Economic

Research 

Report

Number 96

June 2010

United States 

Department 

of Agriculture

Economic 

Research 

Service

Diansheng Dong 

Ephraim Leibtag

Promoting Fruit and Vegetable

Consumption

Are Coupons More Effective

Than Pure Price Discounts?
www.ers.usda.gov

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United States

Department

of Agriculture

www.ers.usda.gov

A Report from the Economic Research Service

Abstract

The U.S. Department of Agriculture administers food and nutrition assistance programs that 

promote fruit and vegetable consumption. But consumption remains relatively low among 

program recipients as well as among the general U.S. population. The perceived high cost of 

produce is often cited as a deterrent to more consumption. This study looks at coupons and 

price discounts, two methods of lowering the cost of fruits and vegetables, and uses household 

purchase data and a consumer demand model to examine each method. Coupons infl uence 

consumer behavior through a price-discount effect and an informational/advertising effect. 

Because of this dual effect, the use of a coupon to increase fruit and vegetable purchases may 

be more effective than a pure price-discount policy or other noncoupon promotion. Assuming 

a coupon usage rate of 10 to 50 percent, lowering prices through a “10 percent off” coupon 

would increase average weekly fruit and vegetable quantities purchased by 2 to 11 percent, as 

compared with a 5- to 6-percent effect for a pure price discount. 

Keywords: fruit and vegetable consumption, coupons, price discounts, consumer 

demand, dual effect of coupons, informational advertising effects

Acknowledgments

For their helpful comments on the report, the authors wish to thank: Steven Yen, 

Professor, Department of Agricultural Economics, University of Tennessee; Timothy 

Richards, Professor, Morrison School of Agribusiness, Arizona State University; ERS 

Food Economics Division colleagues Margaret Andrews, Senior Economist; Fred 

Kuchler, Senior Economist; Hayden Stewart, Economist; and ERS colleague Susan 

Pollack, Senior Economist, Markets and Trade Economics Division. We also thank 

Priscilla Smith for editorial expertise and Wynnice Pointer-Napper for design.

Diansheng Dong, ddong@ers.usda.gov

Ephraim Leibtag, eleibtag@ers.usda.gov

Promoting Fruit and Vegetable 

Consumption

Are Coupons More Effective Than 

Pure Price Discounts?

Economic

Research 

Report

Number 96

June 2010
ii

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Contents

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

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

U.S. Fruit and Vegetable Purchases and Coupon Usage . . . . . . . . . . . . . 3

 Weekly Produce Purchases Are Examined. . . . . . . . . . . . . . . . . . . . . . . . 3

 Coupon User Households Are Characterized . . . . . . . . . . . . . . . . . . . . . . 4

Applying the Marked-Purchase Renewal Model . . . . . . . . . . . . . . . . . . . 8

Price, Season, and Household Characteristics 

 Affect Produce Buying. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

 Price and Information/Advertising . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

 Seasons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

 Household Characteristics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

Application of Results Through a Simulation. . . . . . . . . . . . . . . . . . . . . 12

References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

Appendix A: Marked Purchase Renewal Model 

 With Coupon Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

Appendix B: Calculating Simulation Effects From 

 Elasticity Estimates. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

Recommended citation format for this publication:

Dong, Diansheng, and Ephraim Leibtag. Promoting Fruit and 

Vegetable Consumption: Are Coupons More Effective Than Pure 

Price Discounts? Economic Research Report No. 96, U.S. Dept. of 

Agriculture, Economic Research Service, June 2010.
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Summary

The U.S. Department of Agriculture administers food and nutrition assistance 

programs that promote fruit and vegetable consumption. But consumption 

remains relatively low, with price cited as the main deterrent.

What Is the Issue?

A price-discount strategy in conjunction with existing programs might 

encourage participants in food and nutrition assistance programs to consume more fruits and vegetables. This study looks at coupons and price discounts, two methods of lowering the cost of fruits and vegetables, and uses 

household purchase data and a consumer demand model to determine which 

method may be more successful in encouraging produce consumption. 

What Did the Study Find?

Coupons infl uence consumer behavior through a dual effect—a price-discount 

effect and an informational advertising effect. Because of this dual effect, the 

use of a coupon to increase fruit and vegetable purchases may be more effective than a pure price-discount policy or other noncoupon promotion. 

• For a 10-percent coupon usage rate, lowering prices by 10 percent with 

a coupon would increase average weekly quantity purchases by 2 percent for fruits and 2.1 percent for vegetables. (A “coupon usage” rate is 

defi ned as the percentage of purchases in which households use the coupon when buying fruits and vegetables in a given time period.) A 30-percent usage rate simulation shows a larger effect—over 6 percent for fruits 

and over 6.5 percent for vegetables—while a 50-percent usage rate shows 

just over a 10-percent effect for both fruits and vegetables. 

• By comparison, a pure price discount of 10 percent would likely have 

about a 6-percent effect for both fruits and vegetables. 

• If coupon usage turned out to be less than 30 percent, then the overall effect of coupons would be lower than a pure price-discount policy 

because the price discount applies to everybody (it has a 100-percent 

usage rate).

• The informational effect of coupons might decline as coupon use became 

more common or if coupons were distributed electronically instead of in 

paper form.

• Even a 10-percent increase in purchases of fruits and vegetables—the 

result assuming the highest coupon usage rate—would still leave consumption at about 65 percent of the recommended level of 5 or more 

servings a day. 

The success of attempts to use coupons to increase consumption of fruits 

and vegetable by low-income households would depend on the distribution 

method (paper or electronic), on the number of households that actually use 

the coupons, on the size of the discount offered by the coupon, and on the 

coupon’s ease of use. 
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How Was the Study Conducted?

This analysis relies on data from the 2004 Nielsen Homescan panel. The data 

include household purchase information for fruits and vegetables, coupon 

usage information, and households’ demographic characteristics. The 2004 

panel was made up of 8,482 households that reported purchases of products 

marked with bar codes as well as other purchases.

To estimate the dual effect of coupons on fruit and vegetable demand, the 

marked purchase renewal model was used, including three variables that may 

affect purchase quantity and/or frequency: (1) the gross price paid, (2) an 

indicator variable that tracks whether a coupon was used, and (3) the value 

of a redeemed coupon used during a given shopping trip. Elasticity estimates 

from the analysis then were used to conduct a simulation to compare the 

effect of coupons as compared with a pure price discount on fruit and vegetable purchase behavior.
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Introduction

With growing evidence of an association between increased fruit and vegetable consumption and a reduced risk of obesity-related and other diseases 

such as stroke, cardiovascular disease, diabetes, and cancers, the U.S. 

Departments of Agriculture and Health and Human Services and other 

Federal agencies recommend that individuals consume more fruits and vegetables in their daily diets. Many of USDA’s food and nutrition assistance 

programs, including the Supplemental Nutrition Assistance Program (SNAP) 

(formerly known as the Food Stamp Program), the WIC Farmers’ Market 

Nutrition Program, the Senior Farmers’ Market Nutrition Program, and various informational campaigns provide fi nancial resources, increase the availability of fruits and vegetables, and educate Americans on how to make more 

nutritious food choices. However, Americans are not consuming the recommended amounts of fruits and vegetables (Dong and Lin, 2009).

Households that are eligible to participate in current food assistance programs have expressed the opinion that the high cost of a healthy diet, including fruits and vegetables, prevents them from eating better (Eikenberry and 

Smith, 2007). As part of the Food, Conservation, and Energy Act of 2008 

(2008 Farm Act), Congress authorized $20 million for the Healthy Incentives 

Pilot to determine if incentives provided to SNAP recipients at the point 

of sale would increase the purchase of healthful foods, including fruits and 

vegetables.

We examined the effect of supplementing existing food assistance programs 

with policies that change the effective price of foods to improve consumer 

food choices. A price discount or coupon are two possible options to help 

overcome some of the perceived cost barriers associated with affording a 

healthier diet. Our analysis looked at potential effects of coupons versus 

other price discount plans to encourage fruit and vegetable consumption. We 

used household fruit and vegetable purchase data that include information 

on coupon usage to estimate the impact of coupons on all fruit and vegetable 

purchases, both fresh and processed, and compared the coupon effects to a 

pure price discount. If the effect of a coupon discount were larger than a pure 

price-discount effect, this would imply that a coupon strategy would be more 

effective than just a price discount to increase consumers’ purchases of fruits 

and vegetables. 

