Diansheng Dong and Hayden Stewart

Households’ Choices Among Fluid 

Milk Products: What Happens 

When Income and Prices Change?

Economic

Research

Service

Economic 

Research 

Report 

Number 146

April 2013

United States Department of Agriculture
Economic Research Service 

www.ers.usda.gov

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Dong, Diansheng and Hayden Stewart. Households’ Choices Among Fluid Milk 

Products: What Happens When Income and Prices Change?, ERR-146, U.S. 

Department of Agriculture, Economic Research Service, April 2013.

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United States Department of Agriculture
Economic Research Report Number 146  A Report from the Economic Research Service  April 2013

Abstract

Households have several ways to economize on their purchases at retail food stores 

when prices increase or their incomes fall. This report investigates a household’s 

choice among retail fl uid milk products categorized along three dimensions: three 

levels of fat content, two levels of package size, and organic versus conventional 

methods of production. Nielsen Homescan data from 2007-08 are used to estimate 

a choice model, which accounts for price, income, and other choice determinants. 

Results show that small changes in prices and income have a modest impact on a 

household’s choice among milk products. However, households mitigate the impact 

of more substantial price and income shocks by switching from more expensive 

to less expensive products. We also fi nd that the demand for organic milk is more 

sensitive to swings in income and food prices than is demand for conventional milk.

Keywords: milk purchases, milk prices, dairy product, dairy prices, organic milk, 

household income, household food economizing behavior, Homescan data, fl uid 

milk, recession

Acknowledgments

The authors extend their thanks for helpful comments to Tirtha Dhar, Professor, 

University of British Columbia; Kristin Kiesel, Professor, California State 

University Sacramento, and Economic Research Service colleagues William Hahn 

and Donald Blayney. We also thank Maria Williams for editorial expertise and 

Curtia Taylor for the design.

Diansheng Dong, ddong@ers.usda.gov

Hayden Stewart, hstewart@ers.usda.gov

Households’ Choices Among Fluid 

Milk Products: What Happens 

When Income and Prices Change?
ii Households’ Choices Among Fluid Milk Products: What Happens Economic Research Service, USDA

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

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

Households’ Purchases of Fluid Milk . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

Milk Purchase Choice Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

Many Underlying Factors to Households’ Product Choices . . . . . . . . . . . . . . . . . . . 9

Impact of Price and Income Shocks on Market Composition . . . . . . . . . . . . . . . . 16

Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

Appendix I: The Specifi cation of the Household 

Loyalty Variable (Lijt) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

Appendix II: Estimation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

Contents
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Summary

What Is the Issue?

Many households experienced a decrease in income during the 2007-2009 recession. At the same time, food prices rose. In 2008, the median U.S. household made 

3.6 percent less money after adjustment for infl ation than it did in 2007, while 

prices for fl uid milk at retail food stores rose 11.6 percent in 2007 and 6 percent in 

2008. Households have several ways to economize on their retail food purchases 

when prices increase or their incomes fall. More information on how households 

economize on their purchases may help policymakers better understand the relationship of consumer choices to changes in the economy and to a host of demographic 

variables. 

What Did the Study Find?

Households experiencing an income decrease may look for ways to stretch their 

food dollar, such as seeking out promotions or shopping at less expensive stores like 

supercenters. This study focuses on the type of fl uid milk a household buys. Fluid 

milk that is higher fat, organic, or packaged in small containers is more expensive 

per gallon than milk that is lower fat, conventionally produced, or packaged in 

large containers. Households typically switch to less expensive products when their 

incomes decrease. For instance, households save money by choosing fl uid milk 

products with a lower fat content or by switching from organic to conventional milk. 

Households with an increase in income, however, do not always buy more expensive products: 

A 10-percent increase in household income:

• Raises the probability of purchasing organic milk from 3 to 3.7 percent; 

• Raises the probability of buying low-fat milk (defi ned as “skim and less than 2 

percent fat”) from 47 to 48.6 percent; 

• Lowers the probability of purchasing whole milk (at least 3.25 percent fat) 

from 17 to 15.9 percent;

• Lowers the probability of choosing reduced-fat milk (between 2 and 3.25 

percent fat) from 36 to 35.5 percent; and 

• Has only a small effect on households’ choice among products in different 

container sizes. 

Changes in retail prices also affect a household’s choice among different milk 

products:

• A small (1-percent) increase in prices for all milk products has only a small 

effect on the division of sales among products with different levels of fat 

content and in different package sizes, as well as division of sales between milk 

produced using conventional and organic methods.
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• A large ($1 per gallon or approximately 25-percent) increase in retail milk 

prices is large enough to curb growth in sales of organic milk.

• A large increase in prices for all milk products also increases the probability—

from 47 to 53.9 percent—of purchasing low-fat milk. 

• Even large price shocks have little effect on households’ choice between 

package sizes. The probability of purchasing milk in a container smaller than 1 

gallon decreases from 42 to 40.2 percent.

Overall, when substantial price and income shocks occur, households switch from 

more expensive to less expensive products. This practice may help households 

afford a healthful diet when budgets get tight. However, many lower income 

Americans already (before income reductions or general price increases) purchase 

less expensive items; likewise, lower income households are less likely to choose 

organic milk. This lack of fl exibility may render households already on a tight 

budget more exposed to the effects of price volatility. 

In general, demand for organic milk is more sensitive than demand for conventional 

milk to swings in income and food prices. Past research suggests that many buyers 

of organic milk question conventional production methods and believe organic 

products to be safer and/or more healthful. Nonetheless, during the recent recession, 

when incomes declined and prices rose, growth in organic milk sales stalled. 

How Was the Study Conducted?

We investigate a household’s choice among retail fl uid milk products categorized 

along three dimensions: three levels of fat content, two levels of package size, and 

organic versus conventional methods of production. Categorizing retail products 

along all 3 dimensions yields 12 specifi c products (e.g., low-fat organic milk in a 

1-gallon container). A unique multinomial logit choice model is applied to account 

for past household purchase behavior, price, promotional deal, and seasonality. It 

also accounts for household demographic variables such as income and number of 

household members, as well as the age, employment status, education, and ethnicity 

of the head of household and whether or not the home was owned. We use 2007-

2008 Nielsen Homescan data to estimate the choice model. Finally, using model 

results for each of the 12 specifi c products, we simulate how shocks to prices, 

income, and other demand determinants would affect the probability that a household buys lower fat versus higher fat fl uid milk, conventional or organic products, 

and fl uid milk packaged in a 1-gallon or smaller container.
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Introduction

Households may need to stretch their food dollars either when their incomes 

decrease or when food prices increase. Many Americans experienced both of these 

conditions during the December 2007 to June 2009 recession. This report examines 

the question of how consumers adjust their choices when faced with income and 

price shocks for a staple (in this report, fl uid milk), which is available in a variety of 

retail forms and container sizes.

Households have several ways to economize on their purchases at retail food stores 

when prices increase or their incomes fall. They may buy smaller quantities of 

some foods, but ultimately, they need to eat. Aside from buying less food, Leibtag 

and Kaufman (2003), for example, show that households may adjust their purchase 

behavior by shopping at less expensive stores or substituting less expensive foods. 

This project focuses on the second possibility: we investigate households’ choices 

among fl uid milk products (1) sold in gallon versus less-than-gallon containers, (2) 

produced using organic versus conventional methods, and (3) containing more and 

less milk fat. That is, when prices and income change along with other variables, 

how do households adjust their choices among these substitute fl uid milk products? 

The median U.S. household saw its income fall 3.6 percent in 2008 and 0.7 percent 

in 2009 after adjustment for infl ation.1 In addition, food prices had already begun 

to rise in early 2007. Food price infl ation reached 4 percent in 2007 and 5.5 percent 

in 2008 before moderating to 1.8 percent in 2009.2 Foods that became substantially more expensive included staples like fl uid milk. Prices for milk at retail food 

stores rose 11.6 percent in 2007 and 6 percent in 2008 before ultimately falling 13.2 

percent in 2009.3

The price of 2 percent milk rose above $4 per gallon in many U.S. cities during 

the 2007-08 peak of infl ation.4 Kumcu and Kaufman (2011) show that, in general, 

consumers reacted to the combination of lower incomes and higher food prices over 

these years by economizing on their food purchases. They took advantage of sales, 

promotions, and coupons; substituted comparable, but lower cost foods; and sought 

stores with lower prices and more cost-effective selections.

Fluid milk is a staple of the American diet, and it is especially important to young 

people. Americans consumed about 0.75 cup per day, on average, in 2005-06 

(Sebastian et al., 2010), and during those same years, children ages 2 to 11 

consumed between 1.25 and 1.5 cups per day. Cornick et al. (1994) found that 96.1 

percent of all households bought fl uid milk over a 1-year period in the early 1990s. 

1 Based on data provided by the U.S. Census Bureau. See DeNavas-Walt et al. (2011). 

2 Based on the Consumer Price Index (U.S. city average) as reported by the Bureau of 

Labor Statistics (2012). 

3 Based on the Consumer Price Index (U.S. city average) as reported by the Bureau of 

Labor Statistics (2012). 

4 Through its administration of Federal milk marketing orders, the USDA Agricultural Marketing Service (AMS) generates data on milk supplies, utilization, sales, plant prices, overorder payments, and retail prices for packaged milk. See USDA/AMS (2012).
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Furthermore, the Dietary Guidelines for Americans, 2010 encourages consumption 

of dairy products.5 Americans are advised that consuming enough dairy products 

can improve bone health and lower blood pressure, as well as reduce the risk of 

cardiovascular disease and type 2 diabetes. However, “most” Americans aged 4 and 

over consume less than the recommended quantity of dairy products (p. 38). 

Although milk has long been considered a major food product to provide necessary 

nutrients such as calcium, milk fat has also been viewed as a contributor to obesity 

in America. Fat-free and low-fat fl uid milk provide necessary nutrients, such as 

calcium, with fewer calories than higher fat dairy products. Thus, the type of milk 

a household buys plays a role in its members’ health. Whether or not consumers 

substitute between whole milk and lower fat products will affect not only their 

budgets, but also how closely they adhere to Federal dietary guidelines. 

In addition to affecting health, consumer choices of milk products infl uence dairy 

production trends. One example of such infl uence is in organic dairy production. 

