Modeling taste change in meat demand

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Title:
Modeling taste change in meat demand an application of latent structural equation models
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vi, 131 leaves : ill. ; 28 cm.
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English
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Gao, Xiaoming, 1962-
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Subjects / Keywords:
Meat industry and trade -- United States   ( lcsh )
Food -- Sensory evaluation -- Mathematical models   ( lcsh )
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bibliography   ( marcgt )
theses   ( marcgt )
non-fiction   ( marcgt )

Notes

Thesis:
Thesis (Ph. D.)--University of Florida, 1991.
Bibliography:
Includes bibliographical references (leaves 125-130).
Statement of Responsibility:
by Xiaoming Gao.
General Note:
Vita.

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University of Florida
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notis - AJD0505
oclc - 25682016
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Full Text









MODELING TASTE CHANGE IN MEAT DEMAND:
AN APPLICATION OF LATENT STRUCTURAL EQUATION MODELS














BY


XIAOMING GAO


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



UNIVERSITY OF FLORIDA


1991



















To my parents


Gao Jisheng and Nian Guizhen














ACKNOWLEDGMENTS

It has been a long process to complete this

dissertation. The experience and knowledge I gained through

this study are marvelous and can't be over estimated.

I would like to thank Dr. Scott Shonkwiler, the

chairman of my supervisory committee. He provided me with

the insights of this study and patiently guided me through

this project. I thank he for reading and re-reading many

drafts of this dissertation to correct my English.

I would like to thank Dr. Mark Brown, Dr. Jonq-Yinq

Lee, Dr. Thomas Spreen, and Dr. Yasushi Toda, members of my

supervisory committee, for their guidance and help. The

experience I gained during my M.S. study under the guidance

of Dr. Spreen certainly has a spill-over benefit to this

dissertation in terms of methodology training and writing.

I am grateful to my wife Li for her understanding and

support throughout this study, and the inspiration given by

my 19-month-old daughter Alice. I certainly observed her

changing taste from formula to plain milk in the last year.


iii

















TABLE OF CONTENTS


Page
ACKNOWLEDGMENTS ................................ iii

TABLE OF CONTENTS .............................. iv

ABSTRACT ....................................... v

CHAPTER

1 INTRODUCTION ...................... ....... 1
Problem Statement ..................... 4
Organization ......................... 9

2 LITERATURE REVIEW ....................... 13

3 LATENT VARIABLE MODELS ................... 29
Structural Equation Models ............. 29
State Space Models ..................... 41

4 MODEL SPECIFICATION ..................... 47
Multiple Indicator Models .............. 56
MIMIC Models .......................... 59
DYMIMIC Models ........................ 62

5 ESTIMATION AND RESULTS ................. 63
Multiple Indicator Models .............. 63
Latent AIDS Model .................... 64
Latent Rotterdam Model ............... 69
MIMIC Models .......................... 84
DYMIMIC Models ......................... 97

6 SUMMARY AND CONCLUSION ................... 107

APPENDIX
A SUMMARY OF STUDIES ON STRUCTURAL CHANGE
IN RETAIL MEAT DEMAND ................ 113
B GAUSS PROGRAM FOR MIMIC MODEL ........ 114
C GAUSS PROGRAM FOR DYMIMIC MODEL ........ 118

BIBLIOGRAPHY ................................... 125

BIOGRAPHICAL SKETCH ................ ............. 131










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


MODELLING TASTE CHANGE IN MEAT DEMAND:
AN APPLICATION OF LATENT STRUCTURAL EQUATION MODELS


By
Xiaoming Gao


May 1991

Chairman: J. S. Shonkwiler
Major Department: Food and Resource Economics


Taste or preference comprises an unobservable latent

variable in utility and demand functions. This latent

variable can be estimated by using both its indicator and

causal variables in a structural equations model. It is

widely presumed that taste changes in the last three decades

have significantly affected U.S. consumer demand for meat

products. This dissertation uses both static and dynamic

latent variable models to estimate the latent taste variable

in a U.S. meat demand system. The static latent variable

model is estimated by using factor analysis and causal path

analysis; the dynamic latent variable model uses a state

space model estimated by Kalman filtering and smoothing.

Empirical results show that taste changes have been a

significant factor explaining both declining beef and

increasing poultry per capital consumption. The taste change

is attributed to consumer health concerns over fat and

v








cholesterol intake and demand for convenience food. It is

estimated that consumer taste change has decreased per

capital consumption of beef by twenty-four percent over the

last three decades and increased that of poultry by sixty-

five percent and the trend continues. Taste elasticity is

increasing, showing that consumer are more responsive to

taste changes. This is because health information is more

readily available, consumers are more health conscious, and

demand for convenience increases as more married women are

working.














CHAPTER 1
INTRODUCTION


For the past quarter of century there have been

significant changes in U.S. food consumption patterns. The

per capital consumption of some foods has increased while the

consumption of others has declined. Consumers are

purchasing smaller quantities of dairy products, grains, and

cereals and are consuming more poultry and fish, fat and

oil, fruits and vegetables, potatoes, and sweets. The total

quantity of meat, poultry, and fish consumption is higher

now than in the early 1960s and it has changed little since

the early 1970s.

When we examine the subgroups that make up meat and

dairy products, it is clear that consumers have been

substituting one product for another. Within dairy

products, cheese consumption has increased, while fluid milk

and animal fat consumption has decreased. For fluid milk,

low fat and skim milk consumption is increasing while whole

milk consumption is declining. Now consumers buy more low

fat and skim milk than whole milk. Per capital consumption

of poultry and vegetable fats has more than doubled, while

pork and beef consumption has been stable or increased

little.










Meat production is an important sector in agriculture.

In the 1987, more than 27 percent of gross farm income came

from livestock production (including beef, pork and poultry)

of which, beef and pork production accounts for 60 to 70

percent. While total supply of red meats has been

relatively stable, its share of the total meat supply has

been declining over the past three decades. Poultry

production, on the contrary, has been steadily increasing

over the same period; it now accounts for about 25 percent

of total meat supply. The three products beef, pork, and

poultry make up more than 85 percent of the total U.S. meat

supply, with fish, veal, lamb, and other minor red meats

making up the other 15 percent. The consumption of meat

products takes a great proportion of consumer household food

expenditure. In 1988, for every dollar which the consumer

spent on food at home, approximately 30 cents were allocated

to meats, of which more than half was spent on red meat and

another 20 percent was spent on poultry (Agricultural

Statistics, USDA, 1988).

Red meat and poultry have been and continue to be a

major component of the U.S. food system. Thus, it is not

surprising that changes in the market conditions for this

food group are of great concern and interest to many people.

For producers, market changes may mean the need to adjust

their market strategies and improve their commodity to

satisfy customers; for consumers, changes in market










conditions may mean changing retail prices and availability

of commodities. When we examine per capital meat consumption

over the last twenty years (Figure 1), it is clear that per

capital consumption of meat products has changed

substantially.

It is the task of this research to look at the reasons

for this change. First, we need to keep in mind that

purchasing decisions of consumers are the end result of

complex interactions among economic, sociological and

psychological factors. These factors express themselves in

demand theory as price and income effects, demographic

factors, taste, etc. In addition, the values of economic

variables will be affected by the interaction of factors

such as production level, government policies, and

macroeconomic conditions. When we try to dissect these

factors using econometric models, it is essential that we do

not exclude any of these factors from the analysis which

would render conclusions biased (or inconsistent).

Different studies on meat demand have addressed the impact

of different factors on consumer demand in numerous ways,

and empirical measures of demand parameters differ from

study to study. Model specification, variable

specification, time period of analysis, length of the

observation period, and assumptions about functional form

all affect demand parameter estimates. While researchers

should consider as many factors in demand models as possible










to minimize this biasedness, every study has to focus its

attention on one or few factors in empirical analysis. In

this study, the effect of a change of taste is the focus.

The change of taste for meat can be affected by

different things. One factor is the consumer health concern

over blood cholesterol level and saturated fat intake;

another is convenience, which in itself is influenced by

grading and packing; the third factor is advertising. The

hypothesis that consumers are concerned about their health

and about the role of different foods in human health has

been documented in some public attitude surveys of different

population groups and news reports (Myers,1989). But the

link between attitudes, as expressed in survey responses,

and taste change has not been subjected to rigorous

empirical testing. This research will try to shed some

light on this aspect.



Problem Statement

Since the early '80s, there has been continuous

discussion among agriculture economists concerning possible

structural or taste changes in meat demands, especially beef

and chicken. The debate stimulated even unusual media

coverage (for example, Business Week, 26 August, 28 October,

1985) reflecting public concerns on this issue. These

articles argue that consumer blood cholesterol and other

nutritional and health concerns may have generated a









5
departure in meat demand from old long-term trends, and that

people tend to buy more white meat and less red meat.

Studies finished so far, however, give us mixed results.

Moreover, suspicion has arisen among some researchers

whether the methodologies employed by previous studies were

able to identify structural change (Chalfant & Alston,

1988). More recently, an article by Purcell (1989) blamed

agricultural economists for failing to come to a consensus

on this issue and alarmed industry leaders with regards to

the degree of changing beef demand. The author argues that

because the beef industry did not respond to the changes in

a timely fashion, it has suffered dearly from shrinking

herds, low cattle prices, forced disinvestment and business

losses; consumers also suffered from higher retail prices

and lack of variety.

The consumption patterns of meat products have changed

significantly in the last two decades. Figure 1 shows the

annual per capital consumption patterns (pounds of retail

equivalent) for beef, pork and poultry. Poultry (including

chicken and turkey) consumption has been steadily

increasing; total consumption has increased 70 percent from

1965 to 1988, and chicken itself increased by 72 percent.

The per capital consumption of beef reached its peak in 1976,

and then declined sharply in the second half of the decade.

Compared to beef and pork, the relative price of poultry has

been declining (Figure 2). Relative prices of beef










increased during the period of late 1970s and slightly

decreased in the 1980s. Pork price and consumption have

been relatively stable.

The limited data on relative prices and per capital

consumption, as well as budget shares of meat products, show

that total consumption of beef and poultry has changed and

deviated from old trends. At the first glance, it may be

hypothesized that observed meat consumption changes are

caused by movements in, or fluctuations of, meat prices,

consumer incomes, and the prices of substitute goods, all of

which interact with stable meat demand functions. There is

some credence for this assumption because increasing

consumption of poultry is consistent with decreasing

relative poultry prices and increasing beef prices

(substitutes); and decreasing beef consumption is consistent

with higher beef price and declining substitute prices. In

addition to this assumption, the change in the consumption

pattern may also have been caused by a change in the

structure of meat demand resulting from changes in

demographic variables, demand for convenience foods, and,

above all, from an evolution in consumer preferences driven

by a growing awareness of the health hazard of large intake

of cholesterol and other saturated fats. The identification

of causes of shifts in consumption is extremely important

for industry and agricultural economists. The importance of

this issue prods researchers to look beyond the simple










assumption of stable demand functions. Indeed, if the beef

consumption decline is due to price-income changes, the beef

industry must improve its production efficiency if the

industry is to keep from shrinking further. If, however,

there has been a structural shift in the demand for beef,

the industry needs to pursue the question of why preference

relations have changed and undertake such measures as

advertising, consumer educational programs, grading and

packing changes,etc., which could shift preferences back

toward their original position.

Of course, consumption is determined by the equilibrium

of demand and supply. Consumption changes can come from a

shift in supply, a shift in demand, or a combination of the

two. A difficult task of structural change studies is to

identify the sources of the changes. Supply and demand

conditions should be looked at carefully and some clue on

forces of change be identified before one starts estimating

a sophisticated demand (supply) model, or some form of

supply (demand) instrument should be included into demand

(supply) models if data permits to avoid simultaneous

equation bias. Increases in per capital consumption at

higher inflation-adjusted prices are a sure sign of

increasing demand. However, beef consumption shows us a

different example. From 1979 to 1986, to obtain the same per

capital supply of beef sold, the deflated price of choice

beef at retail had to drop over 32 percent. Meanwhile,









8
production costs increased and farm disinvestment continued;

this evidence points to a scenario of decreasing demand.

Other studies have concluded that the supply shocks are

relatively small and have uniform impacts on all meat

products (Purcell 1989, Thurman 1987).

Beside the practical importance of advising and helping

the meat industry to adjust to changing demand, the

identification of the structure of taste change has

theoretical importance, which, if not fully acknowledged,

can make the estimated demand system neither applicable to

the period before nor after the structural change. Most of

the studies on structural changes have used a demand system,

and have estimated and tested the stability of the

parameters. This approach is valid only if the demand

system is complete, i.e. the prices and quantities of

substitute and complementary goods are included, otherwise

the shift of demand function could be caused by a change in

an excluded price interacting with a stable demand

structure. Furthermore, even with a complete demand system,

which satisfies an acceptable definition of flexibility and

imposes the restrictions of utility maximization, evidence

of structural change may reflect model misspecification of

some kind because important features of the data generating

process are not known (e.g. the specification of utility

function) or are overly simplified. However, the problem

can be solved if we make sure that the analysis is carried










out within a functional form which is at least a second

order Taylor series approximation of the true demand system.

Another alternative is Fourier transform (Wohlgenant, 1984).

