United States

Department of

Agriculture

Estimation of Food

Economic

Research Demand and Nutrient

Service

Bulletin

Technical Elasticities from

Number 1887 Household Survey Data

Kuo S. Huang

Biing-Hwan Lin
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Estimation of Food Demand and Nutrient Elasticities from Household Survey Data.

By Kuo S. Huang and Biing-Hwan Lin, Food and Rural Economics Division, Economic

Research Service, U.S. Department of Agriculture. Technical Bulletin No. 1887.

Abstract

A methodology for estimating a demand system from household survey data is developed

and applied to the 1987-88 Nationwide Food Consumption Survey data. The empirical

results are sets of estimated demand elasticities for households segmented with different

income levels. In addition, we apply these demand elasticities to estimate the implied

nutrient elasticities for low-income households. The estimation results are useful in

evaluating some food policy and program effects related to households of a specific income

level.

Keywords: Demand elasticities, household survey data, and food quality effect.

Acknowledgments

The authors thank Chung L. Huang of the University of Georgia, Steven Carlson of Food and

Nutrition Service, USDA, and Parke Wilde and Mark Jekanowski of the Economic Research

Service for helpful review of the earlier drafts of this report, and J.B. McGraw for editorial

advice.

1800 M Street, NW

Washington, DC 20036-583 1 August 2000
Contents

Page

Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ....... iii

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

Conceptual Framework.. .......................................................................................................... 1

Demand Model Specification............................................................................................. 2

Derivation of Demand Elasticities and Standard Errors.................................................... 4

Measuring Nutrient Demand Elasticities............................................................................ 5

Empirical Application ........................................................................................................... 7

Data Source........................................................................................................................ 7

Estimates of Demand Elasticities for All Samples............................................................. 8

Estimates of Demand Elasticities Segmented by Income ................................................ 11

Estimates of Nutrient Elasticities for Low-Income Households...................................... 12

Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .... 15

Appendix: Review of Deaton’s Approach. .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

Tables. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

ii
Summary

Many food programs, like the Food Stamp Program, are concerned about low-income

households. To evaluate program effects, one needs demand elasticity estimates pertinent to

households of different income levels. Most available demand elasticities, by contrast, are

estimated from time-series data based on average consumer behavior and may not represent

well the households of concern. In this study, we used data from the 1987-88 Nationwide

Food Consumption Survey to estimate demand elasticities for households segmented by

income levels.

We developed an approach for estimating a demand system from household survey data in

this study. We used the unit values of foods available in household surveys as variables to

model a food demand system. Since the unit values of foods reflect market prices and

consumer choices of food quality, we adjusted the estimates by excluding the food quality

effects and obtained a complete set of demand information including own-, cross-price, and

expenditure elasticities. This approach is particularly useful in estimating a demand system

when obtaining time series data is difficult or when the estimates of demand elasticities

across different population groups are required for food policy decisionmakers.

We classified all households into three income groups and then estimated the demand

structures both for the entire sample of households and also for each group of households.

Most estimated demand elasticities were statistically significant and acceptable in sign and

magnitude. Estimates of food quality effects obtained in this study show that food quality

plays a significant role in household budget allocation, and that food quality is an important

factor in modeling a food demand system from household survey data. According to the

estimates, the demand elasticities among income groups were substantially different. We,

therefore, suggest using the demand elasticities of a specific income group (for example, the

low-income group) for food policy analysis when that group of households is of interest.

We also used the estimated demand elasticities for low-income households to measure

nutrient income elasticities-the percentage change in nutrient availability with respect to

changes in household food expenditure. The results indicate that consumption of all 13 food

groups increases as food expenditures increase. Consequently, the nutrient elasticities with

respect to food expenditure and with respect to food stamp benefits were positive for 25

nutrients studied.

iii
Estimation of Food Demand and Nutrient Elasticities

from Household Survey Data

Kuo S. Huang and Biing-Hwan Lin

Introduction

Household food consumption surveys, as conducted in the United States and elsewhere, often

collect detailed information on the quantity and expenditure of food consumed and on the

economic and sociodemographic characteristics of households. This rich database offers

researchers unique opportunities and challenges in analyzing food demands and related policy

issues. Many food policies and programs like the Food Stamp Program are targeted at lowincome households. For evaluating the program effects, most available demand elasticities may

be inadequate, since they are estimated from time-series data based on average consumer

behavior rather than on the behavior of the households of interest. Therefore, estimating crosssection demand relationships from household survey data in order to obtain elasticities

distinguished by household characteristics, such as income, is of interest.

In this study, we develop a new approach for estimating a demand system from household survey

data. We apply this approach to the 1987-88 Nationwide Food Consumption Survey (NFCS)

data to analyze food demands for households segmented into three income levels. Since the

nutrient status of low-income households is a primary concern of various food programs, we use

estimated demand elasticities for low-income households as input information to generate the

nutrient elasticities, which are useful in evaluating the effect of the food stamp benefit on nutrient

availability.

In this report, we first present a conceptual framework with a focus on the specifications of a

demand system and unit value equations and a procedure to measure demand elasticities and

nutrient elasticities. We then present empirical results, including data sources, estimates of

demand elasticities of all samples and for three income groups, and estimates of nutrient

elasticities for low-income households. Finally, we review Deaton’s approach for estimating

demand elasticities from household survey data in the appendix.

Conceptual Framework

A major problem of using household survey data to estimate a demand system lies in its

difficulty in defining price variables. Earlier household budget studies often assumed that prices

are constant, and they focused on fitting the Engel curves. In an attempt to retrieve price effects

Economic Research Service/USDA Food Demand and Nutrient Elasticities/ TB-1887 1
in household survey data, Theil and Neudecker derived conceptual relationships of substitution

and complementarity from the residual variations around the Engel curves. Their methodology,

however, is far from practical in developing a working model for empirical application.

Recently, Deaton, in a series of articles, developed a procedure by using the residuals of

estimated unit value (defined as the ratio of expenditure to quantity) and expenditure share

equations to obtain a system of demand equations. By applying a separability assumption, he

was able to derive information about price effects from the estimated covariance of residuals.

The problem of applying his approach, however, is that there is no guarantee of obtaining

accurate estimates of price responses, because many unexplained factors influence covariance of

residuals, not price variations alone.

Cox and Wohlgenant proposed an alternative approach, which was then adopted in some crosssectional demand analyses, such as Park et al., and Gao et al. They assumed that the deviations

of unit values from regional or seasonal means reflected the quality effects induced by household

characteristics and nonsystematic supply-related factors. By regressing the mean-deviated unit

values on household characteristics, they filtered the quality effects out of unit values to obtain

the quality-adjusted prices for the subsequent demand system estimation. Specifically, qualityadjusted prices were calculated as the sum of an estimated constant term and residuals from

related unit-value equations. A problem with this approach is that the adjusted prices are

random, vary from household to household, and are not consistent with the fact that households

face quite similar market prices in a short survey period.

Demand Model Specification

In our empirical study, based on the NFCS data, we assumed that food consumption at home was

separable from the demands for other goods in the consumer budget. By weak separability, we

then focused on a food-demand structure by allocating at-home food expenditures to various food

categories. Thus, the demand for each food category was represented as a function of at-home

food expenditures and a set of prices for food categories. In addition, only unit values, but not

prices of each food category, are available in the household survey data. The unit value of a food

category reflects its average market price and consumers’ choices of food quality. In fact, the

foods purchased by different households are obviously not homogeneous; rather, the foods are a

collection of different qualities. Beef as a category, for example, includes meat cuts such as

steak and inexpensive ground beef. In this study, we used unit values of food categories as

variables in modeling a food demand system, and the rationale of such a specification is given

below.

Let the average price of the i th food category be p i , the unit value of the food category paid by an

individual household be v i, and the ratio of unit value to average price be λ i. Thus λ i represents a

price structure for the quality choices of a food category by a household. If a household’s choice

of food quality is above average, the ratio λ i should be greater than one; otherwise, for food

quality below average, the ratio λ i should be less than one. By using the household survey data,

the quantity of a food category (say q i ) represents the amount of foods purchased regardless of

2 Economic Research Service/USDA Food Demand and Nutrient Elasticities/ TB-1887
quality. For example, different households may buy the same number of pounds of beef, which

consist of differentcuts. Therefore, the quantity variables that affect consumers’ satisfaction in

the utility function should be the quantities that are adjusted by quality effect as λ i q i. In other

words, for above-average quality of food purchased by a household, the quantity should be

augmented by a factor of λ i. On the other hand, in case of quality of food purchased below

average, the quantity should be reduced by a factor of λ i.

For illustration, let a utility function for a food sector consisting of two food categories be

By maximizing U subject to the food budget constraint

 we can obtain a demand equation expressed as a function of unit values and

income as 1, 2. Moreover, through the duality properties of

demand relationships, we can derive a demand equation from a cost function.

Consider the following cost minimization problem. By minimizing C =

subject to a utility function log U we can derive the conditional factor

demands and then the cost function as

This cost function, which can be

used to generate a demand system, is obviously a function of unit values and utility level. In

general, we may conclude that it is ‘justifiable to substitute unit values for price variables in

modeling a food demand system.

In this study, we adopt a cost function as suggested by Deaton and Muellbauer by replacing unit

values for prices in the function. By applying Shepard’s lemma, we can derive a modified

version of an “Almost Ideal Demand System” (AIDS), in which at-home expenditure share of a

food category is a function of unit values and the related food expenditures as

(1)

where w i is the at-home food expenditure share, m is per capita at-home food expenditures, and

v* is a unit value index defined by

(2)

All subscripts of variables and summation throughout this paper refer to a total of n food

categories ( i, j, k = 1, 2, . . , n ). In practical estimation, log v* is approximated by the logarithm

of the Stone price index (that is, log v* = Σ j w j log v j ) to allow for linear estimation and for

subsequent derivations of demand elasticities. Obviously, this demand system is a first-order

approximation to the general unknown relationships among expenditure share, unit values, and

expenditure. Theoretical properties of adding up, homogeneity, and symmetry are applied

directly to the parameters. They are δ jk = δ kj, Σ j β j = Σ j δ jk = Σ j δ kj = 0, and Σ j α j = 1. On empirical

application, some sociodemographic variables are also included in the demand system to reflect

the nature of household survey data.

Economic Research Service/USDA Food Demand and Nutrient Elasticities/ TB-1887 3
In addition, the magnitude of household income and other characteristics such as size and

composition may affect the choice of food quality. As we would expect, the better-off

households tend to spend more on food and choose more costly, better quality foods. Therefore,

a positive relationship between unit values and per capita household food expenditures exists.

Also, consumers who spend a larger portion of their food budget away from home can be

regarded as valuing taste and convenience more than other consumers may. Because taste and

convenience are two important quality attributes in foods, we expect a positive relationship

between unit values and the share of food away from home in the food budget. Finally, regional

and seasonal dummy variables can be used to capture variations in market prices induced by

transportation costs and seasonal supplies. Accordingly, we can explain the variations of unit

values by using the following equation:

(3)

where f i is an exogenous variable representing the portion of the total food budget spent on food

away from home, Z k is a vector of household sociodemographic variables, and other variables are

the same as in equation 1. For given food prices, the parameter

is defined as the elasticity of unit value with respect to per capita

expenditure for food consumed at home. Houthakker and Prais called this the “elasticity of

quality,” which is an important component that will be used to correct the bias of measuring

Engel relationships directly from equation 1 when food quality effects are ignored.

In summary, for our empirical analysis of household food consumption at home, the proposed

demand model consists of two sets of equations: one is the modified AIDS equation system and

the other is a set of unit value equations. Since the two sets of equations are recursive blocks, it

is well known that unbiased estimates of the recursive-form parameters are obtainable by

estimating each set of equations separately (Goldberger, p. 383). Therefore, the unit value

equations can be estimated by applying ordinary least squares (OLS), while the modified AIDS

model can be estimated by applying seemingly unrelated regressions with parameters constrained

across equations. After the estimation, we are able to obtain a complete set of demand

information including own-, cross-price, and food-expenditure elasticities by excluding the food

quality effects from the estimates.

