United States 

Department of 

Agriculture

Economic

Research

Service

Abigail M. Okrent and Julian M. Alston

The Demand for Disaggregated FoodAway-From-Home and Food-at-Home 

Products in the United States

Economic 

Research 

Report 

Number 139

August 2012
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Recommended citation format for this publication:

Okrent, Abigail M., and Julian M. Alston. The Demand for Disaggregated 

Food-Away-From-Home and Food-at-Home Products in the United States,

ERR-139, U.S. Department of Agriculture, Economic Research Service, 

August 2012. 
United States

Department

of Agriculture

www.ers.usda.gov

A Report from the Economic Research Service

Abstract

Food away from home (FAFH) comprises nearly half of all U.S. consumer food expenditures. Hence, policies designed to influence nutritional outcomes would be incomplete if 

they did not address the role of FAFH. However, because of data limitations, most studies 

of the response of food demand to policy changes have ignored the role of FAFH, and 

those studies that have included FAFH have treated it as a single good. We, therefore, 

estimate demand for 43 disaggregated FAFH and food-at-home (FAH) products, using a 

2-stage budgeting framework. We find that the demands for disaggregated FAFH products 

differ in price responsiveness and tend to be more sensitive to changes in food spending 

patterns than FAH products. Many foods are found to have statistically significant substitution and complementary relationships within and among food groups. Predicted changes 

in quantities based on our estimates that include all goods and services and those estimates 

that include only a subset of foods differ substantially, implying that evaluations of health 

and nutrition policy based on elasticities of demand for only a subset of goods may be 

misleading.

Keywords: Food demand, food away from home (FAFH), demand systems, elasticities.

Acknowledgments

The authors are grateful for comments and suggestions made by Sharon Shewmake from 

Vanderbilt University, colleagues from the Economic Research Service of USDA including 

Abebayehu Tegene, Ephraim Leibtag and Laurian Unnevehr, participants at an Agricultural 

Economics Workshop at North Carolina State University, and three anonymous reviewers, 

which substantially improved this manuscript. We also are thankful to Dale Simms for 

editing the manuscript and Curtia Taylor for design and layout.

Abigail M. Okrent, aokrent@ers.usda.gov

Julian M. Alston

The Demand for Disaggregated FoodAway-From-Home and Food-at-Home 

Products in the United States

Economic 

Research 

Report

Number 139

August 2012
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Contents

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

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

Previous Research on Modeling Demand 

for Food Away From Home . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

Estimation Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

New Estimates of Demand for Disaggregated 

Food-Away-From-Home and Food-At-Home Products . . . . . . . . . . . . 13

First-Stage Estimates of Demand Elasticities 

for Composite Goods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

Conditional Elasticities of Demand for Disaggregated 

Food Products . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

Unconditional Elasticities of Demand for 

Disaggregated Food Products . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

Potential Policy Implications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

Appendix Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

Technical Appendix of Derivations of the Generalized 

Ordinary Differential Demand System (GODDS) . . . . . . . . . . . . . . . . 61
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Summary

What Is the Issue?

Food away from home (FAFH, including limited-service and full-service 

restaurants) constitutes a large and growing portion of the food budget: in 

2009, the annual average household expenditure on FAFH was $2,619, or 

approximately 41 percent of the food budget for an average U.S. household, compared with $1,320, or approximately 29 percent of the food 

budget in 1984. Because FAFH comprises a sizable share of total food 

expenditures and nutritional intake for an average American, disregarding 

the relationships between FAFH and any other subset of foods may produce 

misleading results for formulating nutrition and health policy. Many studies 

have excluded or inadequately represented FAFH, such that the estimates 

only partially capture the effects of policy-induced food price changes on 

consumer demand and nutrition.

Those analyses that included all goods and services treated FAFH as a 

composite good, but disaggregated products in FAFH might differ from 

one another in terms of responsiveness to price- and income-led expenditure changes, nutritional characteristics, or both. Little is known about how 

demands for different types of FAFH respond to price changes, but a handful 

of studies have found that demand responds to changes in income differently 

for full-service food than it does for limited-service food. 

What Did the Study Find?

Statistically significant cross-price relationships exist between and within 

groups of foods. Evidence suggests that demands for FAFH products differ 

from demands for food-at-home (FAH) products. Further, FAFH products 

differ among one another in their nutritional characteristics, quality, and 

responsiveness to changes in prices and expenditure. Specific findings related 

to cross-price relationships and consumer demand for FAFH include: 

•	 The demands for disaggregated FAFH products tend to be more sensitive

to income-induced changes in total expenditures than are FAH products. This finding may explain why the budget share for FAFH products 

dipped during the recent recession, while the budget shares for many 

FAH products increased. During December 2007-June 2009, monthly 

total expenditures fell 0.51 percent for the average American. In addition, 

the prices of most FAH products, which are mostly gross substitutes for 

FAFH products, fell relative to the prices of the FAFH products. Hence, 

income-induced changes in total expenditures and the relative affordability of FAH versus FAFH products caused demand for FAFH to fall.

•	 The demand for full-service FAFH responds much more readily to price

changes than does the demand for limited-service FAFH and other FAFH 

(including vending machines, mobile food vendors, and school and 

employee sites). 
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•	 Compared with the demands for foods commonly deemed “unhealthy”

(e.g., cheese, white bread, cakes and cookies, frozen foods), the demands 

for many products commonly deemed “healthy” (fruits and vegetables,

nonwhite bread, fish, and seafood) tend to be much less responsive to 

price changes. For example, the demand for nonwhite bread is much 

less price-elastic than the demand for white bread, and the demand for 

cookies and cakes is one of the most price-elastic. 

•	 Many of these “healthy” and “unhealthy” foods show statistically significant substitution and complementary relationships within and among 

food groups—a finding that complicates any analysis trying to predict the 

effects of policy-induced price changes on food demands and nutritional 

outcomes. 

•	 Using forecasts of price and total expenditure changes between 2011 and

2012 to predict food consumption changes over the same span, we found 

that predictions based on estimates of (conditional) demand elasticities 

that ignore the total effects of substitutions and complementarities differ 

substantially—sometimes even taking opposite signs—from predictions 

based on estimates of (unconditional) demand elasticities that include 

all goods and services. For example, consumption of each disaggregated 

dairy product was predicted to increase approximately 0.5-1 percent in 

2012 when using unconditional demand elasticities, but to decrease a 

similar amount according to conditional elasticities. Similar contradictions in forecast changes in consumption between the two sets of demand 

elasticities are found for pork, poultry, eggs, sugar and sweets, and frozen 

foods.

•	 The substantial cross-price relationships between products in different

groups suggest that nutrition policy analysis based on demand elasticities 

for small groups of products is likely to be misleading. 

How Was the Study Conducted?

Using the 1998–2010 Consumer Expenditure Survey diary section, we 

constructed a monthly time series of household expenditures by aggregating 

detailed weekly expenditure data into 43 products (i.e., 3 FAFH products, 

38 FAH products, alcoholic beverages, and a nonfood composite), and then 

averaged these data over households for a given month. We then matched the 

average monthly expenditures to monthly consumer price indices. 

We estimated demand for the 43 products using 2-stage budgeting, where the 

representative consumer allocates expenditures for market goods and services 

to groups of goods in the first stage, and then chooses products within each 

group of goods in the second stage. First, we estimated demand for eight 

food groups (cereals and bakery products, dairy, meat and eggs, fruits and 

vegetables, nonalcoholic beverages, other FAH, and FAFH/alcoholic beverages), and a nonfood composite good. Second, we modeled the second-stage 

allocation of expenditures on the eight food groups as weakly separable 

groups—a structure that allowed us to estimate demand for goods in a given 

group without considering demand for goods in other groups. 
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Using demand elasticity estimates from the first- and second-stage allocations, we approximated “unconditional” demand elasticities, which consider

the total expenditure for all goods and services. We then computed the 

changes in food quantities implied by forecasted changes in prices and 

personal consumption expenditures between 2011 and 2012. The computation used the two sets of demand elasticities and compared the simulated 

changes to show the influence of intergroup substitution on measures of 

changes in total nutritional intake.
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Introduction

Food away from home (FAFH) is a sizable component of total food 

consumption and the nutritional intake of U.S. adults and children. FAFH 

also, therefore, constitutes a large and growing portion of the food budget: 

in 2009, the annual average household expenditure on FAFH was $2,619, or 

approximately 41 percent of the food budget for an average U.S. household, 

compared with $1,320, or approximately 29 percent of the food budget in 

1984 (U.S. Department of Labor, Bureau of Labor Statistics, 2010a).

Recent findings suggest that FAFH may contribute significantly to obesity 

and poor dietary quality in the United States. Several studies have found 

that the nutritional content of FAFH is poor compared with food consumed 

at home (FAH) (Lin, Guthrie, and Frazao, 1999; Jeffrey et al., 2006; Todd, 

Mancino, and Lin, 2010). In addition, some types of FAFH (e.g., limitedservice FAFH, vending machines, and lunch trucks) may be nutritionally 

worse than others.1 Consumer proximity to limited-service restaurants—

especially proximity to dense concentrations of limited-service restaurants—has been found to contribute to obesity (Chou, Grossman, and Saffer, 

2004; Davis and Carpenter, 2009; Currie et al., 2010). Conversely, Binkley 

(2008) found that—although food from limited-service restaurants tended 

to be more energy-dense and nutritionally inferior to food from full-service 

restaurants—meals from limited-service restaurants tended to be smaller. On 

the whole, the evidence suggests that consuming FAFH may have dramatic 

effects on dietary quality and body weight and that different types of FAFH 

may affect dietary quality and individual body weight differently. 

Given the potential significance of FAFH for dietary quality and nutrition, 

policies designed to influence nutritional outcomes should address the role 

of FAFH. However, because most studies of the response of food demand 

to policy changes have disregarded the role of FAFH, the estimates from 

these studies incompletely reflect changes in food consumption and nutrition 

resulting from the policy changes. Those studies that included FAFH treated 

it as a single good, but evidence suggests that FAFH products are heterogeneous in their nutritional characteristics and quality and in how they respond 

to changes in prices and expenditures. 

Some studies have analyzed the relationships between the demands for disaggregated FAFH products and total expenditure or income (i.e., Engel curve 

analysis), but little is known about the effects of either prices or total expenditure on the demand for disaggregated FAFH products. Only a handful of 

studies have estimated the effect of price and total expenditure on demand 

for FAFH as a composite group; to our knowledge, estimates of the effects 

of prices and total expenditure on demand for disaggregated FAFH have not 

been published before now. In addition, demand studies that included FAFH 

as a composite also included fairly aggregated groups of FAH products, 

whereas some economists have argued that more disaggregated products in 

terms of “healthy” and “unhealthy” foods would be more useful for policy

analysis (Andreyeva, Long, and Brownell, 2009). 

1 Throughout this study, the different 

types of FAFH are defined by establishment type. Full-service FAFH 

are establishments that provide food 

services to patrons who order and 

are served while seated (i.e., waiter/

waitress service) and pay after eating. 

Limited-service FAFH are establishments primarily engaged in providing 

food services (except snack and nonalcoholic beverage bars) where patrons 

generally order or select items and pay 

before eating.
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In this study, we estimate the demand for disaggregated FAFH and FAH 

products— including 38 FAH products, 3 FAFH products, alcoholic beverages, and nonfood—as elements of an unconditional system of demand 

equations in a two-stage budgeting process. We find statistically significant 

cross-price relationships, between and within groups of foods, using the 

first- and second-stage estimates—a finding that underscores the potential 

usefulness of considering all foods, not just a subset of foods, in evaluating 

policies targeting nutrition and health outcomes. Using estimates of demand 

elasticities from the first and second stages, we approximate unconditional 

elasticities of demand. In particular, we find that demand for full-service 

FAFH differs from its first-stage aggregate: FAFH and alcoholic beverages. 

Also, demands within the group comprising FAFH and alcoholic beverages 

differ from each other. Likewise, compared with demand for “healthy” foods,

demand for foods commonly deemed “unhealthy” respond differently to

own-price changes. Using the unconditional and conditional sets of demand 

elasticities, we compute predicted changes in consumption of foods implied 

by forecasts of price changes between 2011 in 2012, compare the results, and 

discuss the policy implications of basing analysis on estimates derived from 

conditional versus unconditional demand systems.
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Previous Research on Modeling Demand for Food 

Away From Home

In a recent review of the economic literature on the demand for food, Okrent 

and Alston (2011) found that—in the handful of studies that have estimated 

the demand for FAFH—FAFH was always treated as a composite food. 

The earliest studies of food demand that included FAFH as composite good 

included fairly aggregated foods in other categories as well (Barnes and 

Gillingham, 1984; Craven and Haidacher, 1987; Nayga and Capps, 1992). 

Later studies that included disaggregated FAH products and FAFH used 

fairly restrictive demand systems, which may poorly approximate the actual 

process that generated the data (Park et al., 1996; Raper et al., 2002).2

Piggott (2003); Reed, Levedahl, and Hallahan (2005); and Okrent and Alston 

(2011) used flexible demand systems with time-series data to estimate 

demand for FAFH and FAH products in complete demand systems. Piggott 

(2003) estimated demand for FAH, FAFH, and alcoholic beverages using the 

nested price independent generalized logarithmic (PIGLOG) demand system 

and annual data from 1969 to 1999 (i.e., USDA expenditures matched to the 

Consumer Price Index (CPI)). The nested PIGLOG is very flexible, nesting 

popular models of demand such as the almost ideal demand system (Deaton 

and Muellbauer, 1980a) and the indirect translog (Christensen, Jorgenson, 

and Lau, 1975), as well as globally flexible versions of these models. But 

again, the estimates of demand elasticities for these three food and beverage 

groups may be too aggregated to be useful in studies of nutrition policy. 

Reed, Levedahl, and Hallahan (2005) presented estimates of demand elasticities for an FAFH composite, six FAH products, and a nonfood composite 

using the semiflexible almost ideal demand system (Moschini, 1998) and 

the Consumer Expenditure Survey (CEX) aggregated into a quarterly time 

series matched to the CPI. However, the demands for all of the goods were 

found to have quite large income elasticities (all in the elastic range), which 

violates Engel’s law. Okrent and Alston (2011) argued that—because unit 

roots were detected in the logarithmic transformations of the price indexes 

and budget shares used in their analysis—a differential-demand systems 

model would be appropriate for modeling demand using those data. They 

modeled demand for FAFH, alcoholic beverages, eight FAH products, and 

a nonfood composite using Barten’s synthetic model (Barten, 1993; Brown, 

Lee, and Seale, 1994), which nests four differential-demand systems (i.e., the 

Rotterdam, National Bureau of Research (NBR), Central Bureau of Statistics 

(CBS), and differenced linear almost ideal demand system). All of these 

studies treat FAFH as a single composite good, although the effects of prices 

and expenditure may differ among individual FAFH products.

A few studies analyzed the relationship between demand for disaggregated 

FAFH products and income or total expenditure, assuming that the price of 

food from limited-service restaurants relative to food from full-service restaurants would be the same across households. Using different data sets, Byrne, 

Capps, and Saha (1998) and Stewart et al. (2004) found that income, household size, and labor force participation were statistically significant determinants of expenditure on FAFH for various establishment types. However, to 

our knowledge, no study before this one has evaluated the effects of changes 

in prices and total expenditure on demands for disaggregated FAFH products.

2For the compensated law of demand 

to hold using the LES, all goods must 

be normal and substitutes for each 

other. The linear expenditure system 

(LES) also implies that Engel curves 

are linear. Last, the own-price elasticity 

of demand for each food is approximately proportional to its demand elasticity with respect to total expenditure 

(Deaton and Muellbauer, 1980b, p. 66).
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Data

Like Reed, Levedahl, and Hallahan (2005) and Okrent and Alston (2011), we 

use the Consumer Expenditure Survey (CEX) paired with CPIs to estimate 

the demands for disaggregated FAFH and FAH products, alcoholic beverages, and nonfood. The CEX is a nationwide household survey administered 

every year since 1984 and designed to represent the total U.S. civilian noninstitutionalized population. The CEX consists of two surveys: a diary survey 

and a quarterly interview survey. The diary survey collects detailed data on 

expenditures for frequently purchased items, such as food and apparel, while 

the interview survey obtains detailed data on expenditures for infrequently 

purchased items, such as property, automobiles, and major appliances, and on 

recurring expenses, such as rent, utilities, and insurance premiums. The diary 

survey collects detailed data on FAH and FAFH expenditures for a 2-week 

period. The interview survey contains data on expenditures on aggregate 

food categories, such as FAH and FAFH (U.S. Department of Labor, Bureau 

of Labor Statistics, 2010b). 

The CEX diary data are from cross-sections of households and can be aggregated to construct a weekly, monthly, quarterly, or annual time series of 

average expenditures per consuming unit. Because the CPIs are available 

monthly and annually, we aggregated the CEX diary data to create a monthly 

series. When consuming units reported expenditures for a week that straddled 

2 months, those expenditures were assigned to the month that included 4 or 

more of the days in question. Households that did not report purchasing a 

particular food were assigned a zero. To extrapolate the sample observations 

to the population, we applied the sample weights calculated by the Bureau of 

Labor Statistics (BLS). The CEX public microdata are available from 1980 

through 2010, but we used a subset of the data since it was only in 1998 that 

the CEX began publishing detailed data on FAFH (specifically, food from 

limited-service restaurants, full-service restaurants, vending machines and 

lunch trucks, employee and school sites, and catered affairs).3

We constructed the budget shares as expenditure for each food group divided 

by total expenditures on all goods and services for the first stage, and as 

expenditure for each disaggregated food product divided by expenditures for 

its group for the second stage (table 1). On average, for 1998-2010, nonfood 

constituted the largest share of the budget for all goods and services at 81 

percent, followed by FAFH and alcoholic beverages (8 percent), meat and 

eggs (3 percent), and other FAH (3 percent). Within the FAFH and alcohol 

category, food from limited-service and full-service restaurants constituted 

about 41 percent and 37 percent, respectively, although the average monthly 

share of limited-service FAFH, within FAFH and alcohol, declined over the 

entire period (a linear trend of -0.09 percent per month), while the share of 

full-service FAFH increased (a linear trend of 0.14 percent per month). Other 

FAFH—which includes food from vending machines and mobile vendors, as 

well as employee and school sites—constitutes about 7 percent of the expenditure on FAFH and alcohol, and this share has declined by 0.24 percent 

per month, on average. Expenditure on all of the disaggregated FAFH and 

alcohol products declined relative to expenditure on total goods and services 

during the most recent recession (December 2007-June 2009). This finding 

contrasts starkly with the data on most FAH products, for which expenditure 

3Expenditures on food from catered 

affairs are inconsistent between 1998 

and 2009 in that between 2005 and 

2009, no expenditures on food from 

catered affairs were reported. Hence, 

we exclude catered food from our 

analysis.
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Table 1

Summary statistics and trends for budget shares and prices

Budget shares (%) Consumer price indexes (Jan. 1999=100)

Meana

Std. 

dev.

Avg. monthly growth (%)b

Meana

Std. 

dev.

Avg. monthly real growth (%)c

Jan. 98 - 

Dec. 10

Dec. 07 - 

June 09

Jan. 98 - 

Dec. 10

Dec. 07 - 

June 09

Cereals/bakery 1.66 0.21 -0.12 0.51 114.71 12.90 0.23 0.02

Flour, flour mixes 4.40 0.77 -0.23 1.56 113.84 15.68 0.27 0.05

Breakfast cereals 19.01 1.51 -0.20 0.43 105.40 4.05 0.07 -0.14

Rice, pasta 10.18 1.24 -0.09 1.30 115.89 18.92 0.30 0.09

Non-white bread 11.26 1.01 0.04 0.20 123.93 20.96 0.35 0.14

White bread 7.69 0.73 -0.23 -0.38 122.75 19.73 0.33 0.12

Biscuits, rolls, muffins 9.15 0.87 -0.02 0.52 120.15 17.28 0.30 0.09

Cakes, cookies 17.91 1.62 -0.17 -0.18 113.74 12.60 0.23 0.02

Other bakery products 20.41 1.86 -0.04 -0.02 114.29 10.91 0.20 -0.01

Dairy 1.21 0.11 -0.01 0.03 110.68 11.02 0.28 0.07

Cheese 31.66 2.20 0.07 0.20 111.71 11.53 0.38 0.16

Frozen dairy desserts 17.35 3.00 -0.17 0.32 107.68 7.55 0.18 -0.04

Milk 36.74 2.32 -0.08 -0.94 110.70 13.04 0.22 0.00

Other dairy 14.25 2.15 0.24 0.21 112.11 11.09 0.21 -0.01

Meat and eggs 2.88 0.38 -0.16 0.41 126.17 16.18 0.21 -0.01

Beef 29.09 2.37 -0.22 0.00 135.30 22.95 0.33 0.12

Pork 20.23 1.53 -0.21 0.44 119.61 9.97 0.21 -0.01

Other red meat 13.03 1.19 -0.09 0.00 116.34 11.56 0.21 0.00

Poultry 18.11 1.62 -0.17 0.21 112.85 10.78 0.14 -0.07

Fish 14.75 1.50 -0.07 0.35 111.67 11.51 0.22 0.01

Eggs 4.80 0.77 0.06 0.07 116.70 22.64 0.21 0.00

Fruits and vegetables 1.69 0.19 0.06 0.40 113.57 13.54 0.26 0.04

Apples 6.99 1.14 0.01 -0.29 131.99 22.25 0.33 0.12

Bananas 6.57 0.86 -0.11 0.52 110.56 10.99 0.17 -0.04

Citrus 7.84 1.27 0.13 0.34 128.36 25.40 0.36 0.15

Other fresh fruit 17.59 4.90 0.21 -0.29 95.53 11.49 0.18 -0.04

Potatoes 6.64 0.78 0.00 0.61 134.29 26.39 0.40 0.19

Lettuce 4.88 0.39 0.07 0.30 122.06 16.24 0.21 0.00

Tomatoes 6.95 0.75 0.05 -0.37 93.78 15.53 0.27 0.06

Other fresh vegetables 19.43 1.28 0.08 0.14 118.92 15.52 0.28 0.06

Proc. fruits, vegetables 23.10 2.93 0.06 0.69 115.85 14.63 0.26 0.05

--continued
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Table 1

Summary statistics and trends for budget shares and prices--continued

Budget shares (%) Consumer price indexes (Jan. 1999=100)

Meana

Std. 

dev.