All the theoretical restrictions of a proper demand system

should also be tested and imposed. It is recommended that a

taste variable be specifically stated in the model. This

added dimension of a demand system will correct the

biasedness of other parameter estimates, in terms of omitted

variables, and improve the performance of the model in terms

of satisfying symmetry and homogeneity conditions (Pope et

al. 1980, Stapelton 1984). Relaxing the assumption of

constant taste and incorporating it into a indirect

objective function (cost or utility function) will make the

theoretical structural assumptions tractable.

The proposed research uses the Almost Ideal Demand

System (AIDS) developed by Deaton and Muellbauer (1980) and

the Rotterdam Model as frameworks for demand analysis. Both

of these models have been widely used in demand studies and

can be used to provide statistical tests of demand

properties. Latent taste variables are specifically

included into the objection function, utility and cost

functions, to minimize the problem of misspecification.



Organization

This research will specify a structural equation model

of meat consumption with provision for static and/or dynamic










latent variables to capture taste changes. Tastes or

preferences comprise an unobservable latent variable in the

utility and demand functions. The model used in this study

will trace the path of taste variable changes and

specifically quantify taste changes. The organization of

this dissertation is as follows: chapter 2 will review

previous studies of structural change in meat demand;

chapter 3 reviews and specifies static and dynamic latent

variable models used in this study; chapter 4 shows the

detailed model specification and set-up of the latent

variable model and the selection of cause and indicator

variables; chapter 5 shows results of model estimation and

chapter 6 gives summary and conclusions.










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CHAPTER 2
LITERATURE REVIEW

Many studies on the structural change of meat demand

have been done, but different conclusions were drawn on the

occurrence and timing of the structural change. When a

demand system is estimated, it is usually assumed that

factors not entering into the demand function remain

constant throughout the data period of study. When any of

the "constant" factors changes, the estimated demand

function shifts, this is called structural change. In most

meat demand models previously studied, the quantity or price

is defined as a function of income and prices of related

goods. Taste is assumed constant and not included in the

demand model. When a shift is detected within the data

period, it is then concluded that structural change has

occurred and it is usually attributed to changing consumer

tastes. Nyankori and Miller (1982), Braschler (1983),

Chavas (1983), Thurman (1987), Eales and Unnevehr (1988),

Moschini and Meilke (1989) present evidence that structural

change occurred in meat demands in the 1970's, while

studies by Haidacher et al. (1982), Moschini and Meilke

(1984), Dahlgran (1987), and Chalfant and Alston (1988)

found no such evidence. Most of the studies focused on the









14
red meat consumption. Only Thurman (1987) looked at poultry

market demand closely. All the above studies except

Chalfant and Alston (1988) estimated a demand system and

inferred the occurrence and timing of structural change by

identifying parameter changes.

All tests of structural changes were conducted with

aggregate U.S. time series data. The diversity of empirical

results may be due to a combination of factors, such as (1)

the time span and the periodicity of data, (2) the number of

parameters in the model, (3) the specification of gradual or

abrupt change, (4) functional form, (5) price dependent

versus quantity dependent specification, (6) the degree to

which the theoretical structure is embodied in the empirical

structure. Given the same data set, any of the above

considerations may very well result in different structural

change conclusions.

Studies by Chavas (1983), Frank (1984), and Moschini

and Meilke (1984) attempted to capture the effect of all

other prices by explicitly including a composite price index

of all other commodities. The validity of this aggregate

price index depends on the assumption that these prices

change in proportion. This is a very restrictive assumption

and rarely if ever satisfied. These studies usually

rejected the inclusion of these price indexes in favor of a

simpler version of model which excludes these indices.










Braschler (1982) and Leuthold and Nwagbo (1977)

examined structural changes within single equation models by

allowing abrupt change of parameters at a specific time.

However, the point of structural change is usually

identified by an ad hoc procedure. Even when some

statistical methods are utilized for identifying these

points, the same data are used again for testing, rendering

this whole practice dependent on data mining. Leuthold and

Nwagbo (1977) chose the midpoint of their relatively small

11-year sample of quarterly data as the point of structural

change, and then examined the impact of changing that point

by one year each time. They found no strong evidence of

structural change during the 1964-75 period. Braschler

(1983) used a price dependent, single equation model for

beef and pork, finding evidence of structural change at the

midpoint of his data set. He found that beef structural

change occurred in 1971, pork in 1969. He found that pork

prices are becoming less responsive to available quantities

of pork and beef, more responsive to the quantity of

broilers, and less responsive to changes in real income.

For beef prices, he found that the response to the quantity

of broilers changes from negative to positive, thus the

increasing quantity of broiler consumption led to higher

beef price. Increasing beef price is the result of

increasing beef demand. This not consistent with his

finding on the unfavorable structural changes against beef









16
demand. Although structural change can be elicited by many

different methods, from an intuitive view, we would expect

structural change to occur simultaneously in related

commodities since they would all be affected by the same

factors. We would expect the pork structural change to

occur in the same year as the change in beef structure.

Thus, while Braschler (1983) found a significant change in

his empirical structure, his estimates of the demand

structure are inconsistent with the assumed economic theory.

Frank (1984), Cornell and Sorenson (1986), and Dahlgran

(1986) improved on some of the former studies in several

ways. They employed statistical procedures that allow for

gradual changes in parameters. Gradual changes are more

plausible than abrupt changes in consumption behavior. It

is compatible with habit formation and diffusion of

information among consumers. Frank (1984) and Dahlgran

(1986) also imposed restrictions that structural changes

take place simultaneously among the meat commodities. Frank

(1984) and Dahlgran (1986) found statistically significant

evidence of parameter changes for beef, pork and chicken

occurring around 1973-1975. Cornell and Sorenson (1986),

using annual data for 1950-1982, found evidence of parameter

changes for beef and broilers but not for pork.

Nyankori and Miller (1982), Chavas (1983), Thurman

(1987), Moschini and Meilke (1984) used ad hoc demand

functions to test the consistency of the structural change









17
hypothesis and data. The functions were usually defined in

such a way that a quantity-dependent variable (per capital

consumption of meat) was a function of consumer income and

prices of related goods. Thurman (1987) did an endogeneity

test and found that for poultry demand, price is

predetermined by costs of production while quantity is

determined by price. Dahlgran (1987), Eales and Unnevehr

(1988), and Moschini and Meilke (1989) used complete demand

systems. By way of specification, the allocation of

expenditure for a group of meat commodities can be assumed

to be independent of other commodities outside of this

group.

The system of demand functions for these commodities

should satisfy properties of adding-up, symmetry and

homogeneity. It is a controversial issue that when using

aggregate data these demand properties should still be

satisfied. Christensen and Jorgenson and Lau (1975)

rejected these demand properties using their now famous

translog flexible function forms, and they concluded that

the theory of demand is inconsistent with the evidence.

Later studies by Simmons and Weiserbs (1979) showed that any

flexible functional form is only an accurate local

approximation to a true function. The estimated aggregate

demand function will satisfy demand properties only when

strict forms of individual preferences are assumed. Other

studies obtained almost uniform rejection of demand










restrictions on aggregate data (Deaton and Muellbauer, pp.

74, 1980). Chalfant and Alston (1988) criticized these

parametric functional form studies for failing to

distinguish between the structural change and errors of

specification in their parametric approach and proposed a

non-parametric approach for assessing the structural change

by using the Strong Axioms of Revealed Preferences (SARP).

Haidacher (1983) discussed the issues related to

structural change in demand systems, particularly the issue

of intractability of obtaining direct evidence on structural

change via conventional procedures. He argued that since

demand structure is uniquely determined by the utility

function and the optimizing process, changes in structure

must be a consequences of change in the utility function,

U=F(q). Since the utility function is not directly

observable, the change can only be reflected in the demand

structure (which is unknown) and the observed behavior. Any

observed behavior embodies two potential effects, response

under a given structure and response from a changes in

structure. If the specification of a given structure is not

correct, the null hypothesis of linear demand structure with

constant parameters that are invariant with respect to time

would result in multiple alternative hypotheses rather than

a single one. Each specification results in one more

element in the alternative hypothesis set. Thus, the effort

of obtaining direct evidence on structural change without










assurance of correct specification is futile. Haidacher

proposed an indirect method to test structural changes which

includes testing error of prediction and testing the

/ constant term in an differential demand model. He strongly

favored a complete demand system, arguing that it

corresponds more closely to the classic optimizing model

than most other specifications and provides the greatest

potential for reducing the number of elements in the

alternative hypothesis set due to specification error

through omitted variables.

Chavas (1983) agreed that consumer concern regarding

fat and cholesterol might have produced an important shift

in meat preferences. This preference change can lead to

permanent changes in behavioral relationships, and hence

change the parameters in demand functions. He assumed that

parameters can change randomly from one period to the next,

and used the Kalman Filter specification to identify and

estimate (update) parameter change in a linear demand model.

The identification of the variance of these random elements

is based on the minimization of a prediction error

criterion. Application of the method to U.S. meat demand in

the 1970s identified structural change to have occurred for

beef and poultry, but not pork, in the last part of the

decade. Chavas found that price and income elasticities of

beef have been decreasing in the past few years, while the

income elasticity of poultry has been increasing. This










analysis suggests that data before 1975 may not be very

useful in measuring poultry and beef demand in the 1980s.

In a attempt to minimize the impact of specification

error due to choice of functional form, Moschini and Meilke

(1984) used the flexible Box-Cox transformation in a single-

equation, quantity-dependent model of beef demand. They

found no evidence of structural change over the period 1966-

1981, but do find that price and income elasticities change

with varying levels of prices and income. They correctly

noted that such changes in response parameters do not

necessarily imply structural change. They found that price

elasticity of beef rises as the price of beef increases.

This is plausible because demand would be more sensitive as

this commodity becomes more expensive, as substitutes become

more attractive. They found that income elasticity

decreases as income increases, this is consistent with

Engle's Law and the notion of a saturation point of food

consumption.

Wohlgenant (1982,1986) attempted to explain the cause

of structural change explicitly within the model

specification. He found that parameter changes can be

partially explained by quality changes in meats, which

mainly are changes in protein, carbohydrates, iron,

riboflavin, and ascorbic acid. He found that one-third of

the unexplained decrease in demand for beef and pork and

one-half of the unexplained increase in poultry are due to











quality changes in the respective products. The explained

demand changes are defined as the variation not accounted by

changes in income and prices. His model provides us some

good insights into the casual factors influencing parameter

changes.

Dahlgran (1987) used the Rotterdam model to test

structural changes in meat demand, arguing that the

Rotterdam model is derived from per capital demands rather

than from representative consumer's preference, and that

specification error is diminished by this model. Dahlgran

assumed, based on the length of the gestation and production

cycle for beef and pork and empirical evidence for chicken,

that the annual supplies of beef, pork and chicken are

fixed. This assumption dictates that meat quantities should

be treated as given along with the prices of other foods and

non-food items and that meat prices should be dependent

variables. The time variant paths of the elasticities of

meat demands show that significant changes in the demand

system parameters were detected, and these changes were

consistent with increased substitutability between beef and

chicken. However, the timing and transitory nature of these

changes does not support the contention of a permanent

change in consumers' meat consumption preferences.

Corresponding to the detected model parameter changes, the

meat demand elasticity structure appeared to change

substantially in the 1970s, but in the 1980s it has









22

restabilized. He concluded that the 1970s structure was an

aberration and that the meat markets have since returned to

an elasticity structure that is not very different from that

displayed in the 1960s.

Eales and Unnevehr (1988) used two Dynamic Almost Ideal

Demand Systems (DAIDS), one for aggregated meats and another

for disaggregated meat products. Tests for weak

separability show that consumers choose among meat products

rather than meat aggregates such as "beef" and "chicken".

Therefore, tests for structural change in the meat

aggregates may be biased. They suggested that a full

understanding of meat demand or tests for structural change

require analysis of a disaggregated meat product model.

Tests for structural change in disaggregated products

revealed a different picture of preference changes than the

aggregate model. Two types of significant shifts in meat

demand were identified in meat products: an exogenous

constant annual 6.4% growth in demand for chicken

parts/processed from 1965 to 1985 and a 3.5% decline in

demand for beef table cuts after 1974. Over the entire

period, demand for whole birds declined slightly while

demand for hamburger increased slightly. Growth in

aggregate chicken is apparently due to growth in the demand

for parts/processed. The model identified that hamburger

and whole birds are inferior goods and chicken parts and

beef table cuts are normal goods. Further findings of











disaggregate substitution made the authors refute the

assumption that structural changes come from health

concerns. They argued that a shift due purely to health

concerns would have led to growth in whole birds and a

decline in hamburger, but the contrary is true. While

awareness of cholesterol may be greater among consumers of

higher quality meats, the shift from beef table cuts to

chicken parts/processed must also have been caused by growth

in demand for convenience. They concluded that the chicken

industry has responded to the increased demand for embodied

service in chicken products by marketing new products. This

suggests that the beef industry should develop new products

to stimulate demand.

Moschini and Meilke (1989) tested the hypothesis of

structural change in U.S. meat demand in a four-meat Almost

Ideal Demand System with parameters following a gradual

switching regression model. The results support the notion

that structural change partly explains the observed U.S.

meat consumption patterns. Structural change is

significantly biased against beef, in favor of chicken and

fish, and it is neutral for pork. Bias to structural change

is attributed to changes in expenditure shares in this model

when prices and expenditure are held constant. The

estimated bias for beef implies that a decline of

approximately 6 percent in beef share can be accounted for

by the estimated changing structure at constant prices and










expenditures. One of the interesting conclusions of this

study is that, contrary to other studies which reached

similar conclusions about structural changes, the structural

change did not significantly affect demand elasticities and

elasticities of substitution.