Currently, a number of canned and frozen fruit and vegetable manufacturers 

provide coupons to the general public in order to entice consumers to try new 

products and to increase the quantity of a given product that is purchased 

(increase market share). Some fresh produce distributors and retailers also 

have issued coupons for fresh fruit and vegetables in order to promote sales 

of these items. But the use of coupons for fresh fruits and vegetables is less 

common than the use of coupons for fruits and vegetables overall (including 

dried, frozen, and canned).1 However, if coupons that could be used at any 

store chain or retail outlet type were provided by the Federal Government, 

those coupons might be used by more households than those issued by a 

single manufacturer or retailer since the Government-issued coupons would 

not be brand- or store-specifi c.

1Based on estimates from 2004 

Nielsen Homescan data, described later 

in this report, about 11 and 9 percent of 

households used coupons for fresh fruit 

and vegetable purchases, respectively, 

as compared with about 20 and 12 percent of households that used coupons 

for all fruit and vegetable purchases, respectively, during the course of a year.
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Previous studies have focused on the effect of coupon use on other foods 

and found that coupons have a signifi cant impact on a household’s demand 

for some types of foods. For example, there is a great deal of research that 

has focused on how coupons affect brand switching (Gupta, 1988; Neslin 

et al., 1985; Bawa and Shoemaker, 1987). However, few papers focus on 

how coupons are used to increase the demand for a food category in general. 

Pioneering work by Ward and Davis (1978) and a later study by Lee and 

Brown (1985) investigated the effects of coupons on Florida households’ 

demand for frozen concentrated orange juice. Both studies revealed a signifi -

cant, positive relationship between coupon redemption and product purchases. 

In a study by Dong and Kaiser (2005), coupon usage was found to be effective in expanding household cheese purchases. Although large-scale studies 

of coupons’ effect on the purchases of fruits and vegetables are nonexistent in 

the literature to the best of our knowledge, there has been some recent work 

focusing on the related issue of the impact of vouchers on fruit and vegetable 

purchases. Herman et al. (2008) conducted an experiment by providing $10 

vouchers for the purchase of fresh fruits and vegetables to WIC participants in 

Los Angeles and found statistically signifi cant effects on the servings of fresh 

fruits and vegetables consumed. 

Our objective here is to examine how coupons affect the demand for fruits 

and vegetables. In order to obtain the coupon effects on average fruit and 

vegetable purchases from our data, we investigate coupon infl uence on both 

the quantity and the frequency of a household’s purchases. As a group, U.S. 

households make fruit and vegetable purchases irregularly. Some buy every 

week. Others may purchase once every few weeks. How much a household 

buys each week, on average, depends on the quantities it prefers to consume 

as well as the frequency of these purchase occasions. By determining how 

coupons affect both decisions—how often to buy and how much to buy—we 

are able to establish how coupons impact average weekly purchases. 

It is possible that coupons cause only short-term purchase stockpiling without 

longrun consumption increases, as Helsen and Schmittein maintained (1992). 

We can test this hypothesis by examining coupon effects on both purchase 

frequency and purchase quantities during purchase weeks. 

In addition to the ability to be provided to specifi c subgroups without infl uencing the price for the general population, coupons have a dual effect on 

consumption as compared with pure price discounts (Ward and Davis, 1978). 

First, the price discount associated with the coupon lowers the price for coupon holders. This effect is likely to generate the change in demand predicted 

by Dong and Lin (2009), who found that if prices are lowered by 10 percent, 

U.S. low-income households would increase their fruit purchases by 5.2 percent and their vegetable purchases by 6.9 percent. Secondly, coupons provide 

information about the existence or availability of foods, functioning as an 

“informational stimulant” (Ward and Davis, 1978). In other words, coupons 

remind consumers about the availability of fruits and vegetables, possibly 

causing a household to buy those foods on occasions when the household 

might not have done so otherwise. Due to this dual effect, a coupon-based 

incentive for fruit and vegetable purchases may have a bigger impact on 

demand than would pure price adjustments or increased information alone. 
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U.S. Fruit and Vegetable Purchases 

and Coupon Usage

We used 2004 Nielsen Homescan data to investigate the quantity and frequency of households’ fruit and vegetable purchases as well as their associated coupon usage throughout the year. Nielsen Homescan data include 

information on the fruits and vegetables households bought for at-home consumption as well as the households’ demographic information. Households 

that reported both random-weight and universal price code (UPC) purchases 

are used in this study since a large share of fruits and vegetables are purchased on a random-weight (non-UPC) basis. The data are recorded at the 

purchase/transaction level by households whose members use handheld 

scanners to record purchase information after each shopping trip. Recorded 

information includes the date of purchase, dollars paid, quantities purchased, 

coupon usage, and other product attribute variables, such as fl avor, form, and 

container type. The raw purchase data were aggregated from daily transactions to weekly totals and combined with household demographic information for 8,482 households.

Weekly Produce Purchases 

Are Examined

Weekly purchase quantities and expenditures are defi ned as the sum of quantities and expenditures on all types of fruits or vegetables in all formats, including fresh, frozen, dried, and canned, that are purchased within a given week. 

A total of 52 weeks for each of the households is in our fi nal sample. Among 

these 8,482 households, 131 did not purchase any fruits and 185 did not purchase any vegetables for at-home consumption during the sampling period.

Statistics calculated over purchase and nonpurchase households show that, 

relative to vegetables, fruits are purchased in larger quantities and at higher 

prices (table 1). On average, households purchase 1.56 and 1.02 pounds of 

fruits and vegetables, respectively, each week for at-home consumption. The 

histograms of purchase frequencies for fruits and vegetables of the sampled 

households show that purchasing households buy fruits, on average, in 21 of 

the 52 weeks (40 percent) and vegetables in 18 of the 52 weeks (35 percent) 

(see fi gs. 1 and 2). The average length of time between two purchases is 2.5 

weeks for fruits (52/21 = 2.5) and 2.9 weeks for vegetables (52/18 = 2.9). 

In other words, on average, households make fruit and vegetable purchases 

roughly once every 3 weeks.

A comparison of purchasing and nonpurchasing household characteristics is 

helpful for determining potential determinants of fruit and vegetable demand 

and market penetration. The number of nonpurchase households is small, 

but the demographic differences are noticeable for both fruits and vegetables. Fruit and vegetable purchasers have slightly higher income ($3,000 

to $4,000 more per year), larger household size (2.4 vs. 1.8 household members), and are more likely to have a female head of household employed at 

least 35 hours per week (table 1). This study focuses only on those households that purchased fruits or vegetables in order to estimate the impact of 

coupons on current purchasers. Future research on nonpurchase households 

also would be important in revealing the factors that hinder consumption of 
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fruits and vegetables for those who currently choose not to purchase fruits 

and vegetables at all.

Coupon User Households 

Are Characterized

Household characteristics and purchase statistics for coupon users and nonusers show that among the 8,351 households who purchased fruit, 1,634 used 

coupons at least once during the year (19.57 percent) (table 2). The average 

value of redeemed coupons was about $1.55 in weeks when fruit coupons 

were used, implying about a 16-percent discount on fruit purchases for coupon users during weeks in which they used coupons. Coupon users made 

purchases in about 27 out of the 52 weeks and used coupons in about 4 out of 

these 27 weeks (14.81 percent). 