Derivation of Demand Elasticities and Standard Errors

Since the unit value of a food category is a product of average market prices and a quality choices

index, we can decompose log v j in the AIDS model of equation 1 into the sum of two

components: log p j and log λ j , and their effects on at-home food expenditure share are implicitly

assumed to be the same as showing by an estimate of δ ij. Accordingly, we can derive price and

expenditure elasticities by differentiating equations 1 and 2 with respect to prices and

expenditure to obtain the following elasticity measures:

(4) Own-price elasticity:

4 Economic Research Service/USDA Food Demand and Nutrient Elasticities/ TB-1887
(5) Cross-price elasticity:

(6) Expenditure elasticity:

In particular, the quality-adjusted expenditure elasticity measure showing in equation 6 is

different from that derived from the conventional AIDS model without considering food quality

effect, which is calculated by ( β i/ w i + 1). We, therefore, can measure the bias of estimate as

when quality effects are ignored.

Furthermore, the standard errors of demand elasticities are obtainable by following a method for

computing an asymptotic variance for a function of random variables (Goldberger, p. 124).

Let Φ be the estimated covariance matrix of a vector of parameter estimates α ’s, β ’s, and δ ’s in

the AIDS system, and Var ( π i) be the variance of estimate π i . We can measure the variances of

estimated demand elasticities in terms of Φ and Var ( π i), as follows:

(7)

(8)

(9)

where J a is a vector with entries: 

J b is a vector with entries:

J c is a vector with entries: 

Measuring Nutrient Demand Elasticities

Given the estimated demand elasticities, we can translate them into changes in the total level of

nutrients available for consumption by following the same approach developed in Huang (1996).

To explore the linkage of the demand model to nutrient availability, let a ki be the quantity of the

k th nutrient in a total of k nutrients obtained from a unit of the i th food. The total quantity of that

nutrient, say φ k , obtained from various foods may be expressed as:

(10)

Lancaster (1966) called this equation the “consumption technology” of consumer behavior. This

equation, including all foods consumed, plays a central role in the transformation of food demand

into nutrient availability.

Economic Research Service/USDA Food Demand and Nutrient Elasticities/ TB-1887 5
Suppose a household consumes n foods with a predetermined total food expenditure, m, the

demand for i th food quantity q i can be expressed as:

(11)

Furthermore, the demand system may be expressed by applying the first-order differential

approximation of the conceptual demand relationships as:

(12)

where e ij is a price elasticity of the i th commodity, with respect to a price change of the j th

commodity, and η i is expenditure (or income) elasticity showing the effect of the i th quantity in

response to a change in per capita expenditure. This demand model is a general approximation

of conceptual demand relationships relating to some small change from any given point on the ncommodity demand surface.

By differentiating φ k of equation 10 with respect to price and expenditure and then by

incorporating equation 12, as shown in Huang (1996, p. 22), relative changes in nutrient

consumption can be expressed as a function of relative changes in prices and expenditure:

(13)

where π kj = Σ i e ij α ki q i / ( φ k is a price elasticity measure relating the effect of a change in the j th

food price on the availability of the k th nutrient, and pk = Σ i η i α ki q i/ φ k is an income elasticity

measure relating the effect of a change in income on the availability of that nutrient. In other

words, the measurement of π kj represents the weighted average of all own- and cross-price

elasticities ( e ij’s) in response to a change in the j th price, with each weight expressed as the share

of each food’s contribution to the k th nutrient ( α ki q i / φ k’s). Similarly, the measurement of pk

represents the weighted average of all income elasticities ( η i’s), with each weight again expressed

as the share of each food’s contribution to the k th nutrient.

In measuring the effect of food stamp benefits (as part of total food expenditure) on nutrient

consumption, we need information on the relationship between food stamp benefits and food

expenditure. Letting variable s be the food stamp benefits, the elasticity of food expenditure with

respect to food stamp benefits can be expressed as ( dm/m )/( ds/s ). Thus, the nutrient elasticity

with respect to food stamp benefits can then be derived as:

(14)

6 Economic Research Service/USDA Food Demand and Nutrient Elasticities/ TB-1887
Empirical Application

Data Source

Since the 1930’s, USDA has conducted seven household food consumption surveys on a national

scale: 1936, 1942, 1948 (urban households only), 1955, 1965-66, 1977-78, and 1987-88. The

data have been used to describe food-consumption behavior patterns and to assess the nutritional

content of diets for policy implications related to food production and marketing, food safety,

food assistance, and nutrition education.

Most household surveys before 1965-66 were conducted during the spring. Since 1965-66, all

surveys have been conducted in all four seasons. The 1987-88 Nationwide Food Consumption

Survey (NFCS) included two components: (1) household food used during a 7-day period, and

(2) individual food intakes by household members for a 3-day period. While the householdfood-used component has not been conducted since 1987-88, the individual food-intakes

component was implemented during 1989-91 and 1994-96.

The NFCS 1987-88 provides the most recent data on quantities used and expenditures for foods

by households in the United States. Additionally, the data set contains a wealth of information

about the economic and sociodemographic characteristics of American households. Therefore,

the NFCS 1987-88 data are well suited for analyzing household food-consumption behavior.

The NFCS 1987-88 sample was designed as a self-weighting, multistage, stratified, area

probability sample, representative of households in the 48 contiguous States. The stratification

plan took into account geographic location, degree of urbanization, and socioeconomic

considerations. In total, 13,733 housing units were selected, of which 12,181 (89 percent) were

occupied housing units. After screening, 4,589 households participated in the survey and 4,495

households completed household food-use questionnaires. The response rate for NFCS 1987-88

is lower than the response rates for earlier surveys.

Among those completing the household food use questionnaire, 4,273 households had at least

one member having 10 or more meals from the household food supply, and these households are

called “housekeeping households.” Only housekeeping households should be used for analytical

studies, because these households provide more comprehensive information about home food

practices. Since household income is an important determinant for food use, we included only

those households (4,245) with a positive income, reported or imputed.

In the NFCS 1987-88 data, more than 3,000 food items were defined in accordance with the

similar frequency of use, comparability of products, and nutritional contents. In this study, we

focus on foods consumed at home because households did not report expenditures on each food

item consumed away from home; rather, they reported total expenditures spent on all foods away

from home. We aggregated foods consumed at home into 13 composite food categories, with the

first three digits of food codes listed in parentheses, as follows: beef (441), pork (442), poultry

Economic Research Service/USDA Food Demand and Nutrient Elasticities/ TB-1887 7
(451), other meat (443-447), fish (452), dairy products (400-409), cereal (420-429), bread (430-

439), fats and oils (410-419), eggs (461-462), vegetables (480-495, 511, 521, 541), fruits (501-

503, 512, 522, 542), and juice (530-539).

In computing a unit value for a food category, we first calculated the unit values of individual

items in the category and then aggregated them into the expenditure-weighted average. Some

households did not consume certain food categories; the unit value for nonconsuming households

is treated as “missing” in the analysis of quality choice. Table 1 shows the mean unit values,

percent of households consuming a food category, and the distribution of at-home food

expenditures among the 13 food categories..

Arrays of sociodemographic factors that may influence consumers’ food choices are included in

the analysis. They are per capita household income, per capita at-home food expenditure, awayfrom-home share of the food budget, education level (household head attended college or not),

race (White, Black, Hispanic, and other), urbanization (city, suburb, and rural), region

(Northeast, Midwest, West, and South), household size measured in 21-meal equivalence, and

household composition. The household composition is characterized by 10 groups: children for

age groups 2-5 and 6-11, and male and female separately for age groups 12-17, 18-34, 35-64, and

above 64. Table 1 contains descriptive statistics of the above variables.

In our analysis, we segment the entire sample into three subsamples according to household

income, measured as a percent of the Federal poverty guideline. The poverty guideline

developed by the U.S. Department of Health and Human Services used to implement Federal

food programs varies by household size; it ranged from $5,360 for a household of one person to

$18,520 for a household of eight persons, and an additional $1,800 for each additional person in

a household with more than eight persons, in 1987-88. Some Federal food assistance programs,

such as the Food Stamp Program, have used 130 percent of the poverty level to determine

eligibility for participants. In this study, we classify three income groups: low-income, below

130 percent of the poverty income guidelines; high-income, above 300 percent of the poverty

income guidelines; and the medium-income group falling in between. Accordingly, the

household income groups are distributed as 23.2 percent for low-income, 35.4 percent for

medium-income, and 4 1.4 percent for high-income.

Estimates of Demand Elasticities for All Samples

In our empirical study, we assumed that food consumption at home was separable from the

demands for other goods in the consumer budget. By weak separability, the demand for each

food category can be represented as a function of total food consumption expenditure at home

and a vector of prices for various food categories. The focus of analysis on allocating food

consumption expenditure at home is proper, mainly because the survey data permit us to separate

the consumption expenditure at home into different food categories.

8 Economic Research Service/USDA Food Demand and Nutrient Elasticities /TB-1887
The AIDS model of equation 1 is estimated as a system of linear equations, using the systems

linear regression (SYSLIN) procedure in SAS computer programs. The parametric constraints of

homogeneity and symmetry conditions across the equations are imposed. To avoid singularity in

the variance-covariance matrix, the “fish equation” is deleted from direct estimation because

almost half of Americans do not eat fish weekly. Also, the survey data show that a high

proportion (47 percent) of U.S. households did not consume fish over a l-week period. The

parameter estimates of the fish equation were derived using the homogeneity, symmetry, and

adding-up conditions.

In the process of estimation, we found that some households reported zero consumptionof

certain foods in household food consumption surveys, because of its cost or personal preferences,

or because that food was not purchased during the short survey period. Consequently, it is

possible that consuming and nonconsuming households may react differently to changes in

market conditions, making traditional regression methods inappropriate.

The econometric treatment of zero consumption has received considerable attention in household

demand analyses, and Gould summarized the proliferating literature. A popular procedure in

dealing with zero consumption in estimating demand systems is to use a Heckman-type sample

selection correction factor (Heien and Wessell). This approach is attractive because of the ease

in model estimation, but it does not capture cross-commodity censoring impacts (Gould). In this

study, while our focus is on the treatment of unit value and its relationship with demand

elasticity, we sidestep the zero consumption issue. When a household did not report consuming

a food, the unit value of the food is missing for the household. Mean unit values are used to

replace missing unit values in AIDS estimation. Future research in integrating our approach in

dealing with quality issues and recent developments in treating zero consumption, such as in

Dong et al., and Shonkwiler and Yen, should be encouraged.

Partial estimation results of the AIDS model, including the parameter estimates of price and

expenditure coefficients ( δ ij's and β i

’s), are reported in table 2. The budget share (dependent)

variables of food categories are listed across the top of the table, and the unit value and

expenditure (independent) variables are listed on the left. Presented are the estimated parameters

of a share of particular food category in response to the changes in unit values with estimated

standard errors in parentheses. The empirical results show that most unit values of each food

category have positive effects on the budget shares within that category, and the estimates are

statistically significant at the l-percent level. The only negative effect is for juice, but its

estimate is not statistically significant. The budget share of each food category is also affected by

changes in per capita food expenditure. According to estimates, the budget shares of beef, other

meat, egg, cereal, and bread decrease as total food expenditures increase, while the budget shares

of poultry, fruits, vegetables, and juice increase with an increase in expenditures. These

estimates of price and expenditure effects will be used as basic input information to derive

demand elasticities.