Chalfant and Alston (1988) used a non-parametric

approach to test structural changes in meat demand systems,

arguing that the rejection of the stability hypothesis could

well be due to use of the wrong functional form rather than

a rejection of the economic proposition in parametric

analysis. The advantage of the non-parametric approach is

that it gives a test for stable preferences for market goods

that does not require that they be of a particular form,

such as AIDS. As in the parametric approach, the null

hypothesis is tht there is a stable set of preferences so

that variation in observed quantities consumed can be

explained by changes in relative prices or expenditures.

When consumers obey the Strong Axiom of Revealed Preferences

(SARP), there is a stable demand system that fully explains

observed consumption patterns. This holds because the

strong axiom is equivalent to the existence of a well-

behaved utility function. The axiom does not need hold in

the data when structural changes occur, so a test for

violations of the axiom is capable of identifying changes in

preferences. A check for consistency with the axioms of

revealed preference, applied to the U.S. and Australian meat










data, showed that the data from both countries could have

been generated by stable preferences. The overwhelming

evidence of meat consumption changes may be attributed to

the fact that household production functions have shifted

over time and that meat is being perceived and used

differently by consumers.

The problem with this non-parametric approach is the

power of the test. When total expenditure is increasing

over the sample period, the demand function (of latter time)

would be pushed out to the right, possibly not intersecting

with the comparison supply function (which is independent of

consumer expenditure and should remain in the original

position). When this occurs, no earlier consumption bundle

can be revealed to be preferred to any subsequent bundle, as

all subsequent bundles were unaffordable in the earlier

period, and as a result the model tends to accept the null

hypothesis more often than it should. The non-parametric

model is more appropriate for cross sectional rather than

time series analysis.

Choi and Sosin (1990) used a translog flexible

functional form specification for the underlying indirect

utility function to develop a demand function which has a

smooth logistic function multiplicative term. This logistic

multiplicative term is a function of time trend and

represents smoothing change,of tastes. Structural changes

alter the marginal rates of substitution between goods at










fixed points of prices and quantities, and the

multiplicative term. Their study found evidence of red meat

demand structural changes in mid 1970's. The statistics of

fit are also improved by defining an evolving multiplicative

structural term in the demand function.

A summary of the studies on the structural change in

retail meat demand is in appendix 1.

Other meat demand literature, although not directly

related to the structural change studies, uses cross section

data to analyze the effects of social-economic and

demographic factors on preference formation. Heien and

Pompelli (1988) used USDA 1977 Household Food Consumption

Survey (HFCS) data, estimated an AIDS model for three major

cuts of beef:steak, roast, and ground beef. They found the

impact of certain demographic effects, such as household

size, region, tenancy, and ethnic origin, was generally

quite significant. Black and Hispanic households have

higher preferences for steak and ground beef, but relatively

low preferences for roast. Other demographic variables,

such as employment status, shopper, and occupation, were

generally not significant.

Jensen and Schroeter (1989) used household panel

scanner data on fresh beef demand from a supermarket

universal product code (UPC) scanner system. The product,

price and quantity information for selected panelists'

grocery shopping trips is read by scanners and used to










update computer-based purchase logs for each of a large

number of participating households in a experimental market

area. The extended period of experiment provided data for

time-series and cross-section analysis. The Non-white

ethnic group (eighty percent are Hispanic families in the

sample) consume more fresh beef than white families.

Households headed by a 45 to 64-year-old tend to consume

significantly more beef than do otherwise comparable

households headed by younger or older individuals. This

perhaps is in accordance with other studies that found that

grown children present in households headed by 45- to 64-

year-olds eat more fresh beef than the younger children

typically found in the households of younger parents.

Households headed by a single female consume

disproportionately less beef than do households with two

heads. This finding is perhaps related with demand for

convenience, single mother families usually face more

demands for their time, and beef takes longer to cook. They

also found that college-educated households purchase nearly

.5 lb./month less fresh beef than do households with members

who have no college experience. Families having higher

education have easier access to information relating health

concerns to food intake, and respond more quickly to this

information.

Although the cross section studies can not address the

question of preference change over years, they can lay the









28
theoretic foundation for time series analysis. This

information can then be used for time series studies to

asses the aggregation problem which researchers would

inevitably encounter during their research.














CHAPTER 3
LATENT VARIABLE MODELS


A latent variable is a variable which is not

observable. It is usually represented by a proxy when its

presence is crucial to the model. Other names of latent

variables include unobservable variables, errors of

measurement, errors in the variables, and factors. Taste or

consumer preference can be considered a latent variable. In

this chapter, two approaches to estimating latent variable

models are reviewed. The structural equation static latent

variable model and state space dynamic latent variable model

are used in Chapter 4 to estimate the latent taste variable.



Structural Equation Models

Goldberger (1972b) has a comprehensive review of the

development of latent variable methods in econometrics. In

the early days of econometrics, equations were formulated as

exact relations among unobservable variables, and errors in

the variables provided the only stochastic component in

observations. The emphasis soon shifted entirely to errors

in the equations since the days of the Cowels Commission. A

possible justification for this neglect is that measurement

errors in economic data are negligible, at least in










comparison to behavioral disturbance. However, the real

explanation may have been the misconception that error in

variable models are under-identified. This under-

identification posed difficulty in estimation and testing,

and presented a seeming impasse to econometricians at the

time. In empirical econometrics it is often common to find

"proxy" or "surrogate" variables used freely, with little

effort made to trace out the consequences. It is often

assumed that taste or preference is constant in maximizing

utility functions, so demand functions compatible with this

property of the utility function ignore the latent variable.

When the model is applied to time series price and quantity

data, where taste or preference may have changed over time,

omitting taste change can render estimation inconsistent.

More problematic is the approach to identifying structural

(taste) change in such a model by using surrogate variables

like residual autocorrelation, time trend dummy, etc. The

specification error of omitting a latent variable in the

original model setting along with other specification errors

mentioned by Chalfant and Alston (1988) makes it impossible

to identify structural change caused by taste change of

consumers.

The effect of using a "proxy" instead of true variable

in regression analysis can be demonstrated by the following

model (Fuller, 1987). The classical linear regression model

is defined by











Yt = fxt + e,
and one is unable to observe xt directly, only Zt is

observed directly.

Zt = xt + ut (3.1)
The regression coefficient (A) computed from the observed

variables is biased toward zero.

E{l) = azz'la =P(axx + au)-1xx. (3.2)

As ao becomes greater, (ax + a)'laxx tends to zero.

The latent variable model is usually discussed in the

more general framework of structural equation models. The

term "structural" stands for the assumption that each

equation represents a causal link, rather than a mere

empirical association. Structural equation models are

regression equations with less restrictive assumptions that

allow measurement error in the explanatory as well as the

dependent variables. They routinely include multiple

indicators of latent variables. These models encompass and

extend path analysis, econometrics, and factor analysis.

Unfortunately, they have only been widely used in other

social sciences like sociology, psychology and political

science.

Structural equation models have two major branches,

path analysis and factor analysis, which are often used in

sociology and psychology, respectively. Path analysis was

invented by biometrician Sewall Wright in 1918. It has

three aspects, a path diagram, the equation relating










correlations or covariances to parameters, and the

decomposition of effects. The path diagram is a pictorial

representation of a system of simultaneous relations. It

shows relations between all variables, including

disturbances and errors. The second aspect of path analysis

sets up rules to write the equation that relates the

covariance of variables to the model parameters. It

basically is a moment estimator. The second moment of the

sample data matrix is defined equal to a matrix of

structural parameters. The unknown structural parameters

are estimated by substituting sample covariance for the

population covariance matrix and solving the above equality.

The third aspect of path analysis provides a means to

distinguish direct, indirect, and total effects of one

variable on another. The direct effects are those not

mediated by any other variables; the indirect effects

operate at least through one intervening variable, and the

total effect is the sum of direct and indirect effects.

Wright used his path analysis methods in many latent

variable studies, such as bone size of rabbits, skin color

of guinea pigs, and human intelligence. Wright also wrote

an article in 1925 on estimating supply and demand functions

simultaneously, using the path analysis method to address

identification problems, long before economists had

sufficient knowledge of this problem. Path analysis has

been largely neglected by econometricians ever since its










birth. In the 1960s, sociologists began to realize the

potential of path analysis and the related "partial

correlation" techniques as a means to analyze non-

experimental data. Many studies have been done to analyze

latent variables like political stability, governing power,

democracy, education, etc. In the 1970's, more general and

elaborate matrix methods had developed and they incorporated

path diagrams and other features of path analysis into their

presentations. Path analysis has become more general and

mathematically more elegant, the vocabulary of covariancee

structural", "latent variable", "multiple indicators" has

become commonplace in quantitative sociology.

Factor analysis also has a long history. It was

invented by Spearman in 1904. It emphasizes the relation of

latent factors to observable variables. Factor analysis has

been used in psychology since the 1930's, especially in

educational psychology. Unlike path analysis, factor

analysis was looked at by economists briefly in 1970's, but

the curiosity was soon dismissed as researchers might have

confused factor analysis with principal component analysis

which they view as a mechanical procedure for reducing

dimensionality in regression computations. Even among the

few who understood that factor analysis is more than a data

management technique, the misconception of

underidentification in the errors in variables model

deterred many people. Goldberger (1972b) presented two










reasons that made factor analysis unattractive for

econometricians: (1)economists are not attracted by models

in which variables and parameters are redefined ex post, and

(2) economists are not attracted by model in which all

observable variables are treated symmetrically as effects of

unobservable causes.

The structural equation model rapidly developed since

the 1970's. It combined the newest improvement in both path

analysis and factor analysis and has become a general

approach to latent variable models. It includes path

analysis, factor analysis and classical econometrics as a

special cases. The observed variable can be causes or

effects of latent variables, or observable variables can

directly affect each other. This is an expansion of

restrictive factor analysis where all indicators are viewed

as effects of the latent variables. The work by Joreskog

(1973) and Wiley (1973) completed the generalization of this

model. This model had two parts. The first was a latent

variable model that was similar to the simultaneous equation

model of econometrics except that all variables were latent

variables. The second part was the measurement model that

showed indicators as effects of latent variables as in

factor analysis.

The first component of structural equation system is a

latent variable model (Bollen, pp.319-326, 1989):

n = By + rF + c (3.3)










where, r (mxl) is the vector of latent endogenous random

variables; t (nxl) is the vector of exogenous random

variables; B is an mxm coefficient matrix showing the

influence of latent endogenous variables on each other; r is

the mxn coefficient matrix for the effects of t on T. The

matrix (I-B) is assumed nonsingular. C is the disturbance

vector that is assumed to have an expected value of zero and

is uncorrelated with t. The second component of the

structural equation model is the measurement model:

y = Ay n + E (3.4)

x = A + (3.5)

where the y (pxl) and the x (qxl) vectors are observed

variables; they are also called indicators of latent

variables ) and t. The Ax and A are (pxm) and (qxn)

coefficient matrices showing the relationship of latent

variables to their indicators respectively. The e (pxl) and

6 (qxl) are the errors of measurement for y and x,

respectively. The measurement errors are uncorrelated with

latent variables, and have expected value of zero.

The equations (3.3), (3.4) and (3.5) are general form

of structural equation models. It is clear that the

classical econometric model is only a special case of this

model where Ax and A are identity matrices and the

covariance matrices of measurement errors 0, (pxp) and 86

(qxq) are zeroes. In this case, if B 0, we have a

simultaneous equation system.










y = By + rx + C (3.6)

The equation (3.5) represents a typical factor analysis

model, a special case of the general set-up. The ordinary

measurement error model, where endogenous and exogenous

variables are measured with errors, is also a special case

of the structural equation model, e.g.

q = Bn + rF + C (3.7)

y = n + e (3.8)

x = + 6 (3.9)

where A = Ip and A = Iq and the covariance matrices of

measurement errors 8, and 86 are non-zero.

The estimation of the structural equation model is

somewhat different than with the traditional econometrics

approach. The latter derives from the minimization of the

sum of squared differences of the predicted and observed

dependent variables for each observation. The procedure

used here emphasizes covariances rather than observations.

Instead of minimizing the sum of squared differences of

observed and predicted values, we minimize the difference

between the sample covariances and the covariances predicted

by the model. The fundamental hypothesis for these

structural equation procedures is that the covariance matrix

of the observed variables is a function of a set of

parameters. This fundamental hypothesis is expressed as

S = Z(e) (3.10)

where S is the sample covariance matrix of observed








37
variables, 8 is a vector that contains the model parameters,

and E(8) is the implied covariance matrix written as a
function of 8.

Assuming we have an endogenous set y and an exogenous
set x, the population covariance matrix for y and x is

SVAR(y) COV(x,y) 1
S=I I (3.11)
I COV(y,x) VAR(x) 1
The implied covariance matrix Z(0) is the covariance matrix
written as a function of the free model parameters in 8. It
can be expressed like

[ Z () Z (e) 1
Z(0) = I (3.12)
1 E ,(0) E (0) J
where E y(0) = E(xy'). The exogenous and (or) endogenous

variables x, y can be expressed as functions) of the
parameter vector 0, then, finally ZE,(8) = E(xy') = f(0).

In practice, the population covariances (E) or the
parameters (0) are both unknown, so S is used to substitute
for Z.

