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An agricultural household model for Burkina Faso, West Africa

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Title:
An agricultural household model for Burkina Faso, West Africa
Creator:
May, Charles Alan, 1956-
Publication Date:
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English
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vii, 123 leaves : ; 29 cm.

Subjects

Subjects / Keywords:
Agricultural households ( jstor )
Agriculture ( jstor )
AIDS ( jstor )
Commodities ( jstor )
Economic models ( jstor )
Elasticity of demand ( jstor )
Income elasticity of demand ( jstor )
Mathematical variables ( jstor )
Price elasticity ( jstor )
Prices ( jstor )
Consumption (Economics) -- Econometric models -- Burkina Faso ( lcsh )
Dissertations, Academic -- Food and Resource Economics -- UF
Food and Resource Economics thesis Ph. D
Home economics -- Accounting -- Econometric models ( lcsh )
Genre:
bibliography ( marcgt )
theses ( marcgt )
non-fiction ( marcgt )

Notes

Thesis:
Thesis (Ph. D.)--University of Florida, 1992.
Bibliography:
Includes bibliographical references (leaves 118-121).
Additional Physical Form:
Also available online.
General Note:
Typescript.
General Note:
Vita.
Statement of Responsibility:
by Charles Alan May.

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University of Florida
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University of Florida
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Copyright Charles Alan May. Permission granted to the University of Florida to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
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26699648 ( OCLC )
027909966 ( ALEPH )

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Full Text







AN AGRICULTURAL HOUSEHOLD MODEL
FOR
BURKINA FASO, WEST AFRICA



















By

CHARLES ALAN MAY

















A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA

1992



UNIVERSITY OF FLC1 : L7


































DEDICATION



To Nana Ama and Kwasi














ACKNOWLEDGEMENTS

Many people deserve mention for their inspiration and assistance over the years. Those listed below are few and I risk offending those not included. Omissions are certainly due to space limitation and not purposeful exclusion. The following order of mention is simply chronological.

Ken Shapiro and the CRED team provided my introduction to development economics. I will always be grateful for their confidence. The support of the Center for African Studies and the Food and Resource Economics Department was essential in luring me back to Florida. Non-committee faculty who impacted this study include Drs. Taylor, Langham, and Shonkwiler in the literature review, proposal process and estimation procedures, respectively.

To Chairperson Uma Lele and the other members of my

final committee, particularly Dr. Emerson, many thanks for their guidance through the final write-up and defense process. A special thanks to Bill Messina for providing a haven from everyday concerns while I completed this study.

Finally, the forbearance, patience and love of my wife and son were crucial to the successful completion of this work. They certainly suffered more than I from this singleminded pursuit. To them, all my love and gratitude.

iii














TABLE OF CONTENTS



DEDICATION ... .. .. ... ......... ii

ACKNOWLEDGEMNTS . . . . . . . . i i

ABSTRACT ....................... vi

INTRODUCTION ...... ............ . 1

Problem Statement . ............ 2
Objectives of the Study ......... . 4
Agricultural Household Models . . . . . 4 Layout of the Study . . . . . . . 7
Clientele for the Research ...... . . 9
Background on Burkina . . . . . . . 10
Data . . . . . . . . .. .. 13

LITERATURE REVIEW .... . ........ . 17

Chayanov . . . . . . . . . . 18
Nakajima ... .............. . 21
Lau, Yotopoulos, and Others . . . . . 24
Production in Taiwan . . . . . .. 25
Consumption in Taiwan ........... 26
Production in Thailand . . . . . 28
Consumption in Thailand . . . . . 29
Barnum and Squire ................ 31
Singh, Squire and Strauss ........ . 34
Haughton .............. . .. . 37
Bezuneh, Deaton and Norton .......... 39

THEORY OF THE AGRICULTURAL HOUSEHOLD . . . . 42

Introduction ............. .. .. . 42
The General Theory of an Agricultural Household 43
The Utility PFunction . . . . . . 44
The Income Constraint . . . . . . 45
The Time Constraint . . . . . . 47
The Technology Constraint . . . . 48
Combining Constraints to Yield the Full Income Constraint ............. 48



iv








Solving the General Model . . . . . . 50
Kuhn-Tucker Conditions. ..... . . 50
Profit Effect . . . . . . . . 53

PRODUCTION SIDE OF THE HOUSEHOLD . . . . . 57

Cobb-Douglas Production Function . . . . 58 Estimation Results ................ 65
Production Elasticities . . . . . . 69

CONSUMPTION SIDE OF THE HOUSEHOLD . . . . . 73

Almost Ideal Demand System (AIDS) . . . . 74 Estimation Results ............... 77
Consumption Elasticities . . . . . . 85

PROFIT EFFECT, POLICY IMPLICATIONS AND FUTURE RESEARCH 93

Profit Effect ................ 95
Policy Implications . . . . . . . 101
Future Research . . . . . . . . 105

APPENDIX
RECURSIVITY IN THE AGRICULTURAL HOUSEHOLD MODEL 114 BIBLIOGRAPHY .................... 119

BIOGRAPHICAL SKETCH . . . . . . ...... 123

























V















Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy

AN AGRICULTURAL HOUSEHOLD MODEL
FOR
BURKINA FASO, WEST AFRICA

By

CHARLES ALAN MAY

MAY 1992


Chairman: Dr. Una Lele
Major Department: Food and Resource Economics

Agricultural households are often household-firms which behave as both producers and consumers of goods. Householdfirms may have unexpected economic responses to price changes. When the price of the good both produced and consumed increases, profits will increase for the firm. Increased profits increase household income and consumption of the good. However, a household facing higher prices will normally decrease consumption of that good. The result of these opposing economic forces is explored in this study.

A literature review of agricultural household models

and results from other empirical studies are presented. The theory of the household-firm and its indefinite conclusion on price responsiveness supports the need for empirical


vi








testing. The model requires econometric estimation of both the production and consumption sides of household behavior.

Household level data collected in Burkina Faso during 1984 are used to model production under a Cobb-Douglas specification with land and labor inputs. Results are satisfactory with labor a binding constraint on the production process. Lack of household level agro-climatological information explains the remaining variability in the data.

Household consumption is modeled under an Almost Ideal Demand System (AIDS) with prices and total expenditures as arguments. A linear approximation (LA/AIDS) using the Stone price index is estimated with Full Information Maximum Likelihood (FIML). Encouraging results with significant and correctly signed expenditure and price effects are obtained.

Demand and supply elasticities are derived for the household. Output price elasticity of demand is computed with and without the profit effect resulting in a reduced response, but no sign change. Results are attributed to two factors; first, data were collected during a poor agricultural year and most households were net purchasers of cereals, thereby reducing the profit effect. Secondly, household income diversification strategies in response to highly variable agroclimatic conditions in the Sahel have resulted in less dependence on agricultural output as a source of household income, again resulting in a reduced profit effect.

vii














CHAPTER I
INTRODUCTION

The majority of empirical studies in agricultural

economics are microeconomic in nature. In fact, some would argue that agricultural economics is best characterized as empirical microeconomics. Neoclassical microeconomic theory concerns the firm in production and the household in consumption. In developing countries the majority of agricultural households act as both a firm and a household. They provide their own labor and consume the bulk of their own production. Thus, decisions concerning production, consumption and labor in developing countries often influence each other within household-based economies. That the household is the chosen unit of analysis should come as no surprise to most economists. The foundation of consumption economics is the household. Recall also that the word "economics" originates from ancient Greek and means the "laws that govern the household."

This study outlines an integrated theoretical and empirical approach to deal with agricultural households which are both producers and consumers of goods that originate from the household-firm. A theoretical framework is proposed for a model that integrates both the production and

1








2

consumption aspects of household behavior in developing countries. The resultant agricultural household model is tested on cross-sectional household data from Burkina Faso, West Africa. Drawing on a wealth of production, demographic and expenditure data from the early 1980s in four villages within Burkina, an integrated, consistent, conceptual model is estimated to provide insights into the behavior of agricultural household-firms.

Because these household-firms consume part of their own production they may behave differently in response to price changes. Specifically, an increase in the price of the output they produce may increase their net profits, thereby inducing an increase in income that would counterbalance or outweigh the traditional negative impact on their consumption of that output due to the increase in its price.


Problem Statement

Basic information about household behavior is essential for the formulation of appropriate policy in the agricultural sector of any country, whether the goal of that policy is household welfare or increased production. Price and income elasticities are needed in order to capture and describe the behavioral responses of household producers and consumers to policy shifts. In particular, tax and subsidy policies will be dependent on an accurate determination of supply and demand responses of households. Microlevel








3

information is important in order to guide economic policies that will correctly anticipate individual behavior under a particular policy environment. In other words, will the people under the policy behave as the policy anticipates, or in a different manner?

The advent of structural adjustment policies throughout Africa in the 1980s has made it increasingly important to understand the impact of price changes. Structural adjustment programs, supported by multilateral donor agencies such as the World Bank and the International Monetary Fund, generally insist on increased prices for agriculturally produced goods as an incentive to farmers. However, in economies where producers are also consumers the impact of changes in output prices may not have the desired effect on household consumption or production.

Furthermore, due to the plethora of social and economic structures in developing countries, there is a lack of basic descriptive and quantitative information on agricultural households in different regions. This kind of information is especially lacking in African countries which only gained independence within the last twenty to thirty years and set out to transform their agricultural sectors. As we will find in the literature review, the majority of the agricultural household models that have been performed to date have been for Southeast Asian countries.








4

Objectives of the Study

The principal goal of this study is to determine household response to economic incentives through the determination of elasticities from an agricultural household model that integrates both consumption and production aspects of the household-firm. The specific objectives are to:

1. provide descriptive and quantitative information
concerning the production and consumption behavior
of rural African households,

2. combine both production and consumption aspects of
agricultural households in an integrated econometric model,

3. estimate income and price elasticities of demand
using pooled data,
4. estimate output supply and input demand equations
using cross-sectional data, and

5. introduce and empirically measure the impact
of the "profit effect" on cereal consumption.


Agricultural Household Models

The general class of agricultural household models was chosen as the framework for analysis. These models are especially suited for modeling the behavior of agricultural households in developing economies because of their ability to integrate both consumption and production aspects of the household.

Consisting of a variant of consumer choice theory in

which the production technology is represented in the income








5

constraint by a profit function, agricultural household models are within the neoclassical paradigm. However, they do allow an additional flexibility in modeling with regard to the consumption response of households to exogenous changes via the income term, often called the "profit effect."

It is through the income term that the two sides,

production and consumption, are linked. For an agricultural household that obtains the preponderance of its income from the sale of agricultural commodities, it is the production technology that first dictates income, which is usually modeled via a profit function. However, once this income level is established, it becomes an argument in the determination of the level of indirect utility. The result is a recursive model where production decisions precede and delimit consumption decisions, but not vice versa. The recursive nature of these models is dependent upon the existence of competitive input and output markets.

Recursive decisions are thought to be sequential in that one set of decisions precedes and subsequently sets parameter values for other decisions. Recursive decisions are often described as separable because a set of initial decisions are assumed to be made separate from subsequent decisions. For example, in agricultural household models production decisions are thought to have no influence on the








6

decisions in consumption. In a recursive system the causality is one way and not interactive.

There is a notable difference in price elasticities derived from cross-sectional models that acknowledge the "profit effect" and those that do not. Table 1.1 presents household-based price elasticities from various studies in the literature with and without incorporation of the "profit effect." Note that in several instances the response elasticities changed not only magnitudes but also direction.


TABLE 1.1

AGRICULTURAL PRICE ELASTICITIES
WITH AND WITHOUT THE PROFIT EFFECT

RESPONSE ELASTICITIES WITHOUT (A) AND
WITH (B) THE PROFIT EFFECT
AGRICULTURAL NON-AGRICULTURAL LABOR
COUNTRY COMMODITY COMMODITY SUPPLY
A B A B A B
Taiwan -0.72 0.22 0.13 1.18 0.21 -1.59 Malaysia -0.04 0.38 -0.27 1.94 0.08 -0.57 Korea -0.18 0.01 -0.19 0.81 0.03 -0.13 Japan -0.87 -0.35 0.08 0.61 0.16 -1.00 Thailand -0.82 -0.37 0.06 0.51 0.18 -0.62 Sierra -0.74 -0.66 -0.03 0.14 0.01 -0.09
Leone
Nigeria -0.05 0.19 -0.14 0.57 0.03 -0.06 Adapted from Singh, Squire and Strauss, Aaricultural Household Models, (1986) Table 1-2, pg. 26.








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Layout of the Study

This first chapter begins with an introduction to the reason for studying agricultural household behavior and briefly describes the major characteristics of agricultural household models that integrate both production and consumption sides of household behavior. The clientele for this research are identified followed by background information on Burkina's physical and socioeconomic setting that influenced data collection and interpretation. Finally, the data used to drive the model are described, although more detailed descriptions are available elsewhere.

A literature review reveals that agricultural household models have an extensive and international history with contributions from a variety of scholars and countries. The review points out that models have become increasingly more reflective of reality and that agricultural household models have been infrequently estimated due to the need for extensive data to support their estimation. The majority of models have been estimated from data on Southeast Asian countries. However, in spite of the extensive data demands of these models, their usefulness is in summarizing broad behavioral data within a consistent framework and increasing reflection of actual conditions in developing country agricultural household-firms. The literature review is presented in Chapter II.








8

Chapter III presents the theoretical model based upon the behavioral assumptions of utility and profit maximization. Under these conditions the addition of a "profit effect" is shown to make determination of household response to price changes indeterminate from theory. One must empirically estimate the behavior from primary data for a region or situation of interest. By also assuming a functional labor market, the resulting model can be shown to be recursive with production decisions preceding consumption decisions. A formal presentation of the recursive nature of the model is presented in the Appendix.

The results from estimating the production and consumption sides of the model are presented in Chapters IV and V, respectively. A Cobb-Douglas production function is used to estimate the supply side of the household while an Almost Ideal Demand System (AIDS) is used in estimating the demand side of household behavior. The results are more encouraging from the demand than the production side which directly reflects the quality and level of detail of the underlying data.

The presentation of the combined results of the production and consumption sides of the model are the focus of Chapter VI. In addition, implications for policy formulation in Burkina from this model are discussed. The work is completed by a discussion of possible avenues for future research relevant to understanding household level behavior.








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Clientele for the Research


The clientele for more and better information on

agricultural households begins with the countries themselves and the various policy arms of the government. Other interested parties for this kind of research may include bilateral and multilateral aid agencies. Private and voluntary organizations, which work directly with farming communities in developing countries, could also be interested in information on agricultural household behavior. These parochial interests should not cause us to overlook, or underemphasize, the purely intellectual appeal of modeling a complex phenomenon in order to better understand the world.

The Government of Burkina is the principal clientele for information on agricultural households in Burkina. A better understanding of the agricultural production and consumption behavior of agricultural households in Burkina will be of immediate assistance to planning and policy formulation. In most developing countries, agriculture provides income for the majority of the population, serves as a source of foreign exchange and a productive resource base for the rest of the economy. Without a good basis of information, the agricultural sector may not be utilized to its fullest capacity or may even be impeded by improper policy.

The specific users of this research would begin with

the various policy arms of the government including, but not








10

limited to, the Ministry of Agriculture. Other interested parties may include bilateral or multilateral aid agencies and other African Governments. Other donor agencies and researchers could also be interested in information on agricultural household behavior in Burkina.


Background on Burkina


This section provides background information on Burkina that is particularly relevant to the interpretation of the results form the study. Two areas of information are identified that influenced the data collected and its analysis. An understanding of the conditions prevailing in Burkina in the physical and socioeconomic realms are important to a full appreciation of the research results and their limitations.

The most important physical factor influencing agricultural production in Burkina is the high variability of rainfall. This variability occurs across both space and time. Spatially, the south and southwest of the country are favored by more regular rainfall. Temporally the country has experienced periods of drought, with the most recent episodes during the agricultural seasons of 1983-84 and 1987-88. From a longer-term agroclimatological perspective the 1970s and 1980s were drier than the 1950s and 1960s.

Most agricultural production in Burkina is rain-fed and subject to the vagaries of these sahelian weather patterns. These patterns are characterized by highly localized and








11

uncertain rainfall that results in generally risky agroclimatic production zones. This risk generally increases as one moves from the south to the north of the country.

The four villages selected for study were chosen to

cross these agroclimatic zones. Two villages were chosen in a chronically cereal production deficit zone, while the remaining two came from a transition zone that would normally experience surplus production. The two northwestern deficit villages, M6n6 and Bougar6, are located north and south of the town of Ouahigouya, respectively. The normally surplus villages in the west of the country are located north and south of the major regional town of D6dougou. Tissi is north of this regional capital and Dankui is located south of D6dougou.

The data used in this study are from calendar 1984

which captured the drought reduced agricultural production of 1983-84. Because of the drought, households in the sample were found to have been dominated by more net purchasers than sellers of cereals in the year from which data are available. In order to obtain sufficient cereals to meet their needs households interacted with the market more than would have been expected in a normal year. This was reflected in the data by reduced contributions of own agricultural production as a share of total cereals obtained (both produced and purchased).








12

Cereals are extremely important in the social and

economic setting of Burkina. Consisting mostly of millet and sorghum, with some maize, wheat and rice, cereals compose from seventy to eighty percent of calories and sixty to seventy percent of proteins in the Burkina diet (Haggblade, 1984, p. 10). With just over nine million people, and a population growth rate of roughly three percent per year, Burkina has approximately thirty-two inhabitants per square kilometer. Gains in gross agricultural production in the 1980s have been achieved mostly by increasing the area under cultivation. Advanced agricultural technology and input use are limited with most farming households using land, labor, seed, rainfall and simple agricultural tools to produce a crop.

As mentioned earlier, the success of agricultural

production is dependent upon the rainfall pattern. In order to diffuse agricultural production risk households have developed income diversification strategies. These strategies include diversification via trade, services, migration and mining, among other possibilities. Using Burkina data from approximately the same period as the present study, Reardon, Matlon and Delgado (1988) found households in the northernmost sections of Burkina which obtained only thirty percent of total household income from agriculture. Households in their sample were from villages slightly farther north than those used in the present study. However, similar








13

income and production diversification behavior in the face of risk was found among the households in the present study.


Data


An agricultural household model requires household

production and consumption information, as well as market price data on commodities and labor. This is an extensive information requirement and few data sets are available to support this type of modeling. The data required are most frequently available in cross section. The data used in this study are from Burkina Faso and represent household transactions data on approximately 87 farm households from roughly the 1984 calendar year.

Originally part of a grain marketing study,' the data were collected in households from four villages in two different agroclimatic zones in Burkina. Two villages were from the sahelian northwest while the other two were from the western sudanian zone. After an initial village census of all households, samples were selected in a stratified random fashion by ethnic group. Household budget survey data were collected on a biweekly basis for twelve months. Interviewers lived in the villages, visited the households and interviewed all married inhabitants and those over




I For a detailed presentation of the data instruments and setting from which these data originated, see May (1987).








14

eighteen years of age. A list of all the questionnaires used in the study is provided in Table 1.2.

The biweekly transactions data consisted of information on sales, purchases, consumption, amounts given (wages, gifts, taxes, etc.) and amounts received (salaries, remittances, gifts, etc.) by the household over the previous two weeks. Data on changes in household composition were collected on a monthly basis. Data collected on a quarterly basis included the livestock census and on-farm cereal storage. These two categories are important proxies for wealth in the sahelian agricultural household.

A one-time survey was also conducted to catalogue

household durable goods as companion information on wealth stratification within the villages. Three additional questionnaires were administered on a one-time basis. First was the initial household census which, in addition to normal demographic variables, covered education, dependency status, and other sources of income. Second, a questionnaire was used to measure the physical area of household members' fields by crop. Third, the harvest was measured during the appropriate part of the agricultural year.

"Households" in Africa are not necessarily nuclear and in Burkina many household production and consumption units can be found within one family compound. In order to distinguish household units within the sample the census question-








15


TABLE 1.2

SUMMARY OF QUESTIONNAIRES



NAME MAIN PURPOSE FREQUENCY


VILLAGE establish village demographics ONCE CENSUS for sample selection HOUSEHOLD sample household demographics ONCE CENSUS
FIELD area cultivated to each crop MEASURES or crop mix ON-FARM quantity of foodstuffs stored STORAGE over time HARVEST harvest quantity BIWEEKLY CONSUMPTION quantity and source of foodstuffs consumed
SALES quantity, value, good, reason
and location of sale
PURCHASES quantity, value, good, reason
and location of purchase
AMOUNTS services, salaries, credit, GIVEN gifts, and remittances given BIWEEKLY AMOUNTS services, salaries, credit, RECEIVED gifts, and remittances re- BIWEEKLY ceived
CHANGE IN monitor household composition HOUSEHOLD changes over time COMPOSITION
DURABLE wealth and asset measures GOODS
MEASURING convert local measures to kiUNITS lograms ANIMAL type,number and owner of liveCENSUS stock QUARERLY








16

naires were used in combination with household interviews to determine the appropriate composition of a decision-making unit. Among the criteria used to distinguish a separate household within a compound were common fields, granaries, and consumption and contiguous dwellings.

Information from the biweekly, monthly and annual

survey questionnaires was used in estimating the model that follows. These data served to support the theoretical model presented in Chapter III and the estimates for the production and consumption sides of household behavior presented in Chapters IV and V, respectively. In addition to the analytics of the agricultural household model, a wealth of summary and descriptive information, as well as other economic inquiries concerning household behavior in Burkina, could be supported from this data. However, the following chapters are mainly concerned with the formal modeling of an agricultural household model to organize and interpret this large body of information on rural agricultural households in Burkina.














CHAPTER II
LITERATURE REVIEW



The interest and development of the theory of agricultural households has an international flavor with its beginnings in Imperial Russia, mathematical specification in Japan, and empirical verification in the United States. The idea of recording and studying the actual behavior of peasant farmers began in Russia in the 1880s with the advent of reforms under Alexander I. This highly detailed examination of farm life in pre-Revolutionary Russia formed the basis of inquiry on agricultural households by A.V. Chayanov.

Nakajima, working and publishing mostly in Japan, was the first to work out a neoclassical framework and the comparative statics for the family farm. Although his work was mainly theoretical, Nakajima's writings provided the basis for the testing, modification and subsequent refinement of agricultural household models.

The empirical estimation of agricultural household

models began in the mid-1970s with most of the work coming from the Food Research Institute at Stanford University. Lau and Yotopoulos, working with other scholars from Southeast 17








18

Asia, presented a series of articles using household-based studies of agriculture in Taiwan and Thailand.

More recently, in the 1980s, agricultural household

models have become a useful analytical technique for examining cross-sectional data in developing country agriculture. The World Bank sponsored volume, edited by Singh, Squire, and Strauss (1986), has become the standard volume on agricultural household models. Further developments and concerns about these models are now being expressed in the economic literature on developing country agriculture.


Chavanov


The seminal work on agricultural household models is

that of Alexander Vasilyvich Chayanov on peasant agriculture in pre-Revolutionary Russia (Chayanov 1966, 1986). Chayanov based his theory of the family farm on extensive data collected from regional- and district-level surveys of peasant households after the serfs were emancipated and land reform enacted in 1861.

Chayanov held that agricultural households were unique economic units in that the household "firm" provided the bulk of its needed production inputs (principally labor) while at the same time consuming the bulk of its own production. Because such firms provided their own inputs and consumed what they themselves produced, the impact of their decisions might be different from those expected from the








19

neoclassical theory of the firm.2 As mentioned in the introduction, in a household that produces what it consumes the income effect can cause the nature of household responsiveness to be indeterminate from theory.

The writings of Chayanov only became available to an

English-speaking audience in 1966, but were known to scholars in other parts of the world through earlier translations in German and Japanese. Nakajima cites his exposure to Tschajanow's (sic) writings as an early influence on his subsequent writings about the agricultural household (Wharton, 1969, p. 165). The introduction to Shanin's reissue of Chayanov's writings states that "the impact of the implicit cross-influences cannot be ascertained, but the views of Chayanov and his friends spread fairly broadly through Europe and Asia via the German professional literature of the 1920s (Chayanov, 1986, p. 11)."

Chayanov focused his analysis on those households which used little or no labor, other than that provided by the household itself. He formally defined a "family farm" as an economic unit that normally employed no wage labor in its production process. Because the Chayanovian "family farm" used family labor almost exclusively, wage rates could not be determined and hence profits were indeterminate.



2 However, it can be explained through a constrained optimization model in the neoclassical mode as will be presented in this research.








20

With profits indeterminable, Chayanov proposed a decision rule for the "family farm" that differed from profit maximization. He suggested that the "family farm" equates the satisfaction of family needs with the drudgery of work required. From his intense familiarity with Russian peasant agriculture, Chayanov realized that Russian peasants did not work to achieve profit maximization. Their labor supply and efficiency did not coincide with profit maximizing behavior as they could almost always provide additional labor or work harder but chose not to do so.

Chayanov worked towards producing a separate theory of the "family farm" that would have its own unique analytical techniques. From his labor-consumer balance, equating the drudgery of work to the consumption needs of the household, he concluded that each household would find its own subjective equilibrium. The level of this balance would be influenced by the size of the family and its ratio of working to non-working members.

The "family farm" had a certain resiliency or survival power that the capitalist farm did not. Peasant farms could continue to survive in an environment that would bankrupt capitalist farms or socialist collective farms. They would do so by working longer hours or selling at lower prices, even continuing from year to year yielding no net surplus production. Such behavior required a unique form of analysis








21
of farm household behavior because it could not be adequately explained by existing theoretical constructs.

He also commented on a "natural history" of the household which can be likened to the "life cycle" income theory. For Chayanov this "demographic differentiation" of households was more important in determining their behavior than class differentiation. This idea and others about transforming Russia agriculture would eventually lead Chayanov into conflict with the revolutionaries of post-1917 Russia.

For Chayanov the household economy, although distinctly different from other analytical economic paradigms, exists within and is influenced by the prevailing economic system, be it capitalist or collective. However, the household would incorporate and adapt to its environment while at the same time retaining its conceptual uniqueness and calling for separate analysis. Unfortunately, the complete ramifications of Chayanov's separate economic theory of the agricultural household were never fully expounded as he was caught up in the Stalinist purges and agricultural collectivization of the 1930s and eventually died in 1939 at the age of fiftyone.


Nakajima

Chahiro Nakajima mathematically formalized the work of Chayanov by expounding on the subjective equilibrium of








22

agricultural households.3 The Japanese audience was familiar with the writings of Chayanov at an earlier date than the anglophone audience. Nakajima's work, which itself only became available to a wide anglophone audience in 1969 (Wharton, 1969) allowed for a continuum of households, from those consuming all of their own production and providing all of their labor input (subsistence farms) to those consuming none of their production and purchasing all their labor (commercial farms).

Nakajima's classification of the world's diverse

agricultural production systems along a continuum can be viewed as having two dimensions, consisting of the level of own production consumed by the household and the level of own labor provided by the household. At one extreme was the purely subsistence household consuming all of its own production and providing all of its own labor input. At the other extreme of his continuum was the purely commercial farm which sold all its output and purchased all of its labor input. Nakajima commented that the later extreme was "rarely found" and the former was a "very small percentage" of world farms (Wharton, 1969, p. 165). He clearly recognized that the bulk of the world's farms fell somewhere between these two extremes.



3 "Subjective" because each household can have its own utility function which is maximized subject to an income constraint.








23

In order to capture the diversity of farm production possibilities, Nakajima proposed four models of household behavior. Two models examined the behavior of the pure commercial family farm while two captured the behavior of the semisubsistence or semicommercial family farm. The purely commercial farm models were distinguished by the presence or absence of a competitive labor market. For the pure commercial family farm with a competitive labor market Nakajima noted that this "family farm may be regarded as an economic unit which behaves, in the first phase, as a 'firm' maximizing profit and, in the second phase, as a laborer's household with nonlabor income maximizing utility (Wharton, 1969, p. 180)." This is the first mention in the literature of what has come to be known as the recursive nature of the agricultural household decision-making process.

In deriving the comparative statics for the purely commercial farm models, Nakajima introduced inputs other than fixed land and variable labor. Nakajima examines the impact of fertilizer as another factor of production whose price is determined in a competitive market. He also allows for the addition of multiple outputs in his purely commercial family farm models.

Turning to the two semisubsistence (or semicommercial) models, Nakajima assumed that these households did not have access to a labor market, but were distinguished by having single or multiple output crops. In these models the house-








24

hold provided all of its own labor requirements and consumed some of its own production.

In each of the four cases proposed by Nakajima he

solves for the comparative statics under the assumption of utility maximization. He thus obtains the first-order conditions and equilibrium values of each of the variables in the respective models. He examines the impact of changes in asset income, output price, and family size as well as the effects of technology and seasonality on the comparative statics.

Nakajima's work provided, in addition to his continuum classification and comparative statics, the introduction of a labor market to the theory of the agricultural household. Contrary to Chayanov, Nakajima allowed for the possibility of a labor market exchange by the household. He introduced a market from which the household could obtain or provide labor at a fixed wage rate. Nakajima's work has received renewed attention through the recent publication of a collection of his writings on the subjective equilibrium of the household (Nakajima, 1986).


Lau, Yotopoulos, and Others


The work of Chayanov and Nakajima was empirically

embellished by researchers at the Food Research Institute at Stanford, with support from the World Bank and the Ford Foundation. This research, published principally in the








25

1970s, focused on the empirical workings of the agricultural household theory developed by Chayanov and Nakajima. Data were obtained on the agricultural household economies of two Southeast Asian nations, Taiwan and Thailand.

However, there are notable differences between the

empirical approach of Lau, Yotopoulos, et al., and Chayanov. In the two Southeast Asian production studies they assume profit maximization by the agricultural household, which runs counter to Chayanov's argument that peasant families, particularly in pre-Revolutionary Russia, do not maximize profits.

When the separate studies of production and consumption that follow are combined they yield a complete system estimation for agricultural households. The system is complete in the sense that input demand and output supply equations are estimated for the production side, while commodity demand equations are estimated for the consumption side of agricultural household behavior.


Production in Taiwan


Lau and Yotopoulos, along with Lin (Yotopoulos, Lau, and Lin, 1976), first began their examination of agricultural households with cross-section data from Taiwan. Modeling the production behavior of Taiwanese agricultural households, they assumed a Cobb-Douglas production function and utilized a profit function to describe the underlying








26

technology. This profit function was normalized by output price and specified as being log linear. The profit function was also considered to be "restricted" because it measured current revenue minus current variable costs.

From the Taiwan household data these researchers determined four variable inputs (labor, animal labor, mechanical labor, and fertilizer) and two fixed inputs (land and fixed assets). Input demand and output supply equations were derived from the Normalized Restricted Profit (NRP) function via Hotelling's Lemma. The method of estimation used was Zellner's seemingly unrelated regression, because it is asymptotically efficient for systems of equations that have related error terms (Zellner, 1962).

In this first of many studies on agricultural households, Lau, Yotopoulos and Lin tested for profit maximization and constant returns to scale in production. On the basis of their results they were not able to reject the hypothesis of profit maximizing behavior by Taiwanese agricultural households. Contingent upon profit maximization, they were also unable to reject the hypothesis of constant returns to scale in Taiwanese agriculture. Consumption in Taiwan

Following their earlier work in 1976 on the production behavior of Taiwanese agricultural households, Lau, Yotopoulos and Lin turned to consumption behavior (Lau, Lin and








27

Yotopoulos, 1978). Assuming utility maximization by the household, these researchers employed an indirect utility function to analyze the consumption behavior of agricultural households.

Utilizing a linear logarithmic expenditure system (LLES) they estimated commodity expenditure equations derived from a transcendental logarithmic (henceforth, translog) indirect utility function that is homogeneous of degree one in prices. The commodity expenditure equations for three aggregated commodities (agricultural commodities, non-agricultural commodities and leisure) were derived via Roy's Identity. Household characteristics, such as the size and composition of the household, were included as arguments in the indirect utility function.

The translog indirect utility function is assumed to be homogenous of degree minus one. One implication of this assumption, for both the Taiwanese and subsequent Thai consumption analysis, is that the total expenditure elasticity of demand for each commodity is identically equal to one.

Elasticities for consumption demand, labor supply and marketed surplus with respect to prices, incomes, household composition and household endowment were derived from the


4 This, of course, not does not imply that income elasticities are identically one, because the imputed value of leisure is included as part of total expenditure in these studies.








28

results of the seemingly unrelated regression equations (again using Zellner's method). The hypothesis of utility maximization by Taiwanese households could not be rejected.

Production parameters, such as agricultural output

supply, necessary for the estimation of household income and marketed surplus, were taken from the previous work on Taiwanese production by the same authors. The reader will recall that the output supply was determined using a normalized restricted profit function and Hotelling's Lemma. This profit function has no arguments based upon an underlying preference structure expressed in a utility function. Thus, the production decisions are implicitly assumed to be separable from the consumption decisions. However, because the output supply affects income, consumption decisions are influenced by production decisions.


Production in Thailand


After completing studies on production and consumption behavior in Taiwanese agricultural households, Lau and Yotopoulos turned to the analysis of data from Thailand. Working with other scholars from Japan (Kuroda) and Thailand (Adulavidhaya and Lerttamrab), they examined the production characteristics of Thai households (Adulavidhaya, Kuroda, Lau, Lerttamrab and Yotopoulos, 1979). A Normalized Restricted Profit function was again employed from which they derived input demand and output supply equations with four








29

variable inputs (labor, animal input, mechanical input, fertilizer and seed) and two fixed inputs (land and capital assets). All prices were normalized by output price.

The functional form used was log linear and estimation was by ordinary least squares. They tested for both profit maximization and constant returns to scale, as in the case of Taiwan, with similar results; neither hypothesis could be rejected. A further result was that both factor demand and output supply were sensitive to changes in output price.

Clearly, the work on the Thai data was quite similar to that using the Taiwanese data, but it was reassuring to find that both profit maximization and constant returns to scale held in the two different environments. The authors foretell their future plans for this data when they state that "the next step of the analysis of the Thailand data . also combines the consumption side of the agricultural household (Adulavidhaya, Kuroda, Lau, Lerttamrab and Yotopoulos, 1979, p. 85).


Consumption in Thailand


The consumption analysis of Thai agricultural household data proceeded along the same lines as that outlined for the Taiwanese data (Adulavidhaya, Kuroda, Lau and Yotopoulos, 1984). Utilizing a linear logarithmic expenditure system under the assumption of utility maximization, they described an indirect utility function. Specifying a translog func-








30

tional form for the indirect utility function, household commodity expenditure equations for agricultural commodities, non-agricultural commodities and leisure were derived using Roy's Identity. These three aggregated commodities were deemed important for the analysis of the supply of marketed surplus, the demand for non-agricultural commodities in the agricultural sector, and the income-leisure choice and supply of labor, respectively.

As in the Taiwanese consumption study, homogeneity was assumed, with its subsequent implications, and the estimation technique was Zellner's seemingly unrelated regression analysis. Output supply was taken directly from the earlier study on Thai production which used a normalized restricted profit function. Like the earlier Taiwan study, the Thailand consumption study is different from the traditional Engel curve analysis because of the introduction of family composition information as an independent variable in the utility function. However, in contrast to the earlier Taiwanese study, utility maximization by Thai agricultural households was rejected.

-> Implicit in each of the consumption analyses performed by Lau, Yotopoulos, et al., in both Taiwan and Thailand, is the separability of the production and consumption decisions of the household. The production analyses, in both cases, can stand on their own without further caveats. However, the consumption analysis, with household income partially








31

determined through the profit function, and hence the underlying production technology, is dependent upon the production decisions of the household. The production decisions influence the consumption decisions, but the production decisions are independent of the consumption decisions.

It is clear from the work of Lau, Yotopoulos and

associates that the beginnings of an integrated theoretical framework for the analysis of agricultural households were possible. Heretofore, researchers would focus one entry in the literature on the production side of the household followed by a sequel, the analysis of the consumption side, utilizing the results from the earlier production study. It was now time for a consistent theoretical framework within which to specify agricultural household models for developing countries.


Barnum and Squire


Barnum and Squire, in contrast with the earlier studies outlined above, were the first researchers to incorporate both production and consumption aspects of the household in one paper (Barnum and Squire, 1979a, 1979b). This team of researchers also used cross-sectional agricultural household data from a Southeast Asian country: the Muda River Valley in northwest Malaysia. They were also working in an essen-








32

tially monocultural agricultural environment as in the previous studies of rice-based agricultural economies.

Although Barnum and Squire used the same theoretical foundation as Lau, Yotopoulos and associates, there were differences in the choice of functional form between the two teams. In contrast to the latter's profit function approach to the production side of the problem, Barnum and Squire preferred to directly estimate the production technology. They chose to estimate a Cobb-Douglas specification for the production technology and then derive the profit function and input demand equations.

On the consumption side they were more concerned with

the restrictions involved in the Linear Logarithmic Expenditure System utilized by Lau, Yotopoulos and associates, especially the constrained nature of the expenditure elasticities. They employed a modified Linear Expenditure System which, unlike the LLES, did not require that all expenditure elasticities equal one. However, even with this more flexible functional form, the own price elasticities were restricted to be linearly related to the expenditure elasticities. The LES is derived from the Stone-Geary additive utility function.

Of particular interest to Barnum and Squire was the

impact of the analytical framework of agricultural household models on migration, marketed surplus, technology and the demand for hired labor. They found that the cost of migra-








33

tion was low relative to the marginal productivity of an agricultural laborer, that marketed surplus was not responsive to output price changes, and that increases in output price and technology would positively influence rural wages, thereby having a favorable impact on rural workers dependent upon wage labor.

In spite of the different functional forms used in the estimations of Barnum and Squire versus Lau, Yotopoulos and associates, the outcomes were reasonable. Their elasticities were similar enough with those of Lau, Lin and Yotopoulos to prompt Barnum and Squire to remark on the similarity of preferences for Taiwanese and Malaysian agricultural households (Barnum and Squire, 1979b, p. 77).

As a follow-up, Tamin used Barnum and Squire's data set and a log-linear Cobb-Douglas functional form of a normalized restricted profit function, with four variable inputs and two fixed inputs, to model the production behavior of a cross section of Muda River Valley households (Tamin, 1979). Joint estimation, by Zellner's seemingly unrelated regressions, of the profit function and four factor share equations was undertaken with and without restrictions imposed. Estimation without restrictions allowed hypothesis tests for profit maximization and constant returns to scale, neither of which could be rejected.

Tamin found low own-price elasticities of output supply as well as low fertilizer price elasticities of output








34

supply. He also tested for technical and price efficiency differences between owner-farm households and tenant-farm households with no significant differences in efficiency found.


Singh, Squire and Strauss

The empirical embellishments and refinements on agricultural household models continued throughout the early 1980s. A collection and synthesis of these works was brought together in 1986 under the editorship of Singh, Squire and Strauss (1986). With introductory chapters on the theory of agricultural household models, these writers then presented nine case studies by different authors, including the editors, that utilized the basic framework of a separable, or recursive, agricultural household model.

These models can be characterized as standard optimization problems. The household is assumed to maximize a joint household utility function subject to constraints. There are generally three constraints on the household's decisionmaking process. Utility is maximized subject to budget, time and technology constraints. Prices are assumed to be given in both input and output markets. Such models can be shown to be recursive.5




5 See the Appendix to this study for a rigorous presentation of the recursivity of agricultural household models.








35

Exceptions to this model are the chapters by Roe and

Graham-Tomasi, and Lopez (see also Lopez, 1984) included in the case studies, both of which bring into question the recursivity assumption of this neoclassical model of agricultural households. Roe and Graham-Tomasi bring risk into the household decision-making process and find that the original neoclassical results will only hold under what can be considered severe restricting assumptions (Singh, Squire and Strauss, 1986). Lopez (1984; Singh, Squire and Strauss, 1986) shows that the recursivity will not hold if the household is not indifferent between on-farm and off-farm labor, both in the sense of labor hired and labor supplied. Lopez's work is also important in emphasizing that this literature on agricultural household models is not limited to the study of developing country agriculture, but is also useful in describing agriculture in more industrial nations, in this case Canada.

The remaining seven case studies utilize the basic

model with recursivity intact. Two of the case studies can be considered as complete systems analyses in the tradition of Lau, Yotopoulos, et al., and Barnum and Squire. Singh and Subramanian (Singh, Squire and Strauss, 1986), using data from Korea and Nigeria, model consumption decisions with a Linear Expenditure System while the production side employs a linear program. Their study is characterized by additional commodity disaggregation and multiple crops. Strauss (Singh,








36

Squire and Strauss, 1986) examines households in Sierra Leone to determine the impact of pricing policies on nutritional status, measured as caloric intake. He employs a Quadratic Expenditure System (QES) to determine consumption parameters and a multiple output production function to model the production decisions. In his QES, outputs are related via a constant elasticity of transformation and inputs are linked via a Cobb-Douglas production function.

Using data from Indonesia, Pitt and Rosenweig (Singh, Squire and Strauss, 1986) take Strauss' concern for nutritional effects further to determine impacts on health and from health to labor productivity. Smith and Strauss (Singh, Squire and Strauss, 1986) turn to distributional issues and examine the impacts of price policy on different segments of the rural population in Sierra Leone within the structure of an agricultural household model. Braverman and Hammer (Singh, Squire and Strauss, 1986), with disaggregated commodity data from Senegal, bring the agricultural household model into General Equilibrium analysis. In their model markets clear through import and export adjustments in international trade.

Iqbal (Singh, Squire and Strauss, 1986) examines household borrowing in India by introducing the credit market into the basic model with a two-period model. Finally, Sicular (Singh, Squire and Strauss, 1986) takes a novel approach by using a programming variant of the general








37

agricultural household model to examine the influence of centrally planned quotas and restrictions on Chinese production teams. With these case studies, and the introductory chapters, the editorial work of Singh, Squire and Strauss (1986) provides a rich source of theoretical and empirical work concerning agricultural household models.


Haughton

Haughton stresses the importance of choosing an appropriate functional form for the production function in estimating agricultural household models (Haughton, 1986). He argues that without a theoretically sound specification of a production function the more sophisticated agricultural household models are of little use. The same can be said for the specification of the consumption function. Lopez also stresses the importance of using flexible functional forms in modeling agricultural household models to ensure the minimum amount of restrictions on behavior (Lopez, 1984, p. 62).

In Haughton's study, employing cross-sectional data from western Malaysia (yet another study using data from Southeast Asia), he compares the results from the same data set of different functional forms to represent the underlying production technology of the household. Quantity-based translog and Cobb-Douglas production functions are compared








38

with indirect, normalized price-based translog and quadratic restricted profit functions.6

While citing the differing results obtained by Barnum and Squire versus Tamin on the same Muda Valley data set, Haughton also points out sources of variation, other than functional form, that may influence the empirical measurement of agricultural household response to price changes. First, differences may depend on whether or not the researcher models a single crop as output or derives some total farm output figure. Secondly, data may be from different time periods or regions (not the case in the Muda Valley studies). Finally, how variables are defined, lagged, or chosen for exclusion due to lack of data can influence the results of estimations.

In testing the direct production estimates, Haughton found that in general, "the Cobb-Douglas form is not sustained (Haughton, 1986, p. 213)." However, he goes on to state that "the superiority of a homogenous translog form should not be overstated" (Haughton, 1986, p. 213) principally because both forms gave similar output elasticities. He concludes by arguing that the choice of functional form will depend upon the particular constraints of the available data.




6 Recall that the Cobb-Douglas production function is a special case of the more general translog production function.








39

His results from the translog and Cobb-Douglas restricted profit functions were "disappointing." The share equations were not significant and the estimation was a poor fit. He cites the difficulty in measuring restricted profits because they are a residual and tend to magnify data errors. The choice of how to value on-farm family labor is also cited as a source of these poor results. Recall that it was this same problem which caused Chayanov to conclude that the neoclassical approach to the analysis of agricultural households was inadequate.

Haughton proposed a third possibility, the direct estimation of input demand and output supply equations derived from restricted profit functions, of which the normalized quadratic restricted profit function appeared to be the most promising. This, of course, will require more close attention to the collection of valid price data, in addition to quantities, in the developing country context.


Bezuneh, Deaton and Norton


Bezuneh, Deaton and Norton (henceforth, BDN) used an

agricultural household model approach to examine the various impacts of food aid under a Food-For-Work (FFW) scheme in the Baringo District of Kenya (Bezuneh, Deaton and Norton, 1988). They chose to model the production side of the household with a linear programming (LP) approach and the consumption side with an Almost Ideal Demand System (AIDS).








40

By their choice of an LP model on the production side BDN argue that they can disaggregate commodities (96 activities and 82 constraints), examine the impact of FFW-based capital investment and limit the cost of data collection needed to support the model. The argument for using an AIDS model on the consumption side is that it allows for flexible price and income elasticities. BDN use the linear approximate Stone price index and impose the standard demand conditions of adding-up, homogeneity and symmetry when estimating the AIDS model using an iterative nonlinear Zellner method for seven commodities.

The FFW enters the model directly through a second

(after farm household) production function for obtaining FFW commodities. They also attempt to include a static, twoperiod production component in an attempt to capture investment effects of FFW programs. Another interesting addition by BDN is the incorporation of a minimum consumption requirement resulting in nonseparability between production and consumption decisions. A household that perceives a minimum consumption need will base that perception on the household consumption needs which would then impact production decisions.

The authors found that FFW increased production,

income, capital investment, employment and marketed surplus in the Baringo District. A shift from maize to millet production was attributed to the maize distributed as FFW








41

meeting consumption needs and millet being a more profitable crop. Own price elasticities of demand were negative, as would normally be expected except for the combined millet and sorghum good. The positive own-price elasticity was attributed to the profit effect because a higher price would result in higher incomes, particularly among households participating in the FFW program.














CHAPTER III
THEORY OF THE AGRICULTURAL HOUSEHOLD



Introduction


The agricultural household in a developing country is unique for three major reasons. First, the agricultural household consumes a major part of its own production. The food crops produced in an agricultural household are partly consumed by that household while some is marketed to provide income. Other types of households do not generally consume part of that which they produce. Hence, in an agricultural household the output of the "firm" can greatly influence consumption choices, or levels, via income.

