United States 

Department of 

Agriculture

Economic

Research

Service

Christopher G. Davis, Diansheng Dong, Don P. Blayney, 

and Ashley Owens

An Analysis of U.S. 

Household Dairy Demand 

Technical

Bulletin

Number 1928

December 2010
www.ers.usda.gov

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Recommended citation format for this publication:

Davis, Christopher G., Diansheng Dong, Don P. Blayney, and Ashley Owens. 

An Analysis of U.S. Household Dairy Demand, TB-1928, U.S. Dept. of Agr., 

Econ. Res. Serv. December 2010.

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A Report from the Economic Research Service

Abstract

This report examines retail purchase data for 12 dairy products and margarine from 

the Nielsen 2007 Homescan data. Selected demographic and socioeconomic variables 

included in the Nielsen data are analyzed for their effects on aggregate demand and 

expenditure elasticities for the selected products. A censored demand system is used 

to derive the demand elasticities. The resulting estimates revealed that the magnitudes 

of 10 of the 13 own-price elasticities have absolute values greater than 1; substitute 

relationships are found among most dairy categories; expenditure elasticities are 1 or 

greater for 7 of the 13 products; and demographic and socioeconomic variables are 

statistically signifi cant contributors to dairy demand. 

Keywords: butter, cheese, censored demand, elasticities, bulk ice cream, margarine, 

milk, Nielsen Homescan data, yogurt

*Ashley Owens was a student intern at Economic Research Service during the time 

that this study was in progress.

Acknowledgments

The authors extend their thanks for helpful comments from Economic Research 

Service colleagues Daniel Pick, Richard Stillman, Rachel Johnson, William Hahn, 

and Abebayehu Tegene. They are also appreciative of the contributions of Courtney 

Knauth, editor, and Curtia Taylor, designer, in preparing the report for publication.

Christopher G. Davis, chrisdavis@ers.usda.gov

Diansheng Dong, ddong@ers.usda.gov

Don P. Blayney, dblayney@ers.usda.gov

Ashley Owens*

An Analysis of U.S. 

Household Dairy Demand

Technical

Bulletin

Number 1928

December 2010
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Table of Contents

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

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

Background. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

A Censored Demand System Model with 

Adding-Up Constraint . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

 Elasticity Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

Estimation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

 Sample Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

 Summary of Estimated Demand System Price and 

 Demographic Coeffi cients. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

Compensated Demand Elasticities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

Uncompensated Demand Elasticities . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

Estimated Elasticities of Demographic Variables . . . . . . . . . . . . . . . . . . 17

Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
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Summary

What Is the Issue?

The measurement of the economic effects of food prices and consumer 

incomes on the demand for foods derived from agricultural products is 

important in economic analysis. Consumers allocate spending among a wide 

array of competing products sold at retail outlets across the country. In this 

technical study, the authors estimate how fl uctuation in prices and household 

expenditures, as well as a number of demographic characteristics, affect 

household demand for 12 dairy products and margarine. These empirical 

estimates offer a glimpse of relationships among the 13 product categories—

including ways that consumers use some of the products together or interchangeably—which are of interest to many in the U.S. dairy industry. 

What Did the Study Find?

Using a censored demand system and Nielsen Homescan data for purchase 

of items in the 13 categories, the authors estimated two types of elasticities: 

price and expenditure. The effects of selected demographic variables, based 

on characteristics such as household size and composition, educational level 

and ethnicity of household head, regional location, and household income, are 

also analyzed. The analysts found that:

• Ten of the 13 products have negative own-price elasticities with absolute 

values greater than 1.

• Strong substitution relationships exist among most dairy product 

categories. 

• All of the expenditure elasticities are statistically signifi cant and positive. 

Changes in the overall household dairy expenditure have the largest effect 

on purchases of reduced-fat milk, canned milk, bulk ice cream, refrigerated and frozen yogurts, natural cheese, and cottage cheese.

• Although the infl uence of most demographic variables is relatively 

small, some of them do have statistically signifi cant effects on consumer 

purchases of dairy products:

 Single-person households and households headed by a college-educated 

woman have a positive, statistically signifi cant infl uence on the purchase 

of refrigerated and frozen yogurt and reduced-fat milk.

 Black heads of household have a positive, statistically signifi cant effect 

on the purchase of bulk ice cream, sherbet/ice milk, refrigerated and 

drinkable yogurts, whole and canned milk, and butter. Asian heads of 

household have a positive, statistically signifi cant effect on the purchase 

of all fl uid milks, refrigerated and drinkable yogurts, and bulk ice 

cream.

 Households in the Western, Eastern, and Central regions of the United 

States are more likely to purchase refrigerated yogurt, natural cheese, 

cottage cheese, and butter than those in the Southern region. Households 
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in the Western region are also more likely to purchase frozen and drinkable yogurts and sherbet/ice milk.

 Of the income categories analyzed, households in the two lowest categories—$20,000-$34,999 annually and $19,999 or less—have a positive, statistically signifi cant infl uence on whole and reduced-fat milk 

purchases. Other dairy product purchases that are statistically signifi cant 

and positively infl uenced by households with incomes of $34,999 or less 

include sherbet/ice milk, processed and cottage cheese, and margarine. 

How Was the Study Conducted?

The authors compiled data on retail purchases of dairy products from Nielsen 

Homescan data for 2007. The Nielsen Homescan data provide detailed 

information on dairy product purchases for at-home use by U.S. households, 

allowing the authors to examine consumption patterns among margarine and 

12 categories of dairy products: bulk ice cream, sherbet/ice milk, refrigerated yogurt, frozen yogurt, drinkable yogurt, whole milk, reduced-fat milk, 

canned milk, natural cheese, processed cheese, cottage cheese, and butter. 