Avg. monthly growth (%)b

Meana

Std. 

dev.

Avg. monthly real growth (%)c

Jan. 98 - 

Dec. 10

Dec. 07 - 

June 09

Jan. 98 - 

Dec. 10

Dec. 07 - 

June 09

Nonalcoholic beverages 0.75 0.09 -0.10 0.53 109.10 7.63 0.14 -0.07

Coffee, tea 17.44 2.42 -0.19 0.18 104.68 10.56 0.19 -0.02

Carbonated beverages 35.07 3.85 -0.88 0.11 113.09 10.40 0.27 0.06

Noncarbonated 

beverages 45.20 3.66 0.15 -0.63 106.09 5.53 0.11 -0.11

Frozen beverages 2.29 1.10 0.20 0.53 115.02 15.95 0.16 -0.06

Other FAH 2.76 0.34 0.14 0.53 109.81 8.57 0.16 -0.05

Sugar, sweets 18.75 3.28 -0.05 0.44 111.27 10.79 0.20 -0.01

Fats, oils 16.81 1.86 -0.03 0.53 111.73 12.90 0.23 0.02

Soups 5.93 1.16 0.02 0.72 110.46 6.99 0.13 -0.09

Frozen meals 17.15 1.80 0.26 0.23 104.86 4.74 0.09 -0.12

Snacks 3.73 0.39 0.11 0.44 113.16 11.63 0.21 0.00

Condiments, sauces, 

season.

15.26 1.14 0.15 0.69 108.56 7.76 0.15 -0.07

Miscellaneous FAH 22.37 3.54 0.41 0.16 107.74 5.84 0.11 -0.10

FAFH and alcohol 8.38 0.75 0.00 0.00 116.41 12.92 0.24 0.03

Alcohol 15.55 2.06 0.05 -0.05 110.90 11.44 0.22 0.01

Full service 37.34 2.71 0.14 -0.22 116.29 12.68 0.24 0.02

Limited FAFH 40.61 3.13 -0.09 -0.24 115.55 11.51 0.25 0.04

Other FAFH 6.51 1.67 -0.24 -0.23 109.71 10.29 0.17 -0.05

Nonfood 80.67 1.58 0.00 -0.06 116.43 11.14 0.21 0.00

Sources: U.S. Department of Labor, BLS, Consumer Expenditure Survey (2010a/b). 

Notes: Foods in the first stage are highlighted. 

FAFH = Food away from home, including limited-service and full-service restaurants.

FAH = Food-at-home. 

a The mean expenditure shares for the disaggregated products are conditional on the group expenditure. 

b The average monthly growth rate in the expenditures for the food as a share of total expenditures on goods and services (price) is the coefficient on a linear trend in the ordinary least squares (OLS) regression of the logarithmic transformation of the budget share (price) on the linear 

trend and a constant. 

c The real price is the price index for a particular food divided by the consumer price index for all items.

increased as a share of total goods and services during the recession, with the 

exception of some fruits and vegetables (i.e., bananas, other fresh fruit, and 

tomatoes), some cereals and bakery products (i.e., white bread, cakes and 

cookies, and other bakery products), and milk.

The budget shares for all foods exhibit considerable month-to-month variation. Expenditure on limited-service FAFH decreased from about 4 percent 

to 3 percent of the total budget for all goods and services of an average 

household between 1998 and 2010 (fig. 1). Conversely, the share of the 

total expenditures for goods and services spent on full-service FAFH grew 
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between 1998 and 2007, but fell thereafter. Expenditures on the FAH products with the largest budget shares likewise seemed to reflect the recession’s 

influence, declining as a share of the total budget on goods and services until 

2006, and then increasing thereafter (fig. 2). In contrast, the share of total 

expenditure on other FAH—which consists of sugar and sweets; fats and oils; 

soups; frozen foods; and condiments, sauces, and gravies—was unaffected 

by the recession, remaining flat until 2004 and then growing, unabated.

Most of the food groups in our analysis correspond directly to one of the 

CPIs. However, two of the food groups—other FAFH and FAFH/alcoholic 

beverages—correspond to more than one CPI (U.S. Department of Labor, 

Bureau of Labor Statistics, 2010c). We constructed a composite price index 

for each of these food groups as a harmonic mean of disaggregated price 

indexes, each weighted by its first- or second-stage expenditure share. All 

price indexes are scaled to be equal to 100 in January 1999. 

The price indexes for limited-service and full-service FAFH deflated by 

the CPI for all items seem to track each other, although the commodity 

price shocks in 2007 and 2008 had a much bigger impact on limited-service 

FAFH than on full-service FAFH (fig. 3). The growth in both of these real 

price series is fairly flat until 2008. On the other hand, the real price of other 

FAFH generally declined until 2008. Of the four products, the real price for 

alcoholic beverages exhibits the most price variation from month to month, 

but does not seem to trend up or down over the sample period. Compared to 

the deflated prices of FAFH, the deflated FAH prices decreased dramatically 

after the commodity price shocks in 2008 (fig. 4).

Note: FAFH = Food away from home, including limited-service and full-service restaurants

Source: Authors’ calculations using the Consumer Expenditure Survey (Department of Labor, Bureau of Labor Statistics, 2010a) 

and the Consumer Price Indexes (Department of Labor, Bureau of Labor Statistics, 2010c).

Figure 1

Monthly household budget expenditures for FAFH and alcohol products as a share of total expenditures 

on goods and services, 1998-2010

Budget shares (percentages)

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010

Limited service Full service Other FAFH Alcoholic beverages
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0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010

Note: FAH = Food at home

Source: Authors’ calculations using the Consumer Expenditure Survey (U.S. Department of Labor, BLS, 2010a) and the Consumer 

Price Indexes (U.S. Department of Labor, BLS, 2010c).

Figure 2

Monthly household budget expenditures for selected FAH products as a share of total expenditures 

on goods and services, 1998-2010

Budget shares (percentages)

Cereals and bakery products Dairy Meat and eggs Fruits and vegetables Other FAH

Note: FAFH = Food away from home, including limited-service and full-service restaurants

Source: Authors’ calculations using the Consumer Expenditure Survey (U.S. Department of Labor, BLS, 2010a) and the Consumer 

Price Indexes (U.S. Department of Labor, BLS, 2010c).

Figure 3

Real prices for disaggregated FAFH and alcohol products, 1998-2010

Price index (100=Jan1999)

85

90

95

100

105

110

1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010

Limited service Full service Other FAFH Alcoholic beverages
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Note: FAH = Food at home

Source: Authors’ calculations using the Consumer Expenditure Survey (U.S. Department of Labor, BLS, 2010a) and the 

Consumer Price Indexes (U.S. Department of Labor, BLS, 2010c).

Figure 4

Real prices for selected FAH products, 1998-2010

Price index (100=Jan1999)

80

85

90

95

100

105

110

115

1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010

Cereals and 

bakery products

Meat and eggs Dairy Fruits and 

vegetables

Other FAH
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Figure 5

Food products within the two-stage budgeting framework

Notes: FAFH = Food away from home, including limited-service and full-service restaurants

FAH = Food-at-home 

Demand for market goods and services assumed to be separable from demand decisions about leisure and savings.

Cereals and 

bakery

Flour, flour 

mixes

Breakfast 

cereals

Rice, pasta

Nonwhite

bread

White bread

Biscuits, 

rolls, 

muffins

Cakes, 

cookies

Other 

bakery

Meat and 

eggs

Beef

Pork

Other red 

meat

Poultry

Fish

Eggs

Dairy

Cheese

Milk

Ice cream, 

frozen 

desserts

Other

dairy

Fruits and 

vegetables

Apples

Bananas

Citrus

Other fresh 

fruits

Lettuce

Tomatoes

Potatoes

Other fresh 

vegetables

Processed 

fruits and 

vegetables

Nonalcoholic 

beverages

Coffee and 

tea

Carbonated 

beverages

Noncarbonated 

beverages

Frozen 

beverages

Other FAH

Sugar and 

sweets

Fats and 

oils

Soups

Snacks

Frozen 

foods

Condiments, 

sauces, 

seasonings

Misc. FAH

FAFH and 

alcohol

Limited 

service

Full service

Other 

FAFH

Alcoholic 

beverages

Nonfood

Total goods and services

Estimation Approach

Given that we have a limited number of observations and a large number of 

parameters to estimate, we assume that a representative household purchases 

goods in a two-stage budgeting process (Strotz 1957, 1959; Gorman, 1959; 

Barten, 1977), as follows. First, consumers allocate their budget for all goods 

and services among composite groups, including six FAH groups, FAFH and 

alcoholic beverages, and nonfood (fig. 5). Second, assuming that the seven 

food groups are weakly separable, consumers then choose disaggregated food 

products within each of the groups, conditional on expenditure for that group. 

We estimate the first- and second-stage demands for nonfood and disaggregated food products. We then use the first- and second-stage estimates to 

approximate “unconditional” elasticities of demand for disaggregated food

products.4

4“Unconditional” in this context

means conditional on total expenditure on food, alcoholic beverages, and 

nonfood. 
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Estimation of First- and Second-Stage Demand

Since unit roots are often detected in time-series data, Gao and Shonkwiler 

(1993) suggested working with difference models rather than level-data 

models because the consequences of differencing when it is not needed are 

much less serious than those of failing to difference when it is appropriate. 

Hence, we opted to use the Generalized Ordinary Differential Demand 

System (GODDS) (Barten, 1993; Eales, Durham, and Wessells, 1997) to 

estimate demands in both the first and second stages. 

The GODDS nests several commonly used differential demand systems, 

including the Rotterdam model (Theil, 1965; Barten, 1966); the Central 

Bureau of Statistics (CBS) model (Keller and van Driel, 1985); the 

differenced linear almost ideal demand system (DLAIDS) (Deaton and 

Muellbauer, 1980a); and the National Bureau of Research (NBR) model 

(Neves, 1987). The GODDS is

(1) dwn = (cn + φ1wn)d ln Q + ∑ N

k = 1[dnk + φ2wn(δnk – wk)]d ln pk ,

where cn and dnk are expenditure and price coefficients to be estimated, 

respectively; φ1 and φ2 are nesting coefficients; δnk is the Kronecker delta; wn

is a t × 1 vector of expenditure shares for good n; pk is a t × 1 vector of prices 

of good k; and Q is a t × 1 vector of Divisia volume indexes (see appendix 

for more details on this model). The values of φ1 and φ2 that generate the 

various nested models in GODDS are

(2) φ1 = –1, φ2 = 1 Rotterdam model

(3) φ1 = 0, φ2 = 0 DLAIDS

(4) φ1 = 0, φ2 = 1 CBS model

(5) φ1 = –1, φ2 = 0 NBR model.

Restrictions from demand theory can also be imposed a priori or tested,

(6) ∑N

n = 1din = 0,

(7) ∑N

n = 1dni = 0, ∑Nn = 1cn = –φ1,

(8) dik = dki,

(i.e., homogeneity, adding-up, and symmetry, respectively). The formulas for 

the price and expenditure elasticities of demand for the GODDS are

(9) ηik = 

dik – ciwk

wi

 + (φ2 – 1)δik – (φ1 + φ2 )wk,

(10) ηiM = 

ci – φ1wi + wi 

wi

.
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Approximating Unconditional Elasticities of Demand 

Many studies model only the second stage of the two-stage budgeting 

process, and some have argued that the resulting conditional elasticities of 

demand are a useful approximation to the unconditional elasticities (Capps 

and Havlicek, 1984; Heien and Pompelli, 1988; Gao and Spreen, 1994). 

However, the conditions that allow conditional elasticities of demand to 

approximate unconditional elasticities do not hold empirically.5 Hence, we 

approximate the unconditional elasticities of demand by assuming consumers 

purchase goods in a two-stage budgeting process, and use the first- and 

second-stage elasticities of demand to approximate the unconditional elasticities of demand.

Carpentier and Guyomard (2001) approximated unconditional elasticities 

of demand using an approximation to the Slutsky substitution terms that are 

assumed to be weakly separable. Denoting the superscript as representing the 

composite group and the subscript as representing the elementary good, they 

approximated the unconditional Marshallian expenditure (η

iM) and price (ηij

) 

elasticities of demand as

(11) η

iM

 ≈ ηI

iM ηIM,

(12) η

ij

 ≈ δIJ ηI

ij

 + wJ

j 

ηI

iM ηJjM (δIJ / ηJjM

+ ηIJ) + wJ

j 

wJ ηIM ηI

iM(ηJjM

 – 1),

where 

ηI

iM = expenditure elasticity for good i ∈ I conditional on expenditure for 

group I,

ηIM = expenditure elasticity for composite group I with respect to total 

expenditure, M,

ηI

ij = Marshallian elasticity of demand for good i ∈ I with respect to price j ∈

J conditional on I = J,

ηIJ = Marshallian elasticity of demand for composite group I with respect to 

composite price J,

wJ

j

 = budget share for good j ∈ J conditional on J,

wJ = budget share for composite group J,

δIJ = 





 =

0, otherwise

11, if I = J , if I J

0, otherwise .

We use the formulas in (11) and (12) and our first- and second-stage estimates of elasticities of demand to approximate unconditional elasticities of 

demand for disaggregated food products. The approximate unconditional 

elasticities of demand satisfy the restrictions implied by homogeneity, 

symmetry, and Cournot and Engel aggregation.

5Gao and Spreen (1994) and Heien 

and Pompelli (1998) argued that conditional elasticities of demand for meat 

are appropriate when the aggregate 

price elasticity of demand for meat is 

close to one in magnitude. However, 

Okrent and Alston (2011) found that 

the aggregate own-price elasticity of 

demand for meat is considerably less 

than one. 
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New Estimates of Demand for 

Disaggregated Food-Away-From-Home 

and Food-at-Home Products 

To estimate the GODDS, we augmented equation (1) in two ways. First, 

because our data are discrete, we approximated the infinitesimal changes 

with their discrete counterparts:

(13) dwn ≈ Δwn = wn,t – wn,t–12, ∀n = 1,...,N,

(14) dpn ≈ Δln pn = ln pn,t – ln pn,t–12, ∀n = 1,...,N,

(15) d ln Q ≈ Δ ln M – ∑N

n = 1

Δln pn, where = (wn,t + wn,t–12), ∀n = 1,...,N.

Seale, Marchant, and Basso (2003) recommended twelfth-differencing rather 

than first-differencing the data when monthly data are used in estimation. In 

addition, we detected unit roots at seasonal frequencies for many of the logarithmic transformations of the prices and expenditure shares (see appendix 

tables A.1. and A.2).6 Second, we included a constant in each equation that 

acts as a linear trend term when modeling differenced data. To avoid singularity of the variance-covariance matrix, we left out the nonfood equation for 

the first-stage estimation, and used Engel and Cournot aggregation conditions 

(i.e., equation (7)) to recover the parameter estimates of nonfood demand; 

likewise, we left out equations for other bakery products, other dairy, eggs, 

processed fruits and vegetables, frozen beverages, and miscellaneous FAH in 

the estimation of the respective second-stage allocations. The GODDS was 

estimated for the first- and second-stage allocations using iterated feasible 

generalized least squares, which yield maximum-likelihood estimates of 

the demand parameters and imply that the system estimates are invariant to 

which of the equations is deleted (Kmenta and Gilbert, 1968; Barten, 1969).7

We first tested whether the data support restrictions associated with any of 

the nested models (i.e., equations (2)-(5)) using the likelihood ratio statistic. 

The restrictions associated with the DLAIDS model cannot be rejected for 

most of the estimated models of second-stage allocations; the model for fruits 

and vegetables is an exception (table 2). This model implies that the Engel 

curves of products within these second-stage allocations are of the form used 

by Working (1943) and Leser (1963) (i.e., wn = αn + βnlnM, where M is total 

expenditure and wn is the budget share for product n), and both the Slutsky 

substitution and marginal budget terms vary over time. All of the nesting 

restrictions on parameters are rejected in the second-stage model of demand 

for fruits and vegetables, while none of the nesting parameter restrictions is 

rejected in the second-stage model of demand for dairy. 

In the first-stage allocations, the restrictions associated with the NBR and 

Rotterdam models cannot be rejected; the NBR and Rotterdam models 

assume constant marginal budget shares. The model restrictions associated 

with the CBS model, which has price coefficients similar to the Rotterdam 

model (i.e., constant Slutsky substitution terms) and an income coefficient 

similar to the DLAIDS, cannot be rejected for the second-stage models of 

demand for meat and eggs, dairy, and FAFH/alcohol. Hence, because the 

restrictions associated with multiple nested models cannot be rejected in 

6Unlike annual data, monthly data 

could have a unit root at the zero 

frequency (i.e., standard longrun unit 

root where first-differencing would 

have to be applied to render the series 

stationary) or at seasonal frequencies 

corresponding to the number of cycles 

per year. For example, the data-generating process may cycle every 6 months 

and be nonstationary, which implies 

that a unit root occurs at that frequency. 

The goal of the procedure developed 

by Hylleberg et al. (1990) is to test 

hypotheses about a particular unit root 

without taking a stand on whether other 

seasonal or zero frequency (longrun) 

unit roots are present. The estimation 

equations included a constant, a time 

trend, and lagged dependent variables, 

and the set of lags was determined 

using the Bayesian Information 

Criterion (BIC) and inspection of the 

partial autocorrelation for each series.

7We checked that our estimates were 

indeed invariant to the equation omitted 

by arbitrarily leaving out different 

equations in the first- and second-stage 

estimation, re-estimating the parameters and standard errors, and recovering 

the parameters and standard errors of 

the excluded equation using adding-up. 

We found our estimates to be invariant 

to any choice of equation omitted in 

estimation.
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Table 2

Likelihood ratio statistics for nested models

Model Expenditure group Likelihood ratio statistic

Rotterdam 

(φ1 = -1, φ2 = 1)

Total goods and services 3.37 [0.19]

Cereals and bakery 19.65 [0.00]

Meat and eggs 6.57 [0.04]

Dairy 3.86 [0.14]

Fruits and vegetables 56.69 [0.00]

Nonalcoholic beverages 13.38 [0.00]

Other FAH 17.24 [0.00]

FAFH and alcohol 12.56 [0.00]

DLAIDS 

(Differenced 

linear almost ideal 

demand system)

(φ1 = φ2 = 0)

Total goods and services 15.16 [0.00]

Cereals and bakery 5.74 [0.06]

Meat and eggs 0.47 [0.79]

Dairy 0.83 [0.66]

Fruits and vegetables 11.55 [0.00]

Nonalcoholic beverages 3.92 [0.14]

Other FAH 4.10 [0.13]

FAFH and alcohol 5.62 [0.06]

CBS (Central Bureau of Statistics)

(φ1 = 0, φ2 = 1)

Total goods and services 17.59 [0.00]

Cereals and bakery 7.14 [0.03]

Meat and eggs 2.66 [0.26]

Dairy 2.62 [0.27]

Fruits and vegetables 14.65 [0.00]

Nonalcoholic beverages 6.56 [0.04]

Other FAH 6.17 [0.05]

FAFH and alcohol 3.81 [0.15]

NBR (National Bureau of Research)

(φ1 = -1, φ2 = 0)

Total goods and services 0.50 [0.78]

Cereals and bakery 18.25 [0.00]

Meat and eggs 5.33 [0.07]

Dairy 1.79 [0.41]

Fruits and vegetables 52.70 [0.00]

Nonalcoholic beverages 11.26 [0.00]

Other FAH 15.30 [0.00]

FAFH and alcohol 14.10 [0.00]

Source: Authors’ calculations.

Notes: The bracketed terms are p-values for the null hypothesis that the nesting restrictions 

are supported by the data.

FAFH = Food away from home, including limited-service and full-service restaurants.

FAH = Food-at-home..
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some cases (as with the estimates of first-stage allocations and second-stage 

models of demand for dairy and meat/eggs), but are completely rejected in 

others (as with second-stage model of demand for fruits and vegetables), 

we present elasticities of demand for the GODDS model for all of the firstand second-stage allocations, including those cases where a more restrictive model could have been used. It has been argued that the GODDS and 

its reparameterization, Barten’s synthetic model, are not merely artificial 

composites of known differential demand systems, but can be viewed as 

demand systems in their own right (Eales, Durham, and Wessells, 1997; 

Matsuda, 2005).

We then tested whether the data supported the restrictions of homogeneity 

(equation 6) and symmetry (equation 8) from demand theory for the first- and 

second-stage estimates based on the GODDS (table 3). For the first-stage 

estimates, homogeneity and symmetry were rejected. Many of the secondstage estimates supported symmetry, except fruits and vegetables and other 

FAH. Homogeneity is supported only in the nonalcoholic beverage and 

FAFH/alcoholic beverages second stages.8 Since we find some support for 

both symmetry and homogeneity restrictions, we model the first and second 

stages using the GODDS and with these restrictions. 