Table 1

U.S. household weekly average purchases of fruits and vegetables, 2004

Fruits Vegetables

NonpurchasersAll 

purchasers

Purchasers 

with 2 or 

more 

purchase 

weeks

NonpurchasersAll 

purchasers

Purchasers 

with 2 or 

more 

purchase 

weeks

Purchases

Number of households 131 8,351 8,145 185 8,297 8,096

Average quantity purchased per week, all weeks 

(pounds) 1.56 1.60 1.02 1.03

Average quantity purchased per week, purchase 

weeks (pounds) 3.84 3.91 2.89 2.90

Number of purchase weeks 21.1 21.3 18.3 18.5

Unit value (dollars/pound) 1.63 1.63 1.47 1.47

Household characteristics

Household income (dollars) 51,183 54,320 54,332 50,149 54,364 54,371

Household size (number of people) 1.80 2.39 2.39 1.75 2.39 2.39

Age of female head (years) 48.8 51.9 52.0 49.6 51.9 51.9

Employment of female head (proportion)1 0.66 0.45 0.45 0.68 0.45 0.45

Education of female head (proportion)2 0.37 0.40 0.40 0.50 0.40 0.40

White households (proportion) 0.68 0.68 0.68 0.71 0.68 0.68

Black households (proportion) 0.15 0.14 0.14 0.16 0.14 0.14

Hispanic households (proportion) 0.07 0.08 0.08 0.05 0.08 0.08

Asian households (proportion) 0.02 0.03 0.03 0.03 0.03 0.03

Other race households (proportion) 0.08 0.07 0.07 0.05 0.07 0.07

East (proportion) 0.21 0.22 0.22 0.29 0.22 0.22

South (proportion) 0.44 0.39 0.39 0.32 0.39 0.39

West (proportion) 0.18 0.22 0.22 0.24 0.22 0.22

Central (proportion) 0.17 0.17 0.17 0.15 0.17 0.17

1Employment of female head: the female head of the household is employed at least 35 hours a week.

2Education of female head: the female head of the household had at least some college education.

Source: USDA, Economic Research Service.
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Figure 1

Fruit purchasing frequency among U.S. households, 2004

Number of buying households 

Source: USDA, Economic Research Service.

Weeks in 2004 when households bought fruits

0

50

100

150

200

250

300

0

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2

3

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43

44

45

46

47

48

49

50

51

52

Figure 2

Vegetable purchasing frequency among U.S. households, 2004

Number of buying households 

Source: USDA, Economic Research Service.

Weeks in 2004 when households bought vegetables

0

50

100

150

200

250

300

0

1

2

3

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Fewer households used coupons for purchasing vegetables. Among the 8,297 

vegetable-purchasing households, 1,000 used coupons (12.1 percent). The 

redeemed coupon values for vegetables were smaller in absolute terms than 

those for fruits, but similar as a share of the average amount spent. On average, $1.23 was redeemed over those weeks when coupons were used, implying about a 20-percent discount on vegetable purchases for coupon users 

during weeks in which they used coupons. However, households who used 

vegetable coupons used them a little more often relative to fruits. Among the 

23.4 weeks in which vegetables were purchased, these households used vegetable coupons in 3.77 weeks (16.32 percent).

Table 2

U.S. household weekly average purchases of fruits and vegetables with or without coupons, 2004

Fruits Vegetables

All With 

coupons

Without 

coupons

Low 

income1 All With 

coupons

Without 

coupons

Low 

income

Purchases

Number of households 8,351 1,634 6,717 1,241 8,297 1,000 7,297 1,241

Quantity purchased over all 

 weeks (pounds) 1.56 2.19 1.42 1.53 1.02 1.37 0.97 1.02

Quantity purchased over purchase 

 weeks (pounds) 3.84 4.21 3.75 3.63 2.89 3.04 2.87 2.92

Quantity purchased over coupon-

 redeemed purchase weeks (pounds) 5.77 5.77 0 5.38 4.04 4.04 0 3.60

Number of purchase weeks 21.1 27.1 19.7 21.9 18.3 23.4 17.6 18.2

Unit value (dollars/pounds) 1.63 1.71 1.61 1.58 1.47 1.53 1.46 1.42

Coupon usage

Coupon value over redeemed 

weeks (dollars) 1.55 1.55 0 1.53 1.23 1.23 0 1.19

Number of coupon-redeemed weeks 0.78 4.05 0 0.66 0.45 3.77 0 0.34

Household characteristics

Household income (dollars) 54,320 57,518 53,542 17,794 54,364 56,939 54,010 17,892

Household size (number of people) 2.39 2.61 2.33 2.78 2.39 2.51 2.38 2.79

Age of female head (years) 51.9 51.8 52.0 51.9 51.9 53.2 51.8 51.8

Employment of female head (proportion) 0.45 0.38 0.47 0.18 0.45 0.35 0.47 0.18

Education of female head (proportion) 0.40 0.42 0.40 0.20 0.40 0.43 0.40 0.20

White households (proportion) 0.68 0.75 0.66 0.70 0.68 0.75 0.67 0.69

Black households (proportion) 0.14 0.10 0.15 0.16 0.14 0.10 0.14 0.16

Hispanic households (proportion) 0.08 0.06 0.09 0.12 0.08 0.06 0.03 0.13

Asian households (proportion) 0.03 0.04 0.03 0.01 0.03 0.04 0.09 0.01

Other race households (proportion) 0.07 0.05 0.08 0.01 0.07 0.05 0.07 0.01

East (proportion) 0.22 0.27 0.21 0.20 0.22 0.28 0.21 0.19

South (proportion) 0.39 0.33 0.40 0.46 0.39 0.28 0.41 0.46

West (proportion) 0.22 0.20 0.23 0.18 0.22 0.23 0.22 0.18

Central (proportion) 0.17 0.20 0.16 0.26 0.17 0.21 0.18 0.27

1The low income group includes households that have income up to 185 percent of the poverty level.

Source: USDA, Economic Research Service.
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Compared with nonusers, coupon users purchased a greater quantity of food, 

paid higher original prices, and bought both fruits and vegetables more often. 

Household characteristics of coupon users and nonusers are quite different 

for some variables. On average, coupon users appear to have higher household incomes and larger household sizes. They also include a lower proportion of employed female heads, but a higher proportion of college-educated 

female heads. In terms of ethnicity, Caucasian households are more likely to 

use coupons than African-American households. Interestingly, coupon usage 

appears to be related to residential regions. Households in the South purchase 

vegetables more frequently, but redeem fewer coupons relative to people 

in other regions, such as those in the West and Central States. This may be 

caused by different levels of coupon availability across regions due to advertisers’ different geographic strategies. The regional differences in coupon 

redemption also could be due to differences in food shopping behavior and/or 

store format type availability across U.S. regions.2 2See Leibtag (2006) for additional 

discussion of regional differences in 

store format types.
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Applying the Marked-Purchase 

Renewal Model 

Using the Homescan data as described, we estimated the dual effect of fruit 

and vegetable coupons and other variables on fruit and vegetable purchases. 

Coupons can provide information to consumers to alter their preferences 

as well as create a price discount to increase the likelihood of purchases. 

We separated the informational or advertising effect of coupons from the 

price-discount effect for both purchase quantity and frequency by using the 

marked-purchase renewal model originally developed by Cox and Oakes 

(1984) and later applied by Boizot, Robin, and Visser (2001). A statistical 

analysis follows (for more details, see appendix A).

The marked-purchase renewal model allows us to determine how coupons 

impact both the quantity and frequency of a household’s food purchases. 

Specifi cally, the marked-purchase renewal model has two equations: one for 

the quantity purchased3 and one for the interpurchase time (time between 

purchases). The interpurchase time measures the number of weeks elapsed 

between purchases. For example, if a household made a purchase in 26 out 

of 52 weeks, that household was recorded as typically allowing 2 weeks to 

elapse between purchases. Therefore, the interpurchase time is the inverse of 

the purchase frequency.

Households who bought fruits and vegetables on fewer than two occasions 

total are not included in this statistical analysis since no interpurchase time 

could be calculated for those households. However, we do not believe that 

dropping these households has a major impact on our analysis since the 

number of very infrequent buyers who purchased fruits and vegetables during only 1 week during the year are 337 (4.0 percent) and 386 (4.6 percent), 

respectively. Given the small proportion of dropped households (see table 1, 

columns 3 and 6), possible selection bias is expected to be negligible.

