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Credit and efficiency : an analysis of traditional food production systems in southeastern Minas Gerais, Brazil

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Credit and efficiency : an analysis of traditional food production systems in southeastern Minas Gerais, Brazil
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Food production systems in southeastern Minas Gerais, Brazil
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Gomes, Aloisio Teixeira, 1948-
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xii, 111 leaves : ill. ; 28 cm.

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Agricultural land ( jstor )
Allocative efficiency ( jstor )
Crops ( jstor )
Discriminants ( jstor )
Efficiency metrics ( jstor )
Farmers ( jstor )
Farms ( jstor )
Herpes zoster ( jstor )
Production efficiency ( jstor )
Production functions ( jstor )
Agricultural assistance -- Brazil ( lcsh )
Agricultural credit -- Brazil ( lcsh )
Agricultural productivity -- Brazil ( lcsh )
Dissertations, Academic -- Food and Resource Economics -- UF
Food and Resource Economics thesis Ph. D
Rural conditions -- Brazil ( lcsh )
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bibliography ( marcgt )
non-fiction ( marcgt )

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Thesis:
Thesis (Ph. D.)--University of Florida, 1984.
Bibliography:
Bibliography: leaves 107-110.
General Note:
Typescript.
General Note:
Vita.
Statement of Responsibility:
by Aloisio Teixeira Gomes.

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CREDIT AND EFFICIENCY:
AN ANALYSIS OF TRADITIONAL FOOD PRODUCTION SYSTEMS
IN SOUTHEASTERN MINAS GERAIS, BRAZIL









By

ALOISIO TEIXEIRA GOMES


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




UNIVERSITY OF FLORIDA


1984













ACKNOWLEDGMENTS


The author wishes to express his gratitude and appreciation to Dr. Harold Evan Drummond, chairman of the supervisory committee, for his guidance, patience, and encouragement during the preparation of this dissertation. Gratitude is also expressed to Dr. William G. Boggess, co-chairman of the supervisory committee, and Dr. Timothy G. Taylor, member of the supervisory committee, for their valuable assistance. Appreciation and thanks are also extended to Dr. J. Scott Shonkwiler and Dr. William G. Blue, members of the supervisory committee, for their time and assistance.

Special recognition is given to Dr. W. W. McPherson, former

graduate coordinator in the Department of Food and Resource Economics, and to Dr. Max R. Langham, present graduate coordinator, for their assistance and guidance during the author's study program at the University of Florida.

The author also appreciates the very rewarding experience and good times shared with colleagues, friends, staff, and faculty of the Department of Food and Resource Economics.

The data used in this study were collected by the Department of

Agricultural Economics of the Federal University of Vicosa, Brazil. All of the staff of that department had some input into this study. Their permission to use the data is gratefully acknowledged.








Finally, the author is especially grateful to the Empresa

Brasileira de Pesquisa Agropecuaria for providing financial support for the author's graduate study.













TABLE OF CONTENTS


Page


ACKNOWLEDGMENTS ...........

LIST OF TABLES ...............

LIST OF FIGURES ...........

ABSTRACT ..... ...............

CHAPTER

I INTRODUCTION ...........


. . . ii . . . vii


. . . . . . . . . . . x


Problem Definition . ... Objectives of the Study Organization of the Study


II GENERAL CHARACTERISTICS OF THE
THE PRODEMATA PROGRAM . ...


STUDY REGION AND


Introduction .... ..................
The Agricultural Economy of the State of
Minas Gerais .... ................
General Characteristics of the Zona da Mata The Agricultural Sector of the Zona da Mata
The Integrated Rural Development Program for
the Zona da Mata Region ..........

III THE PRODEMATA SAMPLE ..... ...............

Introduction .... ..................
The Sample ...... ..................
The Data ...........................
Sample Characteristics ................
Farm Size and Land Resources ............
Levels of Input Use .............
Labor . . . . . . . . . . . . . . . . .
Fixed Capital
Operating Expenses ..............


8 8 8

. . . . 14 S. .. 17








CHAPTER


IV EFFICIENCY MEASUREMENT ..... ...............

Introduction ...........................
Efficiency and Frontier Functions .......
Conceptual Framework .... ...............
The Model . . . . . . . . . . . . . . . .
Farrell Measures of Efficiency .......
Estimation Procedure ..............
Corrected Ordinary Least Squares (COLS)
Estimation . . . . . . . . . . . . . . .
Maximum Likelihood (ML) Estimation ....

V EMPIRICAL RESULTS .................

Model Estimation *. .................
Frontier Production Function .........
Frontier Cost Function .............
Efficiency Measures ..............
Technical Efficiency ..............
Results . . . . . . . . . . . . . .
Comparison by Tenancy ....... Comparison by Group ........ Allocative Efficiency ..........
Results .
Comparison by Tenancy . . . . . . . Comparison by Group ........ Total Productive Efficiency .......
Summary of Findings ...................


VI DISCRIMINANT ANALYSIS OF PARTICIPATION CHOICE

Introduction .... ................


Linear Discriminant Model


Evaluating the Discriminant Function . . .
Differences between Groups .......
Relative Importance of the Variables Classification Ability .........
Selection of Discriminant Variables .
Analysis and Results ............
Technical and Allocative Efficiency by
Discriminant Analysis Groups . . . . . .

VII SUMMARY AND CONCLUSIONS ...........


76
S. . . 76 . . . . 76

. . . . 79 S. .. 79
. .. . 80
. .. . 80
* . . . 81
. ... 83

* . . . 86


The Problem, Objectives, and Procedures .... Summary of the Findings ............
Implications and Policy Issues ............
Limitations and Suggestions for Further Research


. . . 96


Page


0









APPENDIX Page

A LABOR USED PER HECTARE IN SHARECROPPED AREAS ...... ..99 B BASIC DATA'AND'DEFINITIONS ....... ............... 101

C TEST OF THE EQUALITY OF THE AVERAGE EFFICIENCY
MEASURES BETWEEN PARTICIPANTS AND NONPARTICIPANTS
IN THE PRODEMATA PROGRAM ..... ................ .... 104

REFERENCES ......... ........................... ..... 107

BIOGRAPHICAL SKETCH ....... ...................... .I.I. il













LIST OF TABLES


Page


Table


2-1 Distribution of farms and farm receipts by size
class, Minas Gerais, 1974-75 ...........

2-2 Urban, rural, and total population of the state of
Minas Gerais, 1950-75 ..... ...............

2-3 Urban, rural, and total population of Zona da Mata,
1950-75 ....... .....................

2-4 Land use and number of farms by activity, Zona da
Mata, 1975 . . . . . . . . . . . . . . . . . . . .

2-5 Land tenure partern, Zona da Mata, 1975 ........

3-1 Sample composition by class of producer and participation in the PRODEMATA program, Zona da Mata, 1981-82 ....... .....................


. . . . 10 S. .. 12


. . . . 13 . . . . 16 . . . . 18


3-2 Description of the different groups of farmers who
were interviewed according to ownership of land and
management structure, and the corresponding need for
adjustments of production factors, Zona da Mata,
1981-82 ....... .. ......................

3-3 Average farm size by land use, class of producer, and
participation in the PRODEMATA program, Zona daMata,
1981-82 ........ ........................

3-4 Average labor used per farm, labor per hectare, and
labor cost, by class of producer and participation
in the PRODEMATA program, Zona da Mata, 1981-82 . . ..

3-5 Average capital stock per farm in buildings, machinery
and equipment, and work and production animals, Zona
da Mata, 1981-82 . . . . . . . . . . . . . . . . .

3-6 Average fixed capital per hectare and per man-day by
class of producer and participation in the PRODEMATA
program, Zona da Mata, 1981-82 . ........ .








Table Page

3-7 Average operating expenses per farm by class of producer and participation in the PRODEMATA
program, Zona da Mata, 1981-82 .... .. .............. 35

3-8 Average operating expenses per hectare and per man-day by class of producer and participation
in the PRODEMATA program, Zona da Mata, 1981-82 ... ...... 37

5-1 Corrected ordinary least squares (COLS) and maximum likelihood (ML) estimates of the frontier production
function for each group of farmers, Zona da Mata,
1981-82 ........ .......................... ... 58
5-2 Sunmmary statistics for the frontier production function disturbance distributions for each group
of farmers, Zona da Mata, 1981-82 ... ............. ... 60

5-3 Derived COLS and ML estimates for the cost function frontier for each group of farmers, Zona da Mata,
1981-82 ....... ... ... ... ... ... ....63
5-4 Average efficiency indices (calculated via COLS estimates) for each group of farmers and by tenancy
category, Zona da Mata, 1981-82 ... .............. ... 65

5-5 Average efficiency indices (calculated via ML estimates) for each group of farmers and by tenancy
category, Zona da Mata, 1981-82 ... .............. ... 66
5-6 Output/input ratios obtained by sharecroppers and by the owners in the Zona da Mata, 1981-82 .... ........ 68

5-7 Efficiency index ratios between participant and nonparticipant farmers, Zona da Mata, 1981-82 .... ........ 70

6-1 Discriminant coefficients, overall means, group
means, and t-test levels of significance for differences in mean values between participants and
nonparticipants ....... ...................... ... 84

6-2 Ranking of the importance of each variable in the
discriminant analysis ..... ................... ... 87

6-3 Test for significant differences between the
technical efficiency index averages of subgroups defined by actual participation in the PRODEMATA program and socio-economic characteristics which
would have predicted participation according to the
discriminant analysis, Zona da Mata, 1981-82 . ....... ... 89


viii








Table Page

6-4 Test for significant differences between the allocative efficiency index averages of subgroups defined by actual participation in the PRODEMATA program and socio-economic characteristics which would have predicted participation according to
the discriminant analysis, Zona da Mata, 1981-82 .. ..... 91

A-1 Regression equations estimates of labor used
(expressed in logarithms) in each crop as a function of the cultivated area, also expressed in
logarithms .... .... ........................ ... 99

C-1 Test for significant differences between the efficiency averages derived from COLS estimates for
participants and nonparticipants in the PRODEMATA
program ... ... .. ......................... ... 104
C-2 Test for significant differences between the efficiency averages derived from ML estimates for participants and nonparticipants in the PRODEMATA
program ........ .......................... ... 105













LIST OF FIGURES


Figure Page

2-1 Brazil, state of Minas Gerais, and the Zona da Mata region ....... ... ....................... 9

4-1 Efficient unit isoquant .... ................. .... 40













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


CREDIT AND EFFICIENCY:
AN ANALYSIS OF TRADITIONAL FOOD PRODUCTION SYSTEMS IN SOUTHEASTERN MINAS GERAIS, BRAZIL

By
Aloisio Teixeira Gomes

April 1984

Chairman: H. Evan Drummond
Co-Chairman: William G. Boggess Major Department: Food and Resource Economics

Over the past two decades one of the primary policy actions

designed to increase productivity, and hence income, of poor rural people in Brazil has been the provision of agricultural credit at subsidized rates of interest. There is a lack of consensus regarding the need for and effectiveness of such credit programs. Various farm-level production studies have provided conflicting results concerning the effect of credit policies on productivity and efficiency of traditional farming.

This study provides an evaluation of the Integrated Rural Development Program (PRODEMATA) for the low-resource farmers in the Zona da Mata, a region in the state of Minas Gerais, Brazil. The PRODEMATA program includes credit combined with technical assistance from the extension service.








The focus of the study was on the technical and allocative

efficiency of participant and nonparticipant farmers in the PRODEMATA program. Full frontier production functions were estimated using a maximum likelihood approach. The production frontiers generated dualcost frontiers which were used to estimate the technical and allocative efficiency of each sample observation. The average participant had statistically significant higher technical efficiency than nonparticipants, but statistically significant lower allocative efficiency.

A discriminant analysis approach was used to identify pre-existing socio-economic differences between partipants and nonparticipants. When the sample was stratified into homogeneous socio-economic groups, it was clear that the differences in technical efficiency between participants and nonparticipants were due to the PRODEMATA program rather than other pre-existing fundamental differences between the two groups. However, it was impossible to determine if the differences in allocative efficiency were caused by PRODEMATA participation alone.













CHAPTER I
INTRODUCTION

The agricultural sector is of fundamental importance to the

economies of most developing countries. In Brazil, even though agricultural contributions to the economy are being given increasing priority and many efforts have been made to promote rural development, much of the population lives in conditions of extreme poverty, the worst of which is concentrated in the rural areas.

Rural development programs in Brazil have often emphasized improvements in farm productivity. Development strategies based on technological change designed to increase agricultural output and the incomes of poor rural people have been considered of crucial importance to overall plans of economic growth and development.

A common strategy to encourage the adoption of new and/or more

productive technologies has been to provide adequate agricultural credit at subsidized rates. A typical credit program allows the development agency to monitor farmers' production practices and to subsidize indirectly the adoption of new technologies. In the last two decades, agricultural credit has been viewed as an important catalyst in development efforts in most low-income countries and various types of agricultural credit programs have been started in these less developed countries. The objectives or goals of credit programs and the concern about their performance fall into three categories: (a) the








economic efficiency of the activities financed, (b) the ability of the program to serve neglected portions of the rural population, and (c) the financial viability of the institution through which funds are administered (Donald, 1976).

In Brazil, agricultural credit expanded very rapidly at the same time that agricultural growth rates accelerated. The emphasis of most programs has been to provide credit to farmers through normal banking channels (Meyer et al., 1973), the idea being that all farmers, including small producers, will benefit by the distribution of agricultural credit through the existing commercial banking system. This study is concerned with the effectiveness of agricultural credit in achieving the goals of a specific development program for low-resource farmers in BrazilPRODEMATA, the Integrated Rural Development Program for the Zona da Mata, a region in the state of Minas Gerais.


Problem Definition

The Zona da Mata is one of the most backward regions of rural southeastern Brazil. The region, despite its favorable location near large urban centers of southeastern Brazil, is considered a depressed area. The relative abundance of labor and relatively low crop yields are characteristic of its traditional agriculture.

The PRODEMATA program was designed as part of a continued effort toward the revitalization of the agricultural economy of the Zona da Mata. An implicit hypothesis in the project's design is the belief that growth in productivity and farmers' income occur through increased access to inputs and that the ability of farmers to adopt these inputs is related to the availability of credit.








The need for and effectiveness of credit programs in traditional agriculture have frequently been debated in the literature. In the early 1960s, Schultz (1964) introduced the "poor but efficient" theory casting doubt upon the benefits of providing credit to traditional farmers. Professor Schultz utilized the works of Tax (1963) and Hopper (1957) to support the hypothesis that "there are comparatively few significant inefficiencies in the allocation of the factors of production in traditional agriculture" (Schultz, 1964, p. 37). He argued that in traditional agriculture most profitable opportunities had been exhausted and, thus, there is no need for employment of outside capital. If this is the case, credit programs to encourage the use of additional inputs will result in a misallocation of resources and will introduce inefficiencies into a production system which will remain poor and become inefficient.
Various farm-level production studies have been conducted in

Brazil to analyze the effects of credit programs on capital formation, productivity, and efficiency of traditional agriculture. Rao (1970), analyzing the economics of credit in southern Brazil, indicated that there was considerable underutilization of capital on small farms and that the provision of credit to relieve capital shortages and increase output would be necessary. Nelson (1971), however, in his study in Riberao Preto (Sao Paulo, Brazil), concluded that farmers could not increase income by applying more capital inputs because of technological barriers. He argued that credit programs would have little impact on capital formation and income unless these technological constraints were overcome.








White and Seabra (1973) pointed out that internal capital accumulation through savings is very difficult among small farmers in the Zona da Mata and that credit plays a major role as a source of additional capital. On the other hand, some studies have shown a tendency for the extension service (which must approve all institutional credit) to work mainly with the owners of larger farms in Brazil. As a result, large farmers have a greater access to credit than do small farmers, who may well have a greater need for credit.

There is also disagreement in analyses of resource allocation in traditional agriculture in Brazil. Nehman (1973), in his study of agricultural credit in a depressed area of Sao Paulo, showed that capital inputs were being well allocated by large farmers with borrowed capital. He found misallocation of capital inputs, however, by the small farmers who had the lowest potential return on increases in operating capital and no potential return for increasing working assets.
Garcia (1975) found in two regions of the state of Minas Gerais that small farmers were not efficient, demonstrating excessive labor use. Graber (1976) and Teixeira (1976) also concluded that poor resource allocation of acquired production factors existed among small farmers in Brazil.

Drummond (1972), in his study, compared two regions of the state of Minas Gerais, Brazil, which were felt to be polar opposites in their fundamental characteristics. The findings led to the conclusion that "the agriculture in the traditional region of Muriae is neither more nor less efficient in the use of available resources than in the commercially oriented region of Capinopolis" (p. 151). This result




5



supports the position that traditional agriculture is not necessarily inefficient.

Steitieh (1971) enlarged on the study of resource allocation through the analysis of productivity and productivity change of all inputs in crop production at the farm level in Brazil. The general conclusion derived from his results is that increased investment in inputs alone is not the answer to increasing crop production. He argued that "better management, information and utilization of resources is as important and should be equally emphasized if any benefit is to be expected from increasing expenditures on these inputs" (p. 96). The implication of this argument is that while credit availability may increase access to inputs, there is no guarantee that these inputs will be used in such manner as to realize the full potential of output gains.
Even though these studies represent only a small sample of the

large body of research on traditional agriculture in Brazil, they serve to illustrate the divergence of opinion and results concerning the allocative efficiency of traditional farmers, and hence the effectiveness of agricultural credit programs.
This study will attempt to evaluate and analyze the impact of the supervised agricultural credit extended through the PRODEMATA program. The analysis focuses on the effects of the program on the technical and allocative efficiencies of farms in the Zona de Mata region of the state of Minas Gerais, Brazil. Unlike previous studies analyzing inefficiency on farms which used an "average" production function, this analysis is undertaken in terms of a "frontier" production function.








Objectives of the Study

The general purpose of this researchwas to analyze the effectiveness of the use of supervised credit in achieving the goals of the PRODEMATA project. The specific objectives of the study were

1. To evalute farm and farmers' characteristics which are associated with participation in the PRODEMATA and can distinguish between participants and nonparticipants in the program

2. To analyze the effectiveness of the PRODEMATA in stimulating the adoption of more productive technologies in traditional agriculture

3. To analyze the effects of the PRODEMATA on the allocative and technical efficiency of resource use


Organization of the Study

This study is divided into seven chapters. In the introductory chapter the research problem and objectives are presented. Chapter II provides a brief description of the study region, with emphasis given to a discussion of specific features of its agricultural sector. A summary of the scope of the PRODEMATA program is also presented in this chapter. In Chapter III the sampling plan and the data used in this study are discussed. A descriptive presentation of characteristics of the sampled farms is also developed in this chapter where aspects related to resource endowment and levels of resource use are discussed. Chapters IV and V are devoted to the efficiency analyses. In Chapter IV efficiency measurement is reviewed, the empirical model is presented, and the procedures used in the analysis are explained. Chapter V contains the empirical results. In Chapter VI a discriminant analysis




/




approach is used to distinguish between participants and nonparticipants in the PRODEMATA. The theoretical and empirical models are discussed, the results are analyzed, and an application is shown where the results are integrated to the efficiency analysis. Finally, in Chapter VII the major findings of the research are summarized, implications and policy recommendations are derived, limitations of the study are discussed, and suggestions for further research are explored.













CHAPTER II
GENERAL CHARACTERISTICS OF THE STUDY REGION AND THE PRODEMATA PROGRAM

Introduction

This chapter presents selected characteristics of the study area and of the PRODEMATA project. The initial sections deal with structural characteristics of the farm sector in the state of Minas Gerais and the geographic setting of the study. Some of the major characteristics of the agricultural economy of the Zona da Mata are presented. An overview of the World Bank-sponsored PRODEMATA project concludes the chapter.

The Agricultural Economy of the State of Minas Gerais

The Zona da Mata region is located in the southeastern part of the state of Minas Gerais, bordering the state of Rio de Janeiro and Espirito Santo (see Figure 2-1). The agricultural sector of Minas Gerais is of great importance for the state itself as well as the whole country. The 1975 Agricultural Census registered 454,465 farms in the state. The predominance of small farms is clearly shown in Table 2-1. About 28 percent of the farms in the state have fewer than 10 hectares and 81 percent of the farms have fewer than 100 hectares. Total receipts of all farmers in the crop year 1974-75 were about 15 billion cruzeiros (approximately $4,000 per farm). While farms which are larger than 100 hectares represent only 19 percent of the total units, they receive about 61 percent of the total receipts of the sector.












N







Brazil1






Espirito Santo /Paul o Rio de Janeiro asilia









Minas Gerais Zoria da Mata


Brazil, state of Minas Gerais, and the Zona da Mata region


Figure 2-1.









Table 2-1. Distribution of farms and farm receipts by size class, Minas Gerais, 1974-75


Farms Receipts Class of Percentage Cumulative Percentage Cumulative Average farm Number of total percentage Amount of total percentage per farm


(ha) (Cr$1,000) (Cr$1,000)

<10 128,273 28.23 28.23 1,188,551 7.66 7.66 9,266 10-20 73,043 16.07 44.30 891,782 5.75 13.41 12,209 20-50 104,471 22.99 67.29 1,981,101 12.77 26.18 18,963 50-100 62,033 13.65 80.94 2,088,101 12.94 39.12 33,661 100-200 42,686 9.39 90.33 2,323,400 14.98 54.10 54,430 >200 43,959 9.67 100.00 7,121,348 45.90 100.00 162,000

Total 454,465 100.00 15,594,283 100.00 34,313


Source: Minas Gerais, Rio


Fundacao Instituto Brasileiro de Geografia e Estatistica (FIBGE), Censo Agropecuario de de Janeiro, 1975.








The total population of Minais Gerais in 1975 was 12,550,000 inhabitants, of which 41 percent lived in rural areas. During the period 1950-1975 the percentage of rural population decreased, primarily because of a rapid increase in the urban population (Table 2-2). Since 1960, incentives for rural to urban migration have caused the rural population to decrease in absolute terms.

General Characteristics of the Zona da Mata

The Zona da Mata region covers an area of 36,012 km2, which is 6.1 percent of the total area of the state of Minas Gerais. The climate is generally mild with a temperature that averages about 22'C. Annual rainfall averages 1,400 mm, with a dry period occurring from April to September.
The Zona da Mata (literally translated as the forested zone) is

characterized by a topography of rolling hills and sharp rock outbreaks, not unlike the topography of much of Appalachia in the United States. Soils are moderately to highly weathered and relatively high in clay. Those from higher elevations are dominated by Red Yellow Latosols (Oxisols) and those from terraces by Red Yellow Podzols (Ultisols) (Resende, 1980). Some relatively fertile soils occur along narrow valleys.
The total population of the Zona da Mata was about 1.6 million

inhabitants in 1975 (Table 2-3). Similar to the pattern of the state of Minas Gerais, the percentage of the rural population has been decreasing since 1950, with only 49 percent of the total population living in rural areas in 1975.








Table 2-2.


Urban, rural, and total population of the state of Minas Gerais, 1950-75


Year Urban Rural Total


--------------------- thousands----------------1950 2,322.9 5,459.3 7,782.2 (29.8)a (70.2)
1960 3,825.2 5,832.5 9,657.7 (39.6) (60.4)
1970 6,060.3 5,427.1 11,487.4 (52.8) (47.2)
1975b 7,350.7 5,199.9 12,550.6 (58.6) (41.4)


Source: Fundacao Instituto Brasileiro de Geografia e Estatistica (FIBGE), Anuario Estatistico do Brasil, 1955 and 1978 issues.
aNumbers in parentheses are percentages of the total population.
bEstimated by FIBGE, Anuario Estatistico do Brasil, 1978.








Table 2-3. Urban, rural, and total population of Zona da Mata, 1950-75



Urban Rural Total


------------------- thousands-----------------1950 385.1 898.2 1,283.3 (30.0)a (70.0)

1960 567.2 955.8 1,532.0 (37.2) (62.8)

1970 795.6 805.2 1,600.8 (49.7) (50.3)
1975b 834.6 789.1 1,623.7 (51.4) (48.6)


Source: Fundacao Instituto Brasileiro de Geografia e Estatistica (FIBGE), Anuario Estatistico do Brasil, 1955, 1965, 1975, and 1978 issues.
aNumbers in parentheses are percentages of the total population.
Estimated by FIBGE, Anuario Estatistico do Brasil, 1978.








The social infrastructure in the region is poor. Health and education services are very limited. Mortality rates are high, especially among infant and preschool children, as a consequence of widespread malnutrition and disease.

Educational opportunities are limited. The investment in education by the state is low, resulting in a lack of facilities and generally low quality of teaching services. As a consequence of this inadequate system, the labor force in the region has a poor educational background. According to the 1970 census, 60 percent of the agricultural workers in the region had no formal education (FIBGE, 1978). The illiteracy rate among the 5-14 year old age group was about 55 percent in 1975 (FIBGE, 1978).

The Agricultural Sector of the Zona da Mata

The Zona da Mata region was one of the first areas of central

Brazil to be colonized. As a result of a mining boom in the early part of the seventeenth century, an incipient agriculture began to develop in the area. For many years the region played an important role in supplying agricultural products to the mining population.

The settlement process was intensified with the introduction of

coffee around 1830. Coffee found favorable soil and climatic conditions in the Zona da Mata along with the advantage given by its proximity to major markets.
Until the first quarter of the twentieth century, the Zona da Mata was a leading economic region of the state and the nation, experiencing constant growth fueled by the coffee boom. However, depleted soil conditions coupled with inadequate conservation techniques during the coffee








era resulted in reduced yields and increased production costs (UFV, 1971). Simultaneously, competition from coffee growers in southern states led to a process of economic decline in the Zona da Mata.

Coffee, once dominant in the region, has become relatively less important as a result of the comparative advantage of the southern producers and government programs to eradicate coffee plantations during the mid-1960s. These programs accelerated the economic decline of the the Zona da Mata because areas released by the eradicated coffee have been put primarily into unimproved pastures for cattle raising. The dramatic and sudden shift from labor-intensive coffee to laborextensive pastures has resulted in a serious problem of unemployment and underemployment in the agricultural sector (Bandetra, 1970). Moreover, since coffee generates a relatively high net income per hectare, the region has many small farms which were economically viable when in coffee but which are marginal, at best, in pasture.

Dairy farming now is the most important source of income for agriculture in Zona da Mata. The region has become an important milk supplier forthe Rio de Janeiro area. The predominance of the livestock subsector is illustrated in Table 2-4. More than 70 percent of the productive land in the Zona da Mata is now in pastures and nearly all farm units have some pasture (FIBGE, 1975). The most important annual crops in the region are corn, rice, beans (edible beans), sugarcane, and tobacco. Corn and beans are frequently intercropped. Coffee and fruit (including citrus) are the main perennial crops. Garlic and tomatoes are the primary vegetable crops. They are produced for shipment to the Rio de Janeiro market.








Table 2-4. Land use and number of farms by activity, Zona da Mata, 1975


Land use Farms Activity Area (ha) Percentage Number Percentage Pasture 2,166,654 70.3 59,812 88.6 Annual crops 382,840 12.4 58,173 86.2 Perennial crops 113,379 3.7 25,786 38.2 Forests 343,239 11.1 38,961 57.7 Other 76,428 2.5 11.049 16.4

Total 3,082,540a 100 67.474 .b


Source: Fundacao Instituto Brasileiro de Geografia a Estatistica (FIBGE), Censo Agropecuario de Minas Gerais (Rio de Janeiro, 1975).
aTotal does not include unproductive lands.
bPercentages do not total 100 because of farm enterprise diversification.








Concentration in the land tenure pattern in the Zona da Mata

exacerbates the economic problems of the region. As shown in Table 2-5, of the 67,474 farms in the area, about 33 percent are smaller than 10 hectares, 76 percent have less than 50 hectares, and 89 percent have less than 100 hectares. Those farm units with more than 100 hectares hold about 55 percent of the area's land resource (FIBGE, 1975).

Given the difficulty of stimulating structural changes, most efforts to address the problems of the region have focused on improvements in the allocation of the available resources and the efficiency with which those resources are employed. Agricultural credit, technical services, and investments to improve social infrastructure are some of the alternatives which have been selected to address the problems of the region.

The Integrated Rural Development Program for the Zona da Mata Region
The Integrated Rural Development Program for the Zona da Mata region of the state of Minas Gerais (PRODEMATA) is a World Bank-sponsored project.1 It was designed-as part of a continuing effort to revitalize the agricultural economy of the Zona da Mata. The target population is the large number of small landowners and sharecroppers in the region.

The general purpose of PRODEMATA is to induce agricultural development in the Zona da Mata and to upgrade the welfare of the target population. These objectives are to be achieved through a series of incentives




1For more details concerning the project, see World Bank (1976).








Land tenure pattern, Zona da Mata, 1975


Cumulative Percentage
Class of
farm (ha) Number of Farms Area (ha) Percentage of farms Percentage of area

<10 22,171 107,061 32.9 3.4 (32.9)a (3.4)
10-20 12,583 168,164 51.5 8.7 (18.6) (5.3)

20-50 16,379 533,238 75.8 25.2 (24.3) (16.8)
50-100 8,627 609,139 88.6 44.8 (12.8) (19.3)
100-200 4,996 694,606 96.0 66.8 (7.4) (22.0)
>200 2,718 1,050,910 100.0 100.0 (4.0) (33.2)
Total 67,474 3,163,118 --..