Organic dairy farmers represent a small but growing share of the overall market for 

fl uid milk. To qualify for certifi cation under USDA’s National Organic Program, 

conventional milk producers must undergo a process that can be challenging and 

costly (McBride and Greene, 2009). To help cover those costs and support the 

recent growth in organic dairy farming, farmers have largely relied on the willingness of many consumers to pay a premium for organic milk. Smith et al. (2009), for 

example, fi nd that the organic premium for a half-gallon of low-fat milk is between 

72 and 88 percent, depending on whether the milk is also branded. Because of 

the fi nancial risk involved, conventional milk producers thinking of switching to 

organic production need information not only on consumers’ willingness to pay, but 

on the robustness of that willingness, in the face of price and income shocks. 

In this report, we investigate a household’s choice among retail fl uid milk products categorized along three dimensions: three levels of fat content,6 two levels of 

package size (“1 gallon” and “less-than-gallon sized”), and organic versus conventional methods of production. Categorizing retail products along all 3 dimensions 

(e.g., low-fat organic milk in a 1-gallon container) yields 12 specifi c products. We 

estimate a choice model that allows predicting the effects of changes in prices and 

income, among other factors, on a household’s choices among the 12 products. 

Results obtained in this study may help policymakers better understand the relationship of consumer choices to changes in the economy and to a host of demographic 

variables.

5 The Dietary Guidelines for Americans is issued by the USDA and the U.S. Department 

of Health and Human Services to provide evidence-based nutrition information and advice for 

people age 2 and older. It also serves as the basis for Federal food and nutrition education 

programs.

6 Low-fat milk is defi ned as less than 2 percent fat including skim; reduced-fat is between 

2 and 3.25 percent fat; and whole is at least 3.25 percent fat.
Economic Research Service, USDA 3

Households’ Purchases of Fluid Milk

When prices rise or incomes fall, consumers tend to reduce the quantity of milk that 

they consume by a proportionally smaller amount. A review of existing research 

by Andreyeva et al. (2010) identifi es 26 studies that estimate the price elasticity 

of demand for milk using either time series or cross-sectional data. The average 

reported estimate was -0.59, meaning that if the price of milk were to increase 

(or decrease) by 10 percent, the expected decrease (or increase) in the quantity 

consumed would be only 6 percent. However, during the past recession, despite the 

rise of milk prices and fall of incomes, quantities of milk consumed were unusually stable. Loss-adjusted food availability data reveal that per capita consumption 

remained about 14.5 gallons per person per year (USDA-ERS, 2012). 

In a recession or when prices increase, households may seek to economize in ways 

other than consuming less of staple foods. One way is shopping at less expensive 

stores. Dong and Stewart (2012) show that, after an income decrease, a household 

is more likely to buy fl uid milk at a supercenter than at either a traditional grocery 

store or club warehouse. Another way that households may economize is by substituting less expensive products for more expensive ones. 

For the analysis, we use 2007 and 2008 Nielsen Homescan data to investigate a 

household’s choices among retail milk products. Nielsen maintains a consumer 

panel that demographically and geographically represents the continental United 

States. Participating households from all 48 contiguous States are given scanners 

to keep in their homes. After a shopping occasion, panelists use these scanners to 

record food purchases, including the Universal Product Code (UPC), the quantities 

bought, the amount of money paid, the purchase date, and price promotions, if any. 

The data are likewise daily transaction data and include purchases at all grocery 

retail stores. Homescan panelists do not record purchases at foodservice outlets 

including restaurants and, most importantly, in the case of fl uid milk, schools. 

It is possible that some households make mistakes when reporting information to 

Nielsen (e.g., some may fail to report all purchases because the recording process 

is time consuming). However, Einav et al. (2008) analyze the accuracy of these 

data and fi nd that errors in Homescan data are of the same order of magnitude as 

reporting errors in Government-collected data sets commonly used to measure earnings and employment status. 

The Homescan data used in this study include information on purchases by 24,110 

households. For each of these, Nielsen provides detailed information on each transaction as well as information on each household’s demographic characteristics and 

county of residence. 

The data confi rm that most American households buy fl uid milk. Although prices 

rose in 2007, the Homescan data show that 95.2 percent of households still bought 

fl uid milk that year, about 0.9 percent less than reported by Cornick et al. (1994). In 

2008, 94.8 percent of households bought fl uid milk. 

Retail food stores typically offer a wide array of fl uid milk products. We divide this 

array along three dimensions (table 1). The fi rst of these dimensions is fat content, 

with levels defi ned as whole (at least 3.25 percent fat), reduced-fat (between 2 and 
4 Households’ Choices Among Fluid Milk Products: What Happens Economic Research Service, USDA

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3.25 percent milk fat), and low fat (less than 2 percent milk fat). Other product 

dimensions include package size (i.e., gallon or in smaller sized packages), and, 

fi nally, whether milk is produced by conventional or organic methods. 

Dividing retail milk products along all 3 dimensions produces 12 distinct milk 

products. For example, conventionally produced, low-fat milk in a gallon container 

is the most frequently bought product (28 percent of all purchases), while organic 

whole and organic reduced-fat milk sold in gallon containers tie for least frequently 

bought (both with less than 0.1 percent of total sales). The prices used in this report 

are average daily prices paid by households for each of the 12 different milk products.7 Over 2007-08, the least expensive product was conventional low-fat milk 

sold by the gallon for $3.27 (table 1). The most expensive was organic whole milk 

sold in a less-than-gallon container at $7.28 per gallon. 

7 For each given date, the prices for each of the 12 products are the average prices 

across households that purchased the products on that date. If no households purchased any 

of the 12 products on that particular date, we instead use that week’s average prices. 

Table 1

Fluid milk products and marketing variables

Purchase frequency annual and seasonal

Fluid milk product descriptions

(by fat content, container size, and means 

of production)

Average 

daily price 

Average daily 

share of sales 

made on a deal Annual Winter Spring Summer Fall

Dollars 

per gallon Percent Percent

 1. Whole, 1 gallon, conventional 3.57 14.6 8.8 8.8 8.9 8.7 9.1

 2. Reduced-fat, 1 gallon, conventional 3.38 17.5 20.8 20.7 20.6 20.7 21.1

 3. Low-fat, 1 gallon, conventional 3.27 19.7 27.5 27.5 27.5 27.6 27.4

 4. Whole, less than gallon, conventional 5.30 9.9 7.8 8.0 7.6 7.8 7.9

 5. Reduced-fat, less than gallon, conventional 5.04 13.3 14.0 13.9 14.0 14.1 13.8

 6. Low-fat, less than gallon, conventional 4.93 15.3 18.1 18.1 18.4 18.1 17.6

 7. Whole, 1 gallon, organic 5.60 20.2 0.1 0.1 0.1 0.1 0.1

 8. Reduced-fat, big 1 gallon, organic 5.24 11.7 0.1 0.1 0.1 0.1 0.2

 9. Low-fat, 1 gallon, organic 5.21 18.8 0.3 0.3 0.3 0.3 0.4

10. Whole, less than gallon, organic 7.28 19.0 0.5 0.5 0.5 0.5 0.4

11. Reduced-fat, less than gallon, organic 7.19 17.7 0.7 0.7 0.7 0.7 0.7

12. Low-fat, less than gallon, organic 7.15 21.3 1.3 1.4 1.3 1.4 1.2

Note: Average daily prices for each of the 12 products are the average prices over all the dates of the year. Other values in the table are 

proportions. Gallon-sized containers of conventional low-fat or skim milk accounted for 27.5 percent of all purchases annually and were the 

most often purchased product.

Low-fat milk is defi ned as less than 2 percent fat including skim; reduced-fat is between 2 and 3.25 percent fat; and whole is at least 3.25 

percent fat.

Source: Calculated by authors using 2007-08 Nielsen Homescan data.
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Products may have also been purchased while being promoted by either a manufacturer or a store. Promotional deals include manufacturer coupons, store coupons, 

and store features, among others. The promotional deal variable is the share of each 

day’s purchases of each product that were made on promotion. 

What are the most purchased types of milk products? When the 2007-2008 retail 

market is sorted according to products’ fat content, low-fat and skim milk accounted 

for 47 percent of all purchases by U.S households; reduced-fat milk accounted for 

36 percent; and whole milk accounted for 17 percent of all purchases. Regarding 

container size and organic purchases, the research shows that households bought 

milk in a gallon-sized container 58 percent of the time, and all six organic products 

collectively accounted for about 3 percent of all purchases.

Casual observation reveals that food retailers often sell whole, reduced-fat, and 

low-fat milk for the same price, but, on average, they sell higher fat products at a 

higher price. Consider prices paid for conventional milk packaged in a less-thangallon container. Consumers paid $4.93 per gallon for low-fat milk versus $5.30 for 

similarly packaged, conventionally produced, whole milk (table 1)—a premium of 

$0.37 per gallon. Under Federal milk marketing orders, the minimum price paid to 

farmers for fl uid milk is higher for higher fat products. Fat extracted from fl uid milk 

is valuable because it is used to make other dairy products like cream and butter.

Cornick et al. (1994) and, more recently, Davis et al. (2010) examine the effects of a 

household’s income and demographic characteristics on its purchases of whole and 

lower fat milk products. Davis et al. (2010) fi nd that Black households and households with young children purchase more whole milk than other households. By 

contrast, high-income households and households whose female head of household 

has attended college tend to buy more lower fat products.

Another of this report’s product dimensions considers the variety of fl uid-milk 

package sizes, the most common being the gallon container. Buying milk this 

way costs less per gallon. Consumers paid $3.27 for conventional low-fat milk in 

a gallon container versus $4.93 per gallon for this same type of milk in smaller 

containers—a premium of $1.66 per gallon (table 1). Though it stands to reason 

that lower income households might economize by purchasing products in larger 

containers, Leibtag and Kaufman (2003) fi nd that lower income households are 

less likely to take advantage of economy-sized packages for ready-to-eat cereal, 

meat, poultry, fruits, vegetables, and cheese, among other products. One possible 

explanation is that households living on a tight budget cannot afford to “stock up” 

on staples. Another is that lower income households have less storage space in their 

homes. The data used by Leibtag and Kaufman (2003) did not include fl uid milk.

The study’s third product dimension tracks whether fl uid milk purchases were 

produced using organic or conventional methods. McBride and Greene (2009) note 

that conventional dairy farmers switching to organic production must make changes 

in animal husbandry, alter land and crop management, and secure organic feed, 

among other endeavors. The process can be challenging and costly. Sales of organic 

milk have, nonetheless, grown rapidly since the 1990s. 
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Chronicling this growth, Dupuis (2000) notes that many buyers of organic milk 

question conventional production methods and believe organic products to be safer 

and/or more healthful. The use of the hormone Recombinant Bovine Somatotropin 

(rBST) to increase production yields was once particularly controversial. Several 

studies have since measured the premium that some consumers are willing to pay 

for organic milk. As noted above, Smith et al. (2009) demonstrate that this premium 

can be substantial. Kiesel and Villas-Boas (2007) fi nd that the USDA organic seal 

increases the probability of purchasing organic milk. 