The Nielsen database includes not only economic data such as product prices, 

but also demographic and location information. The authors used the data to 

derive estimates of own- and cross-price elasticities and expenditure elasticities for the 13 product categories, employing a censored demand system. 
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Introduction

A wide array of milk and dairy products is offered by the U.S. dairy industry 

to consumers. Over the past two decades, dairy demand analyses have 

been conducted at the aggregated and disaggregated levels, using panel and 

cross-sectional data. Although several methods have been used to derive 

dairy demand parameter estimates, one of the most popular has been the 

Almost Ideal Demand System (AIDS) model and its many variations. (See, 

for example, Chouinard et al. (2010), Huang and Lin (2000), Maynard and 

Veeramani (2003), Maynard and Liu (1999), and Heien and Wessells (1990)). 

In this study, a censored demand system used by Dong, Gould, and Kaiser 

(2004) is employed to estimate the demand for four major dairy categories: 

fl uid milk, ice cream, yogurt, and cheese. These four broad categories are 

disaggregated into three fl uid milks, two ice creams, three yogurts, and three 

cheeses, plus butter and margarine. The objective of the study is to estimate 

demand elasticities with respect to retail prices, expenditure, and several 

demographic variables. 
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Background

While there are numerous studies focusing on aggregated dairy products, few 

display an analysis of the many disaggregated products for dairy goods available in retail stores. The authors make no effort to catalog the relevant earlier 

studies. One of the studies most comparable to the present analysis was 

conducted by Chouinard et al. (2010). Using weekly Information Resources 

Incorporated’s (IRI) InfoscanTM scanner data for the years 1997 through 

1999, Chouinard estimated price and income elasticities at the city level from 

an Incomplete Almost Ideal Demand System that is linear in income and 

linear and quadratic in prices. Findings showed that the own-price elasticities for 1-percent milk (–0.88), 2-percent milk (–0.79), no-fat or skim milk 

(–0.62), whole milk (–0.74), natural cheese (–0.72), processed cheese (–0.77), 

shredded cheese (–0.25), butter (–0.41), ice cream (–0.80), and fl avored 

yogurt (–0.77) were smaller than the elasticities estimated by our censored 

demand system at the household level. 

Maynard and Liu (1999) estimated three separate models, a quantitydependent double-log specifi cation, a linearized AIDS model, and a differential demand system model, using weekly national average retail scanner 

data from Nielsen (formerly referred to as A.C. Nielsen) for the years 1996 

through 1998. Results from the linearized AIDS model, which is the model 

most similar to that used in the present study, revealed that own-price elasticities for fl avored milk, shredded cheese, frozen yogurt, and frozen novelties 

were elastic. The estimates from the differential demand system also showed 

these dairy products to be elastic, but provided elastic results for butter and 

ice cream in addition. 

In the two studies above, Chouinard et al. and Maynard and Liu avoided the 

data-censoring problem by aggregating the data from household to city or 

national level. Heien and Wessells (1990) applied the AIDS model to estimate a demand system that includes 11 food items, with a focus on dairy. In 

their study, a two-step censored regression approach was compared with an 

uncensored approach, using data retrieved from USDA’s 1977-78 household 

food consumption survey (HFCS). Own-price elasticities for milk, cheese, 

cottage cheese, butter, margarine, and ice cream were all inelastic under the 

censored demand estimation, but were elastic for ice cream, cottage cheese, 

and butter. The uncensored demand model expenditure elasticities were lower 

for all items than they were for the censored demand model, ranging from 

0.61 to 0.89. 

A study by Boehm and Babb (1975) used two separate models without 

censoring to estimate price and expenditure elasticities at the market level for 

dairy products, using cross-sectional and time-series data from the United 

Dairy Industry Association. Findings from the model showed that national 

average own-price elasticities for whole milk (–1.70), 2% milk (–1.33), buttermilk (–1.52), cottage cheese (–1.29), processed cheese (–1.71), and canned 

milk (–1.33) were all elastic, while other dairy products such as ice cream 

(–0.42), ice milk (–0.56), American cheese (–0.44), butter (–0.76), and 

yogurt (–0.31) were less than 1 in magnitude. All of the expenditure elasticity 

estimates for the above dairy products were also less than 1. 
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A Censored Demand System Model 

with Adding-Up Constraint

The present study uses Nielsen 2007 Homescan data, which provide detailed 

dairy product purchases at the retail level for at-home use by U.S. households. 

Household demographic variables are also collected and combined with the 

purchase data. An analyst needs to address the data-censoring problem when 

using these household data, particularly for a system of demand analysis. 

Normally, not every product from the system will be purchased by any given 

household for the data survey period (1 year). Ignoring this nonpurchase issue 

could lead to biased parameter estimates (Wales and Woodland, 1983). To 

solve this censoring problem, we defi ne the share equations as:

(1) * SA P Y =+ + + γξε ln ln ,

where S* is a column vector of latent expenditure shares on M products. 

Equation 1, the AIDS model specifi ed by Deaton and Muellbauer (1980), is 

derived from the price-independent generalized logarithmic (PIGLOG) utility 

function for a consumer. P is a column vector of the associated M product 

prices, and *

*

P

y Y = is the defl ated total dairy expenditure, with y* as total 

expenditure and P* as a translog price index. The ε is a column vector of M

error terms. 

In order to obtain the effects of household demographic variables on dairy 

demand, we incorporate these variables into the AIDS model through transformation of the intercept A of equation 1. We follow Abdulai (2002) by 

defi ning the intercept of equation 1 as:

(2) A = β 0 + β X ,

where X is a column vector of N demographic variables. The translog price 

index P* is defi ned as:

(3) *

0

1 ln 'ln (ln ) ' (ln ) 2

P AP P P =+ + α γ . 

In equations 1, 2, and 3, β0 (M x 1), β (M x N), γ (M x M), ξ (M x 1), and α 0

(a scalar) are parameters to be estimated.

The latent expenditure shares of equation 1 are derived from the utility 

maximization problem under the budget constraint, and they must sum to 

1 (adding-up). The adding-up and other theoretical constraints, such as 

symmetry and homogeneity, are attained through parameter restrictions. 