(FIBGE), Censo Agropecuario de


Source: Fundacao Instituto Brasileiro de Geografia e Estatistica Minas Gerias (Rio de Janeiro, 1975).
aNumbers in parentheses are percentages of the total.


Table 2-5.








to increase farm production, enhance farm productivity and income, and improve living conditions for the rural population in general. The incentives include

1. Provision of agricultural credit combined with technical services including extension, research and demonstration facilities, and cooperative organization, and

2. Investments in health, sanitation, and education.

The major component of the PRODEMATA program is agricultural credit, which accounts for 60 percent of the.:total .JJS$139 million of project costs. Most of the credit is available only for sharecoppers and small farmers who own less than 100 hectares. These low interest loans are designed. for on-farm investment, the purchase of hired labor and other inputs, reforestation, and land reclamation projects.

The agricultural extension component coupled with the agricultural research and demonstration program is the main production support service. Extension, which has been directed primarily at large farmers in the past, is to be enlarged and redirected toward small farmers. The development of applied agricultural research and the demonstration of improved agronomic practices are to focus on the production system of small farmers. These components are to be executed by the state's agencies for agricultural extension (EMATER-MG) and agricultural research (EPAMIG), respectively. The production support services, including a plan concerning the improvement of cooperatives in Zona da Mata, represent about 21 percent of the total project costs.








Investments in health and education are designed to improve the

social infrastructure. Health services are to be improved by providing health care posts throughout the area. Investments are to be made in sanitation programs and action plans for nutritional improvements, in order to diminish morbidity and mortality from diseases caused by deficient sanitary and nutritional conditions. Emphasis is to be given to pregnant and nursing women, to children under five years of age, and to vaccination against communicable diseases.

With respect to education, the project includes construction and improvement of primary schools and vocational centers, training of teaching staff, and promotion of instructional programs to provide basic knowledge of agricultural technology for farm families.













CHAPTER III
THE PRODEMATA SAMPLE


Introduction

This chapter presents the sampling plan and some descriptive

statistics for the sample. In the initial sections the sampling procedures and the data used in this study are discussed. A descriptive analysis of the farmers sampled in Zona da Mata is presented to conclude the chapter.


The Sample

In order to measure the progress of the PRODEMATA project, comprehensive surveys of the target population were conducted annually from 1977 to the present. These data, which are used in this study, were collected by the Department of Agricultural Economics of the Federal University of Vicosa. The data include information concerning crop and livestock production, land use, input and output prices, sales and onfarm consumption, input use, technology, credit use, tenancy, off-farm work, cooperative membership, and sociodemographic information.

The geographical boundaries of the survey area were defined on the basis of the regional divisions used by the state's extension agency for administrative purposes. In each region four municipios (counties) were selected for inclusion in the sample. Two of the municipios were randomly chosen and the other two were selected based on the presence of








a large target population or specific crops of interest to PRODEMATA (e.g., tobacco and sugarcane). The following municipios were chosen to be included in the sample:

1. Region of Juiz de Fora: Alto Rio Doce, Juiz de Fora, Santos Dumont, Sao Joao Nepomuceno

2. Region of Muriae: Carangola, Leopoldina, Manhuacu, Muriae

3. Region of Vicosa: Ervalia, Ponte Nova, Raul Soares, Uba

The sample included both landowners and sharecroppers. In each administrative region at least 50 sharecroppers were interviewed with a minimum of 12 for each municipio.

The sample was surveyed annually and analyses of consistency of the data were performed. These analyses provided the basis for the elimination and substitution of some producers. Also, some substitution occurred over the years due to the death of respondents or the sale of farms. Thus, over time the original data file was modified, resulting in the creation of files with fewer respondents but, presumably, with a higher degree of credibility and consistency.
For the purpose of this study, data from the 1981-82 crop year survey were used. Some data from the previous surveys were also used to determine the history of PRODEMATA participation of each producer included in the 1981-82 survey. The composition of the sample is shown in Table 3-1.

The Data

The unit of analysis for this study is the farm management unit. This takes into account the total area managed by the respondent,









Table 3-1. Sample composition by class of producer and participation in the PRODEMATA program, Zona da Mata,
1981-82


Class of producer

Owners (by farm size in hectares)
Total
Sharecroppers 0-10 10.01-50 50.01-100 >100 sample



Participants 4 32 104 27 15 182
(7)a (29) (56) (51) (60) (42) Nonparticipants 57 77 83 26 10 253
(93) (71) (44) (49) (40) (58) Total 61 109 187 53 25 435

aNumbers in parentheses are percentages.








irrespective of whether the land is owned, rented, or utilized under a sharecropper agreement. Since the questionnaires were designed to record only the quantities of inputs purchased by the respondent, some adjustments were required in those cases in which some part of the management unit was sharecropped. The sharecropped areas are cultivated under an agreement between landowner and the sharecropper. In the most prevalent arrangement, the owner provides all the land, the sharecropper provides all the labor, and the purchased inputs are equally provided by both. This arrangement was assumed to hold throughout the sample.
The situations which required adjustments in the raw data are summarized in Table 3-2. In case I the respondent is the sole provider of all inputs and labor for the total cultivated area. In this case no adjustments were necessary.

In case II the respondent provides all the inputs and labor only to the area which is not cultivated under a sharecropper agreement. The inputs to the sharecropped area are purchased by both owners and sharecroppers, and all labor is provided by the sharecropper.

In case III the respondent provides all labor and one half of the inputs for all of the management unit. The other half of the inputs is purchased by the owner.

The total quantity of purchased inputs] used in cases II and III was calculated in the following manner:



:fThe set of purchased inputs included seeds, fertilizer, pesticides, draft animal services, and mechanized services.









Table 3-2.


Description of the different groups of farmers who were interviewed according to ownership of land and management structure and the corresponding need for adjustments of production factors, Zona da Mata, 1981-82


Adjustment required
Respondent Ownership of land and (cases) management structure Purchased inputs Labor


I. Owner The respondent owns or rents and manages all of the management unit. No sharecropping exists. No No

II. Owner The respondent owns or rents all of the management unit but part of it is sharecropped. The sharecropped portion is considered part of the management unit of the owner. Yes Yes

Ill. Sharecropper The respondent owns no land. The sharecropper manages all of the management unit which is an entire sharecropped area. Yes No








{i x (T + S) (3.1)



where

thh
Ilij is the estimated total amount of the it input which was used for the jth crop on a particular farm

Qij is the amount of i th input provided by the respondent for the Sth crop

T. is the area of the jth crop cultivated by the owner (for sharecroppers, Tj = 0), and

S. is the area of the jth crop cultivated by the sharecropper.

The total quantity of labor used in the sharecropped areas of land owned by the interviewee (case II) was estimated assuming that all labor used was provided by the sharecroppers. In order to determine labor requirements on sharecropped land, regression equations were estimated for sharecroppers in the sample. For each crop,2 labor used was considered as a function of the cultivated area for the respective crop. The following model was specified:

log L =b + b log S. (3.2)


where

L. is the amount of sharecropper labor used in the jth crop

S. is the sharecropped area in the jth crop, and
b0 and b, are estimated parameters of the model


2Rice, corn, beans (edible beans), corn-beans intercropped, tobacco, sugarcane, and coffee.








The parameter estimates, which are shown in Appendix A, were used to adjust the total labor use in the following manner: For each respondent, the labor used on the sharecropped area for crop j was estimated by Equation (3.2). This procedure was repeated for each crop cultivated in the sharecropped area and the sum of the labor values thus obtained gives the total amount of labor used in the sharecropped areas of the management unit. This total was then added to the quantity of labor used in the nonsharecropped area as reported by the respondent (owner) in the survey.
After all inputs and labor adjustments were made, economic variables were defined at various levels of aggregation. Appendix B includes a listing of the variables relevant to this study and explains how each is defined.


Sample Characteristics
In the following sections a descriptive analysis of the farmers sampled is presented in order to give a more thorough understanding of the sample by describing some general characteristics of the farming system in the Zona da Mata region. It should be pointed out that all figures refer to the 1981-82 crop year and that participant farmers are those producers who had used PRODEMATA-sponsored credit during at least one year since the initiation of the program.


Farm Size and Land Resources
The farm size in this study was measured in hectares of productive land, which is defined as the sum of cropland and land in pastures. In the sample, about 85 percent of the total farm land was used for








crops or pastures in the 1981-82 agricultural year. The other 15 percent of the total land area was in forests, was occupied with buildings and structures, or was unused. These findings are consistent with those of Silva (1981), who found productive land to be 83 percent of the total farm land during the 1977-78 crop year.
As indicated in Table 3-3, the average area of productive land for the 435 farmers in the sample was about 29.10 hectares, with sizes ranging from 0.1 to 230.50 hectares. For the whole sample, the size of the total productive land of the participant farms was roughly 1.5 times that of the nonparticipant farms. This difference is even more apparent with respect to cropland in the two groups.

Patterns of land allocation show that, on the average, farmers utilized about 25 percent of their productive land in cropping activities and 75 percent for pastures. The percentage of land used for crops increased as the size of the holdings diminished. In fact, the owners of the smallest farms (0-10 hectares) allocated about 63 percent of their land to crops. This negative association between the percentage of land in crops and farm size reflects the emphasis placed on subsistence crops by the smaller producers. On the other hand, the owners of larger farms had a higher proportion of their land in pasture, emphasizing livestock activities.

Levels of Input Use

Labor
The Zona de Mata is a region of chronic unemployment and underemployment in rural areas. As a result, the wage rate in the rural








Table 3-3.


Average farm size by land use, class of producer, and participation in the PRODEMATA program, Zona da Mata, 1981-82


Class of producer

Owners (by farm size in hectares)
_______________________________________-Total Sharecroppers 0-10 10.01-50 50.01-100 >100 sample


--------------------------------------hectares -----------------------------


Crop land


Participants
Nonparticipants Sample average Pasture land

Participants
Nonparticipants Sample average Productive land

Participants Nonparticipants Sample average


6.65 4.63 4.77


0.0
0.0 0.0


6.65 4.63
4.77


4.68
2.65 3.25


1.80 1. 99 1 .93


6.48
4.64 5.18


8.24 4.89 6.75


17.74 17.29 17.54


25.98 22.18 24.30


15.45 11.69
13.61


54.13 61.94 57.96


69.58
73.63
71.57


21.66
15.52 19.20


106.06 139.41
119.40


127.72
154.93 138.60


9.76 5.27
7.15


27.23
18.15 21.95


36.98 23.42
29.10








sector is low compared with that of most of the other regions in the state of Minas Gerais (EPAMIG-Informe Agropecuario-1977-82, several issues). This low wage rate, combined with topographic characteristics which to a large extent constrain the use of mechanization, leads to the predominance of labor as the primary resource in the area.

Overall, the average amount of labor used was 414 man-days per farm. As Table 3-4 shows, those farmers producing on a smaller scale tended to use more labor per hectare of productive land than those producing on a larger scale. For example, sharecroppers and owners in the range of 0-10 hectares used about 45 man-days per hectare, whereas those with more than 100 hectares used only 8 man-days per hectare.
As far as participation in the PRODEMATA program is concerned, the level of labor used per hectare was lower for participant sharecroppers and the smallest participant farmers than for these same categories of nonparticipants. The opposite situation was found for the three other farm size categories. Overall, the participant farms used less labor per hectare than nonparticipants.


Fixed Capital
The fixed capital stock is composed of three major categories:

buildings, including animal facilities but excluding houses; machinery and equipment; and draft animals and livestock. The sample data on fixed capital are shown in Table 3-5. The data represent the value of the fixed capital stock as estimated and reported by farmers.

As expected, the larger the farm, the higher the value of the

capital stock. Most of the capital stock on the larger farms is for the









Table 3-4. Average labor used per farm, labor per hectare, and labor cost, by class of producer and participation in the PRODEMATA program, Zona da Mata, 1981-82



Class of producer

Owners (by farm size in hectares)
Sample
Sharecropper 0-10 10.01-50 50.01-100 >100 average

-----------------------------Equivalent man-days -----------------------------Labor used
Participants 231.2 256.6 483.9 944.3 1122.8 559.3 Nonparticipants 205.6 154.8 308.4 711.8 1053.4 309.4 Sample average 207.3 184.7 406.0 830.3 1095.1 414.0

Labor per hectare
Participants 36.5 40.6 20.9 14.0 8.9 22.7 Nonparticipants 45.5 43.3 15.7 10.0 7.0 29.9 Sample average 44.9 42.5 18.6 12.0 8.1 26.9 Labor costa ---------------------------Thousands of cruzeiros--------------------------Sample average 88.993 79.291 174.295 356.447 470.126 177.730

a The estimated labor cost is based on the estimated average annual wage paid for daily labor of one
equivalent man-day, Cr$429.30 (equivalent to US$2.42 at the exchange rate of July, 1982; US$1.00 = Cr$177.54).







Table 3-5. Average capital stock per farm in buildings, machinery and equipment, and work and production
animals, Zona da Mata, 1981-82


Class of producer


Owners (by farm size in hectares)


Sharecroppers


0-10


10.01


--- - - - - - -- - - - - - -thousands of


Capital in buildings
Participants
Nonparticipants
Sample average

Capital in machinery
Participants
Nonparticipants Sample average Capital in Animals
Participants
Nonparticipants Sample average

Total capital stock
Participants Nonparticipants Sample average


0.0
0.228
0.213


7.625 20.500 19.655


24.650
31.652 31. 193


32. 275
52. 380 51.062


361.446 182.949 235.352


150.509 94.789 111.147


88.943 71.423 76.566


600.899 349.162 423.066


724.533 434.218 595.676


353.485 144.456 260.708


543.877 415.378 486.843


1,621.895
994.052 1,343.228


Sample
50.01-100 >100 average cruzeiros--------------------------


1,286.485 1,037.365 1,164.275


772.985 726.584 750.222


1,198.481 1,076.688 1,138.733


3,257.951 2,840.638 3,053.231


1,843.633 1,765.669 1,812.447


719. 700 731.600 724.460


1,994. 586 2,361.600
2,141.391


4,557.919 4,858.869 4,678. 299


820.370 374.578 561.093


402.612 184.444 275.723


669.153
369.130 494.657


1,892.135
928.153 1,331.474








dairy enterprise, which is consistent with the observed correlation bebetween large size and the dairy enterprises.

For the whole sample the value of the capital stock averaged about Cr$1,331,000 (about US$7,500), with the average for participant farms being twice that of nonparticipant farms. The relative composition of the total capital stock was about the same for nonparticipant and participant farms.
Fixed capital stock per hectare decreased as the farm size increased (Table 3-6). This result illustrates the extensive characteristic of the livestock activities on larger farms with respect to the use of land. On the average, participants used more fixed capital per hectare than their nonparticipant counterparts.

As expected, fixed capital per unit of labor increased with farm size. In the Zona da Mata region most larger farms have a significant dairy enterprise. Since dairying requires substantial fixed capital investments in the form of structures and the dairy herd itself, it is not surprising that fixed capital use is positively correlated with the size of the farm. On the other hand, the dairy enterprise uses relatively less labor than do crop activities. Therefore, fixed capital per unit of labor increases with farm size. The comparison of this ratio between participant and nonparticipant farmers shows that participants used slightly more fixed capital per man-day than nonparticipant farmers.


Operating Expenses

Operating expenses increased with farm size similar to the fixed capital stock pattern (Table 3-7). Overall, the operating expenditures of participant farms were 2.8 times those of nonparticipant farms.









Table 3-6. Average fixed capital per hectare and per man-day by class of producer and participation in
the PRODEMATA program, Zona da Mata, 1981-82


Class of producer

Owners (by farm size in hectares)
Sample
Sharecropper 0-10 10.01-50 50.01-100 >100 average

----------------------------- thousands of cruzerios------------------------Fixed capital stock
per hectare

Participants 5.348 98.305 62.003 49.592 35.908 63.149 Nonparticipants 12.558 89.493 48.649 39.922 31.417 51.370 Sample average 12.085 92.080 56.076 44.848 34.112 56.299 Fixed capital stock
per man-day

Participants 0.129 2.661 3.406 4.352 4.878 3.465 Nonparticipants 0.340 3.234 4.037 4.422 5.337 3.051 Sample average 0.326 3.066 3.686 4.386 5.062 3.224








Table 3-:7. Average operating expenses per farm by class of producer and participation in the PRODEMATA
program, Zona da Mata, 1981-82


Class of producer

Owners (by farm size in hectares) Sample
Sharecropper 0-10 10.01-50 50.01-100 >100 average

-----------------------------thousands of cruzerios------------------------Operating expenses
per farm
Participants 44.750 124.944 322.584 760.705 966.591 399.802 Nonparticipants 52.185 58.874 127.031 353.503 850.946 141.312 Sample average 51.698 78.270 235.788 560.946 920.333 249.462








Operating expenses per hectare decreased as the farm size increased as was the case for fixed capital (Table 3-8). The level of operating expenses per hectare was higher for the participant owners in all categories, particularly for those with farms in the 10.01-100 hectare range. This evidence may indicate that farmers in the mid-size categories have adopted modern inputs more intensively. If this is the case, they may be more receptive to the PRODEMATA program.

Operating expenses per man-day increased as the farm size increased. Comparisons between participant and nonparticipant farmers show that participant owners had many more expenditures per man-day than did nonparticipant owners. This seems to indicate that larger farmers, particularly participant owners, tended to substitute expenditures on operating inputs for labor.







Table 3-8. Average operating expenses per hectare and per man-day by class of producer and participation
in the PRODEMATA program, Zona da Mata, 1981-82


Class of producer

Owners (by farm size in hectares)
Sample
Sharecroppers 0-10 10.01-50 50.01-100 >100 average

----------------------------thousands of cruzerios------------------------Operating expenses
per hectare

Participants 7.200 19.434 12.798 11.675 7.605 13.247 Nonparticipants 12.743 14.265 6.027 4.907 5.060 9.894 Sample average 12.379 15.783 9.793 8.355 6.587 11.297 Operating expenses
per man-day

Participants 0.176 0.492 0.639 0.757 0.739 0.629 Nonparticipants 0.325 0.376 0.362 0.486 0.615 0.381 Sample average 0.316 0.410 0.516 0.624 0.689 0.484













CHAPTER IV
EFFICIENCY MEASUREMENT


Introduction

Most of the production studies which have been conducted in Brazil have fit production functions to cross-sectional data. The ordinary least squares (OLS) method, or some variant, has been used as the estimation procedure assuming the disturbances, which account for random shocks and error measurement, to be normally distributed. Because these models generate predicted values that may be smaller than observed values, the fitted production functions which result are actually average functions. However, the theoretical definition of a production function is given in terms of the maximum output rate obtained from a given set of inputs. Therefore, as the usually estimated functions are in fact average functions, they do not correspond to the theoretical notion of a production function. Unless technical efficiency is accommodated by a neutral scaling of the average functions, many inferences regarding allocative efficiencies may be incorrect. The framework used in this study takes into consideration this criticism of the traditional approach through the use of frontier production functions.

The first section of this chapter reviews the elements of the original Farrell approach to efficiency measurement and some contemporary efforts utilizing frontier functions. The conceptual framework








and the model to be used in this study are presented in the second section. The third section summarizes the estimation procedures employed to estimate a frontier production function.


Efficiency and Frontier Functions

Generally, three types of inefficiency are considered in the literature. The first is technical inefficiency, which arises from the failure to produce maximum output from a specified bundle of inputs. The second is allocative inefficiency, which results from the utilization of inputs in nonoptimal proportions for a given set of input prices. Allocative efficiency requires the equalization of marginal rates of substitution with input price ratios. The third is scale inefficiency, which arises from the failure to produce at the point where marginal cost and output price are equal.

Beginning with the work of Farrell (1957), a number of researchers have attempted to measure a "frontier" or "efficient" production function. Farrell introduced a technique by which the efficiency of a production process could be measured a-ndany observed-inefficiencies broken down into technical and allocative components.

The standard of efficiency used by Farrell was the frontier unit isoquant. Assume that X and X2 are the only inputs used in the production of output (Y) and that the firm's production function (a technical frontier) is given by Y = f(Xl,X2). Furthermore, assume that the production function is homogeneous of degree one in inputs so that it may be written as 1 = f(X1/Y,X2/Y). That is, the frontier technology can be characterized by the unit isoquant, denoted 10 in Figure 4.1.






















X2/Y


xI /Y


Efficient unit isoquant


Figure 4-1.








Let point XA in Figure 4.1 represent the firm's actual factor combination (XA,XA) used to produce unit output I0. The ratio of inputs
1inatio

needed to produce 10 to the inputs actually used to produce I1, oxB/oxA, measures the technical efficiency as defined by Farrell. Now assume for some set of input prices, that the line PP' is the firm's isocost line for which the cost of producing 10 is minimized with input combination XE. This isocost line intersects OXA at XC. Farrell's index of allocative efficiency is OX C/OX B, since the cost of point XC is the same as that of allocatively efficient point XE, and is less than that of technically efficient point XB. The overall productive efficiency is then calculated as the product of technical and allocative indices and is given by the ratio oxC/oxA. That is, Farrell efficiency measures associate a deviation from the frontier isoquant with technical inefficiency and a deviation from the cost minimizing input ratios with allocative inefficiency.

The efficient unit isoquant is not observable. Farrell's method of estimating the frontier isoquant involves the construction of an envelope of the observed input-output ratios by linear programing techniques. An index of technical efficiency can then be developed for each observation where the index is equal to the ratio of the maximum possible output to the observed output. This procedure has two main advantages: (1) it provides an estimate of technical efficiency for each individual observation and (2) it is not based on any specific mathematical model of the frontier. However, the method possesses two serious limitations:

(1) it presumes constant returns to scale and (2) it is quite sensitive to extreme observations or outliers. Also, there are statistical difficulties with this deterministic nonparametric frontier. Since no








assumptions are made about the properties of the disturbances, the parameters are not estimated in any statistical sense. They are simply computed via mathematical programming techniques.

Since the pioneering work of Farrell, several studies have been

evaluated production efficiencies-.using the frontier concept. Aigner and Chu (1968) expressed the frontier in a simple mathematical form. They specified a Cobb-Douglas production frontier requiring all observations to be on or below the frontier. This was accomplished by assuming that the disturbance term of the fitted function was one-sided. Following Farrell's approach, estimates were obtained by solving constrained programming problems, i.e., either by linear programming minimizing the sum of the absolute values of the residuals or by quadratic programming minimizing the sum of'squared residuals, subject to the constraint that each residual be nonpositive. As in Farrell's method the parameters were quite sensitive to extreme observations.

To compensate for this problem, Timmer (1971) proposed that the linear programming technique be modified to allow a certain proportion of the observations to be above the frontier as a device to reduce the effect of extreme measurement error on the estimates. While this procedure probably solves the outlier problem, it is purely arbitrary and has no statistical basis (Lee and Tyler, 1978).

The lack of identifiable statistical properties of the full frontier estimators, as proposed by Aigner and Chu (1968), has been pointed out by several authors (Lee and Tyler, 1978; Aigner, Lovell, and Schmidt, 1977; Greene, 1980). Schmidt (1976), however, pointed out that if the disturbance term has an exponential distribution, the Aigner and Chu








linear programming procedure is equivalent to a maximum likelihood estimator, while their quadratic programming estimator is a maximum likelihood estimator if the disturbance is half-normal. That the "estimators" are maximum likelihood is of little practical value, since the usual regularity conditions for the application of maximum likelihood are violated (Schmidt, 1976). Therefore, the statistical properties of the estimators cannot be established.

Greene (1980) examined the problem in programing models which

arises because the range of the disturbance depends upon the parameters being estimated. By considering the properties of maximum likelihood estimators, Greene shows that the irregular nature of the estimators is a consequenc-eof the choice of the disturbance distribution. He suggests an alternative estimator in which the disturbance has a gamma distribution with certain restrictions on the distribution parameters. Given these restrictions, and some additional assumptions (Greene, 1980), maximum likelihood estimation may be used as the usual case and standard errors for parameter estimates may be obtained.

More recently, frontier models have been specified by a stochastic frontier, or "composed error" model (Aigner et al., 1977; Meeusen and Broeck, 1977). The central idea behind the stochastic frontier approach is that the error term is composed of two components, a symmetric disturbance and a one-sided efficiency disturbance. The symmetric component allows for variation of the frontier across firms and represents the effects of random variation outside the control of the firm. The onesided component captures the deviation from the frontier function due to technical inefficiency.








A weakness of the stochastic frontier model is the impossibility

of decomposing the residuals into their components (Forsund et al., 1980). Therefore, it is not possible to estimate technical or allocative ineffiencies for a given observation.

Even though frontier estimators have some weaknesses, it seems clear that frontier functions are recognized as superior to Farrell's unit isoquant, notably in their statistical properties. An approach to efficiency measurement which combines Farrell's efficiency indices and frontier methods was proposed by Kopp (1981). Using Farrell's efficiency measure concepts in conjuction with full frontier production functions, Kopp's approach produces estimates of technical, allocative, and overall productive efficiency for each sample observation. The method does not require assumptions concerning homogeneity or homotheticity thus placing few restrictions on the form of the production function.

In a subsequent paper Kopp and Diewert (1982) proposed to measure technical and allocative efficiencies using the full frontier cost function. This method, which relies on duality theory, requires no direct knowledge of the parameters of the primal production frontier and provides efficiency measures in a relatively simple manner.

The possibility of measuring the total productive efficiency and its components at every data point constitutes a major advantage of the full frontier function. However, as Kopp (1981) recognizes, whenever one estimates a full frontier, sensitivity to outliers will be a problem and measures of technical efficiency can be underestimated.







Conceptual Framework

It is well known that either the cost function or the production

function can be used to define a production technology. Also, it has been shown that both technical and allocative efficiency measures can be obtained from the production function frontier or from the cost function frontier.

In this study, efficiency measurement follows Kopp and Diewert's

(1982) approach closely, relying on a full frontier cost function. Essentially, the method decomposes the deviations from a full frontier cost function into Farrell measures of technical and allocative efficiency. Unfortunately, the data on input prices which are necessary for estimation of the cost function were not available for this study. Therefore, a self-dual production function was estimated. This allows the analytical derivation of the corresponding cost function and thus the derivation of efficiency measures using the procedure proposed by Kopp and Diewert.1

The Model

Let the production function be specified as


Yi = f(TiLi'Mi) i = 1, . . ,n (4.1) where Yi is the output and T, Li, and Mi are, respectively, land, labor, and intermediate material inputs to the production process of the ith firm,2 and n is the sample size. Assuming that the firm's production

1Even though the efficiency measures can be derived directly from the full frontier production function, they were derived from the full frontier cost function in this study for reasons of computational convenience.
2A description of these variables is presented in Appendix B.








technology is characterized by a Cobb-Douglas production function, the model can be written in logarithmic form as

knYi =ZY n a + a 1n Ti + a 2 n Li + 3 kn Mi i=1,...,n (4.2)


where Bj(j = 1,2,3) are the unobserved parameters and a is the constant term.
The Cobb-Douglas production function has long been a target of criticism because of its admittedly restrictive properties. Recently, generalized functional forms have been suggested to allow the estimation of nonrestrictive substitution characteristics for production structures containing many inputs (Diewert, 1971; Christensen, Jorgenson, and Lau, 1973). By far the most widely used has been the translog function. However, alongside of the many advantages association with the generalized forms, a major disadvantage is the impossibility of providing an explicit dual solution for the cost function corresponding to the production function. Consequently, it is difficult to see exactly how the error term in one function relates to the error in the other function.

Since the focus of this study is not directed toward an analysis of the structure of production, but rather toward efficiency measures derived from cost function, the Cobb-Douglas function should provide a reasonable specification because of its self-dual characteristic.

The stochastic specification of the Cobb-Douglas production function given in Equation (4.2) can be expressed by










kn Y =n ax + z k. 9n Xij - ui = 1, . . . , n


j = 1, . . . , 3 (4.3)


where X is the vector of inputs (T, L, M), cx and $ are the vectors of fixed and unknown parameters to be estimated, and u is a random disturbance.

The deterministic part of Equation (4.3) gives the maximum value of the output Y, given the set of inputs T, L, and M. The disturbance u captures technical inefficiency as well as other random factors.

Following Schmidt and Lovell (1979), the dual cost frontier C(Y,P), where P is a vector of input prices, can be analytically derived from Equation (4.3),


kn C. = k + Z y. Zn P. + Y Yi + 1u 1 1j r 1 r 1


where C is the cost of the technically and allocatively efficient input set corresponding to output Y and input prices PT' PL' and PM' P is the vector of input prices (PT' PL' PM)' r is the sum of the j's (0 = 1,2,3), y is the vector of parameters of the cost function (in this case, yj : /r), and k is the intercept of the cost function, defined as


1 1 3
k = kn r- n - 9.n I









From the derived cost function, technical, allocative, and total

productive efficiency measures can be obtained following the methodology set forth in Kopp and Diewert (1982) as discussed in the next section. Farrell Measures of Efficiency

Consider Figure 4.1 which depicts the frontier unit isoquant for a linear homogeneous production technology which employs two factors Xl and X2 to produce some output Y. The assumption of a linear homogeneous technology can be relaxed by considering I0 as the technically efficient isoquant for some level of output obtained from a general full frontier production function. Assume that in Figure 4.1 point XA denotes the observed input levels, XA = (X~,X~) that produce output Y*. Given a 1' 2
set o inpu prics P 1' (P, that define the isocost line PP', the input levels at point E, XE = (XE XE), denote the technically and allo1' 2
catively efficient input levels.