Economic Research Service/USDA Food Demand and Nutrient Elasticities /TB-1887 9
The parameter estimates of sociodemographic variables are not reported in the table, but they are

available upon request. The results indicate that larger households allocate more of their food

expenditure to beef and pork, and less to bread and juice. Households headed by those who

attended college allocate more of their food budgets to poultry, fruits, and vegetables, and less for

beef, pork, other meat, and eggs. In terms of differences by race, Black households allocated

more of their food budgets for pork, poultry, other meat, fish, eggs, and juice than White

households, but less for dairy, bread, and fruits. City and suburban households allocated less of

their food budgets for pork and fats, and more for fruits and juice than rural households. We also

found significant regional and seasonal differences in food budget allocation. For example,

households in the West devoted a greater proportion of their food budget to dairy products and

fruits than other households and less to pork and other meat. Family composition influences

food budget allocation; households with more children ages 2-5 tended to spend more of their

food budgets on dairy products.

The unit value equation 3, which is specified as a function of per capita food expenditure and

some sociodemographic variables, was estimated by OLS (see table 3). The overall goodness-offit for the equations appears to be satisfactory in the standard of analyzing household survey data,

with R2 values in a range of 6 to 15 percent. For all 13 food categories, per capita food

expenditure had a positive effect on the unit values of each category, with estimates statistically

significant at the l-percent level. Because both the unit value and food expenditure are

expressed in logarithmic terms, the parameter estimate ( π i) represents the elasticity of quality,

the percentage change in unit value in response to a change in food expenditure. The elasticity of

quality varied greatly among food categories, from 0.06 for eggs to 0.34 for dairy products. In

particular, the estimates of quality elasticities for dairy products, beef, poultry, fish, fats, bread,

fruits, and vegetables exceed 0.15, signifying the importance of food quality effects in

consumers’ food choices.

Other estimates showed that the share of food expenditure consumed away from home has a

positive effect on the unit values of all food categories. A household having a larger share of

food expenditure away from home can be regarded as having a higher preference for taste or

convenience, or both, in foods, and hence the household tends to purchase value-added foods that

cost more. Household size, measured in 21-meal equivalence, has a negative effect on the unit

value, a result consistent with economies of scale, because a large family may enjoy discounts for

buying bulk foods. Households with college-educated heads paid a significantly higher unit

value for all foods, except for eggs, than other households. Non-Hispanic white households

tended to pay more for poultry, other meat, bread, and juice than other households. Unit values

varied significantly across some regions and seasons,- reflecting regional and seasonal variations

in market prices.

On the basis of equations 4 to 9, we can generate demand elasticities and their standard errors, as

shown in table 4. Most own-price elasticities, except for eggs, were significant at the l-percent

level. The demands for dairy, fruits, and vegetables were relatively more price elastic than those

for other food categories, with elasticities ranging from -0.72 to -1.01, while the estimated

own-price elasticities for meat categories were -0.35 for beef, -0.69 for pork, -0.64 for poultry,

10 Economic Research Service/USDA Food Demand and Nutrient Elasticities /TB-1887
and -0.39 for fish. The own-price elasticities were substantially larger than those obtained from

time-series data such as in Huang (1993), in which the estimates of price elasticities were less

than -0.4 in absolute value for most food categories.

The estimates of expenditure elasticities with and without adjustments of food quality effects are

listed in the last two columns of table 4. The results show that the measurement of elasticities by

ignoring the quality adjustment would yield upward bias comparable to the adjusted elasticities

in a range from14 to 44 percent. The adjusted expenditure elasticities of fruits, vegetables, and

juice were 1.16, 1.04, and .98 greater than those of other foods, while the estimates for bread,

eggs, other meats, dairy, and cereals were less elastic, with elasticity estimates ranging from 0.58

to 0.68. The food expenditure elasticities could be larger than income elasticities because the

elasticities of food expenditure with respect to changes in income are in general less than 1, as

found in Park et al.

Estimates of Demand Elasticities Segmented by Income

By following the same estimation procedure outlined for all samples, we can estimate the

demand structure for each group-low-, medium-, and high-income, separately. As mentioned

earlier, we classified three income groups based on the poverty income guideline. The lowincome households are below 130 percent, and the high-income households are above 300

percent of the poverty income guidelines, while the medium-income households fall between the

two. The demand elasticities are reported in table 5 for high-income households, table 6 for

medium-income households, and table 7 for low-income households. The estimates for lowincome households will be used as input information to generate nutrient elasticities in the next

section of this report. For purposes of comparison, we report the own-price, expenditure, and

quality elasticities of the three household income groups in table 8.

A comparison of own-price elasticities among different income groups shows that the estimates

did not vary systematically across income groups. For example, the price elasticity of beef for

the low-income group was 0.29, compared with 0.41 for the high-income group. But the price

elasticity of pork for the low-income group was 0.72, relatively higher than that of 0.67 for the

high-income group. Similarly, the estimated expenditure elasticities did not vary systematically

across income groups. On the other hand, the estimated quality elasticities of the low-income

group were in general lower than those of the medium- and high-income groups, as expected,

because high-income households likely choose higher quality foods and value taste and

convenience more than low-income households.

To provide an indicator of the amount of difference in the estimated demand elasticities among

the three income groups, we calculated the coefficient of variation (CV) for these elasticity

estimates. The CV is calculated as the percentage of standard deviation to its mean in absolute

Economic Research Service/USDA Food Demand and Nutrient Elasticities /TB-1887 11
value. The differences in the own-price elasticities for pork, poultry, dairy, cereal, vegetables,

fruit, and juice were relatively small among income groups, with the CV estimates being less

than 10 percent. An exceptionally high CV estimate for eggs was a result of insignificant

elasticities for the medium- and high-income groups.

The differences in the expenditure elasticities among income groups, except for other meat, eggs,

and juice, were also relatively small, with CV estimates less than 10 percent. The difference in

food quality elasticities among income groups, however, was relatively large. For example, the

CV estimates of meat and fish categories are in a range from 24 to 37 percent. In general, higher

income households appeared to have higher food quality elasticities, especially for beef, pork,

poultry, and fish. Nevertheless, the empirical results suggest that low-income households also

devoted substantial food expenditures toward improving food quality, with the quality elasticities

ranging from a high of 28 percent for dairy products to a low of 4 percent for eggs.

Estimates of Nutrient Elasticities for Low-Income Households

The Food Stamp Program (FSP) is the largest domestic food-assistance program, costing the

Federal Government nearly $19 billion each year and serving an average of 20.8 million persons

per month in 1998 (USDA). An objective of the FSP is to improve the diets of low-income

people by providing food stamps to eligible households to increase their food expenditure. In

this section, we measure how food stamps influence the nutrient content of diets in low-income

households.

The FSP had its origins as a coupon-based food program during the Great Depression era, but it

was relatively short-lived. A coupon-based food program was resurrected in the early 1960’s, but

only on a limited pilot basis. The program became available in all States and counties starting in

1975. The existence of hunger in the United States and the rapid growth of the FSP spurred

empirical studies of its effectiveness. The literature on the effect of FSP on food consumption

has proliferated since the release of NFCS 1977-78 data, and this rich literature was reviewed by

Fraker in 1990.

The literature has shown that the food stamp benefits increase food expenditure and nutrient

availability, but that literature has some drawbacks. First, most studies are quite dated, analyzing

data collected before 1980. Before 1979, food stamps were purchased at a discount. This

purchase requirement was eliminated in 1979. Second, attention has focused increasingly on

overconsumption of fat, saturated fat, cholesterol, and sodium rather than underconsumption of

other nutrients. Third, previous studies employed ad hoc econometric models in which nutrient

availability was regressed on food stamp participation/benefit and sociodemographic variables,

excluding prices. In our study, food expenditures were allocated among food groups according

to prices and sociodemographic variables. Given demand elasticities, the nutrient elasticities can

be derived to estimate the effect of food expenditure on nutrient availability.

12 Economic Research Service/USDA Food Demand and Nutrient Elasticities /TB-1887
Using the mean values of the nutrient share of each food in the consumption of the 13 food

groups by low-income households (table 9), we can transform low-income household

expenditure elasticities (table 7) into nutrient elasticities with respect to food expenditures based

on equation 13. These nutrient expenditure elasticities, adjusted and unadjusted for food quality

effect, are reported in table 10. To derive the nutrient elasticities with respect to food stamp

benefits, we need the information pertaining to the effect of food stamps on food expenditure.

Many researchers have estimated the relationship between food expenditures and food stamp

benefits. Fraker’s review indicates that each additional dollar of food stamps would stimulate

roughly 20-45 cents of at-home food expenditure, while each additional dollar of regular income

would result in 5-10 cents of at-home food expenditure. These figures are estimated using much

earlier survey data, with NFCS 1977-78 being the latest. Recently, Levedahl used USDA’s San

Diego Cash-Out Demonstration data in 1990-91 and found a marginal propensity to spend 26

cents for each dollar of food stamps and an elasticity of 0.054.

By using Levedahl’s estimate of elasticity, we can estimate the nutrient elasticities with respect to

food stamp benefits according to equation 14. Because each percent of food stamp benefit would

result in only a 0.054 percent change in food expenditure, the nutrient elasticity with respect to

food stamps as shown in table 10 is quite small compared with the nutrient elasticity with respect

to food expenditure. The results in the table indicate that consumption of all 13 food groups rises

when total food expenditure increases. Consequently, the nutrient elasticities with respect to

either food expenditure or food stamp benefit are positive for all 25 nutrients reported in NFCS

1987-88.

Economic Research Service/USDA Food Demand and Nutrient Elasticities /TB-1887 13
Conclusion

Many food programs like the Food Stamp Program are concerned about low-income households.

To evaluate program effects, we need to know the demand elasticity estimates for the targeted

households. In this study, we developed a new approach for estimating a demand system from

household survey data. To overcome the difficulty of obtaining price data, we used the unit

value of each food category as variables in modeling a modified Almost Ideal Demand System.

Since the unit values reflect both market prices and consumers’ choices of food quality, we

further calculated the quality-adjusted own-price, cross-price, and expenditure elasticities.

The developed methodology was successfully applied to the 1987-88 Nationwide Food

Consumption Survey data. The empirical results are sets of estimated demand elasticities for

households segmented at three different income levels. These demand elasticities were further

applied to estimate the implied nutrient elasticities for low-income households. The significant

estimates of food quality effects obtained in this study show that food quality plays a significant

role in household budget allocation, and is an important factor in modeling a food demand

system from household survey data. The estimation results are useful in evaluating some food

policy and program effects that are related to households of a specific income level.

For various reasons, a household may report no consumption of a particular food in the survey.

The treatment of zero consumption in cross-section demand estimation has received increasing

attention in the literature. In this study, we focused on the treatment of unit value and its

relationship with demand elasticity and sidestepped the zero-consumption issue. Future research

in integrating our approach in dealing with quality issues and recent developments in treating

zero consumption would be useful.

14 Economic Research Service/USDA Food Demand and Nutrient Elasticities /TB-1887
References

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Food stamps,” American Journal of Agricultural Economics. 65(1983): 685-693.

Basiotis, P.P., S.R. Johnson, K. Morgan, and A. Chen. “Food stamps, Food Costs, Nutrient

Availability, and Nutrient Intake.” Journal of Policy Modeling. 9(1987): 383-404.

Butler, J.S., and J.E. Raymond. “The Effect of the Food Stamp Program on Nutrient Intake,”

Economic Inquiry. 34(1996): 781-798.

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Deaton, A. J., and J. Muellbauer. “An Almost Ideal Demand System,” American Economic

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Deaton, A. “Panel Data from Time Series of Cross-Sections,” Journal of Econometrics

30(1985): 109-126.

Deaton, A. “Estimation of Own- and Cross-Price Elasticities from Household Survey Data,”

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Household Expenditure Patterns: Theory and Spanish Evidence,” Journal of Political Economy.

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Deaton, A. “Price Elasticities from Survey Data: Extensions and Indonesian Results,” Journal of

Econometrics. 44(1990): 281-309.

Devaney, B., and R. Moffitt. “Dietary Effects of the Food Stamp Program,” American Journal of

Agricultural Economics. 73(1991): 202-211.