The second reason why agricultural households are distinctly different from other households is that they provide their own labor as a major part of the inputs used in the production process. The combination of being the major provider of inputs and the major consumer of output allows for the possibility of unique behavior on the part of an agricultural household. In this chapter we will outline a general theory of this type of agricultural household.

The third distinguishing characteristic of agricultural households in developing countries is the nature of the 42








43

management process. For example, in a developing country management techniques and practices may involve the use of multiple households acting as one unit, sources of income may be determined by kinship patterns, and cultural practices and preferences may influence choices.

The problem of theoretically modelling an agricultural household can be framed in the standard techniques of constrained optimization. The household can be assumed to optimize an objective function, in this case utility, subject to a series of constraints. These constraints generally include information concerning the limitations on behavior due to income, time, and technology.


The General Theory of an Agricultural Household


The general model used in this study can be succinctly written as a constrained optimization problem as follows:

MAX U = U(X.,,,X,) (3.1) subject to:

(i) P,Xa + PXm + w(L-F) < P.Q

(ii) X, + F = T
(iii) Q = Q(L,A)


maximizing utility subject to constraints due to income (i), time (ii), and technology (iii), respectively. The goods consumed are the crop produced by the household, X,; goods purchased on the market, X; and the leisure time available








44

to the household, X,. Prices for goods and services are the price of the agricultural commodity, P,, market commodities, P,, and wages, w. Total time, T, is allocated to agricultural labor supplied by the household, F, and leisure, X,. Agricultural output, Q, is the product of total labor (L) and land, A.

Leisure time is broadly defined in this model to

incorporate any activity undertaken by the household that is related to own agricultural production. This is a key point in analyzing the behavior of sahelian agriculturalists. Recent studies have found that as much as seventy percent of total household income in extremely risky agroclimatic zones comes from non-agricultural production (Reardon, Matlon and Delgado, 1988 and Staatz, D'Agostino and Sundberg, 1990). In this model the diversified income strategy in response to agricultural risk is captured as exogenous income.


The Utility Function


The agricultural household is assumed to function under a joint utility function for the household as a distinct unit. In this particular theory there is no concern for the intrahousehold distribution of resources. Although such distributional issues are important (see Folbre, 1986), the data from which the model will be estimated is not sufficiently disaggregated to allow examination of the issues concerning intrahousehold distribution. Thus, the model will








45

assume a joint utility function for the household. A utility function which, when maximized for the household unit as a whole, is assumed to maximize utility for its individual members.

Household utility maximization is assumed to be a

function of the goods consumed by the household. In this case, the goods consumed are the crop produced by the household, goods purchased on the market, and the leisure time available to the household. The resulting utility function is:

U = U(Xa,X.,X) (3.2) with Xa a vector of agricultural goods, X, a vector of market goods, and X, the leisure consumed by the household.

The utility function is assumed to behave in accordance with standard theory. It is considered to be quasi-concave in its arguments and its partial derivatives are positive. Of course, the quantities appearing as arguments in the utility function are assumed to be nonnegative. Other household characteristics can be added as arguments in this utility function. Examples include number of dependents, level of education, and other socioeconomic factors. The Income Constraint


As outlined above, this optimization is subject to

certain constraints. In the general agricultural household model the objective function is constrained by three re-








46

strictions on the household's actions. The first constraint can be written such that the household expenditures are less than or equal to the income available to the household, or

PX, + P.X. + w(L-F) < P.Q. (3.3) The inequality holds due to possible zero level expenditures or savings by the household. Household consumption consists of expenditures on agricultural goods, PX,; market goods, P.Y. and expenditure on hired agricultural labor, w(L-F).

The quantity of agricultural labor hired by the household is the difference between total labor input on the farm

(L) and the total quantity of labor, on and off-farm, supplied by the household (F). Here, wage rates are assumed equivalent between on-farm and off-farm labor implying that the household is indifferent between these two types of labor. The household income is derived from agricultural goods whose quantity, Q, represents gross production. Subsequently, the value of agricultural goods sold by the household, PQ, represents agriculturally based income.

It is interesting and instructive to note that the term w(L-F) may appear on either side of the income constraint. In other words, it may be construed as either an expenditure or an income term. This is due to the expression (L-F) which can be either positive or negative. If total labor input, L, is greater than that supplied by the family, F, then the expression is positive and the farm household employs labor from off-farm to make up the difference. In this case the








47

expression w(L-F), the value of the employed labor, is interpreted as an expenditure and employed on the left-hand side of equation 3.3.

On the other hand, if family labor supplied, F, is

greater than the total labor input, L, then the expression (L-F) is negative and the household is supplying labor to the off-farm market. The value term w(L-F) is then interpreted as the return to off-farm labor supplied by the household and is counted as an addition to income. In formal specification of the income constraint equation the labor value term would be subtracted from other right-hand side terms to ensure that the "negative" quantity (L-F) is positively valued.


The Time Constraint


The household has the opportunity of utilizing its

total endowment of time in either leisure or labor. Therefore, the sum of the amount of time spent in leisure, X,, and that spent in family labor input, F, must be equal to the total time available, T. In equational form this gives the identity:

X, + F = T. (3.4) This equality holds if one assumes that all slack time is leisure. However, if some slack time is considered lost due to illness, weather or other factors then the equality becomes an inequality (less than or equal).








48

Other possible behavioral characteristics could be modeled through the time constraint. One example is the inclusion of a cultural variable, C, that reflects the minimum amount of time devoted by the household to community or cultural activities. Not all leisure time is devoted to cultural activities, thus X, : C.


The Technology Constraint


The technology constraint represents the production technology that is employed by the household in combining inputs to produce output. A general production function can be used to represent this underlying technology and is written as:

Q = Q(L,A) (3.5) where L is variable labor input and A is the fixed area under cultivation. This production function is assumed to be quasi-convex and increasing in inputs.


Combining Constraints to Yield the Full Income Constraint


The three constraints outlined above can be combined into one constraint in order to simplify the problem. Substituting both the time and technology constraints into the income constraint and rearranging gives:

Y = P,X, + PmXm + wX, 5 PaQ(L,A) wL + wT (3.6) which can be interpreted as a variant on Becker's "full income" (Becker, 1965).








49

The expenditure side of the household's "full income" constraint is now augmented by the value of the household's leisure time, wX,. The income side consists of the value of agricultural production, PQ(L,A), the value of the household's entitlement of time, wT, and is diminished by the value of total labor utilized by the farm, wL. Note that the value of agriculturally based gross income can be given by [PQ(L,A)-P.X]. This can also be interpreted as the value of marketed surplus, where P,Q(L,A) is the value of gross agricultural production of the household and PaX, the value of agricultural goods consumed by the household.'

Note that the full income constraint in the agricultural household model contains an element of income whose value is generated using the household's production technology. The combined term, PQ(L,A) wL, on the income side of the "full income" constraint, represents household profits from agricultural activity. These profits, r, can be written as: T = P,Q(L,A) wL (3.7) and could be determined via a profit function that can be specified so as to be representative of the underlying technology employed by the household.

While the optimization problem is still framed as a consumption problem in which the household is assumed to



This assumes that all agricultural goods not consumed by the household are sold on the market and not given away in non-market exchanges which may not always be the case.








50

maximize utility, one can begin to see how the production decisions may, in fact, influence consumption decisions through the income term in the full income constraint.


Solving the General Model


With the substitutions and rearrangements of the income constraint outlined in the previous section, the original optimization problem can be restated as: MAX U = U(X.,Xm,X) (3.8) subject to:

(i) PaX. + PmXm + wX, 5 wT + P,Q(L,A) wL.

The agricultural household has choice variables concerning the amount of agricultural goods to consume (X,), amount of market goods to consume (Xm), amount of leisure to consume (XI), and total labor input supplied to the farm

(L), assuming that acreage under cultivation is fixed (A). The household, under the assumption of utility maximization, will seek to optimize the levels of these four choice variables.


Kuhn-Tucker Conditions


In its most general form this model consists of a

nonlinear objective function subject to a nonlinear constraint. The solution to a nonlinear programming model is described by the Kuhn-Tucker conditions which consist of








51

marginal, non-negativity and complementary slackness components (Intriligator, 1971, p. 49).

Write the generalized Lagrangian function as:

= U(X,,Xm.,X) + '(Y" PmX. P.X, wX1) (3.9) where A is the Lagrangian multiplier and Y' is the value of full income that results from profit maximizing behavior such that:

Y' = wT + PQ(L',A) W1' 2 PmX. + P,X + wX, (3.10)

= wT + i'(P, w,A)

where L' is the labor input level under the assumptions of maximized profits, i', and fixed area under cultivation, A. Note that, consistent with duality theory, the underlying production technology can be modeled either via a production function, Q(.), or an indirect profit function, n'(.).

The Kuhn-Tucker marginal conditions at the point of the

optimum (X,', X.', X,', A') are:

ao/ax,' = au/ax MP, < 0 (3.11)

o8/ax" .= au/axm Pm < 0 a/ax, = au/ax Aw < 0

a/80" = Y" PmXm" P.X," wX," 2 0

The Kuhn-Tucker non-negativity conditions state that

X," > 0, X.' 2 0, X,' > 0, A* > 0 (3.12) thus the choice variables and the multiplier are all limited to the non-negative orthant. The multiplier, A, is the marginal utility of full income.








52

The Kuhn-Tucker complementary slackness conditions given by:

(8/ax') (X,*) = 0 (3.13) (a/aX,') (X.') = 0

(a/lax') (X,') = 0

(01/=) (.) =o

serve to emphasize the possibility that an interior solution, where the first order partial derivative of the objective function must equal zero, may not exist. However, whether the solution occurs at a boundary or an interior point, the complementary slackness condition states that the choice variables or the first order partial, or both, must be equal to zero.

The marginal conditions of equation 3.11 involve four equations and four unknowns and, if all are binding as one would expect in this model, can be solved to give the demand equations for the three choice variables.2 These demand equations can be written as:

Xi = Xi (P,Pm,w,Y) i = a,m,l (3.14) which is the neoclassical result that demand is dependent upon prices and income.

However, in an agricultural household the full income variable, Y', is determined by the household's production


2 One would expect all conditions to be binding since X', Xm*, XL, and g" would all be expected to be positive in a smallholder household, therefore equation 3.13 suggests that equality hold in each equation 3.11.








53

technology through equation 3.10. In equation 3.10 the only endogenous variable utilized in the characterization of the production technology is total labor, L. Thus, production decisions are made separate from consumption decisions; they are separable decisions. The recursive nature of the model becomes evident as consumption decisions are seen to be dependent upon production decisions, but not vice versa.3


Profit Effect


The major result of the agricultural household model is the introduction of the profit effect. As outlined in the Introduction, the profit effect can counterbalance traditional neoclassical theory of household behavior with respect to price changes. This section outlines an example of the profit effect through an increase in output price and its implications for consumption.

The total change in quantity demanded, dX,, with a

change in output price, dP,, can be determined by totally differentiating the appropriate demand equation. Totally differentiate the demand for the agricultural good (equation

3.14) and divide by the change in its own-price, assuming that the prices of market goods and wages are exogenous, to give

dX./dP. = aX,/aPa + (aXa/aY') (dY'/dP,) (3.15)


3 For a more rigorous presentation of the recursivity of the model see the Appendix.








54

where the term BX,/P, is the standard substitution effect of neoclassical demand theory. The change in the quantity consumed of a good given a change in its own price is negative, if the commodity in question is not an inferior good. Thus, the first term on the right hand side of equation 3.15 is unambiguously negative for a normal good.

The second term on the right hand side of equation 3.15, (aX,/aY')(dY'/dP,), represents the profit effect. A change in the price of the agricultural good changes profits, and hence full income, through equation 3.10. This change in full income will, in turn, change the quantity demanded of the agricultural good, via the demand equation (eq. 3.14).

It remains to determine the sign of this profit effect in order to derive the full impact of a change in the price of an output which is consumed by the household. First, note that maximized full income (Y') given by equation 3.10 is a function of price levels (P,, w) whose total differential is given by:

dY = (aY/apa) (dP,) + (aY'/aw) (dw) (3.16) or, when w is unchanged:

dY'/dP. = aYP/aP,. (3.17) Substituting from equation 3.17, the profit effect term of equation 3.15 may be rewritten as:

(ax,/aY') (aY'/aP) = (aY'/aP.)dP.. 3.18)








55

Second, from equation 3.10, a7'/aP = X, and aY'laP X,, therefore

ay*/ap = af/aP, (3.19) But Hotelling's Lemma states that a7/aP, = Q which allows us to rewrite the profit effect term as:

(aY*/aP,)dP, = (af/aP,)dP, = (Q)dP, (3.20) a term whose sign can be determined. The profit effect is therefore the product of the quantity produced and the change in price. Because quantities, Q, are always positive the sign of the profit effect is determined by the sign of the price change under study. The result is analogous to the well known result that the effect of an income increase is positive for a normal good.

A direct example will help make the impact of this result clear. The total change in the quantity of the agricultural good consumed by the household with a change in the price of that good is given by: dX./dP, = ax,/ap, + (Xa)dP,. (3.21) As stated earlier, the first term on the right hand side is the familiar substitution effect which is negative for a normal good. The second term on the right hand side has been defined as the profit effect. With an increase in output price the profit effect is unambiguously positive while the substitution effect is negative. Thus, the substitution and profit effects work in different directions with the same price change.








56

Therefore, the total effect of an increase in the price of an agricultural good produced and consumed by the household can have three possible outcomes. An increase in the price of the agricultural good may cause a decrease in consumption via a dominant substitution effect; an increase in consumption due to a dominant profit effect; or, the two effects could balance each other resulting in no measurable effect on household consumption due to an output price increase. The relative impacts of these two effects on the response of an agricultural household is indeterminate from theory. Thus, the particular response for any agriculturally based household economy must be determined through empirical means.














CHAPTER IV
PRODUCTION SIDE OF THE HOUSEHOLD


In this chapter the rationale for choosing a particular approach to estimating the production side of the household and a functional form are outlined. The Cobb-Douglas production function was chosen for estimation and is presented in the first section. Derivations of the input demand, profit function and profit-maximized output supply equations are also presented in the first section. The results of the ordinary least squares (OLS) estimation of the Cobb-Douglas production function are presented in section two. Production side elasticities are computed in section three, particularly the output price elasticity of profits needed for calculating the profit effect in Chapter VI.

The data used for estimating the production side of the agricultural household model came from a grain marketing study performed in Burkina that roughly coincided with calendar 1984. The data, while richly detailed on the consumption side, did not particularly focus on household production information. However, production relevant data were measured that would allow an uncomplicated characterization and estimation of the household production system. The data used in estimating the production side included 57








58

household field size by crop, harvest figures, labor force employed by the household (both family and non-family), expenditures on variable inputs and durable goods held by the household.

The area under cultivation in cereals by household,

predominantly millet and sorghum, was aggregated to give a measure of land under cultivation. Labor was obtained from household demographic and composition changes plus use of market labor. Output was measured from the harvest figures and converted to kilograms of cereal using threshing rates determined for each household during the survey.


Cobb-Douglas Production Function


The alternatives considered for estimating the production side of the model were to use either a production or a profit (cost) function. A Cobb-Douglas production function was eventually chosen for three main reasons. First, the available data were more suited to a Cobb-Douglas production function than a profit (or cost) function approach. For example, a representative cost for land is extremely difficult to capture in the African agricultural setting. Second, actual factor use, and hence a production function, was preferred over factor input prices, and a profit (cost) function, because the former were available from the survey. Furthermore, factor input prices were not expected to vary significantly across households in a cross-sectional data








59

set. The third consideration was the ease of estimation, given that the consumption side of the model would take considerable time for data preparation, estimation and refinement a more straight forward production side estimation was preferred. Statistical testing of the appropriateness of the Cobb-Douglas approach in this case was also undertaken. In comparisons against other specifications, notably the translog and constant elasticity of substitution (CES), the Cobb-Douglas specification was not rejected.

A Cobb-Douglas production function consistent with the production constraint (Eq. 3.5) takes the specific form Q = aoAaLa (4.1) where Q is total output, A is the area under cultivation (assumed fixed in the short-term) and L is the labor utilized in producing output. The expansion of this form to include variable inputs and capital is straight forward. The o variable is a technological efficiency parameter that indicates the present state of technology. This can be seen from equation 4.1 by noting that for given values of the other production inputs (A and L), the value of to will have a proportional effect on the size of output (Q).

For estimation purposes equation 4.1 is linearly transformed by taking natural logarithms to yield

InQ = Ina0 + allnA + a2lnL (4.2)








60

Note that the output supply elasticities can be obtained directly from the parameter estimates of the linearly transformed Cobb-Douglas production function because

CQL = (aQ/aL)L/Q = alnQ/alnL = a2. (4.3)
Factor demand equations are obtained from the first order conditions of profit maximization that equate the value of the marginal product of a factor to its wage cost, assuming perfectly competitive markets or a7/aL = P,(aQ/aL) = w. (4.4) Thus, the household will employ labor, in this case both on-farm labor and off-farm labor, until the marginal product of the marginal worker equals the real wage rate.

Note that equation 4.4 has only one endogenous variable, L, and, thus, can be solved in terms of P,, w, the parameters of the production function and the fixed area of land, A. The general solution to equation 4.4 can now be written as:

L' = L'(P,,w,A). (4.5) This result is important because none of the other

endogenous or choice variables appear in equation 4.5, which emphasizes that household consumption decisions do not impinge on production decisions in this model. Thus, production decisions are made separate from consumption decisions; they are separable decisions.

Multiplying both sides of equation 4.4 by L/Q gives

P,(aQ/aL)L/Q = wL/Q (4.6)








61

which can be solved for the household demand for labor as L = a2(P,/w)Q. (4.7) where Pa is the output price of the agricultural commodity and w is the wage rate.

The restricted profit equation (profits minus variable costs) is then given by

f = P,Q(A,L) wL (4.8) which, with substitution from equation (4.7), simplifies to: w = a1P,Q (4.9) when a, + a2 = 1.

The profit-maximized output supply equation can then be obtained by substituting the input demand equation (eq. 4.7) in the original Cobb-Douglas production function (eq. 4.1) which simplifies to:


6oQ (4.10)



In addition to the above Cobb-Douglas specification, a translog model was estimated that included squared terms for the two factor inputs and an interaction term between these inputs. Since the Cobb-Douglas model is a special case of the translog model, the former can be tested as a restricted case of the latter. When the appropriate F-test was performed the hypothesis that the Cobb-Douglas model was appropriate was not rejected at the 99% level of significance.








62

The Cobb-Douglas specification was also tested against the CES production function. Once estimated, the CES was tested for constant returns to scale (unable to reject at the 95% level of significance) and then reestimated with this restriction imposed. The resulting CES with constant returns to scale was tested against the Cobb-Douglas. Again the Cobb-Douglas specification was not rejected at the 99% level of significance (nor at the 95% level of significance, contrary to the test against the translog). With these results the Cobb-Douglas estimates were retained for the model estimation.

Other concerns entered into the choice of the CobbDouglas specification. The needs of the agricultural household model, functional form tractability and data availability constraints precluded the use of a translog approach in the present case. Recall, that the main production side result required for the agricultural household model is the responsiveness of profits to changes in output price. Unfortunately, "it is not possible to derive the first order conditions for profit maximization and substitute them into the translog production function to give a price-based translog production function (Haughton, 1986, p. 207)" as was done with the Cobb-Douglas specification.

An alternative approach would have been to derive the restricted profit function from a direct production function. Again tractability is a problem as "this works neatly








63

in the Cobb-Douglas case, it is not analytically possible for a translog production (sic) (Haughton, 1986, p. 209)." The direct specification of a profit, or cost, function would require information on input prices that is not available in the Burkina data. Profit and cost function approaches were unavailable because the input price data were not sufficient to support estimation. Furthermore, it is particularly difficult to value the two major inputs in the African agricultural household production system; family labor input and land to farm production.

Choice of specification can often have constraining

impacts on model results that must be noted prior to estimation. The impact of using a Cobb-Douglas specification on the resulting production side elasticity estimate have been mentioned by other writers. Previous studies have shown that the estimates of direct (quantity-based) production functions generally result in larger elasticity estimates than indirect (price-based) production functions. "Once again the direct estimates show far greater responsiveness (Haughton, 1986, p. 215)."

Other a priori constraints on the results that are

specific to a Cobb-Douglas specification include constant unitary elasticity of substitution, input elasticities of output that are invariant to output level, and strictly positive input quantities. In spite of these restrictions,








64

the Cobb-Douglas approach can give useful results as Haughton points out:

However, the superiority of a homogenous translog
form over the Cobb-Douglas form should not be
overstated; both have fairly close fits . Depending on what issue is being addressed, the
simpler Cobb-Douglas form may be adequate, Both
give essentially similar output elasticities with respect to inputs (at the geometric mean values of
the variables). (Haughton, 1986, p. 213)

Awareness of these and other impacts of model specification should be retained and used to temper the interpretation of the final results.

Additional explanatory variables, other than land and labor, were also created from the raw household data to represent expenditures on variable inputs (fertilizer, seed, insecticides, etc.) and capital inputs (durable good holdings as a proxy). Their inclusion in the model did not add additional explanatory value and hence were not retained for the final estimation. Moreover, few households in the sample reported using inputs other than land and labor.

Another likely omitted explanatory variable is farm

management. Surrogate variables based on the age and educational level of the head of household were added to the basic model to capture the variance of management capability across households. The resulting specifications did not add explanatory power to the model with management proxies based on age, head of household educational level and maximum educational obtained within the household. These results can be explained by the lack of significant variance in levels








65

of education across households in the sample. Thus, the final estimating equation for the production side of the household model was the Cobb-Douglas specification using land and labor as explanatory variables for output.


Estimation Results


This section presents the results from the ordinary

least squares (OLS) estimation of a Cobb-Douglas production function fitted to Burkina household data on output, area under cultivation and labor. Both the endogenous and exogenous variables were measured in volume rather than value form. Three dummy variables were added to the basic model to account for any differences in the production function across villages. Of course, the model with all dummy variables coefficients equal to zero holds for the fourth village in the sample (in this case Village 1).

Land and labor are normally considered endogenous

(decision) variables with rental and wage rates exogenously determined. With land and labor decisions endogenously determined a simultaneity problem would arise in estimating a Cobb-Douglas function with OLS. However, other work on the Cobb-Douglas specification (Zellner, Kmenta and Dreze, 1966) has shown that if output is stochastic and the householdfirm is assumed to maximize expected profits, then the resulting error terms of the OLS estimation are independent of the included endogenous variables. The result is that OLS








66

estimation of a Cobb-Douglas land-labor specification yields consistent parameter estimates assuming expected profit maximization.

The econometric model of household production behavior was first estimated with no restrictions on the parameter estimates. The resulting estimates were then tested to determine if the sum of the parameters on land and labor was significantly different from unity (i.e., constant returns to scale). The statistical test of this linear constraint would not allow rejection of the null hypothesis that the sum of the parameter estimates was one at the 95% level of significance. A confidence interval on the sum of the parameter estimates was determined at the 95% level of significance. The resulting range was from 0.71 to 1.59. The model was re-estimated under the restriction that a, + a2 = 1. Note that the presence of CRS is consistent with profit maximization because of the assumption of fixed land under cultivation.

Results from both the unrestricted and restricted

models are presented in Table 4.1. Note that the t-statistic values are significant at the 95% level for land, labor and the Village 2 dummy variable in both the unrestricted and restricted equations.

The R-squared values for both the unrestricted and

restricted equations are not particularly high indicating that the model explains roughly 40% of the variance in








67

output. This kind of result is not surprising, particularly for primary, cross-section data. Barnum and Squire's (1979a,b) Cobb-Douglas estimation in a monocropping environment explained roughly 67% of the variation in output. Haughton (1986) reported R-squared values of around 50%.


TABLE 4.1

UNRESTRICTED AND RESTRICTED
COBB-DOUGLAS PRODUCTION FUNCTION ESTIMATES

UNRESTRICTED RESTRICTED PARAMETER t-STAT PARAMETER t-STAT
ESTIMATE ESTIMATE
Intercept 0.597 0.45 1.072 0.94 In (Land) 0.414 3.38 0.394 3.32
In (Labor) 0.739 3.26 0.606
Village 2 -1.778 -5.48 -1.747 -5.45 Village 3 -0.350 -1.02 -0.344 -1.01 Village 4 -0.107 -0.33 -0.131 -0.41
R 0.419 0.417



The definition of inputs and output variables could

account for some of the unexplained variation remaining in the production estimation. For example, the output variable is an aggregate measure over both millet and sorghum. The assumption of a single production function for cereals may be a source of additional variability in the output variable. Although the major cereals, millet and sorghum, are generally aggregated together, a multicrop production








68

function could possibly add explanatory power. Further error could originate in the measures used for the explanatory variables, particularly labor. Labor quality can vary significantly across household, market and work party labor sources (Saul, 1983).

Omitted variables could also help explain the reduced R-squared value. The most likely exogenous variable that would add information to explain variable output would be one that captured the highly variable climatology of the Sahel. Unfortunately, this type of information, or a suitable surrogate, is not available at the household level. The village dummy variables add significant explanatory value to the model and can be interpreted as capturing some of the agroclimatological variation across the villages.

Another possible missing variable that could help

interpret the lack of explanatory power is the quality of land. The variability of the quality of land is significant across households and could improve explanatory power in a revised estimate. Unfortunately, this variable, or a proxy, were not available for inclusion in this estimation.

Using the restricted estimation results from Table 4.1 the production side equations needed to proceed with the agricultural household model can be determined. The production function (for Village 1) can now be written as

InQ = 1.07 + 0.39*lnA + 0.61*lnL, (4.11) the household demand for labor is








69

L = 0.61*(P,/w)Q, (4.12) the restricted profit function is r' = 0.39*PaQ, (4.13) and the profit-maximized output equation becomes Q" = 7.2*A*(P/w)"2. (4.14)


Production Elasticities


This section outlines the derivation and calculation of the production side elasticities relevant to the agricultural household model. Using the parameter estimates from the previous section, a table of input demand and output supply elasticities is constructed. These elasticities are interpreted for their significance to production decisions and will be used in Chapter VI to determine the direction and magnitude of the profit effect and its impact on household output price responsiveness.

The coefficients on land and labor can be interpreted as the output supply elasticities, as was demonstrated through equation 4.3. Similarly, the restricted equation estimates can be used to determine the relative shares accruing to land and labor. From Table 4.1 it can be determined that the share for land is 39% while that of labor is 61%. In the same fashion, the impact on output of a 10% increase in labor is slightly less than twice that of a similar increase in land.








70

Barnum and Squire's Malaysia data indicated the reverse of the Burkina figures with 62 and 29% shares for land and labor, respectively. The balance being the shares of other variable inputs (8 percent) and capital (1 percent). This can be taken to imply that agriculture in Burkina is constrained more by labor than land. Thus, greater returns could be expected from addressing labor constraints than land constraints, although both would have a significant positive impact on production.

Production side elasticities more directly relevant to the agricultural household model can be directly computed from the output supply (eq. 4.10), labor demand (eq. 4.7) and profit (eq. 4.9) equations.' The resulting elasticity values and the formulas from which these estimates were derived are presented in Table 4.2.

In general, the results from Table 4.2 are consistent with earlier studies including Barnum and Squire (1979a,b) and Haughton (1986), both using Malaysian data. From the first two diagonal elements of Table 4.2, the own-price elasticities of output and labor can be interpreted. Output produced is very (positively) responsive to changes in the price of that output (in this case cereal price). As previously mentioned above, these direct, or quantity based,




I Taking logarithms of both sides of these three equations simplifies the derivation of the elasticity formulas.








71

estimates are expected to imply greater responsiveness than those based upon indirect or price based estimates.


TABLE 4.2

PRODUCTION SIDE ELASTICITY ESTIMATES ELASTICITIES
VARIABLES
OUTPUT LABOR PROFIT
(Q) DEMAND (L) (t)
OUTPUT PRICE (P.) 1.56 2.56 2.56

(elasticity equation) (a2/a) (1/a,) (1/a,)
WAGE RATE (w) -1.56 -2.56 -1.56

(elasticity equation) (-a2/aI) (-a2-a/aI) (-a/,)
TECHNOLOGY PARAMETER 2.56 2.56 2.56
(ao)
(elasticity equation) (1/al) (1/a,) (1/a,)



The high responsiveness of demand for labor to changes in the wage rate is also clear from Table 4.2. The value of

-2.56 compares to -2.57 found by Haughton using Malaysian data and a Cobb-Douglas production function. Similarly, Barnum and Squire, using data from a more well-to-do area of Malaysia and a Cobb-Douglas production function approach, found -1.47. Assuming increasing population growth the high price responsiveness of household demand for labor can be expected to limit unemployment in the agricultural sector.

In addition to increasing output, an increase in output price will also induce greater demand for labor and higher profits. Wage rate elasticities have the expected negative








72

responsiveness for the elasticities listed in Table 4.2. An increase in the wage rate can be expected to reduce the demand for labor, thereby reducing both output and profits. Note that the direct influence on labor demand is greater than the induced declines in both output and profits indicating that labor is not the sole factor input in the household production process. Finally, the significance of technological change is high and can be expected to increase demand for labor, output and profits.

What is needed from this production side in terms of

the agricultural household model is the impact of changes in output price on profits, the output price elasticity of profit. Table 4.2 reports a value of 2.56 for this elasticity implying that profits are highly responsive to output price changes. Haughton found this elasticity using a direct approach to be 3.06 while the indirect approach gave 1.89. The value for Burkina in Table 4.2 (2.56) is approximately halfway between these two extremes.














CHAPTER V
CONSUMPTION SIDE OF THE HOUSEHOLD


This chapter presents the consumption side of the household model. The consumer choice between goods to consume and labor to supply, modeled by an almost ideal demand system (AIDS), is presented in the first section. Estimation results from the AIDS model and restrictions from the neoclassical theory of demand (homogeneity and symmetry) are examined in the second section of this chapter. In the final section, expenditure, own and cross-price elasticities are calculated.

The data used to estimate the consumption side of the agricultural household are also from the Burkina grain marketing study. Recall that the household level survey from this marketing study provided the data for estimating the production side of the household in the previous chapter. Expenditure data from the same households used in Chapter IV are used in this chapter to estimate the consumption side of the household. These expenditures were obtained from fortnightly recall interviews in each household. The expenditure data were complemented with questionnaires designed to acquire information on quantities given (wages, gifts, exchanges, etc.) and received (salaries, gifts, remittances, 73








74

etc.). The final size of the sample set of households used was limited to the 87 households which had complete annual data on both production and consumption.


Almost Ideal Demand System (AIDS)


There are several alternative approaches to solving and estimating a system of demand equations. These include the linear expenditure system (LES), the log-linear expenditure system (LLES) and the Rotterdam approaches. Each of these systems approaches has its advantages and disadvantages depending upon the needs of the analysis.

Demand systems that are derived from an additive utility function, such as the LES, necessitate strong separability of preferences and, possibly, own price elasticities restricted to linear relations of expenditure elasticities. The LES is derived from the Stone-Geary additive utility function. The LLES, on the other hand, requires expenditure elasticities equal to unity, which would inappropriately restrict the present study.

Another possible specification for the consumption side that would provide an opportunity to test the consequences of the neoclassical theory of demand is the Rotterdam model. The Rotterdam model is consistent with utility maximization for a linearly logarithmic utility function and has a similar specification to the AIDS configuration. However, unlike the AIDS, the Rotterdam model is not derived from








75

explicit preferences and demand functions (Deaton and Muellbauer, 1980a, p. 317).

The crucial points for choosing a functional form for the agricultural household model is the need for unrestrained elasticities and compatibility with theory. Prior restrictions resulting from the choice of functional form could limit the impact of the profit effect on consumer demand via the full income constraint.

Because of the need for a functional form that does not restrict parameter estimate values and related elasticities the almost ideal demand system of Deaton and Muellbauer was chosen for this study (Deaton and Muellbauer, 1980a). The AIDS model provides great flexibility for estimation and testing as Deaton and Muellbauer point out:


the Almost Ideal Demand System (AIDS), gives
an arbitrary first-order approximation to any
demand system; it satisfies the axioms of choice
exactly; it aggregates perfectly over consumers
without invoking parallel linear Engel curves; it
has a functional form which is consistent with
known household budget data; it is simple to
estimate, largely avoiding the need for non-linear
estimation; and it can be used to test the restrictions of homogeneity and symmetry through
linear restrictions on fixed parameters. (Deaton
and Muellbauer, 1980a, p. 312)


Most importantly for the present study, the AIDS model provides for flexible price and income elasticities which are necessary in estimating a household model because price and expenditure responses are the major points of interest. One should not constrain the elasticities to any particular








76

value (like the LLES), or range of values, in order that the full responsiveness of household expenditures to price and income changes can be captured.

Derived from utility maximization via a cost function

by way of Shephard's Lemma, the AIDS model can be succinctly written as


W, = a,+ 3, $log{ "I + 'Y7 logpi (5.1) where the share of expenditures allocated to good i (budget shares; wi = piq,/m) are determined as a function of the price of good j (p) and total expenditure (m) on all the goods being examined. Note that changes in relative prices impact on budget allocations via the gamma terms and changes in real expenditure impact via the beta coefficients. The beta coefficients can be interpreted as measuring necessities (1<0) or luxuries (>0) depending on their sign.

The only non-linear element in the AIDS model of

equation 5.1 is the price index term (log P) that deflates the value of total expenditure. From the derivation of the AIDS model this price index is defined as

log P = + ak log p, + logpk logpj (5.2) k j k

The non-linear AIDS price index (logP) of equation 5.2 is often estimated by the Stone price index (logP') which is given as








77

logP: =Ew, logp, (5.3)


The Stone price is an expenditure share weighted linear price index which is approximately proportional to P', if prices are highly collinear.

AIDS models that utilize the linear approximate (LA) Stone price index of equation 5.3 are often designated as LA/AIDS models. Having employed the Stone price index, the present study is an LA/AIDS model. The distinction between estimation of the AIDS, with the non-linear price index, and the LA/AIDS, with the linear Stone approximation, will be important in determining the appropriate computing formulas for elasticities of demand in section three below.


Estimation Results

For estimation purposes the household level data were pooled by considering each household separately over four time periods within the twelve month data collection period. Ray used a similar pooling technique to create panel data in estimating an AIDS model on household budget data from India (Ray, 1982). The benefits and costs of panel data over cross sections is discussed in other sources (Ashenfelter, Deaton and Solon, 1986).

The four time periods correspond to the different

seasons in the agricultural sector of Burkina where behavior can be expected to vary. The four periods, corresponding to








78

quarters, are referred to as the cold (December to February), hot (March to May), rainy (June to August) and harvest (September to November) seasons.

Roughly 140 individual commodities were found in the raw data from the 87 households. These commodities were aggregated to four goods, plus labor supplied. The four goods were cereals (containing all cereal products), tobacco and beverages (including beer, soda and kola), other foods (non-cereal food purchases), and other non-food purchases. Time spent in leisure activities (broadly defined as all non-farm activities) was determined by subtracting the amount of agricultural labor time supplied by the household from the total time available. Thus, leisure is determined as the residual of the difference between household labor supplied on-farm and total time available.

Neoclassical demand theory is based upon a set of

preference axioms and a linear budget constraint. Several restrictions on systems of demand equations can be derived from these two basic units of theory. These restrictions are known as adding-up, homogeneity of degree zero in prices, symmetry and negativity of price effects. Adding-up requires that the sum of the expenditures across all goods equal total expenditure and originates from the linear budget constraint.

Homogeneity of degree zero in prices implies that equal proportionate changes in both prices and expenditure will








79

not change the resulting demand. This is also known as the absence of money illusion, implying that consumers make consumption decisions upon relative prices, not absolute price levels. Homogeneity is also derived from the linear budget constraint.

Symmetry implies that the price effects of quantity

demanded across any two goods will be identical. Acceptance of symmetry insures that the underlying preference structure is consistent. Negativity refers to the negative relation between the demand for a good and its own price, which is often called the "law of demand." These last two results derive from the specific axioms of preference underlying neoclassical demand theory. Deaton and Muellbauer provide details on the linear budget constraint, axioms of preference, and the derived constraints of demand (Deaton and Muellbauer, 1980b).

Full Information Maximum Likelihood (FIML) was chosen

as the preferred method of estimating the AIDS model because it is invariant with respect to choice of equation dropped in the demand system (Greene, 1990, p. 528). Recall that in systems of demand estimation all commodity demand functions can not be included in the estimating procedure because this produces a singular covariance matrix. A singular covariance matrix results in an undefined likelihood function. Therefore, one of the system's equations is dropped in order to insure non-singularity of the covariance matrix. The parame-








80

ters of the dropped equation are then obtained from the adding-up conditions.

Both the unrestricted and restricted estimates were used to test the restrictions of homogeneity and symmetry using the likelihood ratio test. Adding-up is assured by dropping one of the equations, in this case the labor supplied by the household. In the AIDS model the testable restrictions imply the following
R n
E a,=1 0 =0 (5.4)
i=O i1 i.1


Y=o 0 (5.5)


=y Yj (5.6)



for adding-up (5.3), homogeneity (5.4) and symmetry (5.5), respectively.

The unrestricted and restricted FIML estimates for the intercept, expenditure and own-price parameters of the LA/AIDS are presented in Table 5.1. Both homogeneity and symmetry were imposed in obtaining the restricted parameter estimates reported in Table 5.1 The results are encouraging with twelve and eleven of the fifteen coefficients listed being significantly different from zero (t-statistics greater than two) for the unrestricted and restricted estimations, respectively. Most of the significant changes in t-statistic values occur with the intercept terms.








81

TABLE 5.1

UNRESTRICTED AND RESTRICTED ESTIMATES OF THE LA/AIDS MODEL

UNRESTRICTED RESTRICTED ESTIMATE t-STAT ESTIMATE t-STAT INTERCEPT a -0.520 -5.61 -0.014 -0.23 a2 -0.165 -3.43 -0.039 -1.84 a3 0.009 0.11 0.141 4.31 a4 -0.091 -0.99 -0.032 -0.69 a5 1.767 11.86 0.945 9.84 EXPENDITURE B1 0.047 5.79 0.052 5.94 82 0.022 8.97 0.023 8.71 B3 0.010 1.84 0.004 0.84 84 0.030 3.16 0.021 2.73 B5 -0.111 -6.98 -0.100 -7.06 OWN-PRICE 71 0.111 16.78 0.075 10.29 72 0.022 -2.50 0.019 8.71 73 0.036 20.58 0.036 18.43 74 0.028 7.08 0.030 8.21 75 -0.049 -2.93 0.067 5.57



Note that the expenditure parameter estimates are

positive for four out of the five goods in both the unrestricted and restricted models. As mentioned earlier, the AIDS configuration allows for classification of goods as necessities and luxuries depending upon the sign of the beta coefficients. Inspection of Table 5.1 results in the conclusion that cereals, tobacco and beverages, other foods and other non-food are all luxuries in the rural economy of Burkina. This is not surprising given the low absolute levels of incomes in the Sahel.








82

The share of total expenditures allocated to the

consumption of leisure increases with increasing income. Recall that the labor supply equation is related to leisure demand through the total time available (X, = T L). The share estimated in this system is wL/m, which decreases with increasing income, thereby increasing wX1/m. The broadly determined leisure variable is the only luxury in this system. Interpretation of the price parameters in the AIDS model requires calculation of the relevant elasticity estimates which are presented in the next section.

The likelihood values for both the restricted and

unrestricted models were differenced, multiplied by two and compared to the chi-squared statistic to perform the likelihood-ratio test for the validity of the restrictions. The restrictions were rejected at the 95% level of significance. Symmetry and homogeneity were imposed separately and also tested. Both were rejected at the 95% level of significance.

The rejection of the restrictions derived from neoclassical demand theory is not unusual in empirical studies. "The restrictions of homogeneity and symmetry . are consistently rejected by the data (Deaton and Muellbauer, 1980b, p. 80)." In tests of the restrictions Ray found "that homogeneity is only marginally rejected for the household AIDS" (Ray, 1982, p. 360). In contrast, the "symmetry restriction is decisively rejected for the rural sector but only marginally for the urban sector" (Ray, 1982, p. 360).








83

In general, Ray's results found that the rural data were more likely to reject the demand restrictions than the urban data. This result was also dependent on whether or not household size effects were included in the model. The important point for this study is the choice between the unrestricted or restricted estimates in determining the demand elasticities. The decision is between statistically rejected restrictions from theory versus the results obtained from the theoretical structure employed.

Both unrestricted and restricted parameter estimates were used in deriving the consumption elasticities with no exceptional difference in elasticity values, particularly the expenditure elasticities. Therefore, restricted estimates were retained for the elasticity computations of the next section. It is not uncommon to impose theoretical restrictions in AIDS models without reporting significance tests (Bezuneh, Deaton and Norton, 1988).

The cross-price parameter estimates provided in Table 5.2 were not as impressive as those presented in Table 5.1. A total of 25 cross price parameters were estimated, or estimated and derived in the case of restrictions. The number of statistically significant cross price parameter estimates, at the 95% level, numbered 8 and 12 in the unrestricted and restricted models, respectively.








84

TABLE 5.2

UNRESTRICTED AND RESTRICTED ESTIMATES OF THE LA/AIDS MODEL

UNRESTRICTED RESTRICTED ESTIMATE t-STAT ESTIMATE t-STAT GOOD 1 to 2 -0.006 -1.16 -0.015 -7.19 3 -0.001 -0.25 -0.011 -3.49 4 -0.002 -0.58 -0.015 -3.99 5 0.027 1.99 -0.033 -3.70 GOOD 2 to 1 -0.008 -2.50 -0.015 -7.19 3 -0.002 -0.91 -0.003 -1.86 4 0.001 0.69 -0.0005 -0.34 5 0.016 2.32 -0.0008 -0.24 GOOD 3 to 1 -0.023 -4.48 -0.011 -3.49 2 -0.005 -1.43 -0.003 -1.86 4 -0.005 -2.15 -0.002 -1.05 5 0.005 0.39 -0.019 -5.29 GOOD 4 to 1 -0.044 -4.59 -0.015 -3.99 2 -0.003 -0.55 -0.0005 -0.34 3 0.004 0.88 -0.002 -1.05 5 0.002 0.22 -0.012 -2.79 GOOD 5 to 1 -0.036 -2.57 -0.033 -3.70 2 -0.007 -0.92 -0.0008 -0.24 3 -0.037 -6.53 -0.019 -5.29 4 -0.021 -3.99 -0.012 -2.79



This percentage of statistically significant parameter estimates (one-third to one-half) from an AIDS estimation compares favorably with other studies. Deaton and Muellbauer reported 22 out 64 parameter estimates from British data with t-statistics greater than two (Deaton and Muellbauer, 1980a). Using Kenyan data, Bezuneh, Deaton and Norton found








85

85 out of 124 parameter estimates that were more than twice their standard errors, but this figure included both cross price and other parameters (Bezuneh, Deaton and Norton, 1988). Finally, Ray's Indian data resulted in 21 out of 32 cross price parameter estimates with greater than "unit t values (Ray, 1982, p. 357)." Inspection of Ray's results reveals that 10 out of the 32 cross price estimates had tstatistics greater than two.

The poorer performance of the parameter estimates for cross-price behavior can be attributed to the difficulties arising from aggregation across commodities. The four tangible consumables in this study consisted of varying numbers of individual commodities. Two of the goods created from the disaggregated data were composed of around ten commodities, namely Cereals (Good 1, 11 commodities) and Tobacco and Beverages (Good 2, 9 commodities). Other foods (Good 3) and other non-food (Good 4) were composed of 71 and 51 commodities, respectively. The difficulty in determining cross-price behavior from this level of aggregation is not surprising. Similarly, it is not surprising that the most significant cross price parameters arose for the least diverse good grouping (i.e., Good 1, cereals).


Consumption Elasticities


Consumption elasticities from the AIDS model have

received considerable attention in recent years. Various








86

authors have used different elasticity computing formulas. The issue has been how to determine the price, both compensated and uncompensated, and income (expenditure) elasticities of demand. The problem derives from the use of the Stone price index as an approximation of the price deflator used in the AIDS model. Thus, the problem is between the linear approximate AIDS (LA/AIDS) and the non-linear AIDS (AIDS) computing formulas for price and income demand elasticities.

From equation 5.3 it is clear that the Stone price

index is a function of the budget shares indicating that the budget share variable is endogenously determined. These shares are generally assumed to be constant when taking derivatives to derive elasticity computing formulas for the LA/AIDS. The confusion arises in the use of non-linear AIDS computing formulas where the shares are endogenous in computing elasticities for the LA/AIDS. Green and Alston, using the same data set under LA/AIDS and AIDS, have found that the use of AIDS computing formulas in calculating LA/AIDS elasticities will result in significantly different elasticity estimates than those from the non-linear AIDS (Green and Alston, 1990). Green and Alston present the correct elasticity computing formula for use with the LA/AIDS model.

AIDS elasticity computing formulas, with variable

expenditure shares, should not be used with estimations of








87

the LA/AIDS, where expenditure shares are assumed invariant to changes in income. Assuming that the expenditure shares are invariant to income level is equivalent to assuming homothetic preferences (i=0 for all i), in which case the elasticity computing formulas are the same for both the AIDS and the LA/AIDS. However, if preferences are not assumed to be homothetic then the choice of computing formula is important.

In a follow-up article Green and Alston presented the correct LA/AIDS computing formulas for the uncompensated, compensated and expenditure elasticities (Green and Alston, 1991). The demand elasticity computing formulas for the LA/AIDS result in a system of simultaneous equations solved by matrix algebra. This was the approach used in computing the uncompensated and income compensated elasticities presented.

The uncompensated and income compensated elasticities are presented in Tables 5.3 and 5.4, respectively. The elasticity directions and values are reasonable for both prices and incomes. All own price elasticities are negative, as would be expected from rational consumers. Rural Burkina households adhere to the law of demand just as any other household. Own price elasticities are somewhat inelastic which could be due to the overall low level of consumption in the rural Sahel.