Given the set of reference input prices P* = (PI,P2) and output Y*, the Farrell efficiency measures are given by


Technical efficiency (TE) = (P* � xB)/(P* � XA)


Allocative efficiency (AE) = (P* � xC)/(P* � XB) (4.5)


Total productive efficiency (PE) = (P* xC)/CP* � XA)

where P* xA = Z P* Xj is the actual cost of the inefficient input set;
j=l j i
P* xB= jl Pt XB is the cost of the technically efficient input set;
C
and * X j=l jt X is the cost of the technically and allocatively
j i j .








efficient input set, which is given by the cost-minimizing-input-demand equations. The input combination XA is known since it is the observed vector of inputs. Assuming that P* and Y* are known, it is necessary to obtain the values for XC and XB in order to evaluate technical, allocative, and total productive efficiency. The values for X and XB can be estimated using the production function (4.3) and its corresponding cost function (4.4), in which the input vectors shown in Figure 4.1 and the reference input price vectors are Xt (Tt, Lt, Mt)tA,BCE and = (P*, P*, P*), respectively. The input combination XE can be found from the frontier cost function C(Y*,P*). By Shephard's lemma (Diewert, 1971),


aC(Y*,P*)
apiP P;Y-Y*;,=T,L,M


gives the system of cost-minimizing-input-demand equations (point E in Figures 4.1) for T, L, and M, which, according to the cost function specification (4.4), can be written, in exponential form, as


TE Y1 C(Y*,P*)/P*


LE = y2 C(Y*,P*)/Pt (4,6)


ME = y3 C(Y*,P*)/P*


where


C(Y*,P*) = K P*Yl PY2 PY3 yYy
T ~L ~M








Y1= 1/r; Y2 = a2; Y3 = a3/r; yy = y/r


K : ek, and

k and r are as previously defined

The input bundle XC lies on the ray intersecting XA with the origin (Figure 4.1). The location of XC is determined by the intersection of this ray and the cost plane P* - XE = C(Y*,P*). Thus XC= XCxA where XC = C(Y*,P*)/(P* � XA). Therefore, the technically and allocatively efficient input set (TC, LC, MC) is given by


TC = [C(Y*,P*)/(P* � XA)J TA


LC = [C(Y*,P*)/(P* � xA) LA (4.7)


M = [C(Y*,P*)/(P* � XA)A MA

The bundle XB lies on the efficient isoquant and on the ray joining XA with the origin. Thus, XB can be expressed as


TB X BTA


LB X BLA (4.8)


MB X BMA for someX B

Since the bundle XB lies on the efficient surface, it will represent the efficient bundle for some set of input prices W* = (W*, W*, WM). Thus, T' L ~ hs








Shephard's lemma is applicable for the price vector W*, and XB can also be expressed as


TB = LB


MB =


Y1 C(W*,Y*)/W* Y2 C(W*,Y*)/W* Y3 C(W*,Y*)/W


(4.9)


C(W*,Y*) = K WT W*


W*Y3 y.YY
M


The equations in (4.8) and (4.9) can be solved by normalizing one input price (i.e., let W* WT/WT 1). Then the model may be expressed in terms of normalized prices and the equation in (4.9) can be rewritten

as


B y C(W*,Y*) LB = Y2 C(W*,Y*)/WL MB = Y3C(W*,Y*)


since W*_ 1


(4.10)


^* 'l *Y2 ^Y3 YY ^ .*. C(W*,Y*) = K 1 W ; W = W/WT and


where


where







The term X B can be eliminated from Equations (4.8) by dividing the left-hand side vector by MB and by dividing the right-hand side vector by X BMA The resultant equations are of the form


LB/MB LA /MA e
(4.11)

TB/MB T AA/MA 2


where 01 and 02 are fixed constants given that TA, LA, and MA are observed values.
From equations in (4.10) and (4.11) the following results can be derived:

LB/MB Y2C(W*'Y*) Y3CI.*,Y*) Y2 1
LB/M - e

L ^M 'Y2 W*
L 3Y3 =61




and


BB Y3 C(W*,Y*) W,
/M YjC(W*,Y*) A' ' i 2 M 3Y3


W* Y3 2


Thus,

* Y2 3 Y2 e2 L Y30 elYl2 Yl 6







and the equations in (4.9) can be solved for TB, LB, and MB. After the bundles (TC, LC, MC) and (TB, LB, MB) are determined, the efficiency measures as previously defined may be calculated.


Estimation Procedure

The estimation of the production function given in Equation (4.3) was performed using the procedures described in Greene (1980). Two distinct estimators were utilized to obtain parameter estimates of the full frontier model. The first is a corrected ordinary least squares estimator with an intercept adjustment (COLS). This procedure assumes that the frontier is a neutrally scaled average function. The second procedure is maximum likelihood estimation (ML) process. The full frontier production function was fitted using the two estimators for each group of farmers based upon whether or not they participated in the PRODEMATA program.

Corrected Ordinary Least Squares (COLS) Estimation
Assume the production function as specified in (4.3). If, with the exception of a nonzero mean for the disturbance, all of the assumptions of the Gauss-Markov theorem are assumed to apply to the specification in (4.3), then it can be shown that ordinary least squares (OLS) provides consistent estimates of , but that the estimate of the intercept is inconsistent. However, the OLS intercept estimator is consistent for a + p, where p = (E(u).
Greene (1980) has shown that, regardless of the distribution of u, the OLS residuals can be used to derive consistent estimates for a. Denote the smallest OLS residual by e(l). By definition, e(l) < 0.






Let a be the estimated value of Zn a. Assuming a > 0, then subtracting e(l) from 3 yields e! = [kn Yi - (a - e(1)) - Zaj kn Xij] or, equivalently, e [(& - e(l)) + Zj Zn Xij) - kn Yi]. The corrected estimate & & e(l) has been shown by Greene to be a consistent estimate. The resulting residuals (i.) will be nonnegative with the equality ii = 0 holding at one observation.

Although estimates for all parameters of the frontier function can be obtained using this simple modification of the OLS estimator, the results are appropriate only if the errors are symmetrically distributed. If this is the case, then the frontier function is simply a scaled version of the average function. Therefore, measures for the marginal rate of substitution and allocative efficiency derived from Equation (4.3) will produce the same result in either COLS or OLS.

The distribution of u in Equation (4.3) can be of different shapes. As a consequence, the parameter estimates of the frontier and average functions can be quite different depending on the degree of skewness of the distribution. Greene (1980) points out that a maximum likelihood estimation which takes into account the distribution of u should be more efficient than COLS, particularly if the error distribution is highly skewed.

Maximum Likelihood (ML) Estimation

Consider the model as specified in (4.3). The disturbance u is

assumed to have a gamma distribution, i.e., u n. G(X,Z). In addition, the restrictions X > 0 and Z > 2 are necessary to ensure that the likelihood function is well behaved (Greene, 1980). Given this disturbance specification, then the necessary regularity conditions required for ML and the usual asymptotic properties of ML estimators are satisfied. The log







likelihood function for the model is


log L = n Z log X - n log r(Z) + (Z - 1) 7 log ui - x 7 ui (4.12)

1 1
where u i = kn a + Ea i kn Xij - Zn Yi. By using the method of squaring to impose the restrictions that X > 0 and Z > 2, the log likelihood function becomes
log L = n(Z2 + 2) log X - n log r(Z2 + 2) + (Z2 + 1) 7 log u.




- 7 ui (4.13)
1

where

Z, = vT -2 and X. =


The maximization of (4.13) can be accomplished by minimizing the negative of the log likelihood function with respect to the parameter vector 0' = (X., Z., a, ). The method used to obtain the parameter estimates is a modified method of scoring utilized by Greene (1980). The convergence criterion in the iterative procedure was that the individual change in the estimates for a and the $'s from the sth iteration to the next were smaller than 10-4. The starting values for a and a were the consistent estimates obtained from the COLS procedure outlined above. Consistent starting values for X* and Z. were slightly more difficult to obtain. Denote ^2(e) = S2 and E(e) = e as the variance and the mean of the modified set of residuals. Given that e = Z/X and S2 = Z/X 2 are consistent estimates for 2(e) and E(e), respectively, X = e/S and Z = 2/2 are appropriate consistent starting values for X and Z. Since any








continuous function of a consistent estimator is itself consistent (Kmenta, 1971, p. 166), substituting X2 for X and Z + 2 for Z the starting values for X, and Z, are then determined as


:j = and Z, = - 2]



The ability to obtain the ML estimator with all the desirable

properties for the estimates constitutes a major advantage of Greene's (1980) formulation. Furthermore, since the gamma distribution can be asymmetric, ML estimation of the parameter vector 4' should be more efficient than OLS which does not account for this fact. In general, the gain in efficiency obtained by ML is related to the degree of skewness of the distribution which is approximated by 2/V2-. Greene suggests the ratio Z/(Z - 2) as an indicator of the relative asymptotic efficiency of ML over COLS. Therefore, the smaller the value of Z the greater the degree of skewness and the greater the gain in efficiency.

The degree of skewness also has some implications with respect to the relationship between the frontier and average functions. Suppose the process generating the disturbances is such that the error distribution is fairly symmetric. The estimate of Z will tend to be large and the frontier function will tend to be a neutrally scaled version of the average function. On the contrary, if the distribution is highly skewed, the frontier function will be a nonneutrally scaled transform of the average function.













CHAPTER V
EMPIRICAL RESULTS

This chapter is divided into two major sections, In the first

section the estimated full frontier production functions and the corresponding frontier cost functions are analyzed. In the second section estimates of efficiency measures derived from the frontier estimates are considered.


Model Estimation

Full frontier Cobb-Douglas production functions were estimated

using sample data for participants and nonparticipants in the PRODEMATA program. These frontier production functions generated the dual cost frontiers which were analytically derived. Corrected ordinary least squares (COLS) and maximum likelihood (ML) estimation procedures were used in this study. The estimates obtained for the frontier production functions and the derived estimates for the frontier cost function are discussed below.


Frontier Production Function

The full frontier parameter estimates for both groups of farmers are presented in Table 5-1. As expected, all input coefficients


IA description of the variables used for estimation is presented in Appendix B.








Table 5-1.


Corrected ordinary least squares (COLS) and maximum production function for each group of farmers, Zona


likelihood (ML) estimates of the frontier da Mata, 1981-82


Intermediate
Method Constant Land Labor materials


COLS

Participants 3.08973 0.08547 0.70995 0.24388 1.03930 (0.34333)a (0.05124) (0.09454) (0.05246) (0.06567) Nonparticipants 4.78728 0.12272 0.58316 0.28222 0.98810 (0.22210) (0.03805) (0.06173) (0.03572) (0.02892)


ML

Participants 3.34963 0.04813 0.79484 0.25345 1.09643
(b) (0.04478) (0.05871) (0.05117) (0.03432) Nonparticipants 4.99502 0.09571 0.65965 0.25227 1.00764
(b) (0.03009) (0.03416) (0.03383) (0.01419)


a Numbers in parentheses are asymptotic standard errors of the coefficients. Greene (1980) argued that it is not clear what standard error is appropriate for the COLS intercept estimate. He suggested that the original estimate of the standard error obtained from OLS shoud be a good approximation.
bLess than l0-7.







estimates are positive. In addition, with the exception of the land coefficients in the participant group, all coefficients are significantly different from zero at the 1 percent level of statistical significance.

In comparing the results obtained by ML with those obtained by COLS, some slight differences were observed. In general, the differences were relatively more pronounced in the estimates for participant farmers. As expected, the ML estimates for the intercept term are higher than those of the COLS for both groups of farmers. The land coefficient estimates are relatively much smaller in the ML procedure than in the COLS procedure, especially for the participant group. Even though these differences are relatively large on a percentage basis, they are less than one COLS standard error of the respective land coefficients.

In general, the differences between the ML and COLS estimates

were not very large. In no case was the difference between the estimates greater than a single COLS standard error of the respective coefficent.

The differences between the ML and COLS estimates depend on the skewness of the disturbance distribution as mentioned in the previous chapter. Because the degree of skewness is approximated by 2/VT for the gamma distribution, large values of the Z parameter of the disturbance distribution imply a less skewed distribution. Therefore, in light of the relatively large estimates (2) obtained for the Z parameter (Table 5-2), the similarities which were found between the ML and COLS are not surprising.

Table 5-2 provides a comparison of the estimated ML distribution parameters for the two groups of farmers. The skewness measures for








Table 5-2. Summary statistics for the frontier production function disturbance distributions for each
group of farmers, Zona da Mata, 1981-82


Summary measures


Mean ,(ZI/X) Variance (Z/X) Asymptotic efficiency ratio (Z/Z-2) Skewness (2//Z) Degrees of excess (6/Z)


Group of farmers

Participants Nonparticipants

8.3475 11.6493 (0.8843)a (1.0422) 16.3315 35.2710 (1.7146) (3.1375) 1.9565 3.0277 0.2344 0.2599 1.1396 1.0601 0.4949 0.3368 0.3674 0.1701


aNumbers in parentheses are asymptotic standard errors of the estimates.










the participants are about 1.5 times that of the nonparticipants. This finding indicates that the estimated disturbance distribution tended to be more symmetrically distributed in the case of the nonparticipants than in that of the participants.

The degree of excess is a measure of nonnormality. It approaches zero as the error distribution tends toward normality. Since the estimated degree of excess is twice as great for the participant group as-for the nonparticipant group, the error distribution is closer to normality in the case of nonparticipant farmers. As a result of these findings, only a marginal gain in statistical efficiency was obtained for the group of nonparticipants when the ML procedure was used. The asymptotic ratio efficiency was 1.0601; i.e., the gain in statistical efficiency was about 6 percent. Thus, the frontier function can be viewed as an approximation of a neutrally scaled version of the average function in the case of nonparticipant farmers.

For the participant group the results are somewhat different.

The value of 16.3315 for Z gives an asymptotic efficiency ratio of 1.1396. Consequently, the gain in statistical efficiency was about 14 percent. This greater gain in statistical efficiency is a consequence of a more skewed disturbance distribution in this group as compared with that of the nonparticipants. As a result, the frontier function for the participant group is less related to the average function than is the case with the nonparticipant group.









Frontier Cost Function

For each production frontier the dual cost frontier was derived analytically. The results are presented in Table 5-3. From the estimated parameters and the corresponding standard errors, it can be seen that, except for the coefficients for the price of land in the participant group, all coefficients are significantly different from zero at the 1 percent level of statistical significance.

The coefficients in the cost function represent the cost shares for the use of each input. Labor accounts for the greatest share of the total cost. This is not surprising. Labor is a relatively abundant factor in the Zona da Mata. High unemployment, coupled with low wages, may contribute to a high level of labor use.

The estimated labor share is consistent with the actual pattern of labor use found in the sample. As shown in Chapter III, labor costs accounted for more than 60 percent of the variable input costs. This high labor share is also consistent with the findings of Silva (1981) which show that labor costs accounted for about 70 percent of input costs in most enterprises analyzed in the Zona da Mata in the 1977-78 crop year.


Efficiency Measures
The derived cost function frontiers provide the necessary information to calculate efficiency estimates for each observation. The reference prices used to compute technical and allocative efficiency are the following: (a) for land, the average rent paid per hectare of productive land in the survey year (Cr$2780.00); (b) for labor, the average









Table 5-3.


Derived COLS and ML estimates da Mata, 1981-82


for the cost function frontier for each group of farmers, Zona


Method Constant PT PL PM Y


COLS

Participants -2.16692 0.08224 0.68310 0.23465 0.96218 (0.04949)a (0.06175) (0.04578) (0.08724) Nonparticipants -3.91673 0.12419 0.59018 0.28562 1.01204 (0.03981) (0.05112) (0.04388) (0.03539)
ML

Partici pants -2.34605 0.04389 0.72494 0.23116 0.91205 (0.04016) (0.05371) (0.06763) (0.01945) Nonparticipants -4.10950 0.09498 0.65465 0.25036 0.99242 (0.02888) (0.05119) (0.03538) (0.01711)


aNumbers in parentheses are asymptoticstandarderrors., hey were obtained viaan approximate formula for the determination of the variance of resulting estimators which are nonlinear functions of the unrestricted estimators (Kmenta, 1971, pp. 442-45).







wage paid for daily labor of one equivalent man-day during the agricultural year (Cr$429.30); and (c) for intermediate material inputs, an aggregate index of the price paid by producers for agricultural inputs in the state of Minas Gerais2 (Cr$227.02 per unit of intermediate material input).

For an individual firm it is reasonable to assume that the supply of inputs is perfectly elastic. Therefore, input prices can be taken as fixed, exogenous variables. Moreover, since the Zona da Mata region is a fairly small region, it may be assumed that all farmers face the same set of prices. Therefore, the selection of a single vector of prices for all sampled farms is a reasonable assumption.

Tables 5-4 and 5-5 show the average efficiency measures which were calculated using the procedure outlined in Chapter IV, Equations (4.5). The results are given for both the COLS and ML estimates. These results are discussed below.


Technical Efficiency

Results. A notable feature of the findings is the low level of technical efficiency estimates compared to the much larger measures of allocative efficiency. The unduly low technical efficiency may be due in part to the full frontier specification. As pointed out previously, this method is highly sensitive to outliers. The high degree of technical inefficiency may also be a result of the degree of traditionalism in the agriculture of the region. As was mentioned in Chapter II, the


2The Centro de Estudos Agricolas of the Fundacao Getulio Vargas (FGV) pulishes a monthly index of prices paid and received by farmers in each state of Brasil. The index used corresponds to the average for the 1981-82 crop year, calculated by FGV with 1966 used as the base year (price = 100).








Table 5-4.


Average efficiency indices (calculated via COLS estimates) for each group tenancy category, Zona da Mata, 1981-82


of farmers and by


Class of producer (by farm sige in hectares)

Owners
Efficiency Sample indices Sharecroppers 0-10 10.01-50 50.01-100 >100 average

Technical efficiency
Participants 0.731 0.321 0.320 0.365 0.373 0.340 (O.ll9)a (0.021) (0.015) (0.028) (0.037) (0.011) Nonparticipants 0.104 0.070 0.082 0.074 0.076 0.082 (0.07) (0.004) (0.011) (0.006) (0.009) (0.04) Allocative efficiency
Participants 0.926 0.859 0.793 0.710 0.666 0.785 (0.048) (0.022) (0.012) (0.021) (0.022) (0.009) Nonparticipants 0.878 0.907 0.889 0.828 0.764 0.881 (0.020) (0.011) (0.010) (0.022) (0.035) (0.007) Total Productive
efficiency
Participants 0.665 0.274 0.252 0.252 0.243 0.264 (0.089) (0.019) (0.012) (0.016) (0.022) (0.009) Nonparticipants 0.091 0.062 0.069 0.062 0.058 0.071 (0.007) (0.004) (0.007) (0.006) (0.006) (0.003)


aNumbers in parentheses are asymptotic standard


errors of the means.








Table 5-5.


Average efficiency indices (calculated via ML tenancy category, Zona da Mata, 1981-82


estimates) for each group of farmers and by


Class of producer (by farm size in hectares) Owners
Efficiency Sample indices Sharecroppers 0-10 10.01-50 50.01-100 >100 average


Technical efficiency
Participants 0.394 0.179 0.174 0.195 0.202 0.185 (0.066)a (0.011) (0.007) (0.014) (0.021) (0.006) Nonparticipants 0.071 0.050 0.059 0.053 0.056 0.058 (0.005) (0.003) (0.008) (0.004) (0.006) (0.003) Allocative efficiency
Participants 0.901 0.834 0.749 0.658 0.608 0.743 (0.047) (0.022) (0.012) (0.021) (0.022) (0.010) Nonparticipants 0.880 0.894 0.850 0.772 0.703 0.856 (0.020) (0.012) (0.011) (0.023) (0.035) (0.008) Total productive
efficiency
Participants 0.349 0.148 0.129 0.125 0.119 0.136 (0.046) (0.010) (0.006) (0.007) (0.011) (0.004) Nonparticipants 0.063 0.043 0.047 0.042 0.038 0.049 (0.005) (0.002) (0.004) (0.004) (0.004) (0.002)


aNumbers in parentheses are asymptotic standard


errors of the means.








Zona da Mata experienced its heyday several decades ago when coffee was the leading enterprise in the area. Thus, it is possible that the region is still in an adjustment process from the coffee eradication program sponsored by the government in the mid-1960's. Some farms with high degrees of efficiency may already have achieved this adjustment. In a very traditional area, however, it is not surprising for the adjustment to come slowly; therefore, the high degree of technical inefficiency may reflect this slow pace of adjustment.

Comparison by tenancy. In both the COLS and ML estimates technical efficiency tends to be quite uniform across different sizes of owned farms. However, one result which stands out is the higher technical efficiency of the sharecroppers compared to that of the owners, especially in the case of the participant farmers. The technical efficiency indices for the participant sharecroppers should be regarded with the utmost caution since they are based upon a very small number of observations. In addition, this class of producers has no tradition of participation in supervised credit programs. However, the nonparticipant sharecroppers, whose number in the sample is much greater, also had a relatively higher technical efficiency than the nonparticipant owners.

The better performance by the sharecroppers may have several

plausible explanations. First, since most sharecropping contracts are verbal and short term, sharecroppers do not usually cultivate perennial crops or maintain livestock under the sharecropping agreement. Thus, the level of output per unit of input used was much higher in the case of the sharecroppers (Table 5-6). These higher output/input ratios








Table 5-6. Output/input ratios obtained by sharecroppers and by the
owners in the Zona da Mata, 1981-82


Unit of
Class of Output ntermediate producers Output/land Output/labor materials (Cr$/ha) (Cr$/man day) (Cr$) Sharecroppers 85,000 2,055 35.75


Owners 42,000 1,966 5.64


for the sharecroppers may also partially be explained by the higher crop yields obtained by this class of producers compared to the owners. The sharecroppers, using their own labor can exert better control over their activities and so may obtain higher productivity than their owner counterparts who tend to hire labor.

A second explanation for the higher technical efficiency presented by the sharecroppers may be the prevalence of intercropping in the region. Corn is intercropped with beans by most of the producers, particularly by sharecroppers and the smallest farmers. Vieira (1978) pointed out this fact and suggested that the intercropping practice is both a resource-use-optimization strategy and a means to ensure diversified diets and income sources.

Finally, it is possible that the sharecroppers use less labor per unit of cropland as compared to the owners, which may contribute to the former's better performance. Sharecroppers frequently have offfarm jobs as an important source of income. Thus, it may be argued









that sharecroppers have a very accurate perception of the opportunity cost of their labor which is explicitly specified by off-farm jobs. As a consequence, sharecroppers may tend to use their labor more efficiently in the sharecropped areas in order to increase their labor availability for off-farm opportunities. On the other hand, the opportunity cost of labor for the owners may be much less explicit than is the case with the sharecroppers. Thus, it is possible that the owners use more labor in crop areas than would be recommended, a situation which contributes to a decrease in their level of efficiency.

Comparison by group. For ease of comparison between the efficiency measures obtained for participants and nonparticipants in the PRODEMATA program, Table 5-7 presents the ratio of the participant to nonparticipant efficiency. This table was taken directly from Tables 5-4 and 5-5.

The-efficiency measures derived from COLS and ML show that, on the average, technical efficiency for the participants was about three to four times higher than for the nonparticipants.3 On the average, the technical efficiency measures obtained via the derived cost function when the ML estimates were used (Table 5-5) are 0.185 for the participants and 0.058 for the nonparticipants.4



3In Appendix C it is demonstrated that, under certain assumptions, the technical efficiency averages for the two groups are statistically different in each tenancy class and in the sample as a whole.
4These figures are fairly close to the values of the technical efficiency measures estimated directly by the disturbance distribution as suggested by Greene (1980). As pointed out in the specification of Equation (4.3), the disturbance term u captures technical inefficiency in production and other random factors. Under the assumption that u has a gamma distribution, i.e., u '\ G(X,Z), Greene pointed out that the average technical efficiency may be estimated by (X/X+l)Z. The average values of technical efficiency estimated via the efficiency distribution were 0.1578 for the participant farmers and 0.054 for the nonparticipant farmers.








Table 9-7. Efficiency index ratios between participant and nonparticipant farmers, Zona da Mata, 1981-82 COLS ML
Efficiency indices Participants Nonparticipants Ratio Participants Nonparticipants Ratio Technical efficiency 0.340 0.082 4.15 0.185 0.058 3.19 Allocative efficiency 0.785 0.881 0.89 0.743 0.856 0.87 Total productive
efficiency 0.264 0.071 3.72 0.136 0.049 2.77










The much higher technical efficiency shown by the participants indicates that the sampled farms participating in the PRODEMATA program tended to be grouped closer to their frontier than were the nonparticipating farms. This pattern also holds for different farm sizes. That is, technical efficiency is always greater for the PRODEMATA participants than for the nonparticipants, irrespective of farm size. These results could suggest that the PRODEMATA program exerted a substantial impact on technical efficiency.


Allocative Efficiency
Results. Data in Tables 5-4 and 5-5 show that both groups of farmers were much more efficient in an allocative sense than in a technical sense. Relatively high levels of allocative efficiency were found when either the COLS or the ML estimates were used.
The similarity between the allocative efficiency indices derived from the COLS and ML estimates is a consequence of the similarity of the COLS and ML frontiers. This is particularly noticeable for the nonparticipant group. Since the COLS frontier for this group can be viewed as an approximation of a neutrally scaled version of the average function, the marginal rates of substitution between inputs will be very similar whether derived from the COLS frontier or from an average function. Therefore, allocative efficiency measures for this group will be similar whether derived from the frontier function or from an average function.










Comparison by tenancy. Unlike in the case of technical efficiency, the high levels of allocative efficiency tend to decrease slightly as farm size increases. These results appear to support the argument that traditional agriculture, especially among the smaller farmers, is not necessarily inefficient in allocating resources.

The high degree of allocative efficiency presented by the sharecroppers and smaller farmers may be a response to the severe restriction in resources faced by these producers. In addition, since these classes of producers raise food crops as their primary activity, they may strive more for better resource allocation.

Comparison by group. In comparing the allocative efficiency between the two groups, the results indicate that the nonparticipants had indices which were greater than those of the participants.5 Initially this is surprising. However, there may be several explanations for these findings. First, it may be argued that nonparticipant farmers, facing more restrictions in resources, might be forced into allocative efficiency. Second, it is possible that participant farmers face difficulties in adjusting to marginal conditions for the best allocation because of the effects of the learning process in adopting new agricultural practices.



5In Appendix C a statistical test indicates that, with the exception of sharecroppers, the allocative efficiency averages for the two groups are statistically different in each tenancy class and in the sample as a whole.










Finally, an alternative explanation for this result is that additional capital made participant farmers less efficient. It is possible that participant farmers had been allocatively efficient prior to PRODEMATA but that with additional capital resources flowing into their production systems, some inefficiencies may have been introduced. This possible drop in efficiency may have occurred because of changes in the quantity of inputs used or in their relative prices. Certainly, if allocative efficiency existed before the initiation of the PRODEMATA program and if this program induced changes, then it is quite likely that allocative efficiency was disrupted. As cited in Chapter I of this study, some authors have argued that few significant inefficiencies in the allocation of the factors exist in traditional agriculture. Thus, the findings of this study appear to corroborate the argument that farmers in traditional agriculture, although poor, allocate their resources efficiently.


Total Productive Efficiency

Tables 5-4 and 5-5 also show the figures obtained for total productive efficiency. Since this efficiency measure is defined as the product of technical and allocative efficiencies, there is no need to present a full discussion of these findings, which reflect the pattern already discussed for the two components of total productive efficiency. However, a result which should be noted is related to a comparison of the results by groups. The participant group was found to be considerably more efficient. Although this group is at a slight









disadvantage in the allocative efficiency component, its higher technical efficiency was strong enough to put it in a slightly better position in total productive efficiency.


Summary of Findings
1. The average technical efficiency of the participant group was significantly greater than for the nonparticipant group in each tenancy class and in the sample as a whole.
2. Technical efficiency levels and farm size seem to be unrelated; i.e., technical efficiency indices for the owners tended to be quite uniform across different sizes of farm. However, the average technical efficiency by the sharecroppers was significantly higher than that by the owners.
3. Both groups of farmers had relatively high levels of allocative efficiency. The nonparticipant group had an average allocative efficiency which was higher than that of the participant group for all tenancy classes (except sharecroppers) and for the whole sample.

While statistically significant differences have been found

between participants and nonparticipants in both technical and allocative efficiency (Tables C-l and C-2, Appendix), it remains to be determined whether such differences are a consequence of participation in PRODEMATA, or of other farm or farmer characteristics that are associated with participation in the program. That is, the measured differences in technical and allocative efficiency may be caused by PRODEMATA participation or may be simply associated with participation, both of which are caused by some third factor.









As shown in Chapter III, those farmers who participated in

PRODEMATA have larger farms, own more capital, and use more purchased inputs than nonparticipants. Could it be that these and other fundamental differences between participants and nonparticipants which existed prior to the initiation of PRODEMATA are the cause of the estimated differences in technical and allocative efficiency rather than participation in the program itself? The next chapter deals with this question.













CHAPTER VI
DISCRIMINANT ANALYSIS OF PARTICIPATION.CHOICE


Introduction
The analysis described in this chapter is designed to determine

which farmer attributes are associated with participation in the PRODEMATA program. A discriminant model was used to examine numerous characteristics of farms and farmers in an attempt to determine which of them were best able to distinguish between participants and nonparticipants in the program.
The initial sections of this chapter deal with methodological considerations, including definitions, basic assumptions, and the theoretical model used in discriminant analyses. In the final section, the empirical model used is formally presented and the results are examined.