Despite these fi ndings, growth in organic milk sales stalled during the recent recession. Organic products accounted for 2.7 percent of all U.S.-marketed fl uid milk 

in December 2007 at the onset of the recession.8 That share was nearly unchanged 

at 2.8 percent in December 2009, about 6 months after the recession had ended. 

Growth did eventually recover along with the economy. Organic products accounted 

for 3.9 percent of all milk marketed in the United States in December 2011.

When prices rise or incomes fall, do buyers of organic milk switch back to conventional products? And what determines which consumers choose to buy organic 

milk and which continue to choose conventional products? Dhar and Foltz (2005) 

estimate a demand model for organic milk products, conventional milk labeled as 

rBST-free, and unlabeled conventional milk. They fi nd that the demand for organic 

products is more price sensitive than the demand for unlabeled conventional products. Also, they confi rm that unlabeled conventional milk is a substitute for organic 

milk. A later study by Alviola and Capps (2010) fi nds that the demand for organic 

milk is also relatively more sensitive to changes in income. Moreover, the demand 

for organic milk varies with a person’s level of education, race, ethnicity, and 

household size, among other things. College-educated households in particular are 

more likely to exhibit a preference for organic milk over conventional products. 

Milk Purchase Choice Model

Our review of existing research on the demand for milk by American households 

reveals that households make purchase choices based partly on the attributes of 

the available products and partly on prices and the use of promotional deals. For 

example, Dhar and Foltz (2005) fi nd that the demand for organic products is price 

sensitive, although other studies like Smith et al. (2009) also show that some households are willing to pay a signifi cant premium. These households may feel that 

organic products are safer and/or more healthful. 

Also important are a household’s own characteristics, which can cause it to exhibit 

a preference for a particular type of milk product. These characteristics include not 

only income and demographics, as discussed above, but also past purchase history. 

Guadagni and Little (1983) demonstrate that habit formation can signifi cantly affect 

food choices. Specifi cally, in a study of a household’s choice among various ground 

coffee products, Guadagni and Little (1983) demonstrate that a household may 

choose a particular type of product and thereafter exhibit a tendency to choose that 

same product in the future. Among the demographic characteristics of households, it 

has been demonstrated that income, level of educational attainment, household size, 

8 See USDA Agricultural Marketing Service (AMS) (2012).
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race, and ethnicity, among other factors, can infl uence the type of milk a household 

consumes (e.g., Davis et al., 2010).

We now estimate a choice model that accounts for the major determinants of a 

household’s choice among fl uid milk products. The multinomial logit model has 

been widely used to study a household’s choice among food products in general. 

However, the standard form of this model does not account for all of the key choice 

determinants. To obtain a satisfactory model, we instead start by defi ning a consumer’s utility over the 12 milk products analyzed in this report. For household i, the 

utility to buy food product j at time t is defi ned as follows:

(1) , 

where j

 is an intercept that captures the contribution to consumer utility of the 

attributes associated with food product j. Xjt is a vector of marketing variables, such 

as prices and any promotional deals for product j at time t. Xjt may also account 

for the season of the year. β and θ are vectors of parameters to be estimated. Lijt is 

a household characteristic variable whose value is determined by the household’s 

demographic characteristics (Zi

) and past purchasing history Yijt-1 prior to time t. 

Yijt-1 can be defi ned as a (t-1) x 1 vector of 0’s and 1’s with the rth element equal 

to 1 if household i purchased product j at time r and equal to zero otherwise. In 

research on choice models, Lijt is commonly called the “loyalty variable,” because 

it accounts for a household’s past purchase history, among other things. Finally, as 

in Guadagni and Little (1983), we assume that household utility further contains a 

random component, εijt. 

Alternative approaches for modeling a household’s choice among competing food 

products include the random coeffi cient logit model. This model allows for household heterogeneity by assuming that β is randomly distributed across households. 

However, the estimation of a random coeffi cient model usually requires the evaluation of high order probability integrals. Therefore, the model in (1) is relatively 

much easier to estimate. Also, we can use Lijt to differentiate utility Uijt among 

households. We can, therefore, explicitly model the effects of household demographic variables and a household’s past purchase history, as discussed further 

below—something not possible using a traditional random coeffi cient logit model.

The specifi cation of the loyalty variable, Lijt, to incorporate household characteristics into choice models is a subject of much research. Guadagni and Little (1983) 

propose a specifi cation that uses a weighted average of past choice behavior. Recent 

choices are weighted more heavily. Fader and Lattin (1993) propose an alternative specifi cation in which habits can change with sudden, unforeseen events. For 

example, a promotional campaign may cause a consumer to try a new product. 

However, both studies ignore household demographics. Dong and Stewart (2012) 

expand on Fader and Lattin’s (1993) approach by additionally including household 

demographics in Lijt. In this study, we follow Dong and Stewart (2012) to account 

for both household demographics and past purchase behavior in specifying variable 

Lijt (See appendix I.) 

A household chooses among products to maximize utility. The probability that 

household i selects product j at time t is therefore pijt = Prob (Uijt > Uikt) for all k
8 Households’ Choices Among Fluid Milk Products: What Happens Economic Research Service, USDA

 When Income and Prices Change? ERR-146 

not equal to j. If we further assume the random component in utility, εijt, is an independently distributed random variable with a type II extreme value (double exponential) distribution, the value of pijt is

(2) 

∑=

= J

l

U

U

ijt

ilt

ijt

e

e

p

1

,

which serves as the basis of our multinomial logit choice model. 

An assumption of the multinomial logit model is that the odds ratios, pj /pk, based 

on equation (2) are independent of the other alternatives. This assumption is the 

so-called “Independence from Irrelevant Alternatives” (IIA), and it stipulates that 

the choice alternatives in the model are mutually independent. If this assumption is violated, systematic errors will occur in the predicted choice probabilities 

(Guadagni and Little 1983). We use the Hausman-McFadden approach (Hausman 

and McFadden, 1984) to test the validity of this assumption for the empirical model. 

Another assumption of the model is that households choose only one type of milk 

at a time. For example, if household i bought two types milk at time t, we would 

treat these purchases as two separate purchase occasions on which one type of milk 

was bought. Dube (2004) developed a model that can handle multiple purchase 

units using a Poisson model to predict the number of consumption occasions across 

all household members. However, similar to the random coeffi cient logit model, 

Dube’s (2004) model also requires evaluating high order probability integrals. In 

our data, only 5.25 percent of all purchases were made on the same day as another 

type of milk was bought. 

The log likelihood function for this multinomial logit choice model, given a 

purchase history (yijt), can be written as

(3) 1 11

ln ln

NJT

ijt ijt

i jt

L yp = === ∑∑∑

where N is the total number of households, T is the total number of purchase occasions, and J is the total number of alternative products to be chosen. Model estimates can be obtained from maximizing equation (3).

The marginal effect of X, the seasonality and marketing variables, on the product 

choice probabilities can be derived from equation (2) for household i as

(4) 

⎪

⎩

⎪

⎨

⎧

− ≠

− =

= ∂

∂

P P if l j

P P if l j

X

P

ij il

ij ij

l

ij

,

(1 ) ,
Economic Research Service, USDA Households’ Choices Among Fluid Milk Products: What Happens 9

When Income and Prices Change? ERR-146

where Pij is the average probability of household i purchasing product j over all the 

purchase occasions. The associated elasticity can be written as: 

for l = j and for l ≠ j, where Xl is 

the vector of average seasonality and marketing variables associated with product l

over all the purchase occasions.

The household variables Zi

 are incorporated into the household loyalty variable Lijt. 

The elasticity of product choice probability with respect to Zi

 can be derived from 

equation (2) as

(5) i

J

l i

il

il

il

i

ij

ij ij

i

i

ij

jZ Z

Z

L

L

P

Z

L

P L

Z

Z

P ⋅ ∂

∂ − ∂

∂ = ∂∂ = ∑=

) 1 1 (

1

where all the variables are the average values over all the purchase occasions by 

household i. 

We use the Homescan data described above to create all the variables needed 

in both X and Z. The marketing variables (X) used in this study include milk 

price, promotional deal, and seasonal dummies (table 1). Based on previous milk 

purchase studies, we include the following among demographic variables: household income, household size, age, employment, education level of the female 

household head, and household ethnicity in Z. The presence of small children and 

teenagers usually infl uences household milk consumption, so we further include 

binary variables to indicate if households have small children (younger than 6) 

and young teenagers (between 13 and 17). We also include a dummy variable to 

indicate single-person households, because single people may behave differently 

from other types of households regarding food purchases. To capture variation in 

milk demand across households living in rural/suburban communities and innercity neighborhoods, we include a population density variable (the population per 

square mile in a household’s county of residence). Summary statistics for the 

demographic variables are provided in table 2.

Many Underlying Factors to Households’ Product Choices

The multinomial logit model in equation (2) was estimated using the data on 

24,110 Homescan households over 730 days (the 2 years of 2007 and 2008). Each 

household could have bought milk on each of these days. Households made an 

average of 58 purchases during the 2 years. The total number of milk purchases 

(observations) in the data is 1,390,263. The log likelihood in equation (3) was 

maximized using GAUSS software. The standard errors of the estimated parameters were then obtained from the inverse of the numerically evaluated Hessian 

matrix of the likelihood function (parameter estimates, standard errors, and the 

value of the log likelihood function evaluated at these parameter estimates are 

reported in the appendix II). 

As mentioned above, the multinomial logit choice model assumes IIA. To test 

this assumption, we follow Hausman and McFadden (1984). We re-ran the model 

including only the six conventional milk products and dropping all six of the 
10 Households’ Choices Among Fluid Milk Products: What Happens Economic Research Service, USDA

 When Income and Prices Change? ERR-146 

organic milk products. Suppose γ0 is the vector of all the parameter estimates for 

the subset model with the variance-covariance matrix 0, and γ1 is the vector of 

the associated parameter estimates with γ0 for the full model with the variancecovariance matrix 1. Then,

(6) 

has a chi-square distribution with the degrees of freedom r when IIA is true, where 

r is the rank of 1- 0. In our test, 2 = 96.8 with 89 degrees of freedom. The 

5-percent critical value for the test is 112, which implies that we cannot reject IIA at 

the 0.05 signifi cance level. 