Define E(O) to be the implied covariance matrix with
estimated 6 replacing 0. The residual matrix (S E(O))

indicates how close Z(O) is to S. The unknown parameters

can be estimated by minimizing residuals or a function of a
residual matrix. This function (also called the fitting
function), F(S, Z(O)), has the following properties: scalar,
non-negativity, equals to zero only when S = Z(O), and

continuous in S and Z(O). Minimization of fitting functions










satisfying these properties leads to consistent estimators

of 0 (Bollen, pp.106, 1989). There are a few such fitting

functions. Maximum likelihood (ML) is the one proposed

here.

The maximum likelihood method (ML) is the most widely

used fitting function in general structural models. The

fitting function that is minimized is

Fi = T/21ogI Z(O)1 + T/2tr(S EZ'(0)) (3.13)

The derivation of Fm is from the assumption that

variables x and y are normally distributed, and the

fundamental hypothesis S = Z (0) holds. If we combine y and

x into a single (p+q)xl vector z, for a random sample of T

independent observations of z, its log likelihood function

is (Bollen, 1989):


-T(p+q) T
logL(0) = ------ n(27r)-(T/2)lnI Z(8)I -(l/2)Ez'-1(8) z (3.14)
2 i=l

The logL(0) and the negative Fm are equivalent, the

log likelihood is maximized when Fmt is minimized.

For the general structural equation models defined by

(3.3)-(3.5), the elements of the implied covariance E(0)

are:

xx(0) = E (xx') = Ax A A' + 8 (3.15)
where 9 stands for the covariance matrix of latent variables

t. The covariance of y can be written as a function of the

unknown model parameters that are stacked in the vector, 8.

The Z (8)is










Y (0) = E(yy')
= E [(Ay n + e)(Ay tI + e)']

= AyE(q7')A'y + e, (3.16)
It can be further broken down by substituting the reduced

form of equation (3.3), that is, v = (I B)'I(rf + C), in

equation (3.16) and simplifying

,yy(e) = A (I B) '(rr' + Y)[(I B)'1]'A' + e,
(3.17)
where 7 stands for the covariance matrix of errors in the

equations C. Using similar argument, we have

E (0) = E(yx')

= E [(Ay t + e)( Ax + 6)']

= AyE(qE')A',

= A(I-B)'rFA'x (3.18)

The implied covariance matrix of the general structural

equation (3.12) is

[ A(I-B)-'(rr'+T)[(I-B)y']'/A'y +e, A(I-B)-'rA'x 1
Z(0) = 1
S AxF' [ (I-B)-1] 'A' AIxA' +e, I
(3.19)
The classical econometric regression model is a special case

of this general expression when latent variables are

measured without error. The least square estimator is

equivalent to the above estimator when all variables are

observable. Suppose the linear regression model is

expressed as

y = rx + C (3.20)










where both the variables x and y are observable. The

implied covariance matrix for this regression model is

\ rtr'+Y ro 1
E(0) = I I (3.21)
1 or' 0 J
This is a special case of (3.19) when Ax=A=I, and e,=e,=0.

We want the sample covariance matrix to be equal to the

implied covariance matrix

SVAR(y) COV(x,y) 1 [ rFr'+T r[
I I = I I (3.22)
I COV(y,x) VAR(x) i [ 0r' J

then COV(x,y) = rO = r VAR(x), r = COV(x,y)/COV(x). This

is the same as the conventional Least Square estimator.

The Multiple-indicator and Multiple-cause (MIMIC) model

originally formulated by Zellner (1970) and then extended by

Goldberger (1972, 1977) is a special case of the general

latent variable model when latent variable E is observable.

The latent variable q has indicators y, and itself is a

function of cause variable x.

n = Bn + rx + ( (3.23)

y = Ay n + E (3.24)

It is not enough to estimate the coefficients of the

latent variable only, sometimes it is necessary to estimate

the latent variable itself. This is done by a GLS estimator

which uses estimated latent variable coefficients. For

instance, the latent taste variable E can be calculated by

estimating a GLS model if only (3.3) is considered (Fuller

1987, Shonkwiler and Ford 1989).











(I -B)Y = FE + C (3.25)

= (fr' J'f) l AI- 1(1--l )Y (3.26)


State Space Model

Another way to estimate the time variant taste variable

is to use state space form. This is a term widely used in

engineering literature for describing a system in which

parameters follow a dynamic path. State form is often

solved by a filtering method, and is sometimes called the

Kalman filter. The fact that state space form techniques

provide an ideal framework for estimating equations with

latent variables has been increasingly recognized by

economists, see Harvey and Phillips (1979), Pagan (1980),

Engle and Watson (1981,1985), Engle et al (1985), Burmeister

and Wall (1987), Slade (1989). The specification is as

follows:

Yt = BEt + rxt + et (3.27)

st = $ St-1 + 6Ft + t (3.28)
Equations (3.27) are the measurement equations, where Yt is

a (nxl) vector of observations on n dependent variables, B

is a fixed matrix of order (nxj), and Et is an jxl vector of

unobserved state variables. Xt is a (nxk) matrix of

observable variables with the parameter vector r, etc.

Equations (3.28) are the transition equations for the state

variables, with 0 a fixed matrix of order jxj, Ft is an

(jxm) matrix of observations on m nonstochastic variables,








42
and 6 is an (mxl) coefficient vector. Latent variables can

be included in the state variable vector E. et and t are

normal disturbance vectors with zero means and covariance

matrices ne and nf, respectively. et and At are assumed to

be serially uncorrelated, uncorrelated with each other for

all t and uncorrelated with B.

For n 0, the parameter vector is random. Similarly,

for 1 or Ft*0, we have systematic parameter variation.

If ft is the estimate of Et using observations through t and

Et is the covariance matrix of it, Kalman filtering gives

the following sequential estimator of at in the model of

equations (3.27) and (3.28)

t =t/t-1 + Gt[Yt Bt~t/t-1 -xtF] (3.29)
with covariance matrix

-t = t/t-1 GtBtt/t-1 (3.30)
where Gt is the gain of the filter, t/,t-1 and Zt/,-1 are prior

estimators of state variables and their covariance matrix,

respectively. They are defined as

Gt = tt-1B't[Bt t/t-1B't + ne]'1 (3.31)

9t/t-1 = I At-1 + Ft6t (3.32)

Etit-1 = C t-1 't + n (3.33)
The prior estimators are the predictions of period t

using actual information available in period t-l. The

posterior estimate of Et, given in (3.29), is simply the

prior estimate of t/t-1, plus the prediction error (Yt -

Bt t/t-1) weighted by the gain of the filter. The gain of the










filter can be shown to be the coefficient of the least

squares regression of Et on the prediction error (Yt-B~ tt.1),

conditional on Yt-1 (Meinhold and Singpurwalla, 1983).

Similarly, the posterior variance Et in (3.30) is the prior

variance Et/t.1 minus the positive semi-definite matrix

GtBtEt/t-. If the parameters of equation (3.30) are known,
then the estimator in (3.29) gives the minimum variance,

unbiased estimator of Et.

The aim of filtering is to find the expected value of

the state vector Et conditional on the information available

at time t, that is E(St/Yt). The aim of smoothing is to

take account of the information made available after time t.

The mean of the distribution of Et, conditional on all the

sample, may be written as E(Et/YT) and is known as a

smoothed estimator. Since the smoothed estimator is based

on more information than the filtered estimator, it

generally will have a MSE smaller than that of the filtered

estimator.

The fixed interval smoothing algorithm used in this

study consists of a set of recursions which start with the

final quantities, ET and E, given by the Kalman filter and

work backwards. The equations are

Et/T =Et +Et*(Et+l/T --tl t) (3.34)

E t/T =zt +t (t+l/T -Zt*l/t) t (3.35)
where


(3.36)


Et* =Et ft+*1 Et+l1t' t=T-1,... 1










with ET/ =ET and E =ET.

As shown in Harvey (1989) the likelihood function of

the unknown parameters in (3.27)-(3.28) is easily formed.

Let "t denote the innovations in yt, yt E(yt/Yt-l .. ,yl, zt

,...,zl); and let Gt denote the variance of nt. the log

likelihood can be written as

t
L(8) = constant -1/2 E (logGtl + 7'tGt-1it) (3.37)
t=l

where 8 is the vector of unknown parameters. The

innovations and their variances are easily calculated using

the Kalman filter. Note that the innovation variance is

equal to the gain of Kalman filter G,.

The state space model of (3.27)-(3.28) can be estimated

by using the EM methods suggested by Watson and Engle

(1983). This technique was originally developed by Dempster

et al (1977) for maximizing a likelihood function in the

presence of missing observations. It consists of two steps:

an estimation and a maximization step which are iterated to

convergence. The maximization step calculates the maximum

likelihood estimates of all the unknown parameters

conditional on a full data set. The estimation step

constructs estimates of the sufficient statistics of the

problem conditional on the observed data and the parameters.

In the state space model, the unobservables are treated just

like missing observations. The estimation step consists of

a Kalman filter smoother which gives sufficient statistics










of the latent variable. When the latent variable is

estimated, the maximum likelihood estimates could then be

calculated by forming the appropriate sample moment matrices

necessary for the multivariate regression problem. Putting

these two steps together, we have an algorithm. From an

initial guess of the parameters we use a Kalman filter and

smoother, a signal extraction procedure, to estimate the

latent variable(s) and its variance. Combining these with

the observed data we form the appropriate moment matrices

and obtain new parameters using standard regression

formulae. These new parameter estimates are used to form

new estimates of the latent variable(s), and the procedure

is repeated until convergence.

The Kalman filter requires a value of the mean and

variance of E0 as an initialization. When these starting

values are not known, they must be constructed. Different

methods should be used depending on whether the stochastic

process generating Et is stationary. When Et is stationary,

as is the case here, starting values can be computed from

the first J observations by setting Beso =0 and EO/O =KI,

where K is a large scaler.

Upon convergence of the estimation algorithm, the

Kalman smoother can be run to obtain an estimate of the

prior conditioned on the parameter estimates. With the

prior estimate so obtained, the estimation and smoothing

process is repeated until both constant parameters and










priors match. In any case, the initial value will not

affect the estimation of state variables when the sample is

large (Watson, 1983).

The EM method is an iterative two step method, it is

better than some other state space estimators such as the

Scoring method (Pagan, 1980). This maximizes the state

space likelihood (3.37), with respect to all latent

variables as well as parameters, using numerical derivatives

for the score and information matrix. It is equivalent to

recursively substituting the transition equation into the

measurement equation, and maximizing the likelihood function

of the reduced function.













CHAPTER 4
MODEL SPECIFICATION


As reviewed in the previous section, economists are

traditionally suspicious of latent variables. More so in

the case of applied consumption analysis perhaps because a

profession's intellectual tastes change slowly" (Pollak,

1978). Nevertheless it is time to reconsider some of the

old wisdom toward taste formation and taste change.

Among those who are suspicious or pessimistic of taste

modeling are some of the best known economists such as

Milton Friedman and George Stigler. Friedman (1962) writes:

Despite these qualifications, economic theory proceeds
largely to take wants as fixed. This is primarily a case of
division of labor. The economist has little to say about
the formation of wants; this is the province of the
psychologists. The economist's task is to trace the
consequences of any given set of wants. The legitimacy of
and justification for this abstraction must rest ultimately,
in this case as with any other abstraction, on the light
that is shed and the power to predict that is yielded by the
abstraction. (p.13)

It is perhaps reasonable to argue that it is the

psychologist's work to figure out how the taste change takes

place. However, just as Friedman emphasizes the proper test

of validity of this division of labor is its power to

predict, the current need to estimate taste formation and

taste change has largely come from empirical demand

analysis, like meat demand analysis. The taste (structural)










change makes many econometric models which used pre-change

data perform poorly in prediction in recent years (Purcell,

1989). The declining predictive power of meat models

suggests the inclusion of a taste variable in these models

to improve their performance.

Stigler and Becker (1977) used household production

theory to establish theoretically that taste can be treated

as stable over time and among people. This is done by

translating "unstable tastes" into variables in the

household production function for commodities. By

specifying demand models this way, all changes in behavior

are explained by changes in prices and incomes. The

household production theory assumes that the ultimate

objectives of choice are commodities produced by each

household with market goods, own time, knowledge and perhaps

other inputs. Knowledge, for instance, can be produced by

advertising and health information. An increase in

advertising may lower the shadow prices of a commodity to

the household and thereby increase its demand for the market

output, because the household is made to believe correctly

or incorrectly that it gets a greater output of the

commodity from a given input of the advertised product.

Consequently, advertising affects consumption in this

formulation not by changing taste, but by changing shadow

prices. That is, a movement along a stable demand curve for

household produced commodities is seen as generating the








49
apparently unstable demand curves of market goods and other

inputs. The change of demands for household produced

commodities are independent of taste changes, taste change

will not shift demand function for household produced goods.

Taste changes will only be able to change the shadow prices

"of the household produced commodities. Household production

theory is difficult to implement empirically. In this study

we will estimate demand functions in market goods space. In

this case the taste variable would enter into the demand

equation directly.

There are a number of ways to incorporate taste

formation into the analysis of household behavior. Some of

the methods of incorporating advertisement effects into

demand models can be used here (Green 1985, Brown and Lee

1989). Advertisement and taste are related latent

variables, the former affects the latter. The traditional

utility function assumes that consumer tastes are constant.