Linear Discriminant Model

The basic idea of discriminant analysis is that a linear discriminant function exists which will, as best as possible, classify farmers into predetermined statistically separate groups. The discriminant function is of the form

D = d1Z1 + d2z2 + d3z3 + . + dkzk (6.1)


where the dependent variable D is the discriminant score, the d's are discriminant coefficients, and the z's are the values of the k discriminant variables used in the analysis.









The estimation problem is to assign values to dl,d2,d3,...,dk, that maximize the ratio of the variance between the group means to the

variance within groups. Let d equal the vector of discrimin.ant coefficients and Z equal the population vector of the k discriminant variables. Thus, if D = d'Z has mean d'Z1 in group l and d'Z2 in group 2 and if the covariance matrix of Z = E in both groups, the discriminant function is that one which maximizes


(d'Z1 - d'Z2)2

d'Ed

By differentiating this expression with respect to d and setting the derivations equal to zero, the d's are found to be proportional to Z_-l(ZI - Z2). Since Zl, Z2, and Z are generally unknown, they are estimated as 7l' Z2' and S, where Z1 and Z2 are the sample mean vectors of the discriminant variables for the two groups, and S is the pooled estimate of the common E. Therefore, an estimate of the vector d is given by d = S -l( 1 - 1

Once the discriminant function is specified, the cutoff point between the two groups is determined. The cutoff point is used for classification purposes of subsequent observations. According to Morrison (1976), an observation will be classified as belonging to group 1 if


Z'S1-IzI - Z2) - I/2(Zl + Z2)1 S-1 (ZI - Z2) > log P (6.2a)


or in group 2 if

1Further detail on discriminant analysis theory is presented in Morrison (1976).








z's-1(7l - 12) - 1/2 (_Zl + Z2)l S-1 (Y1 _ z2) < log P (6.2b)


where the strictness of the equality is arbitrary for continuous variables; P is given by

p2C (1.12)
plC (211)

where p1 and P2 are prior probabilities, i.e., the probabilities of classifying an observation into group 1 or into group 2, respectively; and C(il)i=l,2; j=l,2; ij is the cost of misclassifying an observation from the jth group as being from the ith group. In the absence of other information, if the misclassification costs are assumed to be equal and the prior probabilities of each population to be one-half, then P = 1 and the classification rule states that an observation should be classified in group 1 if


Z's-I (Yl - Y2) > 1/2 (Y1 + z2) s-I (Z1 - Y2) (6.3)


and in group 2 otherwise.

The expression Z'S1(zI - Y2) in (6.3) is the population linear discriminant function which gives the discriminant score for each individual observation when evaluated for the discriminant variables of that particular observation. The expression 1/2 (ZI + 12) S (Z - 2 is the point midway between the means of the discriminant functions for each group.









Evaluating the Discriminant Function

The performance of the discriminant function can be evaluated in terms of three major aspects: (1) the significance of the observed differences between groups, (2) the relative importance of each variable in the discriminant function, and (3) the ability of the model to classify future observations.

Differences between Groups

To test for differences between groups a Chi-square test is used (Gau, 1978) where the null hypothesis is that the sample group mean vectors are equal. By employing Wilk's lambda,

Iwl
A =-W
ITI


where W is the pooled within-groups sum-of-squares matrix and T is the total sum of squares, a test statistic can be calculated by


H = N- 1 - Kn A


where

N = total sample size

K = number of explanatory variables

G = number of groups

The calculated H, which is distributed as a Chi-square with K(G - 1) degrees of freedom, may be used to test the null hypothesis.









Relative Importance of Variables

The relative importance of each variable in the discriminant function can be measured by either of two methods: (1) ranking variables according to the size of their standardized coefficient, or (2) ranking variables according to the size of their weighted discriminant coefficients.

The standardized coefficient method weights each coefficient in the discriminant model by its standard deviation. Essentially, the standardized coefficients scale the discriminant coefficients in a similar way to the beta coefficient used in regression analysis. The absolute value of each standardized coefficient represents the relative discriminatory power of the variable in the discriminant function.

Joy and Tollefson (1975) argue that the standardized coefficient

method is not appropriate to assess the importance of variables in a discriminant function. They suggest using a weighted discriminant coefe ijl ) where di(i=l,...,k) is the estimated discriminant
f c e t d l - . t h t
coefficient, and Zjk is the mean of the j variable for the kth group. Classification Ability

The ability of the discriminant function to classify future observations is suggested by the apparent error rate. This rate is defined as the fraction of observations in the sample which are misclassified by the estimated discriminant function.

In the following sections the theory of discriminant analysis

described above is applied to the PRODEMATA data, beginning with a discussion of the discriminant variables included in the empirical model and followed by an analysis of the results.










Selection of Discriminant Variables

The explanatory variables were chosen from a large number of socioeconomic characteristics of each farm unit interviewed. From this set of characteristics, only those which were less likely to be affected by the PRODEMATA program were selected as potential candidates for the analysis. This is because if variables which might have been affected were used, it would be difficult to separate the cause of the participation from the effect of the participation.

When two or more variables were found to be highly correlated,

only one was included, as otherwise it would be difficult to determine which one is exerting the greater discriminant effect in the function. The final configuration of the discriminant model included the following variables:2

Crop land (CROLAN)

Pasture land (PASLAN)

Fixed capital stock (FIXK)

Cooperative membership (COOP)

Age of the respondent (AGE), and

Education level of the respondent (EDUC)
A brief discussion of the expected influence of each variable is presented below.
Crop land. Crop farmers use far more purchased inputs per hectare than is the case for livestock. This may imply that producers with


2A description of these variables is presented in Appendix B.









larger areas in crops have greater borrowing requirements and thus a greater need to participate in a credit program such as PRODEMATA.

Pasture land. The PRODEMATA program was derected toward small farmers, who tend to be crop oriented; larger farmers who have larger areas in pastures may be less interested in entering the program. Therefore, farmers with more pasture land would be less likely to participate in the program.
Fixed capital. Farmers who have more assets may also have greater flexibility in making changes in technology. Therefore, they would be more likely to participate in the program.

Cooperative membership. This characteristic was taken as a proxy for the degree of information available to the farmers. It is assumed that members of farm cooperatives have more complete knowledge about specific credit programs than nonmembers and, therefore, may have a greater tendency to participate in the PRODEMATA program. In addition, cooperative members probably are accustomed to working with the extension service and institutional credit sources. Finally, they may have better records than nonmembers which would make it easier for them to obtain credit.

Age. The need for credit may vary inversely with age since older farmers should have achieved higher levels of capital accumulation than is the case for younger farmers.

Education. The educational level among the farmers in the area is very low. In the sample, about 30 percent of the farmers were illiterate and 66 percent had four years or less of formal education. This low









educational level may influence the willingness to accept a formal loan which requires a substantial amoung of paper work and visits to the bank. Therefore, less educated farmers may prefer to obtain their loans from informal sources, rather than to participate in a supervised credit program.

Analysis and Results

The estimated model includes all six variables described above:


D = d0 + d1 CROLAN+ d2 PASLAN+ d3 FIXK+ d4 COOP+ d5 AGE+ d6 EDUC


The coefficients for this six-variable function were estimated

using the "direct" method of the SPSS subprogram discriminant (Nie et al., 1975). The results are presented in Table 6-1. The overall means of the discriminant variables for all farmers, the means for each group of farmers, and student t-statistics, to test the null hypothesis that the means for each group were equal, are also presented in Table 6-1.

To estimate the average discriminant score for each group, the group means were substituted in the estimated equation. The result was Dp = 0.48747 and DNP : -0.35067 for participants and nonparticipants, respectively.
Given that the cost of misclassification are the same and assuming the prior probabilities were equal, then the cutoff point can be calculated by substituting the overall means into the estimated discriminant function. The result was DCp Z 0.0. All producers with discriminant scores above zero would be classified as potential participants, whereas









Table 6-1. Discriminant coefficients, overall means, group means, and t-test levels of significance for
differences in mean values between participants and nonpartTicipants


Group means ProbaEstimated discriminant Overall bility Variables coefficients variable means Participants Nonparticipants I!1


CROLAN PASLAN

FIXK COOP AGE EDUC Constant term


0.07252106

-0. 00802323 0.00021614 0.88115770

-0. 03980932 0.07523472 1.19030600


7.151

21. 950 1 4331.474

0.223 54.643

2.103


9.759

27.228 1,892.135

0.324 52.090

2.490


5.274 18.153 928.153 0.150 56.470 1.820


0.0001 0.0036 0.0001 0.0010 0.0001

0.0004








producers with discriminant scores below zero would be classified as potential nonparticipants.

The signs of the discriminant coefficients were, in general, as

expected. For example, the coefficient for age has a negative sign which implies that younger farmers are more likely to participate in the program. The positive signs of the coefficients for education and cooperative membership were also expected. These signs imply that cooperative members and more educated farmers tend to participate more in the program. The positive sign of crop land also seems logical, suggesting that farmers with larger crop areas tend to participate more in the PRODEMATA program. The negative sign for pasture may be a consequence of the PRODEMATA design that emphasizes modern inputs and stresses credit for small farmers. For the fixed capital stock, the sign was positive and consistent with expectations.

The model classified 77.5 percent of nonparticipants correctly, but only 57.7 percent of participants correctly. Overall, the model classified 69.2 percent of the 435 observations correctly.
To assess the degree of separation established by the discriminant function, the Chi-square test described previously was performed. The null hypothesis tested was that the population group mean vectors were equal. The computed Chi-square value of 68.148 (with 6 degrees of freedom) is significant at the 1 percent level, and the null hypothesis was rejected. This result implies that the discriminant model has established a statistically significant separation between the groups.

The relative importance of the six variables was determined by ranking them using both of the procedures discussed earlier. These








rankings are shown in Table 6-2. The ranking pattern was similar for both the standardized coefficients and the weighted coefficients, In both rankings cropland is shown to have contributed the most to separation of participants and nonparticipants, while education had the smallest contribution. Age and fixed capital alternated as the second and third most important variables in the standardized coefficients and weighted coefficients. Both methods ranked cooperative participation and pasture land fourth and fifth, respectively.
The findings of the discriminant analysis showed that there are some socio-economic characteristics capable of distinguishing between participants and nonparticipants in the PRODEMATA program. When the same procedure was applied to three groups (nonparticipants, participants for one or two years, and participants for three or more years), it failed to establish a statistically significant distinction between the three groups.

Technical and Allocative Efficiency by Discriminant Analysis Groups
In this section an attempt is made to answer the question raised at the end of Chapter V regarding the cause of the differences between participants and nonparticipants in both technical and allocative efficiency. To test the hypothesis that differences in estimated efficiencies were due to the effects of PRODEMATA on farmers who actually participated in the program rather than farm or farmers' characteristics, two-way contingency tables were developed.
For each group of participant and nonparticipant farmers, two subgroups were defined based upon whether or not these farmers were







Table 6-2. Ranking of the importance of each variable in the discriminant analysis


Rank by standardized coefficients Rank by weighted coefficients Standardized Weighted Rank Variable coefficienta Variable coefficienta First CROLAN (0.543) CROPLAN (0.325) Second AGE (-0.429) FIXK (0.208) Third FIXK (0.362) AGE (0.174) Fourth COOP (0.359) COOP (0.153) Fifth PASLAN (-0.258) PASLAN (-0.072) Sixth EDUC (0.142) EDUC (0.050)


aRanks are determined by the absolute value of the coefficients.








predicted to participate by the discriminant analysis of the socio-economic characteristics of each sample observation. The average technical and allocative efficiency was calculated for each of the resulting four subgroups. Each of these means was then tested to determine if it was different from the means of the other subgroups in a statistically significant fashion.
In terms of technical efficiency the PRODEMATA program indeed

exerted a substantial impact. This is shown by making comparisons along the rows of the contingency table in Table 6-3. The average technical efficiency of farmers with similar socio-economic characteristics as determined by the farmer's predictive classification was significantly greater for farmers who participated in the program than for those who did not. This result is independent of the socio-economic grouping of the sample. That is, among those farmers predicted to be nonparticipants by the discriminant analysis because of small crop land, lower education levels, etc., there was still a statistically significant difference in technical efficiency between actual participants and nonparticipants. This strongly suggests that the higher technical efficiency of participant farmers is a consequence of PRODEMATA participation rather than other pre-existing, fundamental differences.

Comparisons in a column-wise fashion produced quite different results. When averages for techincal efficiency werecompared for farmers of the same group in terms of actual participation but with different socio-economic characteristics, no significant differences were detected. This finding confirms that the underlying socio-economic differences between the participant and nonparticipant subsamples were not the:cause of the observed differences in technical efficiency between the two




Full Text

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CREDIT AND EFFICIENCY: AN ANALYSIS OF TRADITIONAL FOOD PRODUCTION SYSTEMS IN SOUTHEASTERN MINAS GERAIS, BRAZIL By ALOISIO TEIXEIRA GOMES A DISSERTATION PRESENTED TO THE GRADUATE COUNCIL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 1984

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ACKNOWLEDGMENTS The author wishes to express his gratitude and appreciation to Dr. Harold Evan Drummond, chairman of the supervisory committee, for his guidance, patience, and encouragement during the preparation of this dissertation. Gratitude is also expressed to Dr. William G. Boggess, co-chairman of the supervisory committee, and Dr. Timothy G. Taylor, member of the supervisory committee, for their valuable assistance. Appreciation and thanks are also extended to Dr. J. Scott Shonkwiler and Dr. William G. Blue, members of the supervisory committee, for their time and assistance. Special recognition is given to Dr. W. W. McPherson, former graduate coordinator in the Department of Food and Resource Economics, and to Dr. Max R. Langham, present graduate coordinator, for their assistance and guidance during the author's study program at the University of Florida. The author also appreciates the very rewarding experience and good times shared with colleagues, friends, staff, and faculty of the Department of Food and Resource Economics. The data used in this study were collected by the Department of Agricultural Economics of the Federal University of V.icosa, Brazil. All of the staff of that department had some input into this study. Their permission to use the data is gratefully acknowledged. n

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Finally, the author is especially grateful to the Empresa Brasileira de Pesquisa Agropecuaria for providing financial support for the author's graduate study. i ii

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TABLE OF CONTENTS Page ACKNOWLEDGMENTS ii LIST OF TABLES vii LIST OF FIGURES x ABSTRACT xi CHAPTER I INTRODUCTION I Problem Definition 2 Objectives of the Study 6 Organization of the Study 6 II GENERAL CHARACTERISTICS OF THE STUDY REGION AND THE PRODEMATA PROGRAM 8 Introduction 8 The Agricultural Economy of the State of Minas Gerais 8 General Characteristics of the Zona da Mata 11 The Agricultural Sector of the Zona da Mata 14 The Integrated Rural Development Program for the Zona da Mata Region 17 III THE PRODEMATA SAMPLE 21 Introduction 21 The Sample 21 The Data 22 Sample Characteristics 27 Farm Size and Land Resources 27 Levels of Input Use 28 Labor 28 Fixed Capital 30 Operating Expenses 33 iv

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CHAPTER Page IV EFFICIENCY MEASUREMENT 38 Introduction 38 Efficiency and Frontier Functions 39 Conceptual Framework 45 The Model 45 Farrell Measures of Efficiency 48 Estimation Procedure 53 Corrected Ordinary Least Squares (COLS) Estimation 53 Maximum Likelihood (ML) Estimation 54 V EMPIRICAL RESULTS 57 Model Estimation 57 Frontier Production Function 57 Frontier Cost Function 62 Efficiency Measures 62 Technical Efficiency 64 Results 64 Comparison by Tenancy 67 Comparison by Group 69 Allocative Efficiency 71 Results 71 Comparison by Tenancy 72 Comparison by Group 72 Total Productive Efficiency 73 Sunmary of Findings 74 VI DISCRIMINANT ANALYSIS OF PARTICIPATION CHOICE 76 Introduction 76 Linear Discriminant Model 76 Evaluating the Discriminant Function 79 Differences between Groups 79 Relative Importance of the Variables 80 Classification Ability 80 Selection of Discriminant Variables 81 Analysis and Results 83 Technical and Allocative Efficiency by Discriminant Analysis Groups 86 VII SUMMARY AND CONCLUSIONS 92 The Problem, Objectives, and Procedures 92 Summary of the Findings 93 Implications and Policy Issues 95 Limitations and Suggestions for Further Research ... 96 V

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APPENDIX P^ A LABOR USED PER HECTARE IN SHARECROPPED AREAS 99 B BASIC DATA 'AND 'DEFINITIONS 101 C TEST OF THE EQUALITY OF THE AVERAGE EFFICIENCY MEASURES BETWEEN PARTICIPANTS AND NONPARTICIPANTS IN THE PRODEMATA PROGRAM 104 REFERENCES 107 BIOGRAPHICAL SKETCH Ill VI

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LIST OF TABLES Table Page 2-1 Distribution of farms and farm receipts by size class, Minas Gerais, 1974-75 10 2-2 Urban, rural, and total population of the state of Minas Gerais, 1950-75 12 2-3 Urban, rural, and total population of Zona da Mata, 1950-75 13 2-4 Land use and number of farms by activity. Zona da Mata, 1975 16 25 Land tenure partem. Zona da Mata, 1975 18 31 Sample composition by class of producer and participation in the PRODEMATA program. Zona da Mata, 1981-82 23 3-2 Description of the different groups of farmers who were interviewed according to ownership of land and management structure, and the corresponding need for adjustments of production factors. Zona da Mata, 1981-82 25 3-3 Average farm size by land use, class of producer, and participation in the PRODEMATA program. Zona da Mata, 1981-82 29 3-4 Average labor used per farm, labor per hectare, and labor cost, by class of producer and participation in the PRODEMATA program. Zona da Mata, 1981-82 31 3-5 Average capital stock per farm in buildings, machinery and equipment, and work and production animals. Zona da Mata, 1981-82 32 3-6 Average fixed capital per hectare and per man-day by class of producer and participation in the PRODEMATA program. Zona da Mata, 1981-82 34 vii

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Table Page 3-7 Average operating expenses per farm by class of producer and participation in the PRODEMATA program, Zona da Mata, 1981-82 35 3-8 Average operating expenses per hectare and per man-day by class of producer and participation in the PRODEMATA program. Zona da Mata, 1981-82 37 5-1 Corrected ordinary least squares (COLS) and maximum likelihood (ML) estimates of the frontier production function for each group of farmers. Zona da Mata, 1981-82 58 5-2 Summary statistics for the frontier production function disturbance distributions for each group of farmers. Zona da Mata, 1981-82 60 5-3 Derived COLS and ML estimates for the cost function frontier for each group of farmers. Zona da Mata, 1981-82 63 5-4 Average efficiency indices (calculated via COLS estimates) for each group of farmers and by tenancy category. Zona da Mata, 1981-82 65 5-5 Average efficiency indices (calculated via ML estimates) for each group of farmers and by tenancy category. Zona da Mata, 1981-82 66 5-6 Output/input ratios obtained by sharecroppers and by the owners in the Zona da Mata, 1981-82 68 57 Efficiency index ratios between participant and nonparticipant farmers. Zona da Mata, 1981-82 70 61 Discriminant coefficients, overall means, group means, and ;t-test levels of significance for differences in mean values between participants and nonparticipants 84 6-2 Ranking of the importance of each variable in the discriminant analysis 87 6-3 Test for significant differences between the technical efficiency index averages of subgroups defined by actual participation in the PRODEMATA program and socio-economic characteristics which would have predicted participation according to the discriminant analysis. Zona da Mata, 1981-82 89 viii

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Table 6-4 Test for significant differences between the allocative efficiency index averages of subgroups defined by actual participation in the PRODEMATA program and socio-economic characteristics which would have predicted participation according to the discriminant analysis. Zona da Mata, 1981-82 91 A-1 Regression equations estimates of labor used (expressed in logarithms) in each crop as a function of the cultivated area, also expressed in logarithms 99 C-1 Test for significant differences between the efficiency averages derived from COLS estimates for participants and nonparticipants in the PRODEMATA program 104 C-2 Test for significant differences between the efficiency averages derived from ML estimates for participants and nonparticipants in the PRODEMATA program 105 IX

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LIST OF FIGURES Figure Page 2-1 Brazil, state of Minas Gerais, and the Zona da Mata region 9 4-1 Efficient unit isoquant 40 X

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Abstract of Dissertation Presented to the Graduate Council of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy CREDIT AND EFFICIENCY: AN ANALYSIS OF TRADITIONAL FOOD PRODUCTION SYSTEMS IN SOUTHEASTERN MINAS GERAIS, BRAZIL By Aloisio Teixeira Gomes April 1984 Chairman: H. Evan Drummond Co-Chairman: William G. Boggess Major Department: Food and Resource Economics Over the past two decades one of the primary policy actions designed to increase productivity, and hence income, of poor rural people in Brazil has been the provision of agricultural credit at subsidized rates of interest. There is a lack of consensus regarding the need for and effectiveness of such credit programs. Various farm-level production studies have provided conflicting results concerning the effect of credit policies on productivity and efficiency of traditional farming. This study provides an evaluation of the Integrated Rural Development Program (PRODEMATA) for the low-resource farmers in the Zona da Mata, a region in the state of Minas Gerais, Brazil. The PRODEMATA program includes credit combined with technical assistance from the extension service. XI

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The focus of the study was on the technical and allocative efficiency of participant and nonparticipant farmers in the PRODEMATA program. Full frontier production functions were estimated using a maximum likelihood approach. The production frontiers generated dualcost frontiers which were used to estimate the technical and allocative efficiency of each sample observation. The average participant had statistically significant higher technical efficiency than nonparticipants, but statistically significant lower allocative efficiency. A discriminant analysis approach was used to identify pre-existing socio-economic differences between parti pants and nonparticipants. When the sample was stratified into homogeneous socio-economic groups, it was clear that the differences in technical efficiency between participants and nonparticipants were due to the PRODEMATA program rather than other pre-existing fundamental differences between the two groups. However, it was impossible to determine if the differences in allocative efficiency were caused by PRODEMATA participation alone. xn

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CHAPTER I INTRODUCTION The agricultural sector is of fundamental importance to the economies of most developing countries. In Brazil, even though agricultural contributions to the economy are being given increasing priority and many efforts have been made to promote rural development, much of the population lives in conditions of extreme poverty, the worst of which is concentrated in the rural areas. Rural development programs in Brazil have often emphasized improvements in farm productivity. Development strategies based on technological change designed to increase agricultural output and the incomes of poor rural people have been considered of crucial importance to overall plans of economic growth and development. A common strategy to encourage the adoption of new and/or more productive technologies has been to provide adequate agricultural credit at subsidized rates. A typical credit program allows the development agency to monitor farmers' production practices and to subsidize indirectly the adoption of new technologies. In the last two decades, agricultural credit has been viewed as an important catalyst in development efforts in most low-income countries and various types of agricultural credit programs have been started in these less developed countries. The objectives or goals of credit programs and the concern about their performance fall into three categories: (a) the 1

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2 economic efficiency of the activities financed, (b) the ability of the program to serve neglected portions of the rural population, and (c) the financial viability of the institution through which funds are administered (Donald, 1976). In Brazil, agricultural credit expanded very rapidly at the same time that agricultural growth rates accelerated. The emphasis of most programs has been to provide credit to farmers through normal banking channels (Meyer et al., 1973), the idea being that all farmers, including small producers, will benefit by the distribution of agricultural credit through the existing commercial banking system. This study is concerned with the effectiveness of agricultural credit in achieving the goals of a specific development program for low-resource farmers in Brazil— PRODEMATA, the Integrated Rural Development Program for the Zona da Mata, a region in the state of Minas Gerais. Problem Definition The Zona da Mata is one of the most backward regions of rural southeastern Brazil. The region, despite its favorable location near large urban centers of southeastern Brazil, is considered a depressed area. The relative abundance of labor and relatively low crop yields are characteristic of its traditional agriculture. The PRODEMATA program was designed as part of a continued effort toward the revitalization of the agricultural economy of the Zona da Mata. An implicit hypothesis in the project's design is the belief that growth in productivity and farmers' income occur through increased access to inputs and that the ability of farmers to adopt these inputs is related to the availability of credit.

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3 The need for and effectiveness of credit programs in traditional agriculture have frequently been debated in the literature. In the early 1960s, Schultz (1964) introduced the "poor but efficient" theory casting doubt upon the benefits of providing credit to traditional farmers. Professor Schultz utilized the works of Tax (1963) and Hopper (1957) to support the hypothesis that "there are comparatively few significant inefficiencies in the allocation of the factors of production in traditional agriculture" (Schultz, 1964, p. 37). He argued that in traditional agriculture most profitable opportunities had been exhausted and, thus, there is no need for employment of outside capital. If this is the case, credit programs to encourage the use of additional inputs will result in a mi sal location of resources and will introduce inefficiencies into a production system which will remain poor and become inefficient. Various farm-level production studies have been conducted in Brazil to analyze the effects of credit programs on capital formation, productivity, and efficiency of traditional agriculture. Rao (1970), analyzing the economics of credit in southern Brazil, indicated that there was considerable underutilization of capital on small farms and that the provision of credit to relieve capital shortages and increase output would be necessary. Nelson (1971), however, in his study in Riberao Preto (Sao Paulo, Brazil), concluded that farmers could not increase income by applying more capital inputs because of technological barriers. He argued that credit programs would have little impact on capital formation and income unless these technological constraints were overcome.

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4 White and Seabra (1973) pointed out that internal capital accumulation through savings is very difficult among small farmers in the Zona da Mata and that credit plays a major role as a source of additional capital. On the other hand, some studies have shown a tendency for the extension service (which must approve all institutional credit) to work mainly with the owners of larger farms in Brazil. As a result, large farmers have a greater access to credit than do small farmers, who may well have a greater need for credit. There is also disagreement in analyses of resource allocation in traditional agriculture in Brazil. Nehman (1973), in his study of agricultural credit in a depressed area of Sao Paulo, showed that capital inputs were being well allocated by large farmers with borrowed capital. He found misal location of capital inputs, however, by the small farmers who had the lowest potential return on increases in operating capital and no potential return for increasing working assets. Garcia (1975) found in two regions of the state of Minas Gerais that small farmers were not efficient, demonstrating excessive labor use. Graber (1976) and Teixeira (1976) also concluded that poor resource allocation of acquired production factors existed among small farmers in Brazil . Drummond (1972), in his study, compared two regions of the state of Minas Gerais, Brazil, which were felt to be polar opposites in their fundamental characteristics. The findings led to the conclusion that "the agriculture in the traditional region of Muriae is neither more nor less efficient in the use of available resources than in the commercially oriented region of Capinopolis" (p. 151). This result

PAGE 17

5 supports the position that traditional agriculture is not necessarily inefficient. Steitieh (1971) enlarged on the study of resource allocation through the analysis of productivity and productivity change of all inputs in crop production at the farm level in Brazil, The general conclusion derived from his results is that increased investment in inputs alone is not the answer to increasing crop production. He argued that "better management, information and utilization of resources is as important and should be equally emphasized if any benefit is to be expected from increasing expenditures on these inputs" (p. 96), The implication of this argument is that while credit availability may increase access to inputs, there is no guarantee that these inputs will be used in such manner as to realize the full potential of output gains . Even though these studies represent only a small sample of the large body of research on traditional agriculture in Brazil, they serve to illustrate the divergence of opinion and results concerning the allocative efficiency of traditional farmers, and hence the effectiveness of agricultural credit programs. This study will attempt to evaluate and analyze the impact of the supervised agricultural credit extended through the PRODEMATA program. The analysis focuses on the effects of the program on the technical and allocative efficiencies of farms in the Zona de Mata region of the state of Minas Gerais, Brazil, Unlike previous studies analyzing inefficiency on farms which used an "average" production function, this analysis is undertaken in terms of a "frontier" production function.

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6 Objectives of the Study The general purpose of this research was to analyze the effectiveness of the use of supervised credit in achieving the goals of the PRODEMATA project. The specific objectives of the study were 1. To evalute farm and farmers' characteristics which are associated with participation in the PRODEMATA and can distinguish between participants and nonparticipants in the program 2. To analyze the effectiveness of the PRODEMATA in stimulating the adoption of more productive technologies in traditional agriculture 3. To analyze the effects of the PRODEMATA on the allocative and technical efficiency of resource use Organization of the Study This study is divided into seven chapters. In the introductory chapter the research problem and objectives are presented. Chapter II provides a brief description of the study region, with emphasis given to a discussion of specific features of its agricultural sector. A summary of the scope of the PRODEMATA program is also presented in this chapter. In Chapter III the sampling plan and the data used in this study are discussed. A descriptive presentation of characteristics of the sampled farms is also developed in this chapter where aspects related to resource endowment and levels of resource use are discussed. Chapters IV and V are devoted to the efficiency analyses. In Chapter IV efficiency measurement is reviewed, the empirical model is presented, and the procedures used in the analysis are explained. Chapter V contains the empirical results. In Chapter VI a discriminant analysis

PAGE 19

7 approach is used to distinguish between participants and nonparticipants in the PRODEMATA. The theoretical and empirical models are discussed, the results are analyzed, and an application is shown where the results are integrated to the efficiency analysis. Finally, in Chapter VII the major findings of the research are summarized, implications and policy recommendations are derived, limitations of the study are discussed, and suggestions for further research are explored.