88

TABLE 5.3

UNCOMPENSATED DEMAND ELASTICITIES FOR THE LA/AIDS


ELASTICITY OF DEMAND WITH RESPECT TO COMMODITY
Price of Commodity Group GROUP In- I
come 1 2 3 4 5 1) Cereals 1.35 -0.72 -0.06 -0.07 -0.09 -0.40
2) Tobacco and 1.83 -0.49 -0.52 -0.11 -0.08 -0.63
Beverages
3) Other Foods 1.06 -0.12 -0.03 -0.65 -0.02 -0.24
4) Non-Food 1.35 -0.23 -0.00 -0.04 -0.69 -0.39

5) Labor Supply 0.72 -0.02 -0.00 -0.03 0.001 -0.67




TABLE 5.4

COMPENSATED DEMAND ELASTICITIES FOR THE LA/AIDS


ELASTICITY OF DEMAND WITH RESPECT TO COMMODITY
Price of Commodity Group GROUP Income 1 2 3 4 5 1) Cereals 1.35 -0.42 -0.01 0.07 0.02 0.33 2) Tobacco and 1.83 -0.09 -0.44 0.08 0.08 0.36 Beverages

3) Other Foods 1.06 0.12 0.02 -0.54 0.07 0.34 4) Non-Food 1.35 0.08 0.05 0.10 -0.57 0.34 5) Labor Supply 0.72 0.14 0.02 0.05 0.07 -0.28



The income (expenditure) responsiveness of three of the five goods categories are significantly elastic. The high degree of income responsiveness of tobacco and beverages is








89

striking and may indicate the increasing integration of rural demand with goods produced in other sectors and regions. The only locally produced commodity included in Good 2 is sorghum beer. The exception to the high degree of income responsiveness is the labor supply that while still positive allows for the intuitively appealing result of increased consumption of leisure with increasing income.

The compensated demand elasticities of Table 5.4 allow direct interpretation of goods as complements, substitutes or independent commodities. The value of most cross price elasticities are very small, the exception again being the labor supply elasticities. Most goods appear to be slight gross substitutes with the only possible gross complements being cereals with tobacco and beverages. In general, using large aggregate commodity groups the own price elasticities are more responsive than the cross price elasticities. The cross price elasticities tend to reflect the income effect over the substitution effect in aggregate data.

Results from other studies using AIDS models at the

household level tend to reinforce the conclusion of reasonable estimates from this side of the model. Ray found differing responses between rural and urban consumers using a non-linear FIML estimation of the AIDS model from Indian budget data (Ray, 1982). Ray's food group was a necessity and the other non-food group was a luxury. Most price elasticities had the correct signs and the most prominent








90

exception (other non-food) was attributed to aggregation error. Ray's expenditure elasticity for the food group was 0.71 while the price elasticity was -0.68 from rural time series data. Pooled data estimates resulted in higher estimates for both elasticities.

All but one of the own-price elasticities for the goods modeled by Bezuneh, Deaton and Norton using Kenyan data had the expected (negative) sign for both participants and nonparticipants in a Food-For-Work (FFW) scheme (Bezuneh, Deaton and Norton, 1988). The exception was the millet and sorghum good which had a positive own-price elasticity. The authors attributed the sign change of the uncompensated ownprice elasticity to the impact of the profit effect (elasticity estimates for AIDS without the profit effect were not reported). The increase in demand for the millet and sorghum good with an increase in its price was credited to the increased income for farm households from higher prices.

The positive uncompensated own-price elasticity (0.67) was found for FFW participants and not among non-participants whose elasticity estimate (-0.53) was similar to that determined for Burkina (-0.72). Compensated price elasticities for the more comparable (to Burkina) non-participant sample were even more striking. The Kenyan non-participant millet and sorghum own-price elasticity was -0.49 compared to a similar cereals elasticity for Burkina of -0.42. Nonfood uncompensated and compensated elasticities were also








91

similar between non-participant Kenyans and the Burkina sample (-0.72 and -0.62 for Kenya with -0.69 and -0.57 for Burkina, respectively).

Expenditure elasticities between the Kenya and Burkina data also compare favorably. Again comparing the results from the non-participant Kenyan sample with the Burkina data the expenditure elasticities for cereals were 1.04 and 1.35, respectively. The participant Kenyan households had an cereals expenditure elasticity of 1.53.

A final comparison is possible between rural and urban consumer behavior in Burkina derived from an LA/AIDS estimation. Savadogo and Brandt report elasticities for urban Burkina from 1982-83 which could be used to compare with the present rural results (Savadogo and Brandt, 1987). These authors found high uncompensated own price elasticities of demand for domestic cereals that ranged from -1.80 to -2.85, depending upon wealth category; wealthier households being more responsive. The income elasticity for locally produced cereals ranged from 0.63 to 1.13 with a sample mean of 0.94. Again, wealthier households were more responsive than less well off households.

The most appropriate comparison between the urban and rural elasticities is between the lowest income urban and the average rural household. The rural price and expenditure elasticities found in the present study are significantly different from those found by Savadogo and Brandt. Recall








92

that the uncompensated own price elasticity for cereals was

-0.72, while the expenditure elasticity was 1.35. The implication is that rural households are less responsive to price changes and more responsive to income changes than urban households.

However, the comparisons between these two studies requires a significant caveat. The urban data, while estimated under an LA/AIDS model, used the non-linear AIDS elasticity computing formulas for deriving parameter estimates and subsequent elasticities. The Green and Alston result reported above implied that the resulting elasticity estimates would be incorrect.

Fortunately, Savadogo and Brandt also ran their data

under an LES and reported the results. Using LES the income elasticity of demand for domestic cereals for the lower 25th wealth percentile was 1.29. This value compares favorably with the 1.35 value found for rural Burkina. The very different price elasticities can be explained by the choice of elasticity estimating formula and the lack of sufficient price variation in the urban data (Savadogo and Brandt, 1987, p. 32). In both the urban and rural models cereal demand is responsive to price changes, but further differences can be expected to arise once the profit effect is brought to bear. Urban consumers are not expected to be as widely influenced by a profit effect because they are generally not producers of the good they themselves consume.














CHAPTER VI
PROFIT EFFECT, POLICY IMPLICATIONS AND FUTURE RESEARCH


This chapter combines the results from both the production and consumption sides of the agricultural household to determine the importance of the profit effect on consumption of cereals in rural Burkina. After presenting the results in section one, the implications for policy in Burkina will be explored in section two. Finally, this chapter and the dissertation will close with some suggestions for avenues of future research that have become evident while undertaking the present effort.

The econometric results from both the production and

consumption sides, presented in the final sections of chapters IV and V, respectively, were encouraging. Although the production and consumption side estimates are interesting, the purpose of this study is to use these results to measure the impact of the profit effect on consumption of the major commodity; cereals. The conclusion that remains from the previous chapters is that extreme departures from rational behavior were not found in the behavior of rural Burkina households. The results obtained for Burkina were also similar to findings from other studies. This tends to reinforce the view that rural households behave in an 93




Full Text
101
Finally, recall the discussion in Chapter IV on the
choice of functional form that implied increased responsive
ness using a direct production function specification,
particularly the Cobb-Douglas approach. Thus, the output
price elasticity of profit is expected to be higher than it
would be under other specifications. From the profit effect
equation (eq. 6.3) this would imply that the profit effect
observed could be somewhat overstated in this instance
which, if corrected, would further reduce the impact of the
profit effect in the current setting.
Policy Implications
The impact of including the production induced profit
effect in determining household consumption response is
clear from the results of the previous section. The absolute
value of all but one of the estimated output price elastici
ties of demand decreased in value. Thus, traditional ap
proaches to demand estimation would have overstated the
magnitude of household responsiveness to price changes. This
is important to keep in mind when interpreting consumption
elasticities from traditional demand approaches in economic
systems characterized by household-firms. The impact of
increasing prices on profits will serve to mitigate the
overall negative impact on demand.
The emergence of household income diversification
strategies in response to variable agricultural production


Ill
framework for the treatment of stocks could be implemented
in the present model given additional time and effort to
work from the raw data and incorporate changes in the
present model.
The spatial variability of price and quantity data can
be used to determine price elasticities of demand and allow
disaggregation of the consumption side of the present model
from the same data set. This would provide insights into
price effects across specific commodities within the rural
Burkina consumption bundle. A rural consumer price index
could be created for monitoring household level impacts of
price changes on a regular basis. If found to be correlated
with certain locations or household characteristics this
information could be used for targeting interventions to
reach those households most in need. Deaton has outlined an
approach for determining disaggregated price elasticities of
demand from spatially varying data (Deaton, 1989).
Two major assumptions underlying the model presented in
this research are that households are profit maximizers and
that markets are perfectly competitive. Perhaps in the
present setting the latter is a more specious assumption
than the former. In both cases, modifications to the present
model could be undertaken to better reflect reality. Ellis
presents a very useful introduction and comparison of a
variety of household models with differing decision-making


91
similar between non-participant Kenyans and the Burkina
sample (-0.72 and -0.62 for Kenya with -0.69 and -0.57 for
Burkina, respectively).
Expenditure elasticities between the Kenya and Burkina
data also compare favorably. Again comparing the results
from the non-participant Kenyan sample with the Burkina data
the expenditure elasticities for cereals were 1.04 and 1.35,
respectively. The participant Kenyan households had an
cereals expenditure elasticity of 1.53.
A final comparison is possible between rural and urban
consumer behavior in Burkina derived from an LA/AIDS estima
tion. Savadogo and Brandt report elasticities for urban
Burkina from 1982-83 which could be used to compare with the
present rural results (Savadogo and Brandt, 1987). These
authors found high uncompensated own price elasticities of
demand for domestic cereals that ranged from -1.80 to -2.85,
depending upon wealth category; wealthier households being
more responsive. The income elasticity for locally produced
cereals ranged from 0.63 to 1.13 with a sample mean of 0.94.
Again, wealthier households were more responsive than less
well off households.
The most appropriate comparison between the urban and
rural elasticities is between the lowest income urban and
the average rural household. The rural price and expenditure
elasticities found in the present study are significantly
different from those found by Savadogo and Brandt. Recall


117
(9) Gc(dQc) + G.(dQ.) + GL (dL) + Gv(dV) = 0
matrix as:
Uu
Uun
Uu,
-w
Uml
Urn,
-Pm
U*
Uan
Uaa
~Pa
-w
~Pm
Pa
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0 0
0 0
0 0
0 0
Lg G
H cc H ca H cL
G G G,
H M fji
-Gl
H
to
0
0
0
0
la.
la.
M
La
la
LL
II VC ^ 9v
G
M
0 0
0 0
0 0
0 0
G G
H f
O.
^ S
fed to
form a
9x9
dX,
~ Hdw~
dXa
PdPa
d/i
*
Qc
=
-dqc
dQc
-Pa
Qc
dpL
dQc
£?(-)
dg.
0
M
L. 1
which is clearly block recursive.
Note that each submatrix block above is itself a
bordered Hessian matrix. The upper left block contains the
information for the utility maximization problem while the
lower right matrix contains the necessary information to
solve the profit maximization problem. Because full income
is determined in the production block the consumption block
is dependent upon the result of the production block for its
own solution. The system is block recursive in that the
consumption decisions are partially determined by the
outcome of the production decisions. However, the consump
tion decisions have no impact on the production decisions.


29
variable inputs (labor, animal input, mechanical input,
fertilizer and seed) and two fixed inputs (land and capital
assets). All prices were normalized by output price.
The functional form used was log linear and estimation
was by ordinary least squares. They tested for both profit
maximization and constant returns to scale, as in the case
of Taiwan, with similar results; neither hypothesis could be
rejected. A further result was that both factor demand and
output supply were sensitive to changes in output price.
Clearly, the work on the Thai data was quite similar to
that using the Taiwanese data, but it was reassuring to find
that both profit maximization and constant returns to scale
held in the two different environments. The authors foretell
their future plans for this data when they state that "the
next step of the analysis of the Thailand data also
combines the consumption side of the agricultural household
(Adulavidhaya, Kuroda, Lau, Lerttamrab and Yotopoulos, 1979,
p. 85).
Consumption in Thailand
The consumption analysis of Thai agricultural household
data proceeded along the same lines as that outlined for the
Taiwanese data (Adulavidhaya, Kuroda, Lau and Yotopoulos,
1984). Utilizing a linear logarithmic expenditure system
under the assumption of utility maximization, they described
an indirect utility function. Specifying a translog func-


53
technology through equation 3.10. In equation 3.10 the only
endogenous variable utilized in the characterization of the
production technology is total labor, L. Thus, production
decisions are made separate from consumption decisions; they
are separable decisions. The recursive nature of the model
becomes evident as consumption decisions are seen to be
dependent upon production decisions, but not vice versa.3
Profit Effect
The major result of the agricultural household model is
the introduction of the profit effect. As outlined in the
Introduction, the profit effect can counterbalance tradi
tional neoclassical theory of household behavior with
respect to price changes. This section outlines an example
of the profit effect through an increase in output price and
its implications for consumption.
The total change in quantity demanded, dXa, with a
change in output price, dPa, can be determined by totally
differentiating the appropriate demand equation. Totally
differentiate the demand for the agricultural good (equation
3.14) and divide by the change in its own-price, assuming
that the prices of market goods and wages are exogenous, to
give
dXa/dPs = 3X./3P, + (dXa/dY*) (dY*/dPJ (3.15)
3 For a more rigorous presentation of the recursivity of
the model see the Appendix.


Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy
AN AGRICULTURAL HOUSEHOLD MODEL
FOR
BURKINA FASO, WEST AFRICA
By
CHARLES ALAN MAY
MAY 1992
Chairman: Dr. Urna Lele
Major Department: Food and Resource Economics
Agricultural households are often household-firms which
behave as both producers and consumers of goods. Household-
firms may have unexpected economic responses to price
changes. When the price of the good both produced and
consumed increases, profits will increase for the firm.
Increased profits increase household income and consumption
of the good. However, a household facing higher prices will
normally decrease consumption of that good. The result of
these opposing economic forces is explored in this study.
A literature review of agricultural household models
and results from other empirical studies are presented. The
theory of the household-firm and its indefinite conclusion
on price responsiveness supports the need for empirical
vi


CHAPTER I
INTRODUCTION
The majority of empirical studies in agricultural
economics are microeconomic in nature. In fact, some would
argue that agricultural economics is best characterized as
empirical microeconomics. Neoclassical microeconomic theory
concerns the firm in production and the household in con
sumption. In developing countries the majority of agricul
tural households act as both a firm and a household. They
provide their own labor and consume the bulk of their own
production. Thus, decisions concerning production, consump
tion and labor in developing countries often influence each
other within household-based economies. That the household
is the chosen unit of analysis should come as no surprise to
most economists. The foundation of consumption economics is
the household. Recall also that the word "economics" origi
nates from ancient Greek and means the "laws that govern the
household."
This study outlines an integrated theoretical and
empirical approach to deal with agricultural households
which are both producers and consumers of goods that origi
nate from the household-firm. A theoretical framework is
proposed for a model that integrates both the production and
1


88
TABLE 5.3
UNCOMPENSATED DEMAND ELASTICITIES FOR THE LA/AIDS
COMMODITY
GROUP
ELASTICITY OF DEMAND WITH RESPECT TO
In
come
Price of Commodity Group
1
2
3
4
5
1) Cereals
1.35
-0.72
-0.06
-0.07
-0.09
-0.40
2) Tobacco and
Beverages
1.83
-0.49
OJ
in

o
1
-0.11
-0.08
-0.63
3) Other Foods
1.06
-0.12
-0.03
-0.65
-0.02
-0.24
4) Non-Food
1.35
-0.23
-0.00
-0.04
-0.69
-0.39
5) Labor Supply
0.72
-0.02
-0.00
-0.03
0.001
-0.67
TABLE 5.4
COMPENSATED DEMAND ELASTICITIES FOR THE LA/AIDS
COMMODITY
GROUP
ELASTICITY OF DEMAND WITH RESPECT TO
In
come
Price of Commodity Group
1
2
3
4
5
1) Cereals
1.35
-0.42
-0.01
0.07
0.02
0.33
2) Tobacco and
Beverages
1.83
-0.09
-0.44
0.08
0.08
0.36
3) Other Foods
1.06
0.12
0.02
-0.54
0.07
0.34
4) Non-Food
1.35
0.08
0.05
0.10
-0.57
0.34
5) Labor Supply
0.72
0.14
0.02
0.05
0.07
-0.28
The income (expenditure) responsiveness of three of the
five goods categories are significantly elastic. The high
degree of income responsiveness of tobacco and beverages is


106
As mentioned above, individual estimations of either
production or consumption would have benefitted from addi
tional degrees of freedom. For example, this would have
provided the opportunity to examine subsets of households
within the sample. A larger sample size is usually prefera
ble, but cost limitations can restrict the number of house
holds surveyed. However, it is important to emphasize that
existing and regular data collection instruments exist in
most countries and could be slightly modified to meet the
needs of household modeling. The inclusion of both produc
tion and consumption data needs in collecting household
survey data should be stressed in this instance. Often the
existing surveys focus on either production or consumption
without realizing that with minimal additions both sides of
household level behavior could be captured.
This study would have gained additional explanatory
power if particular data elements on both sides of the
household model had been of stronger quality. From the
results of the production side of the model it is clear that
subsequent studies on household production and consumption
behavior should be as concerned about collecting information
on prices and quantities of inputs used in production as
budget surveys are on prices and quantities consumed by the
household. The absence of price and quantity data of agri
cultural inputs limited the specification of the production
side of the model and resulted in the use of a less flexible


32
tially monocultural agricultural environment as in the
previous studies of rice-based agricultural economies.
Although Barnum and Squire used the same theoretical
foundation as Lau, Yotopoulos and associates, there were
differences in the choice of functional form between the two
teams. In contrast to the latter's profit function approach
to the production side of the problem, Barnum and Squire
preferred to directly estimate the production technology.
They chose to estimate a Cobb-Douglas specification for the
production technology and then derive the profit function
and input demand equations.
On the consumption side they were more concerned with
the restrictions involved in the Linear Logarithmic Expendi
ture System utilized by Lau, Yotopoulos and associates,
especially the constrained nature of the expenditure elas
ticities. They employed a modified Linear Expenditure System
which, unlike the LLES, did not require that all expenditure
elasticities equal one. However, even with this more flexi
ble functional form, the own price elasticities were re
stricted to be linearly related to the expenditure elastici
ties. The LES is derived from the Stone-Geary additive
utility function.
Of particular interest to Barnum and Squire was the
impact of the analytical framework of agricultural household
models on migration, marketed surplus, technology and the
demand for hired labor. They found that the cost of migra-


26
technology. This profit function was normalized by output
price and specified as being log linear. The profit function
was also considered to be "restricted" because it measured
current revenue minus current variable costs.
From the Taiwan household data these researchers
determined four variable inputs (labor, animal labor,
mechanical labor, and fertilizer) and two fixed inputs (land
and fixed assets). Input demand and output supply equations
were derived from the Normalized Restricted Profit (NRP)
function via Hotelling's Lemma. The method of estimation
used was Zellner's seemingly unrelated regression, because
it is asymptotically efficient for systems of equations that
have related error terms (Zellner, 1962) .
In this first of many studies on agricultural house
holds, Lau, Yotopoulos and Lin tested for profit maximiza
tion and constant returns to scale in production. On the
basis of their results they were not able to reject the
hypothesis of profit maximizing behavior by Taiwanese
agricultural households. Contingent upon profit maximiza
tion, they were also unable to reject the hypothesis of
constant returns to scale in Taiwanese agriculture.
Consumption in Taiwan
Following their earlier work in 1976 on the production
behavior of Taiwanese agricultural households, Lau, Yotopou
los and Lin turned to consumption behavior (Lau, Lin and


65
of education across households in the sample. Thus, the
final estimating equation for the production side of the
household model was the Cobb-Douglas specification using
land and labor as explanatory variables for output.
Estimation Results
This section presents the results from the ordinary
least squares (OLS) estimation of a Cobb-Douglas production
function fitted to Burkina household data on output, area
under cultivation and labor. Both the endogenous and exoge
nous variables were measured in volume rather than value
form. Three dummy variables were added to the basic model to
account for any differences in the production function
across villages. Of course, the model with all dummy vari
ables coefficients equal to zero holds for the fourth
village in the sample (in this case Village 1).
Land and labor are normally considered endogenous
(decision) variables with rental and wage rates exogenously
determined. With land and labor decisions endogenously
determined a simultaneity problem would arise in estimating
a Cobb-Douglas function with OLS. However, other work on the
Cobb-Douglas specification (Zellner, Kmenta and Dreze, 1966)
has shown that if output is stochastic and the household-
firm is assumed to maximize expected profits, then the
resulting error terms of the OLS estimation are independent
of the included endogenous variables. The result is that OLS


8
Chapter III presents the theoretical model based upon
the behavioral assumptions of utility and profit maximiza
tion. Under these conditions the addition of a "profit
effect" is shown to make determination of household response
to price changes indeterminate from theory. One must empiri
cally estimate the behavior from primary data for a region
or situation of interest. By also assuming a functional
labor market, the resulting model can be shown to be recur
sive with production decisions preceding consumption deci
sions. A formal presentation of the recursive nature of the
model is presented in the Appendix.
The results from estimating the production and consump
tion sides of the model are presented in Chapters IV and V,
respectively. A Cobb-Douglas production function is used to
estimate the supply side of the household while an Almost
Ideal Demand System (AIDS) is used in estimating the demand
side of household behavior. The results are more encouraging
from the demand than the production side which directly
reflects the quality and level of detail of the underlying
data.
The presentation of the combined results of the produc
tion and consumption sides of the model arc the focus of
Chapter VI. In addition, implications for policy formulation
in Burkina from this model are discussed. The work is
completed by a discussion of possible avenues for future
research relevant to understanding household level behavior.


38
with indirect, normalized price-based translog and quadratic
restricted profit functions.6
While citing the differing results obtained by Barnum
and Squire versus Tamin on the same Muda Valley data set,
Haughton also points out sources of variation, other than
functional form, that may influence the empirical measure
ment of agricultural household response to price changes.
First, differences may depend on whether or not the re
searcher models a single crop as output or derives some
total farm output figure. Secondly, data may be from differ
ent time periods or regions (not the case in the Muda Valley
studies). Finally, how variables are defined, lagged, or
chosen for exclusion due to lack of data can influence the
results of estimations.
In testing the direct production estimates, Haughton
found that in general, "the Cobb-Douglas form is not sus
tained (Haughton, 1986, p. 213)." However, he goes on to
state that "the superiority of a homogenous translog form
should not be overstated" (Haughton, 1986, p. 213) princi
pally because both forms gave similar output elasticities.
He concludes by arguing that the choice of functional form
will depend upon the particular constraints of the available
data.
6 Recall that the Cobb-Douglas production function is a
special case of the more general translog production function.


86
authors have used different elasticity computing formulas.
The issue has been how to determine the price, both compen
sated and uncompensated, and income (expenditure) elastici
ties of demand. The problem derives from the use of the
Stone price index as an approximation of the price deflator
used in the AIDS model. Thus, the problem is between the
linear approximate AIDS (LA/AIDS) and the non-linear AIDS
(AIDS) computing formulas for price and income demand
elasticities.
From equation 5.3 it is clear that the Stone price
index is a function of the budget shares indicating that the
budget share variable is endogenously determined. These
shares are generally assumed to be constant when taking
derivatives to derive elasticity computing formulas for the
LA/AIDS. The confusion arises in the use of non-linear AIDS
computing formulas where the shares are endogenous in
computing elasticities for the LA/AIDS. Green and Alston,
using the same data set under LA/AIDS and AIDS, have found
that the use of AIDS computing formulas in calculating
LA/AIDS elasticities will result in significantly different
elasticity estimates than those from the non-linear AIDS
(Green and Alston, 1990). Green and Alston present the
correct elasticity computing formula for use with the
LA/AIDS model.
AIDS elasticity computing formulas, with variable
expenditure shares, should not be used with estimations of


97
or more succinctly as
Vzx = {Vzx ) + {Vzy ) [Vy.) (v.x) (6*3)
where the left hand term is the total elasticity with the
profit effect and Z is the good consumed (Xa,Xm, or X,) The
first term on the right hand side of equation 6.3 is the
price elasticity of demand. The remaining three terms on the
right hand side are the expenditure elasticity of demand,
profit elasticity of expenditures and the exogenous variable
(price) elasticity of profits. Note that the profit elastic
ity of expenditures simplifies to tt/Y from equation 6.1.
Using the elasticities computed for the production
(Table 4.2) and consumption (Table 5.3) sides of the model
the total effect can be calculated. The principal interest
of this study is the impact of a change in the agricultural
output price on the consumption of cereals (Good 1) by the
household. These elasticities and the profit to full income
ratio (7r/Y) were evaluated at sample means with and without
the profit effect. The resulting agricultural output price
elasticities for the five goods with and without the profit
effect are presented in Table 6.1.
The overall impact of the profit effect is to decrease
the responsiveness of the household to price signals. Note
however, that contrary to the expectations from the majority
of other countries presented in Table 1.1, the Burkina price
elasticities of demand do not change from negative to posi-


43
management process. For example, in a developing country
management techniques and practices may involve the use of
multiple households acting as one unit, sources of income
may be determined by kinship patterns, and cultural practic
es and preferences may influence choices.
The problem of theoretically modelling an agricultural
household can be framed in the standard techniques of
constrained optimization. The household can be assumed to
optimize an objective function, in this case utility,
subject to a series of constraints. These constraints
generally include information concerning the limitations on
behavior due to income, time, and technology.
The General Theory of an Agricultural Household
The general model used in this study can be succinctly
written as a constrained optimization problem as follows:
MAX U = U (X,, Xm, X,) (3.1)
subject to:
(i) PaXa + PmXm + w(L-F) < P.Q
(ii) X, + F = T
(i) Q = Q(L,A)
maximizing utility subject to constraints due to income (i),
time (ii), and technology (iii), respectively. The goods
consumed are the crop produced by the household, Xa; goods
purchased on the market, Xm; and the leisure time available


100
for the sample was 2.5 times greater than average profits.
For the consumption elasticities in Table 6.1 to change
signs, 20 to 25% of total income would have to come from
agricultural production. This would not be an unusual value
to find in most agricultural settings (Reardon, Matlon and
Delgado, 1988 and Staatz, D'Agostino, and Sundberg, 1990),
but in the regions under investigation and in the period
investigated most households sampled did not obtain one
quarter of their full income, which includes valuing total
time available to the household, from agricultural profits.
The valuation of total time available to the household
can also have a significant impact on the n/Y term in the
profit effect equation. As stated earlier, the valuation of
labor is a difficult task in most any setting and this is
particularly true in the Sahel. To make direct comparison of
the present results to the other sahelian studies mentioned
above the valuation of household time must be removed. When
agricultural profits and exogenous income are evaluated for
the sample mean from the present data the total income is
roughly 36,000 French West African Francs (FCFA). This
compares favorably with the range reported by Reardon,
Matlon and Delgado (31-39,000 FCFA). The resulting share of
agricultural profits in total (non-labor evaluated) income
is then found to be around 26%, again very much in line with
the earlier results.


48
Other possible behavioral characteristics could be
modeled through the time constraint. One example is the
inclusion of a cultural variable, C, that reflects the
minimum amount of time devoted by the household to community
or cultural activities. Not all leisure time is devoted to
cultural activities, thus X, > C.
The Technology Constraint
The technology constraint represents the production
technology that is employed by the household in combining
inputs to produce output. A general production function can
be used to represent this underlying technology and is
written as:
Q = Q(L,A) (3.5)
where L is variable labor input and A is the fixed area
under cultivation. This production function is assumed to be
quasi-convex and increasing in inputs.
Combining Constraints to Yield the Full Income Constraint
The three constraints outlined above can be combined
into one constraint in order to simplify the problem.
Substituting both the time and technology constraints into
the income constraint and rearranging gives:
Y = P.X. + PmXm + WX, < P,Q(L,A) WL + wT (3.6)
which can be interpreted as a variant on Becker's "full
income" (Becker, 1965).


69
L = 0.61*(P,/w)Q,
(4.12)
the restricted profit function is
TTr = 0.39*PaQ,
and the profit-maximized output equation becomes
Q* = 7.2*A* (Pa/w) 028.
(4.14)
(4.13)
Production Elasticities
This section outlines the derivation and calculation of
the production side elasticities relevant to the agricultur
al household model. Using the parameter estimates from the
previous section, a table of input demand and output supply
elasticities is constructed. These elasticities are inter
preted for their significance to production decisions and
will be used in Chapter VI to determine the direction and
magnitude of the profit effect and its impact on household
output price responsiveness.
The coefficients on land and labor can be interpreted
as the output supply elasticities, as was demonstrated
through equation 4.3. Similarly, the restricted equation
estimates can be used to determine the relative shares
accruing to land and labor. From Table 4.1 it can be deter
mined that the share for land is 39% while that of labor is
61%. In the same fashion, the impact on output of a 10%
increase in labor is slightly less than twice that of a
similar increase in land.


CHAPTER IV
PRODUCTION SIDE OF THE HOUSEHOLD
In this chapter the rationale for choosing a particular
approach to estimating the production side of the household
and a functional form are outlined. The Cobb-Douglas produc
tion function was chosen for estimation and is presented in
the first section. Derivations of the input demand, profit
function and profit-maximized output supply equations are
also presented in the first section. The results of the
ordinary least squares (OLS) estimation of the Cobb-Douglas
production function are presented in section two. Production
side elasticities are computed in section three, particu
larly the output price elasticity of profits needed for
calculating the profit effect in Chapter VI.
The data used for estimating the production side of the
agricultural household model came from a grain marketing
study performed in Burkina that roughly coincided with
calendar 1984. The data, while richly detailed on the
consumption side, did not particularly focus on household
production information. However, production relevant data
were measured that would allow an uncomplicated character
ization and estimation of the household production system.
The data used in estimating the production side included
57


89
striking and may indicate the increasing integration of
rural demand with goods produced in other sectors and
regions. The only locally produced commodity included in
Good 2 is sorghum beer. The exception to the high degree of
income responsiveness is the labor supply that while still
positive allows for the intuitively appealing result of
increased consumption of leisure with increasing income.
The compensated demand elasticities of Table 5.4 allow
direct interpretation of goods as complements, substitutes
or independent commodities. The value of most cross price
elasticities are very small, the exception again being the
labor supply elasticities. Most goods appear to be slight
gross substitutes with the only possible gross complements
being cereals with tobacco and beverages. In general, using
large aggregate commodity groups the own price elasticities
are more responsive than the cross price elasticities. The
cross price elasticities tend to reflect the income effect
over the substitution effect in aggregate data.
Results from other studies using AIDS models at the
household level tend to reinforce the conclusion of reason
able estimates from this side of the model. Ray found
differing responses between rural and urban consumers using
a non-linear FIML estimation of the AIDS model from Indian
budget data (Ray, 1982). Ray's food group was a necessity
and the other non-food group was a luxury. Most price
elasticities had the correct signs and the most prominent


18
Asia, presented a series of articles using household-based
studies of agriculture in Taiwan and Thailand.
More recently, in the 1980s, agricultural household
models have become a useful analytical technique for examin
ing cross-sectional data in developing country agriculture.
The World Bank sponsored volume, edited by Singh, Squire,
and Strauss (1986), has become the standard volume on
agricultural household models. Further developments and
concerns about these models are now being expressed in the
economic literature on developing country agriculture.
Chavanov
The seminal work on agricultural household models is
that of Alexander Vasilyvich Chayanov on peasant agriculture
in pre-Revolutionary Russia (Chayanov 1966, 1986). Chayanov
based his theory of the family farm on extensive data
collected from regional- and district-level surveys of
peasant households after the serfs were emancipated and land
reform enacted in 1861.
Chayanov held that agricultural households were unique
economic units in that the household "firm" provided the
bulk of its needed production inputs (principally labor)
while at the same time consuming the bulk of its own produc
tion. Because such firms provided their own inputs and
consumed what they themselves produced, the impact of their
decisions might be different from those expected from the


16
naires were used in combination with household interviews to
determine the appropriate composition of a decision-making
unit. Among the criteria used to distinguish a separate
household within a compound were common fields, granaries,
and consumption and contiguous dwellings.
Information from the biweekly, monthly and annual
survey guestionnaires was used in estimating the model that
follows. These data served to support the theoretical model
presented in Chapter III and the estimates for the produc
tion and consumption sides of household behavior presented
in Chapters IV and V, respectively. In addition to the
analytics of the agricultural household model, a wealth of
summary and descriptive information, as well as other
economic inquiries concerning household behavior in Burkina,
could be supported from this data. However, the following
chapters are mainly concerned with the formal modeling of an
agricultural household model to organize and interpret this
large body of information on rural agricultural households
in Burkina.


108
most likely require detailed information on soil quality and
agroclimatic conditions. Millet prefers sandy soils and is
more tolerant to drought than sorghum. Short of collecting
new data, an index could be constructed to determine appro
priate weights for the aggregation of millet and sorghum
rather than the equal weights approach utilized here.
The specification used for the consumption side was a
linear approximate AIDS (LA/AIDS). The appropriateness of
this linear approximation could be tested by estimating the
non-linear AIDS and testing for statistical significance.
This would require using a non-linear estimation technique
which is not difficult given the present state of desktop
computing power. Such a test would determine whether the
Stone price index and approximation is sufficiently differ
ent from the true AIDS. Elasticities could be calculated and
compared for the LA/AIDS and true AIDS.
Green and Alston have reported preliminary comparisons
using the same data set that found no significant differenc
es in the elasticity estimates between the LA/AIDS and the
AIDS (Green and Alston, 1990). They emphasize that this
result holds as long as the correct elasticity computing
formulas are used for the respective models. In concluding,
these authors point out that their results may be "an
artifact of the particular data set we analyzed (Green and
Alston, 1990, p. 444)" and call for Monte Carlo studies for
testing whether LA/AIDS is close to true AIDS. The present


84
TABLE 5.2
UNRESTRICTED AND RESTRICTED ESTIMATES OF THE LA/AIDS MODEL
UNRESTRICTED
RESTRICTED
ESTIMATE
t-STAT
ESTIMATE
t-STAT
GOOD 1 to 2
-0.006
-1.16
-0.015
-7.19
3
-0.001
-0.25
-0.011
-3.49
4
-0.002
-0.58
-0.015
-3.99
5
0.027
1.99
-0.033
-3.70
GOOD 2 to 1
-0.008
-2.50
-0.015
-7.19
3
-0.002
-0.91
-0.003
-1.86
4
0.001
0.69
-0.0005
-0.34
5
0.016
2.32
-0.0008
-0.24
GOOD 3 to 1
-0.023
-4.48
-0.011
-3.49
2
-0.005
-1.43
-0.003
-1.86
4
-0.005
-2.15
-0.002
h*

O
U1
5
0.005
0.39
-0.019
-5.29
GOOD 4 to 1
-0.044
-4.59
-0.015
-3.99
2
-0.003
-0.55
-0.0005
-0.34
3
0.004
0.88
-0.002
-1.05
5
0.002
0.22
-0.012
-2.79
GOOD 5 to 1
-0.036
-2.57
-0.033
-3.70
2
-0.007
-0.92
-0.0008
-0.24
3
-0.037
-6.53
-0.019
-5.29
4
-0.021
-3.99
-0.012
-2.79
This percentage of statistically significant parameter
estimates (one-third to one-half) from an AIDS estimation
compares favorably with other studies. Deaton and Muellbauer
reported 22 out 64 parameter estimates from British data
with t-statistics greater than two (Deaton and Muellbauer,
1980a). Using Kenyan data, Bezuneh, Deaton and Norton found


APPENDIX
RECURSIVITY IN THE AGRICULTURAL HOUSEHOLD MODEL
A major characteristic of the agricultural household
model is the recursive nature of the decision making pro
cess. A natural extension of the first order conditions from
the optimization problem of the agricultural household model
leads to a clear understanding of the recursive nature of
the neoclassical theory of the agricultural household. In
this Appendix the analytics that lead to recursivity under
the assumption of competitive markets are presented in
detail.1
Begin with the optimization problem as:
MAX U = U(X.,Xm/X,) (A-l)
subject to
(i) P.X, + PmXm + wX, = wT + qcQc + PaQa qvV wL + E
(ii) G(Qc,QaiV,L,K) = 0,
a classical optimization problem subject to equality con
straints.2 Household utility is assumed to be a function of
the consumption of three commodities; an agricultural good,
1. This section owes substantially to the Chapter 2
Appendix by Strauss (Singh, Squire and Strauss, 1986).
2 The nonlinearity and inequalities of the previous
presentation have been excluded to aid in the presentation.
113


79
not change the resulting demand. This is also known as the
absence of money illusion, implying that consumers make
consumption decisions upon relative prices, not absolute
price levels. Homogeneity is also derived from the linear
budget constraint.
Symmetry implies that the price effects of quantity
demanded across any two goods will be identical. Acceptance
of symmetry insures that the underlying preference structure
is consistent. Negativity refers to the negative relation
between the demand for a good and its own price, which is
often called the "law of demand." These last two results
derive from the specific axioms of preference underlying
neoclassical demand theory. Deaton and Muellbauer provide
details on the linear budget constraint, axioms of prefer
ence, and the derived constraints of demand (Deaton and
Muellbauer, 1980b).
Full Information Maximum Likelihood (FIML) was chosen
as the preferred method of estimating the AIDS model because
it is invariant with respect to choice of equation dropped
in the demand system (Greene, 1990, p. 528). Recall that in
systems of demand estimation all commodity demand functions
can not be included in the estimating procedure because this
produces a singular covariance matrix. A singular covariance
matrix results in an undefined likelihood function. There
fore, one of the system's equations is dropped in order to
insure non-singularity of the covariance matrix. The parame-


58
household field size by crop, harvest figures, labor force
employed by the household (both family and non-family),
expenditures on variable inputs and durable goods held by
the household.
The area under cultivation in cereals by household,
predominantly millet and sorghum, was aggregated to give a
measure of land under cultivation. Labor was obtained from
household demographic and composition changes plus use of
market labor. Output was measured from the harvest figures
and converted to kilograms of cereal using threshing rates
determined for each household during the survey.
Cobb-Doualas Production Function
The alternatives considered for estimating the produc
tion side of the model were to use either a production or a
profit (cost) function. A Cobb-Douglas production function
was eventually chosen for three main reasons. First, the
available data were more suited to a Cobb-Douglas production
function than a profit (or cost) function approach. For
example, a representative cost for land is extremely diffi
cult to capture in the African agricultural setting. Second,
actual factor use, and hence a production function, was
preferred over factor input prices, and a profit (cost)
function, because the former were available from the survey.
Furthermore, factor input prices were not expected to vary
significantly across households in a cross-sectional data


80
ters of the dropped equation are then obtained from the
adding-up conditions.
Both the unrestricted and restricted estimates were
used to test the restrictions of homogeneity and symmetry
using the likelihood ratio test. Adding-up is assured by
dropping one of the equations, in this case the labor
supplied by the household. In the AIDS model the testable
restrictions imply the following
af = l 7y=0 j3, = 0 (5-
1=0 i=l i=l
E^=0 (5.5)
j
7y =7a (5-6)
for adding-up (5.3), homogeneity (5.4) and symmetry (5.5),
respectively.
The unrestricted and restricted FIML estimates for the
intercept, expenditure and own-price parameters of the
LA/AIDS are presented in Table 5.1. Both homogeneity and
symmetry were imposed in obtaining the restricted parameter
estimates reported in Table 5.1 The results are encouraging
with twelve and eleven of the fifteen coefficients listed
being significantly different from zero (t-statistics
greater than two) for the unrestricted and restricted
estimations, respectively. Most of the significant changes
in t-statistic values occur with the intercept terms.


76
value (like the LLES), or range of values, in order that the
full responsiveness of household expenditures to price and
income changes can be captured.
Derived from utility maximization via a cost function
by way of Shephard's Lemma, the AIDS model can be succinctly
written as
(5.1)
where the share of expenditures allocated to good i (budget
shares; w¡ = p¡q¡/m) are determined as a function of the price
of good j (pj) and total expenditure (m) on all the goods
being examined. Note that changes in relative prices impact
on budget allocations via the gamma terms and changes in
real expenditure impact via the beta coefficients. The beta
coefficients can be interpreted as measuring necessities
(j8<0) or luxuries (j8>0) depending on their sign.
The only non-linear element in the AIDS model of
equation 5.1 is the price index term (log P) that deflates
the value of total expenditure. From the derivation of the
AIDS model this price index is defined as
logP = a0 + £ ak log pk + 1 ]T £ 7 V lo(?P* lgP, (5.2)
The non-linear AIDS price index (logP) of equation 5.2 is
often estimated by the Stone price index (logP*) which is
given as


DEDICATION
To Nana Ama and Kwasi


55
Second, from equation 3.10, dn'/dPk = X, and 3Y*/dP. = X,,
therefore
3YV3P. = dn/dPa (3.19)
But Hotelling's Lemma states that dn/dP, = Q which allows us
to rewrite the profit effect term as:
(3Y*/3P. )dP. = (dnr/dP,) dP = (Q)dP, (3.20)
a term whose sign can be determined. The profit effect is
therefore the product of the quantity produced and the
change in price. Because quantities, Q, are always positive
the sign of the profit effect is determined by the sign of
the price change under study. The result is analogous to the
well known result that the effect of an income increase is
positive for a normal good.
A direct example will help make the impact of this
result clear. The total change in the quantity of the
agricultural good consumed by the household with a change in
the price of that good is given by:
dXa/dP, = dX,/dP. + (X,)dP,. (3.21)
As stated earlier, the first term on the right hand side is
the familiar substitution effect which is negative for a
normal good. The second term on the right hand side has been
defined as the profit effect. With an increase in output
price the profit effect is unambiguously positive while the
substitution effect is negative. Thus, the substitution and
profit effects work in different directions with the same
price change.


28
results of the seemingly unrelated regression equations
(again using Zellner's method). The hypothesis of utility
maximization by Taiwanese households could not be rejected.
Production parameters, such as agricultural output
supply, necessary for the estimation of household income and
marketed surplus, were taken from the previous work on
Taiwanese production by the same authors. The reader will
recall that the output supply was determined using a normal
ized restricted profit function and Hotelling's Lemma. This
profit function has no arguments based upon an underlying
preference structure expressed in a utility function. Thus,
the production decisions are implicitly assumed to be
separable from the consumption decisions. However, because
the output supply affects income, consumption decisions are
influenced by production decisions.
Production in Thailand
After completing studies on production and consumption
behavior in Taiwanese agricultural households, Lau and
Yotopoulos turned to the analysis of data from Thailand.
Working with other scholars from Japan (Kuroda) and Thailand
(Adulavidhaya and Lerttamrab), they examined the production
characteristics of Thai households (Adulavidhaya, Kuroda,
Lau, Lerttamrab and Yotopoulos, 1979). A Normalized Re
stricted Profit function was again employed from which they
derived input demand and output supply equations with four


116
(8) d*/dL = juw + OG/dL) = 0
or: (1/m) (di/dh) = -w + (0/jLt) (dG/dL) .
Note that there is no analogous first order condition
for the capital input variable (K) because it is assumed
fixed to the decision maker, although it is not considered
immutable. The final condition involves the production
Lagrangian multiplier as:
(9) d*/dn = G (Qc, Qa, V, L, K) = 0.
The first order conditions represented by the nine
equations in A-3 can be totally differentiated to yield:3
(1) Uh(dX.) + Uta(dXm) + Uu(dX,) M(dw) w(dM) = 0 (A-4)
(2) U^dX.) + lUidXJ + Uml(dX,) MdPJ Pm(d/i) = 0
(3) U(dX.) + U^dXJ + Ujj(dX,) M(dPa) P,(d/i) = 0
(4) -P,(dX.) Pm(dXJ w(dX,) = w(dL) (T-L-X,) (dP.) -
P.(dQ.) (Q.-X.)(dP.) qc(dQc) Qc(dqc) dE + qv(dV) +
V (dqv) + Xm(dPm) = f
(5) 0//i[Gcc(dQc) + Gca(dQJ + GcL (dL) + Gcv(dV) + Gcd(0//x)]
= -dqc
(6) 0//i[Glc(dQc) + G(dQa) + GaL (dL) + Gav(dV) + G.d(0//i)]
= -dP.
(7) 0/M[Glc(dQc) + Gu(dQa) + Gll(dL) + GLv(dV) + GLd(0//i)]
= dw
(8) 0 / M [ Gvc (dQc) + Gva(dQa) + GvL (dL) + Gvv(dV) + Gvd(0//i)]
= dqv
3 Where Uu = d2U/dX,dXa U,,,, = d2U/dX,dXm, U = d2U/ax,dX,, etc.