To estimate the dual effect of coupons on fruit and vegetable demand, we use 

both a continuous variable of the dollar value of coupons used by a household in a given week (coupon discount effect) and a dummy variable indicating whether any coupons were used in a given week. Since the fi rst variable 

accounts for the response to the price effect of a coupon, the dummy variable 

that indicates use of a coupon is assumed to estimate the “nonprice” (informational/advertising) effect that is unique to the dual nature of a coupon. If 

this variable is statistically signifi cant in either the purchase-quantity equation or the purchase-frequency equation, then we view this as evidence of the 

dual effect of coupons. If the combined effect of the coupon price discount 

and informational (dummy variable) effect are larger than the standard price 

effect, this would imply that a coupon strategy would be more effective than a 

pure price discount to increase consumers’ purchases of fruits and vegetables. 

To bolster the accuracy of our results, we also controlled for other factors 

that might infl uence households’ behavior. Those factors included the price 

paid by a household during the previous purchase (lag price), following 

Boizot, Robin and Visser (2001), as well as a dummy variable that indicated 

whether purchases were made using noncoupon promotions such as store 

features or displays. In addition to price and promotion (coupon and other 

3Quantity purchased is defi ned as the 

total pounds of fruits or vegetables a 

household bought in the weeks when it 

made a purchase.
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activities) information, seasonality and a number of household characteristics 

are also incorporated as explanatory variables in the model. Tables 1 and 

2 provide overviews of these household characteristics for purchasers (for 

all purchasers, those purchasers included in the estimation, and low-income 

households) and nonpurchasers as well as coupon users and nonusers.
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Price, Season, and Household 

Characteristics Affect Produce Buying

Price and Information/Advertising

Our results show that coupons have a dual effect on the demand for fruits and 

vegetables. Both the coupon-discount effect and the coupon dummy variable 

(information effect) are statistically signifi cant in both purchase quantity and 

purchase frequency equations (appendix A tables A-1 to A-3). However, to 

compare the effect of coupons to the standard response to a general price 

change, we must account for the fact that differences in prices may be a 

function of differences in the quality of fruits and vegetables purchased by a 

given household in the data. Since our data are aggregated across all fruit and 

vegetable purchases, some of the difference in prices (and subsequent difference in purchase behavior) may be a function of differences in the type of 

produce purchased. Thus, we calculate quality-adjusted elasticity estimates 

of the price effect (as detailed in appendix A) since an unadjusted elasticity 

estimate would be larger in magnitude than the true price elasticity (table 3). 

We fi nd that coupons have a statistically signifi cant effect for both fruit and 

vegetable interpurchase time, reducing the time between purchases both from 

an informational effect and from a coupon-discount effect. The elasticity of 

interpurchase time with respect to the coupon dummy is -12.1 for fruits and 

-8.6 for vegetables. This implies that the use of coupons in a given week 

reduces interpurchase time by about 12 percent for fruit purchases and 8.5 

percent for vegetable purchases. The additional effect of the actual redeemed 

value of the coupon, though statistically signifi cant, is quite small in terms of 

the impact on interpurchase time dropping an additional fraction of a percent 

for both fruits and vegetables (table 3). To put these coupon effects in a broader 

context, note that a standard price effect has a small, but statistically signifi cant 

effect on interpurchase time and the store or other promotion decreases interpurchase time by 0.02 percent for fruits and 3.8 percent for vegetables. 

From both an information and a discount effect, coupons encourage households to buy a greater quantity of fruits and vegetables in the weeks in which 

they make a purchase. For fruits, the use of a coupon in a given week raises 

quantities purchased by 3.9 percent (information/advertising effect), while 

the actual discount value has a small but signifi cant marginal effect (coupondiscount effect) as well. For vegetables, the information/advertising effect is 

even greater, increasing purchase quantities by over 10 percent, with again a 

small, but statistically signifi cant, coupon-discount effect. Comparing these 

coupon effects to other price and promotion options, we fi nd that the qualityadjusted standard price-discount effect would be an increase in fruit purchases of 5.5 percent and vegetable purchases of 5.6 percent for a 10-percent 

decrease in the shelf price, while store-based promotions increase fruit and 

vegetable purchases by 4.0 and 1.6 percent, respectively.

Seasons

Seasonality also plays a role in household fruit and vegetable purchases. 

For fruits, households purchase the least in the winter and most in the summer. For both fruits and vegetables, the time between purchases is longer in 
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summer and fall, but shorter in spring relative to winter. Households buy a 

small, but statistically signifi cant amount more vegetables in the spring relative to other seasons (table 3).

Household Characteristics

Household characteristics shape tastes and preferences for fruits and vegetables 

and are important factors in determining purchase behavior. Higher-income 

households are found to purchase both fruits and vegetables in greater amounts 

and with greater frequency than lower-income households. Larger households 

purchase larger amounts of fruits and vegetables than smaller households, 

which is intuitive, but purchase fruits and vegetables less frequently. 

Regarding household race and ethnicity, Caucasian households are found to 

buy fewer fruits per week relative to all other races, and fewer vegetables relative to Hispanic and Asian households. However, Caucasian households buy 

fruits and vegetables more frequently than African-American households. 

Hispanic households buy fruits most frequently, while Asian households buy 

the largest quantities of vegetables (table 3). As was mentioned before, fruits 

and vegetables in this study include all products (e.g., potatoes) and in all 

formats (e.g., frozen and canned). 

Table 3

Elasticity estimates of purchase and interpurchase time equations for fruits and vegetables

Fruits Vegetables

Purchase 

quantity

Interpurchase 

time

Purchase 

quantity

Interpurchase 

time

Estimate t-ratio Estimate t-ratio Estimate t-ratio Estimate t-ratio

Number of households 3.9024 3.08 -12.083 -5.77 10.027 7.17 -8.5858 4.33

Coupon face-value effect 0.0092 6.26 -0.0004 -3.53 0.0031 2.63 -0.0007 -2.16

Shelf-price effect -0.5466(*) -11.16 0.0746 5.44 -0.5652(*) -10.64 0.0064 3.97

Other, noncoupon promotion effect (dummy) 4.0445 7.46 -0.0179 -4.03 1.6068 4.64 -3.8470 -4.31

Household income 0.1046 2.67 -0.0633 -5.35 0.0821 8.74 -0.0473 -3.54

Household size 0.7613 9.12 0.1105 2.26 0.4153 3.48 0.2122 4.81

Age of female head -- -- -0.5678 -19.2 -- -- -0.5202 -10.98

Employment of female head -3.5500 -1.86 9.9305 3.77 -1.5596 -1.21 11.159 4.51

Education of female head 7.5804 3.83 -5.1563 -4.58 4.5077 3.35 -2.6065 -3.99

Black 8.8091 3.25 15.630 3.58 0.5287 0.32 17.066 7.61

Hispanic 14.779 3.93 -7.1803 -2.46 3.9749 1.98 -4.6573 -2.54

Asian 22.662 4.50 0.4979 1.07 18.713 5.77 -8.8954 -4.71

Spring 6.5526 7.22 -5.2757 -2.92 1.5256 2.30 -10.467 -3.35

Summer 39.605 2.43 5.9079 4.79 -0.3275 -0.42 5.5825 2.28

Fall 12.070 6.78 13.812 6.63 -0.7290 -1.23 19.802 4.88

(*) Prices are quality-adjusted. The estimates for unadjusted prices (unit value) are -0.6920 for fruits and -1.0104 for vegetables. 

See appendix A for the details of the adjustment.

(**) For the dummy variable, the elasticity is the percentage change in the dependent variable between the dummy taking the value 0 and 1.

Source: USDA, Economic Research Service.
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Application of Results Through 

a Simulation

In order to get a sense of how the elasticity estimates presented here would 

translate into a hypothetical coupon policy created to increase fruit and vegetable consumption, we conducted a simulation exercise using the following 

scenario. Suppose that a Government agency supplied a paper coupon4 to 

a targeted subpopulation. The coupon would be valid for 10 percent off the 

price of any fruit and vegetable purchased in a given time period. Given the 

inverse relationship of purchase frequency and interpurchase time, we can use 

our elasticity estimates to simulate the impact of this hypothetical 10-percent 

off all fruit and vegetable prices to contrast with a standard (noncoupon) price 

discount. We use the elasticity estimates from table 3 to estimate the impact of 

this coupon plan on fruit and vegetable purchases and compare the dual effect 

from the coupon to the predicted effect from a noncoupon price discount. 