For each of the 12 milk products, we then used the estimation results to calculate 

how much the probability of choosing each product would change with prices, 

promotional deals, income, household size, age, and other variables. Specifi cally, 

we calculated the elasticities of the choice probabilities. For the continuous explanatory variables, the elasticities are evaluated at the means of the explanatory variables 

Table 2

Household variables

Variable Mean Std. Err Min Max

Household income (in dollars) 60,164 40,317 2,500 250,000

Household size (number of people) 2.23 1.17 1 9

Age of female head (in years) 55.99 10.31 22 68

Population density of the household 

residential area 1,547 5,056 0.76 70,924

Employment: = 1 if female head employed; 

= 0 if not 0.41 0.49 0 1

Education: = 1 if female head gained college 

education; = 0 if not 0.38 0.49 0 1

House: = 1 if owned house; = 0 if not 0.81 0.39 0 1

Single: = 1 if household size is 1; = 0 if not 0.27 0.44 0 1

Black: = 1 if household is African American; 

= 0 if other 0.08 0.28 0 1

Hisp: = 1 if household is Hispanic; = 0 if not 0.05 0.22 0 1

AgeC6: = 1 if presence of children 6 and 

below; = 0 if not 0.04 0.19 0 1

AgeC1317: = 1 if presence of children 

between 13 and 17; = 0 if not 0.10 0.29 0 1

The household income was converted to a continuous variable from 33 discrete categories using the 

mean of each category. For the highest category, $250K and above, we use $250K. Similarly, the age 

variable is converted to a continuous variable from the 29 discrete categories provided in the data. 

Source: Calculated by authors using 2007-08 Nielsen Homescan data. 
Economic Research Service, USDA Households’ Choices Among Fluid Milk Products: What Happens 11

When Income and Prices Change? ERR-146

and are best interpreted as the percentage changes in the probability of buying a 

particular milk product with a 1-percent change in the choice determinant. For the 

discrete explanatory variables, the elasticities are the percentage changes in the 

probability of buying a particular milk product when the discrete variable changes 

from 0 to 1. The standard errors of all elasticities were calculated from the Delta 

method proposed by Rao (1973). The results are reported in tables 3 to 5. 

Income and Demographics

Households are hypothesized to switch from higher to lower priced milk products 

when their food budgets get tight. However, when incomes change, it is primarily 

the demand for organic milk products that is affected. Higher income households 

will purchase more organic milk (table 3). The largest increase in purchase probability is for low-fat, organic milk in a small container. On the one hand, buying less 

expensive products may help households with reduced incomes to afford a healthful 

Table 3

Percentage changes in probability of purchasing fl uid milk with respect to a 1-percent change in 

household variables

Percentage changes in purchase probability

WHBC RFBC LFBC WHSC RFSC LFSC WHBO

HH ncome -0.2315* 

(0.0063)

-0.1005* 

(0.0039)

0.0588* 

(0.0046) 

-0.0941* 

(0.0060)

-0.0155* 

(0.0042)

0.1063* 

(0.0038)

0.0410 

(0.1129)

HH size 0.7065* 

(0.0269)

0.5350* 

(0.0191)

0.1873* 

(0.0205)

-0.1750* 

(0.0279)

-0.3726* 

(0.0209)

-0.3892* 

(0.0184)

-1.3897* 

(0.6136)

Age -0.3889* 

(0.0213)

-0.2343* 

(0.0158)

-0.1138* 

(0.0184)

-0.0688* 

(0.0213)

0.1162* 

(0.0175)

0.2490* 

(0.0168)

-2.6212* 

(0.3152)

Employment 0.0034 

(0.0033)

-0.0098* 

(0.0022)

-0.0189* 

(0.0025)

0.0126* 

(0.0032)

0.0161* 

(0.0025)

-0.0002 

(0.0021)

-0.1140 

(0.0647)

Education -0.0663* 

(0.0034)

-0.0302* 

(0.0022)

0.0345* 

(0.0022)

-0.0295* 

(0.0030)

-0.0074* 

(0.0022)

0.0334* 

(0.0018)

0.0023 

(0.0613)

House -0.0248* 

(0.0081)

0.0188* 

(0.0047)

0.0558* 

(0.0057)

-0.1003* 

(0.0070)

0.0078 

(0.0054)

-0.0709* 

(0.0047)

-0.2782* 

(0.1068)

Single 0.1001* 

(0.0085)

0.0589* 

(0.0062)

0.0141* 

(0.0063)

-0.0561* 

(0.0077)

-0.0796* 

(0.0056)

-0.0707* 

(0.0050)

-0.4271* 

(0.1634)

Black 0.0224* 

(0.0012)

-0.0063* 

(0.0010)

-0.0582* 

(0.0019)

0.0319* 

(0.0009)

0.0148* 

(0.0007)

-0.0147* 

(0.0011)

-0.0028 

(0.0211)

Hisp 0.0140* 

(0.0006)

0.0007 

(0.0005)

-0.0036* 

(0.0006)

0.0049* 

(0.0007)

0.0050* 

(0.0005)

0.0015* 

(0.0005)

0.0219* 

(0.0092)

Popdensi -0.0284* 

(0.0023)

-0.0403* 

(0.0016)

0.0032 

(0.0016)

0.0041 

(0.0023)

-0.0179* 

(0.0016)

0.0105* 

(0.0015)

0.1849* 

(0.0388)

AgeC6 0.0148* 

(0.0003)

0.0033* 

(0.0003)

-0.0013* 

(0.0005)

0.0073* 

(0.0006)

0.0017* 

(0.0007)

0.0015* 

(0.0006)

0.0134 

(0.0106)

AgeC1317 -0.0024* 

(0.0010)

0.0008 

(0.0006)

0.0052* 

(0.0007)

-0.0236* 

(0.0019)

-0.0098* 

(0.0012)

-0.0075* 

(0.0011)

0.0487* 

(0.0228)

—continued
12 Households’ Choices Among Fluid Milk Products: What Happens Economic Research Service, USDA

 When Income and Prices Change? ERR-146 

Table 3

Percentage changes in probability of purchasing fl uid milk with respect to a 1-percent 

change in household variables—continued

Percentage changes in purchase probability

RFBO LFBO WHSO RFSO LFSO

HH income 0.6399* 

(0.0884)

0.4860* 

(0.0599)

0.2795* 

(0.0338)

0.2536* 

(0.0236)

0.4503* 

(0.0213)

HH size 0.9937* 

(0.2746)

0.4682* 

(0.2209)

-0.3246* 

(0.1268)

-0.1965 

(0.1147)

-0.6767* 

(0.0831)

Age -0.6132 

(0.4762)

-1.2710* 

(0.1900)

-0.9245* 

(0.1097)

-0.9620* 

(0.0983)

-0.9654* 

(0.0774)

Employment -0.0484 

(0.0399)

-0.0715* 

(0.0303)

-0.0806* 

(0.0158)

-0.1112* 

(0.0136)

-0.0679* 

(0.0102)

Education -0.0209 

(0.0338)

0.1079* 

(0.0292)

0.0368* 

(0.0155)

0.0977* 

(0.0131)

0.0899* 

(0.0097)

House 0.4806* 

(0.2012)

0.1486 

(0.0872)

-0.1821* 

(0.0325)

0.0018 

(0.0364)

-0.1028* 

(0.0270)

Single 0.1715 

(0.0986)

0.1334* 

(0.0677)

0.0581 

(0.0399)

-0.0120 

(0.0323)

-0.1540* 

(0.0238)

Black -0.0257* 

(0.0146)

-0.0527* 

(0.0171)

-0.0059 

(0.0072)

-0.0006 

(0.0057)

-0.0234* 

(0.0051)

Hisp -0.0034 

(0.0099)

0.0003 

(0.0075)

0.0054 

(0.0033)

0.0114* 

(0.0024)

0.0086* 

(0.0022)

Popdensi 0.0870* 

(0.0405)

0.0622* 

(0.0198)

0.1226* 

(0.0103)

0.0259* 

(0.0107)

0.0964* 

(0.0079)

AgeC6 0.0186* 

(0.0072)

0.0082 

(0.0043)

0.0419* 

(0.0020)

0.0050* 

(0.0024)

-0.0012 

(0.0019)

AgeC1317 -0.0040 

(0.0148)

-0.0053* 

(0.0103)

-0.0165* 

(0.0063)

-0.0095* 

(0.0050)

0.0109* 

(0.0035)

Notes: The fi gures in each row are the percentage changes in the probability of buying each of the 12 products (in the top 

row) following a 1-percent increase (or for dichotomous variables from 0 to 1) in each of the household variables (in the fi rst

column). Standard errors are in parentheses and “*” indicates signifi cant at level of 0.05 or better. 

WHBC = Whole, big (1 gallon), conventional; RFBC = Reduced-fat, big, conventional; LFBC = Low-fat, big, conventional; 

WHSC = Whole, small (less than gallon), conventional; RFSC = Reduced-fat, small, conventional; LFSC = Low-fat, small, 

conventional; WHBO = Whole, big, organic; RFBO = Reduced-fat, big, organic; LFBO = Low-fat, big, organic; WHSO = 

Whole, small, organic; RFSO = Reduced-fat, small, organic; LFSO = Low-fat, small, organic 

Low-fat milk is defi ned as less than 2 percent fat including skim; reduced-fat is between 2 and 3.25 percent fat; and whole is 

at least 3.25 percent fat.

HH = Household; Age = age of female head; Popdensi = population density of the household residential area.

Employment: = 1 if female head employed; = 0 if not

Education: = 1 if female head gained college education; = 0 if not

House: = 1 if owned house; = 0 if not

Single: = 1 if household size is 1; = 0 if not

Black: =1 if household is African American; =0 if other

Hisp: = 1 if household is Hispanic; = 0 if not

AgeC6: = 1 if presence of children 6 and below; = 0 if not

AgeC1317: = 1 if presence of children between 13 and 17; = 0 if not

Source: Calculated by authors using 2007-08 Nielsen Homescan data.
Economic Research Service, USDA Households’ Choices Among Fluid Milk Products: What Happens 13

When Income and Prices Change? ERR-146

diet. On the other hand, these households may be more exposed to further income 

decreases and/or price increases. To the extent that they are already purchasing less 

expensive items, they will have less room in their budgets to further economize. 

One exception is the fat content of milk. Consistent with Davis et al. (2010), we 

fi nd a positive association between higher income and the probability of purchasing 

low-fat, conventional milk in a gallon container, which is the least expensive of all 

of our 12 products. Also, larger families are more likely to buy a big container of 

whole, conventional milk than a big container of whole, organic milk. However, 

household size appears to affect primarily the choice of container size. Not surprisingly, larger households tend to buy milk in larger packages. 

The age of the female head of household is another important choice determinant. 