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CHAPTER II GENERAL CHARACTERISTICS OF THE STUDY REGION AND THE PRODEMATA PROGRAM Introduction This chapter presents selected characteristics of the study area and of the PRODEMATA project. The initial sections deal with structural characteristics of the farm sector in the state of Minas Gerais and the geographic setting of the study. Some of the major characteristics of the agricultural economy of the Zona da Mata are presented. An overview of the World Bank-sponsored PRODEMATA project concludes the chapter. The Agricultural Economy of the State of Minas Gerais The Zona da Mata region is located in the southeastern part of the state of Minas Gerais, bordering the state of Rio de Janeiro and Espirito Santo (see Figure 2-1). The agricultural sector of Minas Gerais is of great importance for the state itself as well as the whole country. The 1975 Agricultural Census registered 454,465 farms in the state. The predominance of small farms is clearly shown in Table 2-1. About 28 percent of the farms in the state have fewer than 10 hectares and 81 percent of the farms have fewer than 100 hectares. Total receipts of all farmers in the crop year 1974-75 were about 15 billion cruzeiros (approximately $4,000 per farm). While farms which are larger than 100 hectares represent only 19 percent of the total units, they receive about 61 percent of the total receipts of the sector. 8

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9 A N Figure 2-1 . Brazil , state of Minas Gerais, and the Zona da Mata region

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Table 2-1. Distribution of farms and farm receipts by size class, Minas Gerais, 1974-75 10 E s_ o cn ro o C3^ ro o o CO fO o ro o u oo CM cn CD o 00 o; $#> r\ A > cu CTi CM 00 ro CM (U < Q. ir-“ r“ ro m CD oo -o O r— o ito (U OJ 3 > CT u •»fC 0) +J VO r— 00 CM o o o. C r— r“ o o QJ • • • • • • i. 3 U rN. ro CT^ o ty\ E ^ r— CM ro in o c 3 (U r~ (/) o o. o (/) O. c (U 0) o O 0) (U a: cni— < V to fO LU 4-> 4-> VD ID 00 o o CD c o t£> cr> CTl o CO 0) 4-> • • • • • • • H4 U Lf) CM CM in o U. S14r— o Q; o o. fO u •r“ +j (/> -"“O'. •f“ O CM t— o 00 ro 4J +J o Lf> 00 o o o 00 ro c o UO r>. r— CO CM 4-> 3 #« l/> o r— CO r— • 00 CO r— UJ E 00 cr> 00 00 CM CM on cC %00 CTl o CO in cu o m> «s r— r— CM CM in ro 4<0 (U 0) i. > O) O) •f— ro o •M 4-> ro o CT> ro o 00 cy> o t3 3 O) <_> Q. o S0) r— 0) (/) cni— ro ro CO CT> in CTt o SE +j +j CM o CT^ CD oo VO o DO ic o • • « • • to 0) 4-> oo CM CO cr> o o Lio CM CM o 4-> i>+3 m (U o •4-> r*^ D. •1CT) -4-> i/) C *» l-H o iCO ro 00 CO cr» in o • Sro 00 in CD ro 0) OJ CM o o VO cr> U c #4 •« 0\ ro E 00 ro CM CM OO -O ' 3 3 CM o ID in c Z 3 OJ Uo o • • • r“ CU u f 1 u. #« <4rT3 3 to O o • r* o o o t/)
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The total population of Minais Gerais in 1975 was 12,550,000 inhabitants, of which 41 percent lived in rural areas. During the period 1950-1975 the percentage of rural population decreased, primarily because of a rapid increase in the urban population (Table 2-2). Since 1960, incentives for rural to urban migration have caused the rural population to decrease in absolute terms. General Characteristics of the Zona da Mata 2 The Zona da Mata region covers an area of 36,012 km , which is 6.1 percent of the total area of the state of Minas Gerais. The climate is generally mild with a temperature that averages about 22°C. Annual rainfall averages 1,400 mm, with a dry period occurring from April to September. The Zona da Mata (literally translated as the forested zone) is characterized by a topography of rolling hills and sharp rock outbreaks, not unlike the topography of much of Appalachia in the United States. Soils are moderately to highly weathered and relatively high in clay. Those from higher elevations are dominated by Red Yellow Latosols (Oxisols) and those from terraces by Red Yellow Podzols (Ultisols) (Resende, 1980). Some relatively fertile soils occur along narrow valleys. The total population of the Zona da Mata was about 1.6 million inhabitants in 1975 (Table 2-3). Similar to the pattern of the state of Minas Gerais, the percentage of the rural population has been decreasing since 1950, with only 49 percent of the total population living in rural areas in 1975.

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Table 2-2. Urban, rural, and total Gerais, 1950-75 population of the state of Minas Year Urban Rural Total thousands 1950 2,322.9 5,459.3 7,782.2 (29.8)a (70.2) 1960 3,825.2 5,832.5 9,657.7 (39.6) (60.4) 1970 6,060.3 5,427.1 11,487.4 (52.8) (47.2) 1975^ 7,350.7 5,199.9 12,550.6 (58.6) (41.4) Source: Fundacao Institute Brasileiro de Geografia e Estatistica (FIBGE), Anuario Estatistico do Brasil , 1955 and 1978 issues. ^Numbers in parentheses are percentages of the total population. “Estimated by FIBGE, Anuario Estatistico do Brasil, 1978.

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\d Table 2-3. Urban, rural, and total population of Zona da Mata, 1950-75 Urban Rural Total thousands 1950 385.1 ^ 898.2 1,283.3 (30.0)® (70.0) 1960 567.2 955.8 1,532.0 (37.2) (62.8) 1970 795.6 805.2 1,600.8 (49.7) (50.3) 1975^ 834.6 789.1 1,623.7 (51.4) (48.6) Source: Fundacao Institute Brasileiro de Geografia e Estatistica (FIBGE), Anuario Estatistico do Brasil . 1955, 1965, 1975, and 1978 issues . ^Numbers in parentheses are percentages of the total population. ^Estimated by FIBGE, Anuario Estatistico do Brasil, 1978.

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14 The social infrastructure in the region is poor. Health and education services are very limited. Mortality rates are high, especially among infant and preschool children, as a consequence of widespread malnutrition and disease. Educational opportunities are limited. The investment in education by the state is low, resulting in a lack of facilities and generally low quality of teaching services. As a consequence of this inadequate system, the labor force in the region has a poor educational background. According to the 1970 census, 60 percent of the agricultural workers in the region had no formal education (FIBGE, 1978). The illiteracy rate among the 5-14 year old age group was about 55 percent in 1975 (FIBGE, 1978). The Agricultural Sector of the Zona da Mata The Zona da Mata region was one of the first areas of central Brazil to be colonized. As a result of a mining boom in the early part of the seventeenth century, an incipient agriculture began to develop in the area. For many years the region played an important role in supplying agricultural products to the mining population. The settlement process was intensified with the introduction of coffee around 1830. Coffee found favorable soil and climatic conditions in the Zona da Mata along with the advantage given by its proximity to major markets. Until the first quarter of the twentieth century, the Zona da Mata was a leading economic region of the state and the nation, experiencing constant growth fueled by the coffee boom. However, depleted soil conditions coupled with inadequate conservation techniques during the coffee

PAGE 27

15 era resulted in reduced yields and increased production costs (UFV, 1971). Simultaneously, competition from coffee growers in southern states led to a process of economic decline in the Zona da Mata. Coffee, once dominant in the region, has become relatively less important as a result of the comparative advantage of the southern producers and government programs to eradicate coffee plantations during the mid-1960s. These programs accelerated the economic decline of the the Zona da Mata because areas released by the eradicated coffee have been put primarily into unimproved pastures for cattle raising. The dramatic and sudden shift from labor-intensive coffee to laborextensive pastures has resulted in a serious problem of unemployment and underemployment in the agricultural sector (Banderra, 1970). Moreover, since coffee generates a relatively high net income per hectare, the region has many small farms which were economically viable when in coffee but which are marginal, at best, in pasture. Dairy farming now is the most important source of income for agriculture in Zona da Mata. The region has become an important milk supplier fortheRio de Janeiro area. The predominance of the livestock subsector is illustrated in Table 2-4. More than 70 percent of the productive land in the Zona da Mata is now in pastures and nearly all farm units have some pasture (FIBGE, 1975). The most important annual crops in the region are corn, rice, beans (edible beans), sugarcane, and tobacco. Corn and beans are frequently intercropped. Coffee and fruit (including citrus) are the main perennial crops. Garlic and tomatoes are the primary vegetable crops. They are produced for shipment to the Rio de Janeiro market.

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Table 2-4. Land use and number of farms by activity, Zona da Mata, 1975 Activity Land use Farms Area (ha) Percentage Number Percentage Pasture 2,166,654 70.3 59,812 88.6 Annual crops 382,840 12.4 58,173 86.2 Perennial crops 113,379 3.7 25,786 38.2 Forests 343,239 11.1 38,961 57.7 Other 76,428 2.5 11.049 16.4 Total 3,082,540® 100 67.474 __b Source: Fundacao Institute Brasil eiro de Geografia a Estatistica (FIB6E), Censo Aqropecuario de Minas Gerais (Rio de Janeiro, 1975). ?Total does not include unproductive lands. ^Percentages do not total 100 because of farm enterprise diversification.

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1/ Concentration in the land tenure pattern in the Zona da Mata exacerbates the economic problems of the region. As shown in Table 2-5, of the 67,474 farms in the area, about 33 percent are smaller than 10 hectares, 76 percent have less than 50 hectares, and 89 percent have less than 100 hectares. Those farm units with more than 100 hectares hold about 55 percent of the area's land resource (FIB6E, 1975). Given the difficulty of stimulating structural changes, most efforts to address the problems of the region have focused on improvements in the allocation of the available resources and the efficiency with which those resources are employed. Agricultural credit, technical services, and investments to improve social infrastructure are some of the alternatives which have been selected to address the problems of the region. The Integrated Rural Development Program for the Zona da Mata Region The Integrated Rural Development Program for the Zona da Mata region of the state of Minas Gerais (PRODEMATA) is a World Bank-sponsored project.^ It was designed , as part of a continuing effort to revitalize the agricultural economy of the Zona da Mata. The target population is the large number of small landowners and sharecroppers in the region. The general purpose of PRODEMATA is to induce agricultural development in the Zona da Mata and to upgrade the welfare of the target population. These objectives are to be achieved through a series of incentives 1 For more details concerning the project, see World Bank (1976).

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Cumulative Percentage \b ir> o> tv s. (C o C\J 00 00 • • • • • (U ro 00 in ID CT> C\J ID <0 c Q) U SO) D. (O 4o> CD <0 -M C in CO o C\J , in oo’ ID ro LO 00 CD o o I— <0 1 — 00 4-> fC CO 00 in CO ID CT> ^ CM o oo OO (0 Q) to ^ 00 »— O t— CD CM in oo ID 2: S. in — VD lO^ cC •V fO OO T5 fO C o M to C E ss0) fO 4-> u. Z "O c «3 • in fO 1 4ro C\J O -C o O o OJ o o o O h~ to o CM in CM O to E 1 1 1 1 o (G SV o o o o CM r— ro C\J Ln o A O 4r~ Source: Fundacao Institute Brasileiro de Geografia e Estatistica (FIBGE), Censo Agropecuario de Minas Gerias (Rio de Janeiro, 1975). ^Numbers in parentheses are percentages of the total.

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19 to increase farm production, enhance farm productivity and income, and improve living conditions for the rural population in general. The incentives include 1. Provision of agricultural credit combined with technical services including extension, research and demonstration facilities, and cooperative organization, and 2. Investments in health, sanitation, and education. The major component of the PRODEMATA program is agricultural credit, which accounts for 60 percent of the..:tatal ilS$139 million of project costs. Most of the credit is available only for sharecoppers and small farmers who own less than 100 hectares. These low interest loans are designed, for on-farm investment, the purchase of hired labor and other inputs, reforestation, and land reclamation projects. The agricultural extension component coupled with the agricultural research and demonstration program is the main production support service. Extension, which has been directed primarily at large farmers in the past, is to be enlarged and redirected toward small farmers. The development of applied agricultural research and the demonstration of improved agronomic practices are to focus on the production system of small farmers. These components are to be executed by the state's agencies for agricultural extension (EMATER-MG) and agricultural research (EPAMIG), respectively. The production support services, including a plan concerning the improvement of cooperatives in Zona da Mata, represent about 21 percent of the total project costs.

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zu Investments in health and education are designed to improve the social infrastructure. Health services are to be improved by providing health care posts throughout the area. Investments are to be made in sanitation programs and action plans for nutritional improvements, in order to diminish morbidity and mortality from diseases caused by deficient sanitary and nutritional conditions. Emphasis is to be given to pregnant and nursing women, to children under five years of age, and to vaccination against communicable diseases. With respect to education, the project includes construction and improvement of primary schools and vocational centers, training of teaching staff, and promotion of instructional programs to provide basic knowledge of agricultural technology for farm families.

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CHAPTER III THE PRODEMATA SAMPLE Introduction This chapter presents the sampling plan and some descriptive statistics for the sample. In the initial sections the sampling procedures and the data used in this study are discussed. A descriptive analysis of the farmers sampled in Zona da Mata is presented to conclude the chapter. The Sample In order to measure the progress of the PRODEMATA project, comprehensive surveys of the target population were conducted annually from 1977 to the present. These data, which are used in this study, were collected by the Department of Agricultural Economics of the Federal University of Vicosa. The data include information concerning crop and livestock production, land use, input and output prices, sales and onfarm consumption, input use, technology, credit use, tenancy, off-farm work, cooperative membership, and sociodemographic information. The geographical boundaries of the survey area were defined on the basis of the regional divisions used by the state's extension agency for administrative purposes. In each region four muni ci pi os (counties) were selected for inclusion in the sample. Two of the municipios were randomly chosen and the other two were selected based on the presence of 21

PAGE 34

a large target population or specific crops of interest to PRODEMATA (e.g., tobacco and sugarcane). The following muni ci pi os were chosen to be included in the sample: 1. Region of Juiz de Fora: Alto Rio Doce, Juiz de Fora, Santos Dumont, Sao Joao Nepomuceno 2. Region of Muriae: Carangola, Leopoldina, Manhuacu, Muriae 3. Region of Vicosa: Ervalia, Ponte Nova, Raul Soares, Uba The sample included both landowners and sharecroppers. In each administrative region at least 50 sharecroppers were interviewed with a minimum of 12 for each municipio . The sample was surveyed annually and analyses of consistency of the data were performed. These analyses provided the basis for the elimination and substitution of some producers. Also, some substitution occurred over the years due to the death of respondents or the sal of farms. Thus, over time the original data file was modified, resulting in the creation of files with fewer respondents but, presumably, with a higher degree of credibility and consistency. For the purpose of this study, data from the 1981-82 crop year survey were used. Some data from the previous surveys were also used to determine the history of PRODEMATA participation of each producer included in the 1981-82 survey. The composition of the sample is shown in Table 3-1 . The Data The unit of analysis for this study is the farm management unit. This takes into account the total area managed by the respondent.

PAGE 35

Table 3-1. Sample composition by class of producer and participation in the PRODEMATA program. Zona da Mata, 1981-82 23 (U (O Q. O fO I— to CM CM 00 'cr c^ c» tn Lf> LD 00 CM ' — ' o o A tn o t— to O O Lf> f— ^ CM to 0) slO 4J u cu .E o o 1^ « 00 to to (O to s_ cu c 3 o o I o to i. c cu o scu CO.
PAGE 36

24 irrespective of whether the land is owned, rented, or utilized under a sharecropper agreement. Since the questionnaires were designed to record only the quantities of inputs purchased by the respondent, some adjustments were required in those cases in which some part of the management unit was sharecropped. The sharecropped areas are cultivated under an agreement between landowner and the sharecropper. In the most prevalent arrangement, the owner provides all the land, the sharecropper provides all the labor, and the purchased inputs are equally provided by both. This arrangement was assumed to hold throughout the sample. The situations which required adjustments in the raw data are summarized in Table 3-2. In case I the respondent is the sole provider of all inputs and labor for the total cultivated area. In this case no adjustments were necessary. In case II the respondent provides all the inputs and labor only to the area which is not cultivated under a sharecropper agreement. The inputs to the sharecropped area are purchased by both owners and sharecroppers, and all labor is provided by the sharecropper. In case III the respondent provides all labor and one half of the inputs for all of the management unit. The other half of the inputs is purchased by the owner. The total quantity of purchased inputs^ used in cases II and III was calculated in the following manner: The set of purchased inputs included seeds, fertilizer, pesticides, draft animal services, and mechanized services.

PAGE 37

Table 3-2. Description of the different groups of farmers who were interviewed according to ownership of land and management structure and the corresponding need for adjustments of production factors. Zona da Mata, 1981-82 25 T3 0) i3 cr o; s4 -> c OJ to 3 a so .Q re 3 O. c o OJ to re o i3 Q. to OJ >to to (V (U >>X5 c re -a c re o o. jr to s. (U c 2 o I 4-> re t/) fO s. C 4-^ 4-> in -a (U 4-> CU to C in (/) o. CU .E • (U 4-> 0) a; i-•-> -o Mc sE £ X C 4-) JZ (U E O rO 3 (U 0) 0) 0> 3 1— o «4re M i. O) s•r— o r— in U ro o> to 3 s. C c u 4J • E M O ro So ro o •r•CJ O •rE -C •tJ E Q. C CU o E in o to to Q. in 3 Q. 3 to o; E CU O c CL to E • +J 2 JZ S5 4J O •1“ +J 2 re re E O 4-> u o C E o E CU (U 0) CU L> E CU re 4J iE +J Ms4-> E 0) O E -(-> E re (U E O cn. re O fl3 o o •r* Q. 4-> cu fO s(U c
PAGE 38

where • th I., is the estimated total amount of the i input which was used ij for the crop on a particular farm Q.. is the amount of i * J .th j crop th input provided by the respondent for the T. is the area of the crop cultivated by the owner (for sharecroppers, T. = 0), and «J S. is the area of the crop cultivated by the sharecropper. The total quantity of labor used in the sharecropped areas of land owned by the interviewee (case II) was estimated assuming that all labor used was provided by the sharecroppers. In order to determine labor requirements on sharecropped land, regression equations were estimated for sharecroppers in the sample. For each crop, labor used was considered as a function of the cultivated area for the respective crop. The following model was specified: log Lj = bp + b^ log (3.2) where Lj is the amount of sharecropper labor used in the crop S. is the sharecropped area in the crop, and \) bp and b.j are estimated parameters of the model 2 Rice, corn, beans (edible beans), corn-beans intercropped, tobacco, sugarcane, and coffee.

PAGE 39

27 The parameter estimates, which are shown in Appendix A, were used to adjust the total labor use in the following manner; For each respondent, the labor used on the sharecropped area for crop j was estimated by Equation (3.2). This procedure was repeated for each crop cultivated in the sharecropped area and the sum of the labor values thus obtained gives the total amount of labor used in the sharecropped areas of the management unit. This total was then added to the quantity of labor used in the nonsharecropped area as reported by the respondent (owner) in the survey. After all inputs and labor adjustments were made, economic variables were defined at various levels of aggregation. Appendix B includes a listing of the variables relevant to this study and explains how each is defined. Sample Characteristics In the following sections a descriptive analysis of the farmers sampled is presented in order to give a more thorough understanding of the sample by describing some general characteristics of the farming system in the Zona da Mata region. It should be pointed out that all figures refer to the 1981-82 crop year and that participant farmers are those producers who had used PRODEMATA-sponsored credit during at least one year since the initiation of the program. Farm Size and Land Resources The farm size in this study was measured in hectares of productive land, which is defined as the sum of cropland and land in pastures. In the sample, about 85 percent of the total farm land was used for

PAGE 40

28 crops or pastures in the 1981-82 agricultural year. The other 15 percent of the total land area was in forests, was occupied with buildings and structures, or was unused. These findings are consistent with those of Silva (1981), who found productive land to be 83 percent of the total farm land during the 1977-78 crop year. As indicated in Table 3-3, the average area of productive land for the 435 fanners in the sample was about 29.10 hectares, with sizes ranging from 0.1 to 230.50 hectares. For the whole sample, the size of the total productive land of the participant farms was roughly 1.5 times that of the nonparticipant farms. This difference is even more apparent with respect to cropland in the two groups. Patterns of land allocation show that, on the average, farmers utilized about 25 percent of their productive land in cropping activities and 75 percent for pastures. The percentage of land used for crops increased as the size of the holdings diminished. In fact, the owners of the smallest farms (0-10 hectares) allocated about 63 percent of their land to crops. This negative association between the percentage of land in crops and farm size reflects the emphasis placed on subsistence crops by the smaller producers. On the other hand, the owners of larger farms had a higher proportion of their land in pasture, emphasizing livestock activities . Levels of Input Use Labor The Zona de Mata is a region of chronic unemployment and underemployment in rural areas. As a result, the wage rate in the rural

PAGE 41

Table 3-3. Average farm size by land use, class of producer, and participation in the PRODEMATA program. Zona da Mata, 1981-82 29 0) 1 1 VC LD CO uo LO 00 re 1 CVJ r— OJ o> cn +j s • • • • • . o <0 1 o> ir> 00 r-“ CO t— » CO s( 1 ) c s o 1 VO CNJ o CO o 1 VO LO CVJ o o 1 • * • . r— 1 LO C7N CO A 1 CVJ r— r— o o o o Uf) o m o o o o CO s( 1 ) Q. Q. O So 0) Sre JC C>0 CO 0) re +j o (U 00 in C£> C£) in CM CM CO in cn CO CO CO o »3CTl Cn CO I— O CO 00 CTl on o o o CO O C3 CM CM LO 4J 0) -P cu C O) c O) *o V/) ro fO t/) CL sQ. L. to c a; "O C O) c rtJ (J > c r— 4-> > C U S o. Q. o •P sc £ 3 Sc E 3 Q. rO o <10 4-> <0 o <0 o
PAGE 42

30 sector is low compared with that of most of the other regions in the state of Minas Gerais (EPAMIG— Informe Agropecuario — 1977-82, several issues). This low wage rate, combined with topographic characteristics which to a large extent constrain the use of mechanization, leads to the predominance of labor as the primary resource in the area. Overall, the average amount of labor used was 414 man-days per farm. As Table 3-4 shows, those farmers producing on a smaller scale tended to use more labor per hectare of productive land than those producing on a larger scale. For example, sharecroppers and owners in the range of 0-10 hectares used about 45 man-days per hectare, whereas those with more than 100 hectares used only 8 man-days per hectare. As far as participation in the PRODEMATA program is concerned, the level of labor used per hectare was lower for participant sharecroppers and the smallest participant farmers than for these same categories of nonparticipants. The opposite situation was found for the three other farm size categories. Overall, the participant farms used less labor per hectare than nonparticipants. Fixed Capital The fixed capital stock is composed of three major categories: buildings, including animal facilities but excluding houses; machinery and equipment; and draft animals and livestock. The sample data on fixed capital are shown in Table 3-5. The data represent the value of the fixed capital stock as estimated and reported by farmers. As expected, the larger the farm, the higher the value of the capital stock. Most of the capital stock on the larger farms is for the

PAGE 43

31 I ro CL •o C to O) u 3 "D O SCL O iA U) to U >> «s (/) o u o to C^J CO I -o I— C CO fO o^ QJ •% U to to -»-> •M to o s: (U -C (O •o S(U (C CL C o srvi o ^ « <0 E f— la s~ •> CD E O ii. la Q. M< S(— to < CL I 00 c; to a; 0) CD f— to CL S» E O) to > 00 to SOJ o 3 *o o o. t/) t/) to o (/) 0) sto 4-> u a> JZ 0) N E sto >> u> s. CD c o o A o o I o o ID o LD I o o (/) >> to “O I c: to c 0) to > 3 cr n o CD CD 1 1 OO • • • • • • 1 • a^ o C\J CD VD 1 to o r— CO CSi CJ 1 to oo 1 CO r— CD O r1 • • • • « • I • CM 00 tn 00 CO I o CM LO CD 1 r— o o 1 r— i 00 CO 00 CD o ro CO o o o •OO CVJ VO to o CD N 3 u *0“ VO LT> oo Lf> CD CD o CD r^ CD to CM • • • * « • o • 00 CO VD O LD 00 £ CO o O CM to ro to r— 3 o 1 1 o> (/) o 1 VD 00 CO OO tn 1 CM 0) • • • • • t • CM 1 i VO o OO CM 1 a; bO* o 1 LD tn CO 1 JZ tn 1 CM 1 r— 1 1 •p 3) 1 1 1 c O 1 1 1 1 o 4-> 1 1 TJ •M 1 1 0) C S1 1 t/) CD 0) 1 1 to 1— Q. 1 1 to Q. 1 1 00 > O 1 CM VD oo LD to CD 1 CD to •r— &• • • • 1 •r~ 3 u 1 r— to VD tn 1 • cr 0) 1 00 o o OO 1 CO 4-> CD &1 CM CM CM 1 00 (A *• — to 1 1 o x: 1 1 (J o tyo 1 1 oo o (V to 3 So to l/> CD iA -P CD S-P CD CD £ o> to £ cn CD iA to to 4-> t/) to to to CL CJ 4-> Q. u P £ •rCD a; £ QJ CD to CJ > to CJ > to > CL to CL to -p to •r•P s•r* (A u s. CD CD U 0) O CD to Q. to tJ •p CL Q. •P CL CL Q. s£ E SS£ E iE to O to o to O to o to Dtn CL tn tn to to LD CD • c rN* o 4-bOo sCJ) sO II to o 1—0 >>•— I— -bO•rt/) to o “O • S~ C\J O CO (O >, CLt— 3 Q) <0 ‘i* S o I— (U (O i 2 c (O cu CD 0) c 3) <0 (O -C s_ u OJ X ra -a •> <0 >1 C <0 "O I QJ to Q) to c CD r~ to > 3 cr CD

PAGE 44

Table 3-5. Average capital stock per farm in buildings, machinery and equipment, and work and production animals. Zona da Mata, 1981-82 32 cu 1 O CO ro CM ro CO o QJ 0» 1 rN. ov CM LO CO LO r— re 1 ro LO O VO VO Q. S1 • * • • • • • * * B cn re > 1 C\J VO O CO r^ VO VO C7^ c/) re 1 1 1 CO ro LO CM VO CO 1 1 1 1 ro cr» o o o VO o ro VO o o LO CO o 1 V£) VO VO LO VO ro o 1 • • • • • • • • • o 1 ro LO CM CT> r— r— r— VO r— ro CM ov VO A 1 00 00 rv. cr> ro n— 1 «« 0% 01 01 1 1 1— *— CM CM 1 1 t/> 1 0) 1 Si O 1 Lf> LO LO LO CM CO CO O 1 00 VO 00 CO CM CO CO CO U 1 CO CM CD LO CM VO 0) 1 1 • • • • • • « « • r— 1 VO CM VO o CO VO CO o i/) 00 ro VO CM LO CTi CO C • O C\J O r-* o • fmm o s. •1 •t 0\ Lf> > r“ -a ro CO LO o io c CD C\J VO r*^ CO ro CO Q. — ^ • (0 • • • • • • • o CO lO ro o CO LO VO 4CO r— 3 CVJ ro LO VO CO O so LO ro CM LO (U in c 4-> CO 2 1 ro o 1 r— 1 O 1 1 VO o> CM (Tt CO CO VO o 1 LO O 00 CM VO r— 1 CT) CO LO r— a> LO 1 1 • • • • • • • • o 1 CVJ LO o r-^ 00 r— lO 1 CO CO ro LO CT> r>* 00 1 1 1 CO CM r“ 1/) 1 1 1 S1 a; 1 CL 1 Cl i CO ro LO o LO o CM m o 1 CSJ r— CM o LO Lf) LO 1 O CVJ CM VO LO VO lO VO o 1 • • • • • • • • • 0) 1 o O O o CT> r— S1 CM CM CO ro fO 1 -C 1 00 1 >J (U to to c to to 4-> cu •rOJ CO -P (U C J= C CD E c CD rtJ CO u CA <0 CO to ro ro Q. s. CO 4-> Q. sc •M CL L. OJ E C (U ct C •r— 0) U > CO O > ro u > CO c: Q. ro 3 CL •r" ro +-> 4-> •f“ •f“

Q. Cl CO -M CL Q. c E -M C E C E o CO CO o ro •1“ ro o ro z: 00 Ol O. 2: CO Q. a. z to CO ro C_) Total capital stock Participants 32.275 600.899 1,621.895 3,257.951 4,557.919 1,892.135 Nonparticipants 52.380 349.162 994.052 2,840.638 4,858.869 928.153 Sample average 51.062 423.066 1,343.228 3,053.231 4,678.299 1,331.474

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33 dairy enterprise, which is consistent with the observed correlation bebetween large size and the dairy enterprises. For the whole sample the value of the capital stock averaged about Cr$l ,331 ,000 (about US$7,500), with the average for participant farms being twice that of nonparticipant farms. The relative composition of the total capital stock was about the same for nonparticipant and participant farms. Fixed capital stock per hectare decreased as the farm size increased (Table 3-6). This result illustrates the extensive characteristic of the livestock activities on larger farms with respect to the use of land. On the average, participants used more fixed capital per hectare than their nonparticipant counterparts. As expected, fixed capital per unit of labor increased with farm size. In the Zona da Mata region most larger farms have a significant dairy enterprise. Since dairying requires substantial fixed capital investments in the form of structures and the dairy herd itself, it is not surprising that fixed capital use is positively correlated with the size of the farm. On the other hand, the dairy enterprise uses relatively less labor than do crop activities. Therefore, fixed capital per unit of labor increases with farm size. The comparison of this ratio between participant and nonparticipant farmers shows that participants used slightly more fixed capital per man-day than nonparticipant farmers. Operating Expenses Operating expenses increased with farm size similar to the fixed capital stock pattern (Table 3-7). Overall, the operating expenditures of participant farms were 2.8 times those of nonparticipant farms.