To extend the traditional demand model to include tastes,

the assumption of constant taste must first be relaxed. The

general consumer preference choice can, in general, be

written as (Grandmont, 1983)

Maximize u=u(q, E) (4.1)

subject to p'q = x

where q and p are nxl vectors of quantities and prices

respectively, x is total expenditure or income. The latent

variable S can be a single measure of taste or more










generally a vector of taste measures for commodities. In

this study, one taste measure will be used for all meat

products based on the assumption that health concern is the

major factor of changing tastes, and it influences all meat

demands. However the following discussion may be

generalized to include other measures, such as advertising

and convenience.

The demand equations found by solving (4.1) have the

general form

q, = fi(p, x, E) (4.2)

The indirect utility function and cost function for problem

(4.2) can be written as

u = g(p, x, E) (4.3)

x = c(p, u, S) (4.4)

respectively. Equation (4.3) can be derived from (4.4)

using Roy's identity. The compensated demand equation is

the first derivative of the cost function (4.4) using

Shepard's lemma

ac
hi(p, u, E) = -- (4.5)

The direct approach of allowing taste variables to

appear in the utility (and cost) function generating a

viable demand system is used in this study. A theoretically

plausible demand system, the almost ideal demand system

(AIDS) of Deaton Muellbauer (1980), will serve as the basic

specification. The AIDS model was chosen because of the six










desirable properties mentioned by Deaton and Muellbauer

(1980). In addition, it allows for consistent aggregation

across consumers. The AIDS permits individual demand

function restrictions to hold for aggregate or market demand

functions (Green, 1985). Finally, the AIDS possesses

desirable properties with respect to how income and price

elasticity vary over time (Blanciforti and Green, 1983).

The AIDS satisfies two of the most important prerequisites

of incorporating taste effects into a demand system. First,

the starting function must be general enough to act as a

second-order (or first-order) approximation to any arbitrary

direct or indirect utility function, cost function, or

demand function. It would be ideal if it is a flexible

functional form and be consistent with axioms of choice.

The flexible functional cost form of the AIDS can satisfy

the theoretical properties of concavity, homogeneity,

continuity, positivity, etc. Second, the derived demand

functions must permit the testing of symmetry, homogeneity,

and adding-up. The methods of translating will allow the

incorporation of a latent taste variable into the demand

model and still satisfy all the requisite proprieties (Green

1985, Brown and Lee 1989).

The translating approach is a technique used in demand

analysis to include household composition and habit

formation, which assumes that taste change results in demand

change through income effect. It has the form










qi = ri + qi*(p, x*) (4.6)

where x* is equivalent to a supernumerary income and ri is a

function of the taste variable E. Translating "allows

necessary or subsistence parameters of a demand system to

depend on the demographic variables" (Pollak and Wales,

1981). Rossi (1988) simplified the budget share translating

in AIDS by allowing the aggregate expenditure shares to

depend on a household characteristics factor, which augments

the intercepts of ordinary demand curves, and in this study

is represented by a latent preference shifter S.

The AIDS approximates an arbitrary expenditure or cost

function. The cost function is sufficiently flexible so

that at any single point, all of its first and second

derivatives with respect to prices and utility can be set

equal to these of an arbitrary cost function. Deaton and

Muellbauer specified the AIDS cost function as


In c(u,p)=ao+Eaklnpk+l/2ZTrkiklnpklnpi+uo0pk +E (4.7)
k ki
The demand equations are generated from this cost function

using Shephard's lemma:

wi = a lnc/a Inpi (4.8)

This AIDS model with latent preference variable is called

(LAT/AIDS) through this dissertation:

wi = ai + E rijlnpj + Biln[x/p*] + 0iE +Ci (4.9)

where x is total expenditure on the group of goods being










analyzed, p. is the price of the jth good within the group,

p* is the price index for the group, wi is the share of

total expenditure allocated to the ith good (i.e. wi=

piq,/x), and the price index is approximated by the Stone

index:

In p* = E wk lnpk. (4.10)

The adding-up, homogeneity, and symmetry conditions

hold (4.11-13), respectively, if

E ai = 1, Z rij = 0, E Bi = 0 and E 0i = 0 (4.11)
1 i i i

Z rij = 0, and (4.12)


Tij = Tji (4.13)

because adding-up (4.11) holds, then if symmetry holds,

homogeneity follows. The symmetry condition implies that

the compensated cross price elasticities are equal;

homogeneity condition means that consumer purchases will

remain the same if good prices and income change by the same

percentages, in other words, there is no "money illusion".

A general definition of the uncompensated elasticities

of demand from the AIDS is

Eij = dlnq,/dlnpj
= -6ij + dlnwi/dlnpj

= -6ij + (rij 0i (dlnp*/dlnpj))/w,, (4.14)

where these elasticities refer to allocations within the

group holding constant total group expenditures (x) and all

other prices (Pk, kJj), 6ij is the Kronecker delta (6S. = 1










for i=j; 6i- = 0 for i j). The uncompensated price

elasticities using the Stone index for approximating a price

index are (Green and Alston, 1990)

Eij = -6ij + rij/wi -i/Wi {Wj + E wklnPk(Ekj + kj)} (4.15)
k
The price elasticities can be obtained by solving a

simultaneous equation system. A more widely used

approximation is to assume that expenditure shares are

constant, dlnp*/dlnpj=w then,

eij = -6ij + (ri -Piwj)/wi (4.16)
The expressions for the income and taste elasticities

for LAT/AIDS are given, respectively, by

i = 1 + B,/wi (4.17)

is= iS /w (4.18)

The expression (4.18) gives the taste effects on

changing demand. It represents the percentage change in the

quantity demanded of the ith commodity with respect to a

percentage change in the taste index. This is the primary

index that we are looking for in this study.

Several shortcomings related with the above latent

variable specification and AIDS model should be kept in mind

when we do the further estimation. In the context of a

random objective function, e.g. cost and indirect utility

functions, where the error terms are interpreted as

unobservable factors or measurement errors associated with

the indirect objective function, additive disturbances in

the share equations may be heteroskedastic. In the AIDS









55
model the existence of heteroskedacity could lead to biased

hypothesis testing (Chavas and Segerson, 1987). But when

the unobservable variables are directly incorporated into

the AIDS model, the effect would be similar to a weighted

least square estimates applying to a linear regression

model, the disturbance term will therefore less likely be

heteroskedastic. The LAT/AIDS model in equation (4.9)

assumes that the representative consumer receives

information about health concerns instantaneously. This

assumption can be relaxed by letting the latent taste

variable follow a diffusing path. In a simple "epidemic

model" new information is transferred to consumers either

via other consumers or via the mass media. The probability

of a representative consumer receiving the information may

be represented by draw from a binomial distribution (Putler,

1988). Another simple way to model the slow adjustment of

consumer taste change is to make the taste variable follow

an auto-regressive path. Although the AIDS model is a

flexible functional form, it can impose serious restrictions

on the behavior of own and income elasticities. The demand

for food becomes more inelastic with respect to price as

real income rises (Wohlgenant, 1984).

The Rotterdam model (Theil, 1965) is another demand

system which can be used as a framework for latent taste

analysis. It is a differential demand model and is not

based on a particular utility or cost function, but more










generally, on a first order approximation to the demand

function themselves. The total differential of the demand

equation qi=f(pI,p2,..Pn,x) is

aqi n aqi
dqi dx + E --- dp (4.19)
3x j=l apj

This can be transformed into a log form and have a additive

taste variable term. The right hand side of the Rotterdam

model is similar to the same as first difference form of the

AIDS right hand side. It is expressed as (LAT/Rotterdam)

w, Alnqi = i rijAlnpj + Piwk Alnqk + k iAlnE +e, (4.20)
j k
where expenditure and prices elasticities are

Ai= f,/wi (4.21)
i = Tj i/wi iwj (4.22)

Previous studies using Rotterdam model have shown that it is

a good demand model with negligible approximation errors.

It is linear in parameters and possesses unusually

informative parameters. Although it is not a flexible

functional form, its performance may not be inferior to the

much more complicated, non-linear flexible functional forms.


Multiple Indicator Model
The multiple indicator model is a special case of

general latent variable model outlined in Chapter 3:

n = Bn + rt + c (4.23)

Y = 17 (4.24)
x = Ax + 6 (4.25)










where only one variable is measured with error, and it is

measured by several indicators.

The two indicators of the latent taste variable are a

ratio of low fat milk consumption relative to whole milk

consumption ("MILK") and a cholesterol index ("CHOLE"). The

trends of the two indicators may represent how consumers are

altering consumption patterns because of health concerns.

The milk ratio is increasing because consumers buy more low

fat milk due to concerns about the link of food fat and

cholesterol intake to heart disease. Another indicator is

the cholesterol index which measures the development and

spread of health information linking fat intake and heart

disease. The cholesterol index is from Brown and Schrader

(1990), which is based on the number of citations of the

link between cholesterol and arterial disease in medical

journals. It represents the spread of information on

cholesterol information to consumers and used in this model

to indicate the speed of taste change adjustment.

For the case of LAT/AIDS model, assume, B = 0, A, = I,

E = 0; other variables are

y = [ w,1 w W3 ]'
S= [Inp, Inp np3 ln(x/p*) '

x = [lnpl Inp2 lnp3 ln(x/p*) MILK CHOLE ]'.

In order to make the notation uniform throughout this

dissertation, the general multiple indicator models in

equation (4.23)-(4.25) will be presented in the framework








58
and using same notation as LAT/AIDS (4.9) and LAT/Rotterdam

(4.20). The LAT/AIDS model is given below:

w, = T ,llnp1+T2lnp2+rT3lnp3+8l1n(x/p*)+ 41+CI (4.26)

2 = 7211np1+r22lnp2+ 231np3+221n(x/p*) +2E+C2 (4.27)

3 = T311np1+T32lnP2+T33lnp3+331n(x/p*) 3E+C3 (4.28)
MILK = Ax51 +61 (4.29)

CHOLE = A.,E +62 (4.30)

where var(C)=Y, var(6)=8,.

The nature of share equations (adding-up) makes the

LAT/AIDS model residual covariance matrix singular, so one

of the equation is dropped arbitrarily. Since the system is

estimated by ML, results are invariant to the equation

dropped. This equation is then estimated with one of the

first two equations again. The intercepts are eliminated by

subtracting the means from each variable. In this case, the

difference of original latent variable with its mean, (E-

E), enters into the latent variable equation and

measurement equations. To make the model identifiable, some

constraints are introduced to provide a scale for the latent

variable. The latent preference variable, in this case,

would have the same scale as the first indicator, low fat

milk ratio. This translates to, Ax5s being equal to one.

The implied covariance matrix for this structural

equation model is

S(rr', + 7) rA' 1
(0) = I I (4.31)
I Ax-r' AI, A' + e9 J








59
The variables of LAT/Rotterdam model specification are

expressed as

y = [ wAlnq, w2Alnq2 w3Alnq3 '
S= [Alnp, Alnp2 Alnp3 wkAlnq Ins ]'

x = [Alnp, Alnp2 Alnp3 EWkAlnqk MILK CHOLE ]',

using the same variable definitions as in the expressions

presented above for the LAT/AIDS multiple indicator model.

The LAT/Rotterdam equations are given below:

wAlnql = ,Alnp+2Aln2+3Al+T 2Alp2+T np3+,AWkAlnqk+AlnE+C1
(4.32)
w2Alnq2 = r21Alnp,+r22Alnp2+ 23AlnP3+P2AZWkAlnqk+02AlnE+C2
(4.33)
w3Alnq3 = 73,Alnp,+T32Alnp2+33Alnp3+3AkwkAlnqk+03Aln+
(4.34)
AMILK = A51 AlnE +61 (4.35)

ACHOLE = A)6Aln6 +62 (4.36)

where var(C)=T, var(C)=9, and Ax51=l.



Multiple Indicator Multiple Cause Model

The MIMIC model (3.23-3.24) is based on the argument

that not only do the latent variables have indicators, they

also have a causal relationship expressing them as a

function of some cause variables. In this model, another

factor affecting consumer taste change is augmented into the

model. Taste change is assumed to be affected by both

health concerns and demand for convenience goods. It is

argued by some researchers that a higher proportion of

working women in the population has increased household











demand for easy-to-cook meat such as chicken. The latent

taste variable in the demand system, which is not

measurable, has two indicators; they are the ratio of low

fat milk ("MILK") and per capital consumption of eggs

("EGG"). The trends of the two indicators represent the

results of consumer taste change because of health concerns.

The milk ratio is increasing because consumers buy more low

fat milk; while egg consumption is decreasing because of

health concerns and the demand for convenience at the

breakfast meal (Putler 1989, Shonkwiler and Ford 1989, Brown

and Schrader 1990). In this model, the inverse of egg

consumption is used to make it an increasing series

compatible with the milk ratio indicator. The latent

preference variable is influenced by two cause variables:

the cholesterol information index ("CHOLE") and the

percentage of married working women ("WOM"). The

cholesterol index serves as a cause variable in this set-up

based on our belief that the link of cholesterol intake and

heart disease is arousing consumer concerns and therefore

changing consumer tastes. The working women percentage

represents changes in the family structure and shows the

demand for convenience food.