A key driver of this analysis is the coupon usage rate assumed in the policy 

simulation.5 It is uncertain exactly what share of eligible households that 

receive this coupon would actually use it when making fruit and vegetable 

purchases. Standard manufacturer coupons are usually used at a low rate, 

partially due to the untargeted nature of the distribution of these types of coupons and partially due to the fact that most coupons are brand- or productspecifi c. For example, in the 2004 Homescan data used in this study, coupons 

were used in the purchase of fruits in 3.7 percent of the purchase weeks, 

while coupons were used in 2.5 percent of the purchase weeks for vegetables. 

However, the Homescan data used in our analysis also showed that 12 to 20 

percent of households used coupons at least some of the time when purchasing fruits and vegetables, implying that increasing the frequency of usage by 

current coupon users may be possible. 

Although one might argue that the usage rate in our policy simulation would 

be lower than the observed rate in Homescan since low-income households 

may have lower initial preferences for fruits and vegetables, we believe that 

the usage rate is more likely to be larger because:

1. the targeted (low-income) population would have more ready access 

to the coupons and may be more price-sensitive than the overall 

Homescan population, and

2. the coupons would be usable for all fruits and vegetables, not just a 

specifi c brand or type.

How much higher the usage rate would be is an open question, but there is 

some evidence that a targeted coupon can yield signifi cantly higher usage 

rates. For example, the 2008 Government Accountability Offi ce report Food 

Stamp Program: Options for Delivering Financial Incentives to Participants 

for Purchasing Targeted Foods cites results from pilot studies that show 

usage rates of coupons to targeted groups to be over 80 percent.6 We calculate the effect of the 10-percent coupon at three possible usage rates: 10, 30, 

and 50 percent (table 4).7

4Our analysis is based on conventional paper coupons. Additional testing of 

distribution methods would be needed 

before fully applying our results from 

paper coupons to electronic methods of 

distribution and/or redemption.

5It should be noted at this point that 

some of the coupon research literature 

focuses on coupon redemption rates, 

defi ned as the number of redeemed 

coupons divided by the total number of 

coupons distributed by manufacturers 

and retailers. This redemption rate is 

usually smaller than the coupon usage 

rate discussed and used here. A coupon 

usage rate is defi ned as the percentage of purchases in which households 

use a coupon when buying fruits and 

vegetables in a given time period.

6The 2008 GAO report also discusses 

the relative strengths and weaknesses of 

paper versus electronic coupons.

7Results of the simulation with usage 

rates of 1, 5, and 100 percent are also 

available from the authors upon request 

and details of the simulation estimation 

procedure are provided in appendix B.
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For the 10-percent coupon usage rate case, we fi nd that lowering prices by 

10 percent with a coupon would increase average weekly quantity purchases 

by 2 percent for fruits and 2.1 percent for vegetables, with the informational/

advertising effect comprising 85 percent of the total coupon effect for fruits 

and 89 percent of the total effect for vegetables.8 The 30-percent usage rate 

simulation shows, not surprisingly, a larger effect—over 6 percent for fruit 

and over 6.5 percent for vegetables—while the 50-percent usage rate simulation results show just over a 10-percent effect for each category (table 

4), These overall effects are a function of both aspects of the coupon, with 

the information effect dominating the price-discount effect, not surprising 

given the low relative value of most paper coupons.9 Our results show that 

merely the use of a coupon at all for a given purchase increases the quantities 

purchased over time regardless of the exact amount of the coupon discount 

within the normal range of coupon values (usually anywhere from $0.25 to 

$1.50 off). The sum of the coupon effects can be contrasted with a standard 

(noncoupon) price effect of 6.2 percent for fruit and 5.7 percent for vegetables that would arise from a price discount alone. This implies that the 

effectiveness of a coupon policy as compared with a pure price discount is a 

function of exactly how often consumers actually use the coupons they are 

given. If consumers use coupons more than 30 percent of the time, then the 

effect on fruit and vegetable purchases will be larger than that which would 

result from a pure price discount, assuming that our estimated underlying 

effects do not decline as usage rates rise. If usage turned out to be less than 

30 percent, then the overall effect of coupons would be lower than a pure 

price-discount policy.

8Without reporting a coupon usage 

rate, Ward and Davis found that at the 

price of 0.5 cent/ounce, a 5-cent coupon would increase frozen concentrated 

orange juice purchases by about 30 

percent. They estimate that, at the price 

of 1 cent/ounce, a 5-cent coupon would 

increase frozen concentrated orange 

juice purchases by about 12 percent, 

where the informational/advertising 

effect of a 5-cent coupon would be 

75 percent to 95 percent of the total 

coupon effect given the price range of 

0.5 cent/ounce to 1 cent/ounce.

9The informational/advertising effect 

is 85 to 89 percent of the total effect in 

each of these simulations.

Table 4

Simulation results comparing the percentage changes in purchase quantity and purchase frequency of 

fruits and vegetables for a pure price discount and a 10-percent-off coupon by coupon usage rate, 20041

Fruits Vegetables

Pure 

price 

effect

Coupon effect Pure 

price 

effect

Coupon effect

10% 

usage 

rate

30%

usage 

rate

50%

usage 

rate

10% 

usage 

rate

30%

usage 

rate

50%

usage 

rate

Purchase frequency: Total effect 0.75 1.31 3.98 6.73 0.06 0.91 2.88 4.85

Advertising/information effect 1.30 3.94 6.66 0.90 2.73 4.59

Coupon discount effect 0.01 0.04 0.07 0.01 0.15 0.26

Quantity during purchased weeks: Total effect 5.47 0.69 2.07 3.45 5.65 1.23 3.70 6.16

Advertising/information effect 0.39 1.17 1.95 1.00 3.01 5.02

Coupon discount effect 0.30 0.90 1.50 0.23 0.69 1.14

Average weekly quantity2: Total effect 6.22 2.00 6.11 10.31 5.71 2.14 6.66 11.24

Advertising/information effect 1.69 5.17 8.74 1.90 5.82 9.84

Coupon discount effect 0.31 0.94 1.57 0.24 0.84 1.40

1See appendix B for details of how these calculations are derived from the elasticity estimates of table 3.

2The average weekly quantity effect is the sum of the effect from purchase frequency and quantity purchased during purchased weeks.

Source: USDA, Economic Research Service.
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In our simulation estimates based on the traditional paper coupon, we 

assume that the information effect of coupons would not be diminished 

by an increased use of coupons. One could argue that the informational 

effect of coupons would decline as coupon use became more common 

since the added boost from additional information about the availability of 

discounted fruits and vegetables unique to a coupon would not be as large 

once consumers became accustomed to the coupons. Another argument is 

that the form of coupon distributed may impact usage rates and information 

effects. For example, a paper coupon may have a larger information effect, 

but lower usage rate, than an electronic coupon. However, it may also be 

the case that the coupon price-discount effect would increase with electronic coupons and approach the pure price-discount effect as usage rates 

increase, implying that as long as some positive information effect remains 

from a coupon that coupons would provide a larger overall impact than 

would a pure price discount alone. 

There are also some more general concerns regarding the implementation of 

a coupon policy:

• The data used in our study is for the overall population using coupons available to any consumer, while a targeted coupon policy would be restricted to 

use by only certain consumers and therefore negative stigma associated with 

coupon use may be a problem regarding potential usage rates.

• Our data include all fruit and vegetable purchases (for at-home consumption), but most coupons are not for fresh fruits and vegetables. Previous 

work has shown that coupons work well for branded items. A pilot or test 

program would be appropriate to compare the effect of coupons on fresh 

versus canned/frozen produce to see if the effects we estimate, and then 

simulate from, are, in fact, applicable on a larger scale.

• Coupons have the potential to be sold, if they are transferable. This may 

be a good reason to implement the coupons electronically with a safeguard that ensures exclusive use by the intended individual or group.

• As with any suggested program or policy, the full costs of implementation need to be compared with an estimate of social benefi ts from 

increased consumption of fruits and vegetables and the related health and 

nutritional impacts before any wide-ranging program is implemented.

Additional research or a pilot study could address:

1. how low-income households compare with higher income households in coupon usage.