PAGE 46

34 Q) 0) C7> 1 o LO r— <0 1 «:j“ o> LD LO CVJ Q. 1 r— 00 CVJ O C\J E 0^ • « * • • c rO > 1 00 f— LD oo 00 oo r" 00 (0 { LO LO LO C o fO CL o +-> i. <0 a. •a SI to i(U o 3 XJ o sCL o 10 to to 0 >> to T3 1 c to CM E 00 I i~ 1— 0 ) 00 CX. to to -t-> QJ to SS to 4» to O -O (U ^ to c 5O ivi Q. to 4-> to S•Io> Q. O to SO CL T3 t— X c o o A sOJ o 3 -o o iCL to 0) sto +-> u (U JZ c (U N •f“ to E sfO >> to s(U c 5 o o o o o to o LO I o o o I o (/) o 'f s(U N 3 io to •o c to to 3 o x: •LJ 00 CSJ 00 rv. CM o 00 tc Oi »— 00 oo O • • • • • • LO OO 00 «:}• oo LO LO CSJ CSJ CO CSJ CSJ LO cr> CSJ LO CSJ 00 LO cr> 00 00 "dOO cy^ 'd' oo 00 cr> to to to o O oo CO o LO o •tio to CSJ 00 to ro CO LO LD to oo o «d“ to o CT) (X) VO oo to CO o LO CSJ o • • • * • • CO cri CSJ CSJ CO OO CO O) CO 00 to o LO LO 00 CSJ CSJ 00 LO o oo oo • • • • • • LO CSJ CSJ o o o t|_ LlI o OJ CD LO > -C +J ro CD 4-> • rO LO Q. -M I fO U 00 o OJ x: CD *o CD X) X 0) rO o. 1— Li. L/) CJ CO CD O CD c o> +-> c cn i/i (0 CO 1/) to to fO CL s4-> CL sc: CD C CD (0 o > <0 >1 <0 (J > o. fO 4-> to CL •f— 4-> •r* -a •f— 4-> CJ SCD Q. u U OJ •rfC3 fO c •r“ to Q. Q. CJ ra -M o. Q. SC E E c E fO o 03 "O (0 o ro O. 'Z. 00 CD L. Q. z c/> X QJ •1“ Q.

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Table 3-7. Average operating expenses per farm by class of producer and participation in the PRODEMATA program, Zona da Mata, 1981-82 35 0) < OsJ OJ C\J * CTi to * ro 1 CM r— VD 00 ro ID cr> oo • • • CD o o VD LO CM cn CO CT> ID ro VD O O in cr> • • • o ro o CD in VO 00 lO r— 00 CO ro CO D O • • • CM D CM CM ro ro r— CM o rv. cr> CO CM CO CO CM in 5Q) CL Q. O 6O 0) sfO c/> o in 00 in CO VO • • • CM in in t/> OJ t/> c a; X 0) O) E c S•r" (O 4-> 4ro S0) fO +-> OJ fO f— a. CL c E O (O Z CO

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36 Operating expenses per hectare decreased as the farm size increased as was the case for fixed capital (Table 3-8). The level of operating expenses per hectare was higher for the participant owners in all categories, particularly for those with farms in the 10.01-100 hectare range. This evidence may indicate that farmers in the mid-size categories have adopted modern inputs more intensively. If this is the case, they may be more receptive to the PRODEMATA program. Operating expenses per man-day increased as the farm size increased. Comparisons between participant and nonparticipant farmers show that participant owners had many more expenditures per man-day than did nonparticipant owners. This seems to indicate that larger farmers, particularly participant owners, tended to substitute expenditures on operating inputs for labor.

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Table 3-8. Average operating expenses per hectare and per man-day by class of producer and participation in the PRODEMATA program. Zona da Mata, 1981-82 37 t/) <0 CT> CSJ 00 00 OJ CO CVJ m • • • • • • CO CT> o o o m o CT> LT) CTi o li> 00 ro r— 00 K£> o LO VO VD o o o m in to o in in CO CVJ to cn m VO • • • • • * r— 00 o o o CO 00 cr> CVJ VO CVJ cr> CO VO r-^ o VO 00 LO « • • • • • CVJ VO o o o LO 00 CSJ VO o CO VO 00 C>J ro • • • * • • lO o o o i/) O) CL fO 1 o ro VO in VO o 1 o rs. CSJ r* 1 CVJ ro r— ro CO o 1 • • * • • . (U s1 1 r*^ CVJ CSJ o o o l/> a; e fO cu Q. E <0 u> (U VO c E rc sU (U Q) Q. CL o c to Q. o to CL c ro Ou U s(O CL 0) cn Sq; > to O) CO

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CHAPTER IV EFFICIENCY MEASUREMENT Introduction Most of the production studies which have been conducted in Brazil have fit production functions to cross-sectional data. The ordinary least squares (OLS) method, or some variant, has been used as the estimation procedure assuming the disturbances, which account for random shocks and error measurement, to be normally distributed. Because these models generate predicted values that may be smaller than observed values, the fitted production functions which result are actually average functions. However, the theoretical definition of a production function is given in terms of the maximum output rate obtained from a given set of inputs. Therefore, as the usually estimated functions are in fact average functions, they do not correspond to the theoretical notion of a production function. Unless technical efficiency is accommodated by a neutral scaling of the average functions, many inferences regarding allocative efficiencies may be incorrect. The framework used in this study takes into consideration this criticism of the traditional approach through the use of frontier production functions. The first section of this chapter reviews the elements of the original Farrell approach to efficiency measurement and some contemporary efforts utilizing frontier functions. The conceptual framework 38

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39 and the model to be used in this study are presented in the second section. The third section summarizes the estimation procedures employed to estimate a frontier production function. Efficiency and Frontier Functions Generally, three types of inefficiency are considered in the literature. The first is technical inefficiency, which arises from the failure to produce maximum output from a specified bundle of inputs. The second is allocative inefficiency, which results from the utilization of inputs in nonoptimal proportions for a given set of input prices. Allocative efficiency requires the equalization of marginal rates of substitution with input price ratios. The third is scale inefficiency, which arises from the failure to produce at the point where marginal cost and output price are equal. Beginning with the work of Farrell (1957), a number of researchers have attempted to measure a "frontier" or "efficient" production function. Farrell introduced a technique by which the efficiency of a production process could be measured and any observed ! nefficiencies broken down into technical and allocative components. The standard of efficiency used by Farrell was the frontier unit isoquant. Assume that X-| and X 2 are the only inputs used in the production of output (Y) and that the firm's production function (a technical frontier) is given by Y = f(XpX 2 ). Furthermore, assume that the production function is homogeneous of degree one in inputs so that it may be written as 1 = f(X^/Y,X 2 /Y) . That is, the frontier technology can be characterized by the unit isoquant, denoted Iq in Figure 4.1.

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4U Figure 4-1. Efficient unit isoquant

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41 Let point in Figure 4.1 represent the firm's actual factor combination (XpX^) used to produce unit output Iq. The ratio of inputs B A needed to produce Iq to the inputs actually used to produce Iq, OX /OX , measures the technical efficiency as defined by Farrell. Now assume for some set of input prices, that the line PP' is the firm's isocost line for which the cost of producing Iq is minimized with input combination X^. This isocost line intersects OX at X . Farrell's index of allocative PR C efficiency is OX /OX , since the cost of point X is the same as that of allocatively efficient point X^, and is less than that of technically efp ficient point X . The overall productive efficiency is then calculated as the product of technical and allocative indices and is given by the ratio C A OX /OX . That is, Farrell efficiency measures associate a deviation from the frontier isoquant with technical inefficiency and a deviation from the cost minimizing input ratios with allocative inefficiency. The efficient unit isoquant is not observable. Farrell's method of estimating the frontier isoquant involves the construction of an envelope of the observed input-output ratios by linear programming techniques. An index of technical efficiency can then be developed for each observation where the index is equal to the ratio of the maximum possible output to the observed output. This procedure has two main advantages: (1) it provides an estimate of technical efficiency for each individual observation and (2) it is not based on any specific mathematical model of the frontier. However, the method possesses two serious limitations: (1) it presumes constant returns to scale and (2) it is quite sensitive to extreme observations or outliers. Also, there are statistical difficulties with this deterministic nonparametric frontier. Since no

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42 assumptions are made about the properties of the disturbances, the parameters are not estimated in any statistical sense. They are simply computed via mathematical programming techniques. Since the pioneering work of Farrell, several studies have been evaluated production effi ci end es..using the frontier concept. Aigner and Chu (1968) expressed the frontier in a simple mathematical form. They specified a Cobb-Douglas production frontier requiring all observations to be on or below the frontier. This was accomplished by assuming that the disturbance term of the fitted function was one-sided. Following Farrell's approach, estimates were obtained by solving constrained programming problems, i.e., either by linear prograirming minimizing the sum of the absolute values of the residuals or by quadratic programming minimizing the sum of squared residuals, subject to the constraint that each residual be nonpositive. As in Farrell's method the parameters were quite sensitive to extreme observations. To compensate for this problem, Timmer (1971) proposed that the linear programming technique be modified to allow a certain proportion of the observations to be above the frontier as a device to reduce the effect of extreme measurement error on the estimates. While this procedure probably solves the outlier problem, it is purely arbitrary and has no statistical basis (Lee and Tyler, 1978). The lack of identifiable statistical properties of the full frontier estimators, as proposed by Aigner and Chu (1968), has been pointed out by several authors (Lee and Tyler, 1978; Aigner, Lovell, and Schmidt, 1977; Greene, 1980). Schmidt (1976), however, pointed out that if the disturbance term has an exponential distribution, the Aigner and Chu

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linear programming procedure is equivalent to a maximum likelihood estimator, while their quadratic programming estimator is a maximum likelihood estimator if the disturbance is half-normal. That the "estimators" are maximum likelihood is of little practical value, since the usual regularity conditions for the application of maximum likelihood are violated (Schmidt, 1976). Therefore, the statistical properties of the estimators cannot be established. Greene (1980) examined the problem in programming models which arises because the range of the disturbance depends upon the parameters being estimated. By considering the properties of maximum likelihood estimators, Greene shows that the irregular nature of the estimators is a consequence of the choice of the disturbance distribution. He suggests an alternative estimator in which the disturbance has a gamma distribution with certain restrictions on the distribution parameters. Given these restrictions, and some additional assumptions (Greene, 1980), maximum likelihood estimation may be used as the usual case and standard errors for parameter estimates may be obtained. More recently, frontier models have been specified by a stochastic frontier, or "composed error" model (Aigner et al., 1977; Meeusen and Broeck, 1977). The central idea behind the stochastic frontier approach is that the error term is composed of two components, a symmetric disturbance and a one-sided efficiency disturbance. The symmetric component allows for variation of the frontier across firms and represents the effects of random variation outside the control of the firm. The onesided component captures the deviation from the frontier function due to technical inefficiency.

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A weakness of the stochastic frontier model is the impossibility of decomposing the residuals into their components (Forsund et al . , 1980). Therefore, it is not possible to estimate technical or allocative ineffiencies for a given observation. Even though frontier estimators have some weaknesses, it seems clear that frontier functions are recognized as superior to Farrell's unit isoquant, notably in their statistical properties. An approach to efficiency measurement which combines Farrell's efficiency indices and frontier methods was proposed by Kopp (1981). Using Farrell's efficiency measure concepts in conduction with full frontier production functions, Kopp's approach produces estimates of technical, allocative, and overall productive efficiency for each sample observation. The method does not require assumptions concerning homogeneity or homotheticity thus placing few restrictions on the form of the production function. In a subsequent paper Kopp and Diewert (1982) proposed to measure technical and allocative efficiencies using the full frontier cost function. This method, which relies on duality theory, requires no direct knowledge of the parameters of the primal production frontier and provides efficiency measures in a relatively simple manner. The possibility of measuring the total productive efficiency and its components at every data point constitutes a major advantage of the full frontier function. However, as Kopp (1981) recognizes, whenever one estimates a full frontier, sensitivity to outliers will be a problem and measures of technical efficiency can be underestimated.

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4b Conceptual Framework It is well known that either the cost function or the production function can be used to define a production technology. Also, it has been shown that both technical and allocative efficiency measures can be obtained from the production function frontier or from the cost function frontier. In this study, efficiency measurement follows Kopp and Diewert's (1982) approach closely, relying on a full frontier cost function. Essentially, the method decomposes the deviations from a full frontier cost function into Farrell measures of technical and allocative efficiency. Unfortunately, the data on input prices which are necessary for estimation of the cost function were not available for this study. Therefore, a self-dual production function was estimated. This allows the analytical derivation of the corresponding cost function and thus the derivation of efficiency measures using the procedure proposed by Kopp and Diewert.^ The Model Let the production function be specified as Y^. = f(T.,L.,M.) i = l,...,n (4.1) where Y^. is the output and T^ , L^. , and M^. are, respectively, land, labor, and intermediate material inputs to the production process of the i^*^ 2 firm, and n is the sample size. Assuming that the firm's production ^Even though the efficiency measures can be derived directly from the full frontier production function, they were derived from the full frontier cost function in this study for reasons of computational convenience. 2 A description of these variables is presented in Appendix B.

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46 technology is characterized by a Cobb-Douglas production function, the model can be written in logarithmic form as in Y^. = £,n a + 6-| iln T^. + 62 i = l,...,n (4.2) where 6.-(j = 1,2,3) are the unobserved parameters and a is the constant J term. The Cobb-Douglas production function has long been a target of criticism because of its admittedly restrictive properties. Recently, generalized functional forms have been suggested to allow the estimation of nonrestrictive substitution characteristics for production structures containing many inputs (Diewert, 1971; Christensen, Jorgenson, and Lau, 1973). By far the most widely used has been the translog function. However, alongside of the many advantages association with the generalized forms, a major disadvantage is the impossibility of providing an explicit dual solution for the cost function corresponding to the production function. Consequently, it is difficult to see exactly how the error term in one function relates to the error in the other function. Since the focus of this study is not directed toward an analysis of the structure of production, but rather toward efficiency measures derived from cost function, the Cobb-Douglas function should provide a reasonable specification because of its self-dual characteristic. The stochastic specification of the Cobb-Douglas production function given in Equation (4.2) can be expressed by

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47 Jin = £,n a + Z 3j 5-n u^. i = 1, . . . , n j = 1, .... 3 (4.3) where X is the vector of inputs (T, L, M), a and 3 are the vectors of fixed and unknown parameters to be estimated, and u is a random disturbance. The deterministic part of Equation (4.3) gives the maximum value of the output Y, given the set of inputs T, L, and M. The disturbance u captures technical inefficiency as well as other random factors. Following Schmidt and Lovell (1979), the dual cost frontier C(Y,P), where P is a vector of input prices, can be analytically derived from Equation (4.3), Jin C. = k + Z Y. Jin P + £n Y, + u. (4.4) where C is the cost of the technically and allocatively efficient input set corresponding to output Y and input prices Pj, P|^, and Pj^, P is the vector of input prices (Pj, P|^, Pj^), r is the sum of the 3j's (j = 1,2,3), Y is the vector of parameters of the cost function (in this case, y.: = B-/r), and k is the intercept of the cost function, J J defined as k = Jin r Jin a — £n r r "3 3: n 3.'^ j=i

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From the derived cost function, technical, allocative, and total productive efficiency measures can be obtained following the methodology set forth in Kopp and Diewert (1982) as discussed in the next section. Farrell Measures of Efficiency Consider Figure 4.1 which depicts the frontier unit isoquant for a linear homogeneous production technology which employs two factors X-j and X 2 to produce some output Y. The assumption of a linear homogeneous technology can be relaxed by considering Iq as the technically efficient isoquant for some level of output obtained from a general full frontier A production function. Assume that in Figure 4.1 point X denotes the observed input levels, X^ = (X^,X 2 ), that produce output Y*. Given a set of input prices P* = (P^,P|) that define the isocost line PP', the input levels at point E, X^ = (X^,X 2 ). denote the technically and allocatively efficient input levels. Given the set of reference input prices P* = (P2j^,P^) and output Y*, the Farrell efficiency measures are given by Technical efficiency (TE) = (P* • X^)/(P* • X^) Allocative efficiency (AE) = (P* • X^)/(P* • X^) (4.5) Total productive efficiency (PE) = (P* • X^)/CP* • X^) A _ A where P* • X = p* x. is the actual cost of the inefficient input set; 0 I U vj B B P* • X = P^ Xj is the cost of the technically efficient input set; P P and P* • X = PT X^ is the cost of the technically and allocatively

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49 efficient input set, which is given by the cost-mi nimizing-input-demand /\ equations. The input combination X is known since it is the observed vector of inputs. Assuming that P* and Y* are known, it is necessary to C B obtain the values for X and X in order to evaluate technical, allocative, C B and total productive efficiency. The values for X and X can be estimated using the production function (4.3) and its corresponding cost function (4.4), in which the input vectors shown in Figure 4.1 and the reference input price vectors are X^ = (T^, L^, M^)._. n r r and P* = (P|, P*, P*), respectively. The input combination X^ can be found from the frontier cost function C(Y*,P*). By Shephard's lemma (Diewert, 1971), 8 C(Y*,P*) ^^3 Pj=PJ;Y=Y*;j=T,L,M gives the system of cost-minimizing-input-demand equations (point E in Figures 4.1) for T, L, and M, which, according to the cost function specification (4.4), can be written, in exponential form, as T^ = Yt C(Y*,P*)/P* = Y 2 C(Y*,P*)/P* (4,6) = Y 3 C(Y*,P*)/P* C(Y*,P*) = K P* ^1 where

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50 Yl “ Y2 ~ ^2’ ^3 "^Y K = e*^, and k and r are as previously defined C A The input bundle X lies on the ray intersecting X with the origin r (Figure 4.1). The location of X is determined by the intersection of this ray and the cost plane P* • X^ = C(Y*,P*). Thus X^= where X^ = C(Y*,P*)/(P* • X^). Therefore, the technically and allocatively c c c efficient input set (T , L , M ) is given by T^ = [C(Y*,P*)/(P* • X^)] T^ = [C(Y*,P*)/(P* • X^)] (4.7) = [C(Y*,P*)/(P* • X^)] The bundle X lies on the efficient isoquant and on the ray joining A B X with the origin. Thus, X can be expressed as tB ^ ^B^A lB = ^B^A ( 4.8) = X^M^ for some X^ B Since the bundle X lies on the efficient surface, it will represent the efficient bundle for some set of input prices W* = (W|, Wj^, W*). Thus,

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bl D Shephard's lemma is applicable for the price vector W*, and X can also be expressed as C(W*,Y*)/W* = Y 2 C(W*,Y*)/W* (4.9) = Y 3 C(W*,Y*)/W* where Yi Yo Y^i Yv C(W*,Y*) = K W* ' W* ^ W* Y* The equations in (4.8) and (4.9) can be solved by normalizing one input price (i.e., let 5 W|/W| =1). Then the model may be expressed in terms of normalized prices and the equation in (4.9) can be rewritten as T^ = Y-| C(W*,Y*) since W| E 1 = ^2 C(W*,Y*)/W* (4.10) = Y 3 C(W*,Y*)/W* where C(W*,Y*) = K 1 T3 Yv W* Y* ^ W* = W*/W* and W* = W*/W*

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p The term X can be eliminated from Equations (4.8) by dividing the p left-hand side vector by M and by dividing the right-hand side vector by B A X M . The resultant equations are of the form L^/M^ = lW = (4.11) t-B ,j.B ,wA _ T /M = T /M =02 A A A where B-j and 02 are fixed constants given that T , L , and M are observed values. From equations in (4.10) and (4.11) the following results can be derived: „ „ YjC(W*,Y*) /YoC(W*,Y‘) Y, WX L /M = = e, YJ Wf T2 w* = -= — \ Yje, and tVi^ = YtC(W*,Y*) 'YoC(W*,Y*) Yi ^ r = _L M* = Q Pi* M ^2 ^3 w* = — 0 M Y-] 2 Thus, ^2 ^3 ®1 ^2 0 0 2 1

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53 B B B and the equations in (4.9) can be solved for T , L , and M . After the bundles (T^, L^, M^) and (T^, L^, M^) are determined, the efficiency measures as previously defined may be calculated. Estimation Procedure The estimation of the production function given in Equation (4.3) was performed using the procedures described in Greene (1980). Two distinct estimators were utilized to obtain parameter estimates of the full frontier model. The first is a corrected ordinary least squares estimator with an intercept adjustment (COLS). This procedure assumes that the frontier is a neutrally scaled average function. The second procedure is maximum likelihood estimation (ML) process. The full frontier production function was fitted using the two estimators for each group of farmers based upon whether or not they participated in the PRODEMATA program. Corrected Ordinary Least Squares (COLS) Estimation Assume the production function as specified in (4.3). If, with the exception of a nonzero mean for the disturbance, all of the assumptions of the Gauss-Markov theorem are assumed to apply to the specification in (4.3), then it can be shown that ordinary least squares (OLS) provides consistent estimates of B, but that the estimate of the intercept is inconsistent. However, the OLS intercept estimator is consistent for a + y, where y = (E(u). Greene (1980) has shown that, regardless of the distribution of u, the OLS residuals can be used to derive consistent estimates for a. Denote the smallest OLS residual by By definition, e^-j^ < 0.

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Let a be the estimated value of £n a. Assuming a > 0, then subtracting e^^j from a yields e\ = [£n Yi (a e^^) )ln Xij] or, equivalently, e^ = [(a £n Xij) S,n Yi]. The corrected estimate a = a e^.|^ has been shown by Greene to be a consistent estimate. The resulting residuals (e^. ) will be nonnegative with the equality e^ = 0 holding at one observation. Although estimates for all parameters of the frontier function can be obtained using this simple modification of the OLS estimator, the results are appropriate only if the errors are symmetrically distributed. If this is the case, then the frontier function is simply a scaled version of the average function. Therefore, measures for the marginal rate of substitution and allocative efficiency derived from Equation (4.3) will produce the same result in either COLS or OLS. The distribution of u in Equation (4.3) can be of different shapes. As a consequence, the parameter estimates of the frontier and average functions can be quite different depending on the degree of skewness of the distribution. Greene (1980) points out that a maximum likelihood estimation which takes into account the distribution of u should be more efficient than COLS, particularly if the error distribution is highly skewed. Maximum Likelihood (ML) Estimation Consider the model as specified in (4.3). The disturbance u is assumed to have a gamma distribution, i.e., u 'v G(X,Z). In addition, the restrictions X > 0 and Z > 2 are necessary to ensure that the likelihood function is well behaved (Greene, 1980). Given this disturbance specification, then the necessary regularity conditions required for ML and the usual asymptotic properties of ML estimators are satisfied. The log

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55 likelihood function for the model is log L = n Z log X n log r(Z) + (Z 1) J log u. X J u. (4,12) i i ' where = iln a + Z6^£n Xij S,n Yi. By using the method of squaring to impose the restrictions that X > 0 and Z > 2, the log likelihood function becomes Z* = v'l 2 and X* = /X The maximization of (4.13) can be accomplished by minimizing the negative of the log likelihood function with respect to the parameter vector (}>' = (X*, Z*, a, B). The method used to obtain the parameter estimates is a modified method of scoring utilized by Greene (1980). The convergence criterion in the iterative procedure was that the individual change in the estimates for a and the B's from the s^^ iteration to the -4 next were smaller than 10 . The starting values for a and B were the consistent estimates obtained from the COLS procedure outlined above. Consistent starting values for X* and Z* were slightly more difficult to obtain. Denote o (e) = S and E(e) = e as the variance and the mean of the modified set of residuals. Given that e = Z/X and = Z/X^ are consistent estimates for o^(e) and E(e), respectively, X = e/S^ and Z = e^/S^ are appropriate consistent starting values for X and Z. Since any log L = n(Z* + 2) log X* n log r(Z^ + 2) + (Z^ + 1) j: log u, ( 4 . 13 ) where

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continuous function of a consistent estimator is itself consistent 2 2 (Kmenta, 1971, p. 166), substituting X* for X and Z* + 2 for Z the starting values for X* and Z* are then determined as X* = e 1/2 and Z* = 2 1/2 The ability to obtain the ML estimator with all the desirable properties for the estimates constitutes a major advantage of Greene's (1980) formulation. Furthermore, since the gamma distribution can be asymmetric, ML estimation of the parameter vector $ should be more efficient than OLS which does not account for this fact. In general, the gain in efficiency obtained by ML is related to the degree of skewness of the distribution which is approximated by 2/vT. Greene suggests the ratio Z/(Z 2) as an indicator of the relative asymptotic efficiency of ML over COLS. Therefore, the smaller the value of Z the greater the degree of skewness and the greater the gain in efficiency. The degree of skewness also has some implications with respect to the relationship between the frontier and average functions. Suppose the process generating the disturbances is such that the error distribution is fairly symmetric. The estimate of Z will tend to be large and the frontier function will tend to be a neutrally scaled version of the average function. On the contrary, if the distribution is highly skewed, the frontier function will be a nonneutral ly scaled transform of the average function.

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CHAPTER V EMPIRICAL RESULTS This chapter is divided into two major sections. In the first section the estimated full frontier production functions and the corresponding frontier cost functions are analyzed. In the second section estimates of efficiency measures derived from the frontier estimates are considered. Model Estimation Full frontier Cobb-Douglas production functions were estimated using sample data for participants and nonparticipants in the PRODEMATA program.^ These frontier production functions generated the dual cost frontiers which were analytically derived. Corrected ordinary least squares (COLS) and maximum likelihood (ML) estimation procedures were used in this study. The estimates obtained for the frontier production functions and the derived estimates for the frontier cost function are discussed below. Frontier Production Function The full frontier parameter estimates for both groups of farmers are presented in Table 5-1. As expected, all input coefficients ^A description of the variables used for estimation is presented in Appendix B. 57

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Table 5-1. Corrected ordinary least squares (COLS) and maximum likelihood (ML) estimates of the frontier production function for each group of farmers. Zona da Mata, 1981-82 58 O O C\J oo csj 00 VO r— CTl oo VO 1— +J LT> 00 00 VO ^ •r* 00 VO 00 04 CJi OO O 1— O O CTl O O O o o • • . . • • • (0 f— o o o r— O »— o -C — " — ' -*-> (U 4J CO in •r— 1 — CO VO CM CM LO m TO CO 00 CM ^ 1“ CM 00 0) ro CM CM Lf> ro 1 — CM CO E S^ LO CO ro LO LO LO ro S0) CM O CM O CM O CM O 0) -l-> « • • « • • • • 4-> CO o o o o o o o o C E t-H •o O) =! cn s(0 o CO CTi QJ c (U so cu x: (O x: •o (U 4J in oi 3 in 0} , Lf) VO ro 1— LO VO cn LT5 f— CO VO I— o CTl <0ro r^ 00 JD o CO VO cr> LO LO ro ro o LO O o VO O • • • • • « • o o o o o o o o ' — ^ ' — ' • OI in ra c E O) *r•I(J in •I(U 4OJ 0 U 01 Q. o; o s0) T3 C rr> CO CCTi w f •0C\J o 1— o LT> I— CM 00 00 Lf) O 00 m CM ro on cn -o o o 1 — o o o o o s. . • • . CO So o o o C5 C3 o o -a o C 4co +J o (O •M ... — s C ro ro 00 o ro CM CT5 ro CM 1— VO O 4-> a> ro CM CT> LO ^ iO 00 ^ CO CM ^ -Q 0> -Q C O ro CM OO — o • • • • o ro O ^ o ro -I fO t/) LO to 4-> 4-> C C 10 ro LO ro 4-> CD. 4-> Q. c c •r» ro U ro U Q. Q. •r“ •r* -M •f™ 4-> U SU S•rro •rro -o CD. +-> Cl o SC Sc JZ CO ro o ro o 4-> O. z , a. z 0) o _j CJ> 2:1 C •r— fO -C
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estimates are positive. In addition, with the exception of the land coefficients in the participant group, all coefficients are significantly different from zero at the 1 percent level of statistical significance. In comparing the results obtained by ML with those obtained by COLS, some slight differences were observed. In general, the differences were relatively more pronounced in the estimates for participant farmers. As expected, the ML estimates for the intercept term are higher than those of the COLS for both groups of farmers. The land coefficient estimates are relatively much smaller in the ML procedure than in the COLS procedure, especially for the participant group. Even though these differences are relatively large on a percentage basis, they are less than one COLS standard error of the respective land coefficients. In general, the differences between the ML and COLS estimates were not very large. In no case was the difference between the estimates greater than a single COLS standard error of the respective coefficent. The differences between the ML and COLS estimates depend on the skewness of the disturbance distribution as mentioned in the previous chapter. Because the degree of skewness is approximated by 2/vT for the gamma distribution, large values of the Z parameter of the disturbance distribution imply a less skewed distribution. Therefore, in light of the relatively large estimates (Z) obtained for the Z parameter (Table 5-2), the similarities which were found between the ML and COLS are not surprising. Table 5-2 provides a comparison of the estimated ML distribution parameters for the two groups of farmers. The skewness measures for

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Table 5-2. Summary statistics for the frontier production function disturbance distributions for each group of farmers. Zona da Mata, 1981-82 bu i/i S0) CO 4-> c <0 CL ro c\j O LO CT^ 00 cr> CM 1— cr» o to o u pN. cn CM LO IX) CO to o CM r— O CM o CO 4-> • • • • • • . • • LO ro 00 o r— o o to CL c o zr CO (O a. O o CO 4-> C (0 to IT) CO LT> to LO 5fO a. 00 o t— O o o C>J I > u to c ^ QJ •f" to u CO ( . ^ , a; CM tl15 Cm 0 < MX *'*«s*. 0) 0) < PM CM SmK' U _r-« 4 C cn Q <0 Numbers in parentheses are asymptotic standard errors of the estimates.