The latent variable almost ideal demand system

(LAT/AIDS) of equation (4.9) can be expressed within the

framework of the MIMIC structural equation model (3.23)-

(3.24) with the following specifications (when the third










share equation is dropped):

= [E w1 w ]'

y = [MILK 1/EGG w, w2]'

x = [CHOLE WOM Inp, Inp2 Inp3 ln(x/p*)]'

then for the latent equation part

S, = r,1CHOLE + r,2WOM + C, (4.37)

w2 = B21E + r21npl + r41np2 +r251np3 + r261n(x/p*) + C
(4.38)

w3 = B31, + r331np, + r34ln2 +r351nP3 + r3ln(x/p*) + C
(4.39)

for the measurement equation part

y,= E + 61 (4.40)

y2 = A21Y + 62 (4.41)

Y3 = w1 (4.42)

4 = W2 (4.43)
where var(C)=Y, var(e)=0.

It is very difficult to set up the MIMIC model in the

same notation as the multiple indicator model. In order to

make the notation as close to uniform as possible and easy

to compare, the estimates presented in chapter 5 (table 13)

continue using the notation of LAT/AIDS multiple indicator

model when any pair of parameters have same meaning, for

these parameters unique to MIMIC model the notation still

follows these of (4.39)-(4.43).

The scale constraint makes A11 equal to one. Only the

first variable in n is a latent preference variable which is

measured with error.












Dynamic Multiple Indicator Multiple Cause Model

The Dynamic Multiple Indicator Multiple Cause (DYMIMIC)

model is an extension of the MIMIC model that permits the

latent variable to follow an auto-regressive path. The

possibility that the taste variable is affected by its lag

has intuitive appeal since taste formation is a gradual and

smooth process, which may depend on the its level of

previous period. The state space form is

Yt = B St + Xtr + et (3.27)

St = 0 -1 t_ + Ft6 + t (3.28)
For the LAT/AIDS model

Yt = [Wt w2t w3t milk 1/eggt';
Xt = [Inplt Inp2t Inp3t ln(x/p*)t];

Ft = [CHOLEt WOM ];


and


t = 0 Et-1 + 61CHOLEt + 62WOMt + Alt (4.44)
wt = BEt + r111npit + r21lnp2t +r3lnp3t + r4ln(x/p*)t + el
(4.45)

W2t = B2t + r12lnPt + r22lnP2t +r321nP3t + r42ln(x/P*)t + e2t
(4.46)

3t = B3t + r13lnpt + 231nP2t +331nP3t + r431n(x/p*)t + e3t
(4.47)

MILKIt = B4Et + e4t (4.48)

(1/EGG)2t = B5ET + e5t (4.49)

where var(A))=v, var(e)=Y.

The variable "MILK" and "WOM" etc. in the above

specification are the same as the those of the MIMIC model.















CHAPTER 5
ESTIMATION AND RESULTS


Multiple Indicator Model

The LAT/AIDS and LAT/Rotterdam models are estimated

using the models defined in chapter 4. The results of these

estimations indicate that the latent preference variable has

been significant in both models. The latent preference

variable has a negative effect on the demand of beef, a

positive effect on the demand of poultry, a positive but

insignificant effect on the demand of pork. The latent AIDS

and Rotterdam model yield better statistical performance

than the conventional AIDS and Rotterdam model. The

theoretical assumptions of utility maximization, such as

symmetry, homogeneity and negativity, are satisfied in the

latent models.

The data used in this study are mainly from various

issues of "Food Consumption, Prices, and Expenditure"(USDA).

Aggregate per capital U.S. consumption of beef, pork and

poultry data, along with the average whole country nominal

retail prices are used. The utilization of aggregate price

and quantity data will render testing of demand properties

difficult, as was discussed in the Chapter 2.










Latent AIDS Model

The LAT/AIDS model used in this research is expressed

like

wi = a + E ilnpj + Biln[x/p*] + 0iE +j, (5.1)

x = A E + 6 (5.2)

where the ratio of low fat milk with respect to plain whole

milk, and a cholesterol index citing the number of

publications linking cholesterol intake with heart problems

(Brown and Schrader, 1990) serve as the indicators of latent

taste variable.

The nature of the share equation system makes the

LAT/AIDS model residual covariance matrix singular, so one

of the equations is dropped arbitrarily for estimation. The

intercepts are eliminated by subtracting means of all

observable variables. In this case, the difference of the

original latent variable from its mean, E-E, enters into the

latent variable equation and measurement equations. To make

the model identifiable, some constraints are imposed on the

model. The latent variable has the same scale as the first

indicator, low fat milk ratio. In this case, Ax, equals

one. The residual covariance matrices of both latent

variable and measurement equations, e8 and ', are diagonal.

There is no good statistic to test the goodness of fit

of this structural equation model. One test statistic

proposed by Bollen (1989) which uses a likelihood ratio test

is plagued by its strict assumption about the observable










variable distribution and sample size. An ad hoc goodness

of fit index (GFI) is used in this study to calibrate the

match of S to t The exact distribution of this index is

unknown, but it at least provides us with an overall model

fitness measurement.

GFI= 1 tr[(Zl )2] (5.3)
trC ('sS)2]

The GFI measures the relative amount of the variance and

covariances in S that are predicted by Z. It reaches its

maximum of one when S = t. The GFI of LAT/AIDS model is

0.75, which indicates a fairly good overall fit of the

model.

Table 1 reports the estimates of LAT/AIDS model without

any theoretical constraints except for adding-up which is

automatically satisfied. The estimates of P classify beef

as luxury, pork and poultry as necessity. All but one of

the r coefficients are significantly differently from zero,

having t values absolutely greater than 2. An increase of

poultry price, holding other things constant, has a positive

effect on the expenditure share of poultry. This effect is

not significantly different from zero. The latent variable,

its deviation from mean in this case, has a significant

negative impact on beef consumption and positive impact on

poultry consumption, while its impact on pork consumption is

neutral.










Table 2 gives the latent variable (its deviation from

mean) estimate from equation (5.1). This is a taste index

representing adjustment of consumer taste. The t values

show that the latent variable has been significant through

the data range. The latent taste variable is a monotonic

increasing series which has a breaking point from negative

to positive in early 70's. The monotonic increasing index

of consumer taste should only serve as an indicator showing

the velocity of the change of taste. Whether this index is

increasing or decreasing does not suggest whether the

consumer tastes are "increasing" or "decreasing". We must

keep in mind that the latent taste variable was made to have

the same scale as one of its indicators. So the meaning of

the estimated "increasing" taste variable can only be

determined by comparing signs with its indicator. The taste

index series is a weighted combination of the four

indicators' which all have mean zero. The increasing taste

index shows the part of increasing low fat milk ratio caused

by taste change. Although the taste index changes sign from

negative to positive around 1973, the locus of change

clearly indicates a slow adjustment over the entire sample

period. The last three columns are products of the

estimated latent variable with its coefficients, #(ES-).

These estimates show the total effects of preference change



1. The two indicators in LAT/AIDS equations (5.1) are
residuals of regular AIDS share equation.









67

on the expenditure shares of the three meats. The remainder

effect that is not explained by price and income changes in

the demand models, and solely attributed to taste change.

The signs of coefficients 0 show whether taste change has

positive or negative effects on expenditure shares. The

relative indices of the three latent effects clearly show

that the preference change over the past three decades has

been in favor of poultry and disfavor of beef (Figure 3).

The elasticities with respect to latent preference (Table 3)

show that preference change has a positive effect on poultry

consumption, and this elasticity is growing. Preference

change leads to a decline in beef consumption, and the

reaction becomes more elastic. This is probably because

that as the knowledge about cholesterol spreads, more people

are aware of the link between their food intake and health,

and more people are becoming responsive to health concerns.

The expenditure and price elasticities for average data

are presented in Table 4. Both the correct elasticity form

presented by Green and Alston (1990) and its approximation

assuming constant share expenditure are calculated. The

signs of the elasticities are the same for both estimates

and the numerical estimates are close. This implies that the

shares do remain relatively the same throughout the sample

period, and price changes have little effect on the shares

of expenditures; the changes of expenditure shares depend

primarily on non-price factors, such as preference changes.









68
The expenditure elasticities indicate strongly that beef is

a luxury commodity and pork and poultry are necessity. Pork

and poultry are substitute commodities. The pattern over

time shows that consumers have become more and more

responsive to changes in the price of pork.

The homogeneity and symmetry restrictions are tested,

for the two equation latent variable model, the overall

homogeneity restrictions are not rejected by the likelihood

ratio test (test value is 4.17, x2(2) is 5.99 at 0.05

significant level). The combined homogeneity and symmetry

restrictions are rejected (test value is 16.04, x2(3) is

7.81 at 0.05 level). Taking each of the commodities

separately for the homogeneity test, beef and pork fail to

reject the null hypothesis, while poultry rejects the

restriction. Poultry demand increases when the prices of

poultry, beef and pork increase at the same rate as the

total expenditure, this "money illusion" can be attributed

partially to consumer preference change. The restricted

LAT/AIDS coefficients are presented in table 5.

An iterative procedure can be used to estimate the

latent taste variable. The GLS estimates of taste variable

from equation (3.26) can be used to calculate initial

coefficients estimates for the Maximum Likelihood estimator.

This iteration continues until the latent taste variable

converges. The procedure converges for the above model in

the second iteration, and there is very little gain in doing










the iteration and therefore is not recommended for other

studies.

Latent Rotterdam Model

The Rotterdam model is similar to the first difference

form of the AIDS model. The difference in the dependent

variable is, instead of using Awi, wiAlnqi. Among the

independent variables (wiAlnqi) replaces (Aln[x/p*]).

wiAlnqi = Z. ij Alnpj + BiSwkAlnqk + Oi AlnS + e, (5.4)
3 k
x, = Ax 2 + 6, (5.5)

The coefficients of three equation latent Rotterdam

model are presented in table 6. The overall Goodness of Fit

Index (GFI) for the LAT/Rotterdam model is 0.67. The latent

preference variable is not significantly different from zero

in the three latent equations. This can be attributed to

the fact that after taking first difference form the

variation of the data is decreased dramatically. The

aggregate data used in this study are per capital consumption

and retail prices, they have little variation over the

years. After taking the Logarithm and first difference

form, there is still much less variation left. The

coefficients show the effects of the latent variable on the

dependent variables. The estimated price and expenditure

elasticities are presented in table 7. Pork is ranked as a

luxury commodity in addition to beef. The own price

elasticities are negative, and only beef is price elastic.

The own price elasticity estimation is close to that of the










level data LAT/AIDS estimation. The cross price

elasticities of pork with respect to poultry become negative

in contrast to level data model. The estimated latent

variable increments over the years are presented in table 8.

The changing latent effects show a decreasing beef demand,

and increasing pork and poultry demands.

The model fails to reject the overall homogeneity

restriction. Separate tests indicate that if all prices and

expenditure increases at the same rate, beef demand would

not remain the same; the homogeneity restriction for pork

and poultry applies. The test for combined homogeneity and

symmetry are rejected at the one percent significance level.

The parameter estimates under homogeneity and symmetry

restrictions are in table 9.

The first difference data AIDS model is also estimated

for comparison, the results are in table 10. The parameter

estimates are not very close to the level data results,

indicating a certain degree of model misspecification. The

latent variable is not significant in the three latent

equations, and the results of theoretic restrictions are not

so evidently consistent with the data. The price and

expenditure elasticities are very close to the Rotterdam

results both in signs and values. Especially the own price

elasticities are almost identical from both estimates. The

fact that very close estimates from both first difference

AIDS and Rotterdam indicates that the former as a flexible









71
functional form gives a good approximation for local utility

maximization. The difference between estimates from level

and difference AIDS form may show possible existence of

serial autocorrelation in level model.