2. how coupons made available only to qualifying low-income households would differ in usage as compared with those currently made 

available to the general public.

3. the extent to which coupon usage would differ if coupons were 

distributed via a Government program as compared with manufacturer coupons.
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4. how product or brand-specifi c coupons differ from more general 

coupons.

5. how consumers would respond to a more general coupon that would 

include fresh fruits and vegetables, which do not often have coupons 

available in the current retail environment.10

10One exception to the general lack 

of coupons or price discounts in the 

retail market for fruits and vegetables 

is the recent development of programs 

that provide vouchers for purchase of 

fresh fruits and vegetables at farmers 

markets. Over the past 5 years a number 

of farmers markets, charitable foundations, local governments and nonprofi t 

organizations have collaborated on pilot 

programs to improve the health and 

nutrition of low-income families by offering vouchers that can be used to buy 

fruits and vegetables at farmers markets. 

These vouchers provide what is in 

effect up to a 50-percent discount on 

fruit and vegetable prices and are used 

by over 80 percent of recipients when 

distributed at the point of purchase (at 

the farmers market). Schumacher et al. 

(2009) provides details for a number of 

these programs that are currently run in 

New York, Massachusetts, Maryland, 

and California.
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References

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Brand Choice Behavior,” Journal of Marketing Research (24):370-76.

Blattberg, R., and S. Neslin. 1990. Sales Promotion: Concepts Methods, 

Strategies, Prentice Hall: Englewood Cliffs, NJ.

Boizot, C., J-M Robin, and M. Visser. 2001. “The Demand for Food 

Products: An Analysis of Interpurchase Times and Purchased Quantities,” 

The Economic Journal (April):391-419.

Chintagunta, P., D. Jain, and V. Vilcassim. 1991. “Investigating 

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Cox, D., and D. Oakes. 1984. Analysis of Survival Data, London: Chapman 

and Hall.

Deaton, A. 1990. “Price Elasticities from Survey Data: Extensions and 

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Deaton, A. 1988. “Quality, Quantity, and Spatial Variation of Price,” 

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Deaton, A. 1987. “Estimation of Own- and Cross-Price Elasticities from 

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Dong, D., H.M. Kaiser, and O. Myrland. 2007. “Quantity and Quality Effects 

of Advertising: a Demand System Approach,” Agricultural Economics

(36):313-324.

Dong, D., and H.M. Kaiser. 2005. “Coupon Redemption and Its Effect 

on Household Cheese Purchases,” American Journal of Agricultural 

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Dong, D., and B.H. Lin. December 2009. Fruit and Vegetable Consumption 

by Low-Income Americans: Would a Price Reduction Make a Difference? 

ERR-70, USDA, Economic Research Service. 

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Communities,” Journal of the American Dietetic Association

104(7):1158-1161.

Erdem, T., M. Keane, and B. Sun. 1999. “Missing Price and Coupon 

Availability Data in Scanner Panels: Correcting for the Self-Selection 

Bias in Choice Model Parameters,” Journal of Econometrics

(89):177-196.

Greene, W. 2000. Econometric Analysis, Upper Saddle River, NJ: 

Prentice Hall.
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Gupta, S. 1988. “Impact of Sales Promotion on When, What and How Much 

to Buy,” Journal of Marketing Research (25):342-355.

Helsen, K., and D. Schmittein. 1992. “How Does a Product Market’s Typical PricePromotion Pattern Affect the Timing of Households’ Purchases? An Empirical 

Study Using UPC Scanner Data,” Journal of Retailing 68(3):316-338.

Herman, D., G. Harrison, A. Afi fi , and E. Jenks. 2008. “Effect of a Targeted 

Subsidy on Intake of Fruits and Vegetables among Low-Income Women 

in the Special Supplemental Nutrition Program for Women, Infants, and 

Children,” American Journal of Public Health, Volume 98, No. 1 (January), 

pp. 98-105. 

Jain, D.C., and N.J. Vilcassim. 1991. “Investigating Household Purchase 

Timing Decisions: A Conditional Hazard Function Approach,” Marketing 

Science 10(Winter):1-23.

Kiefer, N.M. 1988. “Economic Duration Data and Hazard Functions,” 

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Lancaster, T., 1990. The Economic Analysis of Transition Data, Cambridge, 

UK: Cambridge University Press.

Lee, J., and M. G. Brown. 1985. “Coupon Redemption and the Demand for 

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Leibtag, E. December 2006. The Impact of Big-Box Stores on Retail Food 

Prices and the Consumer Price Index, ERR33, USDA, Economic 

Research Service.

Neslin, S., C. Henderson, and J. Quelch. 1985. “Consumer Promotions and 

the Acceleration of Product Purchases,” Marketing Science 4(2):147-165.

Park, K., and M. Gomez. March 2004. The Coupon Report: A Study of 

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Schumacher, A., R. Winch, and A. Park. November 2009. Fresh, 

Local, Affordable: Nutrition Incentives at Farmers’ Markets 2009 

Update,Wholesome Wave, Westport, CT, accessed online on at http://wholesomewave.org/news-reports/reports-research/ on 4/1/10. 

Silva-Risso, J.M., and R.E. Bucklin. 2004. “Capturing the Effect of Coupon 

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Management 13(6):442-452.

U.S. Government Accountability Offi ce. July 2008. Food Stamp Program: 

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(August):393-401.
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Appendix A: Marked Purchase Renewal 

Model With Coupon Effects

The marked purchase renewal model is also called a marked failure time 

model (Cox and Oakes, 1984). This model contains two equations: interpurchase time and purchase quantity. The interpurchase time (the duration 

separating consecutive nonzero purchase weeks) represents the failure time, 

and the quantity bought represents the mark. In the marked purchase renewal 

model, each purchase is interpreted as a failure of maintaining the nonpurchase status, and the length (number of weeks) of nonpurchase and the 

amount of purchase are both determined by the household’s demographic and 

social economic variables.

The length of nonpurchase status or the interpurchase time is modeled as a 

random variable that follows a certain probability distribution. By defi nition, 

the distribution of interpurchase times in a market captures the effect of the 

time elapsed since the last purchase on the timing of the next purchase. This 

distribution, in general, is also infl uenced by marketing variables and household characteristics. In the existing literature, the hazard function approach 

is widely used to model the effects on interpurchase time (Kiefer, 1988). The 

hazard function is the conditional probability that an event will occur after a 

given period of time based on the amount of time already passed, contrasted 

with an unconditional probability of the duration of time between two events 

under any circumstances. The hazard function, in other words, is the rate at 

which events occur. By defi nition, the hazard function needs only to be fi nite 

and nonnegative, whereas the probability-density function must also integrate 

to one, so use of the hazard function is easier to model in practice, which 

makes it an intuitively appealing method by which to study purchase-timing 

decisions (Jain and Vilcassim, 1991). 

In our econometric model, we assume that household i faces an occasion to 

purchase a good. The purchase occasion is measured in calendar time, in our 

case, in weeks.1 We further defi ne i Dt as the time in weeks that has passed 

between the last purchase of that good and purchase occasion t

i

. If we use t

i

to index all of household i’s purchase occasions, and t

i

 is the series number 

of 1, 2, until Ti

, then i Dt is the interpurchase time and is a random variable 

that follows a certain distribution. Ti

 is the actual total number of purchase 

occasions or the total number of the interpurchase times household i experiences. The value of Ti

 varies across households. The hazard function of i Dt

can be defi ned as

where 12 34 exp i ii i i t tt t t θ = γ+ γ+ γ+ γ (W V C F ) and i Wt is a vector of household-related variables; i Vt is the unit value (price per pound) paid by household i at time t

i

 without any adjustment for coupon use; i Ct is a dummy 

variable indicating whether at least one coupon was used in a given week or 

not; i Ft is the dollar value sum of all redeemed coupons in a given week; s

are parameters; i

 represents a household-specifi c effect that is not included 

in i Wt , i Vt , i Ct , and i Ft ; and is the hazard parameter.

1The interpurchase time could be 

defi ned as number of days as did, for 

example, Helsen and Schmittlein, 1992. 