When people get older, they are more likely to buy reduced or low-fat conventional 

milk in a smaller container. Other research has shown that fl uid milk consumption 

tends to decrease with age (e.g., Sebastian et al., 2010), suggesting that a gallon 

Table 4

Percentage changes in purchase probability with respect to a 1-percent increase in fl uid milk prices

Percentage changes in purchase probability

WHBC RFBC LFBC WHSC RFSC LFSC WHBO RFBO LFBO WHSO RFSO LFSO

Price

WHBC -0.6153 0.1312 0.1575 0.0649 0.1112 0.1283 0.0005 0.0009 0.0019 0.0034 0.0056 0.0099

RFBC 0.0553 -0.5140 0.1492 0.0615 0.1054 0.1216 0.0005 0.0008 0.0018 0.0032 0.0053 0.0094

LFBC 0.0534 0.1202 -0.4727 0.0595 0.1018 0.1175 0.0005 0.0008 0.0017 0.0031 0.0051 0.0090

WHSC 0.0867 0.1951 0.2341 -0.9050 0.1653 0.1908 0.0007 0.0013 0.0028 0.0051 0.0083 0.0147

RFSC 0.0826 0.1858 0.2228 0.0920 -0.7963 0.1816 0.0007 0.0012 0.0027 0.0048 0.0079 0.0140

LFSC 0.0807 0.1816 0.2187 0.0899 0.1538 -0.7543 0.0007 0.0012 0.0026 0.0047 0.0077 0.0137

WHBO 0.0917 0.2062 0.2475 0.1021 0.1747 0.2017 -1.0579 0.0013 0.0029 0.0054 0.0088 0.0155

RFBO 0.0857 0.1928 0.2314 0.0953 0.1631 0.1885 0.0007 -0.9880 0.0028 0.0050 0.0082 0.0145

LFBO 0.0852 0.1916 0.2298 0.0948 0.1623 0.1874 0.0007 0.0012 -0.9807 0.0050 0.0082 0.0145

WHSO 0.1189 0.2674 0.3209 0.1324 0.2267 0.2615 0.0010 0.0017 0.0038 -1.3659 0.0114 0.0201

RFSO 0.1174 0.2642 0.3171 0.1308 0.2239 0.2583 0.0010 0.0017 0.0038 0.0069 -1.3450 0.0199

LFSO 0.1167 0.2625 0.3150 0.1300 0.2224 0.2566 0.0010 0.0017 0.0037 0.0068 0.0111 -1.3276

Notes: The fi gures in each row are the percentage changes in the probability of buying each of the 12 products (in the top row) following a 

1-percent increase in each product’s price (in the fi rst column). All the elasticities are signifi cant at the level of 0.05 or better.

WHBC = Whole, big (1 gallon), conventional; RFBC = Reduced-fat, big, conventional; LFBC = Low-fat, big, conventional ; WHSC = Whole, small 

(less than gallon), conventional; RFSC = Reduced-fat, small, conventional; LFSC = Low-fat, small, conventional; WHBO = Whole, big, organic; 

RFBO = Reduced-fat, big, organic; LFBO = Low-fat, big, organic; WHSO = Whole, small, organic; RFSO = Reduced-fat, small, organic; LFSO = 

Low-fat, small, organic 

Low-fat milk is defi ned as less than 2 percent fat including skim; reduced-fat is between 2 and 3.25 percent fat; and whole is at least 3.25 percent 

fat.

Source: Calculated by authors using 2007-08 Nielsen Homescan data.
14 Households’ Choices Among Fluid Milk Products: What Happens Economic Research Service, USDA

 When Income and Prices Change? ERR-146 

container may contain more milk than older household members can drink before 

it spoils. Regarding the infl uence of children in a household, the results show 

that presence of small children (6 years old or less) increases the probability of 

buying all types of milk besides conventional, low-fat milk in a 1-gallon container. 

However, the presence of teenagers between ages 13 and 17 has positive effects 

on the probability of buying organic, whole milk in a 1-gallon container, as well as 

conventional, low-fat milk in a 1-gallon container. That the effects differ depending 

on children’s ages suggests that people may start to select different beverages in 

their early teenage years. Similar to past studies, we fi nd a positive association 

between education and the demand for organic milk (e.g., Alviola and Capps, 2010), 

as well as a positive connection between education and the demand for lower fat 

milk products (e.g., Davis et al., 2010). Finally, when a household owns a house, it 

has a higher probability of buying either reduced-fat or low-fat milk in a 1-gallon 

Table 5

Percentage changes in purchase probability with respect to a 1-percent increase in use of fl uid milk 

promotional deals

Percentage changes in purchase probability

WHBC RFBC LFBC WHSC RFSC LFSC WHBO RFBO LFBO WHSO RFSO LFSO

Deal

WHBC 0.1337 -0.0285 -0.0343 -0.0141 -0.0241 -0.0279 -0.0001 -0.0002 -0.0004 -0.0007 -0.0012 -0.0021

RFBC -0.0152 0.1417 -0.0413 -0.0169 -0.0290 -0.0335 -0.0001 -0.0002 -0.0005 -0.0009 -0.0014 -0.0026

LFBC -0.0172 -0.0386 0.1517 -0.0191 -0.0327 -0.0377 -0.0001 -0.0003 -0.0005 -0.0010 -0.0016 -0.0029

WHSC -0.0086 -0.0194 -0.0232 0.0897 -0.0164 -0.0189 -0.0001 -0.0001 -0.0003 -0.0005 -0.0008 -0.0014

RFSC -0.0115 -0.0259 -0.0311 -0.0127 0.1108 -0.0253 -0.0001 -0.0002 -0.0004 -0.0007 -0.0011 -0.0019

LFSC -0.0132 -0.0298 -0.0357 -0.0147 -0.0252 0.1236 -0.0001 -0.0002 -0.0004 -0.0008 -0.0013 -0.0022

WHBO -0.0176 -0.0397 -0.0479 -0.0198 -0.0336 -0.0390 0.2041 -0.0002 -0.0006 -0.0011 -0.0017 -0.0030

RFBO -0.0103 -0.0233 -0.0280 -0.0115 -0.0197 -0.0227 -0.0001 0.1193 -0.0003 -0.0006 -0.0010 -0.0018

LFBO -0.0164 -0.0369 -0.0444 -0.0182 -0.0312 -0.0361 -0.0001 -0.0002 0.1889 -0.0010 -0.0016 -0.0028

WHSO -0.0166 -0.0372 -0.0447 -0.0184 -0.0316 -0.0365 -0.0001 -0.0002 -0.0005 0.1903 -0.0016 -0.0028

RFSO -0.0152 -0.0343 -0.0412 -0.0170 -0.0291 -0.0336 -0.0001 -0.0002 -0.0005 -0.0009 0.1747 -0.0026

LFSO -0.0184 -0.0414 -0.0497 -0.0205 -0.0351 -0.0405 -0.0002 -0.0003 -0.0006 -0.0011 -0.0018 0.2094

Notes: The fi gures in each row are the percentage changes in the probability of buying each of the 12 products (in the top row) following a 

1-percent increase in the use of deals to promote each product (in the fi rst column). All the elasticities are signifi cant at the level of 0.05 or better.

WHBC = Whole, big (1 gallon), conventional; RFBC = Reduced-fat, big, conventional; LFBC = Low-fat, big, conventional ; WHSC = Whole, small 

(less than gallon), conventional; RFSC = Reduced-fat, small, conventional; LFSC = Low-fat, small, conventional; WHBO = Whole, big, organic; 

RFBO = Reduced-fat, big, organic; LFBO = Low-fat, big, organic; WHSO = Whole, small, organic; RFSO = Reduced-fat, small, organic; LFSO = 

Low-fat, small, organic 

Low-fat milk is defi ned as less than 2 percent fat including skim; reduced-fat is between 2 and 3.25 percent fat; and whole is at least 3.25 

percent fat.

Source: Calculated by authors using 2007-08 Nielsen Homescan data.
Economic Research Service, USDA Households’ Choices Among Fluid Milk Products: What Happens 15

When Income and Prices Change? ERR-146

container. Such households may have suffi cient storage space in their homes to 

accommodate larger package sizes. 

Price and Deal Variables

Prices and promotional deals can sway a household’s choice among different milk 

products. Our results reveal that changing the price of any one of the 12 milk products affects the probability that a household buys that specifi c product (table 4). 

However, the magnitude of the response varies widely. Shown in bold along the 

diagonal elements of table 4 are each product’s own-price effects. For example, 

if the price of conventionally produced whole milk sold in a gallon container 

increases by 1 percent, holding all other prices constant, then the probability of 

buying this product decreases by 0.62 percent. Own-price effects are signifi cantly 

larger for organic milk products. Indeed, a 1-percent increase in the price of organically produced whole milk sold in a gallon container lowers the probability of 

buying this product by 1.06 percent. That is, the change in purchase probability is 

proportionally greater than the percentage change in the product’s own price. In 

terms of fat content, we see that whole milk is most sensitive to own-price changes. 

In terms of container size, products sold in less-than-gallon packages are more 

sensitive to own-price changes. In general, the change in purchase probability is 

larger for more expensive products. 

Our results also show that households switch to less expensive products when 

prices rise. Shown in the off-diagonal elements in table 4 are the cross-price effects. 

For example, holding all other prices constant, if the price of a gallon of conventionally produced whole milk increases by 1 percent, the probability of buying 

a gallon of conventionally produced low-fat milk increases by 0.16 percent. As 

shown in table 1, lower fat products tend to cost less than higher fat products. By 

contrast, an increase in the price of conventional milk sold in small containers 

primarily increases the probability that households buy the same type of milk in 

a gallon container. Finally, if the price of any one of the organic milk products 

increases, the probability that a household switches to conventional milk increases 

by more than does the probability the household buys another type of organic milk. 

Our results show that promotional deals and increases in milk price have similar 

effects on purchase probabilities (table 5), but those effects are in opposite directions. In other words, promotional deals may work to counteract the effects of price 

changes.

In our analysis, an increased probability of buying one product—caused either by 

a change in price or the use of promotional deals—must decrease the probability of 

buying 1 or more of the 11 other milk products (tables 4 and 5). Indeed, the fi gures 

in each row of the 2 tables are the percentage changes in the probability of buying 

each of the 12 products following either a 1-percent increase in 1 product’s price 

(table 4) or a 1-percent increase in the use of deals to promote that product (table 5). 