Table 1. The LAT/AIDS Coefficient Estimates (three
equations)


Parameters


Coefficients


Standard Errors


Beef


Pork
T21
T22
T23
02
02
r22

Poultry
T31
732
33
P3
03
%33


Indicator Equation

891
82
12
"x2


0.0571
0.0430
-0.0802
0.2187
-0.0125
0.0066


-0.0355
-0.0353
0.0599
-0.1605
0.0055
0.0052


-0.0329
-0.0081
0.0137
-0.0631
0.0096
0.0024


2.7196
0.6116
0.2413
0.1433
0.3642


0.0124
0.0154
0.0153
0.0329
0.0016
0.0014


0.0099
0.0126
0.0124
0.0264
0.0012
0.0006


0.0099
0.0126
0.0124
0.0264
0.0012
0.0006


0.3280
0.0988
0.0392
0.0467
0.0035














Table 2. Latent Taste Index and The Latent Effects 1950-1987


Year Latent (df) t-value


1950
1951
1952
1953
1954
1955
1956
1957
1958
1959
1960
1961
1962
1963
1964
1965
1966
1967
1968
1969
1970
1971
1972
1973
1974
1975
1976
1977
1978
1979
1980
1981
1982
1983
1984
1985
1986
1987


-2.21674
-2.20548
-2.23767
-2.26602
-2.35647
-2.36819
-2.38446
-2.40489
-2.37804
-2.35694
-2.35666
-2.29845
-2.26666
-2.23729
-2.14364
-2.07982
-2.01281
-1.79195
-1.49630
-1.19689
-0.95950
-0.72038
-0.40989
0.01742
0.33875
0.76292
1.18119
1.65297
1.98365
2.38551
2.85627
3.29228
3.60287
4.02660
4.55500
5.26382
6.21796
7.00791


Beef


-3.32734
-3.31044
-3.35876
-3.40131
-3.53707
-3.55467
-3.57909
-3.60975
-3.56945
-3.53778
-3.53736
-3.44999
-3.40226
-3.35819
-3.21761
-3.12183
-3.02124
-2.68972
-2.24596
-1.79654
-1.44022
-1.08129
-0.61525
0.02614
0.50847
1.14515
1.77297
2.48112
2.97748
3.58066
4.28728
4.94174
5.40793
6.04395
6.83708
7.90103
9.33320
10.51892


Pork


0.02780
0.02766
0.02806
0.02842
0.02955
0.02970
0.02990
0.03016
0.02982
0.02956
0.02955
0.02882
0.02843
0.02806
0.02688
0.02608
0.02524
0.02247
0.01876
0.01501
0.01203
0.00903
0.00514
-0.00022
-0.00425
-0.00957
-0.01481
-0.02073
-0.02488
-0.02992
-0.03582
-0.04129
-0.04518
-0.05050
-0.05712
-0.06601
-0.07798
-0.08789


-0.01227
-0.01221
-0.01239
-0.01255
-0.01305
-0.01311
-0.01320
-0.01331
-0.01317
-0.01305
-0.01305
-0.01273
-0.01255
-0.01239
-0.01187
-0.01152
-0.01114
-0.00992
-0.00828
-0.00663
-0.00531
-0.00399
-0.00227
0.00010
0.00188
0.00422
0.00654
0.00915
0.01098
0.01321
0.01581
0.01823
0.01995
0.02229
0.02522
0.02914
0.03443
0.03880


Poultry

-0.02125
-0.02114
-0.02145
-0.02172
-0.02259
-0.02270
-0.02285
-0.02305
-0.02279
-0.02259
-0.02259
-0.02203
-0.02172
-0.02144
-0.02055
-0.01993
-0.01929
-0.01717
-0.01434
-0.01147
-0.00920
-0.00690
-0.00393
0.00017
0.00325
0.00731
0.01132
0.01584
0.01901
0.02286
0.02738
0.03155
0.03453
0.03859
0.04366
0.05045
0.05960
0.06717












Table 3. Latent Elasticity


Beef


Years

1950
1951
1952
1953
1954
1955
1956
1957
1958
1959
1960
1961
1962
1963
1964
1965
1966
1967
1968
1969
1970
1971
1972
1973
1974
1975
1976
1977
1978
1979
1980
1981
1982
1983
1984
1985
1986
1987


Pork


0.05289
0.05262
0.05339
0.05407
0.05622
0.05650
0.05689
0.05738
0.05674
0.05623
0.05623
0.05484
0.05408
0.05338
0.05115
0.04962
0.04802
0.04275
0.03570
0.02856
0.02289
0.01719
0.00978
-0.00042
-0.00808
-0.01820
-0.02818
-0.03944
-0.04733
-0.05692
-0.06815
-0.07855
-0.08596
-0.09607
-0.10868
-0.12559
-0.14836
-0.16720


-0.03885
-0.03865
-0.03922
-0.03971
-0.04130
-0.04150
-0.04179
-0.04215
-0.04168
-0.04131
-0.04130
-0.04028
-0.03972
-0.03921
-0.03757
-0.03645
-0.03528
-0.03141
-0.02622
-0.02098
-0.01682
-0.01263
-0.00718
0.00031
0.00594
0.01337
0.02070
0.02897
0.03477
0.04181
0.05006
0.05770
0.06314
0.07057
0.07983
0.09225
0.10897
0.12282


Poultry

-0.13407
-0.13338
-0.13533
-0.13705
-0.14252
-0.14323
-0.14421
-0.14544
-0.14382
-0.14254
-0.14253
-0.13901
-0.13708
-0.13531
-0.12964
-0.12579
-0.12173
-0.10837
-0.09049
-0.07239
-0.05803
-0.04357
-0.02479
0.00105
0.02049
0.04614
0.07144
0.09997
0.11997
0.14427
0.17274
0.19911
0.21790
0.24352
0.27548
0.31835
0.37605
0.42383















Table 4. LAT/AIDS Price and Expenditure Elasticities


Price Elasticity (Ray & Alston)
--------------------------------------------------------
Beef Pork Poultry

Beef -1.0967 -0.0462 -0.1983
Pork 0.1385 -0.9554 0.2455
Poultry -0.0114 0.0711 -0.8700

Price Elasticity (constant share assumed)
--------------------------------------------------------
Beef Pork Poultry

Beef -1.1101 -0.0497 -0.2185
Pork 0.1548 -0.9511 0.2702
Poultry 0.0014 0.0744 -0.8506

----------------------------------------------------
Expenditure Elasticity

Beef 1.4161
Pork 0.4919
Poultry 0.6019













Table 5. LAT/AIDS Model With Homogeneity Restriction


Parameters Coefficients Standard Errors
---Beef----------
Beef


Pork
T21
7

r2
Indicator Equations
Indicator Equations


0.0472
0.0436
0.2182
-0.0954
0.0078

-0.0281
-0.0345
-0.1556
0.0343
0.0071

0.2787
0.0300
0.0587
3.6517


0.0122
0.0161
0.0333
0.0074
0.0009

0.0111
0.0146
0.0302
0.0067
0.0008

0.0320
0.0117
0.0067
0.0341


LAT/AIDS Model With Homogeneity and Symmetry Restriction


Parameters Coefficients Standard Errors

Beef


911

*1


Pork


Y2
02

Indicator Equations


82
x2


0.0636
0.0025
0.2744
-0.0941
0.0085

-0.0538
-0.1582
0.0195
0.0076

0.2787
0.0055
0.0554
3.6530


0.0119
0.0107
0.0321
0.0081
0.0011

0.0143
0.0326
0.0156
0.0010

0.0320
0.0007
0.0113
0.0345














Table 6. LAT/Rotterdam Model Estimate


Parameters


Coefficients


Standard Errors


Beef


Pork


Poultry


Indicator Equations
01


x2
Ax2


-0.2359
0.1505
0.0493
0.6185
-0.0851
0.0079


0.1926
-0.1798
0.0257
0.3584
0.0606
0.0075


0.0433
0.0305
-0.0765
0.0268
0.0350
0.0033


0.0240
0.0092
0.0321
3.7450


0.0204
0.0194
0.0222
0.0646
0.0557
0.0009


0.0193
0.0184
0.0210
0.0611
0.0526
0.0009


0.0085
0.0082
0.0094
0.0271
0.0221
0.0004


0.0031
0.0011
0.0037
0.2325
















Table 7. LAT/Rotterdam Price & Expenditure Elasticity


Expenditure Elasticity
---------------------------------------------------------
Beef 1.1767
Pork 1.1345
Poultry 0.1691

Price Elasticity
---------------------------------------------------------
Beef Pork Poultry

Beef -1.0673 -0.0855 -0.0926
Pork 0.0135 -0.9274 -0.0984
Poultry 0.1846 0.1391 -0.5098












LAT/Rotterdam Latent Variable


Years Latent Var. t-value


1950
1951
1952
1953
1954
1955
1956
1957
1958
1959
1960
1961
1962
1963
1964
1965
1966
1967
1968
1969
1970
1971
1972
1973
1974
1975
1976
1977
1978
1979
1980
1981
1982
1983
1984
1985
1986


-0.00030
-0.00084
-0.00062
-0.00251
0.00006
-0.00067
-0.00090
0.00035
0.00068
0.00020
0.00131
0.00081
0.00070
0.00234
0.00150
0.00378
0.02960
0.03978
0.03136
0.02878
0.02629
0.02942
0.03892
0.03918
0.04587
0.04007
0.03948
0.02899
0.03580
0.03301
0.03728
0.03760
0.04585
0.05558
0.06980
0.08406
0.07771


Beef


-0.16309
-0.46014
-0.33915
-1.37129
0.03511
-0.36653
-0.49300
0.19270
0.37328
0.10795
0.71906
0.44360
0.38538
1.27969
0.82020
2.06841
16.20079
21.77008
17.16421
15.75259
14.38736
16.10098
21.29788
21.44239
25.10261
21.92863
21.60608
15.86276
19.59277
18.06276
20.40376
20.57712
25.09254
30.41566
38.19692
46.00508
42.53025


Latent Curve
Pork


0.00003
0.00007
0.00005
0.00021
-0.00001
0.00006
0.00008
-0.00003
-0.00006
-0.00002
-0.00011
-0.00007
-0.00006
-0.00020
-0.00013
-0.00032
-0.00252
-0.00339
-0.00267
-0.00245
-0.00224
-0.00250
-0.00331
-0.00334
-0.00390
-0.00341
-0.00336
-0.00247
-0.00305
-0.00281
-0.00317
-0.00320
-0.00390
-0.00473
-0.00594
-0.00716
-0.00662


-0.00002
-0.00005
-0.00004
-0.00015
0.00000
-0.00004
-0.00005
0.00002
0.00004
0.00001
0.00008
0.00005
0.00004
0.00014
0.00009
0.00023
0.00179
0.00241
0.00190
0.00174
0.00159
0.00178
0.00236
0.00238
0.00278
0.00243
0.00239
0.00176
0.00217
0.00200
0.00226
0.00228
0.00278
0.00337
0.00423
0.00510
0.00471


Poultry


-0.00001
-0.00003
-0.00002
-0.00009
0.00000
-0.00002
-0.00003
0.00001
0.00002
0.00001
0.00005
0.00003
0.00002
0.00008
0.00005
0.00013
0.00104
0.00139
0.00110
0.00101
0.00092
0.00103
0.00136
0.00137
0.00161
0.00140
0.00138
0.00102
0.00125
0.00116
0.00131
0.00132
0.00161
0.00195
0.00245
0.00295
0.00272


Table 8.












LAT/Rotterdam Model With Homogeneity


Parameters Coefficients Standard Errors
Beef
Beef


Pork
721
I22
#2


Indicator Equations

4
e2
Ax2


-0.2059
0.1670
0.7172
-0.1369
0.0102

0.1858
-0.1882
0.3495
0.0594
0.0071

0.0240
0.0092
0.0041
3.7450


0.0210
0.0212
0.0613
0.0706
0.0012

0.0146
0.0148
0.0426
0.0488
0.0008

0.0031
0.0011
0.0009
0.2325


Rotterdam Model With Homogeneity and Symmetry Restricted
---------------------------------------------------------

Parameters Coefficients Standard Errors
Beef
Beef


Pork

Y2
02
Indicator Equations

e1
92


-0.2083
0.1777
0.7224
-0.1352
0.0101

-0.1130
0.6038
-0.0247
0.0106

0.0240
0.0094
0.0041
3.7450


0.0209
0.0171
0.0606
0.0702
0.0012

0.0222
0.0717
0.0727
0.0012

0.0032
0.0011
0.0019
0.2368


Table 9.












Table 10. LAT/AIDS (First Difference Form)


Parameters


Coefficients


Standard Errors


Beef




01
T12
T1

Sy


Pork


Poultry
T31
T32
T33
P3

T33
Indicator Equations

9,
e2
x12
"x2


-0.0035
-0.0258
-0.0291
0.0285
-0.1358
0.0076


0.0375
0.0449
-0.0342
0.0880
0.1114
0.0034


-0.0336
-0.0156
0.0594
-0.1062
0.0393
0.0016


0.0638
0.2490
0.0869
0.0201
0.3645


0.0225
0.0216
0.0237
0.0775
0.0904
0.0014


0.0206
0.0196
0.0215
0.0705
0.0747
0.0004


0.0094
0.0091
0.0099
0.0328
0.0503
0.0036


0.0434
0.0288
0.0100
0.0048
0.0891











Table 11. LAT/AIDS (First Difference Form) Elasticities


Price Elasticities

Beef Pork Poultry

Beef -1.0339 -0.0654 -0.0614
Pork -0.0214 -0.9418 -0.1394
Poultry 0.1247 0.1032 -0.5504

Price Elasticity (approximation)

Beef Pork Poultry

Beef -1.0352 -0.0662 -0.0639
Pork -0.0277 -0.9459 -0.1524
Poultry 0.1399 0.1130 -0.5191

Expenditure Elasticity


Beef 1.0543
Pork 1.2786
Poultry 0.3299











Table 12. LAT/AIDS (First Difference Form) Latent Elasticity


Beef


Years

1950
1951
1952
1953
1954
1955
1956
1957
1958
1959
1960
1961
1962
1963
1964
1965
1966
1967
1968
1969
1970
1971
1972
1973
1974
1975
1976
1977
1978
1979
1980
1981
1982
1983
1984
1985
1986


Pork


-0.01414
0.02522
0.00639
0.01592
0.00312
0.01158
0.00898
0.00505
-0.00066
0.00280
-0.00371
-0.00096
0.00236
-0.00510
-0.00099
-0.00476
-0.02638
-0.02378
-0.02560
-0.02836
-0.02022
-0.01951
-0.05276
-0.02823
-0.03618
-0.05289
-0.05960
-0.02676
-0.04459
-0.05443
-0.05184
-0.03320
-0.05685
-0.06013
-0.09278
-0.09887
-0.10279


0.01930
-0.03442
-0.00871
-0.02173
-0.00426
-0.01581
-0.01225
-0.00690
0.00090
-0.00382
0.00507
0.00131
-0.00322
0.00696
0.00135
0.00650
0.03600
0.03246
0.03494
0.03870
0.02759
0.02662
0.07201
0.03853
0.04938
0.07218
0.08134
0.03653
0.06085
0.07428
0.07075
0.04531
0.07759
0.08207
0.12663
0.13495
0.14029


Average Latent Elasticity


0.00461 0.00609


Poultry

0.01358
-0.02422
-0.00613
-0.01529
-0.00299
-0.01112
-0.00862
-0.00485
0.00064
-0.00269
0.00356
0.00092
-0.00226
0.00490
0.00095
0.00457
0.02533
0.02284
0.02458
0.02723
0.01941
0.01873
0.05067
0.02711
0.03474
0.05079
0.05723
0.02570
0.04282
0.05227
0.04978
0.03188
0.05460
0.05775
0.08910
0.09495
0.09871


-0.00413












MIMIC Model

The GFI of LAT/AIDS model is 0.65, which indicates a

fairly good overall fit for the model. The coefficients of

determination (R2i) for the three LA\AIDS model are very

high, indicating a good fit for individual equations (Table

13). The coefficient of determination for the y measurement

model provides a summary of the joint fit of the y

variables, defined as 1-1je81/IE .