I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality, as
a dissertation for the degree of Doctor of Philosophy.
Urna Lele, Chair
Graduate Research Professor of
Food and Resource Economics
I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequater'^ln scope and quality, as
a dissertation for the degre^of Dpqtor of IJh-ilosophy.
\
Robert D. Emerson
Professor of Food and Resource
Economics
I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality, as
a dissertation for the degree qf-^Doctor of Philosophy.
Chris^Gsr^ftndrew
Professor of Food and Resource
Economics
I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality, as
a dissertation for the degree of Doctor of Philosophy.
R. Hunt Davis, Jr.
Professor of History


107
specification. Particular attention should be addressed to
obtaining relevant and reflective information on the prices
and quantities of different types of labor (household,
market and work party) and land, as well as other inputs.
Other production side information that would have broadened
the analysis include soil qualities and agroclimatic varia
tion across households.
On the consumption side it would have been preferable
to stratify the sample households by some of the wealth
surrogates in order to more fully explore the issue of rural
stratification and possibly different behavior patterns of
households by wealth status. Greater detail on time alloca
tion across and within households would have made the
valuation of total time more accurate. The magnitudes and
degree of diversity of the various income sources other than
agriculture should always be explicitly addressed in the
sahelian context.
Turning to elements of modeling in this context, one of
the first areas of productive inquiry would be in attempting
to integrate a multicrop production function rather than the
single crop specification that was used. The multiple crops
common to rural households may also provide a source of
income to the household. This may be particularly true for
specific subgroups within the household, for example the
women in the household. It may also be productive to distin
guish between millet and sorghum production, but this would


47
expression w(L-F), the value of the employed labor, is
interpreted as an expenditure and employed on the left-hand
side of equation 3.3.
On the other hand, if family labor supplied, F, is
greater than the total labor input, L, then the expression
(L-F) is negative and the household is supplying labor to
the off-farm market. The value term w(L-F) is then inter
preted as the return to off-farm labor supplied by the
household and is counted as an addition to income. In formal
specification of the income constraint equation the labor
value term would be subtracted from other right-hand side
terms to ensure that the "negative" quantity (L-F) is
positively valued.
The Time Constraint
The household has the opportunity of utilizing its
total endowment of time in either leisure or labor. There
fore, the sum of the amount of time spent in leisure, X,,
and that spent in family labor input, F, must be equal to
the total time available, T. In equational form this gives
the identity:
X, + F = T. (3.4)
This equality holds if one assumes that all slack time is
leisure. However, if some slack time is considered lost due
to illness, weather or other factors then the equality
becomes an inequality (less than or equal).


34
supply. He also tested for technical and price efficiency
differences between owner-farm households and tenant-farm
households with no significant differences in efficiency
found.
Singh, Squire and Strauss
The empirical embellishments and refinements on agri
cultural household models continued throughout the early
1980s. A collection and synthesis of these works was brought
together in 1986 under the editorship of Singh, Squire and
Strauss (1986). With introductory chapters on the theory of
agricultural household models, these writers then presented
nine case studies by different authors, including the
editors, that utilized the basic framework of a separable,
or recursive, agricultural household model.
These models can be characterized as standard optimiza
tion problems. The household is assumed to maximize a joint
household utility function subject to constraints. There are
generally three constraints on the household's decision
making process. Utility is maximized subject to budget, time
and technology constraints. Prices are assumed to be given
in both input and output markets. Such models can be shown
to be recursive.5
5 See the Appendix to this study for a rigorous pre
sentation of the recursivity of agricultural household models.


112
rules that includes the basic agricultural household model
employed in the present research (Ellis, 1990).
If the labor market assumption is relaxed the recursiv-
ity of the model is lost and the system becomes simulta
neous. The Appendix to Chapter 2 in Singh, Squire and
Strauss presents the model without a functioning labor
market (Singh, Squire and Strauss, 1986). Low offers a model
in which wage rates are allowed to differ given quality
differences in labor (Low, 1986). This would be interesting
to explore in the Burkina case, if reasonably good labor
market data were available. For instance, Saul reports a
preference ordering for households that ranks family labor
above hired labor above work parties (Saul, 1983).
An often overlooked, but important component, of
household-firms is the nature of intrahousehold decision
making, particularly its impact on health and nutritional
status. Folbre presents an extensive review of this litera
ture, including neoclassical, Marxist, and feminist perspec
tives (Folbre, 1986). Ellis is another source for informa
tion on modeling the inner workings of the agricultural
household (Ellis, 1988). Intrahousehold studies require
extremely disaggregated and extensive consumption, produc
tion and distribution data from the household. This type of
information was not available from the Burkina household
surveys used to estimate the present agricultural household
model except on the consumption side.


77
logpj logp* (5,3)
The Stone price is an expenditure share weighted linear
price index which is approximately proportional to P*, if
prices are highly collinear.
AIDS models that utilize the linear approximate (LA)
Stone price index of equation 5.3 are often designated as
LA/AIDS models. Having employed the Stone price index, the
present study is an LA/AIDS model. The distinction between
estimation of the AIDS, with the non-linear price index, and
the LA/AIDS, with the linear Stone approximation, will be
important in determining the appropriate computing formulas
for elasticities of demand in section three below.
Estimation Results
For estimation purposes the household level data were
pooled by considering each household separately over four
time periods within the twelve month data collection period.
Ray used a similar pooling technique to create panel data in
estimating an AIDS model on household budget data from India
(Ray, 1982). The benefits and costs of panel data over cross
sections is discussed in other sources (Ashenfelter, Deaton
and Solon, 1986).
The four time periods correspond to the different
seasons in the agricultural sector of Burkina where behavior
can be expected to vary. The four periods, corresponding to


Solving the General Model 50
Kuhn-Tucker Conditions 50
Profit Effect 53
PRODUCTION SIDE OF THE HOUSEHOLD 57
Cobb-Douglas Production Function 58
Estimation Results 65
Production Elasticities 69
CONSUMPTION SIDE OF THE HOUSEHOLD 73
Almost Ideal Demand System (AIDS) 74
Estimation Results 77
Consumption Elasticities 85
PROFIT EFFECT, POLICY IMPLICATIONS AND FUTURE RESEARCH 93
Profit Effect 95
Policy Implications 101
Future Research 105
APPENDIX
RECURSIVITY IN THE AGRICULTURAL HOUSEHOLD MODEL 114
BIBLIOGRAPHY 119
BIOGRAPHICAL SKETCH 123
V


31
determined through the profit function, and hence the
underlying production technology, is dependent upon the
production decisions of the household. The production
decisions influence the consumption decisions, but the
production decisions are independent of the consumption
decisions.
It is clear from the work of Lau, Yotopoulos and
associates that the beginnings of an integrated theoretical
framework for the analysis of agricultural households were
possible. Heretofore, researchers would focus one entry in
the literature on the production side of the household
followed by a sequel, the analysis of the consumption side,
utilizing the results from the earlier production study. It
was now time for a consistent theoretical framework within
which to specify agricultural household models for develop
ing countries.
Barnum and Squire
Barnum and Squire, in contrast with the earlier studies
outlined above, were the first researchers to incorporate
both production and consumption aspects of the household in
one paper (Barnum and Squire, 1979a, 1979b). This team of
researchers also used cross-sectional agricultural household
data from a Southeast Asian country: the Muda River Valley
in northwest Malaysia. They were also working in an essen-


21
of farm household behavior because it could not be adequate
ly explained by existing theoretical constructs.
He also commented on a "natural history" of the house
hold which can be likened to the "life cycle" income theory.
For Chayanov this "demographic differentiation" of house
holds was more important in determining their behavior than
class differentiation. This idea and others about transform
ing Russia agriculture would eventually lead Chayanov into
conflict with the revolutionaries of post-1917 Russia.
For Chayanov the household economy, although distinctly
different from other analytical economic paradigms, exists
within and is influenced by the prevailing economic system,
be it capitalist or collective. However, the household would
incorporate and adapt to its environment while at the same
time retaining its conceptual uniqueness and calling for
separate analysis. Unfortunately, the complete ramifications
of Chayanov's separate economic theory of the agricultural
household were never fully expounded as he was caught up in
the Stalinist purges and agricultural collectivization of
the 1930s and eventually died in 1939 at the age of fifty-
one.
Nakaiima
Chahiro Nakajima mathematically formalized the work of
Chayanov by expounding on the subjective equilibrium of


94
economically rational fashion once the structure and con
straints of the rural setting in a particular country are
understood.
This study has reflected some of these constraints by
incorporating the changing composition of the household over
time in calculating labor availability and consumption. The
dynamic nature of African household composition (by age and
gender) requires regular monitoring. In this case household
changes were monitored monthly. It was equally important to
correctly identify the structure of the decision making unit
in the regions studied, as mentioned in the Introduction.
Correct specification of the "households" in the sample
provided the basic unit of analysis which did not necessari
ly correspond to nuclear groupings.
Given the diversity of agroclimatic and social systems
in Africa it is important to use the same (identical)
households on both the production and consumption sides in
estimating an agricultural household model. Other studies
have not always been able to do this (for example, Barnum
and Squire). The encouraging results from the econometric
estimations could possibly be attributed to this fact.
However, this approach has limitations because it restricted
the degrees of freedom in estimation. Only those households
with complete production and consumption data for the entire
year were retained for analysis.


45
assume a joint utility function for the household. A
utility function which, when maximized for the household
unit as a whole, is assumed to maximize utility for its
individual members.
Household utility maximization is assumed to be a
function of the goods consumed by the household. In this
case, the goods consumed are the crop produced by the
household, goods purchased on the market, and the leisure
time available to the household. The resulting utility
function is:
U = U (X,, Xm, X,) (3.2)
with X, a vector of agricultural goods, Xm a vector of
market goods, and X, the leisure consumed by the household.
The utility function is assumed to behave in accordance
with standard theory. It is considered to be quasi-concave
in its arguments and its partial derivatives are positive.
Of course, the quantities appearing as arguments in the
utility function are assumed to be nonnegative. Other
household characteristics can be added as arguments in this
utility function. Examples include number of dependents,
level of education, and other socioeconomic factors.
The Income Constraint
As outlined above, this optimization is subject to
certain constraints. In the general agricultural household
model the objective function is constrained by three re-


82
The share of total expenditures allocated to the
consumption of leisure increases with increasing income.
Recall that the labor supply equation is related to leisure
demand through the total time available (X, = T L) The
share estimated in this system is wL/m, which decreases with
increasing income, thereby increasing wX,/m. The broadly
determined leisure variable is the only luxury in this
system. Interpretation of the price parameters in the AIDS
model requires calculation of the relevant elasticity esti
mates which are presented in the next section.
The likelihood values for both the restricted and
unrestricted models were differenced, multiplied by two and
compared to the chi-squared statistic to perform the likeli
hood-ratio test for the validity of the restrictions. The
restrictions were rejected at the 95% level of significance.
Symmetry and homogeneity were imposed separately and also
tested. Both were rejected at the 95% level of significance.
The rejection of the restrictions derived from neoclas
sical demand theory is not unusual in empirical studies.
"The restrictions of homogeneity and symmetry are
consistently rejected by the data (Deaton and Muellbauer,
1980b, p. 80)." In tests of the restrictions Ray found "that
homogeneity is only marginally rejected for the household
AIDS" (Ray, 1982, p. 360). In contrast, the "symmetry re
striction is decisively rejected for the rural sector but
only marginally for the urban sector" (Ray, 1982, p. 360).


85
85 out of 124 parameter estimates that were more than twice
their standard errors, but this figure included both cross
price and other parameters (Bezuneh, Deaton and Norton,
1988). Finally, Ray's Indian data resulted in 21 out of 32
cross price parameter estimates with greater than "unit t
values (Ray, 1982, p. 357)." Inspection of Ray's results
reveals that 10 out of the 32 cross price estimates had t-
statistics greater than two.
The poorer performance of the parameter estimates for
cross-price behavior can be attributed to the difficulties
arising from aggregation across commodities. The four
tangible consumables in this study consisted of varying
numbers of individual commodities. Two of the goods created
from the disaggregated data were composed of around ten
commodities, namely Cereals (Good 1, 11 commodities) and
Tobacco and Beverages (Good 2, 9 commodities). Other foods
(Good 3) and other non-food (Good 4) were composed of 71 and
51 commodities, respectively. The difficulty in determining
cross-price behavior from this level of aggregation is not
surprising. Similarly, it is not surprising that the most
significant cross price parameters arose for the least
diverse good grouping (i.e., Good 1, cereals).
Consumption Elasticities
Consumption elasticities from the AIDS model have
received considerable attention in recent years. Various


CHAPTER II
LITERATURE REVIEW
The interest and development of the theory of agricul
tural households has an international flavor with its
beginnings in Imperial Russia, mathematical specification in
Japan, and empirical verification in the United States. The
idea of recording and studying the actual behavior of
peasant farmers began in Russia in the 1880s with the advent
of reforms under Alexander I. This highly detailed examina
tion of farm life in pre-Revolutionary Russia formed the
basis of inquiry on agricultural households by A.V. Chay-
anov.
Nakajima, working and publishing mostly in Japan, was
the first to work out a neoclassical framework and the
comparative statics for the family farm. Although his work
was mainly theoretical, Nakajima's writings provided the
basis for the testing, modification and subsequent refine
ment of agricultural household models.
The empirical estimation of agricultural household
models began in the mid-1970s with most of the work coming
from the Food Research Institute at Stanford University. Lau
and Yotopoulos, working with other scholars from Southeast
17


120
Low, Allan. Agricultural Development in Southern Africa:
Farm-Household Economics and the Food Crisis. London:
James Currey, 1986.
May, Charles A. "Farm Level Grain Security in Burkina Faso,"
in The Dynamics of Grain Marketing in Burkina Faso.
Vol. Ill, Research Report 2, Center for Research on
Economic Development, University of Michigan and Inter
national Agricultural Programs, University of Wiscon
sin, Ann Arbor, May 1987.
Nakajima, Chahiro. Subjective Eguilibrium Theory of the Farm
Household. Amsterdam: Elsevier, 1986.
Nakajima, Chahiro. "Subsistence and Commercial Family Farms:
Some Theoretical Models of Subjective Equilibrium," in
Subsistence Agriculture and Economic Development, ed.
by C.R. Wharton, Jr. Chicago: Aldine, 1969, pp. 165-
185.
Reardon, Thomas, Peter Matlon and Christopher Delgado.
"Coping with Household-level Food Insecurity in
Drought-affected Areas of Burkina Faso." World Develop
ment. 16(1988): 1065-1074.
Renkow, Mitch. "Household Inventories and Marketed Surplus
in Semisubsistence Agriculture." American Journal of
Agricultural Economics. 72(1990): 664-675.
Saul, Mahir. "Work Parties, Wages and Accumulation in a
Voltaic Village." American Ethnologist. 10(1983):
77-95.
Savadogo, Kimseyinga and Jon A. Brandt. Household Food
Demand in Burkina Faso with Food Supply-Demand Balance
Projections for 1995. West Lafayette, Indiana: Interna
tional Programs in Agriculture, Purdue University,
1987.
Singh, Inderjit, Lyn Squire and John Strauss (eds.). Agri
cultural Household Models: Extensions. Applications,
and Policy. Baltimore: The Johns Hopkins University
Press, 1986.
Staatz, John M., Victoire C. D'Agostino and Shelly Sundberg.
"Measuring Food Security in Africa: Conceptual, Empiri
cal, and Policy Issues," American Journal of Agricul
tural Economics. 72(1990): 1311-1317.
Tamin, Mokhtar. "Microeconomic Analysis of Production Behav
ior of Malaysian Farms: Lessons From Muda," Food Re
search Institute Studies. 17(1979): 87-98.


27
Yotopoulos, 1978). Assuming utility maximization by the
household, these researchers employed an indirect utility
function to analyze the consumption behavior of agricultural
households.
Utilizing a linear logarithmic expenditure system
(LLES) they estimated commodity expenditure equations
derived from a transcendental logarithmic (henceforth,
translog) indirect utility function that is homogeneous of
degree one in prices. The commodity expenditure equations
for three aggregated commodities (agricultural commodities,
non-agricultural commodities and leisure) were derived via
Roy's Identity. Household characteristics, such as the size
and composition of the household, were included as arguments
in the indirect utility function.
The translog indirect utility function is assumed to be
homogenous of degree minus one. One implication of this
assumption, for both the Taiwanese and subsequent Thai
consumption analysis, is that the total expenditure elastic
ity of demand for each commodity is identically equal to
one.4
Elasticities for consumption demand, labor supply and
marketed surplus with respect to prices, incomes, household
composition and household endowment were derived from the
4 This, of course, not does not imply that income
elasticities are identically one, because the imputed value of
leisure is included as part of total expenditure in these
studies.


5
constraint by a profit function, agricultural household
models are within the neoclassical paradigm. However, they
do allow an additional flexibility in modeling with regard
to the consumption response of households to exogenous
changes via the income term, often called the "profit
effect."
It is through the income term that the two sides,
production and consumption, are linked. For an agricultural
household that obtains the preponderance of its income from
the sale of agricultural commodities, it is the production
technology that first dictates income, which is usually
modeled via a profit function. However, once this income
level is established, it becomes an argument in the determi
nation of the level of indirect utility. The result is a
recursive model where production decisions precede and
delimit consumption decisions, but not vice versa. The
recursive nature of these models is dependent upon the
existence of competitive input and output markets.
Recursive decisions are thought to be sequential in
that one set of decisions precedes and subsequently sets
parameter values for other decisions. Recursive decisions
are often described as separable because a set of initial
decisions are assumed to be made separate from subsequent
decisions. For example, in agricultural household models
production decisions are thought to have no influence on the


81
TABLE 5.1
UNRESTRICTED AND RESTRICTED ESTIMATES OF THE LA/AIDS MODEL
UNRESTRICTED
RESTRICTED
ESTIMATE
t-STAT
ESTIMATE
t-STAT
INTERCEPT a,
-0.520
-5.61
-0.014
-0.23
a2
-0.165
-3.43
-0.039
-1.84
3
0.009
0.11
0.141
4.31
a4
-0.091
-0.99
-0.032
-0.69
5
1.767
11.86
0.945
9.84
EXPENDITURE 6,
0.047
5.79
0.052
5.94
r2
0.022
8.97
0.023
8.71
*3
0.010
1.84
0.004
0.84
B4
0.030
3.16
0.021
2.73
*5
-0.111
-6.98
-0.100
-7.06
OWN-PRICE 7,
0.111
16.78
0.075
10.29
72
0.022
-2.50
0.019
8.71
73
0.036
20.58
0.036
18.43
74
0.028
7.08
0.030
8.21
7s
-0.049
-2.93
0.067
5.57
Note that the expenditure parameter estimates are
positive for four out of the five goods in both the unre
stricted and restricted models. As mentioned earlier, the
AIDS configuration allows for classification of goods as
necessities and luxuries depending upon the sign of the beta
coefficients. Inspection of Table 5.1 results in the conclu
sion that cereals, tobacco and beverages, other foods and
other non-food are all luxuries in the rural economy of
Burkina. This is not surprising given the low absolute
levels of incomes in the Sahel.


78
quarters, are referred to as the cold (December to Febru
ary) hot (March to May), rainy (June to August) and harvest
(September to November) seasons.
Roughly 140 individual commodities were found in the
raw data from the 87 households. These commodities were
aggregated to four goods, plus labor supplied. The four
goods were cereals (containing all cereal products), tobacco
and beverages (including beer, soda and kola), other foods
(non-cereal food purchases), and other non-food purchases.
Time spent in leisure activities (broadly defined as all
non-farm activities) was determined by subtracting the
amount of agricultural labor time supplied by the household
from the total time available. Thus, leisure is determined
as the residual of the difference between household labor
supplied on-farm and total time available.
Neoclassical demand theory is based upon a set of
preference axioms and a linear budget constraint. Several
restrictions on systems of demand equations can be derived
from these two basic units of theory. These restrictions are
known as adding-up, homogeneity of degree zero in prices,
symmetry and negativity of price effects. Adding-up requires
that the sum of the expenditures across all goods equal
total expenditure and originates from the linear budget con
straint.
Homogeneity of degree zero in prices implies that equal
proportionate changes in both prices and expenditure will


11
uncertain rainfall that results in generally risky agrocli-
matic production zones. This risk generally increases as one
moves from the south to the north of the country.
The four villages selected for study were chosen to
cross these agroclimatic zones. Two villages were chosen in
a chronically cereal production deficit zone, while the
remaining two came from a transition zone that would normal
ly experience surplus production. The two northwestern
deficit villages, Mn and Bougar, are located north and
south of the town of Ouahigouya, respectively. The normally
surplus villages in the west of the country are located
north and south of the major regional town of Ddougou.
Tissi is north of this regional capital and Dankui is
located south of Ddougou.
The data used in this study are from calendar 1984
which captured the drought reduced agricultural production
of 1983-84. Because of the drought, households in the sample
were found to have been dominated by more net purchasers
than sellers of cereals in the year from which data are
available. In order to obtain sufficient cereals to meet
their needs households interacted with the market more than
would have been expected in a normal year. This was reflect
ed in the data by reduced contributions of own agricultural
production as a share of total cereals obtained (both
produced and purchased).


36
Squire and Strauss, 1986) examines households in Sierra
Leone to determine the impact of pricing policies on nutri
tional status, measured as caloric intake. He employs a
Quadratic Expenditure System (QES) to determine consumption
parameters and a multiple output production function to
model the production decisions. In his QES, outputs are
related via a constant elasticity of transformation and
inputs are linked via a Cobb-Douglas production function.
Using data from Indonesia, Pitt and Rosenweig (Singh,
Squire and Strauss, 1986) take Strauss' concern for nutri
tional effects further to determine impacts on health and
from health to labor productivity. Smith and Strauss (Singh,
Squire and Strauss, 1986) turn to distributional issues and
examine the impacts of price policy on different segments of
the rural population in Sierra Leone within the structure of
an agricultural household model. Braverman and Hammer
(Singh, Squire and Strauss, 1986), with disaggregated
commodity data from Senegal, bring the agricultural house
hold model into General Equilibrium analysis. In their model
markets clear through import and export adjustments in
international trade.
Iqbal (Singh, Squire and Strauss, 1986) examines
household borrowing in India by introducing the credit
market into the basic model with a two-period model. Final
ly, Sicular (Singh, Squire and Strauss, 1986) takes a novel
approach by using a programming variant of the general


51
marginal, non-negativity and complementary slackness compo
nents (Intriligator, 1971, p. 49).
Write the generalized Lagrangian function as:
* = U(X.,Xm,X,) + M(Y* PmXm PaXa WX,) (3.9)
where /x is the Lagrangian multiplier and Y* is the value of
full income that results from profit maximizing behavior
such that:
Y* = wT + P,Q(L*,A) Wl* > PmXm + P.X. + wX, (3.10)
= wT + 7T*(P,,w,A)
where L* is the labor input level under the assumptions of
maximized profits, 7r*, and fixed area under cultivation, A.
Note that, consistent with duality theory, the underlying
production technology can be modeled either via a production
function, Q(.), or an indirect profit function, 7r(.).
The Kuhn-Tucker marginal conditions at the point of the
optimum (X,*, Xm*, X,*, /x*) are:
d$/dXa* = 3U/dXa* mP* < 0 (3.11)
a*/dxm- = au/axm* Mpm < o
a$/ax,* = du/dx; mw < o
d$/dll' = Y* PmXm* PaXa* WX,* > 0
The Kuhn-Tucker non-negativity conditions state that
Xa* > 0, Xm* > 0, X,* >0, M* > 0 (3.12)
thus the choice variables and the multiplier are all limited
to the non-negative orthant. The multiplier, /x, is the
marginal utility of full income.


33
tion was low relative to the marginal productivity of an
agricultural laborer, that marketed surplus was not respon
sive to output price changes, and that increases in output
price and technology would positively influence rural wages,
thereby having a favorable impact on rural workers dependent
upon wage labor.
In spite of the different functional forms used in the
estimations of Barnum and Squire versus Lau, Yotopoulos and
associates, the outcomes were reasonable. Their elasticities
were similar enough with those of Lau, Lin and Yotopoulos to
prompt Barnum and Squire to remark on the similarity of
preferences for Taiwanese and Malaysian agricultural house
holds (Barnum and Squire, 1979b, p. 77).
As a follow-up, Tamin used Barnum and Squire's data set
and a log-linear Cobb-Douglas functional form of a normal
ized restricted profit function, with four variable inputs
and two fixed inputs, to model the production behavior of a
cross section of Muda River Valley households (Tamin, 1979).
Joint estimation, by Zellner's seemingly unrelated regres
sions, of the profit function and four factor share equa
tions was undertaken with and without restrictions imposed.
Estimation without restrictions allowed hypothesis tests
for profit maximization and constant returns to scale,
neither of which could be rejected.
Tamin found low own-price elasticities of output supply
as well as low fertilizer price elasticities of output


68
function could possibly add explanatory power. Further error
could originate in the measures used for the explanatory
variables, particularly labor. Labor quality can vary
significantly across household, market and work party labor
sources (Saul, 1983).
Omitted variables could also help explain the reduced
R-squared value. The most likely exogenous variable that
would add information to explain variable output would be
one that captured the highly variable climatology of the
Sahel. Unfortunately, this type of information, or a suit
able surrogate, is not available at the household level. The
village dummy variables add significant explanatory value to
the model and can be interpreted as capturing some of the
agroclimatological variation across the villages.
Another possible missing variable that could help
interpret the lack of explanatory power is the quality of
land. The variability of the quality of land is significant
across households and could improve explanatory power in a
revised estimate. Unfortunately, this variable, or a proxy,
were not available for inclusion in this estimation.
Using the restricted estimation results from Table 4.1
the production side equations needed to proceed with the
agricultural household model can be determined. The produc
tion function (for Village 1) can now be written as
InQ = 1.07 + 0.39*lnA + 0.61*lnL, (4.11)
the household demand for labor is


3
information is important in order to guide economic policies
that will correctly anticipate individual behavior under a
particular policy environment. In other words, will the
people under the policy behave as the policy anticipates, or
in a different manner?
The advent of structural adjustment policies throughout
Africa in the 1980s has made it increasingly important to
understand the impact of price changes. Structural adjust
ment programs, supported by multilateral donor agencies such
as the World Bank and the International Monetary Fund,
generally insist on increased prices for agriculturally
produced goods as an incentive to farmers. However, in
economies where producers are also consumers the impact of
changes in output prices may not have the desired effect on
household consumption or production.
Furthermore, due to the plethora of social and economic
structures in developing countries, there is a lack of basic
descriptive and guantitative information on agricultural
households in different regions. This kind of information is
especially lacking in African countries which only gained
independence within the last twenty to thirty years and set
out to transform their agricultural sectors. As we will find
in the literature review, the majority of the agricultural
household models that have been performed to date have been
for Southeast Asian countries.


CHAPTER V
CONSUMPTION SIDE OF THE HOUSEHOLD
This chapter presents the consumption side of the
household model. The consumer choice between goods to
consume and labor to supply, modeled by an almost ideal
demand system (AIDS), is presented in the first section.
Estimation results from the AIDS model and restrictions from
the neoclassical theory of demand (homogeneity and symmetry)
are examined in the second section of this chapter. In the
final section, expenditure, own and cross-price elasticities
are calculated.
The data used to estimate the consumption side of the
agricultural household are also from the Burkina grain
marketing study. Recall that the household level survey from
this marketing study provided the data for estimating the
production side of the household in the previous chapter.
Expenditure data from the same households used in Chapter IV
are used in this chapter to estimate the consumption side of
the household. These expenditures were obtained from fort
nightly recall interviews in each household. The expenditure
data were complemented with questionnaires designed to
acquire information on quantities given (wages, gifts,
exchanges, etc.) and received (salaries, gifts, remittances,
73


4
Objectives of the Study
The principal goal of this study is to determine
household response to economic incentives through the
determination of elasticities from an agricultural household
model that integrates both consumption and production
aspects of the household-firm. The specific objectives are
to:
1. provide descriptive and quantitative information
concerning the production and consumption behavior
of rural African households,
2. combine both production and consumption aspects of
agricultural households in an integrated econome
tric model,
3. estimate income and price elasticities of demand
using pooled data,
4. estimate output supply and input demand equations
using cross-sectional data, and
5. introduce and empirically measure the impact
of the "profit effect" on cereal consumption.
Agricultural Household Models
The general class of agricultural household models was
chosen as the framework for analysis. These models are
especially suited for modeling the behavior of agricultural
households in developing economies because of their ability
to integrate both consumption and production aspects of the
household.
Consisting of a variant of consumer choice theory in
which the production technology is represented in the income


96
realistic results than an examination of each side of the
household economy individually.
Recall from Chapter III that the influence of produc
tion decisions on consumption behavior enter through the
full income constraint as profits. The full income con
straint (equation 3.10) can be rewritten as
Y = 7r(P,,w,A) + wT + E (6.1)
where it is profits and E adds the impact of exogenous income
to the model. Exogenous income includes rents, remittances,
gifts and other sources of income other than agricultural
profits. As will become clear in this section, the extent of
income diversification, as captured by E, in response to
highly variable agroclimatic conditions will have a signifi
cant impact on the profit effect.
The combination of the profit equation from the produc
tion side (equation 4.13), the demand equations from the
consumption side (equation 3.14) and the full income con
straint from above (equation 6.1) provides the complete
agricultural household model. Total differentiation of this
complete household system of equations yields total response
equations to exogenous changes. Written in elasticity form
these equations for a change in an exogenous variable X
(P,,Pm,w or a0) are given by
IdZ X\ sIdZ X\.(dZ Y\ldY ti\I dn X\
(6.2)


121
Wharton, Clifton R., Jr. (ed). Subsistence Agriculture and
Economic Development. Chicago: Aldine, 1969.
Yotopoulos, Pan A., Lawrence J. Lau, and Wuu-Long Lin.
"Microeconomic Output Supply and Factor Demand Func
tions in the Agriculture of the Province of Taiwan."
American Journal of Agricultural Economics. 58(1976):
333-340.
Zellner, Arnold. "An Efficiennt Metthod of Estimating Seem
ingly Unrleated Regressions and Tests for Aggregation
Bias," Journal of the American Statistical Association.
57(1962), 348-368.
Zellner, A. J. Kmenta and J. Dreze. "Specification and
Estimation of Cobb-Douglas Production Function Models."
Econometrica. 34(1966), 784-795.


AH AGRICULTURAL HOUSEHOLD MODEL
FOR
BURKINA FASO, WEST AFRICA
By
CHARLES ALAN MAY
A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
1992
UNIVERSITY OF F10R13A LIBRARIES


60
Note that the output supply elasticities can be obtained
directly from the parameter estimates of the linearly
transformed Cobb-Douglas production function because
£ql = (dQ/dh)L/Q = dlnQ/ainL = a2. (4.3)
Factor demand equations are obtained from the first
order conditions of profit maximization that equate the
value of the marginal product of a factor to its wage cost,
assuming perfectly competitive markets or
dn/d L = P,(3q/3L) = w. (4.4)
Thus, the household will employ labor, in this case both
on-farm labor and off-farm labor, until the marginal product
of the marginal worker equals the real wage rate.
Note that equation 4.4 has only one endogenous vari
able, L, and, thus, can be solved in terms of P,, w, the
parameters of the production function and the fixed area of
land, A. The general solution to equation 4.4 can now be
written as:
L* = L*(P.,w,A) (4.5)
This result is important because none of the other
endogenous or choice variables appear in equation 4.5, which
emphasizes that household consumption decisions do not
impinge on production decisions in this model. Thus, produc
tion decisions are made separate from consumption decisions;
they are separable decisions.
Multiplying both sides of equation 4.4 by L/Q gives
P,(dQ/dL) L/Q = wL/Q (4.6)


102
will continue to mitigate the negative impact of price
changes on the demand for cereals in certain areas. Perhaps
a policy cue can be taken from this pattern of household
behavior in supporting the emerging diversified income
generating possibilities as a means of promoting household
level food security. The impact of large seasonal and annual
price changes in cereals in the Sahel may be better ad
dressed through income programs rather than direct price
interventions. Similarly, increased market dependence would
imply that market based interventions may have greater
impact in rural Burkina than previously thought.
Greater diversification away from own-production will
continue the process of greater market dependence which
argues for increased market information and infrastructure
in these areas than has traditionally been the case. Exist
ing market information systems (MIS) and infrastructure in
the Sahel have focused more on those areas that are surplus
producers than on areas that are moving towards greater
dependence on the market. This is partly due to past deci
sions to locate most MIS in former grain marketing parasta-
tals whose previous mandates had been to exert monopoly
purchasing and resale of cereals. The exception to this is
in Chad whose grain parastatal was never able to establish
the institutional clout of neighboring sahelian states due
to the civil war.


24
hold provided all of its own labor requirements and consumed
some of its own production.
In each of the four cases proposed by Nakajima he
solves for the comparative statics under the assumption of
utility maximization. He thus obtains the first-order
conditions and equilibrium values of each of the variables
in the respective models. He examines the impact of changes
in asset income, output price, and family size as well as
the effects of technology and seasonality on the comparative
statics.
Nakajima's work provided, in addition to his continuum
classification and comparative statics, the introduction of
a labor market to the theory of the agricultural household.
Contrary to Chayanov, Nakajima allowed for the possibility
of a labor market exchange by the household. He introduced a
market from which the household could obtain or provide
labor at a fixed wage rate. Nakajima's work has received
renewed attention through the recent publication of a
collection of his writings on the subjective equilibrium of
the household (Nakajima, 1986).
Lau, Yotopoulos, and Others
The work of Chayanov and Nakajima was empirically
embellished by researchers at the Food Research Institute at
Stanford, with support from the World Bank and the Ford
Foundation. This research, published principally in the


66
estimation of a Cobb-Douglas land-labor specification yields
consistent parameter estimates assuming expected profit
maximization.
The econometric model of household production behavior
was first estimated with no restrictions on the parameter
estimates. The resulting estimates were then tested to
determine if the sum of the parameters on land and labor was
significantly different from unity (i.e., constant returns
to scale). The statistical test of this linear constraint
would not allow rejection of the null hypothesis that the
sum of the parameter estimates was one at the 95% level of
significance. A confidence interval on the sum of the
parameter estimates was determined at the 95% level of
significance. The resulting range was from 0.71 to 1.59. The
model was re-estimated under the restriction that a, + a2 =
1. Note that the presence of CRS is consistent with profit
maximization because of the assumption of fixed land under
cultivation.
Results from both the unrestricted and restricted
models are presented in Table 4.1. Note that the t-statistic
values are significant at the 95% level for land, labor and
the Village 2 dummy variable in both the unrestricted and
restricted equations.
The R-squared values for both the unrestricted and
restricted equations are not particularly high indicating
that the model explains roughly 40% of the variance in




13
income and production diversification behavior in the face
of risk was found among the households in the present study.
Data
An agricultural household model requires household
production and consumption information, as well as market
price data on commodities and labor. This is an extensive
information requirement and few data sets are available to
support this type of modeling. The data required are most
frequently available in cross section. The data used in this
study are from Burkina Faso and represent household transac
tions data on approximately 87 farm households from roughly
the 1984 calendar year.
Originally part of a grain marketing study,1 the data
were collected in households from four villages in two
different agroclimatic zones in Burkina. Two villages were
from the sahelian northwest while the other two were from
the western sudanian zone. After an initial village census
of all households, samples were selected in a stratified
random fashion by ethnic group. Household budget survey data
were collected on a biweekly basis for twelve months.
Interviewers lived in the villages, visited the households
and interviewed all married inhabitants and those over
1 For a detailed presentation of the data instruments and
setting from which these data originated, see May (1987).


63
in the Cobb-Douglas case, it is not analytically possible
for a translog production (sic) (Haughton, 1986, p. 209)."
The direct specification of a profit, or cost, function
would require information on input prices that is not
available in the Burkina data. Profit and cost function
approaches were unavailable because the input price data
were not sufficient to support estimation. Furthermore, it
is particularly difficult to value the two major inputs in
the African agricultural household production system; family
labor input and land to farm production.
Choice of specification can often have constraining
impacts on model results that must be noted prior to estima
tion. The impact of using a Cobb-Douglas specification on
the resulting production side elasticity estimate have been
mentioned by other writers. Previous studies have shown that
the estimates of direct (quantity-based) production func
tions generally result in larger elasticity estimates than
indirect (price-based) production functions. "Once again the
direct estimates show far greater responsiveness (Haughton,
1986, p. 215)."
Other a priori constraints on the results that are
specific to a Cobb-Douglas specification include constant
unitary elasticity of substitution, input elasticities of
output that are invariant to output level, and strictly
positive input quantities. In spite of these restrictions,


54
where the term dX,/dPa is the standard substitution effect of
neoclassical demand theory. The change in the quantity
consumed of a good given a change in its own price is
negative, if the commodity in question is not an inferior
good. Thus, the first term on the right hand side of equa
tion 3.15 is unambiguously negative for a normal good.
The second term on the right hand side of equation
3.15, (dX,/dY*) (dY'/dPa) represents the profit effect. A
change in the price of the agricultural good changes prof
its, and hence full income, through equation 3.10. This
change in full income will, in turn, change the quantity
demanded of the agricultural good, via the demand equation
(eq. 3.14).
It remains to determine the sign of this profit effect
in order to derive the full impact of a change in the price
of an output which is consumed by the household. First, note
that maximized full income (Y*) given by equation 3.10 is a
function of price levels (P,, w) whose total differential is
given by:
dY* = (dY*/dPa) (dP. ) + (3Y*/dw) (dw) (3.16)
or, when w is unchanged:
dY*/dPa = dY*/dPa. (3.17)
Substituting from equation 3.17, the profit effect term of
equation 3.15 may be rewritten as:
(3.18)
(dXa/dY*) (dY*/dPa) = (dY'/dPJdP,.


testing. The model requires econometric estimation of both
the production and consumption sides of household behavior.
Household level data collected in Burkina Faso during
1984 are used to model production under a Cobb-Douglas
specification with land and labor inputs. Results are satis
factory with labor a binding constraint on the production
process. Lack of household level agro-clinatological infor
mation explains the remaining variability in the data.
Household consumption is modeled under an Almost Ideal
Demand System (AIDS) with prices and total expenditures as
arguments. A linear approximation (LA/AIDS) using the Stone
price index is estimated with Full Information Maximum Like
lihood (FIML). Encouraging results with significant and
correctly signed expenditure and price effects are obtained.
Demand and supply elasticities are derived for the
household. Output price elasticity of demand is computed
with and without the profit effect resulting in a reduced
response, but no sign change. Results are attributed to two
factors; first, data were collected during a poor agricul
tural year and most households were net purchasers of
cereals, thereby reducing the profit effect. Secondly,
household income diversification strategies in response to
highly variable agroclimatic conditions in the Sahel have
resulted in less dependence on agricultural output as a
source of household income, again resulting in a reduced
profit effect.
vii


90
exception (other non-food) was attributed to aggregation
error. Ray's expenditure elasticity for the food group was
0.71 while the price elasticity was -0.68 from rural time
series data. Pooled data estimates resulted in higher
estimates for both elasticities.
All but one of the own-price elasticities for the goods
modeled by Bezuneh, Deaton and Norton using Kenyan data had
the expected (negative) sign for both participants and non
participants in a Food-For-Work (FFW) scheme (Bezuneh,
Deaton and Norton, 1988). The exception was the millet and
sorghum good which had a positive own-price elasticity. The
authors attributed the sign change of the uncompensated own-
price elasticity to the impact of the profit effect (elas
ticity estimates for AIDS without the profit effect were not
reported). The increase in demand for the millet and sorghum
good with an increase in its price was credited to the
increased income for farm households from higher prices.
The positive uncompensated own-price elasticity (0.67)
was found for FFW participants and not among non-partici
pants whose elasticity estimate (-0.53) was similar to that
determined for Burkina (-0.72). Compensated price elastici
ties for the more comparable (to Burkina) non-participant
sample were even more striking. The Kenyan non-participant
millet and sorghum own-price elasticity was -0.49 compared
to a similar cereals elasticity for Burkina of -0.42. Non
food uncompensated and compensated elasticities were also


ACKNOWLEDGEMENTS
Many people deserve mention for their inspiration and
assistance over the years. Those listed below are few and I
risk offending those not included. Omissions are certainly
due to space limitation and not purposeful exclusion. The
following order of mention is simply chronological.
Ken Shapiro and the CRED team provided my introduction
to development economics. I will always be grateful for
their confidence. The support of the Center for African
Studies and the Food and Resource Economics Department was
essential in luring me back to Florida. Non-committee
faculty who impacted this study include Drs. Taylor, Lang-
ham, and Shonkwiler in the literature review, proposal
process and estimation procedures, respectively.
To Chairperson Urna Lele and the other members of my
final committee, particularly Dr. Emerson, many thanks for
their guidance through the final write-up and defense
process. A special thanks to Bill Messina for providing a
haven from everyday concerns while I completed this study.
Finally, the forbearance, patience and love of my wife
and son were crucial to the successful completion of this
work. They certainly suffered more than I from this single-
minded pursuit. To them, all my love and gratitude.
iii


50
maximize utility, one can begin to see how the production
decisions may, in fact, influence consumption decisions
through the income term in the full income constraint.
Solving the General Model
With the substitutions and rearrangements of the income
constraint outlined in the previous section, the original
optimization problem can be restated as:
MAX U = U (Xt, Xm, X() (3.8)
subject to:
(i) P.X, + PmXm + WX, < wT + PaQ (L, A) wL.
The agricultural household has choice variables con
cerning the amount of agricultural goods to consume (XJ ,
amount of market goods to consume (Xm) amount of leisure to
consume (X,) and total labor input supplied to the farm
(L), assuming that acreage under cultivation is fixed (A).
The household, under the assumption of utility maximization,
will seek to optimize the levels of these four choice vari
ables.
Kuhn-Tucker Conditions
In its most general form this model consists of a
nonlinear objective function subject to a nonlinear con
straint. The solution to a nonlinear programming model is
described by the Kuhn-Tucker conditions which consist of


39
His results from the translog and Cobb-Douglas re
stricted profit functions were "disappointing." The share
equations were not significant and the estimation was a poor
fit. He cites the difficulty in measuring restricted profits
because they are a residual and tend to magnify data errors.
The choice of how to value on-farm family labor is also
cited as a source of these poor results. Recall that it was
this same problem which caused Chayanov to conclude that the
neoclassical approach to the analysis of agricultural
households was inadequate.
Haughton proposed a third possibility, the direct
estimation of input demand and output supply equations
derived from restricted profit functions, of which the
normalized quadratic restricted profit function appeared to
be the most promising. This, of course, will require more
close attention to the collection of valid price data, in
addition to quantities, in the developing country context.
Bezuneh. Deaton and Norton
Bezuneh, Deaton and Norton (henceforth, BDN) used an
agricultural household model approach to examine the various
impacts of food aid under a Food-For-Work (FFW) scheme in
the Baringo District of Kenya (Bezuneh, Deaton and Norton,
1988). They chose to model the production side of the
household with a linear programming (LP) approach and the
consumption side with an Almost Ideal Demand System (AIDS).


CHAPTER VI
PROFIT EFFECT, POLICY IMPLICATIONS AND FUTURE RESEARCH
This chapter combines the results from both the produc
tion and consumption sides of the agricultural household to
determine the importance of the profit effect on consumption
of cereals in rural Burkina. After presenting the results in
section one, the implications for policy in Burkina will be
explored in section two. Finally, this chapter and the
dissertation will close with some suggestions for avenues of
future research that have become evident while undertaking
the present effort.
The econometric results from both the production and
consumption sides, presented in the final sections of chap
ters IV and V, respectively, were encouraging. Although the
production and consumption side estimates are interesting,
the purpose of this study is to use these results to measure
the impact of the profit effect on consumption of the major
commodity; cereals. The conclusion that remains from the
previous chapters is that extreme departures from rational
behavior were not found in the behavior of rural Burkina
households. The results obtained for Burkina were also
similar to findings from other studies. This tends to
reinforce the view that rural households behave in an
93


37
agricultural household model to examine the influence of
centrally planned quotas and restrictions on Chinese produc
tion teams. With these case studies, and the introductory
chapters, the editorial work of Singh, Squire and Strauss
(1986) provides a rich source of theoretical and empirical
work concerning agricultural household models.
Haughton
Haughton stresses the importance of choosing an appro
priate functional form for the production function in
estimating agricultural household models (Haughton, 1986).
He argues that without a theoretically sound specification
of a production function the more sophisticated agricultural
household models are of little use. The same can be said for
the specification of the consumption function. Lopez also
stresses the importance of using flexible functional forms
in modeling agricultural household models to ensure the
minimum amount of restrictions on behavior (Lopez, 1984, p.
62) .
In Haughton's study, employing cross-sectional data
from western Malaysia (yet another study using data from
Southeast Asia), he compares the results from the same data
set of different functional forms to represent the underly
ing production technology of the household. Quantity-based
translog and Cobb-Douglas production functions are compared


67
output. This kind of result is not surprising, particularly
for primary, cross-section data. Barnum and Squire's (1979-
a,b) Cobb-Douglas estimation in a monocropping environment
explained roughly 67% of the variation in output. Haughton
(1986) reported R-squared values of around 50%.
TABLE 4.1
UNRESTRICTED AND RESTRICTED
COBB-DOUGLAS PRODUCTION FUNCTION ESTIMATES
UNRESTRICTED
RESTRICTED
PARAMETER
t-STAT
PARAMETER
t-STAT
ESTIMATE
ESTIMATE
Intercept
0.597
0.45
1.072
0.94
In (Land)
0.414
3.38
0.394
3.32
In (Labor)
0.739
3.26
0.606
-
Village 2
-1.778
-5.48
-1.747
-5.45
Village 3
-0.350
-1.02
-0.344
-1.01
Village 4
-0.107
-0.33
-0.131
-0.41
R2
0.419
-
0.417
-
The definition of inputs and output variables could
account for some of the unexplained variation remaining in
the production estimation. For example, the output variable
is an aggregate measure over both millet and sorghum. The
assumption of a single production function for cereals may
be a source of additional variability in the output vari
able. Although the major cereals, millet and sorghum, are
generally aggregated together, a multicrop production


114
Xa, a market good, Xm, and leisure, X,. For this discussion
assume that the household crop production vector consists of
two crops; a cash crop, Qc, and a food crop, Qa.
The first constraint, the full income constraint,
equates expenditures and income. Expenditures consist of the
value of agricultural goods, PaXa, the value of market goods,
PmXm, and the value of leisure time consumed, wX,. Income is
composed of the value of the household's time, wT, the value
of a cash crop, qcQc, the value of a food crop, PaQa, minus
the values of variable inputs and labor, qvV and wL, respec
tively, plus exogenous income, E. Examples of exogenous
income sources include remittances, rents and non-farm
income.
The second constraint introduces the limitations on
behavior due to the household production process. An implic
it production function is employed to describe the relation
ship between variable nonlabor inputs, V, total labor input,
L, fixed inputs, K, and output, Q.
The Lagrangian function can now be constructed as:
$ = U (Xa, Xm, X,) (A-2)
+ /x[wT + qcQc + PaQa qvV wL + E]
- /i[PaXa + PmXm + wX,]
+ 6[G(Qc,Qa,V,L,K) ]
from which the first order conditions may be derived. In
this problem the household has seven choice variables
(X,,Xm,X,,Qc,Qa,V,L) and two Lagrangian multipliers (/x and 0)
for a total of nine first order conditions. Three of the


20
With profits indeterminable, Chayanov proposed a deci
sion rule for the "family farm" that differed from profit
maximization. He suggested that the "family farm" equates
the satisfaction of family needs with the drudgery of work
required. From his intense familiarity with Russian peasant
agriculture, Chayanov realized that Russian peasants did not
work to achieve profit maximization. Their labor supply and
efficiency did not coincide with profit maximizing behavior
as they could almost always provide additional labor or work
harder but chose not to do so.
Chayanov worked towards producing a separate theory of
the "family farm" that would have its own unique analytical
techniques. From his labor-consumer balance, equating the
drudgery of work to the consumption needs of the household,
he concluded that each household would find its own subjec
tive equilibrium. The level of this balance would be influ
enced by the size of the family and its ratio of working to
non-working members.
The "family farm" had a certain resiliency or survival
power that the capitalist farm did not. Peasant farms could
continue to survive in an environment that would bankrupt
capitalist farms or socialist collective farms. They would
do so by working longer hours or selling at lower prices,
even continuing from year to year yielding no net surplus
production. Such behavior required a unique form of analysis


109
data could provide a second set to test for significantly
different elasticity estimates.
Further interesting refinements on the present approach
are possible. These include incorporating risk and wealth
effects, disaggregating price elasticities of demand, and
relaxing two major assumptions from the present model,
perfectly competitive markets (both input and output) and
profit maximization. Wealth effects as measured by on-farm
stocks and durable goods, disaggregated price elasticities
and modeling under relaxed assumptions could possibly be
supported by the same data from which the present study was
undertaken.
The incorporation of risk in economic models has been
particularly useful in agricultural economics because of the
inherent uncertainty in agriculture. These risks are very
apparent in the developing country context. In Burkina, and
throughout the Sahel, a highly variable rainfall climatology
is a major determining characteristic of agricultural
performance. As noted in the production chapter, the lack of
reliable household level information to reflect this vari
able was used to explain the relatively low explanatory
power of the estimated production function. Better under
standing of the riskiness of agricultural production systems
in the Sahel would help explain the variability in output.
Unfortunately, the Burkina household data from which the
present work derives does not have suitable household level


72
responsiveness for the elasticities listed in Table 4.2. An
increase in the wage rate can be expected to reduce the
demand for labor, thereby reducing both output and profits.
Note that the direct influence on labor demand is greater
than the induced declines in both output and profits indi
cating that labor is not the sole factor input in the
household production process. Finally, the significance of
technological change is high and can be expected to increase
demand for labor, output and profits.
What is needed from this production side in terms of
the agricultural household model is the impact of changes in
output price on profits, the output price elasticity of
profit. Table 4.2 reports a value of 2.56 for this elastici
ty implying that profits are highly responsive to output
price changes. Haughton found this elasticity using a direct
approach to be 3.06 while the indirect approach gave 1.89.
The value for Burkina in Table 4.2 (2.56) is approximately
halfway between these two extremes.