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Economics. 80(1998): 466-473.

Fraker, T.M. The Effects of Food stamps on Food Consumption: A Review of the Literature.

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Gao, X.M., E.J. Wailes, and G.L. Cramer. “A Synthetic Demand System: An Application to

U.S. Consumer Demand for Rice and Selected Rice Substitutes,” Review of Agricultural

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Agricultural and Resource Economics. 21(1996):68-81.

Heien, D., and CR. Wessell. “Demand Systems Estimation with Microdata: A Censored

Regression Approach,” Journal of Business and Economic Statistics. 8(1990): 365-371.

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Technical Bulletin No. 1821. 1993.

Huang, K.S. “Nutrient Elasticities in a Complete Demand System,” American Journal of

Agricultural Economics. 78(1996): 21-29.

Levedahl, J.W. “A Theoretical and Empirical Evaluation of the Functional Forms Used to

Estimate the Food Expenditure Equation of Food stamp Recipients,” American Journal of

Agricultural Economics. 77(1995): 960-968.

Park, J.L., R.B. Holcomb, K.C. Raper, and O. Capps, Jr. “A Demand Systems Analysis of Food

Commodities by U.S. Households Segmented by Income,” American Journal of Agricultural

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16 Economic Research Service/USDA Food Demand and Nutrient Elasticities /TB-1887
Appendix: Review of Deaton’s Approach

Deaton, in his series of articles starting in 1987, developed a methodology to estimate a complete

demand system including own- and cross-price elasticities from cross-section data.

The unique feature of his approach was its ability to estimate a set of unit value and expenditure

share equations and then recover the price effect from the estimated covariance matrices of

residuals. Since his study represents a major contribution in demand system research, our review

may provide a better understanding of his approach.

In household survey data, for household i in cluster c, there are two equations for good g; one is

the budget share equation and the other is the unit value equation as in the following:

(15)

(16)

where w gic is the budget share of good g in i th household’s budget, x ic is total expenditure on all

goods and services, z ic is a vector of household characteristics, p hc is the price of good h in a total

of the n goods, v gic is the unit value of good g defined as the expenditure on the good divided by

the quantity bought, f gc is a cluster-fixed effect for good g, and u gic and u* gic are random

disturbances.

The expenditure share equation is assumed to be a linear function of the logarithm of total

expenditure, of the prices, and of a vector of household characteristics. Each household in a

cluster is assumed to face the same prices for market goods. The logarithm of the unit value,

which is the logarithm of quality plus the logarithm of price, is a function of the same variables

that appear in the share equation, with the exception of the cluster-fixed effect.

Moreover, consider the budget allocation of a representative consumer; that is, the subscripts of

household i in cluster c are temporarily disregarded, and the equations of cluster means may be

represented as in the following:

(17)

(18)

Since the price variables phc in the model are not observable, it is not possible to estimate the

price coefficients in the equations directly. Deaton developed a two-stage procedure to link the

price effects to the estimated residuals, which are estimated from a model excluding price

variables.

In the first stage of estimation, both equations are estimated separately by OLS with cluster

means subtracted from all data. The subtraction of cluster means removes not only the fixed

effects but also the cluster invariant prices in both equations as in the following:

Economic Research Service/USDA Food Demand and Nutrient Elasticities /TB-1887 17
(19)

(20)

Based on the estimates of β g, γ g, β∗ g and γ∗ g , the residuals associated with each equation can be

generated. Using these estimated residuals, we can estimate the matrices of covariance in each

equation and across equations as 

respectively.

In the second stage of estimation, the first-stage estimates are used to calculate the parts of mean

cluster shares and unit values that are not accounted for by the first-stage variables. To obtain the

covariance matrices, comprised of price components and residuals, we may define ε gc and ε∗ gc as

follows:

(21)

(22)

We then calculate the matrices of covariance associated with ε gc and ε∗ gc as follows:

(23)

(24)

where M is the covariance matrix of the unobservable price vector, Θ is a matrix of θ gh, Ψ is a

matrix of φ gh, and n is the number of households in the cluster.

For given information of S, R, Ω, and Γ, Deaton is able to obtain a matrix B, which is defined by

B = [ S - (1/ n ) Ω]−1 [ R - (1/ n ) Γ ]. Furthermore, he is able to obtain the relationships of Θ and

Ψ by using available information B as a linkage, while the unknown matrix M can be ignored:

(25)

By applying a separability assumption, in which the demand for individual commodities depends

on the associated group expenditures and on the prices of the individual commodities in that

group, Deaton is able to derive information on the price effects from the estimated covariance of

residuals as follows:

18 Economic Research Service/USDA Food Demand and Nutrient Elasticities /TB-1887
(26)

where E is a matrix of all own- and cross-price elasticities, I is an identity matrix, D-1( w g) is a

diagonal matrix with (1/ w g)‘s as entries, and D( ξ g) is a diagonal matrix with (1/ ξ g) as entries, in

which ξ g is defined as β∗ g / [ (1 - β∗ g) w g + β g ].

In addition to complicated matrix multiplication, the main problem of applying Deaton’s

approach is that there is no guarantee of obtaining accurate estimates of price responses, because

the covariance matrices of residuals S, R, Ω, and Γ are influenced by many unexplained factors,

but not by price variations alone. In fact, we applied Deaton’s approach to fit the NFCS 1987-88

data, and the results were deemed unsatisfactory.

Economic Research Service/USDA Food Demand and Nutrient Elasticities /TB-1887 19
Table 1-Descriptive statistics of variables in the 1987-88 Nationwide

Food Consumption Survey

Item

Whole sample Low income Medium income High income

Mean S D Mean SD Mean S D Mea n S D

Price: dollars par pound

Beef

Pork

Poultry

Other meats

Fish

Dairy

Eggs

Fats

Cereals

Bread

Vegetables

Fruits

Juice

Budget share: percent

Beef

Pork

Poultry

Other meats

Fish

Dairy

Eggs

Fats

Cereals

Bread

vegetables

Fruits

Juice

Consuming household: percent

Beef

Pork

Poultry

Other meats

Fish

Dairy

Eggs

Fats

Cereals

Bread

Vegetables

Fruits

Juice

1.73 1.18 1.45 0.94 1.67 1.06

1.51 1.24 1.33 1.14 1.53 1.16

1.09 1.15 0.88 0.94 1.05 1.16

1.53 1.33 1.42 1.18 1.51 1.23

1.94

1.60

1.26

1.62

1.94

1.42

0.49

1.34

1.35

1.23

1.49

2.35

1.09

0.42

1.62 2.07

1.26 0.92

0.49 0.36

1.13 0.63

1.62 0.86

1.20 1.59 1.52 1.94

1.10 0.82 1.17 0.73

0.49 0.26 0.49 0.33

0.98 0.57 1.08 0.61

1.42 0.84 1.64 0.82

1.36 0.73 1.50 0.68

0.83 0.53 0.93 0.47

0.53 0.43 0.61 0.45

0.46 0.45 0.53 0.46

1.26

1.71

1.74

1.03

0.71

0.56

0.65

0.88

0.83

0.62

0.54

0.46

1.56 0.77

0.95 0.56

0.63 0.49

0.53 0.46

12.75 10.60 12.99 11.15

7.25 8.04 7.91 9.11

6.55 7.05 6.53 7.13

4.66 5.73 5.24 5.97

5.10 8.26 4.52 7.97

15.36 8.87 15.60 9.90

1.49 1.59 1.80 1.60

12.77 10.27

7.52 7.95

6.29 6.86

4.83 5.76

4.62 7.48

15.49 8.80

1.60 1.83

3.39 2.67

7.22 5.39

11.19 7.07

13.52 6.69

7.44 6.77

4.11 4.44

12.60

6.64

6.78

4.19

5.84

15.12

1.22

10.56

7.40

7.15

5.52

8.98

8.30

1.29

3.39 2.78 3.55 3.14

6.87 5.41 7.28 6.25

11.10 7.27 10.12 7.47

13.62 7.12 13.49 7.78

7.72 7.17 6.88 7.08

3.30 2.64

6.35 4.86

11.58 7.27

13.78 7.09

8.42 7.49

4.14 4.62 4.09 4.74 4.19 4.71

84.66 36.04

70.08 45.80

73.22 44.29

68.98 46.26

52.72 49.93

98.96 10.13

85.82 34.89

92.93 25.63

92.70 26.02

98.68 11.41

97.79 14.72

84.62 36.08

72.91 44.45

83.06 37.53 86.01 34.70

67.44 46.08 73.48 44.16

84.41

68.66

74.00

65.64

55.97

99.26

82.88

36.28

46.40

43.87

47.50

49.66

a.57

37.68

24.43

25.71

10.07

73.73 44.03 71.95 44.94

71.30 45.26 71.35 45.23

47.26 49.95 52.50 49.95

97.67 15.10 99.47 7.28

88.03 32.47 87.81 32.73

90.26 29.66 93.87 23.99

90.97 28.67 93.60 24.48

97.77 14.78 98.93 10.27

93.63

92.89

98.98

98.18

88.17

76.17

96.45 18.51 98.20 13.30

77.79 41.59 84.94 35.77

13.37

32.31

66.33 47.28 73.42 44.19 42.62

Continued__

20 Economic Research Service/USDA Food Demand and Nutrient Elasticities /TB-1887
Table 1-Descriptive statistics of variables in the 1987-88 Nationwide

Food Consumption Survey-Continued

Whole sample Low income Medium income

Item Mean SD Mean SD Mea n S D

High income

Wean SD

Household income:

Percent of poverty level 316 269 81 33 211 48 538 287

Food expenditure at home:

Dollars per person 18.55 9.99 16.73 9.03 17.81 8.76 20.21 11.17

Away-from-home share

of total food budget 26.63 22.64 16.13 20.24 24.89 21.37 34.01 22.36

Household size 2.43 1.34 2.47 1.55 2.59 1.40 2.26 1.1 3

Education:

Less than college

College

64.83 47.76 87.53 33.06 73.62 44.09 44.60 49.72

35.17 47.76 12.47 33.06 26.38 44.09 55.40 49.72

Race:

83.02 37.55

11.57 31.99

64.60 47.84 84.41 36.29

26.17 43.98 10.39 30.53

9.23 28.96 5.20 22.20

white

Black

Other

92.15 26.90

4.38 20.47

3.47 18.31

Urbanization:

5.42 22.64

23.35 42.31 30.43 46.03 20.92 40.69 21.44 41.06

47.28 49.93 30.43 46.03 45.57 49.82 58.19 49.34

29.38 45.55 39.15 48.83 33.51 47.22 20.36 40.28

City

Suburb

Nonmetro

Region:

Northeast

Midwest

South

west

20.52 40.39

26.20 43.98

34.42 47.52

18.87 39.13

16.23 36.89 20.79 40.59

22.52 41.79 27.51 44.67

45.03 49.78 33.31 47.15

16.23 36.89 18.39 38.75

22.70 41.90

27.13 44.48

29.41 45.58

20.76 40.57

Percent of household members

A g e 0-5

A g e 6-11

Mal e 12-17

Male 18-34

7.12 15.21

6.71 14.34

3.26 9.78

11.30 20.76

9.90 18.23 7.93 15.58

7.96 15.62 8.12 15.69

4.86 12.45

4.80 12.00

3.01 9.08

12.69 22.26

23.46 24.18

5.77 17.05

5.77 17.05

2.55 8.72

13.29 21.92

23.35 24.56

6.23 19.23

3.33 10.37

8.11 18.10

7.47 21.02

7.47 21.02

8.92 19.11

3.96 10.95

12.80 20.49

15.06 26.22

22.48 38.67

12.11 19.54

3.49 10.18

9.03 21.15

9.03 21.15

11.22 19.84

Male 35-64

Male 65 +

Male 65 +

Female 12-17

Female 18-34

15.88 22.27

7.32 19.57

7.32 19.57

3.21 9.85

13.10 21.20

19.44 25.13

12.68 29.14

3.49 10.28

13.07 20.80

17.73 24.41

13.79 29.57

Female 35-64

Female 65 +

Season:

Spring 1987

Summer 1987

Fall 1987

Winter 1987

Spring 1988

Sumner 1998

13.76 34.45

12.06 32.57

15.92 36.59

28.69 45.24

26.57 44.18

2.99 17.04

14.71 35.43 13.72 34.42

14.50 35.23 11.93 32.42

14.40 35.13 15.46 36.16

27.99 44.92 29.11 45.44

13.25 33.92

10.81 31.06

17.18 37.73

28.73 45.26

24.95 43.29 27.18 44.50 26.96 44.39

3.45 18.26 2.60 15.91 3.07 17.26

SD = standard deviation.