Last, we tested for first-order autocorrelation in the first- and secondstage estimates (with homogeneity and symmetry restrictions) using the 

Rao-Breusch-Godfrey test for first-order autocorrelation for the system of 

equations (Edgarton and Shukur, 1999).9 We detected first-order autocorrelation in the second-stage estimates for nonalcoholic beverages only. 

Following Berndt and Savin (1975), we constrained the first-order autocorrelation coefficient to be the same across all equations to preserve adding-up. 

8Deaton and Muellbauer (1980a) 

found that homogeneity is frequently 

rejected.

9Because Edgarton and Shukur 

(1999) found that the power and size of 

the Rao-Breusch-Godfrey test deteriorates as the number of equations 

increases, we also tested for autocorrelation in each equation using the 

Breusch-Godfrey test and did not find 

overwhelming evidence of autocorrelation in the first or second stages (see 

table 4 and appendix tables A.3-A.9).

Table 3

Goodness of fit, tests of autocorrelation, and restrictions from demand theory for all first- and secondstage estimates based on GODDS (Generalized Ordinary Differential Demand System)

Conditional on expenditure for

System 

R2

RaoBreuschGodfrey 

statistic

Likelihood ratio statistics for restrictions from demand theory

Symmetry Homogeneity

Symmetry and 

homogeneity

Total goods and services 0.15 0.64 49.22 [0.00] 22.44 [0.00] 61.28 [0.00]

Cereals and bakery 0.07 0.65 23.78 [0.31] 23.64 [0.00] 45.16 [0.02]

Meat and eggs 0.18 0.30 23.28 [0.05] 18.06 [0.00] 39.78 [0.00]

Dairy 0.20 1.47 4.96 [0.17] 11.92 [0.00] 13.24 [0.05]

Fruits and vegetables 0.08 0.93 60.32 [0.00] 17.02 [0.03] 77.84 [0.00]

Nonalcoholic beverages 0.09 2.19 5.04 [0.17] 0.20 [0.98] 10.50 [0.11]

Other food at home 0.07 0.57 53.00 [0.00] 21.26 [0.00] 74.66 [0.00]

Food away from home/alcohol 0.09 1.85 3.26 [0.35] 4.14 [0.25] 6.28 [0.39]

Source: Authors’ calculations.

Notes: The bracketed terms are p-values for the likelihood ratio tests of the null hypothesis that the restrictions from demand theory are supported by the data. The Rao-Breusch-Godfrey statistic is approximately distributed F(p,q), of which the 5% critical value is (i) 1.39 for the firststage model, with p = 49 and q = 609, and, in the second-stage allocations (ii) 1.39 for cereals and bakery, with p = 49 and q = 609; (iii) 1.46 for 

meat and eggs, with p = 25 and q = 466; (iv) 1.88 for dairy, with p = 9 and q = 290; (v) 1.31 for fruits and vegetables, p = 64 and q = 676; (vi) 

1.88 for nonalcoholic beverages, with p = 9 and q = 319; (vii) 1.67 for other FAH, with p = 16 and q = 536; and (viii) 1.88 for FAFH and alcoholic 

beverages, with p = 9 and q = 288.
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Table 4

First-stage uncompensated elasticities of demand from the GODDS model

Elasticity of demand for

With respect to price of

Cereals 

and 

bakery

Meat and 

eggs Dairy

Fruits and 

vegetables

Nonalcoholic 

drinks

Other 

FAH

FAFH and 

alcohol Nonfood

Cereals and bakery

-0.58 0.05 0.36 -0.31 -0.09 0.25 0.16 0.16

(0.25) (0.12) (0.08) (0.13) (0.15) (0.29) (0.34) (0.29)

Meat and eggs

0.03 -0.31 0.02 0.11 0.08 0.26 0.17 -0.40

(0.07) (0.17) (0.05) (0.09) (0.04) (0.11) (0.32) (0.40)

Dairy

0.49 0.06 -0.05 -0.03 -0.16 -0.44 0.23 -0.21

(0.10) (0.12) (0.09) (0.11) (0.07) (0.16) (0.30) (0.29)

Fruits and vegetables

-0.30 0.18 -0.02 -0.79 0.02 0.58 0.24 0.04

(0.13) (0.15) (0.08) (0.19) (0.09) (0.20) (0.39) (0.36)

Nonalcoholic beverages

-0.21 0.31 -0.25 0.05 -0.65 0.65 -0.05 0.13

(0.32) (0.16) (0.12) (0.20) (0.39) (0.46) (0.51) (0.38)

Other FAH

0.15 0.27 -0.19 0.36 0.18 -0.98 0.45 -0.32

(0.18) (0.11) (0.07) (0.12) (0.12) (0.30) (0.34) (0.28)

FAFH and alcohol

0.03 0.05 0.03 0.05 -0.01 0.14 -0.71 0.20

(0.07) (0.11) (0.04) (0.08) (0.05) (0.11) (0.38) (0.37)

Nonfood

-0.02 -0.05 -0.02 -0.02 -0.01 -0.04 -0.06 -1.00

(0.01) (0.01) (0.00) (0.01) (0.00) (0.01) (0.04) (0.06)

--continued

We then re-estimated the nonalcoholic beverages’ second stage with a 

correction for first-order autocorrelation, using iterated feasible generalized 

nonlinear least squares.10

First-Stage Estimates of Demand Elasticities for 

Composite Goods

The GODDS model seems to fit the monthly data well. The single-equation 

R2 statistics ranged between 0.58 for FAFH and alcohol and 0.77 for cereals 

and bakery products (table 4). The system R2 based on Bewley, Young, and 

Colman (1987) is 0.17, indicating that about 17 percent of the variation in the 

dependent variables in the first stage can be explained by the price terms in 

the GODDS model.11 The constant is significant in the equations for cereal 

and bakery products, meat and eggs, and fruits and vegetables; in particular, 

the estimated constants indicate trends of increasing consumption for cereals 

and bakery products and meat and eggs, and decreasing consumption for 

fruits and vegetables.

All of the own-price elasticities for the first-stage allocations are negative, 

which is consistent with demand theory. Most of the own-price elasticities of 

demand are significant at 10 percent except for dairy, for which the estimate 

10We estimated ρ to be 0.22 for 

nonalcoholic beverages. 

11Bewley, Young, and Colman (1987) 

developed a measure of goodness-of-fit 

for a system of equations model as

system R2 = 1 − 1

1 + LR/(T(n-1)) ,

where LR is twice the difference between the log likelihood of the model in 

(1) and the log likelihood of the model 

with the dependent variable regressed 

on a constant only. We use a variant 

of this measure used by Lee, Brown, 

and Seale (1994) and Brown, Lee, and 

Seale (1994) where LR is twice the 

difference between the log likelihood 

of the model in (1) and the log likelihood of the model with the dependent 

variable regressed on the aggregate 

income term, d ln Q. As Lee, Brown, 

and Seale (1994) and Brown, Lee, and 

Seale (1994) showed, this measure 

is invariant to the equation left out in 

estimation.
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is very small, indicating a very inelastic demand. Demand for nonfood is 

found to be the most responsive to changes in own price (own-price elasticity 

of -1.00), followed by other FAH (own-price elasticity of -0.98). The ownprice elasticity of demand for FAFH and alcohol is -0.71, which compares 

well with the estimate by Reed, Levedahl, and Hallahan (2005), but is 

considerably less than in other studies. Okrent and Alston (2011) found that 

across eight studies the average of the estimates of own-price elasticity of 

demand for FAFH was -1.02 (table 5). In fact, all of this study’s own-price 

elasticities are less than the average across studies reported in Okrent and 

Alston (2011). Our first-stage own-price elasticities are mostly consistent 

with those of Reed, Levedahl, and Hallahan (2005); Huang and Lin (2000); 

and Park et al. (1996).

Of the 56 cross-price elasticities of demand, 20 are statistically significant at 

the 10-percent level of significance. Many of the FAH products (i.e., cereals 

and bakery products, dairy, and other FAH) are gross substitutes for FAFH 

and alcohol, although these relationships are not found to be statistically 

significant. Other FAH is a statistically significant gross substitute for both 

meat/eggs and fruits/vegetables, but a gross complement for dairy. And dairy 

Table 4

First-stage uncompensated elasticities of demand from the GODDS model--continued

Elasticity of demand for

With respect to total 

expenditure R2

Breusch-Godfrey 

statistic Constant

Cereals and bakery

0.01

0.77 1.66

0.0002

(0.05) (0.0001)

Meat and eggs

0.04

0.59 4.90

0.0005

(0.07) (0.0002)

Dairy

0.11

0.74 2.20

0.0001

(0.05) (0.0001)

Fruits and vegetables

0.04

0.66 5.87

-0.0002

(0.06) (0.0001)

Nonalcoholic beverages

0.02

0.70 0.18

0.0000

(0.05) (0.0001)

Other FAH

0.09

0.76 0.08

-0.0003

(0.04) (0.0002)

FAFH and alcohol

0.21

0.58 3.63

0.0003

(0.06)

Nonfood

1.21

na na na

(0.01)

Source: Authors’ calculations using feasible generalized least squares GLS (Stata version 11) with homogeneity and symmetry constraints 

imposed.

Notes: Estimates of elasticities of demand were computed at the mean of the data. Standard errors were bootstrapped using the residual 

method. Total expenditure includes expenditures on durable and nondurable goods and services. The R2 and the Breusch-Godfrey statistic are 

for the individual equations and Breusch-Godfrey statistic is distributed χ2(1), for which the 10% critical value is 2.71.

FAFH = Food away from home, including limited-service and full-service restaurants; FAH = Food at home; GODDS = Generalized Ordinary 

Differential Demand System.
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is also found to be a statistically significant gross complement for nonalcoholic beverages.

Not unexpectedly, demand for nonfood is the most responsive to total expenditure (elasticity of 1.21), followed by demand for FAFH and alcohol (0.21). 

Demands for FAFH and alcohol are twice as responsive to changes in total 

expenditure as the most expenditure-elastic FAH products, namely dairy 

(0.11) and other FAH (0.09). Compared with the total-expenditure elasticities from the studies listed in table 5, the ones here are quite small, mainly 

because the nonfood budget share is 80 percent. 

Conditional Elasticities of Demand for Disaggregated 

Food Products

We estimated demand for disaggregated food products, assuming the products belonged to the following weakly separable groups: cereals and bakery 

products, meat and eggs, dairy products, fruits and vegetables, nonalcoholic 

beverages, other FAH, and FAFH/alcohol. Hence, the elasticities of demand 

for the disaggregated FAH products are conditional on total expenditure for 

the respective group. First-order autocorrelation is not detected in most of 

the second-stage estimates, with the exception of nonalcoholic beverages, 

based on the Rao-Breusch-Godfrey test. The system R2 for the second-stage 

allocations ranges between 0.07 for other FAH and cereals/bakery products 

Table 5

Comparison of first-stage elasticities of demand from this study with previous studies

This study

Reed, Levedahl, 

Hallahan (2005)

Huang and Lin 

(2000)b Park et al. (1996)c

Okrent and Alston 

(2011), table 5

OwnpriceExpenditureOwnprice IncomeOwnpriceExpenditureOwnpriceExpenditure

Number 

of studies 

represented

Average 

own-price 

across 

studies

Cereals and bakery -0.58 0.01 -0.61 1.31 -0.45 0.63 -0.14 0.43 3 -0.86

Meat and eggs -0.31 0.04 -0.61 1.81 -0.41 0.78 -0.45 0.64 8 -0.52

Dairy -0.05 0.11 -0.86 2.25 -0.79 0.67 -0.36 0.57 8 -0.85

Fruits and 

vegetables -0.79 0.04 -0.98 1.60 -0.72 1.07 -0.49 0.65 4 -0.91

Nonalcoholic 

beverages -0.65 0.02 -0.74a 1.04a -1.01 1.04 na na na na

Other FAH -0.98 0.09 -0.40 0.82 -0.58 0.59 11 -0.80

FAFH and alcohol -0.71 0.21 -0.69 1.38 na na -0.96 1.42 8 -1.02

Nonfood -1.00 1.21 -0.86 0.92 na na na na 2 -0.93

Source: Estimates for this study based on the GODDS and average monthly household expenditures based on the Consumer Expenditure 

Survey (U.S. Department of Labor, BLS, 2010a) and the Consumer Price Indexes (U.S. Department of Labor, BLS, 2010c).

a Nonalcoholic beverages included in other FAH category.

b The own-price and expenditure elasticities in this table are simple averages for disaggregated elasticities presented in Huang and Lin (2000) 

within the groups comprising cereals and bakery, meat and eggs, dairy, and fruits and vegetables.

c Estimates for nonpoverty status households only (table 8). The own-price and expenditure elasticities in this table are simple averages for 

disaggregated elasticities presented in Park et al. (1996) within the groups comprising cereals and bakery, meat and eggs, dairy, and fruits/

vegetables. The other FAH category only includes fats and oils.

FAFH = Food away from home, including limited-service and full-service restaurants; FAH = Food-at-home; GODDS = Generalized Ordinary 

Differential Demand System.
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and 0.20 for dairy. For brevity, we report the elasticities of demand, singleequation R2, first-order autocorrelation coefficient, Breusch-Godfrey LM 

statistic, and the trend term in each equation for the second-stage allocations 

in appendix tables A.3-A.9. 

Unconditional Elasticities of Demand for 

Disaggregated Food Products

Using equations (11) and (12) and the estimated elasticities of demand from 

the models of the first- and second-stage allocations, we approximated the 

elasticities of demand for disaggregated FAH and FAFH products conditional on total expenditure for all goods and services. Table 6 shows the ownprice and expenditure elasticities of demand for disaggregated food products 

compared with Huang (1993) and Bergtold, Akobundo, and Peterson 

(2004).12 Appendix table A.10. contains the 43 × 43 matrix of all elasticities. 

The standard errors were bootstrapped using the parametric residual method 

suggested by Green, Hahn, and Rocke (1987).

Cereals and Bakery Products. The demands for flour and prepared flour 

mixes; rice and pasta; and biscuits, rolls, and muffins are almost perfectly 

inelastic; the point estimates are close to zero and not statistically significantly different from zero (table 6). These findings approximate those of 

Huang (1993). By comparison, Bergtold, Akobundu, and Peterson (2004) 

found the own-price elasticity of demand to be closer to -1.0 for rice, pasta, 

and flour, but only the own-price elasticity of demand for pasta was statistically significant. The demands for breakfast cereals and cakes/cookies are 

price-elastic (i.e., elasticities of -1.05 and -1.20, respectively). The demand 

for nonwhite bread is less responsive to changes in price than the demand for 

white bread (elasticities of -0.59 and -1.54, respectively). Most of the crossprice elasticities of demand for foods within the cereals and bakery products 

group are statistically insignificant, although white bread and nonwhite bread 

are statistically significant gross substitutes, and flour/prepared flour mixes 

is a gross substitute for rice and pasta and a gross complement to nonwhite 

bread. Compared with the disaggregated demands of the other groups, the 

demands for all of the cereals and bakery products are relatively expenditure-inelastic, with elasticities ranging between 0.00 and 0.01. Bergtold, 

Akobundu, and Peterson (2004) and Huang (1993) also found the demands 

for disaggregated cereals and bakery products to be expenditure-inelastic 

and even inferior (i.e., expenditure elasticity is less than zero), compared to 

disaggregated products within other food groups. 

Meat and Eggs. Pork and “other red meat” (that is, other than beef and

pork) are price-elastic (own-price elasticities of -1.26 and -1.05), while the 

other products in the meat and eggs group—beef, poultry, fish/seafood, and 

eggs—are price inelastic, with eggs being the most price inelastic (ownprice elasticity of -0.24). The rankings of meat products in terms of their 

price responsiveness are roughly consistent with results from Huang (1993), 

although some of our estimates are statistically significantly smaller, at the 

10-percent level of significance (e.g., pork, other red meat, fish/seafood, and 

eggs). Also, similar to Huang’s findings (1993), beef and pork are statistically significant gross substitutes for each another. Demands for meat 

products are slightly more responsive to changes in total expenditure than 

12Huang (1993) and Bergtold et al. 

(2004) are the only recent studies to 

our knowledge that included a number 

of disaggregated FAH products in their 

estimation of unconditional demand 

systems, such that their results can be 

compared with ours. Huang (1993) 

directly estimated demand for 39 

foods and a nonfood composite using 

quantity indexes constructed from per 

capita disappearance data (ERS) and 

consumer price indexes. The per capita 

disappearance data, however, are not 

direct estimates of retail purchases 

because they are measured as total 

commodity supply less quantities used 

for farm inputs, exports, ending stocks, 

and industrial uses. Hence, the per 

capita disappearance data measure food 

use at a very basic level, do not distinguish between FAFH and FAH, and do 

not measure use of highly processed 

foods such as bakery products and 

frozen dinners in the finished product 

form (although the ingredients in those 

products are included as components 

of less highly processed foods such as 

sugar, flour, vegetables for processing, 

and fresh meat). Bergtold et al. (2004) 

used price and quantity scanner data 

(e.g., IRI Infoscan) and the flexible and 

separable translog multistage demand 

system (Moschini 2001) to estimate 

demand for 49 processed foods and 

an “all-other-goods” composite. One

limitation of their dataset is that it did 

not include information on several key 

food categories, including fresh meats, 

fruits and vegetables, and FAFH, and 

such products were lumped into the 

“all-other-goods” composite in their

model.
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Table 6

Comparison of unconditional elasticities of demand from this study with previous studies

This study

Bergtold, Akobundu, and 

Peterson (2004)a,b Huang (1993)b

Own-price Expenditure Own-price Income Own-price Expenditure

Cereals and bakery

Flour and flour mixes 0.07 0.01 -0.86 0.06 -0.08 0.13

Breakfast cereals -1.05* 0.00 na na na 0

Rice and pasta -0.07 0.01 -0.87 -0.06 0.07 0.15

Nonwhite bread -0.59* 0.00 -0.80 -0.21 na na

White bread -1.54 0.01 na na

Biscuits, rolls, muffins -0.21 0.00 -1.03 -0.55 na na

Cakes and cookies -1.20* 0.01 na na na na

Other bakery products -0.55 0.00 na na na na

Meat and eggs

Beef -0.70* 0.05 na na -0.62 0.39

Pork -1.26* 0.04 na na -0.73 0.66

Other red meat -1.05* 0.02 na na -1.87 -0.57

Poultry -0.81* 0.03 na na -0.45 -0.02

Fish -0.84* 0.03 na na -0.13 0.41

Eggs -0.24* 0.03 na na -0.11 0.29

Dairy

Cheese -0.70* 0.13* -1.18 -0.03 -0.25 0.42

Ice cream -0.23 0.13* -0.88 0.05 -0.08 0.00

Milk -0.10 0.09* -0.80 -0.20 -0.04 0.12

Other dairy -1.04* 0.09* -1.03 0.31 -0.28 0.52

Fruits and vegetables

Apples -0.58* 0.03 na na -0.19 -0.36

Bananas -1.01* 0.05 na na -0.50 0.00

Citrus -1.10* 0.06 na na -0.65 -0.33

Other fresh fruit -0.90* 0.04 na na -0.80 0.34

Potatoes -0.42* 0.03 na na -0.10 0.11

Lettuce -0.84* 0.04 na na -0.09 0.37

Tomatoes -0.58* 0.06 na na -0.62 0.92

Other fresh vegetables -0.94* 0.04 na na -0.26 0.69

Proc. fruits and vegetables -0.77* 0.03 -1.20 -0.29 -0.40 0.56

--continued
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are demands for cereals and bakery products, with expenditure elasticities 

ranging between 0.02 for other red meat and 0.05 for beef. But this effect is 

still small and insignificant compared to the other products in the system.

Dairy. The own-price elasticities of demand for cheese and other dairy are 

statistically different from zero at the 10-percent level of significance (-0.70 

and -1.04, respectively) and much more price-elastic than the demands for 

fluid milk and ice cream/frozen desserts (-0.10 and -0.23, respectively), 

which are not found to be statistically significant. Huang (1993) found 

demand for similar dairy products to be mostly price-inelastic, whereas 

Bergtold, Akobundu, and Peterson (2004) found demand for comparable 

items to be much more elastic. Our results fall between the two studies’ 

findings. Cheese is found to be a statistically significant gross substitute 

for other dairy, which includes yogurt and sour cream. Compared with the 

Table 6

Comparison of unconditional elasticities of demand from this study with previous studies (continued)

This Study

Bergtold, Akobundu, and 

Peterson (2004)a,b Huang (1993)b

Own-price Expenditure Own-price Income Own-price Expenditure

Nonalcoholic beverages

Coffee and tea -0.12 0.02 -0.45 -0.27 -0.18 0.82

Carbonated drinks -0.30 0.01 -1.15 -0.03 na na

Nonfrozen noncarb. drinks -0.44 0.02 -0.65 -0.12 -0.56 0.37

Frozen noncarb. drinks -0.61 0.01 -0.70 -0.14 na na

Other food at home

Sugar and sweets -0.56 0.13* -0.66 -0.16 -0.04 0.21

Fats and oils -0.21 0.08* -0.62 -0.51 -0.13 0.23

Soups 0.19* 0.07* -1.51 0.59 na na

Frozen foods -1.05 0.09* -1.08 -0.27 na na

Snacks -1.14* 0.08* -1.17 -0.10 na na

Condiments, sauces, seas. -1.92* 0.07* -1.00 -0.01 na na

Misc. FAH -1.48* 0.11* -1.17 0.01 na na

Food away from home/alcohol

Alcohol -1.15* 0.32* na na na na

Limited-service -0.13 0.18* na na na na

Full-service -1.96* 0.20* na na na na

Other FAFH -0.43* 0.21* na na na na

Nonfood -1.00* 1.21* -1.00 0.99 -0.98 1.17

* designates statistical significance at the 10-percent level for estimates in this study only.

a Bergtold et al. (2004) presented own-price and expenditure elasticities of demand for four quarters. We averaged the elasticity estimates over 

the quarters. 

b Some of the products in Bergtold et al. (2004) and Huang (1993) did not correspond directly to the products in this study. Hence, we calculated the average own-price and expenditure elasticities of demand for multiple products that corresponded to a product in this study. 