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61 the participants are about 1.5 times that of the nonparticipants. This finding indicates that the estimated disturbance distribution tended to be more symmetrically distributed in the case of the nonparticipants than in that of the participants. The degree of excess is a measure of nonnormality. It approaches zero as the error distribution tends toward normality. Since the estimated degree of excess is twice as great for the participant group as for the nonparticipant group, the error distribution is closer to normality in the case of nonparticipant farmers. As a result of these findings, only a marginal gain in statistical efficiency was obtained for the group of nonparticipants when the ML procedure was used. The asymptotic ratio efficiency was 1.0601; i.e., the gain in statistical efficiency was about 6 percent. Thus, the frontier function can be viewed as an approximation of a neutrally scaled version of the average function in the case of nonparticipant farmers. For the participant group the results are somewhat different. /N The value of 16.3315 for Z gives an asymptotic efficiency ratio of 1.1396. Consequently, the gain in statistical efficiency was about 14 percent. This greater gain in statistical efficiency is a consequence of a more skewed disturbance distribution in this group as compared with that of the nonparticipants. As a result, the frontier function for the participant group is less related to the average function than is the case with the nonparticipant group.

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62 Frontier Cost Function For each production frontier the dual cost frontier was derived analytically. The results are presented in Table 5-3. From the estimated parameters and the corresponding standard errors, it can be seen that, except for the coefficients for the price of land in the participant group, all coefficients are significantly different from zero at the 1 percent level of statistical significance. The coefficients in the cost function represent the cost shares for the use of each input. Labor accounts for the greatest share of the total cost. This is not surprising. Labor is a relatively abundant factor in the Zona da Mata. High unemployment, coupled with low wages, may contribute to a high level of labor use. The estimated labor share is consistent with the actual pattern of labor use found in the sample. As shown in Chapter III, labor costs accounted for more than 60 percent of the variable input costs. This high labor share is also consistent with the findings of Silva (1981) which show that labor costs accounted for about 70 percent of input costs in most enterprises analyzed in the Zona da Mata in the 1977-78 crop year. Efficiency Measures The derived cost function frontiers provide the necessary information to calculate efficiency estimates for each observation. The reference prices used to compute technical and allocative efficiency are the following: (a) for land, the average rent paid per hectare of productive land in the survey year (Cr$2780.00) ; (b) for labor, the average

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Table 5-3. Derived COLS and ML estimates for the cost function frontier for each group of farmers. Zona da Mata, 1981-82 63 -a o O) , — . ... — ^ , — . CO ^ CTi ID ID CM f— »— C\J O OO O ^ ^ f— OsJ CM CD cvj a> CM 0) VD CO I— OO fmmm o» 1— sz cr» o O O O) o CT> O -a • • • • • • . . (V o o rO o o o o i4-> o o 4-ts(O +-> r— to 3 E Sic O 3 V OO 1— o uo 00 *dCO <3CO VD IT) OO CM o CM O CM O CM O X O • • • • • • • o o O O o o o o £ i/^ Q. C Q. O lO .r4-> C U eO C .« > , , , , ?, re O CD 00 CM ^ 1— ID cn ^ S 1— Os. f— r— O'. VO 1— OO 1— O >— •aOO 1— LD LD VO O m o Os. o VD O 8 § . . . . . . . . o o o o o o o o tu ^ (0 •S! f= a to" ^ (Ti CTi I— CTi VD 00 00 CM <— CO 00 rcn 00 £ ^ CM CTi (y> OO O ^ 00 ^ o 00 «!aCM OO *3^ cn CM O) 4-> o o >— O O O o o CO CD • • o o (D CD CD CD -a I-It; to <4-> VO r— o cr» CO C • • o CM CO CM o 1 1 1 1 CO o c_> (/) U) 4-> -l-> C c t/) ro (/> CO Q. CL c •r» c ta U CL +J CL c s. c
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64 wage paid for daily labor of one equivalent man-day during the agricultural year (Cr$429.30); and (c) for intermediate material inputs, an aggregate index of the price paid by producers for agricultural inputs in the state of Minas Gerais (Cr$227. 02 per unit of intermediate material input). For an individual firm it is reasonable to assume that the supply of inputs is perfectly elastic. Therefore, input prices can be taken as fixed, exogenous variables. Moreover, since the Zona da Mata region is a fairly small region, it may be assumed that all farmers face the same set of prices. Therefore, the selection of a single vector of prices for all sampled farms is a reasonable assumption. Tables 5-4 and 5-5 show the average efficiency measures which were calculated using the procedure outlined in Chapter IV, Equations (4.5). The results are given for both the COLS and ML estimates. These results are discussed below. Technical Efficiency Results . A notable feature of the findings is the low level of technical efficiency estimates compared to the much larger measures of allocative efficiency. The unduly low technical efficiency may be due in part to the full frontier specification. As pointed out previously, this method is highly sensitive to outliers. The high degree of technical inefficiency may also be a result of the degree of traditionalism in the agriculture of the region. As was mentioned in Chapter II, the 2 The Centro de Estudos Agricolas of the Fundacao Getulio Vargas (FGV) polishes a monthly index of prices paid and received by farmers in each state of Brasil. The index used corresponds to the average for the 1981-82 crop year, calculated by FGV with 1966 used as the base year (price = 100).

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65 >> •D C E i. to o Q. 3 O scn o (O O) i. o t/1 t— rer— CO 0 ) C 3 1 — 00 o 00 o CO o to o O r— re ro O o . o CO o CM o o o Q. i• • . o • • • • • • • E to re ^ ^ ^ to (U i~ re +-> o (U 0 ) o> to sre >0 to s. (U c 2 o o o o o o LT> o LO o un C>J 1 — CO CVJ CT> o c\i CVJ ot r>. 1 CSJ 1 — 00 •— cr> 1 — 00 ID 1 — to o f— ro o o o o 00 o CVJ O o o o • * • * • • • • « o o o o o o O o O O o o o '' — ^ '' — ' — — ^ ' — CO CO CO o to C'. O o o to CM to CM to o cjto to CO r>. o CO CM reCM CM O CO to to o o o o o o o o o o o o o o o m 00 to CM CO o reto o o o o I— CM o 00 CM CM CM 00 o CM to to r— CM O CM to to o o o o o o o o o o o o o o o o o re > CM -o 00 0) I 4 -> rre 00 I— on 3 I— o <0 (C U -M s; l/> 0) to U “O •o <0 c c •rO M >> u c >> (D S. o U CD •rO) <0 0) u CU >> O) u ro C sto 0 ) c > O) in CO s. 0 ) (J 3 o o o. {/) iA to o ... — s , — ^ ,0^ o r— t— o reCVJ r— ^ ov CVJ ^ r— CVJ CVJ 1 ^ o in CVJ O 1— f— KO O 1 CO O o o CO o ov O CVJ o o o o « • • • • • • • • • « o o o o o o o o o o o o CO S0) CO Q. y.— O. rOV to 00 00 o tn ov r— 1-^ o CO 1— o o CM rer>» CM VO 00 CT> O s. 1— r— • o 00 o VO o O O u • • • o . • . • • • 0) o o o o o o o o d d CO 00 >> u C CO OJ O) •»“ u O T•f-o c CO fO CL S o 3 -o o o c: s. (U Q. •r— u CO -M MO OJ HC/) •M c fO Q. •r— u fO o. CO Q. CJ 4-> CO Q. CO Numbers in parentheses are asymptotic standard errors of the means.

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66 -o c (O to s0) i(O a. 3 0 s01 u (O cu io to O) (O E •f“ -(-> to CM •o CO (U I 4 -> r(O CO t— CD 3 I— o <0 (O o +-> to 0) (O O -O T3 (O C C •ro M >0 O « e: >» (U i. •rO tJ CD QJ re (U u >> u ro C &03 0 ) C > LO I Ln O) jQ reCD CM CO o LD o rec — m o co o reo rtJ 1 — o o o r-^ o 00 o .— o o o Q, • « • • • . . • • • • • E OJ o o o o o o o o o o o o (0 > ^ — 00 ^0 CM to to C3 CM CO in as t— CO reo O CM to o O CM O CO »— F— CO o o CM O o o to O r>. o rO o o [1 » . • • . • • « • • * • • A o o o o o o o o o o o o to 0) O sO . — to to re" reCO I— CM 00 in p^ CM re4-> 1 CD 1— Lf> o to OJ CM CM o reo U I— o o o VO O P^ o r— O o o OJ o • • • . • • • • • • . • o o o o o o o o o o o o o ^ ^ >w«' — £= m •r* to s0) 0) N c •1“ 5 to o E o , — , S. ir> CD CO 0> CM O 1— as VO t-' re<0 1 o tn o ^ »— tn 1 — CM O reo Mf— r— o o o o CO o 1— O o o o • • • • » • • • • • • • >> • o o o o o o o o o o o o o NwO’ Sm** rS. a; o 3 •o 4»«— ^ ^ o cy> f— o ro ^ CM ^ CM CO o CO CM o 1— LO o ro CM tTi 1— •— reo Q. r— rO o o 00 o CO o r— O o o 1 • * • • • • • • • • • • Mo o o o o o o o o o o o o O ' — ^ ' — ' — ^ ' — ' — ^ to to 03 to s0) to Q. .»«— N CL ^ tp r— Lf) r— P^ o o as VO ro in o CTi t£> rs. o o ^ 00 CM VO o sro O o o o CO O ro o o o u • • • • • • • • • • • • 0) o o o o o o o o o o o o u c •r“ c > C •rto <0 4to ro •r“ to ro 4o. 44-> Q. -»-> -M Q. 4c 0) c •r" O c 0) to u fO (J 3 5>S O >> CL 0) Q. •r~ T3 CL u •4-> > •r— 4-> O c -M c to rO o •r— O SScu U SOJ a; U • fmm 4-> to Q. ro •f“ o 4-> Q. ro 4-> CL (J 4-> O. u c &c (j Sc c •rO 03 o O ro o re 4ro o Ho O. 2: r“ cu z 4D. 'Z. 40) r— o OJ U J HcC 1— Numbers in parentheses are asymptotic standard errors of the means.

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67 Zona da Mata experienced its heyday several decades ago when coffee was the leading enterprise in the area. Thus, it is possible that the region is still in an adjustment process from the coffee eradication program sponsored by the government in the mid-1960's. Some farms with high degrees of efficiency may already have achieved this adjustment. In a very traditional area, however, it is not surprising for the adjustment to come slowly; therefore, the high degree of technical inefficiency may reflect this slow pace of adjustment. Comparison by tenancy . In both the COLS and ML estimates technical efficiency tends to be quite uniform across different sizes of owned farms. However, one result which stands out is the higher technical efficiency of the sharecroppers compared to that of the owners, especially in the case of the participant farmers. The technical efficiency indices for the participant sharecroppers should be regarded with the utmost caution since they are based upon a very small number of observations. In addition, this class of producers has no tradition of participation in supervised credit programs. However, the nonparticipant sharecroppers, whose number in the sample is much greater, also had a relatively higher technical efficiency than the nonparticipant owners. The better performance by the sharecroppers may have several plausible explanations. First, since most sharecropping contracts are verbal and short term, sharecroppers do not usually cultivate perennial crops or maintain livestock under the sharecropping agreement. Thus, the level of output per unit of input used was much higher in the case of the sharecroppers (Table 5-6). These higher output/input ratios

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68 Table 5-6. Output/input ratios obtained by sharecroppers and by the owners in the Zona da Mata, 1981-82 Class of producers Output/1 and Output/labor / Unit of Output /intermediate / materials (Cr$/ha) (Cr$/man day) (Cr$) Sharecroppers 85,000 2,055 35.75 Owners 42,000 1,966 5.64 for the sharecroppers may also partially be explained by the higher crop yields obtained by this class of producers compared to the owners. The sharecroppers, using their own labor, can exert better control over their activities and so may obtain higher productivity than their owner counterparts who tend to hire labor. A second explanation for the higher technical efficiency presented by the sharecroppers may be the prevalence of intercropping in the region. Corn is intercropped with beans by most of the producers, particularly by sharecroppers and the smallest farmers. Vieira (1978) pointed out this fact and suggested that the intercropping practice is both a resource-use-optimization strategy and a means to ensure diversified diets and income sources. Finally, it is possible that the sharecroppers use less labor per unit of cropland as compared to the owners, which may contribute to the former's better performance. Sharecroppers frequently have offfarm jobs as an important source of income. Thus, it may be argued

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69 that sharecroppers have a very accurate perception of the opportunity cost of their labor which is explicitly specified by off-farm jobs. As a consequence, sharecroppers may tend to use their labor more efficiently in the sharecropped areas in order to increase their labor availability for off-farm opportunities. On the other hand, the opportunity cost of labor for the owners may be much less explicit than is the case with the sharecroppers. Thus, it is possible that the owners use more labor in crop areas than would be recommended, a situation which contributes to a decrease in their level of efficiency. Comparison by group . For ease of comparison between the efficiency measures obtained for participants and nonparticipants in the PRODEMATA program. Table 5-7 presents the ratio of the participant to nonparticipant efficiency. This table was taken directly from Tables 5-4 and 5-5. The efficiency measures derived from COLS and ML show that, on the average, technical efficiency for the participants was about three to O four times higher than for the nonparticipants. On the average, the technical efficiency measures obtained via the derived cost function when the ML estimates were used (Table 5-5) are 0.185 for the participants and 0.058 for the nonparticipants. ^ 3 In Appendix C it is demonstrated that, under certain assumptions, the technical efficiency averages for the two groups are statistically different in each tenancy class and in the sample as a whole. 4 These figures are fairly close to the values of the technical efficiency measures estimated directly by the disturbance distribution as suggested by Greene (1980). As pointed out in the specification of Equation (4.3), the disturbance term u captures technical inefficiency in production and other random factors. Under the assumption that u has a gamma distribution, i.e., u 'vG(X,Z), Greene pointed out that the average technical efficiency may be estimated by (X/X+1)Z. The average values of technical efficiency estimated via the efficiency distribution were 0.1578 for the participant farmers and 0.054 for the nonparticipant farmers.

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Table '^-7. Efficiency index ratios between participant and nonparticipant farmers. Zona da Mata, 1981-82 70 o CTi •r“ 4-> CO ro Of ro o C>J t/) c CO Q. •r* 00 L£5 o^ U LO LO •r“ o CO o +-> • * • o o o CO O. c o z U) c CO LT> ro •1— u 00 ro •r* 4-^ o o o CO oo LO CTt C\J •P“ •— 00 CO q: o ro • • • So o o COLS CO CL c o «/> M c CO o lO •r“ o ro 00 L£> CM •r* 4^ o CD CD CO O. to > u c: 0) >> o c 0) u (V •nu •r* > *D MC M4-) •r— > U 0) r“ OJ > =3 TD U o c c CO s M<4q; r— O
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71 The much higher technical efficiency shown by the participants indicates that the sampled farms participating in the PRODEMATA program tended to be grouped closer to their frontier than were the nonparticipating farms. This pattern also holds for different farm sizes. That is, technical efficiency is always greater for the PRODEMATA participants than for the nonparticipants, irrespective of farm size. These results could suggest that the PRODEMATA program exerted a substantial impact on technical efficiency. Allocative Efficiency Resul ts . Data in Tables 5-4 and 5-5 show that both groups of farmers were much more efficient in an allocative sense than in a technical sense. Relatively high levels of allocative efficiency were found when either the COLS or the ML estimates were used. The similarity between the allocative efficiency indices derived from the COLS and ML estimates is a consequence of the similarity of the COLS and ML frontiers. This is particularly noticeable for the nonparticipant group. Since the COLS frontier for this group can be viewed as an approximation of a neutrally scaled version of the average function, the marginal rates of substitution between inputs will be very similar whether derived from the COLS frontier or from an average function. Therefore, allocative efficiency measures for this group will be similar whether derived from the frontier function or from an average function.

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72 Comparison by tenancy . Unlike in the case of technical efficiency, the high levels of allocative efficiency tend to decrease slightly as farm size increases. These results appear to support the argument that traditional agriculture, especially among the smaller farmers, is not necessarily inefficient in allocating resources. The high degree of allocative efficiency presented by the sharecroppers and smaller farmers may be a response to the severe restriction in resources faced by these producers. In addition, since these classes of producers raise food crops as their primary activity, they may strive more for better resource allocation. Comparison by group . In comparing the allocative efficiency between the two groups, the results indicate that the nonparticipants had 5 indices which were greater than those of the participants. Initially this is surprising. However, there may be several explanations for these findings. First, it may be argued that nonparticipant farmers, facing more restrictions in resources, might be forced into allocative efficiency. Second, it is possible that participant farmers face difficulties in adjusting to marginal conditions for the best allocation because of the effects of the learning process in adopting new agricultural practices. 5 In Appendix C a statistical test indicates that, with the exception of sharecroppers, the allocative efficiency averages for the two groups are statistically different in each tenancy class and in the sample as a whole.

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73 Finally, an alternative explanation for this result is that additional capital made participant farmers less efficient. It is possible that participant farmers had been allocatively efficient prior to PRODEMATA but that with additional capital resources flowing into their production systems, some inefficiencies may have been introduced. This \ possible drop in efficiency may have occurred because of changes in the quantity of inputs used or in their relative prices. Certainly, if allocative efficiency existed before the initiation of the PRODEMATA program and if this program induced changes, then it is quite likely that allocative efficiency was disrupted. As cited in Chapter I of this study, some authors have argued that few significant inefficiencies in the allocation of the factors exist in traditional agriculture. Thus, the findings of this study appear to corroborate the argument that farmers in traditional agriculture, although poor, allocate their resources efficiently. Total Productive Efficiency Tables 5-4 and 5-5 also show the figures obtained for total productive efficiency. Since this efficiency measure is defined as the product of technical and allocative efficiencies, there is no need to present a full discussion of these findings, which reflect the pattern already discussed for the two components of total productive efficiency. However, a result which should be noted is related to a comparison of the results by groups. The participant group was found to be considerably more efficient. Although this group is at a slight

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74 disadvantage in the allocative efficiency component, its higher technical efficiency was strong enough to put it in a slightly better position in total productive efficiency. Sunmary of Findings 1. The average technical efficiency of the participant group was significantly greater than for the nonparticipant group in each tenancy class and in the sample as a whole. 2. Technical efficiency levels and farm size seem to be unrelated; i.e., technical efficiency indices for the owners tended to be quite uniform across different sizes of farm. However, the average technical efficiency by the sharecroppers was significantly higher than that by the owners. 3. Both groups of farmers had relatively high levels of allocative efficiency. The nonparticipant group had an average allocative efficiency which was higher than that of the participant group for all tenancy classes (except sharecroppers) and for the whole sample. While statistically significant differences have been found between participants and nonparticipants in both technical and allocative efficiency (Tables C-1 and C-2, Appendix), it remains to be determined whether such differences are a consequence of participation in PRODEMATA, or of other farm or farmer characteristics that are associated with participation in the program. That is, the measured differences in technical and allocative efficiency may be caused by PRODEMATA participation or may be simply associated with participation, both of which are caused by some third factor.

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75 As shown in Chapter III, those fanners who participated in PRODEMATA have larger farms, own more capital, and use more purchased inputs than nonparticipants. Could it be that these and other fundamental differences between participants and nonparticipants which existed prior to the initiation of PRODEMATA are the cause of the estimated differences in technical and allocative efficiency rather than participation in the program itself? The next chapter deals with this question.

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CHAPTER VI DISCRIMINANT ANALYSIS OF PARTICIPATION CHOICE Introduction The analysis described in this chapter is designed to determine which farmer attributes are associated with participation in the PRODEMATA program. A discriminant model was used to examine numerous characteristics of farms and farmers in an attempt to determine which of them were best able to distinguish between participants and nonparticipants in the program. The initial sections of this chapter deal with methodological considerations, including definitions, basic assumptions, and the theoretical model used in discriminant analyses. In the final section, the empirical model used is formally presented and the results are examined. Linear Discriminant Model The basic idea of discriminant analysis is that a linear discriminant function exists which will, as best as possible, classify farmers into predetermined statistically separate groups. The discriminant function is of the form D = d,z, + djZj + djZj + . . . -f d|^z^ (6.1) where the dependent variable D is the discriminant score, the d's are discriminant coefficients, and the z's are the values of the k discriminant variables used in the analysis. 76

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77 The estimation problem is to assign values to ,d 2 ,cl 2 , . . . ,d|^, that maximize the ratio of the variance between the group means to the variance within groups. Let d equal the vector of discriminant coefficients and Z equal the population vector of the k discriminant variables. Thus, if D = d'Z has mean d'Z.| in group 1 and d'Z 2 in group 2 and if the covariance matrix of Z = E in both groups, the discriminant function is that one which maximizes (d'Z^ d-Z2)^ d'Ed By differentiating this expression with respect to d and setting the derivations equal to zero, the d's are found to be proportional to E ^(Z.| Z 2 ). Since Z^ 1^, and E are generally unknown, they are estimated as Z.J , Z 2 , and S, where Z-| and 1,^ are the sample mean vectors of the discriminant variables for the two groups, and S is the pooled estimate of the common E. Therefore, an estimate of the vector d is given by d = s-\i^ I 2 ).'' Once the discriminant function is specified, the cutoff point between the two groups is determined. The cutoff point is used for classification purposes of subsequent observations. According to Morrison (1976), an observation will be classified as belonging to group 1 if Z'S'^I^ Z 2 ) 1/2(1^ + I 2 )'' S'^ (Z^ I 2 ) > log P (6.2a) or in group 2 if Vurther detail on discriminant analysis theory is presented in Morrison (1976).

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78 Z'S'^CZ, Zj) 1/2 (Z, + Ij)’ s'l (7, Zj) < log P (6.2b) where the strictness of the equality is arbitrary for continuous variables ; P is given by P 2 C (l.|2) P^C (2|1) where and P 2 are prior probabilities, i.e., the probabilities of classifying an observation into group 1 or into group 2, respectively; and C(i I ^2; j=i ,2; i/j misclassifying an observation from the j group as being from the i^^ group. In the absence of other information, if the misclassifi cation costs are assumed to be equal and the prior probabilities of each population to be one-half, then P = 1 and the classification rule states that an observation should be classified in group 1 if Z'S-'' (Z, Zj) > 1/2 (7^ + s"' (7, 1 ^) (6.3) and in group 2 otherwise. The expression Z'S 1 ^) in (6.3) is the population linear discriminant function which gives the discriminant score for each individual observation when evaluated for the discriminant variables of that particular observation. The expression 1/2 (Z.j + 1 ^)' S“^ (Z.| 1 ^) is the point midway between the means of the discriminant functions for each group.

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79 Evaluating the Discriminant Function The performance of the discriminant function can be evaluated in terms of three major aspects; (1) the significance of the observed differences between groups, (2) the relative importance of each variable in the discriminant function, and (3) the ability of the model to classify future observations. Differences between Groups To test for differences between groups a Chi-square test is used (Gau, 1978) where the null hypothesis is that the sample group mean vectors are equal. By employing Wilk's lambda. where W is the pooled wi thin-groups sum-of-squares matrix and T is the total sum of squares, a test statistic can be calculated by H = where N 1 K + C iln A N = total sample size K = number of explanatory variables G = number of groups The calculated H, which is distributed as a Chi-square with K(G 1) degrees of freedom, may be used to test the null hypothesis.

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80 Relative Importance of Variables The relative importance of each variable in the discriminant function can be measured by either of two methods: (1) ranking variables according to the size of their standardized coefficient, or (2) ranking variables according to the size of their weighted discriminant coefficients. The standardized coefficient method weights each coefficient in the discriminant model by its standard deviation. Essentially, the standardized coefficients scale the discriminant coefficients in a similar way to the beta coefficient used in regression analysis. The absolute value of each standardized coefficient represents the relative discriminatory power of the variable in the discriminant function. Joy and Tollefson (1975) argue that the standardized coefficient method is not appropriate to assess the importance of variables in a discriminant function. They suggest using a weighted discriminant coefficient, ^j2)> where d^. (i=l , . . . ,k) is the estimated discriminant XU coefficient, and is the mean of the variable for the k^^ group. Classification Ability The ability of the discriminant function to classify future observations is suggested by the apparent error rate. This rate is defined as the fraction of observations in the sample which are misclassified by the estimated discriminant function. In the following sections the theory of discriminant analysis described above is applied to the PRODEMATA data, beginning with a discussion of the discriminant variables included in the empirical model and followed by an analysis of the results.

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81 Selection of Discriminant Variables The explanatory variables were chosen from a large number of socioeconomic characteristics of each farm unit interviewed. From this set of characteristics, only those which were less likely to be affected by the PRODEMATA program were selected as potential candidates for the analysis. This is because if variables which might have been affected were used, it would be difficult to separate the cause of the participation from the effect of the participation. When two or more variables were found to be highly correlated, only one was included, as otherwise it would be difficult to determine which one is exerting the greater discriminant effect in the function. The final configuration of the discriminant model included the following 2 variables: Crop land (CROLAN) Pasture land (PASLAN) Fixed capital stock (FIXK) Cooperative membership (COOP) Age of the respondent (AGE), and Education level of the respondent (EDUC) A brief discussion of the expected influence of each variable is presented below. Crop land . Crop farmers use far more purchased inputs per hectare than is the case for livestock. This may imply that producers with 2 A description of these variables is presented in Appendix B.