We use weekly data instead of daily to 

stabilize the estimation of the quantity equation. A great number of daily 

transactions of fruits and vegetables 

are very light, for example, a clove of 

garlic, a bunch of green onions, etc. 

The possible bias of using weekly data 

could be small, since most households 

do grocery shopping on a weekly basis 

according to the 2004 Nielsen panel 

data.

1 (1) i ii t tt i (D ) D , α α− λ = αθ ε
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Equation (1) implies that the hazard function of interpurchase time i Dt (i.e., 

the probability of a household making a purchase given that no purchase 

has been made up to time i Dt ) depends on i Dt , the interpurchase time, in a 

monotonic relationship. Equation (1) belongs to a Weibull family, and the 

hazard function increases in duration ( i Dt ) if  > 1, decreases if  < 1, and is 

constant if  = 1.2 Thus the Weibull distribution captures the various duration dependencies in the value of . Duration dependence indicates that the 

conditional purchase probability increases or decreases with the time elapsed 

since the last purchase. If the probability increases with the time elapsed 

since the last purchase, it is called a positive dependence. If the probability 

decreases with the time elapsed since the last purchase, it is called a negative 

dependence. If the probability remains the same as time elapses since the last 

purchase, it is called an independent duration. In the last case, the conditional 

distribution of i Dt is exponential with parameter it θ . The estimation of (1) 

can be obtained by maximizing the marginal log likelihood function proposed by Boizot, Robin and Visser (2001).

The household purchase amount is defi ned as3 

123 (2) Q ii i i i i tt t t t t = β+ β + β + β + XV C F u

where Q it is the i

th household’s purchases of the commodity (with the commodity index suppressed) at time t

i

; i Xt is a vector of socio-economic and 

demographic variables; i Vt is the logarithm of the unit value (price per 

pound); i Ct is the coupon dummy variable, and i Ft is total dollar value of 

all coupons redeemed in a given week as defi ned in equation (1); s are 

parameters to be estimated; and i

t u is an error term. There are a number of 

ways to incorporate coupon effects into a demand function (e.g., the netprice method (Chintagunta et al., 1991) and the separating-redeemed-value 

method (Dong and Kaiser, 2005)). The net-price method suffers from biased 

model estimates since the coupon discount is included in the net price, while 

the separating-redeemed-value method does not allow for both the price and 

informational effects of coupons to be estimated. We therefore follow the 

method discussed in Silva-Risso and Bucklin (2004) in equations (1) and (2), 

as this seems to be the most appropriate method to capture coupon effects in 

this context. The use of both a coupon dummy and coupon discount value 

is necessary because coupon usage rates increase with coupon face values 

(Blattberg and Neslin, 1990). The potential infl ation or defl ation of redemption rates due to coupon face values can be controlled by incorporating 

redeemed coupon values in the model (Silva-Risso and Bucklin, 2004).

Since i Vt , the unit value (price per pound) in (1) and (2), is derived from the 

observed expenditure and quantity purchased in a given week, it is an endogenous variable not truly independent of the quantity purchased in a given 

week, so we defi ne it as a function of i Zt , a vector of socio-economic and 

demographic variables to address this endogeneity issue:4 

(3) ii i V Z v, tt t = α+

where it v is an error term. In order to capture household heterogeneity effects, 

both i

t u and it v are assumed to have an error component structure (Greene, 

2000). The predicted value of i Vt from equation (3) is used in the estimation 

2The Weibull distribution is a 2-parameter family, in contrast to the 1-parameter 

exponential distribution. First identifi ed 

by Maurice Frechet in 1927 and later 

described in detail by Walloddi Weibull 

in 1951 and named after Weibull, the 

Weibull distribution is more fl exible in 

the statistical analysis of duration data.

3It would be ideal to estimate a structural model in which the interpurchase 

time variable is explicitly included in 

the right hand side of the quantity equation in order to fi nd the direct effect of 

interpurchase time on quantity. But the 

model would be hard to estimate given 

the Weibull distribution of the hazard 

function. The model we estimated is a 

reduced form. Though we don’t have 

the direct effect of interpurchase time 

on quantity, we do have the unbiased 

estimates of coupon effects on both 

interpurchase time and quantity.

4The coupon value, like the unit 

value price, may also be considered 

an endogenous variable. For example, 

Dong and Kaiser (2005) and Erdem, 

Keane, and Sun (1999) address this 

possibility by defi ning an additional 

coupon redemption equation. In their 

studies, the missing values of coupon 

usage for nonpurchase observations 

are determined simultaneously with 

the purchase amount. This procedure is 

necessary to correct for the selectivity 

bias when all the observations including zero purchases are used. In this 

study, however, we avoid the selectivity problem by using only the positive 

purchase observations together with the 

interpurchase time analysis.
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of (1) and (2). The maximum likelihood estimation procedure is adopted to 

obtain parameter estimates of equations (1) to (3).

The parameter estimates of (1) to (3) are presented in appendix tables A-1 to 

A-3. The estimated hazard parameter () for the duration is 1.29 for fruits and 

1.26 for vegetables, and both are greater than 1, indicating that the hazard function increases monotonically. This means that the probability of purchase at the 

present time increases as the time from the last purchase becomes longer. 

The estimated coeffi cients presented in appendix tables A-1 to A-3 can be 

transformed into elasticities. To do so, we evaluate the coeffi cients of interest at the predicted values of the interpurchase time, the quantity purchased 

and the unit value. The prediction of unit values and purchases using (2) 

and (3) is straightforward:

(4) i i E(V ) Z t t = α

123 (5) i ii i i E(Q ) X V C F . ttt t t = β+ β + β + β

The prediction of the time between purchases is a bit more complex, but can 

be obtained as follows. According to Lancaster (1990), the hazard function 

can be rewritten as

(6) i i t t ln(D ) ln( ) ln( ), α α =− θ + π

in which  follows a type 1 extreme value distribution, and

1

12 34 (7) exp i i i i i

/ E(D ) m( ) ( W V C F ), t tt t tα = π ⋅ − γ− γ− γ− γ

where m(1/is the 1/ moment of . The marginal effect of the explanatory variables i Wt , i Vt , i Ct and i Ft on the interpurchase time i Dt can be derived 

as

1

12 34 (8) exp

 

i

ii i i

i

i

t /

tt t t t

t

E(D )

m( ) ( W V C F ) ( ) H

E(D ) .

α ∂

= π ⋅ − γ − γ − γ − γ ⋅ −γ ∂

=− ⋅γ

where 1234 and i ii ii H (W ,V ,C ,F ) ( , , , ). t tt tt = γ= γ γ γ γ

The calculated elasticities for major variables using (4), (5), and (8) are provided in table 3 with one additional adjustment to account for the fact that a 

price measured in unit value terms (in this case, price per pound) for a number of different quality-level fruit or vegetable products mixes both quantity 

and quality changes into any estimated price effect. Since we have defi ned 

fruits and vegetables by aggregating over many different individual products 

whose derived price (unit value) captures not only the marketing price but 

the quality of the aggregate commodity, the unadjusted elasticity derived 

from these derived-price-effect coeffi cients presented in appendix tables A-2 

and A-3 would be inaccurate. If the quantity rather than quality of fruits or 

vegetables is the primary concern of the household, the optimal response to 

an increase in price is to switch to less expensive products with little sacrifi ce 
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in the amount purchased. In this situation, a change in price will generate a 

less-than-proportionate change in unit value. In other words, the same quantity difference will be ascribed to a smaller unit value difference (Dong and 

Kaiser, 2005). As a result, we need to separate the quality effect from the unit 

value effect to obtain the true price effect.