Because households must buy only 1 of the 12 products on any particular occasion 

when they buy milk, the fi gures in each row sum to zero. 
16 Households’ Choices Among Fluid Milk Products: What Happens Economic Research Service, USDA

 When Income and Prices Change? ERR-146 

Impact of Price and Income Shocks on Market Composition

In the December 2007-June 2009 recession, prices increased for fl uid milk and other 

staples. Kumcu and Kaufman (2011) show that, during that recession, consumers 

reacted by looking for ways to economize. We investigate how households adjusted 

their choices among fl uid milk products. However, because many types of price 

and income shocks could again occur, we use our estimated model to simulate the 

effects of some possible future shocks. The elasticities in tables 3-5 are best interpreted as the percentage changes in the probability of buying a particular fl uid milk 

product following 1-percent changes in income, price, and promotional deals, as 

well as changes to other variables. We now use these elasticities to predict changes 

in households’ choices among all 12 fl uid milk products in selected scenarios. 

Consider, for example, a 1-percent price increase for all products. To begin, because 

of the increase in that product’s own price, we note that the probability of buying 

conventionally produced whole milk in a gallon container would decrease by 0.62 

percent. At the same time, because of increases in the prices of the other 11 products, the same purchase probability increases by 0.06 percent, 0.05 percent, 0.09 

percent, 0.08 percent, and so on. In total, summing the own-price and 11 cross-price 

effects in the fi rst column of table 4, we fi nd that the probability of buying conventionally produced whole milk in a gallon container increases by about 0.36 percent 

(table 6). Next, given the product’s baseline market share of 8.8 percent (table 

1), we estimate its new market share under the alternative scenario of a 1-percent 

general price increase. Though the new market share is very slightly higher, it is 

still roughly less than 9 percent (i.e., 0.088 + (0.0036 x 0.088)). After repeating this 

same series of steps for the other 11 products, we can aggregate over our predictions for each individual product to further estimate the re-division of fl uid milk 

sales categorized by fat content, method of production, and package size. This 

would complete simulation results for a 1-percent increase in all fl uid milk prices. 

Notably, we must repeat all calculations for other chosen scenarios. The process of 

calculating each product’s new market share and aggregating over the predictions 

for all 12 products to estimate the re-division of the market categorized along three 

dimensions is a nonlinear process. For example, the impact of 10-percent price 

increase is not simply 10 times the impact of a 1-percent price increase. Finally, 

predictions derived for each scenario can be compared against the baseline scenario. 

Of all fl uid milk purchased by U.S. households in 2007-08, 17 percent was whole, 

47 percent was low-fat, and 36 percent was reduced-fat. Gallon packages accounted 

for about 58 percent of all purchases. Organic products represented about 3 percent 

of all sales. The results of the simulations are shown in tables 6 and 7. Some of the 

scenarios are also provided in fi gure 1. 

Retail fl uid milk prices tend to be volatile, as they fl uctuate with prices that dairy 

farmers receive for milk (Stewart and Blayney, 2011). We examined monthly retail 

milk prices between 2000 and 20119 and fi nd that retail prices typically change by 

1 to 2 percent per month. However, retail prices are also highly cyclical. They can 

trend upward or downward for extended periods of time. The price of a gallon of 

fl uid milk at the high and low points of a cycle can differ by 25 percent or more. To 

begin, in scenario 1 (fi g. 1), we report the effects of a 1-percent increase in price for 

9 Monthly retail prices for conventional whole and conventional reduced-fat milk published 

by the USDA AMS were examined. See AMS (2012).
Economic Research Service, USDA Households’ Choices Among Fluid Milk Products: What Happens 17

When Income and Prices Change? ERR-146

Figure 1

Simulation results for several scenarios

Baseline purchase probability:

Note: Simulations using model results. Retail milk products divided along three dimensions including method of production (organic and 

conventional), fat content (low-fat, reduced-fat, and whole), and container size (gallon or small-sized container).

Source: Calculated by authors using 2007-08 Nielsen Homescan data.

3%

Conventional Organic

36%

47%

Whole Reduced Low fat

42%

Big container Small container

2.6%

35.6%

47.6% 41.8%

35.4%

54% 40.2%

3.7%

35.5%

48.6%

15.9%

97%

17%

58%

97.4%

16.8%

58.2%

>99%

10.6%

59.8%

96.3%

57.4%

42.6%

Scenario 1: Purchase probability after all prices increase by 1 percent

Scenario 2: Purchase probability after all prices increase by $1 per gallon (about 25 percent average)

Scenario 5: Purchase probability after a 10-percent increase in household income

Conventional Organic Whole Reduced Low fat Big Small 

Conventional Whole Reduced Low fat Big Small 

Conventional Whole Reduced Low fat Big Small 
18 Households’ Choices Among Fluid Milk Products: What Happens Economic Research Service, USDA

 When Income and Prices Change? ERR-146 

Table 6

Percentage changes in probability of purchasing fl uid milk with respect to a 1-percent change in household 

variables

Percentage changes in purchase probability

1-percent 

increase 

of all milk 

prices

1-percent 

increase of 

organic milk 

prices

$1 increase 

of all milk 

prices

1-percent 

increase of 

all milk deal

1-percent 

increase of 

organic milk 

deal

1-percent 

increase of 

income

1-person 

increase of 

hhsize

1-year 

increase of 

age

WHBC 0.3590 0.6156 0.7520 -0.0400 -0.5220 -0.2315 0.3168 -0.0069

RFBC 1.6846 1.3847 25.2530 -1.3428 -1.1759 -0.1005 0.2399 -0.0042

LFBC 2.1713 1.6617 34.1143 -1.8164 -1.4140 0.0588 0.0840 -0.0020

WHSC 0.1482 0.6854 2.9480 -0.1579 -0.5823 -0.0941 -0.0785 -0.0012

RFSC 1.0143 1.1731 18.4712 -0.9902 -0.9962 -0.0155 -0.1671 0.0021

LFSC 1.3395 1.3540 24.2571 -1.2984 -1.1512 0.1063 -0.1745 0.0044

WHBO -1.0499 -1.0535 -18.7373 1.0028 1.0070 0.0410 -0.6232 -0.0468

RFBO -0.9742 -0.9804 -18.5919 1.0062 1.0140 0.6399 0.4456 -0.0110

LFBO -0.9502 -0.9637 -18.2438 0.9742 0.9910 0.4860 0.2100 -0.0227

WHSO -1.3125 -1.3368 -17.7120 0.9449 0.9754 0.2795 -0.1456 -0.0165

RFSO -1.2574 -1.2973 -16.9845 0.8955 0.9447 0.2536 -0.0881 -0.0172

LFSO -1.1724 -1.2431 -15.5195 0.8218 0.9085 0.4503 -0.3035 -0.0172

Conventional 6.7167 6.8746 105.79 -5.6455 -5.8410 -0.2765 0.2206 -0.0079

Organic -6.7167 -6.8746 -105.79 5.6455 5.8410 2.1503 -0.5048 -0.1314

Total 00000 1.8738 -0.2842 -0.1393

Note: First column of the table indicates the type of milk product, as follows: WHBC = Whole, big (1 gallon), conventional; RFBC = Reducedfat, big, conventional; LFBC = Low-fat, big, conventional; WHSC = Whole, small (less than gallon), conventional; RFSC = Reduced-fat, small, 

conventional; LFSC = Low-fat, small, conventional; WHBO = Whole, big, organic; RFBO = Reduced-fat, big, organic; LFBO = Low-fat, big, 

organic; WHSO = Whole, small, organic; RFSO = Reduced-fat, small, organic; LFSO = Low-fat, small, organic 

Low-fat milk is defi ned as less than 2 percent fat including skim; reduced-fat is between 2 and 3.25 percent fat; and whole is at least 3.25 

percent fat.

Source: Calculated by authors using 2007-08 Nielsen Homescan data.
Economic Research Service, USDA Households’ Choices Among Fluid Milk Products: What Happens 19

When Income and Prices Change? ERR-146

all milk products. Not surprisingly, as shown in the fi rst two columns of numbers in 

tables 6 and 7 as well as in fi g. 1, a 1-percent change in price has only small impacts 

on the composition of the fl uid milk market. 

The second scenario (table 7 and fi g. 1) simulates the market share changes if prices 

for all 12 milk products rose, as in 2007-08. In those years, higher prices received 

by farmers for milk pushed retail prices for fl uid milk as much as 25 percent higher 

(e.g., Stewart and Blayney, 2011). Although small shocks may have only small 

effects on the market, could such a large shock to prices motivate people to substitute, in signifi cant quantities, less expensive products like conventional milk for 

more expensive products like organic milk? The elasticities are substantially less 

accurate when used to simulate much larger shocks, but may still serve as a very 

general indicator of whether market shares are likely to change only a little or a lot. 

Following the same procedure outlined above, we fi nd that milk price increases of 

$1 per gallon (approximately 25 percent) for all 12 products could slow growth in 

sales of organic milk, just as rising prices and the recession did between 2007 and 

2009. By the simulation, the magnitude of the loss in organic market share could 

nearly equal the overall 2007-08 organic market share of 2 to 3 percent. We again 

caution that this estimate does not precisely measure the likely changes in market 

shares. However, the simulation does indicate that the impact on the organic market 

would be substantial. Likewise, the purchase probabilities decrease from 17 to 10.6 

percent for whole milk; decrease from 36 to 35.4 percent for reduced-fat milk; and 

increase from 47 to 54 percent for low-fat milk. The probability of purchasing milk 

Table 7

Simulation results for purchase probability

Baseline Scenario 1 Scenario 2 Scenario 3 Scenario 4 Scenario 5 Scenario 6 Scenario 7

1-percent 

increase of 

all milk prices

$1 increase 

of all milk 

prices 

1-percent 

increase 

of organic 

milk prices

10-percent 

increase 

of all milk 

deals

10-percent 

increase of 

income

1-person 

increase of 

hhsize

1-year 

increase of 

age

Purchase probability

Conventional 97.0 97.4 100 97.4 90.0 96.3 97.0 97.0

Organic 3.0 2.6 < 1 2.6 10.0 3.7 3.0 3.0

1-gallon container 58.0 58.2 59.8 57.9 56.5 57.4 58.1 57.6

Small container 42.0 41.8 40.2 42.1 43.5 42.6 41.9 42.4

Whole 17.0 16.8 10.6 17.0 21.2 15.9 17.2 17.2

Reduced fat 36.0 35.6 35.4 35.6 35.8 35.5 35.7 35.6

Low fat 47.0 47.6 54.0 47.4 43.0 48.6 47.1 47.2

Total 100 100 100 100 100 100 100 100

Source: Calculated by authors using 2007-08 Nielsen Homescan data.
20 Households’ Choices Among Fluid Milk Products: What Happens Economic Research Service, USDA

 When Income and Prices Change? ERR-146 

in a small container decreases from 42 to 40.2 percent, while the probability of 

buying it in a big container increases from 58 to 59.8 percent.