However, no restriction is imposed to ensure that the latent shares S* lie 

between 0 and 1. To account for this non-negativity and the adding-up of the 

observed shares S, Wales and Woodland (1983) developed a mapping rule, 

later used by Dong, Gould, and Kaiser (2004), which transforms the latent 

shares S* to the observed shares S as:
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(4) 

*

*

*

*

, if 0,

0, if 0,

i

i

j i j

i

S S

S S

S

∈Δ

⎧

⎪ > ⎪ = ⎨

⎪

⎪⎩ ≤

∑

 

 (i = 1, 2,⋯, M),

where the subscript Δ is a set of all positive shares’ subscripts. Equation 4 

guarantees that the observed shares lie between 0 and 1 and sum to unity for 

each observation. Given equations 1 through 4, the likelihood function for 

this model can be derived for estimation.1

Elasticity Evaluation

Given the parameter estimates, demand elasticities of the latent system 

defi ned by equation 1 can be derived using the formula provided by Green 

and Alston (1990). Homogeneity and symmetry are held in these elasticities. 

Demand elasticities of the observed system defi ned by equation 4 can be 

obtained using a simulation procedure developed by Phaneuf, Kling, and 

Herriges (2000) and later applied by Dong, Gould, and Kaiser. Following 

Dong et al., assume R equals replicates of the M error term vectors ε in equation 1. The rth simulated latent share vector, * Sr , evaluated at the sample 

means of the exogenous variables (indicated by a bar over a variable), is:

(5) *

* ln ln r r

Y SA P

P

=+ + + γξ ε ,

where εr

 is the rth replicate of ε. The rth replicate of the i

th observed share is:

(6) 

*

*

*

*

, if 0,

0, if 0.

ir

ir

jr ir j

ir

S S

S S

S

∈Δ

⎧

⎪ > ⎪ = ⎨

⎪

⎪⎩ ≤

∑

The expected observed share vector for R replicates is calculated as a simple 

average of these simulated values:

(7) ∑=

=

R

r

Sr RE S

1

1 ( ) .

If there is a small change in price j, Pj

, then the elasticity vector with respect 

to this price change is:

(8) ( ) ( )/ 2

( ) ( )/ 2

( )

( )

E S E S

E P E P

E P

E S j j

j

j

Q

j + Δ

+ Δ ⋅ Δ

Δ

ψ = −Λ + ,

where Λ j is a vector of 0’s with the j

th element equal to 1, and E(S) is the 

change in the simulated E(S) given the change of expected price, E(Pj

). 

Homogeneity still holds in the elasticities of the observed system because the 

budget constraint (adding-up) is imposed in both latent and observed systems. 

1For more details, refer to Dong, 

Gould, and Kaiser for the derivation of 

the likelihood function and the model 

estimation.
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Most of the empirical estimations of price and expenditure elasticities 

reported in published analyses vary in size due to model specifi cation. This 

study differs from other cross-sectional models in its ability to satisfy both 

non-negativity and the adding-up conditions. The Tobit system estimator 

(Amemiya, 1974) used by Yen, Lin, and Smallwood (2003) addressed 

the non-negativity, but the adding-up restriction is compromised. Other 

approaches, including the maximum entropy estimator of Golan, Perloff, and 

Shen (2001) (also a Tobit system), the sample-selection estimator (Yen and 

Lin, 2006), its two-step alternative (Shonkwiler and Yen, 1999), a semiparametric extension (Sam and Zheng, 2010), and other two-step estimators 

(Perali and Chavas, 2000; Meyerhoefer, Ranney, and Sahn, 2005; Heien and 

Wessells, 1990), also do not satisfy the adding-up constraint. The present 

study also differs in that it uses fi ner distinctions in the product categories 

selected—bulk ice cream, sherbet/ice milk, refrigerated yogurt, frozen 

yogurt, drinkable yogurt, whole milk, reduced-fat milk, canned milk, natural 

cheese, processed cheese, cottage cheese, butter, and margarine—to reduce 

potential aggregation biases in estimation. 

Data

A demand system of 12 dairy products and margarine that were assumed 

separable from other food products is specifi ed and estimated in this study. 

The impact of changes in retail prices, consumer expenditure, and demographic factors on these product purchases is determined. The data underlying the analysis are from Nielsen Homescan data for 2007. A sample of 

the U.S. population was used in the selection process of U.S. consumers 

who agreed to allow their grocery receipts of purchases made during a 

12-month period to be scanned. Thirteen categories were established, using 

the descriptions of the UPC (United Product Code) and designated codes 

for each item. Individual overall quantities and expenditures are reported 

for all 13 products. Prices (unit values) are derived from observed quantities and expenditures after accounting for any coupons or promotions that 

might have been in effect. There are 63,061 households in this study, each of 

which purchased at least 1 of the 13 products in the 2007 data. The purchase 

record is matched to a household record that contains information on the 

size and composition of the household, income, age, race, gender, education 

and occupation of household members, and market location data. Projection 

factors (sample weights) are included in the Nielsen data to be used at the 

household level to provide estimates for the U.S. population. Although some 

researchers have heavily criticized the reliability of Nielsen data, the overall 

accuracy of self-reported data by Homescan panelists seems to be in line 

with many other surveys of this type (Einav, Leibtag, and Nevo, 2008).

Nielsen data contain only retail purchases for “at-home” use. Thus, one of the 

limitations of using the Nielsen data is that any of the 13 products consumed 

“away-from-home” at establishments such as fast food or dine-in restaurants, 

cafeterias, and schools are not included. If the products being analyzed have 

signifi cant “away-from-home” purchases, estimated economic measures such 

as per capita consumption or elasticities must be evaluated with that in mind.
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Estimation Results

Sample Statistics

According to Nielsen 2007 Homescan data, on average, consumers purchased 

more reduced-fat and whole milk than they did any other fl uid-ounce dairy 

products (table 1). Among dry-ounce products, refrigerated yogurt is the one 

most purchased, followed by margarine and processed and natural cheese. 