The equations for MIMIC model in chapter 4 can be

expressed in a compact form as:

w, = a, + E r,jlnpj + Biln[x/p*] + 5iE + ei (5.6)

xi = Ax E + e, (5.7)

St = rkwk +Ci (5.8)
k

Coefficient estimates of LAT/AIDS model are given in

table 13. The parameters of LAT/AIDS model in the latent

variable model (4.38)-(4.39) are replaced by the notation

used in equation (5.6), the rest of the notation follows

equation (4.37) and (4.40)-(4.43). The estimated

coefficients Oi indicate that the latent preference variable

has been significant in beef and poultry demand equations.

The latent preference variable has a negative effect on the

demand for beef, a positive effect on the demand for

poultry, a positive but insignificant effect on the demand

for pork. The latent AIDS model gives better statistical










performance than the conventional AIDS model. The

estimates of pi classifies beef as a luxury, and both pork

and poultry as necessities. That means when income

increases, the expenditure shares of pork and poultry would

decrease while that of beef increases. All but two r,.

coefficients are significantly differently from zero, having

t values absolutely greater than 2. A~2 is 1.13x10-3 which

suggests that decreasing egg consumption (increasing its

inverse) has a positive effect on the latent preference

variable. r,1 and r12 show the effects of the two cause

variables on the latent preference variable. Both of the

coefficients are positive and significant, indicating a

strong relationship exists between the latent taste variable

and two cause variables.

The expenditure and price elasticities for average data

are presented in Table 14. Both the correct price

elasticities using the linear AIDS model presented by Green

and Alston (1990), and its approximation assuming constant

share expenditure, are calculated. The signs of the

elasticities are the same for both estimates and the

numerical values are very close, indicating that the

approximation is useful. On the other hand it implies that

price changes have little effect on shares of expenditure

and that the changes of expenditure shares depends primarily

on non-price factors, such as preference changes. The

expenditure elasticities indicate strongly that beef is a








86
luxury commodity while pork and poultry are necessities. If

pork and poultry prices increase, the quantity of beef

consumption would decrease. On the other hand, an increase

of beef price would elicit substitutive increases in

consumption of pork and poultry. Pork and poultry are

substitute commodities. The pattern over time (estimated

price and expenditure elasticities 1965-1985) shows that

consumers become more responsive to changes in the price of

pork, but less responsive to price changes in beef and

poultry.

The latent variable (with mean zero) is estimated using

the general estimator (3.25)-(3.26). In the MIMIC model,

the cause equation also should be taken into consideration.

The equation (5.7) can be written as x = AxE + e, where Ax

= [1 A,1]', e ~ N(0, 9). The equation (5.8) can be
rewritten as E = wr + CI, where w=[CHOLE WOM]', CI ~ N(0,

Y). Then

t = w t + (x '+e) (X Axwtr) (5.10)
Var( t,) = Ax'(AxAx' + 6) Ax 9 (5.11)

The t values show that the latent variable has been

significant throughout the data range. The latent variable

(deviation from mean) is a increasing series which has a

breaking point from negative to positive in mid 70's. Again

there is no indication that there is an abrupt change of

tastes. The locus of preference change clearly indicates

slow adjustment over the entire sample period. The products









87

of the estimated latent variable with its coefficients, #(E-

S), trace out the total latent effects of preference change

on the expenditure shares of all three meats. The relative

indices of the three latent effects clearly show that

preference changes over the past three decades have been in

favor of poultry and against beef (Figure 3). The

elasticities with respect to latent preferences (Table 15)

show that preference change has a positive and increasing

effect on poultry consumption. Preference change has led to

a decline in beef consumption. Moreover, the elasticities

in table 14 suggest that this decline has become more rapid

in the latest few years. The inclusion of the convenience

demand variable slightly increased consumer taste change

speed (Table 16).

Good indicator and cause variables are important to

structural equation models. But latent structural model

rely much less heavily on these variables than regression

analysis using a taste instrument variable as an exogenous

variable. The estimated taste variable is an optimal

combination of the indicator and cause variables given the

data and structural specifications. Furthermore, the fact

that the parameters 8e11, 8(22 and 711 are significantly

different than zero confirms that the indicator and cause

variables are measured with error and should not be used

individually or together without accounting for this source

of measurement error.










Estimates of latent taste index is used to calculate

the effects of taste on meat demand. It is found that taste

change had decreased per capital beef consumption by 24

percent, had increased pork and poultry consumption by 7 and

65 percent, respectively over the entire data range 1950-

1987 (Table 17). Most of the preference change took effects

after 1970's. From 1970-1987, preference change has

decreased beef demand by 17 percent, increased pork and

poultry demand by 5 and 47 percent. That means about 90

percent of preference change happened after 1970. During

the 80's, preference change continue to occur, and at an

accelerating speed. If the trend in preferences continues

at the present rate, ceteris paribus, the per capital

consumption of beef will continue declining, falling by 19

percent over the next ten years; the consumption of pork

will increase by 6 percent, while the consumption of poultry

will increase by 53 percent over the next 10 years. This

prediction is possibly biased upward since we used taste

change trend of the past 38 years to make the predictions.

It is unlikely that the industry will continue ignoring

changing market conditions in the next decade and make

mistakes as pointed out by Purcell (1989), especially after

so much exposure of the issues in the recent years.

The estimated value of the latent preference variable

can be used to show the effects of the latent preference

variable on price and expenditure elasticities by assuming








89

price and expenditure coefficients vary with the preference

variable. The AIDS model is re-estimated by including

interaction terms (Inp,~) and (ln(x/p*)g in each equation.

This comes by assuming the parameters in LAT/AIDS model are

a function of the latent preference variable:

w, = ai + E rljlnpj + Biln[x/p*] + + (4.9)


Tii=T iO+Ti~ (5.12)

B,=Bi, +Bt (5.13)

Notice the change in the poultry and beef equations (Table

18). The positive interactions of poultry price and the

taste variable, and the negative interaction of expenditure

with the taste variable indicate a damping effect on the

absolute price and expenditure elasticities of poultry.

Consumers are less responsive to price and expenditure

changes when taste change is jointly considered in their

demand model. Increasing the price of poultry decreases

poultry consumption less than would be the case without the

taste change. Increasing the price of beef decreases beef

consumption more than would be the case without the taste

change.













Table 13. MIMIC Model Results


Parameter2


Coefficient


Standart Error


Beef


Pork


Poultry


Indicator Equation
Ay21

(822
9012


Cause Equation

r12



R2
R2;
3
GFI


0.05384
0.04860
-0.07635
0.23463
-0.01306
0.00748


-0.02524
-0.03400
0.06832
-0.15181
0.00231
0.00701


-0.02989
-0.01421
0.00922
-0.08056
0.01073
0.00412


0.00113
0.07508
0.00143
-0.00043


2.55943
1.94706
0.12685


0.985
0.986
0.954

0.65


2. The first 15 parameters uses
following (4.37)-(4.43).


the notation of (5.6), others


0.01264
0.01584
0.01602
0.03411
0.00198
0.00088


0.01157
0.01458
0.01469
0.03091
0.00184
0.00081


0.00680
0.00853
0.00858
0.01789
0.00102
0.00048


0.00009
0.00954
0.00018
0.00003


0.06753
0.72508
0.05626













Table 14. Price and Expenditure Elasticities


Price Elasticities

Beef Pork Poultry
Beef -1.12057 -0.04377 -0.20104
Pork 0.16017 -0.96094 0.27631
Poultry 0.06532 0.06547 -0.87830

Price Elasticity (approximation)

Beef Pork Poultry
Beef -1.13221 -0.04855 -0.21600
Pork 0.17270 -0.95580 0.29242
Poultry 0.07857 0.07091 -0.86127

Expenditure Elasticity

Beef 1.44639
Pork 0.51944
Poultry 0.49166













Latent Elasticities


1950
1951
1952
1953
1954
1955
1956
1957
1958
1959
1960
1961
1962
1963
1964
1965
1966
1967
1968
1969
1970
1971
1972
1973
1974
1975
1976
1977
1978
1979
1980
1981
1982
1983
1984
1985
1986
1987


Pork


0.0948
0.0891
0.0849
0.0814
0.0846
0.0850
0.0784
0.0747
0.0669
0.0705
0.0589
0.0519
0.0499
0.0413
0.0366
0.0299
0.0203
0.0283
0.0288
0.0167
0.0140
0.0167
0.0119
-0.0241
-0.0171
-0.0276
-0.0383
-0.0485
-0.0515
-0.0556
-0.0655
-0.0815
-0.0839
-0.0947
-0.1185
-0.1342
-0.1471
-0.1626


Beef


-0.0214
-0.0183
-0.0195
-0.0189
-0.0202
-0.0210
-0.0207
-0.0198
-0.0180
-0.0193
-0.0168
-0.0150
-0.0144
-0.0123
-0.0113
-0.0093
-0.0061
-0.0086
-0.0092
-0.0054
-0.0044
-0.0055
-0.0041
0.0078
0.0056
0.0095
0.0127
0.0160
0.0172
0.0182
0.0214
0.0261
0.0267
0.0289
0.0374
0.0395
0.0466
0.0473


Poultry

-0.2219
-0.1942
-0.1964
-0.1919
-0.2099
-0.2155
-0.2043
-0.1968
-0.1780
-0.2004
-0.1636
-0.1444
-0.1402
-0.1173
-0.1042
-0.0835
-0.0563
-0.0820
-0.0866
-0.0505
-0.0435
-0.0535
-0.0400
0.0678
0.0546
0.0851
0.1196
0.1434
0.1517
0.1628
0.1881
0.2233
0.2315
0.2536
0.2830
0.3091
0.3294
0.3490


Table 15.












Table 16. Latent Taste Index and The Latent Effects
1950-1987


Year Latent Beef Pork Poultry

1950 -3.4014 0.0444 -0.0079 -0.0365
1951 -3.0493 0.0398 -0.0070 -0.0327
1952 -3.0574 0.0399 -0.0071 -0.0328
1953 -2.9549 0.0386 -0.0068 -0.0317
1954 -3.1261 0.0408 -0.0072 -0.0336
1955 -3.1914 0.0417 -0.0074 -0.0343
1956 -3.0243 0.0395 -0.0070 -0.0325
1957 -2.8886 0.0377 -0.0067 -0.0310
1958 -2.6045 0.0340 -0.0060 -0.0280
1959 -2.7889 0.0364 -0.0064 -0.0299
1960 -2.3541 0.0307 -0.0054 -0.0253
1961 -2.0823 0.0272 -0.0048 -0.0224
1962 -2.0053 0.0262 -0.0046 -0.0215
1963 -1.6819 0.0220 -0.0039 -0.0181
1964 -1.5044 0.0196 -0.0035 -0.0161
1965 -1.2275 0.0160 -0.0028 -0.0132
1966 -0.8273 0.0108 -0.0019 -0.0089
1967 -1.1601 0.0152 -0.0027 -0.0125
1968 -1.2064 0.0158 -0.0028 -0.0130
1969 -0.7057 0.0092 -0.0016 -0.0076
1970 -0.5884 0.0077 -0.0014 -0.0063
1971 -0.7144 0.0093 -0.0016 -0.0077
1972 -0.5192 0.0068 -0.0012 -0.0056
1973 1.0049 -0.0131 0.0023 0.0108
1974 0.7289 -0.0095 0.0017 0.0078
1975 1.1880 -0.0155 0.0027 0.0128
1976 1.6329 -0.0213 0.0038 0.0175
1977 2.0470 -0.0267 0.0047 0.0220
1978 2.1805 -0.0285 0.0050 0.0234
1979 2.3396 -0.0306 0.0054 0.0251
1980 2.7447 -0.0358 0.0063 0.0295
1981 3.3708 -0.0440 0.0078 0.0362
1982 3.4639 -0.0452 0.0080 0.0372
1983 3.8431 -0.0502 0.0089 0.0413
1984 4.7639 -0.0622 0.0110 0.0511
1985 5.2476 -0.0685 0.0121 0.0563
1986 5.8517 -0.0764 0.0135 0.0628
1987 6.2562 -0.0817 0.0144 0.0672









94




Table 17. Meat Demands Changes Caused By Preference Changes
(percentages)


Beef Pork Poultry
---------------------------------------------------------
1950-1987 -0.2400 0.0706 0.6542
1970-1987 -0.1730 0.0509 0.4716
1980-1987 -0.0973 0.0286 0.2653

---------------------------------------------------------

Predictions (By 2000)
-0.1958 0.0576 0.5338