Source: Estimates from this study based on first-stage elasticities of demand (table 4), second-stage elasticities of demand (appendix tables 

A.4-A.9) and formulas derived by Carpentier and Guyomard (2001) in equations (12) and (13).

FAFH = Food away from home, including limited-service and full-service restaurants; FAH = Food-at-home.
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disaggregated demands in the cereals/bakery, meat/eggs, fruits/vegetables, 

and nonalcoholic beverages groups, demands for disaggregated dairy products are almost twice as responsive to changes in total expenditure, with 

expenditure elasticities ranging between 0.09 for milk and other dairy and 

0.13 for cheese and ice cream. Again, these estimated elasticities of demand 

with respect to total expenditure fall generally in between the estimates of 

Bergtold, Akobundu, and Peterson (2004) and Huang (1993). Bergtold, 

Akobundu, and Peterson found cheese and milk to be inferior products (a 

good that decreases in demand when income increases) and the elasticity of 

demand for ice cream and cheese with respect to total expenditure to be close 

to zero.

Fruits and Vegetables. In this group, all of the own-price elasticities are 

statistically significant, with demand for citrus being the most elastic (ownprice elasticity of -1.10) and demand for potatoes being the least elastic 

(own-price elasticity of -0.42). Within the fruits and vegetables group, few of 

the cross-price relationships are statistically significant with the exception of 

processed fruits and vegetables, which is a gross complement to fresh tomatoes. The elasticities of demand for the disaggregated fruits and vegetables 

with respect to total expenditure are small, ranging between 0.03 and 0.06. 

Compared with Huang (1993), the present study finds the demands for disaggregated fruits and vegetables to be generally more price-elastic and more 

expenditure-inelastic.

Nonalcoholic Beverages. Within this group, none of the elasticities of 

demand with respect to price or expenditure elasticities is significant. The 

elasticities of demand with respect to total expenditure are close to zero, 

and the own-price elasticities of demand are small compared with most 

other food products, with the demand for coffee and tea being the least price 

responsive at -0.12. Huang (1993) found the own-price elasticity of demand 

for coffee and tea to be -0.18, while Bergtold, Akobundu, and Peterson 

(2004) found the own-price elasticity for coffee to be -0.45. However, 

Bergtold, Akobundu, and Peterson (2004) found the demand for carbonated 

beverages (averaged across diet and regular cola estimates) to be much more 

price elastic (-1.15) than our estimate for carbonated beverages (-0.30).

Other FAH. Most of the demands for products within the other FAH group 

are price-elastic, with seasonings, condiments, and sauces being the most 

price elastic (-1.92), followed by miscellaneous FAH (-1.48), snacks (-1.14), 

and frozen meals (-1.05). This finding is consistent with Bergtold, Akobundu 

and Peterson (2004), who found sauces and marinades, mayonnaise, relishes, 

and dressings to be generally price elastic. We find the demands for sugars/

sweets and fats/oils to be price-inelastic, but both relationships are statistically insignificant. Compared with the other food product categories, the 

“other FAH” products are the most responsive to changes in their own price 

with the exception of FAFH and alcohol. 

FAFH and Alcohol. The demands for limited-service FAFH and other FAFH 

(vending machines, mobile food vendors, and school/employee sites) are 

the most inelastic in the group (-0.13 and -0.43, respectively). The ownprice elasticity of demand for full-service FAFH is -1.96, and is statistically 

different from the own-price elasticity of demand for limited-service FAFH 

at the 10-percent level of significance. Full- and limited-service FAFH 
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are found to be gross substitutes, although this relationship is not statistically significant. Demand for alcohol is also price-elastic (-1.15). All of the 

FAFH products and alcohol are more than twice as responsive to changes in 

total expenditure compared to the FAH products. Alcohol is the most priceresponsive (0.32), followed by other FAFH (0.21), full-service FAFH (0.20), 

and limited-service FAFH (0.18). 
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Potential Policy Implications

Because disaggregated FAFH and FAH products may differ in responsiveness to prices and total expenditure, as well as in nutritional content, we estimate elasticities using a more disaggregated approach than previously done 

in the literature. Our results show that the demand for full-service FAFH is 

much more responsive than the demand for limited-service FAFH to changes 

in price, and the demands for all FAFH products are at least twice as elastic 

with respect to changes in total expenditure than their FAH counterparts. The 

finding that FAFH products are much more responsive to changes in total 

expenditure—and that these FAFH products are generally gross substitutes 

for many FAH products—can explain why the budget share for these products dipped during the 2007-09 recession, while the budget shares for many 

FAH products increased. In particular, during the period of December 2007-

June 2009, monthly total consumer expenditures fell by about 0.5 percent 

on average, while the prices of most FAH products, which are mostly gross 

substitutes for FAFH products, fell relative to the prices of the FAFH products. Hence, income-induced changes in total expenditures and movements in 

prices of FAH products relative to prices of FAFH products caused demand 

for FAFH to fall during the most recent recession. 

The demands for disaggregated FAH products, which include some foods 

that are considered to be “healthy” and others considered too be “unhealthy,”

also varied in their responsiveness to changes in prices and total expenditure. 

“Healthy” foods—such as nonwhite bread, most fruits and vegetables, and

fish/seafood—are generally less responsive to changes in their own prices 

than their “unhealthy” counterparts. For example, for cereals and bakery

products, we found that the unconditional demand for white bread was much 

more price elastic than the unconditional demand for nonwhite bread, and the 

demand for cookies and cakes was one of the most price elastic within the 

group. Likewise, the unconditional demands for snacks, condiments/sauces/

seasonings, and frozen foods were very price elastic compared with the 

demands for other FAH products. 

However, own-price effects are only one part of an analysis of the effects 

of policy-induced price changes on consumption. The cross-price relationships between “unhealthy” and “healthy” foods are complex; in analyzing

the effect of a change in the price of a “healthy” or “unhealthy” food on the

nutritional outcome of an individual, one must consider the cross-price, as 

well as the own-price, effects. 

To further demonstrate the importance of these cross-price relationships 

and intergroup substitution on the quantities of food consumed, we forecast 

the changes in consumption for several foods between 2011 and 2012—

given forecast changes in prices and total expenditures—and compare the 

predictions based on alternative elasticity measures. We use the “unconditional” demand elasticities reported in appendix table A.10 to obtain forecasts that consider intergroup as well as intragroup substitution; and we use 

the “conditional” demand elasticities reported in appendix tables A.3-A.9

(i.e., conditional on group expenditure) to obtain forecasts that consider 

only intragroup substitution. 
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The forecast changes in prices of food from 2011 to 2012 are taken from the 

CPI forecasts by the U.S. Department of Agriculture, ERS (2011), and the 

forecast changes in prices for nonfood and total expenditures are taken from 

the Federal Reserve Bank of Philadelphia’s Fourth Quarter 2011 Survey 

of Professional Forecasters (2011) (table 7).13 According to the ERS price 

forecasts, the prices of beef, fish/seafood, fats/oils, and cereals/bakery products will increase the most (between 4 and 4.5 percent) from 2011 to 2012, 

whereas the prices for fresh vegetables, eggs, and nonalcoholic beverages 

will increase the least, between 1.5 and 2 percent. The price of nonfood 

products, as proxied by core inflation for 2012, is predicted to increase by 

1.8 percent, while total personal consumption expenditures are predicted to 

increase 1.7 percent.

Using these predicted changes in prices and total expenditure, we forecast 

changes in food quantities using both unconditional and conditional elasticities. Both sets of forecasts indicate decreases in the quantities of disaggregated cereals and bakery products consumed, but the magnitudes differ 

substantially; the forecasts based on the conditional elasticities of demand 

are three to four times larger in absolute terms than the forecasts based on the 

unconditional elasticities of demand. Even though the conditional own-price 

elasticities of demand were not statistically different from the unconditional 

own-price elasticities of demand at the 10-percent level of significance, the 

conditional forecasts disregarded statistically significant intergroup substitution and complementary relationships found in the first stage (i.e., dairy, 

fruits/vegetables, and nonfood). The conditional forecasts followed the same 

pattern for the disaggregated FAFH products. 

The predicted percentage changes in dairy consumption based on the elasticities of demand conditional on dairy expenditure take opposite signs 

compared with the predicted percentage changes based on the unconditional 

elasticities of demand: consumption of each of the disaggregated dairy products is predicted to increase between 0.61 percent and 0.9 percent in 2012 

based on the unconditional demand elasticities, but predicted to decrease 

between 0.63 percent and 0.97 percent based on the conditional demand elasticities. Similar contradictions between the two sets of elasticities are found 

for other food products as well (e.g., pork, poultry, eggs, sugar and sweets, 

frozen foods). Again, dairy—like cereals and bakery products—has several 

statistically significant cross-price relationships between groups of foods at 

the first stage that results in complementary and substitution relationships 

among the disaggregated products in these groups, causing contradictions in 

our forecast changes in quantities consumed depending on which set of elasticities is used.

The substantial cross-price relationships between products in different groups 

lead to two important and related implications. First, the predicted changes 

in quantities of foods consumed based on the conditional demand elasticities pertaining to a weakly separable group are different in magnitude, and 

sometimes in direction of change, than predicted changes in quantities based 

on unconditional elasticities of demand. Second, policy analysis based on 

conditional demand elasticities for a small group of products is likely to be 

misleading. 

13The survey reports the mean 

annualized predictions by professional 

forecasters of changes in headline (all 

items) and core (all items excluding 

food and energy) inflation and personal 

consumption expenditures (PCE). We 

used predicted core inflation and headline PCE to proxy for 2012 predicted 

proportional changes in nonfood price 

and total expenditures, respectively.
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Table 7

Forecast changes in food consumption, 2011 to 2012, based on forecast changes in prices and 

expenditure, using alternative sets of elasticities of demand

Forecast 

changes in 

prices and total 

expenditure

Predicted changes in 

food quantities based on

Predicted changes in 

expenditures based on

Unconditional 

elasticitiesa

Conditional 

elasticitiesb

Unconditional 

elasticitiesa

Conditional 

elasticitiesb

Annual percentage change

Flour and prep. mixes 4.0 -1.25 -4.23 2.75 -0.23

Breakfast cereals 4.0 -0.48 -1.56 3.52 2.44

Rice and pasta 4.0 -1.01 -3.69 2.99 0.31

Nonwhite bread 4.0 -0.44 -1.62 3.56 2.38

White bread 4.0 -0.78 -2.63 3.22 1.37

Biscuits, rolls, muffins 4.0 -0.39 -1.81 3.61 2.19

Cakes and cookies 4.0 -0.84 -2.67 3.16 1.33

Other bakery 4.0 -0.55 -1.92 3.45 2.09

Beef 4.5 -0.39 -3.39 4.11 1.11

Pork 3.5 0.58 -1.75 4.08 1.75

Other red meat 3.0 1.35 0.07 4.35 3.07

Poultry 3.5 0.28 -1.31 3.78 2.19

Fish 4.5 -1.08 -3.11 3.43 1.39

Eggs 1.5 0.75 -0.77 2.25 0.73

Cheese 2.5 0.90 -0.97 3.40 1.53

Ice cream and frozen desserts 2.5 0.87 -0.92 3.37 1.58

Milk 2.5 0.61 -0.63 3.11 1.87

Other dairy 2.5 0.69 -0.71 3.19 1.80

Apples 3.5 -0.70 -1.55 2.81 1.95

Bananas 3.5 -0.62 -2.11 2.88 1.39

Citrus 3.5 -0.91 -2.64 2.59 0.86

Other fruits 3.5 -0.16 -1.45 3.35 2.05

Potatoes 1.5 0.90 0.09 2.40 1.59

Lettuce 1.5 1.02 -0.38 2.52 1.12

Tomatoes 1.5 0.22 -1.55 1.72 -0.05

Other veg. 1.5 1.66 0.27 3.16 1.77

Processed fruits/vegetables 3.5 -0.32 -1.15 3.18 2.35

Coffee and tea 2.0 0.78 -0.16 2.78 1.84

Carbonated drinks 2.0 0.66 -0.31 2.66 1.69

--continued
27

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Economic Research Service/USDA

Table 7

Forecast changes in food consumption, 2011 to 2012, based on forecast changes in prices and 

expenditure, using alternative sets of elasticities of demand (continued)

Forecast 

changes in 

prices and total 

expenditure

Predicted changes in 

food quantities based on

Predicted changes in 

expenditures based on

Unconditional 

elasticitiesa

Conditional 

elasticitiesb

Unconditional 

elasticitiesa

Conditional 

elasticitiesb

Annual percentage change

Nonfrozen noncarbonated drinks 2.0 1.06 -0.35 3.06 1.65

Frozen noncarbonated drinks 2.0 0.44 -0.22 2.44 1.78

Sugar and sweets 2.5 0.56 -2.06 3.06 0.44

Fats and oils 4.0 -0.07 -1.62 3.93 2.38

Soups 3.5 1.86 1.00 5.36 4.50

Frozen foods 3.5 0.63 -1.15 4.14 2.35

Snacks 3.5 -0.08 -1.59 3.42 1.91

Condiments, sauces, seasonings 3.5 -0.80 -2.20 2.70 1.30

Misc. food at home 3.5 -0.13 -2.28 3.37 1.22

Alcohol 3.0 -0.61 -1.93 2.39 1.07

Limited 3.0 -0.42 -1.09 2.58 1.91

Full 3.0 -0.49 -1.22 2.51 1.78

Other food away from home 3.0 -0.51 -1.30 2.49 1.70

Nonfood 1.8 -0.35 na 1.45 na

Notes: Forecast changes in food prices from 2011 to 2012 are based on forecast changes in Consumer Price Index for foods (U.S. Department 

of Agriculture, ERS, 2011); forecast changes in the nonfood price and total expenditure are based on the mean of reported predictions for 

2012 by a sample of professional forecasters for core inflation and headline personal consumption expenditures (Federal Reserve Board of 

Philadelphia, 2011).

a The predictions based on the unconditional elasticities of demand use elasticities of demand reported in appendix table A.10. 

b The predictions based on conditional elasticities of demand use elasticities reported in appendix tables A.3-A.9
28

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Conclusion

Many studies have evaluated the effect of policy-induced price changes on 

food consumption and nutritional outcomes. Several studies have based their 

analysis on demand elasticities for only a subset of foods (i.e., conditional on 

expenditure for a particular group of foods), which ignores important crossprice relationships of foods not included in a given analysis. In particular, 

because FAFH comprises a significant share of total food expenditures and 

nutritional intake for an average American, disregarding the potential crossprice relationship between FAFH and another relevant subset of foods may 

lead to misleading results regarding nutrition and health policy. 

This study is the first to present disaggregated estimates of demand elasticities for different types of FAFH within a complete demand system for 

food, alcohol, and nonfood. We find that the demand for full-service FAFH 

is much more price-elastic than the demand for food from limited-service 

restaurants. All of the disaggregated products within FAFH are much more 

responsive to changes in total expenditure than all of the FAH products. 

Hence, our findings suggest that decreases in total expenditure during the 

most recent recession had a much greater impact on demands for most FAFH 

products than for FAH products. 

We also present disaggregated elasticities of demand for FAH products. 

The demands for products within any group can vary considerably in terms 

of responsiveness to price changes, aggregating groups in policy simulations masks important dissimilarities within food groups in terms of nutrient 

characteristics and responses to prices and total expenditure. In particular, 

the demands for products commonly deemed to be “healthy” (fruits and

vegetables, nonwhite bread, fish and seafood) tend to be much less responsive to own-price changes compared with those commonly deemed to be 

“unhealthy” (e.g., white bread, cakes and cookies, frozen foods, snacks).

Many of these “healthy” and “unhealthy” foods are found to have statistically

significant substitution and complementary relationships within and among 

food groups, which complicates analysis that tries to predict the effects of 

policy-induced changes in prices and income on demands for foods and the 

nutritional outcomes of consumers. Consequently, forecasts of the changes 

of quantities of food based on estimates of conditional demand elasticities 

that ignore the total effects of intergroup substitution and complementarities 

differ substantially in magnitude and sometimes even direction from forecasts based on estimates of unconditional demand elasticities that include all 

goods and services.
29

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Appendix Tables

Appendix table A.1

Test for seasonal unit roots in monthly logarithmic transformation of price series

Seasonal frequency

(Tests of coefficients in HEGY test regression)

0 π π/2 2π/3 π/3 5π/6 π/6

Lag π1=0 π2=0 π3=π4=0 π5=π6=0 π7=π8=0 π9=π10=0 π11=π12=0

Cereals and bakery 4 0.02 -2.65 8.53 7.95 9.47 5.04 10.01

Flour and flour mixes 0 -2.29 -2.97 11.00 13.36 14.47 11.56 15.34

Breakfast cereals 2 -1.16 -3.35 11.48 16.92 10.30 8.45 12.44

Rice and pasta 2 0.09 -3.26 8.25 10.55 10.03 7.58 15.71

Nonwhite bread 9 -2.47 -3.71 8.56 9.97 24.58 8.24 10.15

White bread 1 -3.21 -2.40 7.74 9.15 9.35 9.74 12.75

Biscuits, rolls, muffins 1 -2.25 -2.83 8.02 6.41 8.44 10.72 12.01

Cakes and cookies 9 -0.27 -2.05 9.22 10.54 6.09 4.00 11.29

Other bakery products 9 -4.22 -4.53 3.00 11.86 12.48 2.36 7.37

Meat and eggs 0 -2.90 -4.01 9.89 10.24 14.04 11.71 15.58

Beef 0 -1.78 -3.03 11.84 15.86 10.64 11.51 13.57

Pork 13 0.25 -4.73 2.18 1.88 16.39 17.95 7.60

Other red meat 1 -0.39 -4.03 12.40 9.15 11.68 13.17 6.24

Poultry 0 -3.74 -3.58 13.31 12.36 15.08 11.02 11.42

Fish 2 -3.80 -2.69 11.57 10.39 6.20 11.34 12.46

Eggs 3 -0.95 -3.25 9.53 6.41 7.47 5.75 9.09

Dairy 2 -3.45 -3.58 11.15 11.96 11.09 11.44 10.94

Cheese 4 -2.01 -2.41 13.71 8.40 6.43 11.22 4.91

Ice cream 6 -1.41 -2.84 3.67 8.82 8.10 10.20 10.00

Milk 0 -2.96 -3.81 11.39 17.07 14.23 13.66 16.79

Other dairy 2 -2.83 -2.62 13.24 17.77 15.54 9.62 13.85

Fruits and vegetables 6 -0.44 -4.51 4.99 5.88 2.25 9.35 4.42

Apples 4 -3.09 -3.21 14.39 9.51 9.72 9.33 11.70

Bananas 11 -1.01 -1.73 9.09 7.85 4.83 9.42 9.56

Citrus 9 -3.43 -1.14 7.35 6.85 2.53 13.18 9.54

Other fresh fruit 11 1.79 -4.73 13.94 13.13 7.55 6.99 6.13

Potatoes 2 -2.92 -2.22 12.67 13.27 11.36 7.68 9.86

Lettuce 16 -3.04 -2.62 18.27 4.74 5.88 27.88 11.35

Tomatoes 3 -2.28 -4.13 8.17 7.95 8.25 7.49 6.78

Other fresh vegetables 1 -0.93 -3.73 10.63 11.30 8.56 8.46 8.16

Proc. fruits & vegetables 1 -2.67 -2.40 6.40 8.07 11.16 12.39 13.92

Nonalcoholic beverages 2 -2.24 -2.64 8.23 10.71 9.65 9.96 12.60

Frozen noncarb. drinks 14 -1.14 -1.58 12.34 7.57 0.54 2.18 2.50

Nonfro noncarb. drinks 4 -4.27 -3.94 20.96 25.76 24.76 26.48 16.64

--continued
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Appendix table A.1

Test for seasonal unit roots in monthly logarithmic transformation of price series (continued)

Seasonal frequency

(Tests of coefficients in HEGY test regression)

0 π π/2 2π/3 π/3 5π/6 π/6

Lag π1=0 π2=0 π3=π4=0 π5=π6=0 π7=π8=0 π9=π10=0 π11=π12=0

Carbonated drinks 5 -2.97 -3.69 9.69 16.58 11.72 15.90 20.27

Coffee and tea 9 -3.20 -4.46 8.45 14.32 10.49 2.61 8.73

Sugar and sweets 6 -3.01 -4.33 4.70 3.10 6.18 16.72 4.44

Fats and oils 10 -0.18 -2.82 13.96 7.25 9.36 7.68 4.58

Miscellaneous foods 4 1.72 -3.52 7.66 13.71 8.45 8.99 9.21

Soups 4 -3.44 -3.81 13.07 12.57 17.02 9.07 12.30

Frozen foods 7 -2.53 -3.18 9.42 9.01 8.34 12.96 13.74

Snacks 3 0.03 -2.95 22.36 12.73 11.22 10.66 7.80

Cond., sauces, seas. 2 -2.17 -4.23 4.30 6.54 4.63 13.02 3.59

Other miscellaneous 5 -3.20 -3.09 13.26 8.87 12.24 17.81 7.91

Other FAFH 4 -3.83 -4.53 14.75 17.73 19.15 18.28 26.08

Limited-service FAFH 5 -1.62 -3.44 7.23 7.50 10.40 5.77 8.67

Full-service FAFH 6 -3.50 -3.29 12.70 13.89 8.21 16.55 7.78

Alcoholic beverages 25 -1.04 -4.83 6.44 2.82 1.16 4.38 0.92

Nonfood 4 -2.13 -3.28 10.61 9.89 11.83 11.44 6.13

Note: The HEGY test regressions included a trend, constant, and lagged dependent variables. Beaulieu and Miron (1993) derived the critical 

values from the distributions of the HEGY test statistics for monthly data. The critical values for the test regression with a trend and a constant 

and 240 observations for a 10-percent level of significance are: 

-2.99 for the test of the null hypothesis π1 = 0 versus the alternative π1 < 0 (test of long-run unit root), -2.47 for the test of the null hypothesis π2

= 0 versus the alternative π2 < 0 (test of unit root corresponding to a biannual cycle), and 5.25 for the joint test of the null hypothesis πn = πn-1 = 

0, n = 2, 6, 8, 10, 12 (test of unit root corresponding to seasonal frequencies π/2, 2π/3, π/3, 5π/6 and π/6). 