Dairy expenditures are largest for reduced-fat milk and bulk ice cream, which 

account for almost 42 percent of total dairy expenditures. Natural cheese had 

the highest average price among the seven dry-ounce products, while drinkable yogurt had the highest average price among the six fl uid-ounce products. 

In addition to prices, quantities, and expenditure, demographic-variable 

summary statistics are also displayed in table 1. Variables used in the analysis 

include household size; age of female head of household and dummy variables representing children under the age of 6 years; teenagers 13-17 years; 

single (unmarried) head of household; White, Black, Asian, and Other (other 

race) heads of household; U.S. region (East, Central, Southern, and West); 

and female head educational attainment (up to some college), along with 

seven household income categories ranging from 0 to $150,000 or more per 

year.2 To avoid singularity problems, the demographic dummy variables 

of Southern region, White head of household, and household income of 

$150,000 or more per year are used as the base. 

Summary of Estimated Demand System Price and 

Demographic Coeffi cients 

Tables 2 and 3 show the coeffi cient estimates derived from demand systems 

consisting of 13 different products and 18 demographic variables. A total of 

338 parameters (among them 234 are demographics, 91 are prices, and 13 

are total expenditures) were estimated using the GAUSS software system 

and BHHH maximum likelihood procedure (Berndt et al., 1974). Of the 

234 demographic parameter estimates, 154 are statistically signifi cant at the 

10-percent level or better. All of the own-price coeffi cients are statistically 

different from zero at the 10-percent level of signifi cance except for margarine. Of the 78 cross-price coeffi cients estimated, 58 (74 percent) were statistically signifi cant at the 10-percent level or better. Eleven of the 13 estimated 

expenditure coeffi cients were statistically signifi cant at the 10-percent level 

or better.

2Female head indicates the mother 

of the household. If no female head is 

present in the household, the head will 

be used as a substitute.
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Table 1

Variable defi nitions and sample statistics (sample size = 63,061)

Variable Mean SD % of households purchasing

Quantities (oz or fl oz per household over 12 months)

Bulk ice cream (fl oz) 591.77 801.69 89

Ice milk & sherbet (fl oz) 22.36 104.90 18

Refrigerated yogurt (oz) 316.61 505.48 80

Frozen yogurt (oz) 16.77 137.61 8

Drinkable yogurt (fl oz) 27.13 131.80 18

Whole milk (fl oz) 609.37 1,746.28 49

Reduced-fat milk (fl oz) 2,755.11 3,525.58 27

Canned milk (fl oz) 33.42 117.27 43

Natural cheese (oz) 121.90 173.63 86

Processed cheese (oz) 146.31 164.70 94

Cottage cheese (oz) 85.63 183.61 57

Butter (oz) 82.54 135.25 65

Margarine (oz) 153.80 196.64 74

Expenditures (dollars spent 

per household over 12 months)

Bulk ice cream 32.73 45.04

Ice milk & sherbet 1.09 5.52

Refrigerated yogurt 27.96 44.94

Frozen yogurt 1.03 9.42

Drinkable yogurt 3.34 15.80

Whole milk 16.91 45.93

Reduced-fat milk 70.56 84.68

Canned milk 2.66 8.08

Natural cheese 29.81 40.33

Processed cheese 26.70 29.60

Cottage cheese 9.61 20.63

Butter 13.67 22.07

Margarine 10.56 13.67

Prices (dollars spent per oz or

fl oz over 12 months)

Bulk ice cream ($/fl oz) $0.06 $0.04

Ice milk & sherbet ($/fl oz) 0.05 0.01

Refrigerated yogurt ($/oz) 0.09 0.03

Frozen yogurt ($/oz) 0.09 0.03

Drinkable yogurt ($/fl oz) 0.13 0.04

—Continued
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Table 1

Variable defi nitions and sample statistics (sample size = 63,061) (continued)

Variable Mean SD 

Prices (dollars spent per oz or

fl oz over 12 months)

Canned milk ($/fl oz) 0.09 0.02

Natural cheese ($/oz) 0.27 0.08

Processed cheese ($/oz) 0.20 0.07

Cottage cheese ($/oz) 0.12 0.02

Butter ($/oz) 0.18 0.06

Margarine ($/oz) 0.08 0.04

Demographic variables

Continuous variables:

 Household size - number of members 2.43 1.31

 Average age of female head of household 52.00 11.71

Dummy variables (1 = yes, 0 = otherwise) –

Percent of households: 

 Children less than 6 years old 9%

 Teenagers 13 – 17 years old 13

 Single person household 24

 Eastern region 17

 Central region 27

 Southern region (base) 36

 Western region 20

 Female head of household w/some college 30

 White head of household (base) 84

 Black head of household 9

 Asian head of household 2

 Other head of household 5

 Household income ≤$19,999 11

 Household income $20,000-34,999 20

 Household income $35,000-49,999 19

 Household income $50,000-69,999 20

 Household income $70,000-99,999 18

 Household income $100,000-149,999 10

 Household income ≥$150,000 (base) 2

Note: “fl oz” is fl uid ounce and “oz” is dry ounce. Income is per year.