In the third scenario (table 7 and fi g. 1), we consider the possibility that prices for 

organic and conventional milk products need not move together. Costs for feed and 

other inputs used exclusively by organic dairy farming could rise faster or slower 

than costs for inputs used by conventional dairy farmers. That may have been the 

case in 2011. Neuman (2011) reports that costs for organic farmers rose faster that 

year. 

For the simulation, we consider the effect of a 1-percent increase in the price of the 

six organic products while holding constant prices for the six conventional products. Interestingly, the change in purchase probability for organic products is not 

much larger than the predicted impact of a 1-percent increase in the price of all milk 

products. This difference may refl ect the fact that sales of organic products are more 

sensitive to price changes than sales of conventional products. 

Promotional deals and price increases similarly affect a household’s choice among 

milk products, although in opposite directions. To simulate the impact of promotional deals, we consider a 10-percent increase in promotions for all 12 milk 

products in scenario 4. Large increases in the probability of buying organic milk 

occur. In fact, the purchase probability for any one of the six organic milk products increases from 3 percent in the baseline scenario to 10.5 percent. This fi nding 

underscores the sensitivity of organic milk sales to both retail prices and the use of 

promotional deals. 

For the fi nal simulation, we consider the effects on market composition of shocks 

to income, as well as changes in household size and age. As shown in table 3, the 

effects of the latter two demographic variables are small but statistically signifi -

cant. Rising income increases the probability of purchasing lower fat and organic 

products. 

A 10-percent increase in household income raises the probability of purchasing 

organic milk from 3 to 3.7 percent. A 10-percent increase in income also lowers 

the probabilities of purchasing whole milk from 17 to 15.9 percent and reduced-fat 

milk from 36 to 35.5 percent. The probablility of buying low-fat milk increases 

from 47 to 48.6 percent. Only small changes occur to a household’s choice among 

products in different container sizes. In contrast to household income changes, 

changes in household size and age have no effect on the probabilities of purchasing 

conventional and organic milk, but do affect substantially choice of container size 

(table 7). 
Economic Research Service, USDA Households’ Choices Among Fluid Milk Products: What Happens 21

When Income and Prices Change? ERR-146

Conclusions

During the December 2007 to June 2009 recession, many U.S. household experienced a decrease in income. In addition, food prices rose 4 percent in 2007 and 5.5 

percent in 2008 before moderating to 1.8 percent in 2009. In this study, we examine 

some of the strategies that households use to stretch their food dollar in response to 

income and price shocks. 

 In particular, we focus on how they adjust their choice among fl uid milk products categorized along three dimensions: three levels of fat content, two levels of 

package size, and organic versus conventionally produced products. Though fl uid 

milk is a staple of the American diet, most Americans aged 4 and over do not 

consume enough dairy products. 

Among the key results, households experiencing an income decrease substitute 

less expensive products for more expensive ones. The demand for organic milk is 

particularly sensitive to changes in income. Also, price fl uctuations can infl uence a 

household’s fl uid milk purchases. In the recent past, retail milk prices have fl uctuated by as much as 25 percent. A price increase of this magnitude has little impact 

on whether a household chooses to buy fl uid milk in a 1-gallon or smaller sized 

container. It would decrease the probability that a household buys low-fat milk 

from 47 to 53.9 percent. Moreover, a 25-percent increase in retail fl uid milk prices 

is large enough to reduce growth in sales of organic milk, as happened recently in 

2007-08. 
22 Households’ Choices Among Fluid Milk Products: What Happens Economic Research Service, USDA

 When Income and Prices Change? ERR-146 

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24 Households’ Choices Among Fluid Milk Products: What Happens Economic Research Service, USDA

 When Income and Prices Change? ERR-146 

Appendix I: The Specifi cation of the Household Loyalty 

Variable (Lijt)

Households are heterogeneous with their own specifi c, seemingly idiosyncratic preferences among the products available at retail stores. These preferences may stay 

the same over time, but may also change based on households’ purchase experience. 

For example, suppose that household A derives greater utility from product i than 

does household B at time t. If the two households face the same price and other 

variables are constant, the relative probability between the two households (i.e., the 

purchase probability for product i by household A is bigger than the one for household B) tends to remain the same for future purchases. However, if the households 

each gain more and more experience purchasing product i, they may adjust their 

purchase preferences over time, and the relative purchase probability for product i

between the two households could be reversed. Fader and Lattin (1993) also point 

out that preferences can change with sudden, unforeseen occurrences. Householdspecifi c preferences for given products are unobservable and are associated with 

household-specifi c demographic variables, as well as purchase experience. They 

are the household’s intrinsic loyalty to the products it purchases. They are different 

from the observed purchase probabilities, which also depend on prices, promotional 

deals, and other marketing variables. 

In this study, we follow Fader and Lattin (1993) and Dong and Stewart (2012) to 

defi ne the loyalty probability (Lijt) in equation (1) using the Dirichlet distribution 

and assume that the likelihood of a nonstationary change (a renewal) in the product 

loyalty probabilities for a given household between purchase occasions can be 

described by a Bernouli distribution. We then derive the expected product loyalty 

probabilities (i.e., the Dirichlet posterior probabilities) from the observed choice 

behavior of the household and use these posterior probabilities to form the basis 

of Lijt.

Suppose that there are J products to choose from for a given household to buy 

milk at time t. Absent any information on households’ income and demographic 

characteristics or their prior purchase history, we assume the prior probabilities of 

choosing each of the J products, ρ1, ρ2 

... , ρj

 , follow a Dirichlet distribution with 

parameters θ1, θ2 

... , θj . The pdf of the Dirichlet distribution is

(A1) 1 1

2

1

1

1 2

1 2

1 2 1 2

( ) ( ) ( )

( ) ( , , ) − − −

Γ Γ Γ

Γ + + + = J

J

J

J D J

θ θ θ ρ ρ ρ θ θ θ

θ θ θ

ρ ρ ρ  

  , 

where Γ ⋅( ) is the gamma function, 1

1

J

j

j

ρ

=

∑ = , and all θs are positive. From equation 

(A1) we know

(A2) 

∑=

= J

l

l

j E j

1

( )

θ

θ

ρ , 

where E(.) is expectation operation.
Economic Research Service, USDA Households’ Choices Among Fluid Milk Products: What Happens 25

When Income and Prices Change? ERR-146

The θs are product-specifi c parameters that indicate the relative level of a household’s preference for each product in the absence of any other information. Thus, 

equation (A2) gives the household initial choice (loyalty) probabilities to each of the 

products. However, according to Bayes Theorem, the probabilities can be updated at 

time t using a household’s observed product choice history for milk purchases from 

time 1 through time t - 1, if these data are available. If we use yijr to represent household i’s choice history, and defi ne that yijr equals 1 if household i purchased product 

j at time r and equals zero otherwise, then we can update the probabilities given by 

equation (A1) using a new Dirichlet distribution with the parameters: 

∑ ∑ ∑

−

=

−

=

−

=

+ + +

1

1

1

1

2 2

1

1

1 1 , , ,

t

r

J iJr

t

r

i r

t

r

i r θ y θ y  θ y . Equation (A2) is updated for the new 

expected probability given the purchase history data , as the following:

(A3) 

1

( | )

1

1

1

+ −

+

=

∑

∑

=

−

=

t

y

E y J

l

l

t

r

j ijr

ijt ijr

θ

θ

ρ ,

where t - 1 is the total number of food purchases through time t -1 by household i. 

The model allows for household heterogeneity through ∑

−

=

1

1

t

r

ijr y , the observed 

household purchase history. To further capture heterogeneity caused by household 

demographics, we follow Dong and Stewart (2012) to extend the model through the 

parameterization of θj

, using the vector of household variables, Zit:

(A4) ,

where the parameters γ0j and γ1j are unique to each product. Age, income, household 

size, and other variables may be included in Zit as past studies and economic theory 

suggest. The exponential specifi cation of equation (A4) is to guarantee that θijt is 

positive. 

To allow for any sudden, unforeseen occurrences that might infl uence a household’s 

product choices (for example, the entry and exit of a new brand, a new advertising 

campaign), we expand the Dirichlet probability formulation as a nonstationary 

process.

Nonstationarity in the Dirichlet choice model is assumed to be a renewal process. 

This renewal process may be described as follows: For any given time (purchase 

occasion), the household may renew its choice or loyalty probability because 

of sudden or unforeseen reasons with a probability of 1 - λ, where 0 ≤ λ ≤ 1. As 

described by Fader and Lattin (1993), each renewal constitutes a new draw from the 

original Dirichlet distribution, restarts the purchase history from the renewal point 

until the next renewal, and is independent of previous renewals. Thus, the probability of k purchases elapsing without renewal since the last renewal is (1 - λ) λk

, 

which is geometrically distributed, with λ being constant across households. 
26 Households’ Choices Among Fluid Milk Products: What Happens Economic Research Service, USDA

 When Income and Prices Change? ERR-146 

If a sudden, unforeseen event has changed a household’s product choices, then only 

its behavior since that event provides useful information for predicting its current 

behavior. Given the nonstationary Dirichlet choice process for household i with an 

observed purchase history from occasions 1 to t - 1, the expected loyalty probability 

for product j at time t is given by

(A5) , with

(A6) , and

(A7) , 

where k = 0, 1, ... , t- 1; δk

 is the probability of k purchases elapsing without renewal 

since the last renewal; and yijr equals one if household i purchased product j at time 

r, and equals zero otherwise. When k = 0, we defi ne . θijt is given in 

equation (A4), and λ is a parameter. 