FAFH = Food away from home.

Source: Authors’ calculation of HEGY test for monthly data using logarithmic transformation of consumer price indexes (U.S. Department of 

Labor, BLS, Consumer Expenditure Survey (2010a); U.S. Department of Labor, BLS, Consumer Price Index Database (2010c)).
36

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Appendix table A.2

Test for seasonal unit roots in monthly expenditure share series

Seasonal frequency

(Tests of coefficients in HEGY test regression)

0 π π/2 2π/3 π/3 5π/6 π/6

Lag π1=0 π2=0 π3=π4=0 π5=π6=0 π7=π8=0 π9=π10=0 π11=π12=0

Cereals and bakery 6 -1.18 -1.69 12.24 6.72 3.73 12.05 8.98

Flour and flour mixes 3 0.93 -0.46 1.73 0.51 1.73 0.77 3.06

Breakfast cereals 7 -1.28 -3.01 0.89 4.37 1.58 4.47 1.20

Rice and pasta 8 -3.09 -3.61 1.21 9.57 2.30 9.15 2.06

Nonwhite bread 15 -0.10 -0.56 0.90 1.46 15.48 2.44 1.88

White bread 1 -0.38 -1.89 8.31 4.81 8.43 11.01 5.11

Biscuits, rolls, muffins 3 -1.49 -1.58 13.80 3.34 5.82 2.57 3.68

Cakes and cookies 6 -3.99 -4.54 14.01 5.09 1.49 10.63 2.65

Other bakery products 17 -2.39 -2.38 0.41 1.69 0.06 0.78 0.28

Meat and eggs 3 -2.90 -4.08 14.16 12.22 9.98 8.24 10.49

Beef 8 -1.86 -1.57 1.57 4.72 4.50 7.03 2.11

Pork 3 -2.32 -1.92 1.85 1.38 5.49 3.55 0.85

Other red meat 3 -1.61 -2.42 9.23 16.00 3.01 13.89 2.05

Poultry 11 -0.53 0.15 0.20 0.98 0.18 0.26 0.05

Fish 4 -2.64 -3.05 11.29 4.07 4.92 6.18 3.17

Eggs 2 -0.77 -3.08 7.97 10.58 10.26 9.18 2.82

Dairy 3 -1.98 -2.58 4.65 7.84 7.88 5.58 2.67

Cheese 9 -4.81 -1.34 2.33 5.59 3.61 1.50 0.02

Ice cream 7 -2.98 -2.70 6.71 7.67 4.10 17.46 0.35

Milk 13 -4.37 -3.31 8.01 1.41 2.83 11.63 0.91

Other dairy 2 -4.11 -4.39 10.89 7.16 6.56 10.28 8.06

Fruits and vegetables 1 -0.45 -2.01 14.98 8.27 4.12 19.85 5.78

Apples 11 -4.02 -1.56 1.90 4.21 0.58 8.55 0.51

Bananas 2 1.83 -1.29 2.28 5.03 2.26 3.02 0.78

Citrus 4 2.42 -1.37 3.57 0.42 1.53 2.88 2.97

Other fresh fruit 4 1.15 -2.33 1.43 1.78 0.67 6.82 0.86

Potatoes 0 -1.81 -3.65 10.34 10.50 5.02 9.07 2.36

Lettuce 9 -1.51 -0.96 1.36 7.56 0.82 6.24 3.52

Tomatoes 2 -2.41 -3.64 3.57 4.71 4.84 3.14 4.08

Other fresh vegetables 4 -1.31 -3.12 5.96 6.27 4.60 3.18 2.67

Proc. fruits & vegetables 9 0.09 -0.49 8.39 1.09 0.50 2.88 0.37

Nonalcoholic beverages 1 -2.53 -2.75 12.28 11.49 3.96 8.52 7.36

Frozen noncarb. drinks 5 -0.40 -3.49 8.56 1.86 9.00 8.01 13.40

Nonfro. noncarb. drinks 7 0.53 -3.39 5.19 4.14 1.86 4.08 0.13

Carbonated drinks 4 -2.77 -2.92 10.96 2.36 5.74 5.09 9.65

Coffee and tea 4 0.19 -1.62 6.93 2.72 1.99 6.94 1.07

Sugar and sweets 3 -1.98 -2.78 3.32 5.38 2.52 1.40 1.10

Fats and oils 3 1.06 -2.42 3.47 3.25 3.06 4.77 3.56

--continued
37

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Economic Research Service/USDA

Appendix table A.2

Test for seasonal unit roots in monthly expenditure share series (continued)

Seasonal frequency

(Tests of coefficients in HEGY test regression)

0 π π/2 2π/3 π/3 5π/6 π/6

Lag π1=0 π2=0 π3=π4=0 π5=π6=0 π7=π8=0 π9=π10=0 π11=π12=0

Miscellaneous foods 4 1.73 -1.85 2.42 1.72 1.74 1.79 0.57

Soups 2 -0.67 -1.09 2.59 2.57 0.84 1.82 1.12

Frozen foods 3 0.85 -1.45 2.29 3.56 4.60 4.02 2.49

Snacks 1 -0.55 -2.44 8.03 9.12 9.89 9.95 6.60

Condiments, sauces, 

seasonings 2 -2.03 -1.77 2.48 2.81 1.58 2.91 2.47

Other miscellaneous 6 -2.33 -1.57 3.55 2.01 2.51 9.52 0.59

Other FAFH 1 -1.94 -4.40 9.06 11.84 3.05 14.89 2.63

Limited-service FAFH 8 -1.44 -2.91 3.55 0.90 5.50 10.53 1.52

Full-service FAFH 5 -3.60 -1.11 9.09 7.23 10.53 13.76 1.15

Alcoholic beverages 11 -3.44 -1.21 1.55 5.82 0.43 2.14 0.32

Nonfood 2 -3.46 -3.92 10.41 9.55 4.48 12.57 4.06

Note: See notes to table A.1.

Source: Authors’ calculation of HEGY test for monthly data using aggregated average monthly household expenditures (U.S. Department of 

Labor, BLS, Consumer Expenditure Survey (2010a); U.S. Department of Labor, BLS, Consumer Price Index Database (2010c)).
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The Demand for Disaggregated Food-Away-from-Home and Food-at-Home Products in the United States / ERR-139

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Appendix table A.3

Second-stage estimated elasticities of demand for cereals and bakery products based on the GODDS 

model, 1998-2010

With respect to price of With 

respect 

to cereals 

and bakery 

expenditure R2

BreuschGodfrey 

statistic Constant

Demand 

for

Flour and 

prepared 

flour 

mixes

Breakfast 

cereals

Rice 

and 

pasta

Nonwhite 

bread

White 

bread

Biscuits, 

rolls, 

and muffins

Cakes 

and 

cookies

Other 

bakery

Flour and 

prepared 

mixes

0.07 1.20 0.93 -1.96 -0.37 -0.39 -0.98 -0.33 1.82 0.21 1.27 --0.0022

(0.60) (0.62) (0.52) (0.45) (0.49) (0.60) (0.95) (0.70) (0.21) (0.0008)

Breakfast 

cereals

0.33 -1.13 -0.09 -0.10 -0.06 0.09 0.50 -0.22 0.68 0.11 0.29 0.0039

(0.14) (0.31) (0.18) (0.15) (0.16) (0.20) (0.37) (0.25) (0.09) (0.0016)

Rice and 

pasta

0.41 -0.34 -0.08 -0.10 -0.36 0.20 -0.43 -0.91 1.62 0.21 9.13 -0.0012

(0.22) (0.34) (0.34) (0.21) (0.23) (0.28) (0.47) (0.35) (0.15) (0.0013)

Non-white 

bread

-0.71 -0.17 -0.00 -0.64 0.56 -0.09 0.30 0.04 0.72 0.17 0.73 0.0000

(0.18) (0.25) (0.19) (0.28) (0.24) (0.27) (0.40) (0.29) (0.08) (0.0008)

White 

bread

-0.18 -0.23 -0.42 0.77 -1.57 -0.09 0.56 0.01 1.16 0.03 13.89 0.0006

(0.28) (0.41) (0.30) (0.36) (0.50) (0.45) (0.62) (0.45) (0.13) (0.0009)

Biscuits, 

rolls, and 

muffins

-0.14 0.16 0.31 -0.11 -0.05 -0.25 -1.00 0.30 0.77 0.05 0.01 -0.0002

(0.29) (0.41) (0.31) (0.33) (0.37) (0.62) (0.64) (0.47) (0.12) (0.0011)

Cakes 

and cookies

-0.21 0.44 -0.20 0.14 0.24 -0.55 -1.27 0.24 1.18 0.07 2.80 -0.0005

(0.23) (0.40) (0.27) (0.25) (0.27) (0.33) (0.74) (0.43) (0.12) (0.0020)

Other 

bakery 

-0.03 -0.24 -0.38 0.01 0.03 0.13 0.27 -0.63 0.85 na na na

(0.15) (0.23) (0.17) (0.16) (0.17) (0.21) (0.38) (0.35) (0.08)

Notes: Estimated elasticities of demand were computed at the mean of the data. Standard errors were bootstrapped using the residual method. 

Total expenditure includes expenditures on durable and nondurable goods and services. The R2 and the Breusch-Godfrey statistic are for the 

individual equations and Breusch-Godfrey statistic is distributed χ2(1), for which the 10% critical value is 2.71.

Source: Authors’ calculations using iterated feasible generalized least squares (GLS, Stata version 11) with homogeneity and symmetry constraints imposed.

GODDS = Generalized Ordinary Differential Demand System.
39

The Demand for Disaggregated Food-Away-from-Home and Food-at-Home Products in the United States / ERR-139

Economic Research Service/USDA

Appendix table A.4

Second-stage estimated elasticities of demand for meat based on the GODDS model, 1998-2010

With respect to price of With respect 

to meat 

expenditure R2

BreuschGodfrey 

Demand for Beef Pork statistic Constant

Other 

meat Poultry Fish Eggs

Beef

-0.93 0.15 -0.10 -0.17 -0.23 -0.05 1.34 0.18 3.54 0.0009

(0.19) (0.14) (0.12) (0.11) (0.13) (0.03) (0.07) (0.0022)

Pork

0.30 -1.40 0.09 0.13 -0.16 -0.03 1.08 0.05 4.61 0.0018

(0.20) (0.23) (0.17) (0.15) (0.17) (0.04) (0.07) (0.0016)

Other red meat

-0.02 0.23 -1.12 -0.13 0.50 -0.10 0.63 0.13 0.28 -0.0012

(0.26) (0.26) (0.41) (0.27) (0.29) (0.06) (0.09) (0.0013)

Poultry

-0.11 0.21 -0.11 -0.92 0.15 0.01 0.77 0.10 2.51 0.0013

(0.19) (0.17) (0.20) (0.24) (0.18) (0.04) (0.06) (0.0013)

Fish

-0.34 -0.19 0.40 0.16 -0.94 -0.02 0.93 0.04 1.34 -0.0019

(0.25) (0.23) (0.26) (0.22) (0.31) (0.05) (0.10) (0.0017)

Eggs

-0.14 -0.07 -0.27 0.05 -0.02 -0.26 0.72

na na na

(0.19) (0.17) (0.16) (0.15) (0.16) (0.06) (0.08)

Notes: Estimated elasticities of demand were computed at the mean of the data. Standard errors were bootstrapped using the residual method. 

Total expenditure includes expenditures on durable and nondurable goods and services. The R2 and the Breusch-Godfrey statistic are for the 

individual equations and Breusch-Godfrey statistic is distributed χ2(1), for which the 10% critical value is 2.71.

Source: Authors’ calculations using iterated feasible generalized least squares (GLS, Stata version 11) with homogeneity and symmetry constraints imposed.

Appendix table A.5

Second-stage estimated elasticities of demand for dairy based on the GODDS model, 1998-2010

With respect to price of With respect 

to dairy 

expenditure R2

BreuschGodfrey 

Demand for Cheese statistic Constant

Ice cream and 

frozen desserts Milk

Other 

dairy

Cheese

-1.02 -0.14 -0.31 0.26 1.21 0.08 1.73 -0.0017

(0.21) (0.12) (0.10) (0.17) (0.08) (0.0017)

Ice cream and 

related products

-0.25 -0.43 -0.53 0.04 1.18 0.23 0.00 0.0027

(0.22) (0.23) (0.14) (0.27) (0.13) (0.0014)

Milk

-0.14 -0.18 -0.32 -0.15 0.79 0.38 8.79 0.0028

(0.09) (0.06) (0.08) (0.08) (0.07) (0.0016)

Other dairy

0.69 0.10 -0.40 -1.25 0.85

na na na

(0.37) (0.32) (0.21) (0.52) (0.17)

Notes: Estimated elasticities of demand were computed at the mean of the data. Standard errors were bootstrapped using the residual method. 

Total expenditure includes expenditures on durable and nondurable goods and services. The R2 and the Breusch-Godfrey statistic are for the 

individual equations and Breusch-Godfrey statistic is distributed χ2(1), for which the 10% critical value is 2.71.

Source: Authors’ calculations using iterated feasible generalized least squares (GLS, Stata version 11) with homogeneity and symmetry constraints imposed.
40

The Demand for Disaggregated Food-Away-from-Home and Food-at-Home Products in the United States / ERR-139

Economic Research Service/USDA

Appendix table A.6

Second-stage estimated elasticities of demand for fruits and vegetables based on the GODDS model, 

1998-2010

With respect to price of With 

respect 

to 

fruit/veg. 

expenditure R2

BreuschGodfrey 

statistic Constant

Demand 

for Apples

Bananas CitrusOther 

fruits

PotatoesLettuceTomatoesOther 

veg.

Processed 

fruits/

vegetables

Apples

-0.60 -0.03 0.02 -0.11 -0.11 0.03 -0.05 0.21 -0.13 0.77 0.06 0.01 0.0008

(0.14) (0.11) (0.08) (0.15) (0.10) (0.06) (0.07) (0.16) (0.20) (0.12) (0.0007)

Bananas

-0.07 -1.01 -0.11 0.06 0.01 -0.14 -0.05 0.12 -0.05 1.24 0.05 3.04 0.0004

(0.11) (0.19) (0.08) (0.15) (0.11) (0.06) (0.07) (0.17) (0.25) (0.11) (0.0006)

Citrus

-0.03 -0.10 -1.09 -0.15 -0.10 0.00 0.10 0.05 -0.09 1.41 0.17 0.98 -0.0008

(0.07) (0.07) (0.09) (0.13) (0.07) (0.04) (0.06) (0.12) (0.15) (0.12) (0.0007)

Other 

fruits

-0.06 0.04 -0.04 -0.93 0.03 -0.05 -0.09 -0.11 0.17 1.03 0.00 34.64 -0.0006

(0.06) (0.06) (0.06) (0.14) (0.06) (0.04) (0.05) (0.10) (0.13) (0.10) (0.0014)

Potatoes

-0.11 0.04 -0.07 0.14 -0.45 -0.02 0.10 -0.35 -0.03 0.75 0.17 1.38 0.0007

(0.11) (0.11) (0.08) (0.15) (0.14) (0.06) (0.07) (0.16) (0.21) (0.12) (0.0007)

Lettuce

0.02 -0.17 0.03 -0.16 -0.04 -0.85 0.05 0.12 -0.01 1.01 0.05 1.41 -0.0001

(0.08) (0.08) (0.07) (0.13) (0.08) (0.07) (0.06) (0.13) (0.16) (0.10) (0.0004)

Tomatoes

-0.10 -0.06 0.11 -0.29 0.05 0.01 -0.57 0.00 -0.58 1.43 0.28 1.34 0.0002

(0.07) (0.07) (0.06) (0.12) (0.07) (0.04) (0.08) (0.12) (0.15) (0.12) (0.0007)

Other 

vegetables

0.06 0.05 0.05 -0.09 -0.14 0.03 0.03 -0.98 -0.03 1.01 0.02 6.88 0.0010

(0.06) (0.06) (0.05) (0.09) (0.05) (0.03) (0.04) (0.12) (0.12) (0.08) (0.0012)

Processed 

fruits/

vegetables

-0.04 0.02 0.02 0.18 -0.01 0.01 -0.13 0.03 -0.84 0.77

na na na

(0.06) (0.07) (0.05) (0.09) (0.06) (0.03) (0.04) (0.09) (0.16) (0.09)

Notes: Estimated elasticities of demand were computed at the mean of the data. Standard errors were bootstrapped using the residual method. 

Total expenditure includes expenditures on durable and nondurable goods and services. The R2 and the Breusch-Godfrey statistic are for the 

individual equations and Breusch-Godfrey statistic is distributed χ2(1), for which the 10% critical value is 2.71.

Source: Authors’ calculations using iterated feasible generalized least squares (GLS, Stata version 11) with homogeneity and symmetry constraints 

imposed.
41

The Demand for Disaggregated Food-Away-from-Home and Food-at-Home Products in the United States / ERR-139

Economic Research Service/USDA

Appendix table A.7

Second-stage estimated elasticities of demand for nonalcoholic beverages based on the GODDS 

(Generalized Ordinary Differential Demand System) model, 1998-2010

With respect to price of

With respect to 

nonalcoholic 

beverage 

Demand for expenditure R2 Constant

Coffee and 

tea

Carbonated 

beverages

Nonfrozen 

noncarbonated juices 

and drinks

Frozen noncarbonated 

juices and 

drinks 

Coffee and tea

-0.17 -0.07 -0.31 -0.01 0.56 0.25 -0.0042

(0.26) (0.31) (0.30) (0.08) (0.14) (0.0017)

Carbonated 

beverages

-0.12 -0.58 -0.37 0.01 1.06 0.01 0.0074

(0.15) (0.34) (0.30) (0.07) (0.09) (0.0024)

Nonfrozen 

noncarbonated 

juices and drinks

-0.22 -0.31 -0.61 0.01 1.13 0.18 -0.0048

(0.11) (0.23) (0.27) (0.07) (0.07) (0.0024)

Frozen 

noncarbonated 

juices and drinks 

-0.14 0.25 0.38 -1.37 0.88

na na

(0.59) (1.11) (1.36) (0.91) (0.33)

Notes: Estimated elasticities of demand were computed at the mean of the data. Standard errors were bootstrapped using the residual method. 

Total expenditure includes expenditures on durable and nondurable goods and services. The R2 values are for the individual equations.

Source: Authors’ calculations using iterated feasible generalized least squares (GLS, Stata version 11) with homogeneity and symmetry constraints imposed and with correction for first-order autocorrelation.

Appendix table A.8

Second-stage estimated elasticities of demand for other FAH based on the GODDS model, 1998-2010

With respect to price of With 

respect to 

other FAH 

expenditure R2

BreuschGodfrey 

Demand for statistic Constant

Sugar 

and 

sweets

Fats 

and oils Soups

Frozen 

foods Snacks

Condiments, 

sauces, 

seasonings

Miscellaneous

Sugar and 

sweets

-0.47 -0.06 -0.70 -0.75 0.02 0.63 -0.06 1.39 0.08 0.41 0.0086

(0.73) (0.23) (0.23) (0.46) (0.14) (0.35) (0.56) (0.18) (0.0028)

Fats and oils

0.04 -0.24 -0.19 -0.24 0.02 0.06 -0.27 0.83 0.19 2.06 0.0037

(0.25) (0.16) (0.10) (0.22) (0.06) (0.14) (0.25) (0.10) (0.0013)

Soups

-2.05 -0.48 0.18 0.96 0.05 0.30 0.59 0.45 0.04 0.01 -0.0018

(0.72) (0.28) (0.56) (0.68) (0.27) (0.58) (0.67) (0.18) (0.0009)

Frozen foods

-0.74 -0.26 0.30 -1.06 -0.23 0.07 0.95 0.96 0.05 0.75 -0.0038

(0.50) (0.22) (0.24) (0.62) (0.14) (0.35) (0.47) (0.14) (0.0021)

Snacks

0.22 0.11 0.07 -1.01 -1.15 1.06 -0.10 0.81 0.04 1.31 0.0000

(0.70) (0.27) (0.42) (0.65) (0.47) (0.60) (0.60) (0.16) (0.0005)

Condiments, 

sauces, 

seasonings

0.89 0.08 0.10 0.12 0.26 -1.95 -0.25 0.75 0.12 0.80 0.0008

(0.42) (0.16) (0.22) (0.39) (0.15) (0.44) (0.37) (0.10) (0.0013)

Miscellaneous

-0.01 -0.27 0.11 0.69 -0.03 -0.24 -1.44 1.18

na na na

(0.46) (0.18) (0.18) (0.36) (0.10) (0.25) (0.55) (0.14)

Notes: Estimated elasticities of demand were computed at the mean of the data. Standard errors were bootstrapped using the residual method. 