104
The only negative compensated cross-price elasticity of
demand may propose a unique opportunity for obtaining
additional food security relevant information for policy
makers. It is evident from Table 5.4 that the price of the
tobacco and beverages good moves in a complementary fashion
with cereals. Thus, an increasing price for cereals coupled
with a decreasing demand for tobacco and beverages could be
used as an early warning indicator of food insecurity for
particular regions. Those regions where the profit effect is
expected to predominate would be expected to exhibit the
same change in consumption patterns. The high expenditure
elasticity of demand for tobacco and beverages combined with
a larger proportion of total income form agricultural
profits would be expected to increase consumption of tobacco
and beverages. Monitoring of market demand for the commodi
ties in the tobacco and beverages good (principally, beer,
cigarettes, coffee, soda and cola) would provide additional
information from which to decide if households are making
significant changes in their consumption habits in response
to a price change.
Most striking is the degree of price and income respon
siveness in the rural sector implying that there are oppor
tunities for substitution between broad groups of commodi
ties. This result is important in development planning in
that it serves to reemphasize the importance of the price
variable even in "subsistence" economies. In fact, the


95
Finally, this work has served to reiterate the impor
tance of clearly distinguishing what are properties result
ing from a particular functional form used to model phenom
ena and what are the properties resulting from the data.
This awareness tempered the results from the production side
of the model and influenced the choice of the flexible AIDS
model for the consumption side. One should always be aware
of which results reflect properties of the chosen specifica
tion versus those that arise from the empirical data. This
would seem to be especially important in estimating a system
such as an agricultural household model where theory does
not determine the direction or magnitude of the behavior
under investigation (in this case the profit effect).
Profit Effect
Within the theoretical construct of the agricultural
household model a change in an exogenous variable, such as
the output price of the agricultural commodity produced,
will have standard price and income effects on consumption
plus a reaction in production decisions. The change in
production decisions is captured through its influence on
profits and is referred to as the profit effect. Because
agricultural household models attempt to capture both the
consumption and production responses of the household to
exogenous changes, these models are likely to yield more


BIBLIOGRAPHY
Adulavidhaya, Kamphol, Yoshimi Kuroda, Lawrence J. Lau,
Pichit Lerttamrab and Pan A. Yotopoulos. "A Microeco
nomic Analysis of the Agriculture of Thailand." Food
Research Institute Studies. 17(1979): 79-86.
Adulavidhaya, Kamphol, Yoshimi Kuroda, Lawrence J. Lau, and
Pan A. Yotopoulos. "The Comparative Statics of the
Behavior of Agricultural Households in Thailand."
Singapore Economic Review. 29(1984): 67-96.
Ashenfelter, Orley, Angus Deaton and Gary Solon. Collecting
Panel Data in Developing Countries: Does It Make Sense?
Living Standards Measurement Study Working Paper No.
23, Washington, D.C.: The World Bank, 1986.
Barnum, Howard N. and Lyn Squire. A Model of an Agricultural
Household: Theory and Evidence. World Bank Occasional
Papers No. 27, Baltimore: The Johns Hopkins University
Press, 1979a.
. "An Econometric Application of the Theory of the
Farm Household." Journal of Development Economics.
6(1979b): 79-102.
Becker, Gary S. "A Theory of the Allocation of Time." The
Economic Journal. 75(1965): 493-517.
Bezuneh, Mesfin, Brady J. Deaton and George W. Norton. "Food
Aid Impacts in Rural Kenya." American Journal of Agri
cultural Economics. 70(1988): 181-191.
Chayanov, A.V. The Theory of Peasant Economy. Edited and
introduction by Daniel Thorner, Basile Kerblay and
R.E.F. Smith. Homewood, Illinois: Irwin, 1966.
. The Theory of Peasant Economy: With a New Intro
duction bv Teodor Shanin. Madison: The University of
Wisconsin Press, 1986.
Deaton, Angus. "Household Survey Data and Pricing Policies
in Developing Countries." The World Bank Economic
Review. 3(1989): 183-210.
118


CHAPTER III
THEORY OF THE AGRICULTURAL HOUSEHOLD
Introduction
The agricultural household in a developing country is
unique for three major reasons. First, the agricultural
household consumes a major part of its own production. The
food crops produced in an agricultural household are partly
consumed by that household while some is marketed to provide
income. Other types of households do not generally consume
part of that which they produce. Hence, in an agricultural
household the output of the "firm" can greatly influence
consumption choices, or levels, via income.
The second reason why agricultural households are
distinctly different from other households is that they
provide their own labor as a major part of the inputs used
in the production process. The combination of being the
major provider of inputs and the major consumer of output
allows for the possibility of unique behavior on the part of
an agricultural household. In this chapter we will outline a
general theory of this type of agricultural household.
The third distinguishing characteristic of agricultural
households in developing countries is the nature of the
42


49
The expenditure side of the household's "full income"
constraint is now augmented by the value of the household's
leisure time, wX,. The income side consists of the value of
agricultural production, PaQ(L,A), the value of the house
hold's entitlement of time, wT, and is diminished by the
value of total labor utilized by the farm, wL. Note that the
value of agriculturally based gross income can be given by
[P,Q(L, A) -PaXa] This can also be interpreted as the value of
marketed surplus, where PaQ(L,A) is the value of gross
agricultural production of the household and PaXa the value
of agricultural goods consumed by the household.1
Note that the full income constraint in the agricultur
al household model contains an element of income whose value
is generated using the household's production technology.
The combined term, PaQ(L,A) wL, on the income side of the
"full income" constraint, represents household profits from
agricultural activity. These profits, n, can be written as:
7t = PaQ(L,A) wL (3.7)
and could be determined via a profit function that can be
specified so as to be representative of the underlying
technology employed by the household.
While the optimization problem is still framed as a
consumption problem in which the household is assumed to
1 This assumes that all agricultural goods not consumed
by the household are sold on the market and not given away in
non-market exchanges which may not always be the case.


75
explicit preferences and demand functions (Deaton and
Muellbauer, 1980a, p. 317).
The crucial points for choosing a functional form for
the agricultural household model is the need for un
restrained elasticities and compatibility with theory. Prior
restrictions resulting from the choice of functional form
could limit the impact of the profit effect on consumer
demand via the full income constraint.
Because of the need for a functional form that does not
restrict parameter estimate values and related elasticities
the almost ideal demand system of Deaton and Muellbauer was
chosen for this study (Deaton and Muellbauer, 1980a). The
AIDS model provides great flexibility for estimation and
testing as Deaton and Muellbauer point out:
. the Almost Ideal Demand System (AIDS), gives
an arbitrary first-order approximation to any
demand system; it satisfies the axioms of choice
exactly; it aggregates perfectly over consumers
without invoking parallel linear Engel curves; it
has a functional form which is consistent with
known household budget data; it is simple to
estimate, largely avoiding the need for non-linear
estimation; and it can be used to test the re
strictions of homogeneity and symmetry through
linear restrictions on fixed parameters. (Deaton
and Muellbauer, 1980a, p. 312)
Most importantly for the present study, the AIDS model
provides for flexible price and income elasticities which
are necessary in estimating a household model because price
and expenditure responses are the major points of interest.
One should not constrain the elasticities to any particular


This dissertation was submitted to the Graduate Faculty
of the College of Agriculture and to the Graduate School and
was accepted as partial fulfillment of the reguirements for
the degree of Doctor of Philosophy.
May 1992
X.
Dean,
ege of Agriculture
Dean, Graduate School


35
Exceptions to this model are the chapters by Roe and
Graham-Tomasi, and Lopez (see also Lopez, 1984) included in
the case studies, both of which bring into question the
recursivity assumption of this neoclassical model of agri
cultural households. Roe and Graham-Tomasi bring risk into
the household decision-making process and find that the
original neoclassical results will only hold under what can
be considered severe restricting assumptions (Singh, Squire
and Strauss, 1986). Lopez (1984; Singh, Squire and Strauss,
1986) shows that the recursivity will not hold if the
household is not indifferent between on-farm and off-farm
labor, both in the sense of labor hired and labor supplied.
Lopez's work is also important in emphasizing that this
literature on agricultural household models is not limited
to the study of developing country agriculture, but is also
useful in describing agriculture in more industrial nations,
in this case Canada.
The remaining seven case studies utilize the basic
model with recursivity intact. Two of the case studies can
be considered as complete systems analyses in the tradition
of Lau, Yotopoulos, et al., and Barnum and Squire. Singh and
Subramanian (Singh, Squire and Strauss, 1986), using data
from Korea and Nigeria, model consumption decisions with a
Linear Expenditure System while the production side employs
a linear program. Their study is characterized by additional
commodity disaggregation and multiple crops. Strauss (Singh,


25
1970s, focused on the empirical workings of the agricultural
household theory developed by Chayanov and Nakajima.
Data were obtained on the agricultural household economies
of two Southeast Asian nations, Taiwan and Thailand.
However, there are notable differences between the
empirical approach of Lau, Yotopoulos, et al., and Chayanov.
In the two Southeast Asian production studies they assume
profit maximization by the agricultural household, which
runs counter to Chayanov's argument that peasant families,
particularly in pre-Revolutionary Russia, do not maximize
profits.
When the separate studies of production and consumption
that follow are combined they yield a complete system
estimation for agricultural households. The system is
complete in the sense that input demand and output supply
equations are estimated for the production side, while
commodity demand equations are estimated for the consumption
side of agricultural household behavior.
Production in Taiwan
Lau and Yotopoulos, along with Lin (Yotopoulos, Lau,
and Lin, 1976), first began their examination of agricul
tural households with cross-section data from Taiwan.
Modeling the production behavior of Taiwanese agricultural
households, they assumed a Cobb-Douglas production function
and utilized a profit function to describe the underlying


110
information to reflect the variable rainfall regimes across
households.
Production risk is difficult and costly to obtain at
the household level, but price risk could possibly be
incorporated given the temporal and spatial variability of
the price data. Production risk studies in sahelian agricul
ture would probably require a different scale of analysis,
perhaps at the sub-national, national or regional levels.
Recent authors have outlined the demands of incorporating
risk into the household framework (Finkelshtain and Chal-
fant, 1991).
Wealth rankings in the Sahel are often a function of
on-farm stocks and durable goods held by the household. On-
farm cereal storage is common in the Sahel when cereals are
available. Almost every household has multiple granaries for
storing grain on-farm. The value of these on-farm stocks
would increase as prices increase, resulting in increased
wealth for those households that can store grain. The
presence and/or absence of these goods in a particular
household will affect that household's wealth status and
hence consumption decisions in the recursive household
model. Renkow has recently provided a framework for incorpo
rating levels of on-farm stocks in an agricultural household
model (Renkow, 1990). The results from his empirical estima
tion did not result in significant changes in the calculated
elasticities, although this will not always be the case. His


9
Clientele for the Research
The clientele for more and better information on
agricultural households begins with the countries themselves
and the various policy arms of the government. Other inter
ested parties for this kind of research may include bilat
eral and multilateral aid agencies. Private and voluntary
organizations, which work directly with farming communities
in developing countries, could also be interested in infor
mation on agricultural household behavior. These parochial
interests should not cause us to overlook, or underempha
size, the purely intellectual appeal of modeling a complex
phenomenon in order to better understand the world.
The Government of Burkina is the principal clientele
for information on agricultural households in Burkina. A
better understanding of the agricultural production and
consumption behavior of agricultural households in Burkina
will be of immediate assistance to planning and policy
formulation. In most developing countries, agriculture
provides income for the majority of the population, serves
as a source of foreign exchange and a productive resource
base for the rest of the economy. Without a good basis of
information, the agricultural sector may not be utilized to
its fullest capacity or may even be impeded by improper
policy.
The specific users of this research would begin with
the various policy arms of the government including, but not


56
Therefore, the total effect of an increase in the price
of an agricultural good produced and consumed by the house
hold can have three possible outcomes. An increase in the
price of the agricultural good may cause a decrease in
consumption via a dominant substitution effect; an increase
in consumption due to a dominant profit effect; or, the two
effects could balance each other resulting in no measurable
effect on household consumption due to an output price
increase. The relative impacts of these two effects on the
response of an agricultural household is indeterminate from
theory. Thus, the particular response for any agriculturally
based household economy must be determined through empirical
means.


64
the Cobb-Douglas approach can give useful results as Haugh-
ton points out:
However, the superiority of a homogenous translog
form over the Cobb-Douglas form should not be
overstated; both have fairly close fits De
pending on what issue is being addressed, the
simpler Cobb-Douglas form may be adequate, Both
give essentially similar output elasticities with
respect to inputs (at the geometric mean values of
the variables). (Haughton, 1986, p. 213)
Awareness of these and other impacts of model specification
should be retained and used to temper the interpretation of
the final results.
Additional explanatory variables, other than land and
labor, were also created from the raw household data to
represent expenditures on variable inputs (fertilizer, seed,
insecticides, etc.) and capital inputs (durable good hold
ings as a proxy). Their inclusion in the model did not add
additional explanatory value and hence were not retained for
the final estimation. Moreover, few households in the sample
reported using inputs other than land and labor.
Another likely omitted explanatory variable is farm
management. Surrogate variables based on the age and educa
tional level of the head of household were added to the
basic model to capture the variance of management capability
across households. The resulting specifications did not add
explanatory power to the model with management proxies based
on age, head of household educational level and maximum
educational obtained within the household. These results can
be explained by the lack of significant variance in levels


BIOGRAPHICAL SKETCH
Although born outside of Atlanta in 1956, Charles Alan
May moved to Florida in time to experience Hurricane Donna.
He obtained all of his primary and secondary school educa
tion in Orlando, graduating from Edgewater High School in
1973. In 1977, he graduated from Colorado College in Colora
do Springs, Colorado, with a bachelor's in chemistry and a
Russian minor. After working for a year as an environmental
chemist, he served two years as a Peace Corps volunteer in
Ghana, West Africa, as a secondary school and junior college
teacher. Upon returning to the U.S., he enrolled in a mas
ter's program at the University of Michigan in the School of
Natural Resources.
Through the University of Michigan's Center for Re
search on Economic Development and the University of Wiscon
sin's International Agricultural Programs, Charles joined a
team of researchers examining cereals markets in Burkina
Faso, West Africa. He completed his master's degree in
resource policy, economics and management at the University
of Michigan, in 1987.
After two years of field and stateside work (Burkina
and Madison) Charles enrolled in the Food and Resource
Economics Department (FRED) at the University of Florida
122


44
to the household, X,. Prices for goods and services are the
price of the agricultural commodity, Pa, market commodities,
Pm, and wages, w. Total time, T, is allocated to agricultur
al labor supplied by the household, F, and leisure, X,.
Agricultural output, Q, is the product of total labor (L)
and land, A.
Leisure time is broadly defined in this model to
incorporate any activity undertaken by the household that is
related to own agricultural production. This is a key point
in analyzing the behavior of sahelian agriculturalists.
Recent studies have found that as much as seventy percent of
total household income in extremely risky agroclimatic zones
comes from non-agricultural production (Reardon, Matlon and
Delgado, 1988 and Staatz, D'Agostino and Sundberg, 1990). In
this model the diversified income strategy in response to
agricultural risk is captured as exogenous income.
The Utility Function
The agricultural household is assumed to function under
a joint utility function for the household as a distinct
unit. In this particular theory there is no concern for the
intrahousehold distribution of resources. Although such
distributional issues are important (see Folbre, 1986), the
data from which the model will be estimated is not suffi
ciently disaggregated to allow examination of the issues
concerning intrahousehold distribution. Thus, the model will


AH AGRICULTURAL HOUSEHOLD MODEL
FOR
BURKINA FASO, WEST AFRICA
By
CHARLES ALAN MAY
A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
1992
UNIVERSITY OF F10R13A LIBRARIES

DEDICATION
To Nana Ama and Kwasi

ACKNOWLEDGEMENTS
Many people deserve mention for their inspiration and
assistance over the years. Those listed below are few and I
risk offending those not included. Omissions are certainly
due to space limitation and not purposeful exclusion. The
following order of mention is simply chronological.
Ken Shapiro and the CRED team provided my introduction
to development economics. I will always be grateful for
their confidence. The support of the Center for African
Studies and the Food and Resource Economics Department was
essential in luring me back to Florida. Non-committee
faculty who impacted this study include Drs. Taylor, Lang-
ham, and Shonkwiler in the literature review, proposal
process and estimation procedures, respectively.
To Chairperson Urna Lele and the other members of my
final committee, particularly Dr. Emerson, many thanks for
their guidance through the final write-up and defense
process. A special thanks to Bill Messina for providing a
haven from everyday concerns while I completed this study.
Finally, the forbearance, patience and love of my wife
and son were crucial to the successful completion of this
work. They certainly suffered more than I from this single-
minded pursuit. To them, all my love and gratitude.
iii

TABLE OF CONTENTS
page
DEDICATION ii
ACKNOWLEDGEMENTS iii
ABSTRACT vi
INTRODUCTION 1
Problem Statement 2
Objectives of the Study 4
Agricultural Household Models 4
Layout of the Study 7
Clientele for the Research 9
Background on Burkina 10
Data 13
LITERATURE REVIEW 17
Chayanov 18
Nakajima 21
Lau, Yotopoulos, and Others 24
Production in Taiwan 25
Consumption in Taiwan 26
Production in Thailand 28
Consumption in Thailand 29
Barnum and Squire 31
Singh, Squire and Strauss 34
Haughton 37
Bezuneh, Deaton and Norton 39
THEORY OF THE AGRICULTURAL HOUSEHOLD 42
Introduction 42
The General Theory of an Agricultural Household 43
The Utility Function 44
The Income Constraint 45
The Time Constraint 47
The Technology Constraint 48
Combining Constraints to Yield the Full In
come Constraint 48
iv

Solving the General Model 50
Kuhn-Tucker Conditions 50
Profit Effect 53
PRODUCTION SIDE OF THE HOUSEHOLD 57
Cobb-Douglas Production Function 58
Estimation Results 65
Production Elasticities 69
CONSUMPTION SIDE OF THE HOUSEHOLD 73
Almost Ideal Demand System (AIDS) 74
Estimation Results 77
Consumption Elasticities 85
PROFIT EFFECT, POLICY IMPLICATIONS AND FUTURE RESEARCH 93
Profit Effect 95
Policy Implications 101
Future Research 105
APPENDIX
RECURSIVITY IN THE AGRICULTURAL HOUSEHOLD MODEL 114
BIBLIOGRAPHY 119
BIOGRAPHICAL SKETCH 123
V

Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy
AN AGRICULTURAL HOUSEHOLD MODEL
FOR
BURKINA FASO, WEST AFRICA
By
CHARLES ALAN MAY
MAY 1992
Chairman: Dr. Urna Lele
Major Department: Food and Resource Economics
Agricultural households are often household-firms which
behave as both producers and consumers of goods. Household-
firms may have unexpected economic responses to price
changes. When the price of the good both produced and
consumed increases, profits will increase for the firm.
Increased profits increase household income and consumption
of the good. However, a household facing higher prices will
normally decrease consumption of that good. The result of
these opposing economic forces is explored in this study.
A literature review of agricultural household models
and results from other empirical studies are presented. The
theory of the household-firm and its indefinite conclusion
on price responsiveness supports the need for empirical
vi

testing. The model requires econometric estimation of both
the production and consumption sides of household behavior.
Household level data collected in Burkina Faso during
1984 are used to model production under a Cobb-Douglas
specification with land and labor inputs. Results are satis
factory with labor a binding constraint on the production
process. Lack of household level agro-clinatological infor
mation explains the remaining variability in the data.
Household consumption is modeled under an Almost Ideal
Demand System (AIDS) with prices and total expenditures as
arguments. A linear approximation (LA/AIDS) using the Stone
price index is estimated with Full Information Maximum Like
lihood (FIML). Encouraging results with significant and
correctly signed expenditure and price effects are obtained.
Demand and supply elasticities are derived for the
household. Output price elasticity of demand is computed
with and without the profit effect resulting in a reduced
response, but no sign change. Results are attributed to two
factors; first, data were collected during a poor agricul
tural year and most households were net purchasers of
cereals, thereby reducing the profit effect. Secondly,
household income diversification strategies in response to
highly variable agroclimatic conditions in the Sahel have
resulted in less dependence on agricultural output as a
source of household income, again resulting in a reduced
profit effect.
vii

CHAPTER I
INTRODUCTION
The majority of empirical studies in agricultural
economics are microeconomic in nature. In fact, some would
argue that agricultural economics is best characterized as
empirical microeconomics. Neoclassical microeconomic theory
concerns the firm in production and the household in con
sumption. In developing countries the majority of agricul
tural households act as both a firm and a household. They
provide their own labor and consume the bulk of their own
production. Thus, decisions concerning production, consump
tion and labor in developing countries often influence each
other within household-based economies. That the household
is the chosen unit of analysis should come as no surprise to
most economists. The foundation of consumption economics is
the household. Recall also that the word "economics" origi
nates from ancient Greek and means the "laws that govern the
household."
This study outlines an integrated theoretical and
empirical approach to deal with agricultural households
which are both producers and consumers of goods that origi
nate from the household-firm. A theoretical framework is
proposed for a model that integrates both the production and
1

2
consumption aspects of household behavior in developing
countries. The resultant agricultural household model is
tested on cross-sectional household data from Burkina Faso,
West Africa. Drawing on a wealth of production, demographic
and expenditure data from the early 1980s in four villages
within Burkina, an integrated, consistent, conceptual model
is estimated to provide insights into the behavior of
agricultural household-firms.
Because these household-firms consume part of their own
production they may behave differently in response to price
changes. Specifically, an increase in the price of the
output they produce may increase their net profits, thereby
inducing an increase in income that would counterbalance or
outweigh the traditional negative impact on their consump
tion of that output due to the increase in its price.
Ecfihlea Statement
Basic information about household behavior is essential
for the formulation of appropriate policy in the agricul
tural sector of any country, whether the goal of that policy
is household welfare or increased production. Price and
income elasticities are needed in order to capture and
describe the behavioral responses of household producers and
consumers to policy shifts. In particular, tax and subsidy
policies will be dependent on an accurate determination of
supply and demand responses of households. Microlevel

3
information is important in order to guide economic policies
that will correctly anticipate individual behavior under a
particular policy environment. In other words, will the
people under the policy behave as the policy anticipates, or
in a different manner?
The advent of structural adjustment policies throughout
Africa in the 1980s has made it increasingly important to
understand the impact of price changes. Structural adjust
ment programs, supported by multilateral donor agencies such
as the World Bank and the International Monetary Fund,
generally insist on increased prices for agriculturally
produced goods as an incentive to farmers. However, in
economies where producers are also consumers the impact of
changes in output prices may not have the desired effect on
household consumption or production.
Furthermore, due to the plethora of social and economic
structures in developing countries, there is a lack of basic
descriptive and guantitative information on agricultural
households in different regions. This kind of information is
especially lacking in African countries which only gained
independence within the last twenty to thirty years and set
out to transform their agricultural sectors. As we will find
in the literature review, the majority of the agricultural
household models that have been performed to date have been
for Southeast Asian countries.

4
Objectives of the Study
The principal goal of this study is to determine
household response to economic incentives through the
determination of elasticities from an agricultural household
model that integrates both consumption and production
aspects of the household-firm. The specific objectives are
to:
1. provide descriptive and quantitative information
concerning the production and consumption behavior
of rural African households,
2. combine both production and consumption aspects of
agricultural households in an integrated econome
tric model,
3. estimate income and price elasticities of demand
using pooled data,
4. estimate output supply and input demand equations
using cross-sectional data, and
5. introduce and empirically measure the impact
of the "profit effect" on cereal consumption.
Agricultural Household Models
The general class of agricultural household models was
chosen as the framework for analysis. These models are
especially suited for modeling the behavior of agricultural
households in developing economies because of their ability
to integrate both consumption and production aspects of the
household.
Consisting of a variant of consumer choice theory in
which the production technology is represented in the income

5
constraint by a profit function, agricultural household
models are within the neoclassical paradigm. However, they
do allow an additional flexibility in modeling with regard
to the consumption response of households to exogenous
changes via the income term, often called the "profit
effect."
It is through the income term that the two sides,
production and consumption, are linked. For an agricultural
household that obtains the preponderance of its income from
the sale of agricultural commodities, it is the production
technology that first dictates income, which is usually
modeled via a profit function. However, once this income
level is established, it becomes an argument in the determi
nation of the level of indirect utility. The result is a
recursive model where production decisions precede and
delimit consumption decisions, but not vice versa. The
recursive nature of these models is dependent upon the
existence of competitive input and output markets.
Recursive decisions are thought to be sequential in
that one set of decisions precedes and subsequently sets
parameter values for other decisions. Recursive decisions
are often described as separable because a set of initial
decisions are assumed to be made separate from subsequent
decisions. For example, in agricultural household models
production decisions are thought to have no influence on the

6
decisions in consumption. In a recursive system the causal
ity is one way and not interactive.
There is a notable difference in price elasticities
derived from cross-sectional models that acknowledge the
"profit effect" and those that do not. Table 1.1 presents
household-based price elasticities from various studies in
the literature with and without incorporation of the "profit
effect." Note that in several instances the response elas
ticities changed not only magnitudes but also direction.
TABLE 1.1
AGRICULTURAL PRICE ELASTICITIES
WITH AND WITHOUT THE PROFIT EFFECT
RESPONSE ELASTICITIES WITHOUT (A)
AND
WITH (B) THE PROFIT EFFECT
COUNTRY
AGRICU
commod:
LTURAL
CTY
NON-AGR
COMM
ICULTURAL
ODITY
LABOR
SUPPLY
A
B
A
B
A
B
Taiwan
-0.72
0.22
0.13
1.18
0.21
-1.59
Malaysia
-0.04
0.38
-0.27
1.94
0.08
-0.57
Korea
-0.18
0.01
-0.19
0.81
0.03
-0.13
Japan
-0.87
-0.35
0.08
0.61
0.16
-1.00
Thailand
-0.82
-0.37
0.06
0.51
0.18
-0.62
Sierra
Leone
-0.74
-0.66
-0.03
0.14
0.01
-0.09
Nigeria
-0.05
0.19
-0.14
0.57
0.03
-0.06
Adapted from Singh, Squire and Strauss, Agricultural House
hold Models. (1986) Table 1-2, pg. 26.

7
Layout of the Study
This first chapter begins with an introduction to the
reason for studying agricultural household behavior and
briefly describes the major characteristics of agricultural
household models that integrate both production and consump
tion sides of household behavior. The clientele for this
research are identified followed by background information
on Burkina's physical and socioeconomic setting that influ
enced data collection and interpretation. Finally, the data
used to drive the model are described, although more de
tailed descriptions are available elsewhere.
A literature review reveals that agricultural household
models have an extensive and international history with
contributions from a variety of scholars and countries. The
review points out that models have become increasingly more
reflective of reality and that agricultural household models
have been infrequently estimated due to the need for exten
sive data to support their estimation. The majority of
models have been estimated from data on Southeast Asian
countries. However, in spite of the extensive data demands
of these models, their usefulness is in summarizing broad
behavioral data within a consistent framework and increasing
reflection of actual conditions in developing country
agricultural household-firms. The literature review is
presented in Chapter II.

8
Chapter III presents the theoretical model based upon
the behavioral assumptions of utility and profit maximiza
tion. Under these conditions the addition of a "profit
effect" is shown to make determination of household response
to price changes indeterminate from theory. One must empiri
cally estimate the behavior from primary data for a region
or situation of interest. By also assuming a functional
labor market, the resulting model can be shown to be recur
sive with production decisions preceding consumption deci
sions. A formal presentation of the recursive nature of the
model is presented in the Appendix.
The results from estimating the production and consump
tion sides of the model are presented in Chapters IV and V,
respectively. A Cobb-Douglas production function is used to
estimate the supply side of the household while an Almost
Ideal Demand System (AIDS) is used in estimating the demand
side of household behavior. The results are more encouraging
from the demand than the production side which directly
reflects the quality and level of detail of the underlying
data.
The presentation of the combined results of the produc
tion and consumption sides of the model arc the focus of
Chapter VI. In addition, implications for policy formulation
in Burkina from this model are discussed. The work is
completed by a discussion of possible avenues for future
research relevant to understanding household level behavior.

9
Clientele for the Research
The clientele for more and better information on
agricultural households begins with the countries themselves
and the various policy arms of the government. Other inter
ested parties for this kind of research may include bilat
eral and multilateral aid agencies. Private and voluntary
organizations, which work directly with farming communities
in developing countries, could also be interested in infor
mation on agricultural household behavior. These parochial
interests should not cause us to overlook, or underempha
size, the purely intellectual appeal of modeling a complex
phenomenon in order to better understand the world.
The Government of Burkina is the principal clientele
for information on agricultural households in Burkina. A
better understanding of the agricultural production and
consumption behavior of agricultural households in Burkina
will be of immediate assistance to planning and policy
formulation. In most developing countries, agriculture
provides income for the majority of the population, serves
as a source of foreign exchange and a productive resource
base for the rest of the economy. Without a good basis of
information, the agricultural sector may not be utilized to
its fullest capacity or may even be impeded by improper
policy.
The specific users of this research would begin with
the various policy arms of the government including, but not

10
limited to, the Ministry of Agriculture. Other interested
parties may include bilateral or multilateral aid agencies
and other African Governments. Other donor agencies and
researchers could also be interested in information on
agricultural household behavior in Burkina.
Background on Burkina
This section provides background information on Burkina
that is particularly relevant to the interpretation of the
results form the study. Two areas of information are identi
fied that influenced the data collected and its analysis. An
understanding of the conditions prevailing in Burkina in the
physical and socioeconomic realms are important to a full
appreciation of the research results and their limitations.
The most important physical factor influencing agricul
tural production in Burkina is the high variability of
rainfall. This variability occurs across both space and
time. Spatially, the south and southwest of the country are
favored by more regular rainfall. Temporally the country has
experienced periods of drought, with the most recent
episodes during the agricultural seasons of 1983-84 and
1987-88. From a longer-term agroclimatological perspective
the 1970s and 1980s were drier than the 1950s and 1960s.
Most agricultural production in Burkina is rain-fed and
subject to the vagaries of these sahelian weather patterns.
These patterns are characterized by highly localized and

11
uncertain rainfall that results in generally risky agrocli-
matic production zones. This risk generally increases as one
moves from the south to the north of the country.
The four villages selected for study were chosen to
cross these agroclimatic zones. Two villages were chosen in
a chronically cereal production deficit zone, while the
remaining two came from a transition zone that would normal
ly experience surplus production. The two northwestern
deficit villages, Mn and Bougar, are located north and
south of the town of Ouahigouya, respectively. The normally
surplus villages in the west of the country are located
north and south of the major regional town of Ddougou.
Tissi is north of this regional capital and Dankui is
located south of Ddougou.
The data used in this study are from calendar 1984
which captured the drought reduced agricultural production
of 1983-84. Because of the drought, households in the sample
were found to have been dominated by more net purchasers
than sellers of cereals in the year from which data are
available. In order to obtain sufficient cereals to meet
their needs households interacted with the market more than
would have been expected in a normal year. This was reflect
ed in the data by reduced contributions of own agricultural
production as a share of total cereals obtained (both
produced and purchased).

12
Cereals are extremely important in the social and
economic setting of Burkina. Consisting mostly of millet and
sorghum, with some maize, wheat and rice, cereals compose
from seventy to eighty percent of calories and sixty to
seventy percent of proteins in the Burkina diet (Haggblade,
1984, p. 10). With just over nine million people, and a
population growth rate of roughly three percent per year,
Burkina has approximately thirty-two inhabitants per sguare
kilometer. Gains in gross agricultural production in the
1980s have been achieved mostly by increasing the area under
cultivation. Advanced agricultural technology and input use
are limited with most farming households using land, labor,
seed, rainfall and simple agricultural tools to produce a
crop.
As mentioned earlier, the success of agricultural
production is dependent upon the rainfall pattern. In order
to diffuse agricultural production risk households have
developed income diversification strategies. These strate
gies include diversification via trade, services, migration
and mining, among other possibilities. Using Burkina data
from approximately the same period as the present study,
Reardon, Matlon and Delgado (1988) found households in the
northernmost sections of Burkina which obtained only thirty
percent of total household income from agriculture. House
holds in their sample were from villages slightly farther
north than those used in the present study. However, similar

13
income and production diversification behavior in the face
of risk was found among the households in the present study.
Data
An agricultural household model requires household
production and consumption information, as well as market
price data on commodities and labor. This is an extensive
information requirement and few data sets are available to
support this type of modeling. The data required are most
frequently available in cross section. The data used in this
study are from Burkina Faso and represent household transac
tions data on approximately 87 farm households from roughly
the 1984 calendar year.
Originally part of a grain marketing study,1 the data
were collected in households from four villages in two
different agroclimatic zones in Burkina. Two villages were
from the sahelian northwest while the other two were from
the western sudanian zone. After an initial village census
of all households, samples were selected in a stratified
random fashion by ethnic group. Household budget survey data
were collected on a biweekly basis for twelve months.
Interviewers lived in the villages, visited the households
and interviewed all married inhabitants and those over
1 For a detailed presentation of the data instruments and
setting from which these data originated, see May (1987).

14
eighteen years of age. A list of all the questionnaires used
in the study is provided in Table 1.2.
The biweekly transactions data consisted of information
on sales, purchases, consumption, amounts given (wages,
gifts, taxes, etc.) and amounts received (salaries, remit
tances, gifts, etc.) by the household over the previous two
weeks. Data on changes in household composition were col
lected on a monthly basis. Data collected on a quarterly
basis included the livestock census and on-farm cereal
storage. These two categories are important proxies for
wealth in the sahelian agricultural household.
A one-time survey was also conducted to catalogue
household durable goods as companion information on wealth
stratification within the villages. Three additional ques
tionnaires were administered on a one-time basis. First was
the initial household census which, in addition to normal
demographic variables, covered education, dependency status,
and other sources of income. Second, a questionnaire was
used to measure the physical area of household members'
fields by crop. Third, the harvest was measured during the
appropriate part of the agricultural year.
"Households" in Africa are not necessarily nuclear and
in Burkina many household production and consumption units
can be found within one family compound. In order to distin
guish household units within the sample the census question-

15
TABLE 1.2
SUMMARY OF QUESTIONNAIRES
NAME
MAIN PURPOSE
FREQUENCY
VILLAGE
CENSUS
establish village demographics
for sample selection
ONCE
HOUSEHOLD
CENSUS
sample household demographics
ONCE
FIELD
MEASURES
area cultivated to each crop
or crop mix
QUARTERLY
ON-FARM
STORAGE
quantity of foodstuffs stored
over time
YEARLY
HARVEST
harvest quantity
BIWEEKLY
CONSUMPTION
quantity and source of food
stuffs consumed
BIWEEKLY
SALES
quantity, value, good, reason
and location of sale
BIWEEKLY
PURCHASES
quantity, value, good, reason
and location of purchase
BIWEEKLY
AMOUNTS
GIVEN
services, salaries, credit,
gifts, and remittances given
BIWEEKLY
AMOUNTS
RECEIVED
services, salaries, credit,
gifts, and remittances re
ceived
BIWEEKLY
CHANGE IN
HOUSEHOLD
COMPOSI
TION
monitor household composition
changes over time
MONTHLY
DURABLE
GOODS
wealth and asset measures
ONCE
MEASURING
UNITS
convert local measures to ki
lograms
ONCE
ANIMAL
CENSUS
type,number and owner of live
stock
QUARTERLY

16
naires were used in combination with household interviews to
determine the appropriate composition of a decision-making
unit. Among the criteria used to distinguish a separate
household within a compound were common fields, granaries,
and consumption and contiguous dwellings.
Information from the biweekly, monthly and annual
survey guestionnaires was used in estimating the model that
follows. These data served to support the theoretical model
presented in Chapter III and the estimates for the produc
tion and consumption sides of household behavior presented
in Chapters IV and V, respectively. In addition to the
analytics of the agricultural household model, a wealth of
summary and descriptive information, as well as other
economic inquiries concerning household behavior in Burkina,
could be supported from this data. However, the following
chapters are mainly concerned with the formal modeling of an
agricultural household model to organize and interpret this
large body of information on rural agricultural households
in Burkina.

CHAPTER II
LITERATURE REVIEW
The interest and development of the theory of agricul
tural households has an international flavor with its
beginnings in Imperial Russia, mathematical specification in
Japan, and empirical verification in the United States. The
idea of recording and studying the actual behavior of
peasant farmers began in Russia in the 1880s with the advent
of reforms under Alexander I. This highly detailed examina
tion of farm life in pre-Revolutionary Russia formed the
basis of inquiry on agricultural households by A.V. Chay-
anov.
Nakajima, working and publishing mostly in Japan, was
the first to work out a neoclassical framework and the
comparative statics for the family farm. Although his work
was mainly theoretical, Nakajima's writings provided the
basis for the testing, modification and subsequent refine
ment of agricultural household models.
The empirical estimation of agricultural household
models began in the mid-1970s with most of the work coming
from the Food Research Institute at Stanford University. Lau
and Yotopoulos, working with other scholars from Southeast
17

18
Asia, presented a series of articles using household-based
studies of agriculture in Taiwan and Thailand.
More recently, in the 1980s, agricultural household
models have become a useful analytical technique for examin
ing cross-sectional data in developing country agriculture.
The World Bank sponsored volume, edited by Singh, Squire,
and Strauss (1986), has become the standard volume on
agricultural household models. Further developments and
concerns about these models are now being expressed in the
economic literature on developing country agriculture.
Chavanov
The seminal work on agricultural household models is
that of Alexander Vasilyvich Chayanov on peasant agriculture
in pre-Revolutionary Russia (Chayanov 1966, 1986). Chayanov
based his theory of the family farm on extensive data
collected from regional- and district-level surveys of
peasant households after the serfs were emancipated and land
reform enacted in 1861.
Chayanov held that agricultural households were unique
economic units in that the household "firm" provided the
bulk of its needed production inputs (principally labor)
while at the same time consuming the bulk of its own produc
tion. Because such firms provided their own inputs and
consumed what they themselves produced, the impact of their
decisions might be different from those expected from the

19
neoclassical theory of the firm.2 As mentioned in the intro
duction, in a household that produces what it consumes the
income effect can cause the nature of household responsive
ness to be indeterminate from theory.
The writings of Chayanov only became available to an
English-speaking audience in 1966, but were known to schol
ars in other parts of the world through earlier translations
in German and Japanese. Nakajima cites his exposure to
Tschajanow's (sic) writings as an early influence on his
subsequent writings about the agricultural household (Whar
ton, 1969, p. 165). The introduction to Shanin's reissue of
Chayanov's writings states that "the impact of the implicit
cross-influences cannot be ascertained, but the views of
Chayanov and his friends spread fairly broadly through
Europe and Asia via the German professional literature of
the 1920s (Chayanov, 1986, p. 11)."
Chayanov focused his analysis on those households which
used little or no labor, other than that provided by the
household itself. He formally defined a "family farm" as an
economic unit that normally employed no wage labor in its
production process. Because the Chayanovian "family farm"
used family labor almost exclusively, wage rates could not
be determined and hence profits were indeterminate.
2 However, it can be explained through a constrained
optimization model in the neoclassical mode as will be
presented in this research.

20
With profits indeterminable, Chayanov proposed a deci
sion rule for the "family farm" that differed from profit
maximization. He suggested that the "family farm" equates
the satisfaction of family needs with the drudgery of work
required. From his intense familiarity with Russian peasant
agriculture, Chayanov realized that Russian peasants did not
work to achieve profit maximization. Their labor supply and
efficiency did not coincide with profit maximizing behavior
as they could almost always provide additional labor or work
harder but chose not to do so.
Chayanov worked towards producing a separate theory of
the "family farm" that would have its own unique analytical
techniques. From his labor-consumer balance, equating the
drudgery of work to the consumption needs of the household,
he concluded that each household would find its own subjec
tive equilibrium. The level of this balance would be influ
enced by the size of the family and its ratio of working to
non-working members.
The "family farm" had a certain resiliency or survival
power that the capitalist farm did not. Peasant farms could
continue to survive in an environment that would bankrupt
capitalist farms or socialist collective farms. They would
do so by working longer hours or selling at lower prices,
even continuing from year to year yielding no net surplus
production. Such behavior required a unique form of analysis

21
of farm household behavior because it could not be adequate
ly explained by existing theoretical constructs.
He also commented on a "natural history" of the house
hold which can be likened to the "life cycle" income theory.
For Chayanov this "demographic differentiation" of house
holds was more important in determining their behavior than
class differentiation. This idea and others about transform
ing Russia agriculture would eventually lead Chayanov into
conflict with the revolutionaries of post-1917 Russia.
For Chayanov the household economy, although distinctly
different from other analytical economic paradigms, exists
within and is influenced by the prevailing economic system,
be it capitalist or collective. However, the household would
incorporate and adapt to its environment while at the same
time retaining its conceptual uniqueness and calling for
separate analysis. Unfortunately, the complete ramifications
of Chayanov's separate economic theory of the agricultural
household were never fully expounded as he was caught up in
the Stalinist purges and agricultural collectivization of
the 1930s and eventually died in 1939 at the age of fifty-
one.
Nakaiima
Chahiro Nakajima mathematically formalized the work of
Chayanov by expounding on the subjective equilibrium of

22
agricultural households.3 The Japanese audience was familiar
with the writings of Chayanov at an earlier date than the
anglophone audience. Nakajima's work, which itself only
became available to a wide anglophone audience in 1969
(Wharton, 1969) allowed for a continuum of households, from
those consuming all of their own production and providing
all of their labor input (subsistence farms) to those
consuming none of their production and purchasing all their
labor (commercial farms).
Nakajima's classification of the world's diverse
agricultural production systems along a continuum can be
viewed as having two dimensions, consisting of the level of
own production consumed by the household and the level of
own labor provided by the household. At one extreme was the
purely subsistence household consuming all of its own
production and providing all of its own labor input. At the
other extreme of his continuum was the purely commercial
farm which sold all its output and purchased all of its
labor input. Nakajima commented that the later extreme was
"rarely found" and the former was a "very small percentage"
of world farms (Wharton, 1969, p. 165). He clearly recog
nized that the bulk of the world's farms fell somewhere
between these two extremes.
3 "Subjective" because each household can have its own
utility function which is maximized subject to an income
constraint.