Source: Nationwide Food Consumption Survey 1987-88, USDA.

Economic Research Service/USDA Food Demand and Nutrient Elasticities /TB-1887 21
Table 2-The AIDS model estimates: Results of the 1987-88 Nationwide Food Consumption Survey

Budget share

Variable Beef Pork Poultry O. meat Fish Dairy Egg Fat Cereal Bread Vegetables Fruit Juice

Unit value:

Beef

Pork

Poultry

Other meats

Fish

Fats

Cereal

Bread

Vegetables

Fruits

0.0809 -0.0056 -0.0033 -0.0053 -0.0015 -0.0107 -0.0018 -0.0035 -0.0086 -0.0183 -0.0100 -P.O089 -0.0035

(0.0041) (0.0027) (0.0020) (0.0020) (0.0075) (0.0020) (0.0006) (0.0011) (0.0017) (0.0021) (0.0022) (8.0021) (0.0016)

-0.0056 0.0225

(0.8027) (0.0037)

-0.0001 -0.0023 0.0005 -0.0044 -0.0012 -0.0014 -0.0041 -0.0057 -0.0045 0.0008 0.0056

(0.0019) (0.0021) (0.0072) (0.0017) (0.0007) (0.0012) (0.0017) (0.0020) (0.0021) (0.0020) (0.0017)

-0.0033 -0.0001

(0.0020) (0.0019)

0.0237 -0.0034 -0.0053 -0.0011 -0.0011 -0.0014 -0.0023 -0.0005

(0.0020) (0.0014) (0.0050) (0.0014) (0.0004) (0.0007) (0.0012) (0.0015)

-0.0052 0.0004 -0.0005

(0.0015) (0.0014) (0.0011)

-0.0053 -0.0023

(0.0020) (0.0021)

-0.0034 0.0296 -0.0024 -0.0008 -0.0003 -0.0019 0.0004 -0.0088

(0.0014) (0.0024) (0.0055) (0.0013) (0.0006) (0.0010) (0.0013) (0.0016)

-0.0024 -0.0019 -0.0003

(0.0017) (0.0016) (0.0013)

-0.0015 0.0005

(0.0025) (0.0024)

-0.0053 -0.0024 0.0316 -0.0008 0.0001 -0.0029 -0.0058 -0.0068

(0.0017) (0.0019) (0.0062) (0.0017) (0.0006) (0.0010) (0.0015) (0.0019)

-0.0003 -0.0031 -0.0034

(0.0019) (0.0018) (0.0015)

-0.0107 -0.0044

(0.0020) (0.0017)

-0.0011 -0.0008 -0.0008 0.0306 -0.0018 0.0002 -0.0022 -0.0062

(0.0014) (0.0013) (0.0048) (0.0020) (0.0004) (0.0006) (0.0011) (0.0014)

-0.0013 -0.0009 -0.0009

(0.0014) (0.0014) (0.0010)

-0.0018 -0.0012

(0.0006) (0.0007)

-0.0011 -0.0003 0.0001 -0.0018 0.0140 -0.0011 -0.0016 -0.0039

(0.0004) (0.0006) (0.0019) (0.0004) (0.0007) (0.0005) (0.0005) (0.0005)

-0.0013 -0.0012 0.0011

(0.0005) (0.0005) (0.0005)

-0.0035 -0.0014

(0.0011) (0.0012)

-0.0014 -0.0019 -0.0029 0.0002 -0.0011 0.0204 -0.0046 -0.0042

(0.0007) (0.0010) (0.0030) (0.0006) (0.0005) (0.0010) (0.0007) (0.0009)

-0.0009 -0.0007 0.0018

(0.0009) (0.0008) (0.0008)

-0.0086 -0.0041

(0.0017) (0.0017)

-0.0023 0.0004 -0.0058 -0.0022 -0.0016 -0.0046 0.0300 0.0003

(0.0012) (0.0013) (0.0045) (0.0011) (0.0005) (0.0007) (0.0015) (0.0013)

-0.0042 -0.0009 0.0036

(0.0014) (0.0013) (0.0011)

-0.0183 -0.0057

(0.0021) (0.0020)

-0.0005 -0.0088 -0.0068 -0.0062 -0.0039 -0.0042 0.0003 0.0684

(O-0015) (0.0016) (0.0054) (0.0014) (0.0005) (0.0009) (0.0013) (0.0022)

-0.0092 -0.0034 -0.0019

(0.0017) (0.0016) (0.0013)

-0.0100 -0.0045

(0.0022) (0.0021)

-0.0052 -0.0024 -0.0003 -0.0013 -0.0013 -0.0009 -0.0042 -0.0092

(0.0015) (0.0017) (0.0060) (0.0014) (0.0005) (0.0009) (0.0014) (0.0017)

0.0407 -0.0022 0.0008

(0.0024) (0.0016) (0.0013)

-0.0089 0.0008

(0.0021) (0.0020)

0.0004 -0.0019 -0.0031 -0.0009 -0.0012 -0.0007 -0.0009 -0.0034

(0.0014) (0.0016) (0.0054) (0.0014) (0.0005) (0.0008) (0.0013) (0.0016)

-0.0022 0.0242 -0.0022

(0.0016) (0.0022) (0.0012)

-0.0035 0.0056

(0.0016) (0.0017)

-0.0005 -0.0003 -0.0034 -0.0009 0.0011 0.0018 0.0036 -0.0019

(0.0011) (0.0013) (0.0043) (0.0010) (0.0005) (0.0008) (0.0011) (0.0013)

0.0008 -0.0022 -0.0001

(0.0013) (0.0012) (0.0015)

-0.0112 -0.0036 0.0056 -0.0090 0.0060 -0.0046 -0.0026 0.0003 -0.0145 -0.0300 0.0228 0.0332 0.0076

(0.0038) (0.0030) (0.0026) (0.0021) (0.0084) (0.0031) (0.0006) (0.0010) (0.0019) (0.0024) (0.0025) (0.0025) (0.0017)

AIDS = Almost ideal demand system. Numbers in parentheses are standard errors. To save space, estimates for variables representing social and demographic

characteristics are not reported.
Table 3-Unit value equations: Results of the 1987-88 Nationwide Food Consumption Survey

Variable Beef Pork Poultry Other meat Fish Dairy Egg Fat Cereal Bread Vegetables Fruit Juice

Constant 0.1847 0.5052 -0.1460 0.3575 0.4579 -0.8616 -0.5189 -0.1529 -0.1201 -0.1243 -0.4991 -1.0295 -0.3873

(0.0724) (0.0759) (0.1264) (0.0853) (0.1206) (0.1043) (0.0554) (0.0759) (0.0888) (0.0731) (0.0729) (0.0880) (0.1011)

Food 0.1992 0.1210 0.1593 0.1358 0.2786 0.3377 0.0626 0.2038 0.1006 0.2331 0.1498 0.1841 0.0726

expenditure (0.0152) (0.0158) (0.0269) (0.0178) (0.0254) (0.0220) (0.0119) (0.0157) (0.0185) (0.0153) (0.0152) (0.0189) (0.0220)

Proportion of food 0.1844 0.1779 0.2951 0.1388 0.2550 0.1995 0.0596 0.2362 0.2033 0.2838 0.1670 0.0495 0.0119

exp. away from home (0.0329) (0.0336) (0.0571) (0.0382) (0.0520) (0.0477) (0.0257) (0.0336) (0.0401) (0.0333) (0.0331) (0.0404) (0.0463)

Household size -0.0102 -0.0232 -0.0590 -0.0242 -0.0436 -0.0244 -0.0226 -0.0274 -0.0119 -0.0260 -0.0282 -0.0087 -0.0253

in 21-meal equ. (0.0065) (0.0065) (0.0112) (0.0073) (0.0111) (0.0100) (0.0052) (0.0070) (0.0082) (0.0070) (0.0069) (0.0082) (0.0095)

College 0.0790 0.0629 0.0942 0.0510 0.1164 0.1271 0.0120 0.0832 0.0373 0.0958 0.0814 0.0820 0.1106

(0.0144) (0.0149) (0.0251) (0.0166) (0.0229) (0.0216) (0.0115) (0.0151) (0.0179) (0.0151) (0.0149) (0.0176) (0.0203)

white 0.0163 0.0305 0.2007 0.0849 0.0675 0.1413 -0.0687 -0.0280 0.3507 0.0633 -0.0095 0.0610 0.0390

(0.0288) (0.0305) (0.0477) (0.0335) (0.0480) (0.0436) (0.0225) (0.0313) (0.0361) (0.0309) (0.0299) (0.0361) (0.0413)

Black -0.0519 -0.0788

(0.0340) (0.0353)

-0.1013

(0.0553)

city 0.0842 0.0457 0.0285

(0.0187) (0.0193) (0.0324)

Suburban 0.0660 0.0504

(0.0156) (0.0159)

Northeast 0.0706 0.0432

(0.0213) (0.0225)

0.0726

(0.0278)

0.1203

(0.0362)

-0.0439

(0.0388)

0.0725

(0.0214)

0.0500

(0.0180)

0.0418

(0.0252)

-0.1040

(0.0556)

0.0053

(0.0302)

0.0516

(0.0259)

0.1058

(0.0326)

0.0427 -0.0196

(0.0514) (0.0264)

0.0602 -0.0108

(0.0274) (0.0146)

0.0412 -0.0128

(0.0235) (0.0124)

-0.0525 0.0232

(0.0312) (0.0167)

-0.1192

(0.0368)

0.0511

(0.0194)

0.0611

(0.0165)

-0.0172

(0.0220)

0.0751 -0.0717 -0.1403

(0.0427) (0.0363) (0.0352)

0.0626 0.0753 0.0515

(0.0230) (0.0192) (0.0190)

0.0835 0.0673 0.0376

(0.0196) (0.0164) (0.0162)

0.0397 0.0116 0.0557

(0.0261) (0.0218) (0.0215)

-0.0264

(0.0435)

0.0297

(0.0232)

0.0148

(0.0195)

0.0505

(0.0254)

-0.1176

(0.0488)

-0.0182

(0.0266)

-0.0855

(0.0226)

-0.1959

(0.0295)

Northwest -0.1026 -0.0616 -0.0494 -0.0324 -0.0124 -0.0937 -0.1668 -0.0830 0.0820 -0.0169 0.0287 0.0840 -0.1034

(0.0201) (0.0211) (0.0354) (0.0237) (0.0326) (0.0297) (0.0159) (0.0208) (0.0247) (0.0208) (0.0205) (0.0242) (0.0286)

South -0.0343 -0.0725 -0.0751 -0.0854 -0.0760 -0.0900 -0.1135 -0.1270 -0.0301 -0.0738 0.0030 -0.0010 -0.1999

(0.0195) (0.0205) (0.0338) (0.0233) (0.0314) (0.0287) (0.0154) (0.0201) (0.0239) (0.0201) (0.0198) (0.0236) (0.0282)

Sample size 3618 2995 3131 2950 2253 4226 3665 3970 3961 4215 4177 3616 3119

R-squared 0.13 0.09 0.14 0.09 0.15 0.10 0.09 0.11 0.11 0.13 0.08 0.06 0.07

Meal equ. = meal equivalence. Numbers in parentheses are standard errors. To save space, estimates for the variables

representing season/year and age/sex groups are not reported.
Table 4-Demand elasticities derived from the AIDS model: Case of all sample households

Commodity

Beef

Pork

Poultry

Other meat

Fish

Dairy

Egg

Fat

cereal

Bread

Vegetables

Fruit

Juice

Price Expenditure

Beef Pork Poultry Other meat Fish Dairy Egg Fat Cereal Bread Vegetables Fruit Juice Adj. Unadj.