Total expenditure includes expenditures on durable and nondurable goods and services. The R2 and the Breusch-Godfrey statistic are for the 

individual equations and Breusch-Godfrey statistic is distributed χ2(1), for which the 10% critical value is 2.71.

Source: Authors’ calculations using iterated feasible GLS (Stata version 11) with homogeneity and symmetry constraints imposed.
42

The Demand for Disaggregated Food-Away-from-Home and Food-at-Home Products in the United States / ERR-139

Economic Research Service/USDA

Appendix table A.9

Second-stage estimated elasticities of demand for FAFH (food away from home) and alcohol based on the 

GODDS model, 1998-2010

With respect to price of With respect 

to FAFH 

and alcohol 

expenditure R2

BreuschGodfrey 

Demand for Alcohol statistic Constant

Limitedservice Full-service Other FAFH

Alcohol

-1.13 -2.39 2.17 -0.16 1.53 0.10 6.24 -0.0021

(0.63) (0.66) (0.74) (0.12) (0.16) (0.0020)

Limited-service

-0.89 -0.26 0.31 -0.00 0.84 0.15 4.25 0.0057

(0.27) (0.94) (0.95) (0.06) (0.07) (0.0024)

Full-service

0.92 0.24 -2.08 -0.02 0.94 0.08 21.87 -0.0054

(0.29) (0.88) (0.96) (0.06) (0.08) (0.0027)

Other FAFH

-0.31 -0.06 -0.17 -0.45 0.98

na na na

(0.37) (0.32) (0.21) (0.52) (0.17)

Notes: Estimated elasticities of demand were computed at the mean of the data. Standard errors were bootstrapped using the residual method. 

Total expenditure includes expenditures on durable and nondurable goods and services. The R2 and the Breusch-Godfrey statistic are for the 

individual equations and Breusch-Godfrey statistic is distributed χ2(1), for which the 10% critical value is 2.71.

Source: Authors’ calculations using iterated feasible GLS (Stata version 11) with homogeneity and symmetry constraints imposed.

FAFH = Food away from home, including limited-service and full-service restaurants; FAH = Food at home; GODDS = Generalized Ordinary 

Differential Demand System. 
43

The Demand for Disaggregated Food-Away-from-Home and Food-at-Home Products in the United States / ERR-139

Economic Research Service/USDA

Appendix table A.10`

Estimated unconditional elasticities of demand

With respect to price of

Demand for

Flour, prep. 

mixes

Breakfast 

cereals

Rice and 

pasta

Nonwhite 

bread

White 

bread

Biscuits, 

rolls, muff.

Cakes and 

cookies

Other 

bakery 

products

Flour, prep. mixes

0.07 1.41 0.94 -1.84 -0.32 -0.30 -0.88 -0.14

(0.71) (0.67) (0.56) (0.51) (0.58) (0.68) (1.09) (0.74)

Breakfast cereals

0.32 -1.05 -0.08 -0.05 -0.04 0.12 0.54 -0.15

(0.15) (0.33) (0.19) (0.17) (0.18) (0.21) (0.40) (0.25)

Rice and pasta

0.41 -0.15 -0.07 0.00 -0.31 0.28 -0.34 -0.75

(0.24) (0.36) (0.38) (0.22) (0.27) (0.30) (0.53) (0.36)

Nonwhite bread

-0.72 -0.09 0.00 -0.59 0.58 -0.05 0.34 0.11

(0.20) (0.28) (0.20) (0.30) (0.28) (0.31) (0.45) (0.31)

White bread

-0.18 -0.10 -0.42 0.84 -1.54 -0.04 0.63 0.13

(0.33) (0.44) (0.35) (0.41) (0.58) (0.54) (0.69) (0.47)

Biscuits, rolls, 

muff.

-0.14 0.25 0.31 -0.06 -0.03 -0.21 -0.95 0.38

(0.33) (0.44) (0.34) (0.38) (0.45) (0.71) (0.72) (0.47)

Cakes and 

cookies

-0.22 0.57 -0.19 0.21 0.27 -0.49 -1.20 0.36

(0.27) (0.43) (0.30) (0.28) (0.30) (0.37) (0.81) (0.42)

Other bakery

-0.03 -0.14 -0.37 0.06 0.05 0.17 0.31 -0.55

(0.16) (0.23) (0.18) (0.17) (0.18) (0.21) (0.37) (0.34)

Beef

0.00 0.01 0.01 0.00 0.00 0.00 0.01 0.01

(0.01) (0.01) (0.02) (0.01) (0.01) (0.01) (0.02) (0.02)

Pork

0.00 0.00 0.01 0.00 0.00 0.00 0.01 0.01

(0.01) (0.01) (0.01) (0.01) (0.01) (0.01) (0.02) (0.01)

Other red meat

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

(0.00) (0.01) (0.01) (0.00) (0.00) (0.00) (0.01) (0.01)

Poultry

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

(0.00) (0.01) (0.01) (0.00) (0.01) (0.00) (0.01) (0.01)

Fish

0.00 0.00 0.00 0.00 0.00 0.00 0.01 0.00

(0.01) (0.01) (0.01) (0.01) (0.01) (0.00) (0.01) (0.01)

See notes at end of table.
44

The Demand for Disaggregated Food-Away-from-Home and Food-at-Home Products in the United States / ERR-139

Economic Research Service/USDA

Appendix table A.10

Estimated unconditional elasticities of demand--continued

With respect to price of

Demand for Beef Pork

Other 

red meat Poultry Fish Eggs Cheese

Ice cream 

and frozen 

desserts Milk

Flour, prep. mixes

0.04 0.02 0.01 0.01 0.01 0.00 0.24 0.13 0.19

(0.09) (0.05) (0.02) (0.03) (0.03) (0.01) (0.07) (0.04) (0.06)

Breakfast cereals

0.01 0.01 0.00 0.01 0.00 0.00 0.09 0.05 0.07

(0.03) (0.02) (0.01) (0.01) (0.01) (0.00) (0.03) (0.01) (0.02)

Rice and pasta

0.03 0.02 0.01 0.01 0.01 0.00 0.22 0.12 0.17

(0.08) (0.04) (0.02) (0.03) (0.03) (0.01) (0.06) (0.03) (0.05)

Nonwhite bread

0.01 0.01 0.00 0.01 0.01 0.00 0.10 0.05 0.08

(0.04) (0.02) (0.01) (0.01) (0.01) (0.00) (0.03) (0.01) (0.02)

White bread

0.02 0.01 0.01 0.01 0.01 0.00 0.15 0.08 0.12

(0.06) (0.03) (0.01) (0.02) (0.02) (0.01) (0.05) (0.03) (0.03)

Biscuits, rolls, 

muff.

0.02 0.01 0.00 0.01 0.01 0.00 0.10 0.06 0.08

(0.04) (0.02) (0.01) (0.01) (0.01) (0.00) (0.03) (0.02) (0.02)

Cakes and 

cookies

0.02 0.01 0.01 0.01 0.01 0.00 0.16 0.08 0.12

(0.06) (0.03) (0.01) (0.02) (0.02) (0.01) (0.05) (0.03) (0.04)

Other bakery

0.02 0.01 0.00 0.01 0.01 0.00 0.11 0.06 0.09

(0.04) (0.02) (0.01) (0.02) (0.02) (0.00) (0.03) (0.02) (0.02)

Beef

-0.70 0.33 0.04 0.01 -0.09 0.00 0.01 0.01 0.01

(0.20) (0.15) (0.11) (0.12) (0.12) (0.03) (0.03) (0.01) (0.02)

Pork

0.48 -1.26 0.20 0.28 -0.05 0.01 0.01 0.01 0.01

(0.21) (0.26) (0.18) (0.18) (0.17) (0.04) (0.02) (0.01) (0.02)

Other red meat

0.09 0.32 -1.05 -0.04 0.56 -0.07 0.01 0.00 0.00

(0.26) (0.28) (0.42) (0.30) (0.29) (0.07) (0.01) (0.01) (0.01)

Poultry

0.02 0.31 -0.03 -0.81 0.23 0.04 0.01 0.00 0.01

(0.19) (0.20) (0.22) (0.28) (0.19) (0.04) (0.02) (0.01) (0.01)

Fish

-0.18 -0.06 0.50 0.28 -0.84 0.02 0.01 0.00 0.01

(0.24) (0.24) (0.25) (0.23) (0.30) (0.06) (0.02) (0.01) (0.01)

See notes at end of table.
45

The Demand for Disaggregated Food-Away-from-Home and Food-at-Home Products in the United States / ERR-139

Economic Research Service/USDA

Appendix table A.10

Estimated unconditional elasticities of demand--continued

With respect to price of

Demand for

Other 

dairy Apples Bananas Citrus

Other 

fresh fruits Potatoes Lettuce Tomatoes

Other fresh 

vegetable

Flour, prep. mixes

0.08 -0.03 -0.05 -0.06 -0.10 -0.03 -0.03 -0.06 -0.11

(0.03) (0.01) (0.02) (0.03) (0.05) (0.01) (0.01) (0.03) (0.05)

Breakfast cereals

0.03 -0.01 -0.02 -0.02 -0.04 -0.01 -0.01 -0.02 -0.04

(0.01) (0.01) (0.01) (0.01) (0.02) (0.01) (0.01) (0.01) (0.02)

Rice and pasta

0.07 -0.03 -0.04 -0.06 -0.09 -0.03 -0.02 -0.05 -0.10

(0.02) (0.01) (0.02) (0.03) (0.04) (0.01) (0.01) (0.02) (0.05)

Nonwhite bread

0.03 -0.01 -0.02 -0.02 -0.04 -0.01 -0.01 -0.02 -0.04

(0.01) (0.01) (0.01) (0.01) (0.02) (0.01) (0.01) (0.01) (0.02)

White bread

0.05 -0.02 -0.03 -0.04 -0.06 -0.02 -0.02 -0.04 -0.07

(0.02) (0.01) (0.01) (0.02) (0.03) (0.01) (0.01) (0.02) (0.03)

Biscuits, rolls, 

muff.

0.04 -0.01 -0.02 -0.03 -0.04 -0.01 -0.01 -0.02 -0.05

(0.01) (0.01) (0.01) (0.01) (0.02) (0.01) (0.01) (0.01) (0.02)

Cakes and 

cookies

0.05 -0.02 -0.03 -0.04 -0.07 -0.02 -0.02 -0.04 -0.07

(0.02) (0.01) (0.01) (0.02) (0.03) (0.01) (0.01) (0.02) (0.03)

Other bakery

0.04 -0.01 -0.02 -0.03 -0.05 -0.01 -0.01 -0.03 -0.05

(0.01) (0.01) (0.01) (0.01) (0.02) (0.01) (0.01) (0.01) (0.02)

Beef

0.00 0.01 0.01 0.02 0.03 0.01 0.01 0.01 0.03

(0.01) (0.01) (0.01) (0.01) (0.02) (0.01) (0.01) (0.01) (0.03)

Pork

0.00 0.01 0.01 0.01 0.02 0.01 0.01 0.01 0.02

(0.01) (0.01) (0.01) (0.01) (0.02) (0.01) (0.01) (0.01) (0.02)

Other red meat

0.00 0.00 0.01 0.01 0.01 0.00 0.00 0.01 0.01

(0.00) (0.00) (0.00) (0.01) (0.01) (0.00) (0.00) (0.01) (0.01)

Poultry

0.00 0.00 0.01 0.01 0.02 0.00 0.00 0.01 0.02

(0.01) (0.00) (0.01) (0.01) (0.01) (0.00) (0.00) (0.01) (0.01)

Fish

0.00 0.01 0.01 0.01 0.02 0.01 0.00 0.01 0.02

(0.01) (0.00) (0.01) (0.01) (0.02) (0.00) (0.00) (0.01) (0.02)

See notes at end of table.
46

The Demand for Disaggregated Food-Away-from-Home and Food-at-Home Products in the United States / ERR-139

Economic Research Service/USDA

Appendix table A.10

Estimated unconditional elasticities of demand--continued

With respect to price of

Demand for

Processed 

fruits and 

vegetables

Coffee 

and tea

Carbonated 

beverages

Noncarbonated 

beverages

Frozen 

beverages

Sugar and 

sweets

Fats 

and 

oils Soups Snacks

Flour, prep. mixes

-0.10 -0.02 -0.06 -0.09 0.00 0.12 0.06 0.01 0.01

(0.05) (0.03) (0.12) (0.17) (0.01) (0.16) (0.09) (0.02) (0.02)

Breakfast cereals

-0.04 -0.01 -0.02 -0.03 0.00 0.04 0.02 0.00 0.01

(0.02) (0.01) (0.04) (0.06) (0.00) (0.06) (0.03) (0.01) (0.01)

Rice and pasta

-0.09 -0.02 -0.06 -0.08 0.00 0.10 0.06 0.01 0.01

(0.04) (0.03) (0.11) (0.15) (0.01) (0.15) (0.08) (0.02) (0.02)

Nonwhite bread

-0.04 -0.01 -0.03 -0.03 0.00 0.05 0.02 0.00 0.01

(0.02) (0.01) (0.05) (0.07) (0.00) (0.06) (0.03) (0.01) (0.01)

White bread

-0.06 -0.01 -0.04 -0.06 0.00 0.07 0.04 0.01 0.01

(0.03) (0.02) (0.08) (0.11) (0.00) (0.10) (0.06) (0.01) (0.01)

Biscuits, rolls, 

muff.

-0.04 -0.01 -0.03 -0.04 0.00 0.05 0.03 0.01 0.01

(0.02) (0.01) (0.05) (0.07) (0.00) (0.07) (0.04) (0.01) (0.01)

Cakes and 

cookies

-0.07 -0.01 -0.04 -0.06 0.00 0.08 0.04 0.01 0.01

(0.03) (0.02) (0.08) (0.11) (0.00) (0.11) (0.06) (0.01) (0.01)

Other bakery

-0.05 -0.01 -0.03 -0.04 0.00 0.05 0.03 0.01 0.01

(0.02) (0.01) (0.06) (0.08) (0.00) (0.08) (0.04) (0.01) (0.01)

Beef

0.03 0.01 0.04 0.05 0.00 0.09 0.05 0.01 0.01

(0.02) (0.01) (0.02) (0.03) (0.00) (0.04) (0.02) (0.01) (0.01)

Pork

0.02 0.01 0.03 0.04 0.00 0.07 0.04 0.01 0.01

(0.02) (0.00) (0.02) (0.03) (0.00) (0.03) (0.02) (0.00) (0.00)

Other red meat

0.01 0.00 0.02 0.03 0.00 0.04 0.02 0.00 0.00

(0.01) (0.00) (0.01) (0.02) (0.00) (0.02) (0.01) (0.00) (0.00)

Poultry

0.01 0.01 0.02 0.03 0.00 0.05 0.03 0.01 0.01

(0.01) (0.00) (0.01) (0.02) (0.00) (0.03) (0.01) (0.00) (0.00)

Fish

0.02 0.01 0.03 0.04 0.00 0.06 0.03 0.01 0.01

(0.02) (0.00) (0.02) (0.02) (0.00) (0.03) (0.02) (0.00) (0.00)

See notes at end of table.
47

The Demand for Disaggregated Food-Away-from-Home and Food-at-Home Products in the United States / ERR-139

Economic Research Service/USDA

Appendix table A.10

Estimated unconditional elasticities of demand--continued

With respect to price of

With 

respect to 

Demand for expenditure

Condiments, 

sauces, 

season.

Miscellaneous FAHAlcoholic 

beverages

Limitedservice 

FAFH

Full-service 

FAFH

Other 

FAFH Nonfood

Flour, prep. mixes

0.05 0.12 0.07 0.09 0.11 0.02 0.30 0.01

(0.07) (0.16) (0.17) (0.22) (0.27) (0.05) (0.61) (0.08)

Breakfast cereals

0.02 0.04 0.03 0.03 0.04 0.01 0.11 0.00

(0.03) (0.06) (0.06) (0.08) (0.10) (0.02) (0.23) (0.03)

Rice and pasta

0.05 0.11 0.06 0.08 0.10 0.02 0.26 0.01

(0.06) (0.14) (0.15) (0.20) (0.24) (0.04) (0.54) (0.08)

Nonwhite bread

0.02 0.05 0.03 0.04 0.04 0.01 0.12 0.00

(0.03) (0.06) (0.07) (0.09) (0.11) (0.02) (0.24) (0.03)

White bread

0.03 0.08 0.04 0.06 0.07 0.01 0.19 0.01

(0.05) (0.10) (0.11) (0.14) (0.17) (0.03) (0.39) (0.05)

Biscuits, rolls, 

muff.

0.02 0.05 0.03 0.04 0.05 0.01 0.13 0.00

(0.03) (0.07) (0.07) (0.10) (0.12) (0.02) (0.26) (0.04)

Cakes and 

cookies

0.03 0.08 0.04 0.06 0.07 0.01 0.19 0.01

(0.05) (0.11) (0.11) (0.14) (0.18) (0.03) (0.39) (0.05)

Other bakery

0.02 0.06 0.03 0.04 0.05 0.01 0.14 0.00

(0.03) (0.08) (0.08) (0.10) (0.13) (0.02) (0.28) (0.04)

Beef

0.04 0.09 0.06 0.07 0.09 0.01 -0.54 0.05

(0.02) (0.04) (0.11) (0.14) (0.18) (0.03) (0.60) (0.09)

Pork

0.03 0.07 0.04 0.06 0.07 0.01 -0.43 0.04

(0.02) (0.03) (0.09) (0.11) (0.14) (0.02) (0.48) (0.07)

Other red meat

0.02 0.04 0.03 0.03 0.04 0.01 -0.25 0.02

(0.01) (0.02) (0.05) (0.07) (0.08) (0.01) (0.29) (0.04)

Poultry

0.02 0.05 0.03 0.04 0.05 0.01 -0.31 0.03

(0.01) (0.02) (0.06) (0.08) (0.10) (0.02) (0.35) (0.05)

Fish

0.03 0.06 0.04 0.05 0.06 0.01 -0.37 0.03

(0.01) (0.03) (0.08) (0.10) (0.12) (0.02) (0.42) (0.06)

See notes at end of table.
48

The Demand for Disaggregated Food-Away-from-Home and Food-at-Home Products in the United States / ERR-139

Economic Research Service/USDA

Appendix table A.10

Estimated unconditional elasticities of demand

With respect to price of

Demand for

Flour, 

prep. 

mixes

Breakfast 

cereals

Rice and 

pasta

Non-white 

bread

White 

bread

Biscuits, 

rolls, 

muff.