23
In order to capture the diversity of farm production
possibilities, Nakajima proposed four models of household
behavior. Two models examined the behavior of the pure
commercial family farm while two captured the behavior of
the semisubsistence or semicommercial family farm. The
purely commercial farm models were distinguished by the
presence or absence of a competitive labor market. For the
pure commercial family farm with a competitive labor market
Nakajima noted that this "family farm may be regarded as an
economic unit which behaves, in the first phase, as a 'firm7
maximizing profit and, in the second phase, as a laborer's
household with nonlabor income maximizing utility (Wharton,
1969, p. 180)." This is the first mention in the literature
of what has come to be known as the recursive nature of the
agricultural household decision-making process.
In deriving the comparative statics for the purely
commercial farm models, Nakajima introduced inputs other
than fixed land and variable labor. Nakajima examines the
impact of fertilizer as another factor of production whose
price is determined in a competitive market. He also allows
for the addition of multiple outputs in his purely commer
cial family farm models.
Turning to the two semisubsistence (or semicommercial)
models, Nakajima assumed that these households did not have
access to a labor market, but were distinguished by having
single or multiple output crops. In these models the house-

24
hold provided all of its own labor requirements and consumed
some of its own production.
In each of the four cases proposed by Nakajima he
solves for the comparative statics under the assumption of
utility maximization. He thus obtains the first-order
conditions and equilibrium values of each of the variables
in the respective models. He examines the impact of changes
in asset income, output price, and family size as well as
the effects of technology and seasonality on the comparative
statics.
Nakajima's work provided, in addition to his continuum
classification and comparative statics, the introduction of
a labor market to the theory of the agricultural household.
Contrary to Chayanov, Nakajima allowed for the possibility
of a labor market exchange by the household. He introduced a
market from which the household could obtain or provide
labor at a fixed wage rate. Nakajima's work has received
renewed attention through the recent publication of a
collection of his writings on the subjective equilibrium of
the household (Nakajima, 1986).
Lau, Yotopoulos, and Others
The work of Chayanov and Nakajima was empirically
embellished by researchers at the Food Research Institute at
Stanford, with support from the World Bank and the Ford
Foundation. This research, published principally in the

25
1970s, focused on the empirical workings of the agricultural
household theory developed by Chayanov and Nakajima.
Data were obtained on the agricultural household economies
of two Southeast Asian nations, Taiwan and Thailand.
However, there are notable differences between the
empirical approach of Lau, Yotopoulos, et al., and Chayanov.
In the two Southeast Asian production studies they assume
profit maximization by the agricultural household, which
runs counter to Chayanov's argument that peasant families,
particularly in pre-Revolutionary Russia, do not maximize
profits.
When the separate studies of production and consumption
that follow are combined they yield a complete system
estimation for agricultural households. The system is
complete in the sense that input demand and output supply
equations are estimated for the production side, while
commodity demand equations are estimated for the consumption
side of agricultural household behavior.
Production in Taiwan
Lau and Yotopoulos, along with Lin (Yotopoulos, Lau,
and Lin, 1976), first began their examination of agricul
tural households with cross-section data from Taiwan.
Modeling the production behavior of Taiwanese agricultural
households, they assumed a Cobb-Douglas production function
and utilized a profit function to describe the underlying

26
technology. This profit function was normalized by output
price and specified as being log linear. The profit function
was also considered to be "restricted" because it measured
current revenue minus current variable costs.
From the Taiwan household data these researchers
determined four variable inputs (labor, animal labor,
mechanical labor, and fertilizer) and two fixed inputs (land
and fixed assets). Input demand and output supply equations
were derived from the Normalized Restricted Profit (NRP)
function via Hotelling's Lemma. The method of estimation
used was Zellner's seemingly unrelated regression, because
it is asymptotically efficient for systems of equations that
have related error terms (Zellner, 1962) .
In this first of many studies on agricultural house
holds, Lau, Yotopoulos and Lin tested for profit maximiza
tion and constant returns to scale in production. On the
basis of their results they were not able to reject the
hypothesis of profit maximizing behavior by Taiwanese
agricultural households. Contingent upon profit maximiza
tion, they were also unable to reject the hypothesis of
constant returns to scale in Taiwanese agriculture.
Consumption in Taiwan
Following their earlier work in 1976 on the production
behavior of Taiwanese agricultural households, Lau, Yotopou
los and Lin turned to consumption behavior (Lau, Lin and

27
Yotopoulos, 1978). Assuming utility maximization by the
household, these researchers employed an indirect utility
function to analyze the consumption behavior of agricultural
households.
Utilizing a linear logarithmic expenditure system
(LLES) they estimated commodity expenditure equations
derived from a transcendental logarithmic (henceforth,
translog) indirect utility function that is homogeneous of
degree one in prices. The commodity expenditure equations
for three aggregated commodities (agricultural commodities,
non-agricultural commodities and leisure) were derived via
Roy's Identity. Household characteristics, such as the size
and composition of the household, were included as arguments
in the indirect utility function.
The translog indirect utility function is assumed to be
homogenous of degree minus one. One implication of this
assumption, for both the Taiwanese and subsequent Thai
consumption analysis, is that the total expenditure elastic
ity of demand for each commodity is identically equal to
one.4
Elasticities for consumption demand, labor supply and
marketed surplus with respect to prices, incomes, household
composition and household endowment were derived from the
4 This, of course, not does not imply that income
elasticities are identically one, because the imputed value of
leisure is included as part of total expenditure in these
studies.

28
results of the seemingly unrelated regression equations
(again using Zellner's method). The hypothesis of utility
maximization by Taiwanese households could not be rejected.
Production parameters, such as agricultural output
supply, necessary for the estimation of household income and
marketed surplus, were taken from the previous work on
Taiwanese production by the same authors. The reader will
recall that the output supply was determined using a normal
ized restricted profit function and Hotelling's Lemma. This
profit function has no arguments based upon an underlying
preference structure expressed in a utility function. Thus,
the production decisions are implicitly assumed to be
separable from the consumption decisions. However, because
the output supply affects income, consumption decisions are
influenced by production decisions.
Production in Thailand
After completing studies on production and consumption
behavior in Taiwanese agricultural households, Lau and
Yotopoulos turned to the analysis of data from Thailand.
Working with other scholars from Japan (Kuroda) and Thailand
(Adulavidhaya and Lerttamrab), they examined the production
characteristics of Thai households (Adulavidhaya, Kuroda,
Lau, Lerttamrab and Yotopoulos, 1979). A Normalized Re
stricted Profit function was again employed from which they
derived input demand and output supply equations with four

29
variable inputs (labor, animal input, mechanical input,
fertilizer and seed) and two fixed inputs (land and capital
assets). All prices were normalized by output price.
The functional form used was log linear and estimation
was by ordinary least squares. They tested for both profit
maximization and constant returns to scale, as in the case
of Taiwan, with similar results; neither hypothesis could be
rejected. A further result was that both factor demand and
output supply were sensitive to changes in output price.
Clearly, the work on the Thai data was quite similar to
that using the Taiwanese data, but it was reassuring to find
that both profit maximization and constant returns to scale
held in the two different environments. The authors foretell
their future plans for this data when they state that "the
next step of the analysis of the Thailand data also
combines the consumption side of the agricultural household
(Adulavidhaya, Kuroda, Lau, Lerttamrab and Yotopoulos, 1979,
p. 85).
Consumption in Thailand
The consumption analysis of Thai agricultural household
data proceeded along the same lines as that outlined for the
Taiwanese data (Adulavidhaya, Kuroda, Lau and Yotopoulos,
1984). Utilizing a linear logarithmic expenditure system
under the assumption of utility maximization, they described
an indirect utility function. Specifying a translog func-

30
tional form for the indirect utility function, household
commodity expenditure equations for agricultural commodi
ties, non-agricultural commodities and leisure were derived
using Roy's Identity. These three aggregated commodities
were deemed important for the analysis of the supply of
marketed surplus, the demand for non-agricultural commod
ities in the agricultural sector, and the income-leisure
choice and supply of labor, respectively.
As in the Taiwanese consumption study, homogeneity was
assumed, with its subsequent implications, and the estima
tion technique was Zellner's seemingly unrelated regression
analysis. Output supply was taken directly from the earlier
study on Thai production which used a normalized restricted
profit function. Like the earlier Taiwan study, the Thailand
consumption study is different from the traditional Engel
curve analysis because of the introduction of family compo
sition information as an independent variable in the utility
function. However, in contrast to the earlier Taiwanese
study, utility maximization by Thai agricultural households
was rejected.
Implicit in each of the consumption analyses performed
by Lau, Yotopoulos, et al., in both Taiwan and Thailand, is
the separability of the production and consumption decisions
of the household. The production analyses, in both cases,
can stand on their own without further caveats. However, the
consumption analysis, with household income partially

31
determined through the profit function, and hence the
underlying production technology, is dependent upon the
production decisions of the household. The production
decisions influence the consumption decisions, but the
production decisions are independent of the consumption
decisions.
It is clear from the work of Lau, Yotopoulos and
associates that the beginnings of an integrated theoretical
framework for the analysis of agricultural households were
possible. Heretofore, researchers would focus one entry in
the literature on the production side of the household
followed by a sequel, the analysis of the consumption side,
utilizing the results from the earlier production study. It
was now time for a consistent theoretical framework within
which to specify agricultural household models for develop
ing countries.
Barnum and Squire
Barnum and Squire, in contrast with the earlier studies
outlined above, were the first researchers to incorporate
both production and consumption aspects of the household in
one paper (Barnum and Squire, 1979a, 1979b). This team of
researchers also used cross-sectional agricultural household
data from a Southeast Asian country: the Muda River Valley
in northwest Malaysia. They were also working in an essen-

32
tially monocultural agricultural environment as in the
previous studies of rice-based agricultural economies.
Although Barnum and Squire used the same theoretical
foundation as Lau, Yotopoulos and associates, there were
differences in the choice of functional form between the two
teams. In contrast to the latter's profit function approach
to the production side of the problem, Barnum and Squire
preferred to directly estimate the production technology.
They chose to estimate a Cobb-Douglas specification for the
production technology and then derive the profit function
and input demand equations.
On the consumption side they were more concerned with
the restrictions involved in the Linear Logarithmic Expendi
ture System utilized by Lau, Yotopoulos and associates,
especially the constrained nature of the expenditure elas
ticities. They employed a modified Linear Expenditure System
which, unlike the LLES, did not require that all expenditure
elasticities equal one. However, even with this more flexi
ble functional form, the own price elasticities were re
stricted to be linearly related to the expenditure elastici
ties. The LES is derived from the Stone-Geary additive
utility function.
Of particular interest to Barnum and Squire was the
impact of the analytical framework of agricultural household
models on migration, marketed surplus, technology and the
demand for hired labor. They found that the cost of migra-

33
tion was low relative to the marginal productivity of an
agricultural laborer, that marketed surplus was not respon
sive to output price changes, and that increases in output
price and technology would positively influence rural wages,
thereby having a favorable impact on rural workers dependent
upon wage labor.
In spite of the different functional forms used in the
estimations of Barnum and Squire versus Lau, Yotopoulos and
associates, the outcomes were reasonable. Their elasticities
were similar enough with those of Lau, Lin and Yotopoulos to
prompt Barnum and Squire to remark on the similarity of
preferences for Taiwanese and Malaysian agricultural house
holds (Barnum and Squire, 1979b, p. 77).
As a follow-up, Tamin used Barnum and Squire's data set
and a log-linear Cobb-Douglas functional form of a normal
ized restricted profit function, with four variable inputs
and two fixed inputs, to model the production behavior of a
cross section of Muda River Valley households (Tamin, 1979).
Joint estimation, by Zellner's seemingly unrelated regres
sions, of the profit function and four factor share equa
tions was undertaken with and without restrictions imposed.
Estimation without restrictions allowed hypothesis tests
for profit maximization and constant returns to scale,
neither of which could be rejected.
Tamin found low own-price elasticities of output supply
as well as low fertilizer price elasticities of output

34
supply. He also tested for technical and price efficiency
differences between owner-farm households and tenant-farm
households with no significant differences in efficiency
found.
Singh, Squire and Strauss
The empirical embellishments and refinements on agri
cultural household models continued throughout the early
1980s. A collection and synthesis of these works was brought
together in 1986 under the editorship of Singh, Squire and
Strauss (1986). With introductory chapters on the theory of
agricultural household models, these writers then presented
nine case studies by different authors, including the
editors, that utilized the basic framework of a separable,
or recursive, agricultural household model.
These models can be characterized as standard optimiza
tion problems. The household is assumed to maximize a joint
household utility function subject to constraints. There are
generally three constraints on the household's decision
making process. Utility is maximized subject to budget, time
and technology constraints. Prices are assumed to be given
in both input and output markets. Such models can be shown
to be recursive.5
5 See the Appendix to this study for a rigorous pre
sentation of the recursivity of agricultural household models.

35
Exceptions to this model are the chapters by Roe and
Graham-Tomasi, and Lopez (see also Lopez, 1984) included in
the case studies, both of which bring into question the
recursivity assumption of this neoclassical model of agri
cultural households. Roe and Graham-Tomasi bring risk into
the household decision-making process and find that the
original neoclassical results will only hold under what can
be considered severe restricting assumptions (Singh, Squire
and Strauss, 1986). Lopez (1984; Singh, Squire and Strauss,
1986) shows that the recursivity will not hold if the
household is not indifferent between on-farm and off-farm
labor, both in the sense of labor hired and labor supplied.
Lopez's work is also important in emphasizing that this
literature on agricultural household models is not limited
to the study of developing country agriculture, but is also
useful in describing agriculture in more industrial nations,
in this case Canada.
The remaining seven case studies utilize the basic
model with recursivity intact. Two of the case studies can
be considered as complete systems analyses in the tradition
of Lau, Yotopoulos, et al., and Barnum and Squire. Singh and
Subramanian (Singh, Squire and Strauss, 1986), using data
from Korea and Nigeria, model consumption decisions with a
Linear Expenditure System while the production side employs
a linear program. Their study is characterized by additional
commodity disaggregation and multiple crops. Strauss (Singh,

36
Squire and Strauss, 1986) examines households in Sierra
Leone to determine the impact of pricing policies on nutri
tional status, measured as caloric intake. He employs a
Quadratic Expenditure System (QES) to determine consumption
parameters and a multiple output production function to
model the production decisions. In his QES, outputs are
related via a constant elasticity of transformation and
inputs are linked via a Cobb-Douglas production function.
Using data from Indonesia, Pitt and Rosenweig (Singh,
Squire and Strauss, 1986) take Strauss' concern for nutri
tional effects further to determine impacts on health and
from health to labor productivity. Smith and Strauss (Singh,
Squire and Strauss, 1986) turn to distributional issues and
examine the impacts of price policy on different segments of
the rural population in Sierra Leone within the structure of
an agricultural household model. Braverman and Hammer
(Singh, Squire and Strauss, 1986), with disaggregated
commodity data from Senegal, bring the agricultural house
hold model into General Equilibrium analysis. In their model
markets clear through import and export adjustments in
international trade.
Iqbal (Singh, Squire and Strauss, 1986) examines
household borrowing in India by introducing the credit
market into the basic model with a two-period model. Final
ly, Sicular (Singh, Squire and Strauss, 1986) takes a novel
approach by using a programming variant of the general

37
agricultural household model to examine the influence of
centrally planned quotas and restrictions on Chinese produc
tion teams. With these case studies, and the introductory
chapters, the editorial work of Singh, Squire and Strauss
(1986) provides a rich source of theoretical and empirical
work concerning agricultural household models.
Haughton
Haughton stresses the importance of choosing an appro
priate functional form for the production function in
estimating agricultural household models (Haughton, 1986).
He argues that without a theoretically sound specification
of a production function the more sophisticated agricultural
household models are of little use. The same can be said for
the specification of the consumption function. Lopez also
stresses the importance of using flexible functional forms
in modeling agricultural household models to ensure the
minimum amount of restrictions on behavior (Lopez, 1984, p.
62) .
In Haughton's study, employing cross-sectional data
from western Malaysia (yet another study using data from
Southeast Asia), he compares the results from the same data
set of different functional forms to represent the underly
ing production technology of the household. Quantity-based
translog and Cobb-Douglas production functions are compared

38
with indirect, normalized price-based translog and quadratic
restricted profit functions.6
While citing the differing results obtained by Barnum
and Squire versus Tamin on the same Muda Valley data set,
Haughton also points out sources of variation, other than
functional form, that may influence the empirical measure
ment of agricultural household response to price changes.
First, differences may depend on whether or not the re
searcher models a single crop as output or derives some
total farm output figure. Secondly, data may be from differ
ent time periods or regions (not the case in the Muda Valley
studies). Finally, how variables are defined, lagged, or
chosen for exclusion due to lack of data can influence the
results of estimations.
In testing the direct production estimates, Haughton
found that in general, "the Cobb-Douglas form is not sus
tained (Haughton, 1986, p. 213)." However, he goes on to
state that "the superiority of a homogenous translog form
should not be overstated" (Haughton, 1986, p. 213) princi
pally because both forms gave similar output elasticities.
He concludes by arguing that the choice of functional form
will depend upon the particular constraints of the available
data.
6 Recall that the Cobb-Douglas production function is a
special case of the more general translog production function.

39
His results from the translog and Cobb-Douglas re
stricted profit functions were "disappointing." The share
equations were not significant and the estimation was a poor
fit. He cites the difficulty in measuring restricted profits
because they are a residual and tend to magnify data errors.
The choice of how to value on-farm family labor is also
cited as a source of these poor results. Recall that it was
this same problem which caused Chayanov to conclude that the
neoclassical approach to the analysis of agricultural
households was inadequate.
Haughton proposed a third possibility, the direct
estimation of input demand and output supply equations
derived from restricted profit functions, of which the
normalized quadratic restricted profit function appeared to
be the most promising. This, of course, will require more
close attention to the collection of valid price data, in
addition to quantities, in the developing country context.
Bezuneh. Deaton and Norton
Bezuneh, Deaton and Norton (henceforth, BDN) used an
agricultural household model approach to examine the various
impacts of food aid under a Food-For-Work (FFW) scheme in
the Baringo District of Kenya (Bezuneh, Deaton and Norton,
1988). They chose to model the production side of the
household with a linear programming (LP) approach and the
consumption side with an Almost Ideal Demand System (AIDS).

40
By their choice of an LP model on the production side BDN
argue that they can disaggregate commodities (96 activities
and 82 constraints), examine the impact of FFW-based capital
investment and limit the cost of data collection needed to
support the model. The argument for using an AIDS model on
the consumption side is that it allows for flexible price
and income elasticities. BDN use the linear approximate
Stone price index and impose the standard demand conditions
of adding-up, homogeneity and symmetry when estimating the
AIDS model using an iterative nonlinear Zellner method for
seven commodities.
The FFW enters the model directly through a second
(after farm household) production function for obtaining FFW
commodities. They also attempt to include a static, two-
period production component in an attempt to capture invest
ment effects of FFW programs. Another interesting addition
by BDN is the incorporation of a minimum consumption re
quirement resulting in nonseparability between production
and consumption decisions. A household that perceives a
minimum consumption need will base that perception on the
household consumption needs which would then impact produc
tion decisions.
The authors found that FFW increased production,
income, capital investment, employment and marketed surplus
in the Baringo District. A shift from maize to millet
production was attributed to the maize distributed as FFW

41
meeting consumption needs and millet being a more profitable
crop. Own price elasticities of demand were negative, as
would normally be expected except for the combined millet
and sorghum good. The positive own-price elasticity was
attributed to the profit effect because a higher price would
result in higher incomes, particularly among households
participating in the FFW program.

CHAPTER III
THEORY OF THE AGRICULTURAL HOUSEHOLD
Introduction
The agricultural household in a developing country is
unique for three major reasons. First, the agricultural
household consumes a major part of its own production. The
food crops produced in an agricultural household are partly
consumed by that household while some is marketed to provide
income. Other types of households do not generally consume
part of that which they produce. Hence, in an agricultural
household the output of the "firm" can greatly influence
consumption choices, or levels, via income.
The second reason why agricultural households are
distinctly different from other households is that they
provide their own labor as a major part of the inputs used
in the production process. The combination of being the
major provider of inputs and the major consumer of output
allows for the possibility of unique behavior on the part of
an agricultural household. In this chapter we will outline a
general theory of this type of agricultural household.
The third distinguishing characteristic of agricultural
households in developing countries is the nature of the
42

43
management process. For example, in a developing country
management techniques and practices may involve the use of
multiple households acting as one unit, sources of income
may be determined by kinship patterns, and cultural practic
es and preferences may influence choices.
The problem of theoretically modelling an agricultural
household can be framed in the standard techniques of
constrained optimization. The household can be assumed to
optimize an objective function, in this case utility,
subject to a series of constraints. These constraints
generally include information concerning the limitations on
behavior due to income, time, and technology.
The General Theory of an Agricultural Household
The general model used in this study can be succinctly
written as a constrained optimization problem as follows:
MAX U = U (X,, Xm, X,) (3.1)
subject to:
(i) PaXa + PmXm + w(L-F) < P.Q
(ii) X, + F = T
(i) Q = Q(L,A)
maximizing utility subject to constraints due to income (i),
time (ii), and technology (iii), respectively. The goods
consumed are the crop produced by the household, Xa; goods
purchased on the market, Xm; and the leisure time available

44
to the household, X,. Prices for goods and services are the
price of the agricultural commodity, Pa, market commodities,
Pm, and wages, w. Total time, T, is allocated to agricultur
al labor supplied by the household, F, and leisure, X,.
Agricultural output, Q, is the product of total labor (L)
and land, A.
Leisure time is broadly defined in this model to
incorporate any activity undertaken by the household that is
related to own agricultural production. This is a key point
in analyzing the behavior of sahelian agriculturalists.
Recent studies have found that as much as seventy percent of
total household income in extremely risky agroclimatic zones
comes from non-agricultural production (Reardon, Matlon and
Delgado, 1988 and Staatz, D'Agostino and Sundberg, 1990). In
this model the diversified income strategy in response to
agricultural risk is captured as exogenous income.
The Utility Function
The agricultural household is assumed to function under
a joint utility function for the household as a distinct
unit. In this particular theory there is no concern for the
intrahousehold distribution of resources. Although such
distributional issues are important (see Folbre, 1986), the
data from which the model will be estimated is not suffi
ciently disaggregated to allow examination of the issues
concerning intrahousehold distribution. Thus, the model will

45
assume a joint utility function for the household. A
utility function which, when maximized for the household
unit as a whole, is assumed to maximize utility for its
individual members.
Household utility maximization is assumed to be a
function of the goods consumed by the household. In this
case, the goods consumed are the crop produced by the
household, goods purchased on the market, and the leisure
time available to the household. The resulting utility
function is:
U = U (X,, Xm, X,) (3.2)
with X, a vector of agricultural goods, Xm a vector of
market goods, and X, the leisure consumed by the household.
The utility function is assumed to behave in accordance
with standard theory. It is considered to be quasi-concave
in its arguments and its partial derivatives are positive.
Of course, the quantities appearing as arguments in the
utility function are assumed to be nonnegative. Other
household characteristics can be added as arguments in this
utility function. Examples include number of dependents,
level of education, and other socioeconomic factors.
The Income Constraint
As outlined above, this optimization is subject to
certain constraints. In the general agricultural household
model the objective function is constrained by three re-

46
strictions on the household's actions. The first constraint
can be written such that the household expenditures are less
than or equal to the income available to the household, or
P.X, + + w(L-F) < P.Q. (3.3)
The inequality holds due to possible zero level expenditures
or savings by the household. Household consumption consists
of expenditures on agricultural goods, P.X,; market goods,
PmXm and expenditure on hired agricultural labor, w(L-F).
The quantity of agricultural labor hired by the house
hold is the difference between total labor input on the farm
(L) and the total quantity of labor, on and off-farm,
supplied by the household (F). Here, wage rates are assumed
equivalent between on-farm and off-farm labor implying that
the household is indifferent between these two types of
labor. The household income is derived from agricultural
goods whose quantity, Q, represents gross production.
Subsequently, the value of agricultural goods sold by the
household, P,Q, represents agriculturally based income.
It is interesting and instructive to note that the term
w(L-F) may appear on either side of the income constraint.
In other words, it may be construed as either an expenditure
or an income term. This is due to the expression (L-F) which
can be either positive or negative. If total labor input, L,
is greater than that supplied by the family, F, then the
expression is positive and the farm household employs labor
from off-farm to make up the difference. In this case the

47
expression w(L-F), the value of the employed labor, is
interpreted as an expenditure and employed on the left-hand
side of equation 3.3.
On the other hand, if family labor supplied, F, is
greater than the total labor input, L, then the expression
(L-F) is negative and the household is supplying labor to
the off-farm market. The value term w(L-F) is then inter
preted as the return to off-farm labor supplied by the
household and is counted as an addition to income. In formal
specification of the income constraint equation the labor
value term would be subtracted from other right-hand side
terms to ensure that the "negative" quantity (L-F) is
positively valued.
The Time Constraint
The household has the opportunity of utilizing its
total endowment of time in either leisure or labor. There
fore, the sum of the amount of time spent in leisure, X,,
and that spent in family labor input, F, must be equal to
the total time available, T. In equational form this gives
the identity:
X, + F = T. (3.4)
This equality holds if one assumes that all slack time is
leisure. However, if some slack time is considered lost due
to illness, weather or other factors then the equality
becomes an inequality (less than or equal).

48
Other possible behavioral characteristics could be
modeled through the time constraint. One example is the
inclusion of a cultural variable, C, that reflects the
minimum amount of time devoted by the household to community
or cultural activities. Not all leisure time is devoted to
cultural activities, thus X, > C.
The Technology Constraint
The technology constraint represents the production
technology that is employed by the household in combining
inputs to produce output. A general production function can
be used to represent this underlying technology and is
written as:
Q = Q(L,A) (3.5)
where L is variable labor input and A is the fixed area
under cultivation. This production function is assumed to be
quasi-convex and increasing in inputs.
Combining Constraints to Yield the Full Income Constraint
The three constraints outlined above can be combined
into one constraint in order to simplify the problem.
Substituting both the time and technology constraints into
the income constraint and rearranging gives:
Y = P.X. + PmXm + WX, < P,Q(L,A) WL + wT (3.6)
which can be interpreted as a variant on Becker's "full
income" (Becker, 1965).

49
The expenditure side of the household's "full income"
constraint is now augmented by the value of the household's
leisure time, wX,. The income side consists of the value of
agricultural production, PaQ(L,A), the value of the house
hold's entitlement of time, wT, and is diminished by the
value of total labor utilized by the farm, wL. Note that the
value of agriculturally based gross income can be given by
[P,Q(L, A) -PaXa] This can also be interpreted as the value of
marketed surplus, where PaQ(L,A) is the value of gross
agricultural production of the household and PaXa the value
of agricultural goods consumed by the household.1
Note that the full income constraint in the agricultur
al household model contains an element of income whose value
is generated using the household's production technology.
The combined term, PaQ(L,A) wL, on the income side of the
"full income" constraint, represents household profits from
agricultural activity. These profits, n, can be written as:
7t = PaQ(L,A) wL (3.7)
and could be determined via a profit function that can be
specified so as to be representative of the underlying
technology employed by the household.
While the optimization problem is still framed as a
consumption problem in which the household is assumed to
1 This assumes that all agricultural goods not consumed
by the household are sold on the market and not given away in
non-market exchanges which may not always be the case.

50
maximize utility, one can begin to see how the production
decisions may, in fact, influence consumption decisions
through the income term in the full income constraint.
Solving the General Model
With the substitutions and rearrangements of the income
constraint outlined in the previous section, the original
optimization problem can be restated as:
MAX U = U (Xt, Xm, X() (3.8)
subject to:
(i) P.X, + PmXm + WX, < wT + PaQ (L, A) wL.
The agricultural household has choice variables con
cerning the amount of agricultural goods to consume (XJ ,
amount of market goods to consume (Xm) amount of leisure to
consume (X,) and total labor input supplied to the farm
(L), assuming that acreage under cultivation is fixed (A).
The household, under the assumption of utility maximization,
will seek to optimize the levels of these four choice vari
ables.
Kuhn-Tucker Conditions
In its most general form this model consists of a
nonlinear objective function subject to a nonlinear con
straint. The solution to a nonlinear programming model is
described by the Kuhn-Tucker conditions which consist of

51
marginal, non-negativity and complementary slackness compo
nents (Intriligator, 1971, p. 49).
Write the generalized Lagrangian function as:
* = U(X.,Xm,X,) + M(Y* PmXm PaXa WX,) (3.9)
where /x is the Lagrangian multiplier and Y* is the value of
full income that results from profit maximizing behavior
such that:
Y* = wT + P,Q(L*,A) Wl* > PmXm + P.X. + wX, (3.10)
= wT + 7T*(P,,w,A)
where L* is the labor input level under the assumptions of
maximized profits, 7r*, and fixed area under cultivation, A.
Note that, consistent with duality theory, the underlying
production technology can be modeled either via a production
function, Q(.), or an indirect profit function, 7r(.).
The Kuhn-Tucker marginal conditions at the point of the
optimum (X,*, Xm*, X,*, /x*) are:
d$/dXa* = 3U/dXa* mP* < 0 (3.11)
a*/dxm- = au/axm* Mpm < o
a$/ax,* = du/dx; mw < o
d$/dll' = Y* PmXm* PaXa* WX,* > 0
The Kuhn-Tucker non-negativity conditions state that
Xa* > 0, Xm* > 0, X,* >0, M* > 0 (3.12)
thus the choice variables and the multiplier are all limited
to the non-negative orthant. The multiplier, /x, is the
marginal utility of full income.

52
The Kuhn-Tucker complementary slackness conditions
given by:
(a*/ax.) (X,*) =0 (3.13)
0/3O (O = o
ca*/ax,*) (x,*) = o
0*/a/x) (m*) = o
serve to emphasize the possibility that an interior solu
tion, where the first order partial derivative of the
objective function must equal zero, may not exist. However,
whether the solution occurs at a boundary or an interior
point, the complementary slackness condition states that the
choice variables or the first order partial, or both, must
be equal to zero.
The marginal conditions of equation 3.11 involve four
equations and four unknowns and, if all are binding as one
would expect in this model, can be solved to give the demand
equations for the three choice variables.2 These demand
equations can be written as:
X; = X¡* (P, Pm, w, Y*) i = a,m, 1 (3.14)
which is the neoclassical result that demand is dependent
upon prices and income.
However, in an agricultural household the full income
variable, Y*, is determined by the household's production
2 One would expect all conditions to be binding since X,*,
X,,,*, X,*, and n" would all be expected to be positive in a
smallholder household, therefore equation 3.13 suggests that
equality hold in each equation 3.11.

53
technology through equation 3.10. In equation 3.10 the only
endogenous variable utilized in the characterization of the
production technology is total labor, L. Thus, production
decisions are made separate from consumption decisions; they
are separable decisions. The recursive nature of the model
becomes evident as consumption decisions are seen to be
dependent upon production decisions, but not vice versa.3
Profit Effect
The major result of the agricultural household model is
the introduction of the profit effect. As outlined in the
Introduction, the profit effect can counterbalance tradi
tional neoclassical theory of household behavior with
respect to price changes. This section outlines an example
of the profit effect through an increase in output price and
its implications for consumption.
The total change in quantity demanded, dXa, with a
change in output price, dPa, can be determined by totally
differentiating the appropriate demand equation. Totally
differentiate the demand for the agricultural good (equation
3.14) and divide by the change in its own-price, assuming
that the prices of market goods and wages are exogenous, to
give
dXa/dPs = 3X./3P, + (dXa/dY*) (dY*/dPJ (3.15)
3 For a more rigorous presentation of the recursivity of
the model see the Appendix.

54
where the term dX,/dPa is the standard substitution effect of
neoclassical demand theory. The change in the quantity
consumed of a good given a change in its own price is
negative, if the commodity in question is not an inferior
good. Thus, the first term on the right hand side of equa
tion 3.15 is unambiguously negative for a normal good.
The second term on the right hand side of equation
3.15, (dX,/dY*) (dY'/dPa) represents the profit effect. A
change in the price of the agricultural good changes prof
its, and hence full income, through equation 3.10. This
change in full income will, in turn, change the quantity
demanded of the agricultural good, via the demand equation
(eq. 3.14).
It remains to determine the sign of this profit effect
in order to derive the full impact of a change in the price
of an output which is consumed by the household. First, note
that maximized full income (Y*) given by equation 3.10 is a
function of price levels (P,, w) whose total differential is
given by:
dY* = (dY*/dPa) (dP. ) + (3Y*/dw) (dw) (3.16)
or, when w is unchanged:
dY*/dPa = dY*/dPa. (3.17)
Substituting from equation 3.17, the profit effect term of
equation 3.15 may be rewritten as:
(3.18)
(dXa/dY*) (dY*/dPa) = (dY'/dPJdP,.

55
Second, from equation 3.10, dn'/dPk = X, and 3Y*/dP. = X,,
therefore
3YV3P. = dn/dPa (3.19)
But Hotelling's Lemma states that dn/dP, = Q which allows us
to rewrite the profit effect term as:
(3Y*/3P. )dP. = (dnr/dP,) dP = (Q)dP, (3.20)
a term whose sign can be determined. The profit effect is
therefore the product of the quantity produced and the
change in price. Because quantities, Q, are always positive
the sign of the profit effect is determined by the sign of
the price change under study. The result is analogous to the
well known result that the effect of an income increase is
positive for a normal good.
A direct example will help make the impact of this
result clear. The total change in the quantity of the
agricultural good consumed by the household with a change in
the price of that good is given by:
dXa/dP, = dX,/dP. + (X,)dP,. (3.21)
As stated earlier, the first term on the right hand side is
the familiar substitution effect which is negative for a
normal good. The second term on the right hand side has been
defined as the profit effect. With an increase in output
price the profit effect is unambiguously positive while the
substitution effect is negative. Thus, the substitution and
profit effects work in different directions with the same
price change.

56
Therefore, the total effect of an increase in the price
of an agricultural good produced and consumed by the house
hold can have three possible outcomes. An increase in the
price of the agricultural good may cause a decrease in
consumption via a dominant substitution effect; an increase
in consumption due to a dominant profit effect; or, the two
effects could balance each other resulting in no measurable
effect on household consumption due to an output price
increase. The relative impacts of these two effects on the
response of an agricultural household is indeterminate from
theory. Thus, the particular response for any agriculturally
based household economy must be determined through empirical
means.

CHAPTER IV
PRODUCTION SIDE OF THE HOUSEHOLD
In this chapter the rationale for choosing a particular
approach to estimating the production side of the household
and a functional form are outlined. The Cobb-Douglas produc
tion function was chosen for estimation and is presented in
the first section. Derivations of the input demand, profit
function and profit-maximized output supply equations are
also presented in the first section. The results of the
ordinary least squares (OLS) estimation of the Cobb-Douglas
production function are presented in section two. Production
side elasticities are computed in section three, particu
larly the output price elasticity of profits needed for
calculating the profit effect in Chapter VI.
The data used for estimating the production side of the
agricultural household model came from a grain marketing
study performed in Burkina that roughly coincided with
calendar 1984. The data, while richly detailed on the
consumption side, did not particularly focus on household
production information. However, production relevant data
were measured that would allow an uncomplicated character
ization and estimation of the household production system.
The data used in estimating the production side included
57

58
household field size by crop, harvest figures, labor force
employed by the household (both family and non-family),
expenditures on variable inputs and durable goods held by
the household.
The area under cultivation in cereals by household,
predominantly millet and sorghum, was aggregated to give a
measure of land under cultivation. Labor was obtained from
household demographic and composition changes plus use of
market labor. Output was measured from the harvest figures
and converted to kilograms of cereal using threshing rates
determined for each household during the survey.
Cobb-Doualas Production Function
The alternatives considered for estimating the produc
tion side of the model were to use either a production or a
profit (cost) function. A Cobb-Douglas production function
was eventually chosen for three main reasons. First, the
available data were more suited to a Cobb-Douglas production
function than a profit (or cost) function approach. For
example, a representative cost for land is extremely diffi
cult to capture in the African agricultural setting. Second,
actual factor use, and hence a production function, was
preferred over factor input prices, and a profit (cost)
function, because the former were available from the survey.
Furthermore, factor input prices were not expected to vary
significantly across households in a cross-sectional data

59
set. The third consideration was the ease of estimation,
given that the consumption side of the model would take
considerable time for data preparation, estimation and
refinement a more straight forward production side estima
tion was preferred. Statistical testing of the appropriate
ness of the Cobb-Douglas approach in this case was also
undertaken. In comparisons against other specifications,
notably the translog and constant elasticity of substitution
(CES), the Cobb-Douglas specification was not rejected.
A Cobb-Douglas production function consistent with the
production constraint (Eq. 3.5) takes the specific form
Q = aQAa'Lai (4.1)
where Q is total output, A is the area under cultivation
(assumed fixed in the short-term) and L is the labor uti
lized in producing output. The expansion of this form to
include variable inputs and capital is straight forward. The
a0 variable is a technological efficiency parameter that
indicates the present state of technology. This can be seen
from equation 4.1 by noting that for given values of the
other production inputs (A and L), the value of a0 will have
a proportional effect on the size of output (Q).
For estimation purposes equation 4.1 is linearly
transformed by taking natural logarithms to yield
InQ = lna0 + a,lnA + a2lnL
(4.2)

60
Note that the output supply elasticities can be obtained
directly from the parameter estimates of the linearly
transformed Cobb-Douglas production function because
£ql = (dQ/dh)L/Q = dlnQ/ainL = a2. (4.3)
Factor demand equations are obtained from the first
order conditions of profit maximization that equate the
value of the marginal product of a factor to its wage cost,
assuming perfectly competitive markets or
dn/d L = P,(3q/3L) = w. (4.4)
Thus, the household will employ labor, in this case both
on-farm labor and off-farm labor, until the marginal product
of the marginal worker equals the real wage rate.
Note that equation 4.4 has only one endogenous vari
able, L, and, thus, can be solved in terms of P,, w, the
parameters of the production function and the fixed area of
land, A. The general solution to equation 4.4 can now be
written as:
L* = L*(P.,w,A) (4.5)
This result is important because none of the other
endogenous or choice variables appear in equation 4.5, which
emphasizes that household consumption decisions do not
impinge on production decisions in this model. Thus, produc
tion decisions are made separate from consumption decisions;
they are separable decisions.
Multiplying both sides of equation 4.4 by L/Q gives
P,(dQ/dL) L/Q = wL/Q (4.6)

61
which can be solved for the household demand for labor as
L = a2(P,/w)Q. (4.7)
where Pa is the output price of the agricultural commodity
and w is the wage rate.
The restricted profit equation (profits minus variable
costs) is then given by
7T = P,Q(A,L) wL (4.8)
which, with substitution from equation (4.7), simplifies to:
n = a,P,Q (4.9)
when a, + a2 = 1.
The profit-maximized output supply equation can then be
obtained by substituting the input demand equation (eq. 4.7)
in the original Cobb-Douglas production function (eq. 4.1)
which simplifies to:
cX1
a.
L
w
1/ (l-2>
(4.10)
In addition to the above Cobb-Douglas specification, a
translog model was estimated that included squared terms for
the two factor inputs and an interaction term between these
inputs. Since the Cobb-Douglas model is a special case of
the translog model, the former can be tested as a restricted
case of the latter. When the appropriate F-test was per
formed the hypothesis that the Cobb-Douglas model was
appropriate was not rejected at the 99% level of signifi
cance.

62
The Cobb-Douglas specification was also tested against
the CES production function. Once estimated, the CES was
tested for constant returns to scale (unable to reject at
the 95% level of significance) and then reestimated with
this restriction imposed. The resulting CES with constant
returns to scale was tested against the Cobb-Douglas. Again
the Cobb-Douglas specification was not rejected at the 99%
level of significance (nor at the 95% level of significance,
contrary to the test against the translog). With these
results the Cobb-Douglas estimates were retained for the
model estimation.
Other concerns entered into the choice of the Cobb-
Douglas specification. The needs of the agricultural house
hold model, functional form tractability and data availabil
ity constraints precluded the use of a translog approach in
the present case. Recall, that the main production side
result required for the agricultural household model is the
responsiveness of profits to changes in output price.
Unfortunately, "it is not possible to derive the first order
conditions for profit maximization and substitute them into
the translog production function to give a price-based
translog production function (Haughton, 1986, p. 207)" as
was done with the Cobb-Douglas specification.
An alternative approach would have been to derive the
restricted profit function from a direct production func
tion. Again tractability is a problem as "this works neatly

63
in the Cobb-Douglas case, it is not analytically possible
for a translog production (sic) (Haughton, 1986, p. 209)."
The direct specification of a profit, or cost, function
would require information on input prices that is not
available in the Burkina data. Profit and cost function
approaches were unavailable because the input price data
were not sufficient to support estimation. Furthermore, it
is particularly difficult to value the two major inputs in
the African agricultural household production system; family
labor input and land to farm production.
Choice of specification can often have constraining
impacts on model results that must be noted prior to estima
tion. The impact of using a Cobb-Douglas specification on
the resulting production side elasticity estimate have been
mentioned by other writers. Previous studies have shown that
the estimates of direct (quantity-based) production func
tions generally result in larger elasticity estimates than
indirect (price-based) production functions. "Once again the
direct estimates show far greater responsiveness (Haughton,
1986, p. 215)."
Other a priori constraints on the results that are
specific to a Cobb-Douglas specification include constant
unitary elasticity of substitution, input elasticities of
output that are invariant to output level, and strictly
positive input quantities. In spite of these restrictions,

64
the Cobb-Douglas approach can give useful results as Haugh-
ton points out:
However, the superiority of a homogenous translog
form over the Cobb-Douglas form should not be
overstated; both have fairly close fits De
pending on what issue is being addressed, the
simpler Cobb-Douglas form may be adequate, Both
give essentially similar output elasticities with
respect to inputs (at the geometric mean values of
the variables). (Haughton, 1986, p. 213)
Awareness of these and other impacts of model specification
should be retained and used to temper the interpretation of
the final results.
Additional explanatory variables, other than land and
labor, were also created from the raw household data to
represent expenditures on variable inputs (fertilizer, seed,
insecticides, etc.) and capital inputs (durable good hold
ings as a proxy). Their inclusion in the model did not add
additional explanatory value and hence were not retained for
the final estimation. Moreover, few households in the sample
reported using inputs other than land and labor.
Another likely omitted explanatory variable is farm
management. Surrogate variables based on the age and educa
tional level of the head of household were added to the
basic model to capture the variance of management capability
across households. The resulting specifications did not add
explanatory power to the model with management proxies based
on age, head of household educational level and maximum
educational obtained within the household. These results can
be explained by the lack of significant variance in levels

65
of education across households in the sample. Thus, the
final estimating equation for the production side of the
household model was the Cobb-Douglas specification using
land and labor as explanatory variables for output.
Estimation Results
This section presents the results from the ordinary
least squares (OLS) estimation of a Cobb-Douglas production
function fitted to Burkina household data on output, area
under cultivation and labor. Both the endogenous and exoge
nous variables were measured in volume rather than value
form. Three dummy variables were added to the basic model to
account for any differences in the production function
across villages. Of course, the model with all dummy vari
ables coefficients equal to zero holds for the fourth
village in the sample (in this case Village 1).
Land and labor are normally considered endogenous
(decision) variables with rental and wage rates exogenously
determined. With land and labor decisions endogenously
determined a simultaneity problem would arise in estimating
a Cobb-Douglas function with OLS. However, other work on the
Cobb-Douglas specification (Zellner, Kmenta and Dreze, 1966)
has shown that if output is stochastic and the household-
firm is assumed to maximize expected profits, then the
resulting error terms of the OLS estimation are independent
of the included endogenous variables. The result is that OLS

66
estimation of a Cobb-Douglas land-labor specification yields
consistent parameter estimates assuming expected profit
maximization.
The econometric model of household production behavior
was first estimated with no restrictions on the parameter
estimates. The resulting estimates were then tested to
determine if the sum of the parameters on land and labor was
significantly different from unity (i.e., constant returns
to scale). The statistical test of this linear constraint
would not allow rejection of the null hypothesis that the
sum of the parameter estimates was one at the 95% level of
significance. A confidence interval on the sum of the
parameter estimates was determined at the 95% level of
significance. The resulting range was from 0.71 to 1.59. The
model was re-estimated under the restriction that a, + a2 =
1. Note that the presence of CRS is consistent with profit
maximization because of the assumption of fixed land under
cultivation.
Results from both the unrestricted and restricted
models are presented in Table 4.1. Note that the t-statistic
values are significant at the 95% level for land, labor and
the Village 2 dummy variable in both the unrestricted and
restricted equations.
The R-squared values for both the unrestricted and
restricted equations are not particularly high indicating
that the model explains roughly 40% of the variance in

67
output. This kind of result is not surprising, particularly
for primary, cross-section data. Barnum and Squire's (1979-
a,b) Cobb-Douglas estimation in a monocropping environment
explained roughly 67% of the variation in output. Haughton
(1986) reported R-squared values of around 50%.
TABLE 4.1
UNRESTRICTED AND RESTRICTED
COBB-DOUGLAS PRODUCTION FUNCTION ESTIMATES
UNRESTRICTED
RESTRICTED
PARAMETER
t-STAT
PARAMETER
t-STAT
ESTIMATE
ESTIMATE
Intercept
0.597
0.45
1.072
0.94
In (Land)
0.414
3.38
0.394
3.32
In (Labor)
0.739
3.26
0.606
-
Village 2
-1.778
-5.48
-1.747
-5.45
Village 3
-0.350
-1.02
-0.344
-1.01
Village 4
-0.107
-0.33
-0.131
-0.41
R2
0.419
-
0.417
-
The definition of inputs and output variables could
account for some of the unexplained variation remaining in
the production estimation. For example, the output variable
is an aggregate measure over both millet and sorghum. The
assumption of a single production function for cereals may
be a source of additional variability in the output vari
able. Although the major cereals, millet and sorghum, are
generally aggregated together, a multicrop production

68
function could possibly add explanatory power. Further error
could originate in the measures used for the explanatory
variables, particularly labor. Labor quality can vary
significantly across household, market and work party labor
sources (Saul, 1983).
Omitted variables could also help explain the reduced
R-squared value. The most likely exogenous variable that
would add information to explain variable output would be
one that captured the highly variable climatology of the
Sahel. Unfortunately, this type of information, or a suit
able surrogate, is not available at the household level. The
village dummy variables add significant explanatory value to
the model and can be interpreted as capturing some of the
agroclimatological variation across the villages.
Another possible missing variable that could help
interpret the lack of explanatory power is the quality of
land. The variability of the quality of land is significant
across households and could improve explanatory power in a
revised estimate. Unfortunately, this variable, or a proxy,
were not available for inclusion in this estimation.
Using the restricted estimation results from Table 4.1
the production side equations needed to proceed with the
agricultural household model can be determined. The produc
tion function (for Village 1) can now be written as
InQ = 1.07 + 0.39*lnA + 0.61*lnL, (4.11)
the household demand for labor is

69
L = 0.61*(P,/w)Q,
(4.12)
the restricted profit function is
TTr = 0.39*PaQ,
and the profit-maximized output equation becomes
Q* = 7.2*A* (Pa/w) 028.
(4.14)
(4.13)
Production Elasticities
This section outlines the derivation and calculation of
the production side elasticities relevant to the agricultur
al household model. Using the parameter estimates from the
previous section, a table of input demand and output supply
elasticities is constructed. These elasticities are inter
preted for their significance to production decisions and
will be used in Chapter VI to determine the direction and
magnitude of the profit effect and its impact on household
output price responsiveness.
The coefficients on land and labor can be interpreted
as the output supply elasticities, as was demonstrated
through equation 4.3. Similarly, the restricted equation
estimates can be used to determine the relative shares
accruing to land and labor. From Table 4.1 it can be deter
mined that the share for land is 39% while that of labor is
61%. In the same fashion, the impact on output of a 10%
increase in labor is slightly less than twice that of a
similar increase in land.