Source: Authors’ calculations, using 2007 Nielsen Homescan data.
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Table 2

Censored demand system parameter estimates for demographics

Variable Intercept Household size

Age of female head 

of household

Children ages 6

and younger

Bulk ice cream 0.039* –0.005* 0.001 –0.024*

Sherbet/ice milk –0.026* 0.001* 0.000 –0.002

Refrigerated yogurt 0.207* –0.003 –0.001* 0.017*

Frozen yogurt –0.017* 0.002 0.000 –0.003*

Drinkable yogurt 0.038* –0.003* 0.000* 0.010*

Whole milk 0.335* 0.004* –0.001* 0.076*

Reduced-fat milk –0.379* 0.002 –0.001* –0.035*

Canned milk –0.023* 0.000* 0.001* –0.001*

Natural cheese 0.367* –0.005* –0.001* 0.000

Processed cheese 0.311* 0.005* –0.001* –0.023*

Cottage cheese –0.045* 0.003 0.001* –0.004

Butter 0.106* –0.003 0.001* –0.006

Margarine 0.086* 0.003 0.001* –0.006

Variable

Teenagers 

ages 13-17

Single person 

household

Female head of household 

w/ some college 

Black head of 

household

Bulk ice cream 0.008 0.014* –0.003 0.053*

Sherbet/ice milk 0.000 0.001 0.000 0.008*

Refrigerated yogurt –0.006 0.024* 0.035* 0.012*

Frozen yogurt –0.002* 0.005* 0.001* 0.000

Drinkable yogurt –0.006* 0.005* 0.001 0.007*

Whole milk –0.009 –0.025* –0.035* 0.055*

Reduced-fat milk 0.032* 0.035* 0.020* –0.093*

Canned milk –0.001* –0.006* –0.001 0.020*

Natural cheese –0.006 0.002 0.011* –0.024*

Processed cheese 0.002 –0.017* –0.015* –0.025*

Cottage cheese –0.008* –0.003* –0.001 –0.042*

Butter –0.002* –0.009* –0.001 0.012*

Margarine –0.001 0.025* –0.013* 0.016

—Continued
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Table 2

Censored demand system parameter estimates for demographics (continued)

Variable

Asian head of 

household

Other-race head of 

household Eastern region Central region

Bulk ice cream –0.002 0.000 –0.002* 0.001

Sherbet/ice milk 0.001 0.002 0.010* –0.004

Refrigerated yogurt 0.043* 0.013* 0.037* 0.020*

Frozen yogurt 0.002 –0.002 0.002* –0.003*

Drinkable yogurt 0.011* 0.005* 0.001 0.000*

Whole milk 0.042* 0.039* –0.025* –0.075*

Reduced-fat milk 0.026* –0.025* –0.049* 0.008*

Canned milk 0.011* 0.005* –0.009* –0.002*

Natural cheese –0.056* 0.006 0.016* 0.012*

Processed cheese –0.035* –0.014* –0.022* –0.004*

Cottage cheese –0.031* –0.009* 0.008* –0.033*

Butter –0.008 –0.009* 0.047* 0.024*

Margarine –0.030 –0.007 –0.006 0.001

Variable Western region

Household income 

≤$19,999

Household income 

$20,000–$34,999

Household income 

$35,000–$49,999

Bulk ice cream 0.003* 0.003 0.003 0.003*

Sherbet/ice milk 0.004* 0.001 –0.004 0.004

Refrigerated yogurt 0.037* –0.073* –0.060 –0.054*

Frozen yogurt 0.002 –0.008* –0.006* –0.005*

Drinkable yogurt 0.002 –0.006* –0.011* –0.009*

Whole milk –0.054* 0.081* 0.053* 0.041*

Reduced-fat milk –0.055* 0.002 0.013* 0.007

Canned milk –0.004* 0.003 0.000 0.001

Natural cheese 0.056* –0.024* –0.011* –0.005

Processed cheese –0.040* 0.017* 0.019* 0.023*

Cottage cheese 0.031* 0.007 0.006 0.003

Butter 0.043* –0.046* –0.033* –0.025*

Margarine –0.015 0.047* 0.036* 0.028*

—Continued
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Table 2

Censored demand system parameter estimates for demographics (continued)

Variable

Household income 

$50,000–$69,999

Household income 

$70,000–$99,999

Household income 

$100,000–$149,999

Bulk ice cream –0.015* –0.017* –0.018*

Sherbet/ice milk 0.002 0.001 0.001

Refrigerated yogurt –0.044* –0.032* –0.025*

Frozen yogurt –0.005* –0.002 –0.003*

Drinkable yogurt –0.009* –0.005* –0.005*

Whole milk 0.023* 0.007 0.003

Reduced-fat milk 0.015* 0.016* 0.014*

Canned milk 0.002 0.000 0.000

Natural cheese 0.002 0.007* 0.011*

Processed cheese 0.020* 0.019* 0.014*

Cottage cheese 0.004* 0.000* 0.003

Butter –0.016* –0.007 –0.001

Margarine 0.020 0.012 0.005

Notes: Level of statistical signifi cance: * = 10% or better. Income is per year.

Source: Authors’ calculations using 2007 Nielsen Homescan data.

Table 3

Censored demand system parameter estimates for price and total expenditures

Variable Bulk ice cream Sherbet/ice milk Refrig. yogurt Frozen yogurt Drinkable yogurt

Total expenditure

0.006* –0.002* 0.003* 0.000 –0.002*

Price coeffi cients

Bulk ice cream –0.025*

Sherbet/ice milk –0.003* –0.007*

Refrigerated yogurt 0.005* –0.004* –0.041*

Frozen yogurt 0.002* –0.001* –0.010* –0.013*

Drinkable yogurt 0.002* 0.002* 0.001 –0.006* –0.038*

Whole milk 0.008 0.004* 0.004 0.008* 0.001

Reduced-fat milk –0.024* 0.001 0.031* 0.009* 0.016*

Canned milk –0.001* 0.005* 0.002* 0.001 0.003*

Natural cheese 0.015* 0.002* –0.001 0.003* 0.003*

Processed cheese –0.015* –0.001 0.011* 0.003* 0.006*

Cottage cheese 0.002* 0.004* –0.012* 0.000 0.003*

Butter 0.017* –0.001 –0.003 –0.001 0.001

Margarine –0.017* –0.001 0.017* 0.006* 0.007*

—Continued
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Table 3

Censored demand system parameter estimates for price and total expenditures (continued)