Cakes 

and 

cookies

Other 

bakery 

products Beef

Eggs

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.02

(0.00) (0.01) (0.01) (0.00) (0.00) (0.00) (0.01) (0.01) (0.20)

Cheese

0.05 0.07 0.09 0.05 0.05 0.04 0.12 0.10 0.03

(0.01) (0.02) (0.03) (0.01) (0.02) (0.01) (0.04) (0.03) (0.06)

Ice cream and 

froz. dessert

0.05 0.07 0.09 0.05 0.05 0.04 0.12 0.10 0.03

(0.01) (0.02) (0.03) (0.01) (0.02) (0.01) (0.04) (0.03) (0.06)

Milk

0.03 0.05 0.06 0.03 0.04 0.03 0.08 0.07 0.02

(0.01) (0.01) (0.02) (0.01) (0.01) (0.01) (0.02) (0.02) (0.04)

Other dairy

0.04 0.06 0.07 0.04 0.04 0.03 0.09 0.08 0.02

(0.01) (0.02) (0.02) (0.01) (0.01) (0.01) (0.03) (0.02) (0.04)

Apples

-0.02 -0.03 -0.04 -0.02 -0.02 -0.02 -0.05 -0.04 0.06

(0.01) (0.02) (0.02) (0.01) (0.01) (0.01) (0.02) (0.02) (0.05)

Bananas

-0.03 -0.05 -0.06 -0.03 -0.03 -0.03 -0.08 -0.07 0.09

(0.01) (0.02) (0.03) (0.01) (0.02) (0.01) (0.04) (0.03) (0.08)

Citrus

-0.03 -0.06 -0.07 -0.03 -0.04 -0.03 -0.09 -0.07 0.10

(0.02) (0.03) (0.03) (0.02) (0.02) (0.02) (0.04) (0.04) (0.09)

Other fresh fruits

-0.03 -0.04 -0.05 -0.03 -0.03 -0.02 -0.07 -0.05 0.07

(0.01) (0.02) (0.02) (0.01) (0.01) (0.01) (0.03) (0.03) (0.07)

Potatoes

-0.02 -0.03 -0.04 -0.02 -0.02 -0.02 -0.05 -0.04 0.05

(0.01) (0.01) (0.02) (0.01) (0.01) (0.01) (0.02) (0.02) (0.05)

Lettuce

-0.02 -0.04 -0.05 -0.02 -0.03 -0.02 -0.06 -0.05 0.07

(0.01) (0.02) (0.03) (0.01) (0.01) (0.01) (0.03) (0.03) (0.06)

Tomatoes

-0.03 -0.06 -0.07 -0.04 -0.04 -0.03 -0.09 -0.08 0.10

(0.02) (0.03) (0.04) (0.02) (0.02) (0.02) (0.04) (0.04) (0.09)

Other fresh 

vegetables

-0.02 -0.04 -0.05 -0.02 -0.03 -0.02 -0.07 -0.05 0.07

(0.01) (0.02) (0.02) (0.01) (0.01) (0.01) (0.03) (0.03) (0.06)

See notes at end of table.
49

The Demand for Disaggregated Food-Away-from-Home and Food-at-Home Products in the United States / ERR-139

Economic Research Service/USDA

Appendix table A.10

Estimated unconditional elasticities of demand--continued

With respect to price of

Demand for Pork

Other 

red meat Poultry Fish Eggs Cheese

Ice 

cream 

and 

frozen 

desserts Milk

Other 

dairy Apples

Eggs

0.03 -0.20 0.15 0.06 -0.24 0.01 0.00 0.01 0.00 0.00

(0.19) (0.18) (0.17) (0.17) (0.06) (0.01) (0.01) (0.01) (0.00) (0.00)

Cheese

0.01 0.01 0.01 0.01 0.00 -0.70 0.07 0.15 0.42 0.00

(0.03) (0.01) (0.02) (0.02) (0.01) (0.24) (0.13) (0.13) (0.19) (0.01)

Ice cream and 

froz. dessert

0.01 0.01 0.01 0.01 0.00 0.13 -0.23 -0.08 0.12 0.00

(0.03) (0.01) (0.02) (0.02) (0.01) (0.24) (0.22) (0.16) (0.25) (0.01)

Milk

0.01 0.00 0.01 0.01 0.00 0.13 -0.04 -0.10 -0.03 0.00

(0.02) (0.01) (0.01) (0.01) (0.00) (0.11) (0.07) (0.09) (0.09) (0.01)

Other dairy

0.01 0.00 0.01 0.01 0.00 0.93 0.14 -0.08 -1.04 0.00

(0.02) (0.01) (0.02) (0.02) (0.00) (0.42) (0.29) (0.23) (0.53) (0.01)

Apples

0.03 0.01 0.02 0.02 0.00 -0.01 0.00 0.00 0.00 -0.58

(0.03) (0.01) (0.02) (0.02) (0.00) (0.03) (0.01) (0.02) (0.01) (0.16)

Bananas

0.05 0.02 0.03 0.03 0.01 -0.01 0.00 -0.01 0.00 -0.03

(0.04) (0.02) (0.03) (0.03) (0.01) (0.04) (0.02) (0.03) (0.01) (0.12)

Citrus

0.06 0.02 0.04 0.04 0.01 -0.01 -0.01 -0.01 0.00 0.01

(0.05) (0.02) (0.03) (0.03) (0.01) (0.05) (0.03) (0.04) (0.02) (0.09)

Other fresh fruits

0.04 0.02 0.03 0.03 0.01 -0.01 0.00 -0.01 0.00 -0.03

(0.04) (0.01) (0.02) (0.02) (0.01) (0.04) (0.02) (0.03) (0.01) (0.07)

Potatoes

0.03 0.01 0.02 0.02 0.00 -0.01 0.00 0.00 0.00 -0.09

(0.03) (0.01) (0.02) (0.02) (0.00) (0.03) (0.01) (0.02) (0.01) (0.11)

Lettuce

0.04 0.02 0.03 0.03 0.01 -0.01 0.00 -0.01 0.00 0.05

(0.04) (0.01) (0.02) (0.02) (0.01) (0.03) (0.02) (0.03) (0.01) (0.09)

Tomatoes

0.06 0.02 0.04 0.04 0.01 -0.01 -0.01 -0.01 0.00 -0.06

(0.05) (0.02) (0.03) (0.03) (0.01) (0.05) (0.03) (0.04) (0.02) (0.08)

Other fresh 

vegetables

0.04 0.02 0.03 0.03 0.01 -0.01 0.00 -0.01 0.00 0.09

(0.04) (0.01) (0.02) (0.02) (0.01) (0.03) (0.02) (0.03) (0.01) (0.06)

See notes at end of table.
50

The Demand for Disaggregated Food-Away-from-Home and Food-at-Home Products in the United States / ERR-139

Economic Research Service/USDA

Appendix table A.10

Estimated unconditional elasticities of demand--continued

With respect to price of

Demand for Bananas Citrus

Other 

fresh 

fruits Potatoes Lettuce Tomatoes

Other 

fresh 

vegetable

Processed 

fruits and 

vegetables

Coffee 

and tea

Eggs

0.01 0.01 0.01 0.00 0.00 0.01 0.02 0.01 0.01

(0.01) (0.01) (0.01) (0.00) (0.00) (0.01) (0.01) (0.01) (0.00)

Cheese

0.00 0.00 -0.01 0.00 0.00 0.00 -0.01 -0.01 -0.02

(0.01) (0.02) (0.03) (0.01) (0.01) (0.02) (0.03) (0.03) (0.01)

Ice cream and 

froz. dessert

0.00 0.00 -0.01 0.00 0.00 0.00 -0.01 -0.01 -0.02

(0.01) (0.02) (0.03) (0.01) (0.01) (0.01) (0.03) (0.03) (0.01)

Milk

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.01

(0.01) (0.01) (0.02) (0.01) (0.00) (0.01) (0.02) (0.02) (0.01)

Other dairy

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.01

(0.01) (0.01) (0.02) (0.01) (0.01) (0.01) (0.02) (0.02) (0.01)

Apples

-0.03 0.01 -0.08 -0.09 0.03 -0.06 0.24 -0.06 0.00

(0.12) (0.10) (0.17) (0.11) (0.06) (0.08) (0.17) (0.22) (0.01)

Bananas

-1.01 -0.12 0.10 0.05 -0.13 -0.06 0.16 0.06 0.00

(0.21) (0.10) (0.18) (0.12) (0.07) (0.08) (0.19) (0.28) (0.01)

Citrus

-0.10 -1.10 -0.11 -0.06 0.02 0.09 0.10 0.04 0.00

(0.08) (0.10) (0.15) (0.08) (0.05) (0.07) (0.13) (0.17) (0.01)

Other fresh fruits

0.04 -0.05 -0.90 0.06 -0.04 -0.10 -0.07 0.27 0.00

(0.07) (0.07) (0.15) (0.07) (0.04) (0.06) (0.11) (0.14) (0.01)

Potatoes

0.04 -0.07 0.16 -0.42 -0.01 0.09 -0.32 0.03 0.00

(0.12) (0.09) (0.17) (0.15) (0.06) (0.08) (0.17) (0.23) (0.01)

Lettuce

-0.17 0.03 -0.13 -0.01 -0.84 0.04 0.16 0.08 0.00

(0.09) (0.08) (0.14) (0.09) (0.07) (0.07) (0.15) (0.18) (0.01)

Tomatoes

-0.06 0.10 -0.24 0.09 0.03 -0.58 0.06 -0.45 0.00

(0.08) (0.08) (0.15) (0.07) (0.05) (0.09) (0.14) (0.17) (0.01)

Other fresh 

vegetables

0.06 0.04 -0.06 -0.11 0.04 0.02 -0.94 0.07 0.00

(0.06) (0.05) (0.10) (0.06) (0.04) (0.05) (0.14) (0.13) (0.01)

See notes at end of table.
51

The Demand for Disaggregated Food-Away-from-Home and Food-at-Home Products in the United States / ERR-139

Economic Research Service/USDA

Appendix table A.10

Estimated unconditional elasticities of demand--continued

With respect to price of

Demand for

Carbonated 

beverages

Noncarbonated 

beverages

Frozen 

beverages

Sugar and 

sweets

Fats and 

oils Soups

Frozen 

meals and 

snacks Snacks

Eggs

0.02 0.03 0.00 0.05 0.03 0.00 0.03 0.01

(0.01) (0.02) (0.00) (0.02) (0.01) (0.00) (0.01) (0.00)

Cheese

-0.07 -0.09 0.00 -0.13 -0.07 -0.01 -0.08 -0.02

(0.04) (0.05) (0.00) (0.06) (0.03) (0.01) (0.04) (0.01)

Ice cream and 

froz. dessert

-0.07 -0.09 0.00 -0.13 -0.07 -0.01 -0.08 -0.02

(0.04) (0.05) (0.00) (0.06) (0.03) (0.01) (0.04) (0.01)

Milk

-0.05 -0.06 0.00 -0.09 -0.05 -0.01 -0.06 -0.01

(0.02) (0.04) (0.00) (0.04) (0.02) (0.01) (0.03) (0.00)

Other dairy

-0.05 -0.07 0.00 -0.10 -0.06 -0.01 -0.07 -0.01

(0.03) (0.04) (0.00) (0.05) (0.02) (0.01) (0.03) (0.01)

Apples

0.01 0.01 0.00 0.12 0.06 0.01 0.07 0.01

(0.03) (0.04) (0.00) (0.05) (0.03) (0.01) (0.03) (0.01)

Bananas

0.01 0.02 0.00 0.19 0.10 0.02 0.12 0.02

(0.05) (0.07) (0.00) (0.08) (0.04) (0.01) (0.05) (0.01)

Citrus

0.01 0.02 0.00 0.22 0.11 0.02 0.14 0.02

(0.05) (0.08) (0.00) (0.09) (0.05) (0.01) (0.06) (0.01)

Other fresh fruits

0.01 0.01 0.00 0.16 0.08 0.02 0.10 0.02

(0.04) (0.06) (0.00) (0.07) (0.03) (0.01) (0.04) (0.01)

Potatoes

0.01 0.01 0.00 0.11 0.06 0.01 0.07 0.01

(0.03) (0.04) (0.00) (0.05) (0.03) (0.01) (0.03) (0.01)

Lettuce

0.01 0.01 0.00 0.15 0.08 0.02 0.10 0.02

(0.04) (0.05) (0.00) (0.07) (0.03) (0.01) (0.04) (0.01)

Tomatoes

0.01 0.02 0.00 0.22 0.12 0.02 0.14 0.03

(0.05) (0.08) (0.00) (0.09) (0.05) (0.01) (0.06) (0.01)

Other fresh 

vegetables

0.01 0.01 0.00 0.15 0.08 0.02 0.10 0.02

(0.04) (0.05) (0.00) (0.07) (0.03) (0.01) (0.04) (0.01)

See notes at end of table.
52

The Demand for Disaggregated Food-Away-from-Home and Food-at-Home Products in the United States / ERR-139

Economic Research Service/USDA

Appendix table A.10

Estimated unconditional elasticities of demand--continued

With respect to price of

With 

respect to 

Demand for expenditure

Condiments, 

sauces, 

season.

Miscellaneous FAHAlcoholic 

beverages

Limitedservice 

FAFH

Full-service 

FAFH

Other 

FAFH Nonfood

Eggs

0.02 0.05 0.03 0.04 0.05 0.01 -0.29 0.03

(0.01) (0.02) (0.06) (0.08) (0.09) (0.02) (0.32) (0.05)

Cheese

-0.06 -0.14 0.07 0.09 0.11 0.02 -0.25 0.13

(0.03) (0.06) (0.10) (0.13) (0.16) (0.03) (0.40) (0.06)

Ice cream and 

froz. dessert

-0.06 -0.13 0.06 0.08 0.10 0.02 -0.25 0.12

(0.03) (0.06) (0.10) (0.13) (0.16) (0.03) (0.40) (0.06)

Milk

-0.04 -0.09 0.05 0.06 0.07 0.01 -0.17 0.09

(0.02) (0.04) (0.06) (0.09) (0.10) (0.02) (0.26) (0.04)

Other dairy

-0.05 -0.10 0.05 0.07 0.08 0.01 -0.19 0.10

(0.02) (0.05) (0.07) (0.09) (0.11) (0.02) (0.29) (0.05)

Apples

0.05 0.12 0.04 0.06 0.07 0.01 0.03 0.03

(0.02) (0.05) (0.08) (0.10) (0.13) (0.02) (0.32) (0.04)

Bananas

0.08 0.19 0.07 0.10 0.12 0.02 0.05 0.04

(0.03) (0.08) (0.13) (0.17) (0.20) (0.04) (0.51) (0.07)

Citrus

0.09 0.22 0.08 0.11 0.13 0.02 0.06 0.05

(0.04) (0.09) (0.15) (0.19) (0.23) (0.04) (0.58) (0.08)

Other fresh fruits

0.07 0.16 0.06 0.08 0.10 0.02 0.04 0.04

(0.03) (0.07) (0.11) (0.14) (0.17) (0.03) (0.42) (0.06)

Potatoes

0.05 0.12 0.04 0.06 0.07 0.01 0.03 0.03

(0.02) (0.05) (0.08) (0.10) (0.12) (0.02) (0.31) (0.04)

Lettuce

0.07 0.16 0.06 0.08 0.09 0.02 0.04 0.04

(0.03) (0.07) (0.10) (0.14) (0.16) (0.03) (0.41) (0.06)

Tomatoes

0.10 0.22 0.08 0.11 0.13 0.02 0.06 0.05

(0.04) (0.09) (0.15) (0.19) (0.23) (0.04) (0.58) (0.08)

Other fresh 

vegetables

0.07 0.16 0.06 0.08 0.09 0.02 0.04 0.04

(0.03) (0.06) (0.10) (0.14) (0.16) (0.03) (0.41) (0.06)

See notes at end of table.
53

The Demand for Disaggregated Food-Away-from-Home and Food-at-Home Products in the United States / ERR-139

Economic Research Service/USDA

Appendix table A.10

Estimated unconditional elasticities of demand

With respect to price of

Demand for

Flour, 

prep. 

mixes

Breakfast 

cereals

Rice and 

pasta

Non-white 

bread

White 

bread

Biscuits, 

rolls, 

muff.

Cakes 

and 

cookies

Other 

bakery 

products Beef

Proc. fruits and 

vegetables

-0.02 -0.03 -0.04 -0.02 -0.02 -0.02 -0.05 -0.04 0.06

(0.01) (0.01) (0.02) (0.01) (0.01) (0.01) (0.02) (0.02) (0.05)

Coffee and tea

-0.01 -0.01 -0.02 -0.01 -0.01 -0.01 -0.02 -0.02 0.06

(0.02) (0.03) (0.04) (0.02) (0.02) (0.02) (0.05) (0.04) (0.04)

Carbonated 

beverages

-0.02 -0.03 -0.04 -0.02 -0.02 -0.02 -0.05 -0.04 0.12

(0.03) (0.05) (0.07) (0.03) (0.04) (0.03) (0.09) (0.07) (0.07)

Noncarb. 

beverages

-0.02 -0.03 -0.04 -0.02 -0.02 -0.02 -0.05 -0.04 0.14

(0.04) (0.06) (0.07) (0.04) (0.04) (0.03) (0.09) (0.08) (0.08)

Frozen beverages

-0.01 -0.02 -0.02 -0.01 -0.01 -0.01 -0.03 -0.03 0.09

(0.03) (0.04) (0.05) (0.03) (0.03) (0.02) (0.07) (0.06) (0.07)

Sugar and sweets

0.02 0.03 0.03 0.02 0.02 0.01 0.04 0.04 0.15

(0.02) (0.04) (0.05) (0.02) (0.03) (0.02) (0.06) (0.05) (0.07)

Fats and oils

0.01 0.02 0.02 0.01 0.01 0.01 0.03 0.02 0.09

(0.01) (0.02) (0.03) (0.01) (0.02) (0.01) (0.04) (0.03) (0.04)

Soups

0.01 0.01 0.01 0.01 0.01 0.00 0.01 0.01 0.05

(0.01) (0.01) (0.02) (0.01) (0.01) (0.01) (0.02) (0.02) (0.03)

Frozen foods

0.01 0.02 0.02 0.01 0.01 0.01 0.03 0.02 0.10

(0.02) (0.03) (0.03) (0.02) (0.02) (0.01) (0.04) (0.03) (0.05)

Snacks

0.01 0.02 0.02 0.01 0.01 0.01 0.03 0.02 0.08

(0.01) (0.02) (0.03) (0.01) (0.02) (0.01) (0.04) (0.03) (0.04)

Condiments, 

sauces, seas.

0.01 0.01 0.02 0.01 0.01 0.01 0.02 0.02 0.08

(0.01) (0.02) (0.03) (0.01) (0.01) (0.01) (0.03) (0.03) (0.04)

Misc. FAH

0.01 0.02 0.03 0.01 0.02 0.01 0.04 0.03 0.12

(0.02) (0.03) (0.04) (0.02) (0.02) (0.02) (0.05) (0.04) (0.06)

Alcoholic 

beverage

0.00 0.01 0.01 0.00 0.00 0.00 0.01 0.01 0.03

(0.01) (0.02) (0.02) (0.01) (0.01) (0.01) (0.02) (0.02) (0.07)

See notes at end of table.
54

The Demand for Disaggregated Food-Away-from-Home and Food-at-Home Products in the United States / ERR-139

Economic Research Service/USDA

Appendix table A.10

Estimated unconditional elasticities of demand--continued

With respect to price of

Demand for Pork

Other 

red meat Poultry Fish Eggs Cheese

Ice 

cream 

and 

frozen 

desserts Milk

Other 

dairy Apples

Proc. fruits and 

vegetables

0.03 0.01 0.02 0.02 0.00 -0.01 0.00 0.00 0.00 -0.02

(0.03) (0.01) (0.02) (0.02) (0.00) (0.03) (0.01) (0.02) (0.01) (0.07)

Coffee and tea

0.04 0.01 0.02 0.02 0.01 -0.05 -0.03 -0.04 -0.02 0.00

(0.02) (0.01) (0.01) (0.01) (0.00) (0.03) (0.02) (0.02) (0.01) (0.01)

Carbonated 

beverages

0.07 0.03 0.04 0.04 0.01 -0.10 -0.05 -0.08 -0.03 0.00

(0.04) (0.02) (0.03) (0.03) (0.01) (0.06) (0.03) (0.04) (0.02) (0.01)

Noncarb. 

beverages

0.08 0.03 0.05 0.05 0.01 -0.11 -0.06 -0.09 -0.04 0.00

(0.04) (0.02) (0.03) (0.03) (0.01) (0.06) (0.03) (0.05) (0.02) (0.01)

Frozen beverages

0.05 0.02 0.03 0.03 0.01 -0.07 -0.04 -0.05 -0.02 0.00

(0.04) (0.01) (0.02) (0.02) (0.01) (0.05) (0.03) (0.04) (0.02) (0.01)

Sugar and sweets

0.08 0.03 0.05 0.05 0.01 -0.10 -0.05 -0.08 -0.03 0.03

(0.04) (0.02) (0.03) (0.03) (0.01) (0.04) (0.02) (0.03) (0.02) (0.01)

Fats and oils

0.05 0.02 0.03 0.03 0.01 -0.06 -0.03 -0.05 -0.02 0.02

(0.02) (0.01) (0.01) (0.01) (0.00) (0.03) (0.01) (0.02) (0.01) (0.01)

Soups

0.03 0.01 0.02 0.02 0.00 -0.03 -0.02 -0.03 -0.01 0.01

(0.02) (0.01) (0.01) (0.01) (0.00) (0.02) (0.01) (0.02) (0.01) (0.01)

Frozen foods

0.06 0.02 0.04 0.04 0.01 -0.07 -0.04 -0.05 -0.02 0.02

(0.03) (0.01) (0.02) (0.02) (0.00) (0.03) (0.02) (0.02) (0.01) (0.01)

Snacks

0.05 0.02 0.03 0.03 0.01 -0.06 -0.03 -0.05 -0.02 0.02

(0.02) (0.01) (0.02) (0.02) (0.00) (0.03) (0.01) (0.02) (0.01) (0.01)

Condiments, 

sauces, seas.