-0.3540 -0.0372 -0.0199 -0.0376 -0.0071 -0.0702 -0.0129 -0.0243 -0.0617 -0.1340 -0.0667 -0.0632 -0.0234 0.7368 0.9124

(0.0322) (0.0212) (0.0161) (0.0161) (0.0200) (0.0162) (0.0049) (0.0083) (0.0137) (0.0167) (0.0178) (0.0166) (0.0130) (0.0250) (0.0296)

-0.0702 -0.6867 0.0017 -0.0300 0.0098 -0.0535 -0.0157 -0.0178 -0.0537 -0.0729 -0.0559 0.0150 0.0796 0.8072 0.9502

(0.0375) (0.0510) (0.0259) (0.0289) (0.0332) (0.0246) (0.0098) (0.0159) (0.0237) (0.0282) (0.0299) (0.0277) (0.0231) (0.0356) (0.0409)

-0.0609 -0.0080 -0.6437 -0.0560 -0.0847 -0.0297 -0.0174 -0.0244 -0.0405 -0.0178 -0.0911 -0.0001 -0.0119 0.9003 1.0860

(0.0312) (0.0284) (0.0299) (0.0215) (0.0267) (0.0218) (0.0065) (0.0110) (0.0184) (0.0225) (0.0239) (0.0222) (0.0174) (0.0369) (0.0398)

-0.0894 -0.0363 -0.0603 -0.3554 -0.0426 0.0124 -0.0046 -0.0336 0.0209 -0.1668 -0.0257 -0.0256 0.0005 0.6662 0.8064

(0.0444) (0.0451) (0.0306) (0.0518) (0.0400) (0.0282) (0.0137) (0.0215) (0.0291) (0.0343) (0.0365) (0.0335) (0.0290) (0.0381) (0.0451)

-0.0439 0.0018 -0.1107 -0.0534 -0.3871 -0.0335 0.0011 -0.0604 -0.1215 -0.1460 -0.0225 -0.0689 -0.0723 0.8850 1.1174

(0.1495) (0.1415) (0.0988) (0.1090) (0.1213) (0.0972) (0.0375) (0.0589) (0.0881) (0.1080) (0.1140) (0.1057) (0.0793) (0.1511) (0.1640)

-0.0657 -0.0267 -0.0051 -0.0039 -0.0036 -0.7949 -0.0110 0.0025 -0.0121 -0.0370 -0.0044 -0.0038 -0.0047 0.6715 0.9703

(0.0132) (0.0113) (0.0091) (0.0083) (0.0109) (0.0133) (0.0024) (0.0041) (0.0073) (0.0091) (0.0098) (0.0090) (0.0068) (0.0241) (0.0202)

-0.0997 -0.0672 -0.0593 -0.0152 0.0188 -0.0915 -0.0569 -0.0684 -0.0963 -0.2402 -0.0619 -0.0683 0.0814 0.6604 0.8247

(0.0424) (0.0477) (0.0288) (0.0429) (0.0395) (0.0252) (0.0489) (0.0342) (0.0306) (0.0349) (0.0372) (0.0334) (0.0325) (0.0330) (0.0381)

-0.1037 -0.0422 -0.0420 -0.0556 -0.0853 0.0057 -0.0327 -0.3971 -0.1357 -0.1233 -0.0262 -0.0215 0.0518 0.8164 1.0077

(0.0315) (0.0340) (0.0215) (0.0296) (0.0290) (0.0192) (0.0150) (0.0288) (0.0220) (0.0255) (0.0271) (0.0245) (0.0228) (0.0258) (0.0295)

-0.0987 -0.0449 -0.0191 0.0150 -0.0734 0.0010 -0.0203 -0.0595 -0.5489 0.0285 -0.0326 0.0028 0.0618 0.6803 0.7884

(0.0255) (0.0248) (0.0175) (0.0196) (0.0225) (0.0166) (0.0066) (0.0108) (0.0225) (0.0192) (0.0204) (0.0187) (0.0156) (0.0252) (0.0277)

-0.1306 -0.0316 0.0128 -0.0665 -0.0473 -0.0143 -0.0308 -0.0282 0.0216 -0.3537 -0.0457 -0.0097 -0.0060 0.5781 0.7299

(0.0192) (0.0183) (0.0133) (0.0144) (0.0169) (0.0128) (0.0047) (0.0078) (0.0119) (0.0203) (0.0153) (0.0140) (0.0115) (0.0188) (0.0217)

-0.0950 -0.0455 -0.0491 -0.0256 -0.0110 -0.0352 -0.0119 -0.0119 -0.0425 -0.0859 -0.7238 -0.0291 -0.0010 0.9755 1.1675

(0.0163) (0.0156) (0.0113) (0.0123) (0.0143) (0.0110) (0.0040) (0.0066) (0.0101) (0.0122) (0.0179) (0.0120) (0.0098) (0.0190) (0.0185)

-0.1705 -0.0208 -0.0226 -0.0446 -0.0615 -0.0782 -0.0222 -0.0238 -0.0417 -0.0918 -0.0871 -0.7196 -0.0463 1.1602 1.4306

(0.0276) (0.0260) (0.0190) (0.0202) (0.0240) (0.0185) (0.0064) (0.0108) (0.0168) (0.0203) (0.0216) (0.0282) (0.0162) (0.0298) (0.0319)

-0.1068 0.1225 -0.0253 -0.0170 -0.0925 -0.0501 0.0239 0.0365 0.0754 -0.0664 -0.0056 -0.0672 -1.0109 1.0424 1.1834

(0.0402) (0.0404) (0.0277) (0.0326) (0.0360) (0.0258) (0.0116) (0.0186) (0.0261) (0.0308) (0.0330) (0.0302) (0.0364) (0.0414) (0.0418)

AIDS = Almost ideal demand system. Numbers in parentheses are standard errors.
Table 5-Demand elasticities derived from the AIDS Model: Case of high-income households

commodity Beef

Price Expenditure

Pork Poultry Other meat Fish Dairy Egg Fat Cereal Bread Vegetables Fruit Juice

Pork

Poultry

Other Meat

Fish

Egg

Fat

Cereal

Bread

Vegetables

Fruit

Juice

-0.4080 -0.0381 -0.0342 -0.0164 -0.0048 -0.0934 -0.0090 -0.0226 -0.0796 -0.1344 -0.0680 -0.0206 -0.0036 0.7417

(0.0479) (0.0306) (0.0250) (0.0237) (0.0315) (0.0250) (0.0061) (0.0121) (0.0194) (0.0263) (0.0270) (0.0261) (0.0199) (0.0417)

-0.0726 -0.6729 -0.0127 -0.0284 -0.0542 -0.0282 -0.0185 -0.0012 -0.0062 -0.1687 -0.0595 0.0184 0.1699

(0.0586) (0.0815) (0.0423) (0.0472) (0.0543) (0.0401) (0.0140) (0.0262) (0.0376) (0.0480) (0.0489) (0.0452) (0.0382)

0.7642

(0.0595)

-0.0910 -0.0268 -0.6632 -0.0793 -0.0928 -0.0121 -0.0193 -0.0188 -0.0346 0.0219 -0.1285 0.0128 -0.0189

(0.0464) (0.0410) (0.0463) (0.0319) (0.0419) (0.0335) (0.0081) (0.0161) (0.0260) (0.0353) (0.0363) (0.0345) (0.0267)

0.9320

(0.0604)

-0.0109 -0.0245 -0.0928 -0.2957 -0.0076 0.0673 -0.0029 -0.0814 0.0517 -0.1453 -0.0501 -0.0341 -0.0010

(0.0719) (0.0749) (0.0522) (0.0862) (0.0677) (0.0487) (0.0193) (0.0357) (0.0484) (0.0608) (0.0619) (0.0561) (0.0492)

0.5275

(0.0675)

-0.0382 -0.0763 -0.1079 -0.0275 -0.2386 -0.0395 0.0067 -0.0772 -0.1705 -0.1463 -0.1112 -0.0477 -0.0798

(0.1935) (0.1830) (0.1345) (0.1433) (0.1655) (0.1305) (0.0421) (0.0775) (0.1127) (0.1508) (0.1526) (0.1431) (0.1072)

0.9331

(0.2119)

-0.0797 -0.0132 0.0083 0.0052 -0.0032 -0.7731 -0.0067 0.0121 -0.0224 -0.0502 -0.0043 -0.0147 -0.0056

(0.0201) (0.0170) (0.0145) (0.0130) (0.0181) (0.0202) (0.0032) (0.0065) (0.0107) (0.0149) (0.0154) (0.0147) (0.0110)

-0.0977 -0.1029 -0.0949 -0.0243 0.0433 -0.0863 -0.0491 -0.0348 -0.1583 -0.2110 -0.0402 -0.1305 0.0212

(0.0639) (0.0764) (0.0457) (0.0666) (0.0606) (0.0412) (0.0726) (0.0564) (0.0500) (0.0588) (0.0588) (0.0511) (0.0503)

-0.0987 -0.0089 -0.0306 -0.1203 -0.1295 0.0425 -0.0136 -0.3652 -0.1231 -0.0810 -0.0602 -0.0391 -0.0042

(0.0464) (0.0528) (0.0334) (0.0454) (0.0440) (0.0305) (0.0208) (0.0460) (0.0347) (0.0419) (0.0421) (0.0369) (0.0351)

-0.1474 -0.0008 -0.0164 0.0249 -0.1390 -0.0383 -0.0289 -0.0579 -0.5373 0.0739 -0.0039 -0.0311 0.0541

(0.0383) (0.0391) (0.0278) (0.0317) (0.0358) (0.0262) (0.0095) (0.0179) (0.0352) (0.0320) (0.0326) (0.0297) (0.0256)

-0.1135 -0.0794 0.0452 -0.0545 -0.0457 -0.0239 -0.0186 -0.0112 0.0517 -0.3989 -0.0020 -0.0101 -0.0116

(0.0285) (0.0274) (0.0206) (0.0219) (0.0264) (0.0198) (0.0062) (0.0119) (0.0176) (0.0324) (0.0236) (0.0217) (0.0180)

-0.0907 -0.0436 -0.0638 -0.0375 -0.0474 -0.0366 -0.0059 -0.0186 -0.0215 -0.0580 -0.7087 -0.0300 0.0037

(0.0241) (0.0230) (0.0175) (0.0184) (0.0223) (0.0169) (0.0051) (0.0099) (0.0148) (0.0195) (0.0272) (0.0184) (0.0151)

-0.0975 -0.0205 -0.0108 -0.0520 -0.0511 -0.1043 -0.0249 -0.0295 -0.0625 -0.1053 -0.0909 -0.7523 -0.0606

(0.0392) (0.0355) (0.0279) (0.0278) (0.0353) (0.0274) (0.0074) (0.0144) (0.0225) (0.0300) (0.0309) (0.0409) (0.0232)

-0.0293 0.2595 -0.0258 -0.0199 -0.1067 -0.0403 0.0048 -0.0049 0.0672 -0.0791 0.0229 -0.0894 -1.0387

(0.0602) (0.0606) (0.0436) (0.0491) (0.0560) (0.0412) (0.0146) (0.0276) (0.0390) (0.0499) (0.0509) (0.0467) (0.0563)

0.6511

(0.0370)

0.8039

(0.0552)