Allowing for household heterogeneity through both demographics and past purchase 

history, as well as possible nonstationarity, the specifi cation of the household 

heterogeneity variable becomes 

(A8) 

based on equation (A5), with as given in equation (A6) and δk as 

given in equation (A7). 
Economic Research Service, USDA Households’ Choices Among Fluid Milk Products: What Happens 27

When Income and Prices Change? ERR-146

Appendix II: Estimation Results

Our data appear to fi t the model well. From the appendix table, we see that the 

predicted purchase probabilities for the 12 milk products are quite consistent with 

the data provided in table 1. Also, prices and promotional deals are signifi cant at the 

1-percent level. These marketing variables directly affect product choices and have 

the expected signs. Notably, given the specifi cation of household utility in equation 

(1), these variables have the same coeffi cient (β) for all milk products. However, 

prices and promotions will still have different effects on the purchase probabilities 

for each product, in accordance with equation (4) for the variables’ marginal effects 

(Dong and Stewart, 2012). The product-specifi c constants and some of the seasonal 

dummy variables are also signifi cant at the 1-percent level. The constant and the 

coeffi cient on the seasonal dummy variable for the product conventional, whole milk 

in a gallon container were restricted to zero for the purpose of normalization, so 

that the values for all other products are relative to the value of this product. From 

equation (1), we see that household variables indirectly infl uence milk product 

choices through the household loyalty variable. Many of these variables are signifi -

cant at the 1-percent level, including income, household size, age, and house ownership, among others. The effects of these variables on the purchase probabilities vary 

among milk products. Also signifi cant is λ, the nonstationary probability associated 

with the loyalty variable. It indicates how often a household’s product choices are 

infl uenced by sudden, unforeseen occurrences, such as a new promotional marketing 

campaign. A value near one indicates that such events rarely occurred. 
28 Households’ Choices Among Fluid Milk Products: What Happens Economic Research Service, USDA

 When Income and Prices Change? ERR-146 

Appendix table: Model estimates

Variable WHBC RFBC LFBC WHSC RFSC LFSC

Probability: 0.0866 0.1948 0.2338 0.0964 0.1651 0.1905

Household Variables:

Intercept 3.6185*

(0.1242)

2.2020*

(0.1115)

-3.0533*

(0.1273)

-0.4436*

(0.1474)

-2.416*

(0.1252)

-5.6751*

(0.1178)

Log HH income -0.4046*

(0.0114)

-0.2107*

(0.0089)

0.1214*

(0.0107)

-0.1788*

(0.0119)

-0.0355*

(0.0099)

0.2278*

(0.0091)

Inverse HHsize -1.8928*

(0.0833)

-1.7144*

(0.0714)

-0.5351*

(0.0791)

0.7059*

(0.0980)

1.5431*

(0.0870)

1.6437*

(0.0790)

Age -0.0133*

(0.0007)

-0.0096*

(0.0006)

-0.0052*

(0.0008)

-0.0032*

(0.0008)

0.0035*

(0.0007)

0.0089*

(0.0007)

Employment: 0.0071

(0.0144)

-0.0567*

(0.0121)

-0.1055*

(0.0142)

0.0503*

(0.0155)

0.0749*

(0.0141)

-0.0095

(0.0126)

Education -0.2654*

(0.0148)

-0.1322*

(0.0122)

0.2160*

(0.0136)

-0.1185*

(0.0145)

-0.0176

(0.0129)

0.2174*

(0.0118)

House -0.0707*

(0.0186)

0.0317*

(0.0136)

0.1302*

(0.0168)

-0.2509*

(0.0173)

0.0023

(0.0159)

-0.2107*

(0.0139)

Single 0.4248*

(0.0507)

0.2113*

(0.0420)

0.0696

(0.0449)

-0.5438*

(0.0552)

-0.7905*

(0.0482)

-0.7368*

(0.0439)

Black 0.5798*

(0.0267)

0.0029

(0.0230)

-0.9382*

(0.0356)

0.8941*

(0.0258)

0.5029*

(0.0189)

-0.1755*

(0.0242)

Hisp 0.6030*

(0.0226)

0.1193*

(0.0240)

-0.0664*

(0.0267)

0.2726*

(0.0282)

0.3066*

(0.0223)

0.1491*

(0.0229)

Popdensi -0.0570*

(0.0043)

-0.0923*

(0.0037)

-0.0011

(0.0038)

0.0002

(0.0047)

-0.0466*

(0.0037)

0.0147*

(0.0037)

AgeC6 1.0973*

(0.0195)

0.4731*

(0.0242)

0.1451*

(0.0329)

0.5987*

(0.0355)

0.2941*

(0.0391)

0.2787*

(0.0314)

AgeC1317 -0.0661*

(0.0204)

-0.0007

(0.0208)

0.1191*

(0.0225)

-0.4599*

(0.0359)

-0.2199*

(0.0267)

-0.1733*

(0.0230)

Marketing variables and other parameters:

Constant 0 -0.0004

(0.0133)

0.1521*

(0.0148)

0.2106*

(0.0371)

0.1712*

(0.0324)

0.2630*

(0.0310)

Spring 0 -0.0548*

(0.0184)

-0.1272*

(0.0203)

0.1455*

(0.0198)

0.1378*

(0.0200)

0.0953*

(0.0207)

Summer 0 -0.0155

(0.0205)

-0.1310*

(0.0230)

0.1678*

(0.0223)

0.1950*

(0.0227)

0.0937*

(0.0235)

Fall 0 -0.0347

(0.0278)

-0.2012*

(0.0304)

0.1157*

(0.0288)

0.0713*

(0.0297)

-0.0573

(0.0309)

Milk price -0.1888*

(0.0205)

Milk deal 1.0121*

(0.0724)

λ 0.9963*

(0.0110)

Log likelihood -479,127.99

—continued
Economic Research Service, USDA Households’ Choices Among Fluid Milk Products: What Happens 29

When Income and Prices Change? ERR-146

Appendix table: Model estimates—continued

Variable WHBO RFBO LFBO WHSO RLSO LFSO

Probability: 0.0007 0.0013 0.0028 0.0051 0.0083 0.0146

Household Variables:

Intercept -5.9509*

(2.1401)

-15.5443*

(1.5161)

-11.9883*

(1.0309)

-9.7030*

(0.5970)

-7.7794*

(0.4234)

-11.992*

(0.3630)

Log HH income 0.0577

(0.1650)

0.9360*

(0.1297)

0.7122*

(0.0882)

0.4110*

(0.0501)

0.3762*

(0.0354)

0.6759*

(0.0323)

Inverse HHsize 3.6611*

(1.5713)

-2.4464*

(0.7054)

-1.0996*

(0.5690)

-0.9458*

(0.3291)

0.6192*

(0.3008)

1.8930*

(0.2208)

Age -0.0696*

(0.0083)

-0.0169

(0.0126)

-0.0344*

(0.0050)

-0.0253*

(0.0029)

-0.0266

(0.0026)

-0.0269*

(0.0021)

Employment: -0.4180

(0.2336)

-0.1816

(0.1446)

-0.2660*

(0.1108)

-0.3007*

(0.0578)

-0.4168*

(0.0502)

-0.2593*

(0.0381)

Education 0.0255

(0.2306)

-0.0622

(0.1279)

0.4270*

(0.1113)

0.1577*

(0.0593)

0.3945*

(0.0509)

0.3707*

(0.0383)

House -0.5252*

(0.1961)

0.8713*

(0.3712)

0.2600

(0.1615)

-0.3529*

(0.0605)

-0.0114

(0.0685)

-0.2094*

(0.0515)

Single -2.3133*

(0.8327)

0.7376

(0.5038)

0.5435

(0.3463)

0.1598

(0.2063)

-0.2024

(0.1682)

-0.9503*

(0.1261)

Black 0.0636*

(0.3374)

-0.3034

(0.2339)

-0.7337*

(0.2737)

0.0149

(0.1175)

0.1004

(0.0942)

-0.2725*

(0.0832)

Hisp 0.7175*

(0.2728)

-0.0326

(0.2927)

0.0767

(0.2233)

0.2317*

(0.1000)

0.4140*

(0.0745)

0.3357*

(0.0692)

Popdensi 0.2668*

(0.0574)

0.1226*

(0.0601)

0.0861*

(0.0295)

0.1769*

(0.0154)

0.0325*

(0.0162)

0.1403*

(0.0120)

AgeC6 0.7192

(0.4347)

0.9457*

(0.3012)

0.5158*

(0.1812)

1.9312*

(0.0835)

0.3871*

(0.1005)

0.1274

(0.0815)

AgeC1317 0.7440*

(0.3565)

-0.0796

(0.2331)

-0.1002

(0.1629)

-0.2785*

(0.0993)

-0.1682*

(0.0798)

0.1587*

(0.0561)

Marketing variables and other parameters:

Constant -0.6639*

(0.1280)

-0.5398*

(0.0699)

-0.2341*

(0.0632)

0.3530*

(0.0814)

0.2164*

(0.0762)

0.4907*

(0.0722)

Spring 0.2284

(0.1432)

-0.0776

(0.0999)

-0.0347

(0.0835)

0.2897*

(0.0670)

0.3056*

(0.0510)

0.1197*

(0.0434)

Summer 0.3212*

(0.1396)

0.2462*

(0.1030)

0.2518*

(0.0895)

0.2195*

(0.0752)

0.3821*

(0.0586)

0.1632*

(0.0478)

Fall 0.9846*

(0.1496)

1.1154*

(0.1095)

0.6669*

(0.1090)

0.2169*

(0.0905)

0.4104*

(0.0746)

0.1006

(0.0625)

Milk price -0.1888*

(0.0205)

Milk deal 1.0121*

(0.0724)

λ 0.9963*

(0.0110)

—continued
30 Households’ Choices Among Fluid Milk Products: What Happens Economic Research Service, USDA

 When Income and Prices Change? ERR-146 

Appendix table: Model estimates—continued

Variable WHBO RFBO LFBO WHSO RLSO LFSO

Log likelihood -479,127.99

Source: Calculated by authors using 2007-08 Nielsen Homescan data. Notes: Standard errors are in parentheses. The constant and the coeffi cient of grocery stores in the marketing variables are constrained to be zero. “*”indicates signifi cant at level of 0.05 or better. 

WHBC = Whole, big (1 gallon), conventional; RFBC = Reduced-fat, big, conventional; LFBC = Low-fat, big, conventional ; WHSC = Whole, 

small (less than gallon), conventional; RFSC = Reduced-fat, small, conventional; LFSC = Low-fat, small, conventional; WHBO = Whole, big, 

organic; RFBO = Reduced-fat, big, organic; LFBO = Low-fat, big, organic; WHSO = Whole, small, organic; RFSO = Reduced-fat, small, 

organic; LFSO = Low-fat, small, organic. Low-fat milk is defi ned as less than 2 percent fat including skim; reduced fat is between 2 and 3.25 

percent fat; and whole is at least 3.25 percent fat. HH = Household; Age = age of female head; Popdensi = population density of the household 

residential area. Employment: = 1 if female head employed, = 0 if not; Education: = 1 if female head gained college education, = 0 if not; House: 

= 1 if owned house, = 0 if not; Single: = 1 if household size is 1, = 0 if not; Black: =1 if household is African American, =0 if other; Hisp: = 1 if 

household is Hispanic, = 0 if not; AgeC6: = 1 if presence of children 6 and below, = 0 if not; AgeC1317: = 1 if presence of children between 13 

and 17, = 0 if not.