Variable Whole milk Reduced-fat milk Canned milk Natural cheese Processed cheese

Total expenditure

–0.051* 0.065* 0.003* 0.010* –0.024*

Price coeffi cients

Bulk ice cream

Sherbet/ice milk

Refrigerated yogurt

Frozen yogurt

Drinkable yogurt

Whole milk –0.179*

Reduced-fat milk 0.118* –0.261*

Canned milk 0.011* 0.008* –0.014*

Natural cheese 0.035* 0.054* 0.001 –0.147*

Processed cheese –0.014* 0.016* –0.007* 0.024* –0.006*

Cottage cheese 0.028* 0.012* 0.005* 0.002 0.010*

Butter 0.015* 0.025* –0.006* 0.003* 0.000

Margarine –0.021* –0.004 –0.007* 0.006 –0.026*

Variable Cottage Cheese Butter Margarine

Total expenditure

0.010* –0.001 –0.033*

Price coeffi cients

Bulk ice cream

Sherbet/ice milk

Refrigerated yogurt

Frozen yogurt

Drinkable yogurt

Whole milk

Reduced-fat milk

Canned milk

Natural cheese

Processed cheese

Cottage cheese –0.062*

Butter 0.005* –0.070*

Margarine 0.004* 0.019* 0.0170

Notes: Level of statistical signifi cance: * = 10% or better. 

Source: Authors’ calculations using 2007 Nielsen Homescan data.
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Compensated Demand Elasticities

Two sets of demand elasticities can be derived from the censored AIDS 

model estimates: compensated (Hicksian) and uncompensated (Marshallian). 

According to economic theory, changes in both price and income can infl uence demand. A compensated demand curve allows income to change to 

“compensate” for the price change, while an uncompensated demand curve 

does not. 

The compensated price elasticities for the 13 products are presented in table 

4. Each cell shows the price elasticity for a change in the price of the product 

identifi ed at the top of the column. All own-price elasticities are negative 

and statistically signifi cant at the 10-percent level. The cross-price relationships estimated in large demand systems provide information about how the 

purchase price of one product affects the demand for another product. Of the 

156 compensated cross-price elasticity estimates shown in table 4, 145 (93 

percent) are statistically signifi cant at the 10-percent level. 

Table 4

Estimated compensated price elasticities

Variable Bulk ice cream Sherbet/ ice milk Refrig. yogurt Frozen yogurt Drinkable yogurt

Bulk ice cream –0.77* 0.00* 0.12* 0.01* 0.01*

Sherbet/ice milk 0.05* –1.21* –0.02 –0.04* 0.06*

Refrigerated yogurt 0.16* –0.01* –1.08* –0.05* 0.01

Frozen yogurt 0.17* –0.02 –0.08* –1.26* –0.10*

Drinkable yogurt 0.18* 0.04* 0.13* –0.11* –1.72*

Whole milk 0.09* 0.01* 0.14* 0.03* 0.01*

Reduced-fat milk 0.09* 0.01* 0.17* 0.02* 0.04*

Canned milk 0.11* 0.12* 0.15* 0.03* 0.07*

Natural cheese 0.21* 0.02* 0.09* 0.02* 0.01*

Processed cheese 0.05* 0.00 0.17* 0.01* 0.03*

Cottage cheese 0.17* 0.05* –0.04* 0.00 0.04*

Butter 0.34* –0.01 0.07* –0.01* 0.01

Margarine 0.09* 0.00 0.15* 0.01* 0.01*

Variable Whole milk Reduced-fat milk Canned milk Natural cheese Processed cheese

Bulk ice cream 0.01 0.23* 0.01* 0.18* 0.05*

Sherbet/ice milk 0.17* 0.33* 0.16* 0.20* 0.10*

Refrigerated yogurt 0.06* 0.46* 0.02* 0.12* 0.16*

Frozen yogurt 0.22* 0.45* 0.03* 0.18* 0.16*

Drinkable yogurt 0.11* 0.56* 0.06* 0.17* 0.23*

—Continued
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Table 4

Estimated compensated price elasticities (continued)

Variable Whole milk Reduced-fat milk Canned milk Natural cheese Processed cheese

Whole milk –1.65* 0.73* 0.04* 0.28* 0.10*

Reduced-fat milk 0.26* –1.26* 0.04* 0.26* 0.12*

Canned milk 0.27* 0.55* –1.31* 0.12* –0.06*

Natural cheese 0.20* 0.60* 0.02* –1.61* 0.23*

Processed cheese 0.02* 0.36* –0.04* 0.26* –0.89*

Cottage cheese 0.31* 0.49* 0.07* 0.14* 0.20*

Butter 0.23* 0.61* –0.06* 0.16* 0.12*

Margarine –0.01* 0.31* –0.01* 0.15* 0.06*

Variable Cottage Cheese Butter Margarine

Bulk ice cream 0.04* 0.13* –0.01*

Sherbet/ice milk 0.17* 0.02 0.01

Refrigerated yogurt –0.02* 0.05* 0.14*

Frozen yogurt 0.03* 0.04* 0.19*

Drinkable yogurt 0.09* 0.07* 0.19*

Whole milk 0.12* 0.11* –0.02*

Reduced-fat milk 0.08* 0.13* 0.04*

Canned milk 0.14* –0.09* –0.11*

Natural cheese 0.05* 0.07* 0.09*

Processed cheese 0.07* 0.04* –0.08*

Cottage cheese –1.64* 0.10* 0.10*

Butter 0.07* –1.81* 0.28*

Margarine 0.04* 0.11* –0.90*

Notes: Level of statistical signifi cance: * = 10% or better. Own-price elasticities are in boldface.

Source: Authors’ calculations, using 2007 Nielsen Homescan data.
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Uncompensated Demand Elasticities

Table 5 presents the uncompensated price elasticity estimates for the 13 

product categories purchased by consumers from retail stores. All own-price 

elasticities are negative, statistically signifi cant at the 10-percent level, and are 

relatively similar in size to the compensated own-price elasticities presented 

above. Among the 156 cross-price elasticity estimates, 133 (85 percent) are 

statistically signifi cant at the 10-percent level or better. Expenditure elasticities are also presented in table 5. All of the expenditure elasticities are statistically signifi cant and positive. 