70
Barnum and Squire's Malaysia data indicated the reverse
of the Burkina figures with 62 and 29% shares for land and
labor, respectively. The balance being the shares of other
variable inputs (8 percent) and capital (1 percent). This
can be taken to imply that agriculture in Burkina is con
strained more by labor than land. Thus, greater returns
could be expected from addressing labor constraints than
land constraints, although both would have a significant
positive impact on production.
Production side elasticities more directly relevant to
the agricultural household model can be directly computed
from the output supply (eq. 4.10), labor demand (eq. 4.7)
and profit (eq. 4.9) equations.1 The resulting elasticity
values and the formulas from which these estimates were
derived are presented in Table 4.2.
In general, the results from Table 4.2 are consistent
with earlier studies including Barnum and Squire (1979a,b)
and Haughton (1986), both using Malaysian data. From the
first two diagonal elements of Table 4.2, the own-price
elasticities of output and labor can be interpreted. Output
produced is very (positively) responsive to changes in the
price of that output (in this case cereal price). As previ
ously mentioned above, these direct, or quantity based,
1 Taking logarithms of both sides of these three equa
tions simplifies the derivation of the elasticity formulas.

71
estimates are expected to imply greater responsiveness than
those based upon indirect or price based estimates.
TABLE 4.2
PRODUCTION SIDE ELASTICITY ESTIMATES
VARIABLES
ELASTICITIES
OUTPUT
(Q)
LABOR
DEMAND (L)
PROFIT
(7T)
OUTPUT PRICE (PJ
1.56
2.56
2.56
(elasticity equation)
(a2/a,)
(1/a,)
d/a,)
WAGE RATE (w)
-1.56
-2.56
-1.56
(elasticity equation)
(-a2/a,)
(-a2-a,/a,)
(-a2/a,)
TECHNOLOGY PARAMETER
2.56
2.56
2.56
(<*6)
(elasticity equation)
(1/0!,)
(1/a,)
d/a,)
The high responsiveness of demand for labor to changes
in the wage rate is also clear from Table 4.2. The value of
-2.56 compares to -2.57 found by Haughton using Malaysian
data and a Cobb-Douglas production function. Similarly,
Barnum and Squire, using data from a more well-to-do area of
Malaysia and a Cobb-Douglas production function approach,
found -1.47. Assuming increasing population growth the high
price responsiveness of household demand for labor can be
expected to limit unemployment in the agricultural sector.
In addition to increasing output, an increase in output
price will also induce greater demand for labor and higher
profits. Wage rate elasticities have the expected negative

72
responsiveness for the elasticities listed in Table 4.2. An
increase in the wage rate can be expected to reduce the
demand for labor, thereby reducing both output and profits.
Note that the direct influence on labor demand is greater
than the induced declines in both output and profits indi
cating that labor is not the sole factor input in the
household production process. Finally, the significance of
technological change is high and can be expected to increase
demand for labor, output and profits.
What is needed from this production side in terms of
the agricultural household model is the impact of changes in
output price on profits, the output price elasticity of
profit. Table 4.2 reports a value of 2.56 for this elastici
ty implying that profits are highly responsive to output
price changes. Haughton found this elasticity using a direct
approach to be 3.06 while the indirect approach gave 1.89.
The value for Burkina in Table 4.2 (2.56) is approximately
halfway between these two extremes.

CHAPTER V
CONSUMPTION SIDE OF THE HOUSEHOLD
This chapter presents the consumption side of the
household model. The consumer choice between goods to
consume and labor to supply, modeled by an almost ideal
demand system (AIDS), is presented in the first section.
Estimation results from the AIDS model and restrictions from
the neoclassical theory of demand (homogeneity and symmetry)
are examined in the second section of this chapter. In the
final section, expenditure, own and cross-price elasticities
are calculated.
The data used to estimate the consumption side of the
agricultural household are also from the Burkina grain
marketing study. Recall that the household level survey from
this marketing study provided the data for estimating the
production side of the household in the previous chapter.
Expenditure data from the same households used in Chapter IV
are used in this chapter to estimate the consumption side of
the household. These expenditures were obtained from fort
nightly recall interviews in each household. The expenditure
data were complemented with questionnaires designed to
acquire information on quantities given (wages, gifts,
exchanges, etc.) and received (salaries, gifts, remittances,
73

74
etc.)* The final size of the sample set of households used
was limited to the 87 households which had complete annual
data on both production and consumption.
Almost Ideal Demand System (AIDS)
There are several alternative approaches to solving and
estimating a system of demand equations. These include the
linear expenditure system (LES), the log-linear expenditure
system (LLES) and the Rotterdam approaches. Each of these
systems approaches has its advantages and disadvantages
depending upon the needs of the analysis.
Demand systems that are derived from an additive
utility function, such as the LES, necessitate strong
separability of preferences and, possibly, own price elas
ticities restricted to linear relations of expenditure elas
ticities. The LES is derived from the Stone-Geary additive
utility function. The LLES, on the other hand, requires
expenditure elasticities equal to unity, which would inap
propriately restrict the present study.
Another possible specification for the consumption side
that would provide an opportunity to test the consequences
of the neoclassical theory of demand is the Rotterdam model.
The Rotterdam model is consistent with utility maximization
for a linearly logarithmic utility function and has a
similar specification to the AIDS configuration. However,
unlike the AIDS, the Rotterdam model is not derived from

75
explicit preferences and demand functions (Deaton and
Muellbauer, 1980a, p. 317).
The crucial points for choosing a functional form for
the agricultural household model is the need for un
restrained elasticities and compatibility with theory. Prior
restrictions resulting from the choice of functional form
could limit the impact of the profit effect on consumer
demand via the full income constraint.
Because of the need for a functional form that does not
restrict parameter estimate values and related elasticities
the almost ideal demand system of Deaton and Muellbauer was
chosen for this study (Deaton and Muellbauer, 1980a). The
AIDS model provides great flexibility for estimation and
testing as Deaton and Muellbauer point out:
. the Almost Ideal Demand System (AIDS), gives
an arbitrary first-order approximation to any
demand system; it satisfies the axioms of choice
exactly; it aggregates perfectly over consumers
without invoking parallel linear Engel curves; it
has a functional form which is consistent with
known household budget data; it is simple to
estimate, largely avoiding the need for non-linear
estimation; and it can be used to test the re
strictions of homogeneity and symmetry through
linear restrictions on fixed parameters. (Deaton
and Muellbauer, 1980a, p. 312)
Most importantly for the present study, the AIDS model
provides for flexible price and income elasticities which
are necessary in estimating a household model because price
and expenditure responses are the major points of interest.
One should not constrain the elasticities to any particular

76
value (like the LLES), or range of values, in order that the
full responsiveness of household expenditures to price and
income changes can be captured.
Derived from utility maximization via a cost function
by way of Shephard's Lemma, the AIDS model can be succinctly
written as
(5.1)
where the share of expenditures allocated to good i (budget
shares; w¡ = p¡q¡/m) are determined as a function of the price
of good j (pj) and total expenditure (m) on all the goods
being examined. Note that changes in relative prices impact
on budget allocations via the gamma terms and changes in
real expenditure impact via the beta coefficients. The beta
coefficients can be interpreted as measuring necessities
(j8<0) or luxuries (j8>0) depending on their sign.
The only non-linear element in the AIDS model of
equation 5.1 is the price index term (log P) that deflates
the value of total expenditure. From the derivation of the
AIDS model this price index is defined as
logP = a0 + £ ak log pk + 1 ]T £ 7 V lo(?P* lgP, (5.2)
The non-linear AIDS price index (logP) of equation 5.2 is
often estimated by the Stone price index (logP*) which is
given as

77
logpj logp* (5,3)
The Stone price is an expenditure share weighted linear
price index which is approximately proportional to P*, if
prices are highly collinear.
AIDS models that utilize the linear approximate (LA)
Stone price index of equation 5.3 are often designated as
LA/AIDS models. Having employed the Stone price index, the
present study is an LA/AIDS model. The distinction between
estimation of the AIDS, with the non-linear price index, and
the LA/AIDS, with the linear Stone approximation, will be
important in determining the appropriate computing formulas
for elasticities of demand in section three below.
Estimation Results
For estimation purposes the household level data were
pooled by considering each household separately over four
time periods within the twelve month data collection period.
Ray used a similar pooling technique to create panel data in
estimating an AIDS model on household budget data from India
(Ray, 1982). The benefits and costs of panel data over cross
sections is discussed in other sources (Ashenfelter, Deaton
and Solon, 1986).
The four time periods correspond to the different
seasons in the agricultural sector of Burkina where behavior
can be expected to vary. The four periods, corresponding to

78
quarters, are referred to as the cold (December to Febru
ary) hot (March to May), rainy (June to August) and harvest
(September to November) seasons.
Roughly 140 individual commodities were found in the
raw data from the 87 households. These commodities were
aggregated to four goods, plus labor supplied. The four
goods were cereals (containing all cereal products), tobacco
and beverages (including beer, soda and kola), other foods
(non-cereal food purchases), and other non-food purchases.
Time spent in leisure activities (broadly defined as all
non-farm activities) was determined by subtracting the
amount of agricultural labor time supplied by the household
from the total time available. Thus, leisure is determined
as the residual of the difference between household labor
supplied on-farm and total time available.
Neoclassical demand theory is based upon a set of
preference axioms and a linear budget constraint. Several
restrictions on systems of demand equations can be derived
from these two basic units of theory. These restrictions are
known as adding-up, homogeneity of degree zero in prices,
symmetry and negativity of price effects. Adding-up requires
that the sum of the expenditures across all goods equal
total expenditure and originates from the linear budget con
straint.
Homogeneity of degree zero in prices implies that equal
proportionate changes in both prices and expenditure will

79
not change the resulting demand. This is also known as the
absence of money illusion, implying that consumers make
consumption decisions upon relative prices, not absolute
price levels. Homogeneity is also derived from the linear
budget constraint.
Symmetry implies that the price effects of quantity
demanded across any two goods will be identical. Acceptance
of symmetry insures that the underlying preference structure
is consistent. Negativity refers to the negative relation
between the demand for a good and its own price, which is
often called the "law of demand." These last two results
derive from the specific axioms of preference underlying
neoclassical demand theory. Deaton and Muellbauer provide
details on the linear budget constraint, axioms of prefer
ence, and the derived constraints of demand (Deaton and
Muellbauer, 1980b).
Full Information Maximum Likelihood (FIML) was chosen
as the preferred method of estimating the AIDS model because
it is invariant with respect to choice of equation dropped
in the demand system (Greene, 1990, p. 528). Recall that in
systems of demand estimation all commodity demand functions
can not be included in the estimating procedure because this
produces a singular covariance matrix. A singular covariance
matrix results in an undefined likelihood function. There
fore, one of the system's equations is dropped in order to
insure non-singularity of the covariance matrix. The parame-

80
ters of the dropped equation are then obtained from the
adding-up conditions.
Both the unrestricted and restricted estimates were
used to test the restrictions of homogeneity and symmetry
using the likelihood ratio test. Adding-up is assured by
dropping one of the equations, in this case the labor
supplied by the household. In the AIDS model the testable
restrictions imply the following
af = l 7y=0 j3, = 0 (5-
1=0 i=l i=l
E^=0 (5.5)
j
7y =7a (5-6)
for adding-up (5.3), homogeneity (5.4) and symmetry (5.5),
respectively.
The unrestricted and restricted FIML estimates for the
intercept, expenditure and own-price parameters of the
LA/AIDS are presented in Table 5.1. Both homogeneity and
symmetry were imposed in obtaining the restricted parameter
estimates reported in Table 5.1 The results are encouraging
with twelve and eleven of the fifteen coefficients listed
being significantly different from zero (t-statistics
greater than two) for the unrestricted and restricted
estimations, respectively. Most of the significant changes
in t-statistic values occur with the intercept terms.

81
TABLE 5.1
UNRESTRICTED AND RESTRICTED ESTIMATES OF THE LA/AIDS MODEL
UNRESTRICTED
RESTRICTED
ESTIMATE
t-STAT
ESTIMATE
t-STAT
INTERCEPT a,
-0.520
-5.61
-0.014
-0.23
a2
-0.165
-3.43
-0.039
-1.84
3
0.009
0.11
0.141
4.31
a4
-0.091
-0.99
-0.032
-0.69
5
1.767
11.86
0.945
9.84
EXPENDITURE 6,
0.047
5.79
0.052
5.94
r2
0.022
8.97
0.023
8.71
*3
0.010
1.84
0.004
0.84
B4
0.030
3.16
0.021
2.73
*5
-0.111
-6.98
-0.100
-7.06
OWN-PRICE 7,
0.111
16.78
0.075
10.29
72
0.022
-2.50
0.019
8.71
73
0.036
20.58
0.036
18.43
74
0.028
7.08
0.030
8.21
7s
-0.049
-2.93
0.067
5.57
Note that the expenditure parameter estimates are
positive for four out of the five goods in both the unre
stricted and restricted models. As mentioned earlier, the
AIDS configuration allows for classification of goods as
necessities and luxuries depending upon the sign of the beta
coefficients. Inspection of Table 5.1 results in the conclu
sion that cereals, tobacco and beverages, other foods and
other non-food are all luxuries in the rural economy of
Burkina. This is not surprising given the low absolute
levels of incomes in the Sahel.

82
The share of total expenditures allocated to the
consumption of leisure increases with increasing income.
Recall that the labor supply equation is related to leisure
demand through the total time available (X, = T L) The
share estimated in this system is wL/m, which decreases with
increasing income, thereby increasing wX,/m. The broadly
determined leisure variable is the only luxury in this
system. Interpretation of the price parameters in the AIDS
model requires calculation of the relevant elasticity esti
mates which are presented in the next section.
The likelihood values for both the restricted and
unrestricted models were differenced, multiplied by two and
compared to the chi-squared statistic to perform the likeli
hood-ratio test for the validity of the restrictions. The
restrictions were rejected at the 95% level of significance.
Symmetry and homogeneity were imposed separately and also
tested. Both were rejected at the 95% level of significance.
The rejection of the restrictions derived from neoclas
sical demand theory is not unusual in empirical studies.
"The restrictions of homogeneity and symmetry are
consistently rejected by the data (Deaton and Muellbauer,
1980b, p. 80)." In tests of the restrictions Ray found "that
homogeneity is only marginally rejected for the household
AIDS" (Ray, 1982, p. 360). In contrast, the "symmetry re
striction is decisively rejected for the rural sector but
only marginally for the urban sector" (Ray, 1982, p. 360).

83
In general, Ray's results found that the rural data were
more likely to reject the demand restrictions than the urban
data. This result was also dependent on whether or not
household size effects were included in the model. The
important point for this study is the choice between the
unrestricted or restricted estimates in determining the
demand elasticities. The decision is between statistically
rejected restrictions from theory versus the results ob
tained from the theoretical structure employed.
Both unrestricted and restricted parameter estimates
were used in deriving the consumption elasticities with no
exceptional difference in elasticity values, particularly
the expenditure elasticities. Therefore, restricted esti
mates were retained for the elasticity computations of the
next section. It is not uncommon to impose theoretical re
strictions in AIDS models without reporting significance
tests (Bezuneh, Deaton and Norton, 1988).
The cross-price parameter estimates provided in Table
5.2 were not as impressive as those presented in Table 5.1.
A total of 25 cross price parameters were estimated, or
estimated and derived in the case of restrictions. The
number of statistically significant cross price parameter
estimates, at the 95% level, numbered 8 and 12 in the
unrestricted and restricted models, respectively.

84
TABLE 5.2
UNRESTRICTED AND RESTRICTED ESTIMATES OF THE LA/AIDS MODEL
UNRESTRICTED
RESTRICTED
ESTIMATE
t-STAT
ESTIMATE
t-STAT
GOOD 1 to 2
-0.006
-1.16
-0.015
-7.19
3
-0.001
-0.25
-0.011
-3.49
4
-0.002
-0.58
-0.015
-3.99
5
0.027
1.99
-0.033
-3.70
GOOD 2 to 1
-0.008
-2.50
-0.015
-7.19
3
-0.002
-0.91
-0.003
-1.86
4
0.001
0.69
-0.0005
-0.34
5
0.016
2.32
-0.0008
-0.24
GOOD 3 to 1
-0.023
-4.48
-0.011
-3.49
2
-0.005
-1.43
-0.003
-1.86
4
-0.005
-2.15
-0.002
h*

O
U1
5
0.005
0.39
-0.019
-5.29
GOOD 4 to 1
-0.044
-4.59
-0.015
-3.99
2
-0.003
-0.55
-0.0005
-0.34
3
0.004
0.88
-0.002
-1.05
5
0.002
0.22
-0.012
-2.79
GOOD 5 to 1
-0.036
-2.57
-0.033
-3.70
2
-0.007
-0.92
-0.0008
-0.24
3
-0.037
-6.53
-0.019
-5.29
4
-0.021
-3.99
-0.012
-2.79
This percentage of statistically significant parameter
estimates (one-third to one-half) from an AIDS estimation
compares favorably with other studies. Deaton and Muellbauer
reported 22 out 64 parameter estimates from British data
with t-statistics greater than two (Deaton and Muellbauer,
1980a). Using Kenyan data, Bezuneh, Deaton and Norton found

85
85 out of 124 parameter estimates that were more than twice
their standard errors, but this figure included both cross
price and other parameters (Bezuneh, Deaton and Norton,
1988). Finally, Ray's Indian data resulted in 21 out of 32
cross price parameter estimates with greater than "unit t
values (Ray, 1982, p. 357)." Inspection of Ray's results
reveals that 10 out of the 32 cross price estimates had t-
statistics greater than two.
The poorer performance of the parameter estimates for
cross-price behavior can be attributed to the difficulties
arising from aggregation across commodities. The four
tangible consumables in this study consisted of varying
numbers of individual commodities. Two of the goods created
from the disaggregated data were composed of around ten
commodities, namely Cereals (Good 1, 11 commodities) and
Tobacco and Beverages (Good 2, 9 commodities). Other foods
(Good 3) and other non-food (Good 4) were composed of 71 and
51 commodities, respectively. The difficulty in determining
cross-price behavior from this level of aggregation is not
surprising. Similarly, it is not surprising that the most
significant cross price parameters arose for the least
diverse good grouping (i.e., Good 1, cereals).
Consumption Elasticities
Consumption elasticities from the AIDS model have
received considerable attention in recent years. Various

86
authors have used different elasticity computing formulas.
The issue has been how to determine the price, both compen
sated and uncompensated, and income (expenditure) elastici
ties of demand. The problem derives from the use of the
Stone price index as an approximation of the price deflator
used in the AIDS model. Thus, the problem is between the
linear approximate AIDS (LA/AIDS) and the non-linear AIDS
(AIDS) computing formulas for price and income demand
elasticities.
From equation 5.3 it is clear that the Stone price
index is a function of the budget shares indicating that the
budget share variable is endogenously determined. These
shares are generally assumed to be constant when taking
derivatives to derive elasticity computing formulas for the
LA/AIDS. The confusion arises in the use of non-linear AIDS
computing formulas where the shares are endogenous in
computing elasticities for the LA/AIDS. Green and Alston,
using the same data set under LA/AIDS and AIDS, have found
that the use of AIDS computing formulas in calculating
LA/AIDS elasticities will result in significantly different
elasticity estimates than those from the non-linear AIDS
(Green and Alston, 1990). Green and Alston present the
correct elasticity computing formula for use with the
LA/AIDS model.
AIDS elasticity computing formulas, with variable
expenditure shares, should not be used with estimations of

87
the LA/AIDS, where expenditure shares are assumed invariant
to changes in income. Assuming that the expenditure shares
are invariant to income level is equivalent to assuming
homothetic preferences (j3~0 for all i) in which case the
elasticity computing formulas are the same for both the AIDS
and the LA/AIDS. However, if preferences are not assumed to
be homothetic then the choice of computing formula is impor
tant.
In a follow-up article Green and Alston presented the
correct LA/AIDS computing formulas for the uncompensated,
compensated and expenditure elasticities (Green and Alston,
1991). The demand elasticity computing formulas for the
LA/AIDS result in a system of simultaneous equations solved
by matrix algebra. This was the approach used in computing
the uncompensated and income compensated elasticities
presented.
The uncompensated and income compensated elasticities
are presented in Tables 5.3 and 5.4, respectively. The
elasticity directions and values are reasonable for both
prices and incomes. All own price elasticities are negative,
as would be expected from rational consumers. Rural Burkina
households adhere to the law of demand just as any other
household. Own price elasticities are somewhat inelastic
which could be due to the overall low level of consumption
in the rural Sahel.

88
TABLE 5.3
UNCOMPENSATED DEMAND ELASTICITIES FOR THE LA/AIDS
COMMODITY
GROUP
ELASTICITY OF DEMAND WITH RESPECT TO
In
come
Price of Commodity Group
1
2
3
4
5
1) Cereals
1.35
-0.72
-0.06
-0.07
-0.09
-0.40
2) Tobacco and
Beverages
1.83
-0.49
OJ
in

o
1
-0.11
-0.08
-0.63
3) Other Foods
1.06
-0.12
-0.03
-0.65
-0.02
-0.24
4) Non-Food
1.35
-0.23
-0.00
-0.04
-0.69
-0.39
5) Labor Supply
0.72
-0.02
-0.00
-0.03
0.001
-0.67
TABLE 5.4
COMPENSATED DEMAND ELASTICITIES FOR THE LA/AIDS
COMMODITY
GROUP
ELASTICITY OF DEMAND WITH RESPECT TO
In
come
Price of Commodity Group
1
2
3
4
5
1) Cereals
1.35
-0.42
-0.01
0.07
0.02
0.33
2) Tobacco and
Beverages
1.83
-0.09
-0.44
0.08
0.08
0.36
3) Other Foods
1.06
0.12
0.02
-0.54
0.07
0.34
4) Non-Food
1.35
0.08
0.05
0.10
-0.57
0.34
5) Labor Supply
0.72
0.14
0.02
0.05
0.07
-0.28
The income (expenditure) responsiveness of three of the
five goods categories are significantly elastic. The high
degree of income responsiveness of tobacco and beverages is

89
striking and may indicate the increasing integration of
rural demand with goods produced in other sectors and
regions. The only locally produced commodity included in
Good 2 is sorghum beer. The exception to the high degree of
income responsiveness is the labor supply that while still
positive allows for the intuitively appealing result of
increased consumption of leisure with increasing income.
The compensated demand elasticities of Table 5.4 allow
direct interpretation of goods as complements, substitutes
or independent commodities. The value of most cross price
elasticities are very small, the exception again being the
labor supply elasticities. Most goods appear to be slight
gross substitutes with the only possible gross complements
being cereals with tobacco and beverages. In general, using
large aggregate commodity groups the own price elasticities
are more responsive than the cross price elasticities. The
cross price elasticities tend to reflect the income effect
over the substitution effect in aggregate data.
Results from other studies using AIDS models at the
household level tend to reinforce the conclusion of reason
able estimates from this side of the model. Ray found
differing responses between rural and urban consumers using
a non-linear FIML estimation of the AIDS model from Indian
budget data (Ray, 1982). Ray's food group was a necessity
and the other non-food group was a luxury. Most price
elasticities had the correct signs and the most prominent

90
exception (other non-food) was attributed to aggregation
error. Ray's expenditure elasticity for the food group was
0.71 while the price elasticity was -0.68 from rural time
series data. Pooled data estimates resulted in higher
estimates for both elasticities.
All but one of the own-price elasticities for the goods
modeled by Bezuneh, Deaton and Norton using Kenyan data had
the expected (negative) sign for both participants and non
participants in a Food-For-Work (FFW) scheme (Bezuneh,
Deaton and Norton, 1988). The exception was the millet and
sorghum good which had a positive own-price elasticity. The
authors attributed the sign change of the uncompensated own-
price elasticity to the impact of the profit effect (elas
ticity estimates for AIDS without the profit effect were not
reported). The increase in demand for the millet and sorghum
good with an increase in its price was credited to the
increased income for farm households from higher prices.
The positive uncompensated own-price elasticity (0.67)
was found for FFW participants and not among non-partici
pants whose elasticity estimate (-0.53) was similar to that
determined for Burkina (-0.72). Compensated price elastici
ties for the more comparable (to Burkina) non-participant
sample were even more striking. The Kenyan non-participant
millet and sorghum own-price elasticity was -0.49 compared
to a similar cereals elasticity for Burkina of -0.42. Non
food uncompensated and compensated elasticities were also

91
similar between non-participant Kenyans and the Burkina
sample (-0.72 and -0.62 for Kenya with -0.69 and -0.57 for
Burkina, respectively).
Expenditure elasticities between the Kenya and Burkina
data also compare favorably. Again comparing the results
from the non-participant Kenyan sample with the Burkina data
the expenditure elasticities for cereals were 1.04 and 1.35,
respectively. The participant Kenyan households had an
cereals expenditure elasticity of 1.53.
A final comparison is possible between rural and urban
consumer behavior in Burkina derived from an LA/AIDS estima
tion. Savadogo and Brandt report elasticities for urban
Burkina from 1982-83 which could be used to compare with the
present rural results (Savadogo and Brandt, 1987). These
authors found high uncompensated own price elasticities of
demand for domestic cereals that ranged from -1.80 to -2.85,
depending upon wealth category; wealthier households being
more responsive. The income elasticity for locally produced
cereals ranged from 0.63 to 1.13 with a sample mean of 0.94.
Again, wealthier households were more responsive than less
well off households.
The most appropriate comparison between the urban and
rural elasticities is between the lowest income urban and
the average rural household. The rural price and expenditure
elasticities found in the present study are significantly
different from those found by Savadogo and Brandt. Recall

92
that the uncompensated own price elasticity for cereals was
-0.72, while the expenditure elasticity was 1.35. The
implication is that rural households are less responsive to
price changes and more responsive to income changes than
urban households.
However, the comparisons between these two studies re
quires a significant caveat. The urban data, while estimated
under an LA/AIDS model, used the non-linear AIDS elasticity
computing formulas for deriving parameter estimates and
subsequent elasticities. The Green and Alston result report
ed above implied that the resulting elasticity estimates
would be incorrect.
Fortunately, Savadogo and Brandt also ran their data
under an LES and reported the results. Using LES the income
elasticity of demand for domestic cereals for the lower 25th
wealth percentile was 1.29. This value compares favorably
with the 1.35 value found for rural Burkina. The very
different price elasticities can be explained by the choice
of elasticity estimating formula and the lack of sufficient
price variation in the urban data (Savadogo and Brandt,
1987, p. 32). In both the urban and rural models cereal
demand is responsive to price changes, but further differ
ences can be expected to arise once the profit effect is
brought to bear. Urban consumers are not expected to be as
widely influenced by a profit effect because they are
generally not producers of the good they themselves consume.

CHAPTER VI
PROFIT EFFECT, POLICY IMPLICATIONS AND FUTURE RESEARCH
This chapter combines the results from both the produc
tion and consumption sides of the agricultural household to
determine the importance of the profit effect on consumption
of cereals in rural Burkina. After presenting the results in
section one, the implications for policy in Burkina will be
explored in section two. Finally, this chapter and the
dissertation will close with some suggestions for avenues of
future research that have become evident while undertaking
the present effort.
The econometric results from both the production and
consumption sides, presented in the final sections of chap
ters IV and V, respectively, were encouraging. Although the
production and consumption side estimates are interesting,
the purpose of this study is to use these results to measure
the impact of the profit effect on consumption of the major
commodity; cereals. The conclusion that remains from the
previous chapters is that extreme departures from rational
behavior were not found in the behavior of rural Burkina
households. The results obtained for Burkina were also
similar to findings from other studies. This tends to
reinforce the view that rural households behave in an
93

94
economically rational fashion once the structure and con
straints of the rural setting in a particular country are
understood.
This study has reflected some of these constraints by
incorporating the changing composition of the household over
time in calculating labor availability and consumption. The
dynamic nature of African household composition (by age and
gender) requires regular monitoring. In this case household
changes were monitored monthly. It was equally important to
correctly identify the structure of the decision making unit
in the regions studied, as mentioned in the Introduction.
Correct specification of the "households" in the sample
provided the basic unit of analysis which did not necessari
ly correspond to nuclear groupings.
Given the diversity of agroclimatic and social systems
in Africa it is important to use the same (identical)
households on both the production and consumption sides in
estimating an agricultural household model. Other studies
have not always been able to do this (for example, Barnum
and Squire). The encouraging results from the econometric
estimations could possibly be attributed to this fact.
However, this approach has limitations because it restricted
the degrees of freedom in estimation. Only those households
with complete production and consumption data for the entire
year were retained for analysis.

95
Finally, this work has served to reiterate the impor
tance of clearly distinguishing what are properties result
ing from a particular functional form used to model phenom
ena and what are the properties resulting from the data.
This awareness tempered the results from the production side
of the model and influenced the choice of the flexible AIDS
model for the consumption side. One should always be aware
of which results reflect properties of the chosen specifica
tion versus those that arise from the empirical data. This
would seem to be especially important in estimating a system
such as an agricultural household model where theory does
not determine the direction or magnitude of the behavior
under investigation (in this case the profit effect).
Profit Effect
Within the theoretical construct of the agricultural
household model a change in an exogenous variable, such as
the output price of the agricultural commodity produced,
will have standard price and income effects on consumption
plus a reaction in production decisions. The change in
production decisions is captured through its influence on
profits and is referred to as the profit effect. Because
agricultural household models attempt to capture both the
consumption and production responses of the household to
exogenous changes, these models are likely to yield more

96
realistic results than an examination of each side of the
household economy individually.
Recall from Chapter III that the influence of produc
tion decisions on consumption behavior enter through the
full income constraint as profits. The full income con
straint (equation 3.10) can be rewritten as
Y = 7r(P,,w,A) + wT + E (6.1)
where it is profits and E adds the impact of exogenous income
to the model. Exogenous income includes rents, remittances,
gifts and other sources of income other than agricultural
profits. As will become clear in this section, the extent of
income diversification, as captured by E, in response to
highly variable agroclimatic conditions will have a signifi
cant impact on the profit effect.
The combination of the profit equation from the produc
tion side (equation 4.13), the demand equations from the
consumption side (equation 3.14) and the full income con
straint from above (equation 6.1) provides the complete
agricultural household model. Total differentiation of this
complete household system of equations yields total response
equations to exogenous changes. Written in elasticity form
these equations for a change in an exogenous variable X
(P,,Pm,w or a0) are given by
IdZ X\ sIdZ X\.(dZ Y\ldY ti\I dn X\
(6.2)

97
or more succinctly as
Vzx = {Vzx ) + {Vzy ) [Vy.) (v.x) (6*3)
where the left hand term is the total elasticity with the
profit effect and Z is the good consumed (Xa,Xm, or X,) The
first term on the right hand side of equation 6.3 is the
price elasticity of demand. The remaining three terms on the
right hand side are the expenditure elasticity of demand,
profit elasticity of expenditures and the exogenous variable
(price) elasticity of profits. Note that the profit elastic
ity of expenditures simplifies to tt/Y from equation 6.1.
Using the elasticities computed for the production
(Table 4.2) and consumption (Table 5.3) sides of the model
the total effect can be calculated. The principal interest
of this study is the impact of a change in the agricultural
output price on the consumption of cereals (Good 1) by the
household. These elasticities and the profit to full income
ratio (7r/Y) were evaluated at sample means with and without
the profit effect. The resulting agricultural output price
elasticities for the five goods with and without the profit
effect are presented in Table 6.1.
The overall impact of the profit effect is to decrease
the responsiveness of the household to price signals. Note
however, that contrary to the expectations from the majority
of other countries presented in Table 1.1, the Burkina price
elasticities of demand do not change from negative to posi-

98
tive. The exception is the labor/leisure choice where an
increase in output price does elicit an increase in labor
supplied, thereby decreasing leisure consumed.
TABLE 6.1
OUTPUT PRICE ELASTICITIES WITH AND WITHOUT THE PROFIT EFFECT
OUTPUT PRICE ELASTICITY OF DEMAND
FOR
GOOD
1
GOOD
2
GOOD
3
GOOD
4
GOOD
5
WITHOUT PROFIT EFFECT
-0.72
-0.49
-0.12
-0.23
CM
O

o
1
WITH PROFIT EFFECT
t"
in

o
-0.29
0.00
CO
o

o
1
0.06
Further inspection of Table 1.1 in the Introduction
indicates that not all countries experienced a sign change
in their price elasticities of demand after the profit
effect was introduced. Data from Japan, Thailand and Sierra
Leone indicate that price elasticities of demand remained
negative after including the effects of profits. The profit
effect did, however, mitigate the price responsiveness in
these three countries as was found in the Burkina data.
Two major reasons are suggested for the Burkina re
sults. First, the level of income diversity in this part of
the Sahel serves to reduce the overall impact of the profit
effect through the full income constraint. As households
diversify income sources away from agricultural production

99
the denominator of the n/Y term becomes larger, thereby
reducing the impact of the profit effect.
Several authors have found diversified income strate
gies in this part of sahelian Africa. Reardon, Matlon and
Delgado using data from the same time period and country as
this study reported that in northern Burkina less than 30%
of total income comes from agriculture (Reardon, Matlon and
Delgado, 1988). They argue that this is a rational response
to the highly variable agroclimatic conditions in this part
of the Sahel. Similar results were obtained from household
level surveys in neighboring Mali (Staatz, D'Agostino, and
Sundberg, 1990).
A second complementary explanation for the results
involves the point in time that the survey data were col
lected. The 1984 agricultural season was not a good year.
"Rainfall during the 1984 cropping season was about 40%
below long-term trends (Reardon, Matlon and Delgado,
1988, pg. 1066)." The number of net consumers after a bad
agricultural season is much larger than net sellers. The
result on the profit effect is to reduce the number of
households with significant contributions from agricultural
profits to total income, again serving to reduce the n/Y
ratio.
The sample mean for the n/Y term was 0.04 implying
that, on average, only 4 percent of total income came from
agricultural profits. In fact, the average exogenous income

100
for the sample was 2.5 times greater than average profits.
For the consumption elasticities in Table 6.1 to change
signs, 20 to 25% of total income would have to come from
agricultural production. This would not be an unusual value
to find in most agricultural settings (Reardon, Matlon and
Delgado, 1988 and Staatz, D'Agostino, and Sundberg, 1990),
but in the regions under investigation and in the period
investigated most households sampled did not obtain one
quarter of their full income, which includes valuing total
time available to the household, from agricultural profits.
The valuation of total time available to the household
can also have a significant impact on the n/Y term in the
profit effect equation. As stated earlier, the valuation of
labor is a difficult task in most any setting and this is
particularly true in the Sahel. To make direct comparison of
the present results to the other sahelian studies mentioned
above the valuation of household time must be removed. When
agricultural profits and exogenous income are evaluated for
the sample mean from the present data the total income is
roughly 36,000 French West African Francs (FCFA). This
compares favorably with the range reported by Reardon,
Matlon and Delgado (31-39,000 FCFA). The resulting share of
agricultural profits in total (non-labor evaluated) income
is then found to be around 26%, again very much in line with
the earlier results.

101
Finally, recall the discussion in Chapter IV on the
choice of functional form that implied increased responsive
ness using a direct production function specification,
particularly the Cobb-Douglas approach. Thus, the output
price elasticity of profit is expected to be higher than it
would be under other specifications. From the profit effect
equation (eq. 6.3) this would imply that the profit effect
observed could be somewhat overstated in this instance
which, if corrected, would further reduce the impact of the
profit effect in the current setting.
Policy Implications
The impact of including the production induced profit
effect in determining household consumption response is
clear from the results of the previous section. The absolute
value of all but one of the estimated output price elastici
ties of demand decreased in value. Thus, traditional ap
proaches to demand estimation would have overstated the
magnitude of household responsiveness to price changes. This
is important to keep in mind when interpreting consumption
elasticities from traditional demand approaches in economic
systems characterized by household-firms. The impact of
increasing prices on profits will serve to mitigate the
overall negative impact on demand.
The emergence of household income diversification
strategies in response to variable agricultural production

102
will continue to mitigate the negative impact of price
changes on the demand for cereals in certain areas. Perhaps
a policy cue can be taken from this pattern of household
behavior in supporting the emerging diversified income
generating possibilities as a means of promoting household
level food security. The impact of large seasonal and annual
price changes in cereals in the Sahel may be better ad
dressed through income programs rather than direct price
interventions. Similarly, increased market dependence would
imply that market based interventions may have greater
impact in rural Burkina than previously thought.
Greater diversification away from own-production will
continue the process of greater market dependence which
argues for increased market information and infrastructure
in these areas than has traditionally been the case. Exist
ing market information systems (MIS) and infrastructure in
the Sahel have focused more on those areas that are surplus
producers than on areas that are moving towards greater
dependence on the market. This is partly due to past deci
sions to locate most MIS in former grain marketing parasta-
tals whose previous mandates had been to exert monopoly
purchasing and resale of cereals. The exception to this is
in Chad whose grain parastatal was never able to establish
the institutional clout of neighboring sahelian states due
to the civil war.

103
Even taking into consideration the impact of the profit
effect, the overall responsiveness of rural Burkina house
holds is striking. Rural households can be expected to
respond in an economically intuitive fashion as long as
agricultural profits are less than one-fifth to one-quarter
of total income. The percentage of households in a particu
lar area that will draw greater than 25% of total income
from agriculture will be spatially specific in Burkina due
to the different agroclimatic zones. Thus, those households
living in particularly productive (agriculturally) areas can
be expected to exhibit a sign change on the demand for
cereals from negative to positive. In contrast, those areas
with diversified income strategies will continue to exhibit
the intuitive decrease in consumption with price increases.
It may then be possible to determine the sub-national
impacts of a change in pricing policy.
The highly elastic expenditure elasticities on non-food
and non-local produced (tobacco and beverages) goods demon
strate the significant rural demand for production of goods
from other sectors in the national and regional economy.
Rural households are clearly more integrated with the
national and regional economy (the cola nuts of Good 2 come
from Ghana and Cote d'Ivoire) than some have thought. Given
the greater level of market responsiveness, increased market
integration as a policy goal should be considered.

104
The only negative compensated cross-price elasticity of
demand may propose a unique opportunity for obtaining
additional food security relevant information for policy
makers. It is evident from Table 5.4 that the price of the
tobacco and beverages good moves in a complementary fashion
with cereals. Thus, an increasing price for cereals coupled
with a decreasing demand for tobacco and beverages could be
used as an early warning indicator of food insecurity for
particular regions. Those regions where the profit effect is
expected to predominate would be expected to exhibit the
same change in consumption patterns. The high expenditure
elasticity of demand for tobacco and beverages combined with
a larger proportion of total income form agricultural
profits would be expected to increase consumption of tobacco
and beverages. Monitoring of market demand for the commodi
ties in the tobacco and beverages good (principally, beer,
cigarettes, coffee, soda and cola) would provide additional
information from which to decide if households are making
significant changes in their consumption habits in response
to a price change.
Most striking is the degree of price and income respon
siveness in the rural sector implying that there are oppor
tunities for substitution between broad groups of commodi
ties. This result is important in development planning in
that it serves to reemphasize the importance of the price
variable even in "subsistence" economies. In fact, the

105
implied level of integration with the market that is re
vealed through the income and price elasticities from this
sample would bring into guestion the usefulness of the term
"subsistence" in accurately describing these households.
The distribution of net sellers and net purchasers of
cereals in Burkina and the Sahel can be expected to vary
across the country and over the years. This spatial and
temporal distribution of the net seller/purchaser ratio may
help in identifying those areas where residents would be
expected to gain from an increase in agricultural prices and
where people may migrate to avail themselves of not only a
more favorable agricultural production climate, but also
increased demand for labor. This increased labor demand is
the only sign change result in the sampled data introduced
through the profit effect.
Future Research
Suggestions for further inquiry into the nature of
rural household behavior in Burkina focus on three general
themes. First, the need for improved data collection ele
ments that include what data to collect and how it is
collected. Second, improvements in modeling the data once
collected. Finally, some suggestions on what could be done
to refine the present model or further examine the underly
ing data.

106
As mentioned above, individual estimations of either
production or consumption would have benefitted from addi
tional degrees of freedom. For example, this would have
provided the opportunity to examine subsets of households
within the sample. A larger sample size is usually prefera
ble, but cost limitations can restrict the number of house
holds surveyed. However, it is important to emphasize that
existing and regular data collection instruments exist in
most countries and could be slightly modified to meet the
needs of household modeling. The inclusion of both produc
tion and consumption data needs in collecting household
survey data should be stressed in this instance. Often the
existing surveys focus on either production or consumption
without realizing that with minimal additions both sides of
household level behavior could be captured.
This study would have gained additional explanatory
power if particular data elements on both sides of the
household model had been of stronger quality. From the
results of the production side of the model it is clear that
subsequent studies on household production and consumption
behavior should be as concerned about collecting information
on prices and quantities of inputs used in production as
budget surveys are on prices and quantities consumed by the
household. The absence of price and quantity data of agri
cultural inputs limited the specification of the production
side of the model and resulted in the use of a less flexible

107
specification. Particular attention should be addressed to
obtaining relevant and reflective information on the prices
and quantities of different types of labor (household,
market and work party) and land, as well as other inputs.
Other production side information that would have broadened
the analysis include soil qualities and agroclimatic varia
tion across households.
On the consumption side it would have been preferable
to stratify the sample households by some of the wealth
surrogates in order to more fully explore the issue of rural
stratification and possibly different behavior patterns of
households by wealth status. Greater detail on time alloca
tion across and within households would have made the
valuation of total time more accurate. The magnitudes and
degree of diversity of the various income sources other than
agriculture should always be explicitly addressed in the
sahelian context.
Turning to elements of modeling in this context, one of
the first areas of productive inquiry would be in attempting
to integrate a multicrop production function rather than the
single crop specification that was used. The multiple crops
common to rural households may also provide a source of
income to the household. This may be particularly true for
specific subgroups within the household, for example the
women in the household. It may also be productive to distin
guish between millet and sorghum production, but this would

108
most likely require detailed information on soil quality and
agroclimatic conditions. Millet prefers sandy soils and is
more tolerant to drought than sorghum. Short of collecting
new data, an index could be constructed to determine appro
priate weights for the aggregation of millet and sorghum
rather than the equal weights approach utilized here.
The specification used for the consumption side was a
linear approximate AIDS (LA/AIDS). The appropriateness of
this linear approximation could be tested by estimating the
non-linear AIDS and testing for statistical significance.
This would require using a non-linear estimation technique
which is not difficult given the present state of desktop
computing power. Such a test would determine whether the
Stone price index and approximation is sufficiently differ
ent from the true AIDS. Elasticities could be calculated and
compared for the LA/AIDS and true AIDS.
Green and Alston have reported preliminary comparisons
using the same data set that found no significant differenc
es in the elasticity estimates between the LA/AIDS and the
AIDS (Green and Alston, 1990). They emphasize that this
result holds as long as the correct elasticity computing
formulas are used for the respective models. In concluding,
these authors point out that their results may be "an
artifact of the particular data set we analyzed (Green and
Alston, 1990, p. 444)" and call for Monte Carlo studies for
testing whether LA/AIDS is close to true AIDS. The present

109
data could provide a second set to test for significantly
different elasticity estimates.
Further interesting refinements on the present approach
are possible. These include incorporating risk and wealth
effects, disaggregating price elasticities of demand, and
relaxing two major assumptions from the present model,
perfectly competitive markets (both input and output) and
profit maximization. Wealth effects as measured by on-farm
stocks and durable goods, disaggregated price elasticities
and modeling under relaxed assumptions could possibly be
supported by the same data from which the present study was
undertaken.
The incorporation of risk in economic models has been
particularly useful in agricultural economics because of the
inherent uncertainty in agriculture. These risks are very
apparent in the developing country context. In Burkina, and
throughout the Sahel, a highly variable rainfall climatology
is a major determining characteristic of agricultural
performance. As noted in the production chapter, the lack of
reliable household level information to reflect this vari
able was used to explain the relatively low explanatory
power of the estimated production function. Better under
standing of the riskiness of agricultural production systems
in the Sahel would help explain the variability in output.
Unfortunately, the Burkina household data from which the
present work derives does not have suitable household level

110
information to reflect the variable rainfall regimes across
households.
Production risk is difficult and costly to obtain at
the household level, but price risk could possibly be
incorporated given the temporal and spatial variability of
the price data. Production risk studies in sahelian agricul
ture would probably require a different scale of analysis,
perhaps at the sub-national, national or regional levels.
Recent authors have outlined the demands of incorporating
risk into the household framework (Finkelshtain and Chal-
fant, 1991).
Wealth rankings in the Sahel are often a function of
on-farm stocks and durable goods held by the household. On-
farm cereal storage is common in the Sahel when cereals are
available. Almost every household has multiple granaries for
storing grain on-farm. The value of these on-farm stocks
would increase as prices increase, resulting in increased
wealth for those households that can store grain. The
presence and/or absence of these goods in a particular
household will affect that household's wealth status and
hence consumption decisions in the recursive household
model. Renkow has recently provided a framework for incorpo
rating levels of on-farm stocks in an agricultural household
model (Renkow, 1990). The results from his empirical estima
tion did not result in significant changes in the calculated
elasticities, although this will not always be the case. His

Ill
framework for the treatment of stocks could be implemented
in the present model given additional time and effort to
work from the raw data and incorporate changes in the
present model.
The spatial variability of price and quantity data can
be used to determine price elasticities of demand and allow
disaggregation of the consumption side of the present model
from the same data set. This would provide insights into
price effects across specific commodities within the rural
Burkina consumption bundle. A rural consumer price index
could be created for monitoring household level impacts of
price changes on a regular basis. If found to be correlated
with certain locations or household characteristics this
information could be used for targeting interventions to
reach those households most in need. Deaton has outlined an
approach for determining disaggregated price elasticities of
demand from spatially varying data (Deaton, 1989).
Two major assumptions underlying the model presented in
this research are that households are profit maximizers and
that markets are perfectly competitive. Perhaps in the
present setting the latter is a more specious assumption
than the former. In both cases, modifications to the present
model could be undertaken to better reflect reality. Ellis
presents a very useful introduction and comparison of a
variety of household models with differing decision-making

112
rules that includes the basic agricultural household model
employed in the present research (Ellis, 1990).
If the labor market assumption is relaxed the recursiv-
ity of the model is lost and the system becomes simulta
neous. The Appendix to Chapter 2 in Singh, Squire and
Strauss presents the model without a functioning labor
market (Singh, Squire and Strauss, 1986). Low offers a model
in which wage rates are allowed to differ given quality
differences in labor (Low, 1986). This would be interesting
to explore in the Burkina case, if reasonably good labor
market data were available. For instance, Saul reports a
preference ordering for households that ranks family labor
above hired labor above work parties (Saul, 1983).
An often overlooked, but important component, of
household-firms is the nature of intrahousehold decision
making, particularly its impact on health and nutritional
status. Folbre presents an extensive review of this litera
ture, including neoclassical, Marxist, and feminist perspec
tives (Folbre, 1986). Ellis is another source for informa
tion on modeling the inner workings of the agricultural
household (Ellis, 1988). Intrahousehold studies require
extremely disaggregated and extensive consumption, produc
tion and distribution data from the household. This type of
information was not available from the Burkina household
surveys used to estimate the present agricultural household
model except on the consumption side.