0.8427

(0.0417)

0.7310

(0.0404)

0.5243

(0.0302)

0.9797

(0.0304)

1.1902

(0.0477)

0.9467

(0.0684)

AIDS = Almost ideal demand system. Numbers in parentheses are standard errors.
Table 6-Demand elasticities derived from the AIDS Model: Case of medium-income households

Commodity

Price Expenditure

Beef Pork Poultry Other meat Fish Dairy Egg Fat Cereal Bread Vegetables Fruit Juice

Beef

Pork

Poultry

Other meat

Fish

Dairy

Egg

Fat

Cereal

Bread

Vegetables

Fruit

Juice

-0.2615 -0.0443 -0.0193 -0.0898 -0.0021 -0.0610 -0.0264 -0.0310 -0.0577 -0.1367 -0.0812 -0.1031 -0.0538 0.8016

(0.0530) (0.0357) (0.0261) (0.0272) (0.0320) (0.0274) (0.0097) (0.0134) (0.0232) (0.0275) (0.0293) (0.0267) (0.0213) (0.0416)

-0.0781 -0.6349 -0.0293 -0.0594 -0.0226 -0.0289 -0.0199 -0.0012 -0.0794 -0.0913 -0.0259 0.0474 0.0330

(0.0609) (0.0827) (0.0413) (0.0473) (0.0525) (0.0410) (0.0183) (0.0245) (0.0386) (0.0452) (0.0486) (0.0439) (0.0365)

0.8618

(0.0590)

-0.0417 -0.0348 -0.6317 -0.0323 -0.0752 -0.0115 -0.0087 -0.0280 -0.0439 -0.0256 -0.0320 -0.0210 -0.0006

(0.0529) (0.0490) (0.0499) (0.0370) (0.0437) (0.0380) (0.0129) (0.0180) (0.0316) (0.0377) (0.0402) (0.0367) (0.0290)

0.8536

(0.0651)

-0.2183 -0.0795 -0.0313 -0.2930 0.0165 -0.0067 -0.0022 -0.0226 0.0289 -0.1510 -0.0411 -0.0201 0.0025

(0.0725) (0.0737) (0.0487) (0.0859) (0.0640) (0.0468) (0.0262) (0.0340) (0.0482) (0.0555) (0.0603) (0.0540) (0.0466)

0.6809

(0.0626)

-0.0241 -0.0460 -0.1101 0.0031 -0.4772 -0.0235 -0.0159 -0.0468 -0.0843 -0.2227 0.0336 -0.0710 -0.0269

(0.2739) (0.2627) (0.1777) (0.2045) (0.2168) (0.1829) (0.0810) (0.1051) (0.1646) (0.1975) (0.2102) (0.1904) (0.1442)

0.9086

(0.2785)

-0.0499 -0.0121 -0.0033 -0.0092 -0.0002 -0.8144 -0.0180 -0.0039 -0.0186 -0.0321 0.0174 0.0034 -0.0236

(0.0222) (0.0194) (0.0151) (0.0142) (0.0176) (0.0230) (0.0047) (0.0067) (0.0125) (0.0152) (0.0164) (0.0148) (0.0112)

0.6674

(0.0418)

-0.1795 -0.0735 -0.0177 -0.0020 -0.0279 -0.1368 0.0159 -0.0679 -0.0725 -0.2592 0.0107 -0.0067 0.0946

(0.0778) (0.0861) (0.0512) (0.0792) (0.0718) (0.0471) (0.0886) (0.0589) (0.0564) (0.0636) (0.0701) (0.0609) (0.0581)

0.5622

(0.0606)

-0.1250 -0.0057 -0.0547 -0.0426 -0.0601 -0.0284 -0.0370 -0.3326 -0.1738 -0.1801 -0.0056 -0.0467 0.0608

(0.0509) (0.0545) (0.0338) (0.0485) (0.0461) (0.0315) (0.0279) (0.0447) (0.0358) (0.0407) (0.0447) (0.0391) (0.0360)

0.8507

(0.0421)

-0.0844 -0.0705 -0.0283 0.0188 -0.0409 -0.0189 -0.0178 -0.0747 -0.5244 0.0214 -0.0706 -0.0157 0.0771

(0.0411) (0.0400) (0.0276) (0.0321) (0.0353) (0.0272) (0.0124) (0.0167) (0.0367) (0.0305) (0.0328) (0.0295) (0.0248)

0.7202

(0.0411)

-0.1331 -0.0462 -0.0020 -0.0638 -0.0771 -0.0173 -0.0381 -0.0463 0.0167 -0.3110 -0.0743 -0.0073 0.0107

(0.0315) (0.0304) (0.0213) (0.0240) (0.0270) (0.0213) (0.0091) (0.0124) (0.0198) (0.0332) (0.0252) (0.0226) (0.0186)

0.6400

(0.0312)

-0.1036 -0.0285 -0.0269 -0.0321 0.0084 -0.0132 -0.0060 -0.0064 -0.0629 -0.1050 -0.7436 -0.0378 -0.0205

(0.0271) (0.0266) (0.0184) (0.0212) (0.0234) (0.0185) (0.0082) (0.0110) (0.0173) (0.0204) (0.0301) (0.0196) (0.0164)

0.9778

(0.0320)

-0.2250 0.0214 -0.0401 -0.0384 -0.0548 -0.0516 -0.0114 -0.0318 -0.0524 -0.0730 -0.0910 -0.6614 -0.0335

(0.0464) (0.0446) (0.0313) (0.0351) (0.0390 (0.0316) (0.0131) (0.0178) (0.0288) (0.0342) (0.0366) (0.0469) (0.0271)

1.0877

(0.0500)

-0.1851 0.0516 -0.0085 -0.0111 -0.0301 -0.1113 0.0307 0.0476 0.1154 -0.0064 -0.0579 -0.0432 -0.8997

(0.0666) (0.0670) (0.0448) (0.0548) (0.0584) (0.0434) (0.0226) (0.0296) (0.0437) (0.0506) (0.0550) (0.0489) (0.0591)

0.9868

(0.0680)

AIDS = Almost ideal demand system. Numbers in parentheses are standard errors.
Table 7-Demand elasticities derived from the AIDS model: Case of low-income households

Commodity Price Expenditure

Beef Pork Poultry Other meat Fish Dairy Egg Fat Cereal Bread Vegetables Fruit Juice

Beef

Pork

Poultry

Other meat

Fish

Dairy

Egg

Fat

Cereal

Bread

Vegetables

Fruit

Juice

-0.2929 -0.0679 -0.0125 0.0035 -0.0428 -0.0397 0.0105 -0.0212 -0.0433 -0.1193 -0.0784 -0.0906 -0.0119

(0.0778) (0.0503) (0.0370) (0.0382) (0.0455) (0.0345) (0.0114) (0.0213) (0.0328) (0.0363) (0.0411) (0.0377) (0.0301)

-0.1263 -0.7199 0.0824 -0.0427 0.1383 -0.1034 -0.0018 -0.0691 -0.0947 0.0708 -0.0735 -0.0235 0.0424

(0.0833) (0.1067) (0.0548) (0.0588) (0.0683) (0.0485) (0.0187) (0.0341) (0.0491) (0.0545) (0.0611) (0.0573) (0.0470)

-0.0647 0.0846 -0.5738 -0.0290 -0.0786 -0.0899 -0.0318 -0.0162 -0.0496 -0.0868 -0.1055 -0.0389 -0.0338

(0.0735) (0.0658) (0.0665) (0.0490) (0.0584) (0.0448) (0.0146) (0.0274) (0.0425) (0.0473) (0.0533) (0.0485) (0.0389)

-0.0190 -0.0723 -0.0300 -0.5125 -0.1403 -0.0314 -0.0222 0.0175 -0.0001 -0.1933 0.0046 -0.0105 -0.0105

(0.0954) (0.0887) (0.0616) (0.1017) (0.0803) (0.0518) (0.0264) (0.0445) (0.0560) (0.0627) (0.0703) (0.0671) (0.0578)

-0.1502 0.2350 -0.1071 -0.1626 -0.3638 -0.0688 -0.0135 -0.0981 -0.0706 -0.0683 0.0816 -0.1222 -0.1056

(0.4025) (0.3626) (0.2508) (0.2744) (0.3029) (0.2311) (0.0930) (0.1573) (0.2247) (0.2519) (0.2827) (0.2639) (0.1988)

-0.0611 -0.0605 -0.0316 -0.0107 -0.0203 -0.7818 -0.0088 -0.0017 0.0102 -0.0233 -0.0402 -0.0075 0.0146

(0.0283) (0.0239) (0.0184) (0.0170) (0.0214) (0.0277) (0.0046) (0.0090) (0.0160) (0.0178) (0.0206) (0.0176) (0.0133)

0.0710 -0.0016 -0.0976 -0.0554 -0.0261 -0.0486 -0.1849 -0.0903 -0.0533 -0.2132 -0.1717 -0.0818 0.1100

(0.0828) (0.0822) (0.0535) (0.0770) (0.0750) (0.0409) (0.0979) (0.0605) (0.0502) (0.0563) (0.0628) (0.0635) (0.0612)

-0.1010 -0.1591 -0.0216 0.0276 -0.1234 -0.0020 -0.0483 -0.5094 -0.0935 -0.0893 0.0133 0.0187 0.1006

(0.0783) (0.0759) (0.0507) (0.0657) (0.0685) (0.0405) (0.0307) (0.0640) (0.0471) (0.0527) (0.0590) (0.0581) (0.0530)

-0.0626 -0.0850 -0.0171 0.0170 -0.0294 0.0732 -0.0105 -0.0353 -0.5811 -0.0223 -0.0244 0.0693 0.0139

(0.0588) (0.0532) (0.0383) (0.0402) (0.0475) (0.0349) (0.0124) (0.0229) (0.0483) (0.0382) (0.0430) (0.0394) (0.0320)

-0.1431 0.0705 -0.0309 -0.0849 -0.0176 0.0100 -0.0358 -0.0222 -0.0186 -0.3414 -0.0824 -0.0214 -0.0113

(0.0467) (0.0423) (0.0306) (0.0323) (0.0380) (0.0278) (0.0100, (0.0184) (0.0274) (0.0429) (0.0343) (0.0315) (0.0256)

-0.1227 -0.0628 -0.0547 -0.0061 0.0203 -0.0695 -0.0288 -0.0030 -0.0478 -0.1064 -0.6965 -0.0077 0.0154

(0.0389) (0.0350) (0.0254) (0.0268) (0.0314) (0.0235) (0.0082) (0.0152) (0.0227) (0.0252) (0.0391) (0.0262) (0.0213)

-0.2552 -0.0693 -0.0593 -0.0309 -0.1001 -0.0847 -0.0324 -0.0070 0.0178 -0.1051 -0.0536 -0.6472 -0.0293

(0.0716) (0.0658) (0.0464) (0.0511) (0.0586) (0.0407) (0.0166) (0.0300) (0.0418) (0.0465) (0.0524) (0.0693) (0.0408)

-0.1178 0.0424 -0.0740 -0.0345 -0.1351 -0.0067 0.0380 0.0721 -0.0282 -0.0981 0.0168 -0.0470 -1.0498

(0.0962) (0.0909) (0.0626) (0.0740) (0.0818) (0.0522) (0.0269) (0.0460) (0.0571) (0.0637) (0.0717) (0.0686) (0.0837)

0.6929

(0.0518)

0.8391

(0.0738)

0.9708

(0.0724)

0.8913

(0.0737)

0.8457

(0.3477)

0.7783

(0.0524)

0.7223

(0.0564)

0.8281

(0.0575)

0.6112

(0.0559)

0.6147

(0.0422)

1.0252

(0.0412)

1.2604

(0.0632)

1.2885

(0.0867)

AIDS = Almost ideal demand system. Numbers in parentheses are standard errors.
Table 8-Comparison of own-price, expenditure, and quality elasticities by income groups