Seven of the 13 product categories have expenditure elasticities that are 1 

or greater.

Table 5

Estimated uncompensated price and total expenditure elasticities

Variable Bulk ice cream Sherbet/ice milk Refrig. yogurt Frozen yogurt Drinkable yogurt

Bulk ice cream –0.91* –0.01* 0.01* 0.00* –0.00

Sherbet/ice milk –0.08* –1.21* –0.12* –0.05* 0.05*

Refrigerated yogurt 0.02* –0.02* –1.19* –0.05* –0.00

Frozen yogurt 0.03* –0.03* –0.19* –1.26* –0.11*

Drinkable yogurt 0.05* 0.04* 0.03 –0.11* –1.73*

Whole milk –0.02* 0.01* 0.06* 0.03* 0.00

Reduced-fat milk –0.07* 0.00* –0.05* 0.02* 0.02*

Canned milk –0.04* 0.11* 0.03* 0.03* 0.06*

Natural cheese 0.07* 0.01* –0.02* 0.01* 0.00

Processed cheese –0.07* –0.01* 0.08* 0.00 0.02*

Cottage cheese 0.02* 0.05* –0.15* 0.00 0.03*

Butter 0.20* –0.01* –0.04* –0.02* 0.00

Margarine –0.04* 0.00* 0.05* 0.01* 0.00

Variable Whole milk Reduced-fat milk Canned milk Natural cheese Processed cheese

Bulk ice cream –0.06* –0.05* 0.00* 0.06* –0.07*

Sherbet/ice milk 0.10* 0.08* 0.15* 0.09* –0.01

Refrigerated yogurt –0.01 0.18* 0.01* 0.00 0.04*

Frozen yogurt 0.16* 0.17* 0.02* 0.06* 0.04*

Drinkable yogurt 0.04* 0.30* 0.05* 0.06* 0.11*

Whole milk –1.70* 0.52* 0.03* 0.19* 0.01

Reduced-fat milk 0.19* –1.57* 0.03* 0.12* –0.02*

Canned milk 0.20* 0.26* –1.32* 0.00 –0.19*

—Continued
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Table 5

Estimated uncompensated price and total expenditure elasticities (continued)

Variable Whole milk Reduced-fat milk Canned milk Natural cheese Processed cheese

Natural cheese 0.32* 0.00 0.02 –1.73* 0.10*

Processed cheese –0.04* 0.13* –0.05* 0.16* –0.99*

Cottage cheese 0.23* 0.19* 0.05* 0.01 0.07*

Butter 0.17* 0.34* –0.07* 0.05* 0.01

Margarine –0.08* 0.05* –0.02* 0.03* –0.05*

Variable Cottage Cheese Butter Margarine Total expenditure

Bulk ice cream 0.01* 0.07* –0.06* 1.01*

Sherbet/ice milk 0.13* –0.04* –0.04* 0.93*

Refrigerated yogurt –0.06* –0.01 0.09* 1.00*

Frozen yogurt –0.01 –0.02* 0.14* 1.00*

Drinkable yogurt 0.06* 0.02 0.14* 0.96*

Whole milk 0.10* 0.07* –0.06* 0.77*

Reduced-fat milk 0.04* 0.06* –0.02* 1.14*

Canned milk 0.11* –0.15* –0.17* 1.06*

Natural cheese 0.01* 0.01* 0.03* 1.04*

Processed cheese 0.04* –0.01 –0.12* 0.85*

Cottage cheese –1.68* 0.04* 0.05* 1.10*

Butter 0.04* –1.87* 0.23* 0.97*

Margarine 0.00 0.06* –0.95* 0.94*

Note: Level of statistical signifi cance: * = 10% or better. Own-price elasticities are in boldface.

Source: Authors’ calculations, using 2007 Nielsen Homescan data.
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Estimated Elasticities of 

Demographic Variables 

Table 6 displays the impact of demographic variables on the demand for 

“at-home” dairy products and margarine. Eighteen exogenous demographic 

variables are analyzed in the censored demand model, including household 

size, children under 6 years, teens age 13-17, average age of female heads 

of household, single person household, households living in the Eastern, 

Central, and Western regions of the United States, female heads of household 

who have some college training, Asian, Black, and Other race household 

heads, and six household income categories. Findings from the censored 

demand system show that the size of households is statistically signifi cant 

and positively infl uences the purchase of sherbet/ice milk, drinkable yogurts, 

whole milk, reduced-fat milk, processed cheese, and margarine. Although 

there are more women in the workforce today than 20 years ago, women still 

do the majority of the shopping and cooking for the household (Babble, 2010; 

Casual Kitchen, 2010). Purchases of dairy items, including bulk ice cream, 

sherbet/ice milk, frozen yogurt, canned milk, cottage cheese, and butter, are 

all statistically signifi cant and positively infl uenced by the age of the female 

head of household. 

Single-person heads of household, along with college-educated female heads 

of household, positively infl uenced the purchase of healthy dairy products 

such as refrigerated and frozen yogurt and reduced-fat milk. Black heads 

of household have a positive, statistically signifi cant effect on purchases of 

bulk ice cream, sherbet/ice milk, refrigerated and drinkable yogurts, whole 

and canned milk, and butter. Asian heads of household also have a positive, 

statistically signifi cant effect on purchases of bulk ice cream, refrigerated and 

drinkable yogurts, and all fl uid milks. Households residing in the Eastern, 

Central, and Western regions of the United States have a greater impact on 

refrigerated yogurt, natural and cottage cheese, and butter than other dairy 

products and margarine. Of the income categories analyzed, households 

in the two lowest categories—$20,000-$34,999 annually and $19,999 or 

less—have a positive, statistically signifi cant infl uence on purchases of whole 

and reduced-fat milk. Other dairy products that are statistically signifi cant 

and positively infl uenced by households who make $34,999 or less include 

purchases of sherbet/ice milk, processed and cottage cheese, and margarine. 