In order to do so, we follow Deaton (1987, 1988, 1990). The unit value i Vt

defi ned in equation (3) above encompasses both the exogenous marketing 

price and the product quality chosen by households. To account for the quality differences that exist in our aggregated unit value measures, we use the 

following formula developed in Dong, Kaiser, and Myrland (2007):

(9) [1 ], Q Q QV Q

P V VY Y η =η −η η η / (/)

where Q

P η is the quantity elasticity with respect to the unobserved price index 

(P), which is the quality adjusted price elasticity. Q

V η is the quantity elasticity 

with respect to the observed unit value (V), which can be obtained from the 

estimates of equation (2). Q

Y η is the quantity elasticity with respect to income 

(Y), which can be also obtained from equation (1). V

Y η is the unit value elasticity with respect to income (Y), which can be obtained from the estimates of 

equation (3). Equation (9) gives the true price elasticity that adjusts the quality effect from the estimated unit value elasticity.
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Promoting Fruit and Vegetable Consumption: Are Coupons More Effective Than Pure Price Discount? / ERR-96

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Table A-1

Estimates of interpurchase time equations for fruits and 

vegetables, 2004

Fruits Vegetables

Parameter Standard 

error

Parameter Standard 

error

Intercept -2.0312* 0.0145 -1.9891* 0.0172

Coupon dummy 0.1288* 0.0077 0.0898* 0.0099

Coupon redeemed value 0.0063* 0.0030 0.0254* 0.0048

Log unit value -0.0746* 0.0016 -0.0064* 0.0023

Log unit value lag -0.0517* 0.0015 -0.0156* 0.0022

Promotion 0.0181* 0.0023 0.0392* 0.0027

Spring 0.0542* 0.0045 0.1106* 0.0054

Summer -0.0574* 0.0039 -0.0543* 0.0046

Fall -0.1294* 0.0036 -0.1807* 0.0042

Log household income 0.0633* 0.0012 0.0473* 0.0014

Inverse household size 0.0613* 0.0091 0.1173* 0.0109

Age of female head 0.0109* 0.0001 0.0100* 0.0001

Employment of female head -0.0947* 0.0016 -0.1058* 0.0019

Education of female head 0.0529* 0.0015 0.0264* 0.0018

Children  6 years old 0.1027* 0.0033 -0.0095* 0.0040

Children 13 to 17 years old 0.0024 0.0027 -0.0186* 0.0032

Single-person households -0.0976* 0.0052 -0.1806* 0.0063

Black households -0.1452* 0.0023 -0.1576* 0.0027

Hispanic households 0.0745* 0.0033 0.0477* 0.0040

Asian households -0.0050 0.0042 0.0932* 0.0046

Other race households -0.0598* 0.0035 -0.0329* 0.0045

East 0.0169* 0.0022 0.0626* 0.0027

South -0.0004 0.0020 0.0522* 0.0025

West -0.0118* 0.0022 0.0925* 0.0027

Hazard parameter () 1.2927* 0.0014 1.2550* 0.0017

*statistically signifi cant at the 5-percent level.

Source: USDA, Economic Research Service.
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Promoting Fruit and Vegetable Consumption: Are Coupons More Effective Than Pure Price Discount? / ERR-96

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Table A-2

Estimates of purchase and unit value equations for fruits, 2004

Purchase equation Unit value equation

Parameter Standard 

error

Parameter Standard 

error

Intercept -0.5053 0.6614 0.0010 0.0996

Coupon dummy 0.1623* 0.0591 -- --

Coupon redeemed value 0.7299* 0.0121 -- --

Log unit value -2.7141* 0.3138 -- --

Promotion 0.1682* 0.0239 -- --

Spring 0.2725* 0.0401 -0.0152* 0.0042

Summer 1.6473* 0.0332 -0.0206* 0.0039

Fall 0.4930* 0.0395 -0.0260 0.0041

Log household income 0.4102* 0.0603 0.0402* 0.0089

Inverse household size -1.3564* 0.1457 0.0241* 0.0211

Age of female head -- -- -0.0094* 0.0005

Employment of female head -0.1477 0.0790 0.0060 0.0012

Education of female head 0.3153* 0.0785 0.0393* 0.0118

Black households 0.3664* 0.1068 0.0659* 0.0159

Hispanic households 0.6147* 0.1323 0.0241 0.0198

Asian households 0.9426* 0.1610 -0.0193 0.0275

Other-race households 0.4131* 0.1576 0.0289 0.0196

East -- -- 0.1423* 0.0140

South -- -- 0.0541* 0.0126

West -- -- 0.0241 0.0135

*statistically signifi cant at the 5-percent level.

Source: USDA, Economic Research Service.
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Promoting Fruit and Vegetable Consumption: Are Coupons More Effective Than Pure Price Discount? / ERR-96

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Table A-2

Estimates of purchase and unit value equations for vegetables, 2004

Purchase equation Unit value equation

Parameter Standard 

error

Parameter Standard 

error

Intercept 0.2911 0.5448 -0.3205* 0.0628

Coupon dummy 0.4181* 0.0661 -- --

Coupon redeemed value 0.5129* 0.0247 -- --

Log unit value -4.0835* 0.4790 -- --

Promotion 0.0670* 0.0181 -- --

Spring 0.0636 0.0344 0.0291* 0.0041

Summer -0.0137 0.0404 0.0566* 0.0038

Fall -0.0304 0.0311 0.0099* 0.0041

Log household income 0.3316* 0.0520 0.0640* 0.0056

Inverse household size -0.7344* 0.1128 0.0409* 0.0138

Age of female head -- -- -0.0047* 0.0003

Employment of female head -0.0650 0.0633 0.0102 0.0080

Education of female head 0.1880* 0.0638 0.0335* 0.0077

Black households 0.0220 0.0929 -0.0970* 0.0106

Hispanic households 0.1657 0.0980 -0.0320* 0.0123

Asian households 0.7803* 0.1372 -0.0860* 0.0197

Other-race households 0.0243 0.0435 -0.0430* 0.0183

East -- -- 0.0293* 0.0085

South -- -- -0.0343* 0.0079

West -- -- -0.0581* 0.0086

*statistically signifi cant at the 5-percent level.

Source: USDA, Economic Research Service.
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Promoting Fruit and Vegetable Consumption: Are Coupons More Effective Than Pure Price Discount? / ERR-96

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Appendix B: Calculating Simulation Effects 

From Elasticity Estimates

Given the inverse relationship between interpurchase time and purchase frequency, if the percentage change in interpurchase time is r, the percentage 

change in purchase frequency will be - r for continuous variables such as the 

pure price-discount effect and coupon discount effect presented in table 4 

and (–r/(1+r))*100 for a dummy variable, such as the coupon informational/

advertising effect also presented in table 4. Since the average weekly quantity is the product of purchase frequency and the quantity purchased during 

purchasing weeks, the percentage change in the average weekly quantity with 

respect to the change of a continuous variable (e.g., coupon discount effect) 

is the sum of these two changes. However, the percentage change in the average weekly quantity with respect to the change of a dummy variable (e. g., 

coupon advertising) is the sum of the two changes plus an additional term 

that captures the interaction between the two changes.

The current average coupon value over all purchase occasions is $0.05 for 

fruits and $0.02 for vegetables. Current average price per pound for all purchase occasions is $1.63 for fruits and $1.47 for vegetables. A 10-percent-off 

coupon at the current price level for a 10-percent coupon usage rate implies 

an average redeemed value of $0.0163 ($1.63*0.1*0.1) for fruits and $0.0147 

($1.47*0.1*0.1) for vegetables. This implies that redeemed coupon values 

would increase 33 percent for fruits and 74 percent for vegetables. Similarly, 

the 10-percent-off coupon at the current price level for a 30-percent coupon usage rate implies an average redeemed value of $0.0489 for fruits and 

$0.0441 for vegetables, an increase in redeemed coupon value of 98 and 221 

percent, respectively for fruits and vegetables. For a 50-percent coupon usage 

rate, the average redeemed value would be $0.0815 for fruits and$0.0735 for 

vegetables, implying that redeemed coupon values would increase 163 percent for fruits and 368 percent for vegetables.

The percentage change of interpurchase time and quantity with respect to 

the coupon discount value given the 10-percent-off coupon is *C, where 

C is the percentage change in redeemed coupon value and  is the elasticity of coupon face value. The percentage change of quantity with respect to 

the advertising effect given the 10-percent-off coupon is *C, where C is the 

assumed coupon usage rate and  is the elasticity of coupon advertising. The 

percentage change of interpurchase time with respect to coupon advertising 

given the 10-percent-off coupon is exp(-C)-1, where is the coupon dummy 

coeffi cient in the interpurchase time equation, with C = 10, 30, or 50 percent 

depending on the assumed usage rate.