0.04 0.02 0.03 0.03 0.01 -0.05 -0.03 -0.04 -0.02 0.01

(0.02) (0.01) (0.01) (0.01) (0.00) (0.02) (0.01) (0.02) (0.01) (0.01)

Misc. FAH

0.07 0.03 0.04 0.04 0.01 -0.08 -0.05 -0.07 -0.03 0.02

(0.03) (0.01) (0.02) (0.02) (0.01) (0.04) (0.02) (0.03) (0.01) (0.01)

Alcoholic 

beverage

0.02 0.01 0.01 0.01 0.00 0.02 0.01 0.01 0.01 0.00

(0.04) (0.01) (0.03) (0.02) (0.01) (0.03) (0.02) (0.02) (0.01) (0.01)

See notes at end of table.
55

The Demand for Disaggregated Food-Away-from-Home and Food-at-Home Products in the United States / ERR-139

Economic Research Service/USDA

Appendix table A.10

Estimated unconditional elasticities of demand--continued

With respect to price of

Demand for Bananas Citrus

Other 

fresh 

fruits Potatoes Lettuce Tomatoes

Other 

fresh 

vegetable

Processed 

fruits and 

vegetables

Coffee 

and tea

Proc. fruits and 

vegetables

0.02 0.01 0.20 0.01 0.02 -0.14 0.06 -0.77 0.00

(0.08) (0.06) (0.11) (0.07) (0.04) (0.05) (0.11) (0.20) (0.01)

Coffee and tea

0.00 0.00 0.01 0.00 0.00 0.00 0.01 0.01 -0.12

(0.01) (0.01) (0.02) (0.01) (0.01) (0.01) (0.02) (0.02) (0.21)

Carbonated 

beverages

0.00 0.01 0.01 0.00 0.00 0.01 0.01 0.01 -0.01

(0.02) (0.03) (0.04) (0.01) (0.01) (0.02) (0.05) (0.04) (0.13)

Noncarb. 

beverages

0.01 0.01 0.01 0.00 0.00 0.01 0.01 0.01 -0.07

(0.02) (0.03) (0.05) (0.01) (0.01) (0.03) (0.05) (0.05) (0.11)

Frozen beverages

0.00 0.00 0.01 0.00 0.00 0.00 0.01 0.01 -0.08

(0.02) (0.02) (0.03) (0.01) (0.01) (0.02) (0.04) (0.03) (0.49)

Sugar and sweets

0.04 0.05 0.09 0.02 0.02 0.05 0.10 0.09 0.02

(0.02) (0.02) (0.04) (0.01) (0.01) (0.02) (0.04) (0.04) (0.02)

Fats and oils

0.02 0.03 0.05 0.01 0.01 0.03 0.06 0.05 0.01

(0.01) (0.01) (0.02) (0.01) (0.01) (0.01) (0.02) (0.02) (0.01)

Soups

0.01 0.02 0.03 0.01 0.01 0.02 0.03 0.03 0.01

(0.01) (0.01) (0.02) (0.00) (0.00) (0.01) (0.02) (0.02) (0.01)

Frozen foods

0.03 0.04 0.06 0.02 0.02 0.03 0.07 0.06 0.02

(0.01) (0.02) (0.03) (0.01) (0.01) (0.01) (0.03) (0.03) (0.01)

Snacks

0.02 0.03 0.05 0.01 0.01 0.03 0.06 0.05 0.01

(0.01) (0.01) (0.02) (0.01) (0.01) (0.01) (0.03) (0.02) (0.01)

Condiments, 

sauces, seas.

0.02 0.03 0.05 0.01 0.01 0.03 0.05 0.05 0.01

(0.01) (0.01) (0.02) (0.01) (0.01) (0.01) (0.02) (0.02) (0.01)

Misc. FAH

0.03 0.05 0.08 0.02 0.02 0.04 0.08 0.07 0.02

(0.01) (0.02) (0.03) (0.01) (0.01) (0.02) (0.03) (0.03) (0.02)

Alcoholic 

beverage

0.01 0.01 0.01 0.00 0.00 0.01 0.01 0.01 0.00

(0.01) (0.01) (0.02) (0.01) (0.01) (0.01) (0.03) (0.02) (0.01)

See notes at end of table.
56

The Demand for Disaggregated Food-Away-from-Home and Food-at-Home Products in the United States / ERR-139

Economic Research Service/USDA

Appendix table A.10

Estimated unconditional elasticities of demand--continued

With respect to price of

Demand for

Carbonated 

beverages

Noncarbonated 

beverages

Frozen 

beverages

Sugar and 

sweets

Fats and 

oils Soups

Frozen 

meals and 

snacks Snacks

Proc. fruits and 

vegetables

0.01 0.01 0.00 0.12 0.06 0.01 0.07 0.01

(0.03) (0.04) (0.00) (0.05) (0.03) (0.01) (0.03) (0.01)

Coffee and tea

-0.02 -0.19 -0.01 0.09 0.05 0.01 0.06 0.01

(0.27) (0.27) (0.06) (0.08) (0.04) (0.01) (0.05) (0.01)

Carbonated 

beverages

-0.30 -0.35 -0.01 0.18 0.09 0.02 0.11 0.02

(0.38) (0.39) (0.07) (0.15) (0.08) (0.02) (0.09) (0.02)

Noncarb. 

beverages

-0.27 -0.44 0.02 0.20 0.11 0.02 0.13 0.02

(0.30) (0.37) (0.07) (0.16) (0.09) (0.02) (0.10) (0.02)

Frozen beverages

-0.09 0.32 -0.61 0.12 0.07 0.01 0.08 0.01

(1.09) (1.30) (0.91) (0.13) (0.07) (0.02) (0.08) (0.02)

Sugar and sweets

0.09 0.13 0.00 -0.56 -0.01 -0.66 -0.74 0.03

(0.07) (0.10) (0.00) (0.76) (0.26) (0.23) (0.49) (0.14)

Fats and oils

0.05 0.08 0.00 -0.02 -0.21 -0.16 -0.23 0.03

(0.04) (0.06) (0.00) (0.29) (0.18) (0.11) (0.26) (0.06)

Soups

0.03 0.04 0.00 -2.08 -0.47 0.19 0.96 0.06

(0.03) (0.04) (0.00) (0.74) (0.31) (0.60) (0.77) (0.28)

Frozen foods

0.06 0.09 0.00 -0.81 -0.23 0.33 -1.05 -0.22

(0.05) (0.07) (0.00) (0.53) (0.25) (0.27) (0.72) (0.15)

Snacks

0.05 0.08 0.00 0.16 0.13 0.09 -1.00 -1.14

(0.05) (0.06) (0.00) (0.70) (0.28) (0.44) (0.70) (0.46)

Condiments, 

sauces, seas.

0.05 0.07 0.00 0.84 0.10 0.12 0.13 0.27

(0.04) (0.06) (0.00) (0.45) (0.16) (0.23) (0.43) (0.15)

Misc. FAH

0.08 0.11 0.00 -0.09 -0.23 0.15 0.71 -0.02

(0.06) (0.09) (0.00) (0.48) (0.21) (0.19) (0.41) (0.10)

Alcoholic 

beverage

0.00 0.00 0.00 0.06 0.03 0.01 0.04 0.01

(0.03) (0.04) (0.00) (0.05) (0.03) (0.01) (0.03) (0.01)

See notes at end of table.
57

The Demand for Disaggregated Food-Away-from-Home and Food-at-Home Products in the United States / ERR-139

Economic Research Service/USDA

Appendix table A.10

Estimated unconditional elasticities of demand--continued

With respect to price of

With 

respect to 

Demand for expenditure

Condiments, 

sauces, 

season.

Miscellaneous FAHAlcoholic 

beverages

Limitedservice 

FAFH

Full-service 

FAFH

Other 

FAFH Nonfood

Proc. fruits and 

vegetables

0.05 0.12 0.04 0.06 0.07 0.01 0.03 0.03

(0.02) (0.05) (0.08) (0.10) (0.13) (0.02) (0.32) (0.04)

Coffee and tea

0.04 0.09 -0.01 -0.01 -0.01 0.00 0.07 0.01

(0.03) (0.08) (0.07) (0.10) (0.12) (0.02) (0.24) (0.03)

Carbonated 

beverages

0.08 0.18 -0.01 -0.02 -0.02 0.00 0.13 0.02

(0.06) (0.15) (0.14) (0.19) (0.23) (0.04) (0.45) (0.06)

Noncarb. 

beverages

0.09 0.20 -0.01 -0.02 -0.02 0.00 0.15 0.02

(0.07) (0.16) (0.15) (0.20) (0.25) (0.04) (0.50) (0.06)

Frozen beverages

0.05 0.12 -0.01 -0.01 -0.01 0.00 0.09 0.01

(0.06) (0.13) (0.11) (0.15) (0.18) (0.03) (0.35) (0.05)

Sugar and sweets

0.69 -0.11 0.15 0.20 0.24 0.04 -0.45 0.13

(0.37) (0.58) (0.12) (0.16) (0.20) (0.03) (0.48) (0.06)

Fats and oils

0.09 -0.30 0.09 0.12 0.14 0.02 -0.27 0.08

(0.15) (0.28) (0.08) (0.10) (0.12) (0.02) (0.29) (0.04)

Soups

0.32 0.57 0.05 0.06 0.08 0.01 -0.15 0.04

(0.59) (0.73) (0.05) (0.06) (0.08) (0.01) (0.18) (0.03)

Frozen foods

0.11 0.92 0.10 0.13 0.16 0.03 -0.31 0.09

(0.38) (0.54) (0.09) (0.12) (0.14) (0.02) (0.32) (0.05)

Snacks

1.10 -0.13 0.09 0.11 0.14 0.02 -0.26 0.08

(0.61) (0.63) (0.08) (0.10) (0.12) (0.02) (0.29) (0.04)

Condiments, 

sauces, seas.

-1.92 -0.28 0.08 0.11 0.13 0.02 -0.24 0.07

(0.44) (0.39) (0.07) (0.09) (0.11) (0.02) (0.26) (0.03)

Misc. FAH

-0.19 -1.48 0.13 0.17 0.20 0.03 -0.38 0.11

(0.27) (0.59) (0.11) (0.14) (0.17) (0.03) (0.40) (0.05)

Alcoholic 

beverage

0.02 0.06 -1.15 -2.17 2.37 -0.13 0.31 0.32

(0.02) (0.05) (0.67) (0.73) (0.82) (0.13) (0.68) (0.09)

See notes at end of table.
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Appendix table A.10

Estimated unconditional elasticities of demand

With respect to price of

Demand for

Flour, prep. 

mixes

Breakfast 

cereals

Rice and 

pasta

Non-white 

bread

White 

bread

Biscuits, 

rolls, muff.

Cakes and 

cookies

Other 

bakery 

products

Limited service

0.00 0.00 0.00 0.00 0.00 0.00 0.01 0.00

(0.01) (0.01) (0.01) (0.01) (0.01) (0.00) (0.01) (0.01)

Full service 

0.00 0.00 0.00 0.00 0.00 0.00 0.01 0.00

(0.01) (0.01) (0.01) (0.01) (0.01) (0.01) (0.02) (0.01)

Other FAFH

0.00 0.00 0.00 0.00 0.00 0.00 0.01 0.00

(0.01) (0.01) (0.01) (0.01) (0.01) (0.01) (0.02) (0.01)

Nonfood

0.03 -0.06 0.06 -0.03 0.01 -0.02 0.03 -0.03

(0.01) (0.02) (0.02) (0.01) (0.01) (0.01) (0.02) (0.02)

See notes at end of table.

Appendix table A.10

Estimated unconditional elasticities of demand

With respect to price of

Demand for Beef Pork

Other red 

meat Poultry Fish Eggs Cheese

Ice cream 

and frozen 

desserts

Limited service

0.02 0.01 0.00 0.01 0.01 0.01 0.01 0.01

(0.04) (0.02) (0.01) (0.01) (0.01) (0.02) (0.01) (0.01)

Full service 

0.02 0.01 0.00 0.01 0.01 0.01 0.01 0.01

(0.04) (0.02) (0.01) (0.02) (0.02) (0.02) (0.01) (0.01)

Other FAFH

0.02 0.01 0.00 0.01 0.01 0.01 0.01 0.01

(0.05) (0.03) (0.01) (0.02) (0.02) (0.02) (0.01) (0.01)

Nonfood

0.08 0.01 -0.05 -0.05 -0.02 0.06 0.03 -0.08

(0.02) (0.01) (0.01) (0.01) (0.02) (0.03) (0.02) (0.03)

0.01 0.01 0.01

See notes at end of table.

Appendix table A.10

Estimated unconditional elasticities of demand

With respect to price of

Demand for Beef Pork

Other red 

meat Poultry Fish Eggs Cheese

Ice cream and 

frozen desserts

Limited service

0.02 0.01 0.00 0.01 0.01 0.01 0.01 0.01

(0.04) (0.02) (0.01) (0.01) (0.01) (0.02) (0.01) (0.01)

Full service 

0.02 0.01 0.00 0.01 0.01 0.01 0.01 0.01

(0.04) (0.02) (0.01) (0.02) (0.02) (0.02) (0.01) (0.01)

Other FAFH

0.02 0.01 0.00 0.01 0.01 0.01 0.01 0.01

(0.05) (0.03) (0.01) (0.02) (0.02) (0.02) (0.01) (0.01)

Nonfood

0.08 0.01 -0.05 -0.05 -0.02 0.06 0.03 -0.08

(0.02) (0.01) (0.01) (0.01) (0.02) (0.03) (0.02) (0.03)

0.01 0.01 0.01

See notes at end of table.
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The Demand for Disaggregated Food-Away-from-Home and Food-at-Home Products in the United States / ERR-139

Economic Research Service/USDA

Appendix table A.10

Estimated unconditional elasticities of demand

With respect to price of

Demand for Milk Other dairy Apples Bananas Citrus

Other fresh 

fruits Potatoes Lettuce

Limited service

0.00 0.00 0.00 0.00 0.01 0.00 0.00 0.00

(0.01) (0.00) (0.01) (0.01) (0.01) (0.00) (0.00) (0.01)

Full service 

0.00 0.00 0.00 0.00 0.01 0.00 0.00 0.00

(0.01) (0.00) (0.01) (0.01) (0.01) (0.00) (0.00) (0.01)

Other FAFH

0.00 0.00 0.00 0.01 0.01 0.00 0.00 0.00

(0.01) (0.00) (0.01) (0.01) (0.02) (0.00) (0.00) (0.01)

Nonfood

-0.02 -0.02 0.01 0.03 0.00 -0.02 0.00 0.03

(0.02) (0.01) (0.01) (0.01) (0.02) (0.01) (0.01) (0.01)

0.00 0.00 0.00 0.00 0.01 0.00 0.00 0.00

See notes at end of table.

Appendix table A.10

Estimated unconditional elasticities of demand

With respect to price of

Demand for Tomatoes

Other fresh 

vegetable

Processed 

fruits and 

vegetables

Coffee 

and tea

Carb. 

beverages

Noncarbonated 

beverages

Frozen 

beverages

Sugar and 

sweets

Limited service

0.01 0.01 0.01 0.00 0.00 0.00 0.00 0.03

(0.01) (0.02) (0.01) (0.00) (0.02) (0.02) (0.00) (0.03)

Full service 

0.01 0.01 0.01 0.00 0.00 0.00 0.00 0.04

(0.02) (0.02) (0.01) (0.00) (0.02) (0.02) (0.00) (0.03)

Other FAFH

0.01 0.01 0.01 0.00 0.00 0.00 0.00 0.04

(0.02) (0.02) (0.02) (0.00) (0.02) (0.03) (0.00) (0.03)

Nonfood

0.00 0.06 -0.06 -0.08 0.02 0.05 0.00 0.06

(0.01) (0.03) (0.02) (0.02) (0.03) (0.03) (0.01) (0.03)

0.01 0.01 0.01 0.00 0.00 0.00 0.00 0.03

See notes at end of table.

Appendix table A.10

Estimated unconditional elasticities of demand

With respect to price of

Demand for

Fats and 

oils Soups

Frozen 

foods Snacks

Condiments, 

sauces, seas. Misc. FAH

Alcoholic 

beverages

Limited service

0.02 0.00 0.02 0.00 0.01 0.03 -0.90

(0.01) (0.00) (0.02) (0.00) (0.01) (0.03) (0.31)

Full service 

0.02 0.00 0.02 0.00 0.02 0.04 0.91

(0.02) (0.00) (0.02) (0.00) (0.01) (0.03) (0.31)

Other FAFH

0.02 0.00 0.02 0.00 0.02 0.04 -0.32

(0.02) (0.00) (0.02) (0.00) (0.01) (0.03) (0.32)

Nonfood

-0.03 -0.03 -0.01 -0.01 -0.04 0.03 0.07

(0.02) (0.01) (0.02) (0.01) (0.01) (0.03) (0.02)

0.02 0.00 0.02 0.00 0.01 0.03 -0.90

See notes at end of table.
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The Demand for Disaggregated Food-Away-from-Home and Food-at-Home Products in the United States / ERR-139

Economic Research Service/USDA

Appendix table A.10

Estimated unconditional elasticities of demand

With respect to price of

With 

respect to 

Demand for expenditure

Limitedservice 

FAFH

Full-service 

FAFH

Other 

FAFH Nonfood

Limited service

-0.13 0.42 0.01 0.17 0.18

(1.08) (1.15) (0.07) (0.37) (0.05)

Full service 

0.38 -1.96 -0.01 0.19 0.20

(1.06) (1.10) (0.07) (0.42) (0.06)

Other FAFH

0.08 -0.04 -0.43 0.20 0.21

(0.37) (0.42) (0.18) (0.44) (0.07)

Nonfood

-0.08 -0.05 0.00 -1.00 1.21

(0.03) (0.03) (0.01) (0.07) (0.01)

Notes: Authors’ calculations using first-stage elasticities from table 5, second-stage elasticities 

from tables A.3.-A.9., and Carpentier and Guyomard’s formulas for approximating unconditional elasticities of demand, equations 12 and 13. Standard errors calculated using a residual 

bootstrap (Green, Hahn, and Rocke 1987).

FAFH = Food away from home, including limited-service and full-service restaurants; FAH = 

Food at home.
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The Demand for Disaggregated Food-Away-From-Home and Food-at-Home Products in the United States / ERR-139

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Appendix: Derivations of the Generalized 

Ordinary Differential Demand System 

(GODDS)

The GODDS is a reparameterization of a synthetic model developed by 

Barten (1993) that exploits the fact that the Rotterdam (R), the FDLAIDS 

(F), the NBR (N), and the CBS (C) models can be rewritten so they all have 

the same right-hand-side terms: 

(A.1.0) yR = wnd ln qn = θn d ln Q + ∑ N

j = 1πnjd ln pj,

(A.1.1) yF = dwn = βn d ln Q + ∑ N

j = 1γnjd ln pj,

(A.1.2) yC = wn(d ln qn - d ln Q) = βn d ln Q + ∑ N

j = 1πnjd ln pj,

(A.1.3) yN = dwn + wnd ln Q = θn d ln Q + ∑ N

j = 1γnjd ln pj,

where wn is the budget share for good n, qn is quantity, pn is price, and d ln Q

is the Divisia volume index.1,2

Barten’s general model takes the form: 

αRyR + αCyC + αFyF + αNyN = XΩ,

where yi, i = R, C, N, F is a t × 1 vector of transformed basic endogenous 

variables; X is a t × k matrix of exogenous price and expenditure variables; 

and Ω = αRωR + αCωC + αFωF + αNωN and ωi, i=R, C, N, F compose a k × 

1 vector of coefficients. Without loss of generality, Barten set the sum of 

the α’s to one and solved for αR. Instead of solving for αR in (A.1.4), Eales, 

Durham, and Wessells (1997) solved for αF such that the term on the lefthand side of the final model is the same as the left-hand side term of the 

FDAIDS (i.e., dwn):

(A.1.5) αF = 1 - αR - αC - αN.

Substituting αF from (A.1.5) into (A.1.4) and solving for yF yields,

(A.1.6) yF = αC(yF - yC) + αR(yF - yR) + αN(yF - yN) + XΩ.

Unconstrained estimation of the αs is not possible since αF is a linear combination of αR, αC, and αN. However, (A.1.6) can be rewritten using the fact 

that

(A.1.7) yR - yC + yF - yN = 0,

or 

(A.1.8) (yF - yC) + (yF - yN) - (yF - yR) = 0.

1The Divisia volume index is 

defined as 

 d ln Q = d ln M – ∑N

n = 1wnd ln pn, 

where M is total expenditure on all 

goods. Equivalently, the Divisia volume 

index is

 d ln Q = ∑N

n = 1wnd ln qn.

2The coefficient on the income term 

in the Rotterdam and NBR models 

(i.e., θn) is the marginal budget share 

and is constant, whereas the marginal 

budget shares for the FDLAIDS and 

CBS models (i.e., βn = θn – wn) vary 

with the expenditure shares. Similarly, 

the Slutsky terms are considered to 

be constants in the Rotterdam and 

CBS models (i.e., πnj) but vary with 

expenditure shares in the NBR and 

FDLAIDS models.
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Economic Research Service/USDA

Solving (A.1.8) for yF - yR yields

(A.1.9) (yF - yC) + (yF - yN) = (yF - yR),

and substituting this into (A.1.6) gives 

(A.1.10) yF = (αC + αR) (yF - yC) + (αR + αN)(yF - yN) + XΩ,

 = φ1(yF - yC) + φ2(yF - yN) + XΩ.

The nesting coefficient φ1 measures the difference between the price coefficients in the FDLAIDS model and the price coefficients in the CBS and 

Rotterdam models. The nesting coefficient φ2 measures the difference 

between the marginal budget shares of the FDLAIDS model and marginal 

budget shares of the NBR and Rotterdam models. 

Substituting (A.1.0)-(A.1.3) into (A.1.10) and using 

(A.1.11) dwn = wnd ln qn + wnd ln pn - wnd ln M,

(A.1.12) d ln M = ∑N

n = 1wnd ln pn + ∑Nn = 1wnd ln qn,

the GODDS is

(A.1.13) dwn = (cn + φ1wn)d ln Q + ∑ N

k = 1[dnk + φ2wn(δnk - wk)]d ln pk,

where cn = φ1βn + (1 - φ1)θn and dnk = φ2γnk + (1 - φ2)πn are expenditure and 

price coefficients to be estimated, respectively, φ1 and φ2 are nesting coefficients, δnk is the Kronecker delta, wn is a t × 1 vector of expenditure shares 

for good n, pk is a t × 1 vector of prices of good k, and Q is a t × 1 vector of 

Divisia volume indexes.