Although the infl uence of most demographic variables is relatively small, 

some of them do have statistically signifi cant effects on consumer purchases 

of dairy products. 
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Table 6

Estimated demographic elasticities 

Variable Intercept

Household 

size

Age of 

female head 

of household

Children 

ages 6 and 

younger

Teenagers 

ages 13-17

Singleperson 

household

Female head of 

household w/ 

some college 

Bulk ice cream –0.295* –0.037* 0.248* –0.006 0.002* 0.012* –0.007*

Sherbet/ice milk –1.256* 0.115* 0.069* –0.002 0.000 0.003 0.000

Refrigerated yogurt 0.503* –0.024* –0.229* 0.007* –0.004* 0.027* 0.060*

Frozen yogurt –0.822* 0.005 0.027* –0.005* –0.006* 0.021* 0.010*

Drinkable yogurt 0.193* 0.148* –0.405* 0.015* –0.013* 0.023* 0.008

Whole milk 0.976* 0.045* –0.145* 0.027* –0.005* –0.032* –0.062*

Reduced-fat milk –1.339* 0.013* –0.053* –0.005 0.008* 0.020* 0.016*

Canned milk –0.981* 0.019 0.594* –0.001 –0.004* –0.044* –0.013*

Natural cheese 1.394* –0.059* –0.264* 0.001 –0.004* 0.000 0.018*

Processed cheese 1.289* 0.069* –0.131* –0.009* 0.000 –0.027* –0.035*

Cottage cheese –0.941* –0.079* 0.436* –0.003 –0.011* –0.011* –0.006

Butter 0.814* –0.087 0.646* –0.005* –0.003* –0.030* –0.006*

Margarine –0.158* 0.069* –0.131* –0.009 0.000* –0.027* –0.035*

Variable

Black head of 

household

Asian 

head of 

household

Other race 

head of 

household

Eastern 

region

Central 

region

Western 

region

Household 

income ≤

$19,999

Bulk ice cream 0.022* 0.003* 0.000 0.001 –0.018* –0.004* 0.001

Sherbet/ice milk 0.027* –0.002 0.000 –0.010* –0.005 0.015* 0.014*

Refrigerated yogurt 0.007* 0.005* 0.003* 0.028* 0.023* 0.033* –0.037*

Frozen yogurt 0.002 0.001 –0.002* 0.008* –0.012* 0.007* –0.018*

Drinkable yogurt 0.013* 0.005* 0.004* 0.002 0.003 0.010* –0.012*

Whole milk 0.025* 0.004* 0.008* –0.018* –0.091* –0.046* 0.043*

Reduced-fat milk –0.019* 0.002* –0.002* –0.019* 0.002 –0.025* 0.002*

Canned milk 0.049* 0.006* 0.005* –0.036* –0.011* –0.017 0.009

Natural cheese –0.009* –0.007* 0.002* 0.013* 0.014* 0.055* –0.012*

Processed cheese –0.011* –0.005* –0.003* –0.019* –0.007* –0.041* 0.012*

Cottage cheese –0.041* –0.008* –0.004* 0.016* 0.098* 0.069* 0.010*

Butter 0.015* –0.003* –0.004 0.093* 0.080* 0.101* –0.062*

Margarine –0.001* –0.005* –0.003 –0.019* –0.007* –0.041* 0.012*

—Continued
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Table 6

Estimated demographic elasticities (continued)

Variable

Household income 

$20,000–$34,999

Household income 

$35,000–$49,999

Household income 

$50,000–$69,999

Household income 

$70,000–$99,999

Household income 

$100,000–$149,999

Bulk ice cream –0.006* –0.007* –0.011* –0.012* –0.007*

Sherbet/ice milk 0.021* 0.022* 0.012 0.007 0.004

Refrigerated yogurt –0.054* –0.047* –0.038* –0.026* –0.011*

Frozen yogurt –0.023* –0.016* –0.017* –0.008* –0.006*

Drinkable yogurt –0.042* –0.031* –0.031* –0.018* –0.008*

Whole milk 0.050* 0.037* 0.021* 0.006 0.001

Reduced-fat milk 0.008* 0.004* 0.007* 0.007* 0.003*

Canned milk 0.003 0.005 0.010 0.000 0.000

Natural cheese –0.010* –0.003 0.002 0.006* 0.005*

Processed cheese 0.021* –0.025* 0.021* 0.018* 0.007*

Cottage cheese 0.014* 0.007* 0.007* 0.000* 0.003*

Butter –0.079* –0.057* –0.036* –0.015 –0.001

Margarine 0.022* 0.025* 0.021* 0.018* 0.007

Note: Level of statistical signifi cance: * = 10% or better. Income is per year.

Source: Authors’ calculations, using 2007 Nielsen Homescan data.
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Conclusions

This research estimated demand elasticities that can be used for policy analysis by researchers in academic institutions and policy-oriented agencies. An 

empirical analysis of Nielsen 2007 Homescan retail purchase data was used 

to estimate a censored demand system of margarine and 12 dairy products. 

Results indicate that dairy purchases are infl uenced by price, overall dairy 

expenditure, and demographic factors. Ten of the 12 uncompensated ownprice elasticities for dairy products are statistically signifi cant and elastic with 

respect to changes in retail prices. Similar fi ndings are noted for compensated 

own-price elasticities. 

Other fi ndings reveal that consumers’ purchases of bulk ice cream, refrigerated and frozen yogurts, reduced-fat milk, canned milk, natural cheese, and 

cottage cheese are sensitive to changes in overall dairy expenditures. Strong 

substitution relationships are found among bulk ice cream, reduced-fat milk, 

and natural cheese and other products in the demand system. The three fl uid 

milks—whole milk, reduced-fat milk, and canned milk— are found to be 

strong substitutes for each other. Similar substitution relaionships exist among 

the three cheese products, natural cheese, cottage cheese, and processed 

cheese. 
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