APPENDIX
RECURSIVITY IN THE AGRICULTURAL HOUSEHOLD MODEL
A major characteristic of the agricultural household
model is the recursive nature of the decision making pro
cess. A natural extension of the first order conditions from
the optimization problem of the agricultural household model
leads to a clear understanding of the recursive nature of
the neoclassical theory of the agricultural household. In
this Appendix the analytics that lead to recursivity under
the assumption of competitive markets are presented in
detail.1
Begin with the optimization problem as:
MAX U = U(X.,Xm/X,) (A-l)
subject to
(i) P.X, + PmXm + wX, = wT + qcQc + PaQa qvV wL + E
(ii) G(Qc,QaiV,L,K) = 0,
a classical optimization problem subject to equality con
straints.2 Household utility is assumed to be a function of
the consumption of three commodities; an agricultural good,
1. This section owes substantially to the Chapter 2
Appendix by Strauss (Singh, Squire and Strauss, 1986).
2 The nonlinearity and inequalities of the previous
presentation have been excluded to aid in the presentation.
113

114
Xa, a market good, Xm, and leisure, X,. For this discussion
assume that the household crop production vector consists of
two crops; a cash crop, Qc, and a food crop, Qa.
The first constraint, the full income constraint,
equates expenditures and income. Expenditures consist of the
value of agricultural goods, PaXa, the value of market goods,
PmXm, and the value of leisure time consumed, wX,. Income is
composed of the value of the household's time, wT, the value
of a cash crop, qcQc, the value of a food crop, PaQa, minus
the values of variable inputs and labor, qvV and wL, respec
tively, plus exogenous income, E. Examples of exogenous
income sources include remittances, rents and non-farm
income.
The second constraint introduces the limitations on
behavior due to the household production process. An implic
it production function is employed to describe the relation
ship between variable nonlabor inputs, V, total labor input,
L, fixed inputs, K, and output, Q.
The Lagrangian function can now be constructed as:
$ = U (Xa, Xm, X,) (A-2)
+ /x[wT + qcQc + PaQa qvV wL + E]
- /i[PaXa + PmXm + wX,]
+ 6[G(Qc,Qa,V,L,K) ]
from which the first order conditions may be derived. In
this problem the household has seven choice variables
(X,,Xm,X,,Qc,Qa,V,L) and two Lagrangian multipliers (/x and 0)
for a total of nine first order conditions. Three of the

115
first order conditions involve decision rules for the
quantities of goods consumed (X,,Xm/X,), two involve decision
rules for the quantities of goods produced (Qc,Qa) two
involve the quantities of inputs employed in the production
process (V,L), and the final two involve the Lagrangian
multipliers.
The three consumption based first order conditions are
given by:
(1) a$/dX. = dU/dX. MPa = 0 (A-3)
(2) di/dxm = du/dxm MPm = o
(3) d$/dX, = dU/dX, juw = 0
and the corresponding consumption Lagrangian multiplier
condition is:
(4)d/d/x = WT + qcQc + PaQa qvV wL + E PaXa PmXm wX,
= w(T L X,) + Pa(Qa X.) + qcQc + E qvV PmXm
= 0.
The first order conditions for the two output decisions
are given as:
(5) di/dQc = /xqc + (dG/dQc) = 0
or: (1/M) (3$/3Qc) = qc + (6/M) (dG/dQc)
and (6) d*/dQ, = /iP, + 6(dG/dQa) = 0
or: (1/m) (3*/3Q.) = Pa + (0/m) (3G/3Q.)
The first order conditions for the two input decisions
are given as:
(7) di/dV = -Mqv + e(3G/3V) = 0
or:
(1/M) (3*/9V) = -qv + (6/M) (dG/dV)

116
(8) d*/dL = juw + OG/dL) = 0
or: (1/m) (di/dh) = -w + (0/jLt) (dG/dL) .
Note that there is no analogous first order condition
for the capital input variable (K) because it is assumed
fixed to the decision maker, although it is not considered
immutable. The final condition involves the production
Lagrangian multiplier as:
(9) d*/dn = G (Qc, Qa, V, L, K) = 0.
The first order conditions represented by the nine
equations in A-3 can be totally differentiated to yield:3
(1) Uh(dX.) + Uta(dXm) + Uu(dX,) M(dw) w(dM) = 0 (A-4)
(2) U^dX.) + lUidXJ + Uml(dX,) MdPJ Pm(d/i) = 0
(3) U(dX.) + U^dXJ + Ujj(dX,) M(dPa) P,(d/i) = 0
(4) -P,(dX.) Pm(dXJ w(dX,) = w(dL) (T-L-X,) (dP.) -
P.(dQ.) (Q.-X.)(dP.) qc(dQc) Qc(dqc) dE + qv(dV) +
V (dqv) + Xm(dPm) = f
(5) 0//i[Gcc(dQc) + Gca(dQJ + GcL (dL) + Gcv(dV) + Gcd(0//x)]
= -dqc
(6) 0//i[Glc(dQc) + G(dQa) + GaL (dL) + Gav(dV) + G.d(0//i)]
= -dP.
(7) 0/M[Glc(dQc) + Gu(dQa) + Gll(dL) + GLv(dV) + GLd(0//i)]
= dw
(8) 0 / M [ Gvc (dQc) + Gva(dQa) + GvL (dL) + Gvv(dV) + Gvd(0//i)]
= dqv
3 Where Uu = d2U/dX,dXa U,,,, = d2U/dX,dXm, U = d2U/ax,dX,, etc.

117
(9) Gc(dQc) + G.(dQ.) + GL (dL) + Gv(dV) = 0
matrix as:
Uu
Uun
Uu,
-w
Uml
Urn,
-Pm
U*
Uan
Uaa
~Pa
-w
~Pm
Pa
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0 0
0 0
0 0
0 0
Lg G
H cc H ca H cL
G G G,
H M fji
-Gl
H
to
0
0
0
0
la.
la.
M
La
la
LL
II VC ^ 9v
G
M
0 0
0 0
0 0
0 0
G G
H f
O.
^ S
fed to
form a
9x9
dX,
~ Hdw~
dXa
PdPa
d/i
*
Qc
=
-dqc
dQc
-Pa
Qc
dpL
dQc
£?(-)
dg.
0
M
L. 1
which is clearly block recursive.
Note that each submatrix block above is itself a
bordered Hessian matrix. The upper left block contains the
information for the utility maximization problem while the
lower right matrix contains the necessary information to
solve the profit maximization problem. Because full income
is determined in the production block the consumption block
is dependent upon the result of the production block for its
own solution. The system is block recursive in that the
consumption decisions are partially determined by the
outcome of the production decisions. However, the consump
tion decisions have no impact on the production decisions.

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Becker, Gary S. "A Theory of the Allocation of Time." The
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BIOGRAPHICAL SKETCH
Although born outside of Atlanta in 1956, Charles Alan
May moved to Florida in time to experience Hurricane Donna.
He obtained all of his primary and secondary school educa
tion in Orlando, graduating from Edgewater High School in
1973. In 1977, he graduated from Colorado College in Colora
do Springs, Colorado, with a bachelor's in chemistry and a
Russian minor. After working for a year as an environmental
chemist, he served two years as a Peace Corps volunteer in
Ghana, West Africa, as a secondary school and junior college
teacher. Upon returning to the U.S., he enrolled in a mas
ter's program at the University of Michigan in the School of
Natural Resources.
Through the University of Michigan's Center for Re
search on Economic Development and the University of Wiscon
sin's International Agricultural Programs, Charles joined a
team of researchers examining cereals markets in Burkina
Faso, West Africa. He completed his master's degree in
resource policy, economics and management at the University
of Michigan, in 1987.
After two years of field and stateside work (Burkina
and Madison) Charles enrolled in the Food and Resource
Economics Department (FRED) at the University of Florida
122

123
(UF) in 1985. While a Ph.D. student in FRED he began con
sulting work for Tulane University's Center for Interna
tional Health and Development. In 1988, Charles took a leave
of absence from UF as a fellow at the Institute of Interna
tional Economics in Kiel, Germany. This year-long program,
with participants from several countries, was an intensive
program in international macroeconomics, trade, development
and finance.
Upon returning to the U.S. in 1989, Charles was em
ployed by Tulane University as the staff economist on the
Famine Early Warning System (FEWS) Project outside of
Washington, D.C. Charles is presently employed with this
project and returned to UF to complete his Ph.D. disserta
tion in the fall of 1991.

I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality, as
a dissertation for the degree of Doctor of Philosophy.
Urna Lele, Chair
Graduate Research Professor of
Food and Resource Economics
I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequater'^ln scope and quality, as
a dissertation for the degre^of Dpqtor of IJh-ilosophy.
\
Robert D. Emerson
Professor of Food and Resource
Economics
I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality, as
a dissertation for the degree qf-^Doctor of Philosophy.
Chris^Gsr^ftndrew
Professor of Food and Resource
Economics
I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality, as
a dissertation for the degree of Doctor of Philosophy.
R. Hunt Davis, Jr.
Professor of History

This dissertation was submitted to the Graduate Faculty
of the College of Agriculture and to the Graduate School and
was accepted as partial fulfillment of the reguirements for
the degree of Doctor of Philosophy.
May 1992
X.
Dean,
ege of Agriculture
Dean, Graduate School




92
that the uncompensated own price elasticity for cereals was
-0.72, while the expenditure elasticity was 1.35. The
implication is that rural households are less responsive to
price changes and more responsive to income changes than
urban households.
However, the comparisons between these two studies re
quires a significant caveat. The urban data, while estimated
under an LA/AIDS model, used the non-linear AIDS elasticity
computing formulas for deriving parameter estimates and
subsequent elasticities. The Green and Alston result report
ed above implied that the resulting elasticity estimates
would be incorrect.
Fortunately, Savadogo and Brandt also ran their data
under an LES and reported the results. Using LES the income
elasticity of demand for domestic cereals for the lower 25th
wealth percentile was 1.29. This value compares favorably
with the 1.35 value found for rural Burkina. The very
different price elasticities can be explained by the choice
of elasticity estimating formula and the lack of sufficient
price variation in the urban data (Savadogo and Brandt,
1987, p. 32). In both the urban and rural models cereal
demand is responsive to price changes, but further differ
ences can be expected to arise once the profit effect is
brought to bear. Urban consumers are not expected to be as
widely influenced by a profit effect because they are
generally not producers of the good they themselves consume.


7
Layout of the Study
This first chapter begins with an introduction to the
reason for studying agricultural household behavior and
briefly describes the major characteristics of agricultural
household models that integrate both production and consump
tion sides of household behavior. The clientele for this
research are identified followed by background information
on Burkina's physical and socioeconomic setting that influ
enced data collection and interpretation. Finally, the data
used to drive the model are described, although more de
tailed descriptions are available elsewhere.
A literature review reveals that agricultural household
models have an extensive and international history with
contributions from a variety of scholars and countries. The
review points out that models have become increasingly more
reflective of reality and that agricultural household models
have been infrequently estimated due to the need for exten
sive data to support their estimation. The majority of
models have been estimated from data on Southeast Asian
countries. However, in spite of the extensive data demands
of these models, their usefulness is in summarizing broad
behavioral data within a consistent framework and increasing
reflection of actual conditions in developing country
agricultural household-firms. The literature review is
presented in Chapter II.


71
estimates are expected to imply greater responsiveness than
those based upon indirect or price based estimates.
TABLE 4.2
PRODUCTION SIDE ELASTICITY ESTIMATES
VARIABLES
ELASTICITIES
OUTPUT
(Q)
LABOR
DEMAND (L)
PROFIT
(7T)
OUTPUT PRICE (PJ
1.56
2.56
2.56
(elasticity equation)
(a2/a,)
(1/a,)
d/a,)
WAGE RATE (w)
-1.56
-2.56
-1.56
(elasticity equation)
(-a2/a,)
(-a2-a,/a,)
(-a2/a,)
TECHNOLOGY PARAMETER
2.56
2.56
2.56
(<*6)
(elasticity equation)
(1/0!,)
(1/a,)
d/a,)
The high responsiveness of demand for labor to changes
in the wage rate is also clear from Table 4.2. The value of
-2.56 compares to -2.57 found by Haughton using Malaysian
data and a Cobb-Douglas production function. Similarly,
Barnum and Squire, using data from a more well-to-do area of
Malaysia and a Cobb-Douglas production function approach,
found -1.47. Assuming increasing population growth the high
price responsiveness of household demand for labor can be
expected to limit unemployment in the agricultural sector.
In addition to increasing output, an increase in output
price will also induce greater demand for labor and higher
profits. Wage rate elasticities have the expected negative


41
meeting consumption needs and millet being a more profitable
crop. Own price elasticities of demand were negative, as
would normally be expected except for the combined millet
and sorghum good. The positive own-price elasticity was
attributed to the profit effect because a higher price would
result in higher incomes, particularly among households
participating in the FFW program.


83
In general, Ray's results found that the rural data were
more likely to reject the demand restrictions than the urban
data. This result was also dependent on whether or not
household size effects were included in the model. The
important point for this study is the choice between the
unrestricted or restricted estimates in determining the
demand elasticities. The decision is between statistically
rejected restrictions from theory versus the results ob
tained from the theoretical structure employed.
Both unrestricted and restricted parameter estimates
were used in deriving the consumption elasticities with no
exceptional difference in elasticity values, particularly
the expenditure elasticities. Therefore, restricted esti
mates were retained for the elasticity computations of the
next section. It is not uncommon to impose theoretical re
strictions in AIDS models without reporting significance
tests (Bezuneh, Deaton and Norton, 1988).
The cross-price parameter estimates provided in Table
5.2 were not as impressive as those presented in Table 5.1.
A total of 25 cross price parameters were estimated, or
estimated and derived in the case of restrictions. The
number of statistically significant cross price parameter
estimates, at the 95% level, numbered 8 and 12 in the
unrestricted and restricted models, respectively.


98
tive. The exception is the labor/leisure choice where an
increase in output price does elicit an increase in labor
supplied, thereby decreasing leisure consumed.
TABLE 6.1
OUTPUT PRICE ELASTICITIES WITH AND WITHOUT THE PROFIT EFFECT
OUTPUT PRICE ELASTICITY OF DEMAND
FOR
GOOD
1
GOOD
2
GOOD
3
GOOD
4
GOOD
5
WITHOUT PROFIT EFFECT
-0.72
-0.49
-0.12
-0.23
CM
O

o
1
WITH PROFIT EFFECT
t"
in

o
-0.29
0.00
CO
o

o
1
0.06
Further inspection of Table 1.1 in the Introduction
indicates that not all countries experienced a sign change
in their price elasticities of demand after the profit
effect was introduced. Data from Japan, Thailand and Sierra
Leone indicate that price elasticities of demand remained
negative after including the effects of profits. The profit
effect did, however, mitigate the price responsiveness in
these three countries as was found in the Burkina data.
Two major reasons are suggested for the Burkina re
sults. First, the level of income diversity in this part of
the Sahel serves to reduce the overall impact of the profit
effect through the full income constraint. As households
diversify income sources away from agricultural production


15
TABLE 1.2
SUMMARY OF QUESTIONNAIRES
NAME
MAIN PURPOSE
FREQUENCY
VILLAGE
CENSUS
establish village demographics
for sample selection
ONCE
HOUSEHOLD
CENSUS
sample household demographics
ONCE
FIELD
MEASURES
area cultivated to each crop
or crop mix
QUARTERLY
ON-FARM
STORAGE
quantity of foodstuffs stored
over time
YEARLY
HARVEST
harvest quantity
BIWEEKLY
CONSUMPTION
quantity and source of food
stuffs consumed
BIWEEKLY
SALES
quantity, value, good, reason
and location of sale
BIWEEKLY
PURCHASES
quantity, value, good, reason
and location of purchase
BIWEEKLY
AMOUNTS
GIVEN
services, salaries, credit,
gifts, and remittances given
BIWEEKLY
AMOUNTS
RECEIVED
services, salaries, credit,
gifts, and remittances re
ceived
BIWEEKLY
CHANGE IN
HOUSEHOLD
COMPOSI
TION
monitor household composition
changes over time
MONTHLY
DURABLE
GOODS
wealth and asset measures
ONCE
MEASURING
UNITS
convert local measures to ki
lograms
ONCE
ANIMAL
CENSUS
type,number and owner of live
stock
QUARTERLY


99
the denominator of the n/Y term becomes larger, thereby
reducing the impact of the profit effect.
Several authors have found diversified income strate
gies in this part of sahelian Africa. Reardon, Matlon and
Delgado using data from the same time period and country as
this study reported that in northern Burkina less than 30%
of total income comes from agriculture (Reardon, Matlon and
Delgado, 1988). They argue that this is a rational response
to the highly variable agroclimatic conditions in this part
of the Sahel. Similar results were obtained from household
level surveys in neighboring Mali (Staatz, D'Agostino, and
Sundberg, 1990).
A second complementary explanation for the results
involves the point in time that the survey data were col
lected. The 1984 agricultural season was not a good year.
"Rainfall during the 1984 cropping season was about 40%
below long-term trends (Reardon, Matlon and Delgado,
1988, pg. 1066)." The number of net consumers after a bad
agricultural season is much larger than net sellers. The
result on the profit effect is to reduce the number of
households with significant contributions from agricultural
profits to total income, again serving to reduce the n/Y
ratio.
The sample mean for the n/Y term was 0.04 implying
that, on average, only 4 percent of total income came from
agricultural profits. In fact, the average exogenous income


22
agricultural households.3 The Japanese audience was familiar
with the writings of Chayanov at an earlier date than the
anglophone audience. Nakajima's work, which itself only
became available to a wide anglophone audience in 1969
(Wharton, 1969) allowed for a continuum of households, from
those consuming all of their own production and providing
all of their labor input (subsistence farms) to those
consuming none of their production and purchasing all their
labor (commercial farms).
Nakajima's classification of the world's diverse
agricultural production systems along a continuum can be
viewed as having two dimensions, consisting of the level of
own production consumed by the household and the level of
own labor provided by the household. At one extreme was the
purely subsistence household consuming all of its own
production and providing all of its own labor input. At the
other extreme of his continuum was the purely commercial
farm which sold all its output and purchased all of its
labor input. Nakajima commented that the later extreme was
"rarely found" and the former was a "very small percentage"
of world farms (Wharton, 1969, p. 165). He clearly recog
nized that the bulk of the world's farms fell somewhere
between these two extremes.
3 "Subjective" because each household can have its own
utility function which is maximized subject to an income
constraint.


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TABLE OF CONTENTS
page
DEDICATION ii
ACKNOWLEDGEMENTS iii
ABSTRACT vi
INTRODUCTION 1
Problem Statement 2
Objectives of the Study 4
Agricultural Household Models 4
Layout of the Study 7
Clientele for the Research 9
Background on Burkina 10
Data 13
LITERATURE REVIEW 17
Chayanov 18
Nakajima 21
Lau, Yotopoulos, and Others 24
Production in Taiwan 25
Consumption in Taiwan 26
Production in Thailand 28
Consumption in Thailand 29
Barnum and Squire 31
Singh, Squire and Strauss 34
Haughton 37
Bezuneh, Deaton and Norton 39
THEORY OF THE AGRICULTURAL HOUSEHOLD 42
Introduction 42
The General Theory of an Agricultural Household 43
The Utility Function 44
The Income Constraint 45
The Time Constraint 47
The Technology Constraint 48
Combining Constraints to Yield the Full In
come Constraint 48
iv


87
the LA/AIDS, where expenditure shares are assumed invariant
to changes in income. Assuming that the expenditure shares
are invariant to income level is equivalent to assuming
homothetic preferences (j3~0 for all i) in which case the
elasticity computing formulas are the same for both the AIDS
and the LA/AIDS. However, if preferences are not assumed to
be homothetic then the choice of computing formula is impor
tant.
In a follow-up article Green and Alston presented the
correct LA/AIDS computing formulas for the uncompensated,
compensated and expenditure elasticities (Green and Alston,
1991). The demand elasticity computing formulas for the
LA/AIDS result in a system of simultaneous equations solved
by matrix algebra. This was the approach used in computing
the uncompensated and income compensated elasticities
presented.
The uncompensated and income compensated elasticities
are presented in Tables 5.3 and 5.4, respectively. The
elasticity directions and values are reasonable for both
prices and incomes. All own price elasticities are negative,
as would be expected from rational consumers. Rural Burkina
households adhere to the law of demand just as any other
household. Own price elasticities are somewhat inelastic
which could be due to the overall low level of consumption
in the rural Sahel.


6
decisions in consumption. In a recursive system the causal
ity is one way and not interactive.
There is a notable difference in price elasticities
derived from cross-sectional models that acknowledge the
"profit effect" and those that do not. Table 1.1 presents
household-based price elasticities from various studies in
the literature with and without incorporation of the "profit
effect." Note that in several instances the response elas
ticities changed not only magnitudes but also direction.
TABLE 1.1
AGRICULTURAL PRICE ELASTICITIES
WITH AND WITHOUT THE PROFIT EFFECT
RESPONSE ELASTICITIES WITHOUT (A)
AND
WITH (B) THE PROFIT EFFECT
COUNTRY
AGRICU
commod:
LTURAL
CTY
NON-AGR
COMM
ICULTURAL
ODITY
LABOR
SUPPLY
A
B
A
B
A
B
Taiwan
-0.72
0.22
0.13
1.18
0.21
-1.59
Malaysia
-0.04
0.38
-0.27
1.94
0.08
-0.57
Korea
-0.18
0.01
-0.19
0.81
0.03
-0.13
Japan
-0.87
-0.35
0.08
0.61
0.16
-1.00
Thailand
-0.82
-0.37
0.06
0.51
0.18
-0.62
Sierra
Leone
-0.74
-0.66
-0.03
0.14
0.01
-0.09
Nigeria
-0.05
0.19
-0.14
0.57
0.03
-0.06
Adapted from Singh, Squire and Strauss, Agricultural House
hold Models. (1986) Table 1-2, pg. 26.


23
In order to capture the diversity of farm production
possibilities, Nakajima proposed four models of household
behavior. Two models examined the behavior of the pure
commercial family farm while two captured the behavior of
the semisubsistence or semicommercial family farm. The
purely commercial farm models were distinguished by the
presence or absence of a competitive labor market. For the
pure commercial family farm with a competitive labor market
Nakajima noted that this "family farm may be regarded as an
economic unit which behaves, in the first phase, as a 'firm7
maximizing profit and, in the second phase, as a laborer's
household with nonlabor income maximizing utility (Wharton,
1969, p. 180)." This is the first mention in the literature
of what has come to be known as the recursive nature of the
agricultural household decision-making process.
In deriving the comparative statics for the purely
commercial farm models, Nakajima introduced inputs other
than fixed land and variable labor. Nakajima examines the
impact of fertilizer as another factor of production whose
price is determined in a competitive market. He also allows
for the addition of multiple outputs in his purely commer
cial family farm models.
Turning to the two semisubsistence (or semicommercial)
models, Nakajima assumed that these households did not have
access to a labor market, but were distinguished by having
single or multiple output crops. In these models the house-


105
implied level of integration with the market that is re
vealed through the income and price elasticities from this
sample would bring into guestion the usefulness of the term
"subsistence" in accurately describing these households.
The distribution of net sellers and net purchasers of
cereals in Burkina and the Sahel can be expected to vary
across the country and over the years. This spatial and
temporal distribution of the net seller/purchaser ratio may
help in identifying those areas where residents would be
expected to gain from an increase in agricultural prices and
where people may migrate to avail themselves of not only a
more favorable agricultural production climate, but also
increased demand for labor. This increased labor demand is
the only sign change result in the sampled data introduced
through the profit effect.
Future Research
Suggestions for further inquiry into the nature of
rural household behavior in Burkina focus on three general
themes. First, the need for improved data collection ele
ments that include what data to collect and how it is
collected. Second, improvements in modeling the data once
collected. Finally, some suggestions on what could be done
to refine the present model or further examine the underly
ing data.


2
consumption aspects of household behavior in developing
countries. The resultant agricultural household model is
tested on cross-sectional household data from Burkina Faso,
West Africa. Drawing on a wealth of production, demographic
and expenditure data from the early 1980s in four villages
within Burkina, an integrated, consistent, conceptual model
is estimated to provide insights into the behavior of
agricultural household-firms.
Because these household-firms consume part of their own
production they may behave differently in response to price
changes. Specifically, an increase in the price of the
output they produce may increase their net profits, thereby
inducing an increase in income that would counterbalance or
outweigh the traditional negative impact on their consump
tion of that output due to the increase in its price.
Ecfihlea Statement
Basic information about household behavior is essential
for the formulation of appropriate policy in the agricul
tural sector of any country, whether the goal of that policy
is household welfare or increased production. Price and
income elasticities are needed in order to capture and
describe the behavioral responses of household producers and
consumers to policy shifts. In particular, tax and subsidy
policies will be dependent on an accurate determination of
supply and demand responses of households. Microlevel


19
neoclassical theory of the firm.2 As mentioned in the intro
duction, in a household that produces what it consumes the
income effect can cause the nature of household responsive
ness to be indeterminate from theory.
The writings of Chayanov only became available to an
English-speaking audience in 1966, but were known to schol
ars in other parts of the world through earlier translations
in German and Japanese. Nakajima cites his exposure to
Tschajanow's (sic) writings as an early influence on his
subsequent writings about the agricultural household (Whar
ton, 1969, p. 165). The introduction to Shanin's reissue of
Chayanov's writings states that "the impact of the implicit
cross-influences cannot be ascertained, but the views of
Chayanov and his friends spread fairly broadly through
Europe and Asia via the German professional literature of
the 1920s (Chayanov, 1986, p. 11)."
Chayanov focused his analysis on those households which
used little or no labor, other than that provided by the
household itself. He formally defined a "family farm" as an
economic unit that normally employed no wage labor in its
production process. Because the Chayanovian "family farm"
used family labor almost exclusively, wage rates could not
be determined and hence profits were indeterminate.
2 However, it can be explained through a constrained
optimization model in the neoclassical mode as will be
presented in this research.


12
Cereals are extremely important in the social and
economic setting of Burkina. Consisting mostly of millet and
sorghum, with some maize, wheat and rice, cereals compose
from seventy to eighty percent of calories and sixty to
seventy percent of proteins in the Burkina diet (Haggblade,
1984, p. 10). With just over nine million people, and a
population growth rate of roughly three percent per year,
Burkina has approximately thirty-two inhabitants per sguare
kilometer. Gains in gross agricultural production in the
1980s have been achieved mostly by increasing the area under
cultivation. Advanced agricultural technology and input use
are limited with most farming households using land, labor,
seed, rainfall and simple agricultural tools to produce a
crop.
As mentioned earlier, the success of agricultural
production is dependent upon the rainfall pattern. In order
to diffuse agricultural production risk households have
developed income diversification strategies. These strate
gies include diversification via trade, services, migration
and mining, among other possibilities. Using Burkina data
from approximately the same period as the present study,
Reardon, Matlon and Delgado (1988) found households in the
northernmost sections of Burkina which obtained only thirty
percent of total household income from agriculture. House
holds in their sample were from villages slightly farther
north than those used in the present study. However, similar


115
first order conditions involve decision rules for the
quantities of goods consumed (X,,Xm/X,), two involve decision
rules for the quantities of goods produced (Qc,Qa) two
involve the quantities of inputs employed in the production
process (V,L), and the final two involve the Lagrangian
multipliers.
The three consumption based first order conditions are
given by:
(1) a$/dX. = dU/dX. MPa = 0 (A-3)
(2) di/dxm = du/dxm MPm = o
(3) d$/dX, = dU/dX, juw = 0
and the corresponding consumption Lagrangian multiplier
condition is:
(4)d/d/x = WT + qcQc + PaQa qvV wL + E PaXa PmXm wX,
= w(T L X,) + Pa(Qa X.) + qcQc + E qvV PmXm
= 0.
The first order conditions for the two output decisions
are given as:
(5) di/dQc = /xqc + (dG/dQc) = 0
or: (1/M) (3$/3Qc) = qc + (6/M) (dG/dQc)
and (6) d*/dQ, = /iP, + 6(dG/dQa) = 0
or: (1/m) (3*/3Q.) = Pa + (0/m) (3G/3Q.)
The first order conditions for the two input decisions
are given as:
(7) di/dV = -Mqv + e(3G/3V) = 0
or:
(1/M) (3*/9V) = -qv + (6/M) (dG/dV)


14
eighteen years of age. A list of all the questionnaires used
in the study is provided in Table 1.2.
The biweekly transactions data consisted of information
on sales, purchases, consumption, amounts given (wages,
gifts, taxes, etc.) and amounts received (salaries, remit
tances, gifts, etc.) by the household over the previous two
weeks. Data on changes in household composition were col
lected on a monthly basis. Data collected on a quarterly
basis included the livestock census and on-farm cereal
storage. These two categories are important proxies for
wealth in the sahelian agricultural household.
A one-time survey was also conducted to catalogue
household durable goods as companion information on wealth
stratification within the villages. Three additional ques
tionnaires were administered on a one-time basis. First was
the initial household census which, in addition to normal
demographic variables, covered education, dependency status,
and other sources of income. Second, a questionnaire was
used to measure the physical area of household members'
fields by crop. Third, the harvest was measured during the
appropriate part of the agricultural year.
"Households" in Africa are not necessarily nuclear and
in Burkina many household production and consumption units
can be found within one family compound. In order to distin
guish household units within the sample the census question-


30
tional form for the indirect utility function, household
commodity expenditure equations for agricultural commodi
ties, non-agricultural commodities and leisure were derived
using Roy's Identity. These three aggregated commodities
were deemed important for the analysis of the supply of
marketed surplus, the demand for non-agricultural commod
ities in the agricultural sector, and the income-leisure
choice and supply of labor, respectively.
As in the Taiwanese consumption study, homogeneity was
assumed, with its subsequent implications, and the estima
tion technique was Zellner's seemingly unrelated regression
analysis. Output supply was taken directly from the earlier
study on Thai production which used a normalized restricted
profit function. Like the earlier Taiwan study, the Thailand
consumption study is different from the traditional Engel
curve analysis because of the introduction of family compo
sition information as an independent variable in the utility
function. However, in contrast to the earlier Taiwanese
study, utility maximization by Thai agricultural households
was rejected.
Implicit in each of the consumption analyses performed
by Lau, Yotopoulos, et al., in both Taiwan and Thailand, is
the separability of the production and consumption decisions
of the household. The production analyses, in both cases,
can stand on their own without further caveats. However, the
consumption analysis, with household income partially


59
set. The third consideration was the ease of estimation,
given that the consumption side of the model would take
considerable time for data preparation, estimation and
refinement a more straight forward production side estima
tion was preferred. Statistical testing of the appropriate
ness of the Cobb-Douglas approach in this case was also
undertaken. In comparisons against other specifications,
notably the translog and constant elasticity of substitution
(CES), the Cobb-Douglas specification was not rejected.
A Cobb-Douglas production function consistent with the
production constraint (Eq. 3.5) takes the specific form
Q = aQAa'Lai (4.1)
where Q is total output, A is the area under cultivation
(assumed fixed in the short-term) and L is the labor uti
lized in producing output. The expansion of this form to
include variable inputs and capital is straight forward. The
a0 variable is a technological efficiency parameter that
indicates the present state of technology. This can be seen
from equation 4.1 by noting that for given values of the
other production inputs (A and L), the value of a0 will have
a proportional effect on the size of output (Q).
For estimation purposes equation 4.1 is linearly
transformed by taking natural logarithms to yield
InQ = lna0 + a,lnA + a2lnL
(4.2)


10
limited to, the Ministry of Agriculture. Other interested
parties may include bilateral or multilateral aid agencies
and other African Governments. Other donor agencies and
researchers could also be interested in information on
agricultural household behavior in Burkina.
Background on Burkina
This section provides background information on Burkina
that is particularly relevant to the interpretation of the
results form the study. Two areas of information are identi
fied that influenced the data collected and its analysis. An
understanding of the conditions prevailing in Burkina in the
physical and socioeconomic realms are important to a full
appreciation of the research results and their limitations.
The most important physical factor influencing agricul
tural production in Burkina is the high variability of
rainfall. This variability occurs across both space and
time. Spatially, the south and southwest of the country are
favored by more regular rainfall. Temporally the country has
experienced periods of drought, with the most recent
episodes during the agricultural seasons of 1983-84 and
1987-88. From a longer-term agroclimatological perspective
the 1970s and 1980s were drier than the 1950s and 1960s.
Most agricultural production in Burkina is rain-fed and
subject to the vagaries of these sahelian weather patterns.
These patterns are characterized by highly localized and


46
strictions on the household's actions. The first constraint
can be written such that the household expenditures are less
than or equal to the income available to the household, or
P.X, + + w(L-F) < P.Q. (3.3)
The inequality holds due to possible zero level expenditures
or savings by the household. Household consumption consists
of expenditures on agricultural goods, P.X,; market goods,
PmXm and expenditure on hired agricultural labor, w(L-F).
The quantity of agricultural labor hired by the house
hold is the difference between total labor input on the farm
(L) and the total quantity of labor, on and off-farm,
supplied by the household (F). Here, wage rates are assumed
equivalent between on-farm and off-farm labor implying that
the household is indifferent between these two types of
labor. The household income is derived from agricultural
goods whose quantity, Q, represents gross production.
Subsequently, the value of agricultural goods sold by the
household, P,Q, represents agriculturally based income.
It is interesting and instructive to note that the term
w(L-F) may appear on either side of the income constraint.
In other words, it may be construed as either an expenditure
or an income term. This is due to the expression (L-F) which
can be either positive or negative. If total labor input, L,
is greater than that supplied by the family, F, then the
expression is positive and the farm household employs labor
from off-farm to make up the difference. In this case the


119
Deaton, Angus and John Muellbauer. "An Almost Ideal Demand
System." American Economic Review. 70(1980a): 312-36.
. Economics and Consumer
Behavior^ Cambridge: Cambridge University Press, 1980b.
Ellis, Frank. Peasant Economics: Farm Households and Agrar
ian Development. Cambridge: Cambridge University Press,
1988.
Finkelshtain, Israel and James A. Chalfant. "Marketed Sur
plus Under Risk: Do Peasants Agree with Sandmo?" Ameri
can Journal of Agricultural Economics. 73(1991): 557-
567.
Folbre, Nancy. "Cleaning House: New Perspectives on House
holds and Economic Development." Journal of Development
Economics. 22(1986): 5-40.
Green, Richard and Julian M. Alston. "Elasticities in AIDS
Models." American Journal of Agricultural Economics.
72(1990):442-445.
. "Elasticities in AIDS
Models: A Clarification and Extension." American Jour
nal of Agricultural Economics. 73(1991):874-875.
Greene, William H. Econometric Analysis. New York: Macmil
lan, 1990.
Haggblade, Steve. An Overview of Food Security in Upper
Volta: A Report Prepared for USAID/Upper Volta. Oua
gadougou: USAID, 1984.
Haughton, Jonathan. "Farm Price Responsiveness and the
Choice of Functional Form: An Application to Rice
Cultivation in West Malaysia." Journal of Development
Economics. 24(1986): 203-223.
Intriligator, Michael D. Econometric Models. Techniques, and
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Hall, 1978.
Lau, Lawrence J., Wuu-Long Lin, and Pan A. Yotopoulos. "The
Linear Logarithmic Expenditure System: An Application
to the Consumption-Leisure Choice." Econometrica.
46(1978): 843-868.
Lopez, Ramon E. "Estimating Labor Supply and Production
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Economic Review. 24(1984): 61-82.


40
By their choice of an LP model on the production side BDN
argue that they can disaggregate commodities (96 activities
and 82 constraints), examine the impact of FFW-based capital
investment and limit the cost of data collection needed to
support the model. The argument for using an AIDS model on
the consumption side is that it allows for flexible price
and income elasticities. BDN use the linear approximate
Stone price index and impose the standard demand conditions
of adding-up, homogeneity and symmetry when estimating the
AIDS model using an iterative nonlinear Zellner method for
seven commodities.
The FFW enters the model directly through a second
(after farm household) production function for obtaining FFW
commodities. They also attempt to include a static, two-
period production component in an attempt to capture invest
ment effects of FFW programs. Another interesting addition
by BDN is the incorporation of a minimum consumption re
quirement resulting in nonseparability between production
and consumption decisions. A household that perceives a
minimum consumption need will base that perception on the
household consumption needs which would then impact produc
tion decisions.
The authors found that FFW increased production,
income, capital investment, employment and marketed surplus
in the Baringo District. A shift from maize to millet
production was attributed to the maize distributed as FFW


74
etc.)* The final size of the sample set of households used
was limited to the 87 households which had complete annual
data on both production and consumption.
Almost Ideal Demand System (AIDS)
There are several alternative approaches to solving and
estimating a system of demand equations. These include the
linear expenditure system (LES), the log-linear expenditure
system (LLES) and the Rotterdam approaches. Each of these
systems approaches has its advantages and disadvantages
depending upon the needs of the analysis.
Demand systems that are derived from an additive
utility function, such as the LES, necessitate strong
separability of preferences and, possibly, own price elas
ticities restricted to linear relations of expenditure elas
ticities. The LES is derived from the Stone-Geary additive
utility function. The LLES, on the other hand, requires
expenditure elasticities equal to unity, which would inap
propriately restrict the present study.
Another possible specification for the consumption side
that would provide an opportunity to test the consequences
of the neoclassical theory of demand is the Rotterdam model.
The Rotterdam model is consistent with utility maximization
for a linearly logarithmic utility function and has a
similar specification to the AIDS configuration. However,
unlike the AIDS, the Rotterdam model is not derived from


103
Even taking into consideration the impact of the profit
effect, the overall responsiveness of rural Burkina house
holds is striking. Rural households can be expected to
respond in an economically intuitive fashion as long as
agricultural profits are less than one-fifth to one-quarter
of total income. The percentage of households in a particu
lar area that will draw greater than 25% of total income
from agriculture will be spatially specific in Burkina due
to the different agroclimatic zones. Thus, those households
living in particularly productive (agriculturally) areas can
be expected to exhibit a sign change on the demand for
cereals from negative to positive. In contrast, those areas
with diversified income strategies will continue to exhibit
the intuitive decrease in consumption with price increases.
It may then be possible to determine the sub-national
impacts of a change in pricing policy.
The highly elastic expenditure elasticities on non-food
and non-local produced (tobacco and beverages) goods demon
strate the significant rural demand for production of goods
from other sectors in the national and regional economy.
Rural households are clearly more integrated with the
national and regional economy (the cola nuts of Good 2 come
from Ghana and Cote d'Ivoire) than some have thought. Given
the greater level of market responsiveness, increased market
integration as a policy goal should be considered.


123
(UF) in 1985. While a Ph.D. student in FRED he began con
sulting work for Tulane University's Center for Interna
tional Health and Development. In 1988, Charles took a leave
of absence from UF as a fellow at the Institute of Interna
tional Economics in Kiel, Germany. This year-long program,
with participants from several countries, was an intensive
program in international macroeconomics, trade, development
and finance.
Upon returning to the U.S. in 1989, Charles was em
ployed by Tulane University as the staff economist on the
Famine Early Warning System (FEWS) Project outside of
Washington, D.C. Charles is presently employed with this
project and returned to UF to complete his Ph.D. disserta
tion in the fall of 1991.


52
The Kuhn-Tucker complementary slackness conditions
given by:
(a*/ax.) (X,*) =0 (3.13)
0/3O (O = o
ca*/ax,*) (x,*) = o
0*/a/x) (m*) = o
serve to emphasize the possibility that an interior solu
tion, where the first order partial derivative of the
objective function must equal zero, may not exist. However,
whether the solution occurs at a boundary or an interior
point, the complementary slackness condition states that the
choice variables or the first order partial, or both, must
be equal to zero.
The marginal conditions of equation 3.11 involve four
equations and four unknowns and, if all are binding as one
would expect in this model, can be solved to give the demand
equations for the three choice variables.2 These demand
equations can be written as:
X; = X¡* (P, Pm, w, Y*) i = a,m, 1 (3.14)
which is the neoclassical result that demand is dependent
upon prices and income.
However, in an agricultural household the full income
variable, Y*, is determined by the household's production
2 One would expect all conditions to be binding since X,*,
X,,,*, X,*, and n" would all be expected to be positive in a
smallholder household, therefore equation 3.13 suggests that
equality hold in each equation 3.11.


61
which can be solved for the household demand for labor as
L = a2(P,/w)Q. (4.7)
where Pa is the output price of the agricultural commodity
and w is the wage rate.
The restricted profit equation (profits minus variable
costs) is then given by
7T = P,Q(A,L) wL (4.8)
which, with substitution from equation (4.7), simplifies to:
n = a,P,Q (4.9)
when a, + a2 = 1.
The profit-maximized output supply equation can then be
obtained by substituting the input demand equation (eq. 4.7)
in the original Cobb-Douglas production function (eq. 4.1)
which simplifies to:
cX1
a.
L
w
1/ (l-2>
(4.10)
In addition to the above Cobb-Douglas specification, a
translog model was estimated that included squared terms for
the two factor inputs and an interaction term between these
inputs. Since the Cobb-Douglas model is a special case of
the translog model, the former can be tested as a restricted
case of the latter. When the appropriate F-test was per
formed the hypothesis that the Cobb-Douglas model was
appropriate was not rejected at the 99% level of signifi
cance.


70
Barnum and Squire's Malaysia data indicated the reverse
of the Burkina figures with 62 and 29% shares for land and
labor, respectively. The balance being the shares of other
variable inputs (8 percent) and capital (1 percent). This
can be taken to imply that agriculture in Burkina is con
strained more by labor than land. Thus, greater returns
could be expected from addressing labor constraints than
land constraints, although both would have a significant
positive impact on production.
Production side elasticities more directly relevant to
the agricultural household model can be directly computed
from the output supply (eq. 4.10), labor demand (eq. 4.7)
and profit (eq. 4.9) equations.1 The resulting elasticity
values and the formulas from which these estimates were
derived are presented in Table 4.2.
In general, the results from Table 4.2 are consistent
with earlier studies including Barnum and Squire (1979a,b)
and Haughton (1986), both using Malaysian data. From the
first two diagonal elements of Table 4.2, the own-price
elasticities of output and labor can be interpreted. Output
produced is very (positively) responsive to changes in the
price of that output (in this case cereal price). As previ
ously mentioned above, these direct, or quantity based,
1 Taking logarithms of both sides of these three equa
tions simplifies the derivation of the elasticity formulas.


62
The Cobb-Douglas specification was also tested against
the CES production function. Once estimated, the CES was
tested for constant returns to scale (unable to reject at
the 95% level of significance) and then reestimated with
this restriction imposed. The resulting CES with constant
returns to scale was tested against the Cobb-Douglas. Again
the Cobb-Douglas specification was not rejected at the 99%
level of significance (nor at the 95% level of significance,
contrary to the test against the translog). With these
results the Cobb-Douglas estimates were retained for the
model estimation.
Other concerns entered into the choice of the Cobb-
Douglas specification. The needs of the agricultural house
hold model, functional form tractability and data availabil
ity constraints precluded the use of a translog approach in
the present case. Recall, that the main production side
result required for the agricultural household model is the
responsiveness of profits to changes in output price.
Unfortunately, "it is not possible to derive the first order
conditions for profit maximization and substitute them into
the translog production function to give a price-based
translog production function (Haughton, 1986, p. 207)" as
was done with the Cobb-Douglas specification.
An alternative approach would have been to derive the
restricted profit function from a direct production func
tion. Again tractability is a problem as "this works neatly