Commodity Own-price elasticity Expenditure elasticity Quality elasticity

All Low Medium High CV All Low Medium High CV All Low Medium High CV

sample income income income percent sample income incom e income percent sample incom e income income percent

Beef -0.3540 -0.2929 -0.2615 -0.4080 19.6

(0.0322) (0.0778) (0.0530) (0.0479)

Pork -0.6867 -0.7199 -0.6349 -0.6729 5.1

(0.0510, (0.1067) (0.0827) (0.0815)

Poultry -0.6437 -0.5738 -0.6317 -0.6632 5.9

(0.0299) (0.0665) (0.0499) (0.0463)

0.7368 0.6929 0.8016 0.7417

(0.0250) (0.0518) (0.0416) (0.0417)

6.0

5.1

0.1992 0.1147 0.1680 0.2314

(0.0152) (0.0281) (0.0257) (0.0263)

0.1210 0.0706 0.1051 0.1339

(0.0158) (0.0328) (0.0266) (0.0262)

0.1593

(0.0269)

0.0893

(0.0499)

0.1159

(0.0493)

0.1989

(0.0436)

0.1358

(0.0178)

0.0833

(0.0342)

0.1516

(0.0303)

0.1275

(0.0302)

0.2786

(0.0254)

0.1927

(0.0535)

0.2060

(0.0440)

0.3447

(0.0404)

0.3377

(0.0220)

0.2778

(0.0489)

0.3406

(0.0373)

0.3420

(0.0342)

0.0626

(0.0119)

0.0428

(0.0196)

0.0740

(0.0204)

0.0615

(0.0218)

0.2038

(0.0157)

0.1752

(0.0329)

0.1775

(0.0279)

0.2087

(0.0241)

0.1006

(0.0185)

0.1380

(0.0405)

0.0963

(0.0313)

0.0401

(0.0291)

0.2331

(0.0153)

0.2116

(0.0338)

0.2152

(0.0265)

0.2132

(0.0233)

0.1498

(0.0152)

0.1077

(0.0323)

0.1750

(0.0255)

0.1173

(0.0246)

0.1841 0.1249 0.2047 0.1819

0.1841 0.1249 0.2047 0.1819

(0.0189, (0.0385) (0.0330) (0.0301)

0.0726 0.0677 0.0558 0.0716

(0.0220) (0.0462) (0.0385) (0.0345)

27.8

0.8072 0.8391 0.8618 0.7642 25.1

(0.0356) (0.0738) (0.0590) (0.0595)

0.9003

(0.0369)

0.9708

(0.0724)

0.8536

(0.0651)

0.9320

(0.0604)

Other Meat -0.3554 -0.5125 -0.2930 -0.2957 28.0 0.6662 0.8913 0.6809 0.5275

(0.0518) (0.1017) (0.0859) (0.0862) (0.0381) (0.0737) (0.0626) (0.0675)

Fish -0.3871 -0.3638 -0.4772 -0.2386 27.1 0.8850 0.8457 0.9086 0.9331

(0.1213) (0.3029) (0.2168) (0.1655) (0.1511, (0.3477) (0.2785) (0.2119)

Dairy -0.7949 -0.7818 -0.8144 -0.7731 2. 3 0.6715 0.7783 0.6674 0.6511

(0.0133) (0.0277) (0.0230) (0.0202) (0.0241) (0.0524) (0.0418) (0.0370)

Egg -0.0569 -0.1849 0.0159 -0.0491 115.1

(0.0489) (0.0979) (0.0886) (0.0726)

Fat -0.3971 -0.5094 -0.3326 -0.3652 19.1

(0.0288) (0.0640) (0.0447) (0.0460)

0.6604

(0.0330)

0.7223

(0.0564)

0.5622

(0.0606)

0.8039

(0.0552)

5.3

21.3

34.7

23.4

4.1

8.1

27.7

9.4

14.4

1.1

21.6

0.8164 8.2

(0.0258)

Cereal -0.5489 -0.5811 -0.5244 -0.5373 4.4 0.6803

(0.0225) (0.0483) (0.0367) (0.0352) (0.0252)

Bread -0.3537

(0.0203)

Vegetables -0.7238

(0.0179)

Fruit -0.7196

Fruit -0.7196

(0.0282)

-0.3414

(0.0429)

-0.3110

(0.0332)

-0.3989 10.4

(0.0324)

0.5781

(0.0188)

-0.6965

(0.0391)

-0.7436

(0.0301)

-0.7087 2.8

(0.0272)

0.9755

(0.0190,

0.8281 0.8507

(0.0575) (0.0421)

0.6112 0.7202

(0.0559) (0.0411)

0.6147 0.6400

(0.0422) (0.0312)

1.0252 0.9778

(0.0412) (0.0320)

0.8427

(0.0417)

0.7310

(0.0404)

0.5243

(0.0302)

0.9797

(0.0304)

-0.6472 -0.6614

-0.6472 -0.6614

(0.0693) (0.0469)

-0.7523 6.8

-0.7523 6.8

(0.0409)

43.9

0.7

7.9

8.4

2.2

6.0

6.0

14.2

22.3

1.1602 1.2604 1.0877 1.1902

1.1602 1.2604 1.0877 1.1902

(0.0298) (0.0632) (0.0500) (0.0477)

1.0424 1.2885 0.9868 0.9467

(0.0414) (0.0867) (0.0680) (0.0684)

19.7

19.7

Juice -1.0109

(0.0364)

-1.0498 -0.8997 -1.0387 6. 9

(0.0837) (0.0591) (0.0563)

10.3

Numbers in parentheses are standard errors. The CV (coefficient of variation) measures the degree of variation among the three elasticity estimates.

The CV is calculated as the percentage of standard deviation to its mean in absolute value.
Table 9-Food share of nutrient for low-income households

Nutrient Beef Pork Poultry Other meat Fish Dairy Egg Fat Cereal Bread Vegetables Fruit Juice Total

Energy

Protein

Total fat

Saturated fat

Cholesterol

Carbohydrate

Fiber

Vitamin A

Carotene

Vitamin E

Vitamin c

Thiamin

Riboflavin

Niacin

Vitamin B-6

Folate

Vitamin B-12

Calcium

Phosphorus

Magnesium

Iron

Zinc

Copper

Sodium

Potassium

10.38 7.80 4.86 4.38 1.02 14.13 2.03 13.17 14.30 14.81 8.13 2.89

18.59 8.39 12.29 5.69 4.06 19.06 4.33 0.29 9.25 8.96 7.63 0.79

15.89 13.51 5.91 6.94 0.56 14.64 2.61 27.84 1.80 7.33 2.49 0.36

18.12 13.87 4.75 7.35 0.35 26.34 2.28 18.00 1.20 5.57 1.86 0.26

16.80 8.44 11.43 7.42 2.57 14.95 32.40 2.97 0.24 2.68 0.11 0.00

0.00 0.08 0.05 0.44 0.21 11.23 0.18 0.74 31.46 26.28 16.43 7.64

0.00 0.01 0.01 0.07 0.09 0.53 0.00 0.08 23.27 16.89 45.82 11.69

0.00 0.02 2.10 7.28 0.18 11.07 2.59 9.66 11.93 1.02 48.60 3.82

0.00 0.00 0.00 0.10 0.00 3.61 0.01 3.49 0.23 0.97 82.17 6.46

1.50 1.42 1.71 1.02 1.31 6.42 2.49 47.53 11.45 8.48 12.21 3.61

0.17 2.37 0.71 4.77 0.09 4.11 0.00 0.03 7.93 0.19 36.18 17.28

2.27 11.00 1.43 3.62 0.63 8.57 0.89 0.14 33.56 21.28 10.06 2.63

6.80 3.96 3.65 4.93 0.88 30.09 6.47 0.35 21.24 12.70 5.98 1.95

13.50 6.99 12.50 5.43 3.48 2.22 0.09 0.02 28.53 14.48 10.08 1.54

7.80 5.80 8.22 3.62 1.84 9.02 2.09 1.32 25.19 3.85 19.71 8.48

1.82 0.51 2.18 3.51 0.55 8.35 3.96 0.34 28.14 10.82 27.43 4.33

26.65 5.09 3.97 21.18 6.54 21.39 3.69 0.58 10.37 0.53 0.01 0.00

0.79 0.49 0.78 0.95 1.06 63.06 1.68 0.75 9.90 10.75 7.24 1.52

10.51 5.05 5.41 1.81 2.42 43.77 4.20 0.00 14.54 7.77 4.39 0.00

5.94 2.51 3.63 1.76 2.25 21.15 1.19 0.23 18.01 12.27 22.39 4.88

10.02 2.32 3.83 4.08 1.18 3.37 2.66 0.30 38.00 17.47 13.75 1.55

28.30 6.78 7.49 6.43 1.33 17.30 2.70 0.18 13.50 6.07 8.64 0.79

5.62 2.91 2.91 7.60 1.52 5.44 0.37 0.14 17.22 15.34 31.11 5.59

2.70 9.24 1.86 12.53 1.85 14.64 1.53 9.59 13.78 21.15 10.21 0.08

8.31 3.99 3.51 2.65 1.97 22.48 1.35 0.37 5.32 4.97 31.17 7.49

Percent

2.10

0.68

0.13

0.05

0.00

5.27

1.54

1.73

2.95

0.85

26.18

3.92

1.00

1.12

3.08

8.05

0.00

1.04

0.14

3.78

1.48

0.49

4.21

0.83

6.41

100

100

100

100

100

100

100

100

100

100

100

100

100

100

100

100

100

100

100

100

100

100

100

100

100

Source: Nationwide Food Consumption Survey 1987-88, USDA.
Table 10-Nutrient elasticities with respect to food expenditure and food stamp

benefit for low-income households

Food expenditure Food stamp benefit

Nutrien t Unadjuste d Adjuste d Unadjuste d Adjuste d

Calorie s 0.99 0 0.804 0.0534 0.0434

Protei n 0.98 1 0.788 0.0530 0.042 5

Total fat 0.96 1 0.772 0.0519 0.0417

Sat. fat 0.960 0.76 5 0.0519 0.0413

Sat. fa t 0.96 0 0.76 5 0.0519 0.0413

Cholestero l 0.893 0.708 0.0482 0.0382

Carbohydrat e 1.03 4 0.85 7 0.0559 0.0463

Fibe r 1.11 6 0.926 0.0603 0.0500

Vitamin A 1.07 5 0.892 0.0580 0.0482

Caroten e 1.16 4 0.97 1 0.0629 0.052 5

Vitamin B 0.992 0.827 0.0536 0.0447

Vitamin C 1.177 0.98 5 0.0636 0.0532

Vitamin C 1.177 0.985 0.0636 0.0532

Thiami n 1.00 5 0.817 0.0543 0.044 1

Riboflavi n 0.967 0.784 0.0522 0.0424

Niaci n 1.01 8 0.826 0.0549 0.0446

Vitamin B6 1.073 0.876 0.0580 0.0473

Folat e 1.059 0.87 9 0.0572 0.0474

Vitamin B1 2 0.958 0.767 0.0517 0.0414

Calciu m 0.94 5 0.770 0.0510 0.0416

Phosphat e 0.958 0.773 0.0518 0.041 8

Magnesia n 1.034 0.849 0.0558 0.0458

Iro n 1.023 0.839 0.0552 0.0453

Zin c 1.014 0.814 0.0547 0.0439

Coope r 1.052 0.866 0.0568 0.046 8

Sodiu m 0.943 0.76 5 0.0509 0.0413

Potassiu m 1.068 0.875 0.0576 0.0473

Note: This table contains nutrient expenditure elasticities with respect to food expenditure or food stamp benefit.

In each case, the elasticities with adjusted and unadjusted food quality effects are reported.
United States Department of Agriculture

Economic Research Service

1800 M Street, NW

Washington, DC 20036-5831

http://www.ers.usda.gov