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82 larger areas in crops have greater borrowing requirements and thus a greater need to participate in a credit program such as PRODEMATA. Pasture land . The PRODEMATA program was derected toward small farmers, who tend to be crop oriented; larger farmers who have larger areas in pastures may be less interested in entering the program. Therefore, farmers with more pasture land would be less likely to participate in the program. Fixed capital . Farmers who have more assets may also have greater flexibility in making changes in technology. Therefore, they would be more likely to participate in the program. Cooperative membership . This characteristic was taken as a proxy for the degree of information available to the farmers. It is assumed that members of farm cooperatives have more complete knowledge about specific credit programs than nonmembers and, therefore, may have a greater tendency to participate in the PRODEMATA program. In addition, cooperative members probably are accustomed to working with the extension service and institutional credit sources. Finally, they may have better records than nonmembers which would make it easier for them to obtain credit. Age . The need for credit may vary inversely with age since older farmers should have achieved higher levels of capital accumulation than is the case for younger farmers. Education . The educational level among the farmers in the area is very low. In the sample, about 30 percent of the farmers were illiterate and 66 percent had four years or less of formal education. This low

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83 educational level may influence the willingness to accept a formal loan which requires a substantial amoung of paper work and visits to the bank. Therefore, less educated farmers may prefer to obtain their loans from informal sources, rather than to participate in a supervised credit program. Analysis and Results The estimated model includes all six variables described above: D = dp + d^ CROLAN + d^ PASLAN + d3 FIXK + d^ COOP + d^ AGE + dg EDUC The coefficients for this six-variable function were estimated using the "direct" method of the SPSS subprogram discriminant (Nie et al., 1975). The results are presented in Table 6-1. The overall means of the discriminant variables for all farmers, the means for each group of farmers, and student t-statistics, to test the null hypothesis that the means for each group were equal, are also presented in Table 6-1. To estimate the average discriminant score for each group, the group means were substituted in the estimated equation. The result was Dp = 0.48747 and = -0.35067 for participants and nonparticipants, respectively. Given that the cost of misclassification are the same and assuming the prior probabilities were equal, then the cutoff point can be calculated by substituting the overall means into the estimated discriminant function. The result was D^p = 0.0. All producers with discriminant scores above zero would be classified as potential participants, whereas

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Table 6-1. Discriminant coefficients, overall means, group means, and ^-test levels of significance for differences in mean values between participants and nonparticipants 84 I fO -p o SD. -Pi o o 00 o o o o o o o o o o o o o o o o o d d d o to c fC cu B CO -p c CL oo OO o o o LO m ir> CM o CSJ r— r— r— 00 •r* 4J &(0 lA 00 CO CM cn d to LO Q. c o I to •p c CPi 00 LT) O o fO LT> CM CO CM 00 r LO 1 means r“ o 00 OO 00 LO LO P-^ CM o ro 0^ CT^ CM to f— ^ r— * • • • • • o; ^ r— r“ o CM > ro O s» fO > CM 00 00 to I \ c O (U CM CM LO O OO O cn TLO o CM 00 CM 00 •r(J CM 00 O CO LO O -D -tpN. o o 00 CO P-^ CT> C4o o o CO O O •o ^ • . • • • o 1 1 ro O 4-> to LlJ

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85 producers with discriminant scores below zero would be classified as potential nonparticipants. The signs of the discriminant coefficients were, in general, as expected. For example, the coefficient for age has a negative sign which implies that younger farmers are more likely to participate in the program. The positive signs of the coefficients for education and cooperative membership were also expected. These signs imply that cooperative members and more educated farmers tend to participate more in the program. The positive sign of crop land also seems logical, suggesting that farmers with larger crop areas tend to participate more in the PRODEMATA program. The negative sign for pasture may be a consequence of the PRODEMATA design that -emphasizes modern inputs and stresses credit for small farmers. For the fixed capital stock, the sign was positive and consistent with expectations. The model classified 77.5 percent of nonparticipants correctly, but only 57.7 percent of participants correctly. Overall, the model classified 69.2 percent of the 435 observations correctly. To assess the degree of separation established by the discriminant function, the Chi-square test described previously was performed. The null hypothesis tested was that the population group mean vectors were equal. The computed Chi-square value of 68.148 (with 6 degrees of freedom) is significant at the 1 percent level, and the null hypothesis was rejected. This result implies that the discriminant model has established a statistically significant separation between the groups. The relative importance of the six variables was determined by ranking them using both of the procedures discussed earlier. These

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86 rankings are shown in Table 6-2. The ranking pattern was similar for both the standardized coefficients and the weighted coefficients. In both rankings cropland is shown to have contributed the most to separation of participants and nonparticipants, while education had the smallest contribution. Age and fixed capital alternated as the second and third most important variables in the standardized coefficients and weighted coefficients. Both methods ranked cooperative participation and pasture land fourth and fifth, respectively. The findings of the discriminant analysis showed that there are some socio-economic characteristics capable of distinguishing between participants and nonparticipants in the PRODEMATA program. When the same procedure was applied to three groups (nonparticipants, participants for one or two years, and participants for three or more years), it failed to establish a statistically significant distinction between the three groups. Technical and Allocative Efficiency by Discriminant Analysis Groups In this section an attempt is made to answer the question raised at the end of Chapter V regarding the cause of the differences between participants and nonparticipants in both technical and allocative efficiency. To test the hypothesis that differences in estimated efficiencies were due to the effects of PRODEMATA on farmers who actually participated in the program rather than farm or farmers' characteristics, two-way contingency tables were developed. For each group of participant and nonparticipant farmers, two subgroups were defined based upon whether or not these farmers were

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87 to >5 tc c rO C <0 c su to •r* D u ro ) c ro q: ro +-> to 4-> C o; •r* U •f— MMO) O u *o a; N •r— “O ro •D C ro 4-> to >> c ro a: T-l C LO 00 CO OJ o OJ o IT) LD CO CVJ f— r— o O 0>I^ • • • * • • o o o O o o o 1 0) z r— < 2: X) _J < ro o. Q_ o o X UJ O to ZD U q; »-H CD O < CD ro C_) Li. C o o. UJ •oro CJ 4-> N C •rO “O * 1 so fO *r-D t*« c ^ro o; 4^ O to u cu ro ro CO CM 00 CM a; CSJ VD LO LO ID CO CO CM r— 4J • • • • • • o o o o o o tf1 »w-* 1 O o a: o o X D. O O O to < D. O c 4-^ to s= o •o s4-> JZ 4-> JC 4-> ro s. o 3 t4X a: •r^ 0> -C O •rU. 00 1— u. Uto c OJ u t+O) o u 0) D ro > “D 0) “D
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88 predicted to participate by the discriminant analysis of the socio-economic characteristics of each sample observation. The average technical and allocative efficiency was calculated for each of the resulting four subgroups. Each of these means was then tested to determine if it was different from the means of the other subgroups in a statistically significant fashion. In terms of technical efficiency the PRODEMATA program indeed exerted a substantial impact. This is shown by making comparisons along the rows of the contingency table in Table 6-3. The average technical efficiency of farmers with similar socio-economic characteristics as determined by the farmer's predictive classification was significantly greater for farmers who participated in the program than for those who did not. This result is independent of the socio-economic grouping of the sample. That is, among those farmers predicted to be nonparticipants by the discriminant analysis because of small crop land, lower education levels, etc., there was still a statistically significant difference in technical efficiency between actual participants and nonparticipants. This strongly suggests that the higher technical efficiency of participant farmers is a consequence of PRODEMATA participation rather than other pre-existing, fundamental differences. Comparisons in a column-wise fashion produced quite different results. When averages for techincal efficiency were compared for farmers of the same group in terms of actual participation but with different socio-economic characteristics, no significant differences were detected. This finding confirms that the underlying socio-economic differences between the participant and nonparticipant subsamples were not the '.cause of the observed differences in technical efficiency between the two

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89 Table 6-3. Test for significant differences between the technical efficiency index averages of subgroups defined by actual participation in the PRODEMATA program and socio-economic characteristics which would have predicted participation according to the discriminant analysis. Zona da Mata, 1981-82 Subgroups defined by socio-economic characteristics typical of: Subgroups defined by actual participation in PRODEMATA Participants Nonparticipants Z-statistic Participants 0.189 ^ 0.061 15.07* * (0.006)® (0.001) n = 111 n = 64 Nonparticipants 0.180 0.058 10.07* (0.008) (0.003) n = 71 n = 189 Z statistic 0.68 0,49 ^Numbers in parentheses are standard errors of the means; n is the number of observations in each subgroup. *The average technical efficiency between the subgroups is significantly different at the 1 percent level.

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90 groups. Stated conversely, it appears that PRODEMATA participation has caused an improvement in the technical efficiency of program participants. As far as allocative efficiency is concerned, the PRODEMATA program had a negative impact (Table 6-4). That is, among farmers with the same set of socio-economic characteristics, the average allocative efficiency was smaller for farmers who did participate in the program than for those who did not. However, when the averages for allocative efficiency were compared in a column-wise fashion for the two subgroups of actual participant farmers, significant differences also were found. Actual participants who had similar socio-economic characteristics of nonparticipants had higher allocative efficiency than those who participated and had characteristics of participants. Therefore, the observed differences in allocative efficiency were not caused by PRODEMATA_participation alone, but also by differences in the farmer's socio-economic characteristics. These results confirm the difficulty of improving allocative efficiency in traditional agriculture and suggest that the PRODEMATA program may have actually caused a slight disruption in allocative efficiency in the Zona da Mata region.

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91 Table 6-4. Test for significant differences between the allocative efficiency index averages of subgroups defined by actual participation in the PRODEMATA program and socio-economic characteristics which would have predicted participation according to the discriminant analysis. Zona da Mata, 1981-82 Subgroups defined by actual participation Subgroups defined by socio-economi c in PRODEMATA Noncharacteristics typical of: Participants participants ^-statistic Participants 0.714 0.844 (0.017) (0.014) n = 111 n = 64 Nonparticipants 0.788 0.861 (0.017) (0.017) n = 71 n = 189 Z statistic 3.65* * 0.96 ^Numbers in parentheses are standard errors of the means; n is the number of observations in each subgroup. *The average allocative efficiency between the subgroups is significantly different at the 1 percent level.

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CHAPTER VII SUMMARY AND CONCLUSIONS This chapter includes an overview of the problem studied, the research objectives, the procedures used, and the results obtained. Based on the results, some implications and policy recommendations are derived and suggestions for further research explored. The Problem, Objectives, and Procedures Rural poverty has been of increasing concern among policy makers in Brazil. Development strategies based on technological change designed to increase productivity, and hence the income, of poor rural people have been considered of crucial importance to overall plans of economic growth and development. The logical basis of these programs is the belief that growth in productivity occurs through the use of modern inputs and that farmers will adopt these inputs if agricultural credit is available. There is a lack of consensus regarding the need for and effectiveness of credit programs in the context of traditional agriculture. In Brazil, various farm-level production studies evaluating the effectiveness of credit programs in improving productivity and enhancing resource allocation have shown conflicting results. This research was directed toward the evaluation of the Integrated Rural Development Program of supervised agricultural credit for the Zona da Mata region of the state of Minas Gerais, Brazil (PRODEMATA). 92

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93 The emphasis of the study focuses on the technical and allocative efficiency of participant and nonparticipant farmers in the PRODEMATA program. The basic objective is to determine whether or not participation in the PRODEMATA program had measurable effects on producer efficiency. The efficiency analyses were undertaken by means of frontier production functions. Full frontier production functions were estimated for participants and nonparticipants in the PRODEMATA program. The estimated frontier production functions were obtained via two estimation procedures: corrected ordinary least squares (COLS) and maximum likelihood (ML). For each production frontier the dual cost frontier was derived analytically. The derived cost function frontiers were used to measure the technical and allocative efficiency of each sample observation. Summary of the Findings The data used in this study were obtained from sample data of 435 Zona da Mata farmers, collected by the Department of Agricultural Economics of the Federal University of Vicosa in Brazil in 1982. The sample was divided into two groups: those which had participated in the supervised credit program of PRODEMATA at any time during the project's life and those which did not. The participant farmers in the sample had more productive land, used more total labor, owned more fixed capital, and spent more money on intermediate inputs than did the nonparticipants. In terms of resource use per hectare of productive land, the participants used less labor, more fixed capital, and more intermediate inputs than nonparticipants. The findings from the efficiency analysis show that, on the average, farmers had levels of technical efficiency which varied from 5 percent

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94 to 35 percent depending on the group and the estimation method used. Allocative efficiency levels varied from 75 percent to 85 percent indicating that the sample farmers were much more efficient in an allocative sense than in a technical sense. Technical efficiency levels were quite uniform across owned farm sizes. However, sharecroppers' technical efficiency was significantly higher than that of owners. Allocative efficiency tended to decrease as farm size increased. A comparison between participant and nonparticipant farmers shows that while participants had higher technical efficiency, the nonparticipants had higher allocative efficiency. An evaluation of these findings by use of a discriminant analysis approach to correct for the underlying differences between participant and nonparticipant farmers strongly suggested that the observed differences in technical efficiency between participants and nonparticipants were due to the PRODEMATA program. However, differences in allocative efficiency were less clearly related to participation in the PRODEMATA program. The PRODEMATA program is a supervised credit program. Borrowers must work closely with the extension service to obtain credit. Thus, PRODEMATA is a package program that includes both credit and technical assistance from the extension service. The basic results of this study suggest that the technical assistance component of PRODEMATA has been beneficial by improving technical efficiency. They also suggest that the credit component of the PRODEMATA program may have actually disrupted allocative efficiency, at least in the short run.

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95 Implications and Policy Issues Perhaps the most striking finding of this study is the very low level of average technical efficiency found among Zona da Mata farmers. Most farmers in the sample are operating at points well below the estimated frontier production function. The implication of such evidence is obvious: there is a pervasive need to adopt existing advanced technologies in the area. The role of agricultural research and extension in this process is critical. The relatively higher level of technical efficiency of sharecroppers relative to that of owners deserves special attention. Even though the sharecroppers operate with strong resource limitations,, they produce a substantial proportion of the aggregate food supply in the Zona da Mata (Leite, 1981). Nonetheless, the participation of this group in the PRODEMATA program has been negligible. Therefore, the implementation of development programs especial ly directed toward sharecroppers should be encouraged. Among the ov/ners, technical efficiency and the size of farms are not inextricably associated. This result implies that the efforts to improve technical efficiency among traditional farmers in the Zona da Mata will bring similar effects whether directed toward smaller or larger farmers. The seemingly high level of allocative efficiency found for farmers in the sample leads to an important theoretical implication— Shultz's (1964) "poor but efficient within existing technologies" hypothesis is supported. Moreover, his contention that what is needed is more human capital (i.e., knowledge) rather than physical resources is also substantiated by the findings of this study.

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96 Limitations and Suggestions for Further Research Certainly this study has some limitations. These limitations, coupled with the provocative results of this study, demonstrate the need for continuing research in the area. The results of the study suggest as a starting point further analysis directed toward sharecroppers. Even though sharecroppers were targeted as important beneficiaries of the PRODEMATA program, the great majority of these producers have not received credit or technical assistance. In addition, it seems that no attempt has been made to adjust PRODEMATA to the sharecroppers' behavior or their production system. This study analyzed efficiency at the firm level, but it did not differentiate firms by enterprise mixes. Since major differences can be found on farms with different enterprise mixes, a possible extension of this study would be to pursue a less aggregative treatment of the farm units in the area. Perhaps separate studies of crop-oriented farms and farms which emphasize livestock as their most important activity are warranted. All analyses in this study have been based on static economic models. Because the sample data used in this study are available over a limited time series, it seems feasible to bring the all important time element into future analyses. Further research investigating the efficiency of production in a dynamic perspective may improve considerably the approach utilized in this study. Such evaluation could examine the effects of PRODEMATA on changes in farming patterns over time and how these changes are associated with changes in production efficiency.

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97 The low degree of technical efficiency found in this study may be partially explained by the importance of risk aversion in the behavior of agricultural firms in traditional agriculture. No risk component was considered in this study and very little is known empirically about risk preferences and the attitudes of small farmers. The benefits of explicit consideration of these aspects would be substantiatial . Finally, further refinements in the frontier production function approach used in this study are needed. As mentioned previously, the full frontier model is highly sensitive to outliers. Measures of technical efficiency may be severely underestimated when extreme observations or erroneous data are present in the sample. Specifications such as the "composed error" model proposed by Aigner et al. (1977), which allows for variation of the frontier outside the control of the firm, may bring substantial improvements in the results of studies such as this.

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APPENDICES

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APPENDIX A LABOR USED PER HECTARE IN SHARECROPPED AREAS In this appendix the estimated parameters for the model (3.2) discussed in Chapter III are presented. The results are shown in Table A-1. Table A-1. Regression equations estimates of labor used (expressed in logarithms) in each crop as a function of the cultivated area, also expressed in logarithms Crops Constant term Cultivated area R^ Number of observations Rice 3.8256 , 0.5523* 0.37 40 (0.1171)® (0.1151) Corn 3.3707 0.7891* 0.36 52 (0.1457) (0.1465) Corn-beans 2.5811 0.1696 0.01 30 (0.2241) (0.2819) Beans 3.2513 0.6372* 0.55 24 (0.1016) (0.1215) ^Numbers in parentheses are standard errors of the coefficients. *Coefficient significantly different from zero at the 1 percent level of statistical significance. Because of the very small number of sharecroppers interviewed who cultivated tobacco, coffee, or sugarcane, the estimated amount of labor used per hectare for each of these crops was taken as the sample average. 99

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100 It was found that the average number of man-days used per hectare for tobacco, coffee, and sugarcane was 86.75, 30.72, and 21.25, respectively.

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APPENDIX B BASIC DATA AND DEFINITIONS Data Source and Procedures The data used in this study were obtained from sample data of 435 farmers col 1 ected by the Department of Agri cul tural Economi cs of the Federal University of Vicosa in Brazil . The data were collected in July 1982 through direct interviews of farmers and refer to the 1981-82 crop year. After the field work, the data were checked for inconsistencies and codified in accordance with previously designed manuals (UFV, 1977-1982). The data, which included more than 2,000 variables per observation, were recorded on tape at the Federal University of Vicosa. A copy of the tape and the code manuals was made available for this study through the cooperation of the Department of Agricultural Economics. At the University of Florida, greatly condensed data files were created for the purpose of this study. The labor data, which included detail by category of workers, by sex, and by age was aggregated to equivalent man-days, a standard unit of labor as defined below. These labor data were then adjusted if some part of the management unit of the owner respondents was sharecropped. The adjustment procedure is described in Chapter III and Appendix A. Much of the raw data on variable inputs was measured in physical quantities used. In these cases, the price paid per unit, as reported by each respondent, was used to calculate the value of expenditures. In those cases where the respondent had sharecropped areas as part of the 101

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102 management unit, adjustments were performed to obtain the total expenditure for each input for the total management unit. This adjustment procedure is described in Chapter III. Most data on fixed inputs were recorded in physical units. Unit prices provided by the respondents were used to determine the value of each category of fixed inputs. Output data were recorded for each enterprise. Data on quantity produced, sold, consumed, and paid to sharecroppers were reported for each enterprise. The market price for each product, as estimated by the individual respondents, was used to compute the value of crop production, livestock production, and total production obtained by each farmer during the 1981-82 agricultural year. The output variable used in this study is the aggregate value of production of each enterprise during the crop year. No adjustments were made for inventory adjustments. To the extent that some grain produced is fed to livestock, there may be some double counting in the estimation of output. However, livestock feeding in the region is not common, so any bias introduced by this measurement procedure is expected to be small. Definitions Cruzeiro . The monetary unit of Brazil. The average exchange rate during the 1981-82 agricultural year was Cr$179.38 = US$1.00. At the time of interviewing (July 1982), the official exchange rate was Cr$177.54 = US$1.00. Hectare . Measure of land equal to 2.471 acres.

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103 Crop land . Area used for annual or perennial crops. It includes land owned, land rented from others, and land used with a sharecropper agreement. Pasture land . Area used for livestock production. It includes natural pastures and cultivated forages. Total productive land . Sum of crop land and pasture land. Labor . Total amount of labor used in a production unit during the 1981-82 agricultural year. It was measured in equivalent man-days. Equivalent man-day . A unit measure of labor defined as equal to 1.0 for one day of work by males between the ages of 16 and under 65 years; 0.75 for adult females and 0.5 for those under equal to 15 years or above 65 years. Fixed capital . The value of all buildings including animal and storage facilities (but excluding houses), machinery and equipment, draft animals and livestock. It is measured in cruzeiros, according to the market value as estimated by the respondent. Operating expenses or intermediate material inputs . The value of all inputs used (purchased and/or produced) in crop production, such as seeds, chemical and organic fertilizers, pesticides, draft animal services, mechanized services, and the value of inputs used (purchased and/or produced) in livestock production such as feed and medicines. Output . The value of all production obtained from the agricultural activities during the 1981-82 agricultural year. It is measured in cruzeiros and includes the cash sales of crop and livestock products, and the value of this product when produced and consumed on the farm or paid to sharecroppers.

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APPENDIX C TEST OF THE EQUALITY OF THE AVERAGE EFFICIENCY MEASURES BETWEEN PARTICIPANTS AND NONPARTICIPANTS IN THE PRODEMATA PROGRAM If it is assumed that the efficiency measures for an individual observation in each group are independent random variables identically distributed, the central limit theorem can be applied (Bhattacharyya and Johnson, 1977). Thus, the estimated values of the efficiency measures in Chapter VI may be tested for the differences between the averages 2 of the two groups of farmers. Using the variances of each group (S^ and 2 S 2 )s one may calculate the test statistic Z as where X-j and ^2 are the estimated efficiency measures for each group, and n-j and n^ are the respective number of observations. The results of this test are summarized in Table C-1 for the efficiency measures estimated from the COLS estimates and in Table C-2 for the efficiency measures estimated from the Ml estimates. 104

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Table C-1. Test for significant differences between the efficiency averages derived from COLS estimates for participants and nonparticipants in the PRODEMATA program 105 M u •p* * * *K p CM r— cn CO to C\J CT^ 00 (Ti • • • • • •p ro O rLO ro ro > O c (U u 4-> <0 U o in -P c ro I CL C •»“ O U Z •!“ s. fO Q. to c rO O. -P s. ro a. to M *r-P rO to > U c 0) 0) to c fO OI -Ic o o 2: -P s. rO CL C <0 Q. -P S. rC D. Vp SO 00 C3^ CO VO • • • • • • o o o o o o 4C CO CM CD CM CM 00 o o 00 to o to a; 0) sV4sro Mro -P cu to U to 0) u ro JC ro (0 •P o 4-> sU o o O CU (U OJ in 0) C7) > -C 1 1 x: ro <0 • o o o o 0) Oil— • o > ^ (1) 1 CD o ro 1 — > o in A ^ 0) (U Q. •p E c ro a tn u I 0) Cl CU -p (0 c O) S(U “O >5 c: ro o c OJ p ro to *P CL ro Q. U S* ro CL C o •o c ro to •P C ro CL ro CL o u c O)

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Table C-2. Test for significant differences between the efficiency ;ayerages derived from ML estimates for participants and nonparticipants in the PRODEMATA program 106 >1 a c cu •f“ u Q) •r* 4-> (O (J o u) hsj *r-P fO cn t/> -P C 00 00 •r“ o ro Lf) o O cr> 00 LO C£> •r• • • • 4J o o o o o a c (U •r“ U 0) to u c u cu s. C A 3 I Q. C •»“ o u z: •!“ -p 5ro Q. (/) <0 CL -P s. CO a. so OJ u iA 3 (/) to o I— sO Q. O o CO 00 00 o ro (/) 0) Cl CL O Su 0^ sCO JC 00 * * * * * Je s0) r— CO CO 00 CSJ CL ro o • • » CM LO CO CSJ 00 00 o CM ro LO 0) Lf) o Lf) s00 00 0> • uC3 o o o »4O o m o in o tA so; c 2 o iA 0) s u a; o Lf) I ro ir> o iA 0) L. to •p u a; o o o Lf) iO Lf) o LO O) CsJ o OJ to O) to 00 a; to -D >> C to u c cn a; i. to iA Sto o. c o c "O c to iA •P c to CL to o. o >> o c Q} o cu 0) C 7 ) (O s(U > re O) >— ^ a; h“ ^ (c CL'* »— * C cy u 'Significantly different at the 5 percent level.

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REFERENCES Aigner, D. J., and S. F. Chu. "On Estimating the Industry Production Function." American Economic Review 58 (1968): 826-839. Aigner, D. J., C. A. K. Lovell, and P. Schmidt. "Formulation and Estimation of Stochastic Frontier Production Function Models." Journal of Econometrics 6 (1977): 21-27. Bandeira, A. L. "Analise dos Efeitos da Politica de Erradi cacao de Cafeeiros, Caratinga e Manhuacu, Minas Gerais." M.S. thesis, Universidade Federal de Vicosa, 1970. Bhattacharyya, G. K., and R. A. Johnson. Statistical Concepts and Methods . New York: John Wiley & Sons, 1977. Christensen, R., D. W. Jorgensen, and L. R. Lau. "Transcendental Logarithmic Production Frontiers." Review of Economics and Statistics 55 (1973): 28-45. Diewert, W. E. "An Application of the Shephard Duality Theorem: A Generalized Leonti ef Production Function." Journal of Political Economy 79 0971 ): 481-507. Donald, G. Credit for Small Farmers in Developing Countries . Colorado: Westview Press, 1976. Drummond, H. E. "An Economic Analysis of Farm Enterprise Diversifications and Associated Factors in Two Regions of Minas Gerais, Brazil." Ph.D. thesis, Purdue University, 1972. Empresa de Pesquisa Agroprecuaria de Minas Gerais (EPAMIG). Informe Agropecuario , Belo Horizonte, M.G.: EPAMIG, 1977-1982. Farrell, M. J. "The Measurement of Productive Efficiency." Journal of the Royal Statistical Society Series A, General, 120 (1957) : 253-281. Forsund, F. R., C. A. K. Lovell, and P. Schmidt. "A Survey of Frontier Production Functions and of Their Relationship to Efficiency Measurement." Journal of Econometrics 13 (1980): 5-25. Fundacao Getulio Vargas (FGV). Indices Agropecuarios . Monthly Publicacation. Rio de Janeiro, Brasil: FGV, 1982. ' 107

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108 Fundacao Institute Brasileiro de Geografia e Estatistica (FIB6E). Anuario Estatistico do Brasil . Rio de Janeiro: FIBGE, 1955, 1965, 1975, and 1978 issues. Garcia, J. C. "Analise de Alocacao de Recursos por Proprietaries e Parceiros em Areas de Agriculture de Subsistencia. " M.S. thesis, Universidade Federal de Vicosa, 1975. Gau, G. W. "A Note on the Assessment of the Results in Discriminant Analysis." Decision Sciences 9 (1978): 341-345. Graber, K. L. "Factors Explaining Farm Production and Family Earnings of Small Farmers in Brazil." Ph.D. thesis, Purdue University, 1976. Greene, W. H. "Maximum Likelihood Estimation of Econometric Frontier Functions." Journal of Econometrics 13 (1980): 27-56. Hopper, D. "The Economic Organization of a Village in North Central India." Ph.D. thesis, Cornell University, 1957. Joy, M. 0., and J. 0. Tollefson. "On the Financial Applications of Discriminant Analysis." Journal of Financial and Quantitative Analysis 10 (1975): 723-739. Kmenta, J. Elements of Econometrics . New York: Macmillan Publishing Company, Inc., 1971. Kopp, R. J. "The Measurement of Productive Efficiency: A Reconsideration." Quarterly Journal of Economics 96 (1981): 477-503. Kopp, R. J., and W. E. Diewert. "The Decomposition of Frontier Cost Function Deviations into Measures of Technical and Allocative Efficiency. Journal of Econometrics 19 (1982): 319-331. Lee, L. F., and W. G. Tyler. "The Stochastic Frontier Production Function and Average Efficiency: An Empirical Analysis." Journal of Econometrics 7 (1978): 385-390. Leite, C. A. M. "Economic Efficiency of Grain Production Systems for Traditional Agriculture in Southeastern Minas Gerais, Brazil." Ph.D. thesis, Michigan State University, 1981. Meyer, R. L., D. W. Adams, and N. Rask. Rural Capital Markets and Small Farmers and Brazil, 1960-1972 . Small Farmer Credit in South America; Country papers prepared for the Agency for International Development Spring Review of Small Farmer Credit, Vol . III. Washington, D.C.: AID, 1973. Meeusen, W. , and J. Broeck. "Efficiency Estimation from Cobb-Douglas Production Functions with Composed Error." International Economic Review 18 (1977): 435-444.

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109 Morrison, D. F. Multivariate Statistical Methods . New York: McGrawHill Book Company, 1976. Nehman, 6. I. "Small Farmer Credit Use in a Depressed Community of Sao Paulo, Brazil." Ph.D. thesis, Ohio State University, 1973. Nelson, W. C. "An Economic Analysis of Fertilzer Utilization in Brazil." Ph.D. thesis, Ohio State University, 1971. Nie, N. H., C. H. Hull, J. G. Jenkins, K. Steinbrenner, and D. H. Bent. Statistical Package for the Social Sciences . New York: McGrawHill Book Company, 1975. Rao, B. P. "The Economics of Agricultural Credit Use in Brazil." Ph.D. thesis, Ohio State University, 1970. Resende, M. Classificacao e fisica do solo . Universidade Federal de Vicosa, Vicosa, Minas Gerais, Brasil, 1980: p. 135. Schmidt, P. "On the Statistical Estimation of Parametric Frontier Production Functions." Review of Economics and Statistics 58 (1976): 238-239. Schmidt, P., and C. A. K. Lovell. "Estimating Technical and Allocative Inefficiency Relative to Stochastic Production and Cost Frontiers." Journal of Econometrics 9 (1979): 343-366. Schultz, T. W. Transforming Traditional Agriculture . New Haven: Yale University Press, 1964. Silva, C. A. B. "Factors Affecting Enterprise Choice: An Analysis of Traditional Food Production in Southeastern Minas Gerais, Brazil." Ph.D. thesis, Michigan State University, 1981. Steitieh, A. M. "Input Productivity and Productivity Change of the Crop Enterprise in Southern Brazil." Ph.D. thesis, Ohio State Univesity, 1971. Tax, S. Penny Capitalism . Chicago: University of Chicago Press, 1963. Teixeira, T. D. "Resource Efficiency and the Market for Family Labor: Small Farms in the Sertao of Northeast Brazil." Ph.D. thesis, Purdue University, 1976. Timmer, C. P. "Using a Probabilistic Frontier Production Function to Measure Technical Efficiency." Journal of Political Economy 79 (1971): 776-794. Universidade Federal de Vicosa (UFV). Diagnostico Economico da Zona da Mata . Vicosa: Imprensa Uni versitaria, 1971.

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no Uni vers idade Federal de Vicosa (UFV). Programa de Desenvol vimento Integrado da Zona da Mata, MG-PRODEMATA: Manual de Codificacao . Vicosa, M.6., Brasil: UFV, 1977-1982. Vieira, C. "Cultivo Consorciado do Milho com Feijao." Informe Agropecuario 46 (1978): 42-44. White, T. , Jr., and D. Seabra. Credito Agricola na Zona da Mata de Minas Gerais . Monografia No. 9. Rio de Janeiro: IPEA, 1973. World Bank. Brazil-Staff Project Report of the Integrated Rural Development Project in the State of Minas Gerais. Report No. 1291 BR. Mimeographed. Washington, 1976.

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BIOGRAPHICAL SKETCH Aloisio Teixeira Gomes was born in Uba, Minas Gerais, Brazil, on March 6, 1948. He was graduated in 1970 with the degree of Bachelor of Science in Agricultural Engineering from the Universidade Federal de Vicosa, Minas Gerais, and in 1975 with the degree of Master of Science in Agricultural Economics from the Universidade Federal do Rio Grande do Sul, Brazil. From 1971 to 1973, he worked for the Empresa de Assistencia Tecnica e Extensao Rural de Minas Gerais. Since 1974 he has been working for the Empresa Brasileira de Pesquisa Agropecuaria, a federal government agency that carries out agricultural research in Brazil. In the fall of 1979, he began doctoral studies at Michigan State University. In the fall of 1980 he transferred to the Department of Food and Resource Economics, at the University of Florida, where he continued his graduate studies in agricultural economics. He is a member of the American Agricultural Economics Association, the Sociedade Brasileira de Economistas Rurais, and the Associacao Mineira dos Engenheiros Agronomos. Ill

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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. H. Evan .Drummond.,, Chairman 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. William 6. Boggess, Co-C^SPirman Assistant 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. Associate 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. Assistant Professor of Food and Resource Economics

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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. Wflllam G. Blue Professor of Soil Science This dissertation was submitted to the Graduate Faculty of the College of Agriculture and to the Graduate Council, and was accepted as partial fulfillment of the requirements for the degree of Doctor of Philosophy. April 1984 Dean for Graduate Studies and Research