The persistence of healthy behaviors in food purchasing∗†
Marit Hinnosaar‡
June 2022

Abstract
When a policy gives temporary incentives for healthy behaviors, how long does theimpact last? The U.S. Special Supplemental Nutrition Program for Women, Infants, andChildren gives food vouchers to young children and their mothers. Using household-level
scanner data, I study the reform of the program that introduced vouchers for healthierproducts. The difference-in-differences analysis shows that the reform makes purchases
healthier during the program participation in the product categories most targeted by
the reform (bread and milk). However, the effect is not always persistent. For bread,the effect decreases significantly within a couple of years after participants exit the
program. Demand model estimates imply that price differences between healthy andunhealthy products play a large role in decreasing the program’s impact. Therefore,∗

Researcher(s) own analyses calculated (or derived) based in part on data from Nielsen Consumer LLC
and marketing databases provided through the NielsenIQ Datasets at the Kilts Center for Marketing Data
Center at The University of Chicago Booth School of Business. The conclusions drawn from the NielsenIQ
data are those of the researcher(s) and do not reflect the views of NielsenIQ. NielsenIQ is not responsible for,
had no role in, and was not involved in analyzing and preparing the results reported herein.
†
I thank Alex Mas, Andre Trindade, Andrea Pozzi, Aureo de Paula, Avi Goldfarb, Aviv Nevo, David Rivers,
Erich Battistin, Garrett Johnson, Giovanni Mastrobuoni, Greg Veramendi, Isis Durrmeyer, Janet Currie,Jian-Da Zhu, Kim P. Huynh, Kosuke Uetake, Mario Pagliero, Michael Kummer, Toomas Hinnosaar, andseminar participants at the Collegio Carlo Alberto, Duke University, IFS, LSE, Royal Holloway, Universityof Bristol, University of East Anglia, University of Edinburgh, University of Essex, University of Houston,
University of Nottingham, University of Pittsburgh, University of Tennessee, Risky Health Behaviors workshop
at HCHE, Economics of Health Behaviours and Health Information workshop in London, IIOC, EARIE,
JEI, Econometric Society European Winter Meeting, and Dondena Workshop on Public Policy for helpfulcomments and suggestions. Earlier versions of the paper were titled “How long do healthy habits last? The
role of prices”.
‡
University of Nottingham and CEPR, e-mail: marit.hinnosaar@gmail.com.

1some differences in the persistence can be explained by the relatively higher prices ofhealthy foods. Counterfactual analysis shows that a modest post-program subsidy might
be a sustainable way to lengthen the program’s impact and lead to long-term healthierpurchases.

JEL codes: D12, I12, L66, I38
Keywords: Consumer behavior, dietary choices, long-term policy effects, WIC, foodsubsidy

1

Introduction

Obesity is a public health problem that leads to higher medical care costs and imposes
negative externalities (Cawley, 2015). One cause of obesity is an unhealthy diet. While adiet might be an individual’s optimal choice given budget and other constraints, the negative
externalities of obesity provide a rationale for government intervention. Indeed, governments
use various policies to improve diets, like fat and sugar taxes and regulation of nutrition
labeling and advertising. To reduce costs, policies, such as vouchers and subsidies on healthy
foods, often target specific products and give only temporary incentives. When designing andevaluating such policies, it is important to consider both their short- and long-term impacts.
This paper studies three questions. First, what is the impact of healthy food subsidies
on consumption? Second, how long does the impact last after the subsidies end? Third,
what role do prices have in affecting the persistence of the policy impact? Often, the healthy
product is more expensive than its unhealthy substitute. A price-sensitive person, evenwhen she otherwise prefers a healthy option, might not buy it because of the price difference.
Therefore, temporary incentives might not change the long-run behavior even if these didchange preferences.
Specifically, I study a U.S. federal program, the Special Supplemental Nutrition Program2

for Women, Infants, and Children (WIC). WIC gives vouchers for specific foods to children
up to their fifth birthday and their mothers. The program provides a good setting for the
study. The 2009 WIC policy reform changed the composition of food vouchers, introducing
vouchers for healthier products. By providing free healthy products for a few years, thepost-reform program gives temporary incentives to eat more healthily.
In the analysis, I use NielsenIQ household-level scanner data of grocery purchases. The
dataset includes information on households’ demographic characteristics and WIC status. I
focus on the product categories included in the WIC food vouchers. To compute the productprices, I also use the NielsenIQ Retail Scanner Data.
To estimate the short- and long-term impacts of the healthy food subsidies, I use the WIC
program reform that changed the composition of the food vouchers and introduced vouchers
for healthier products. The advantage of the dataset is observing the same household in threestates—before, while, and after receiving the WIC subsidies. I examine two groups of WIC
households—those exposed to the old program and those exposed to the new program—andcompare their within-household changes in purchases when the households start and stop
receiving the vouchers. The main empirical strategy is a difference-in-differences analysis withhousehold and time period fixed effects. A possible concern with the identification strategy isthe existence of time-varying factors specific to the households that receive the post-reform
WIC subsidies. While households starting to receive the subsidies either pre- or post-reform
are likely to be subject to similar shocks (related to the child’s birth), they might choose tostop receiving the vouchers because post-reform vouchers are different. To address the concern,
I also examine changes in purchases when households become ineligible for the vouchers
when the child becomes five years old. I perform a number of additional robustness checks,
including providing the heterogeneity-robust difference-in-differences estimates proposedby de Chaisemartin and D’Haultfœuille (2020a,b) to correct for the possible bias of thetwo-way fixed effects estimator when treatment effects are heterogeneous, and propensity
3

score matching estimators.
I find that the program reform makes purchases healthier during the program participationin the product categories most targeted by the reform. Specifically, it changed purchasesof bread and milk, as the post-reform vouchers were restricted to whole wheat bread andlow-fat milk. For bread, the effect decreases significantly within a couple of years afterparticipants exit the program. For milk, the estimates are imprecise and don’t allow rulingout that the effect is persistent. Typically, healthy products tend to be more expensive thanunhealthy alternatives, but in the case of milk, in some regions, it is the opposite; that is, thehealthy option is cheaper. Using exogenous regional differences in milk pricing, I show thatwhen we restrict attention to states where the healthy option is not cheaper, the long-term
impact is smaller than the short-term. The reform also modified the quantity of products inthe vouchers. There are no statistically significant short- or long-term effects on the total
quantities purchased of any of the products in the WIC vouchers: bread, milk, fruits andvegetables, juice, eggs, and cereals. But for several products, the estimates are imprecise anddon’t allow rejection of sizable positive or negative effects. Note that we don’t necessarily
expect sizable effects on total quantities because the vouchers are smaller than the typicalconsumption for several products.
To examine the long-term impact of healthy food subsidies on preferences and separate itfrom the role of prices, I estimate a demand model. I model demand using a discrete choicerandom coefficient multinomial logit model, allowing the long-term stock of past consumption
to affect current tastes. Again, the policy reform provides an exogeneous variation in thepast consumption, helping to identify its effect. Using the demand model estimates, I run
a counterfactual analysis to study how to lengthen the program’s impact. Demand model
estimates imply that price differences between healthy and unhealthy products play a largerole in decreasing the program’s impact. Thus, some differences in the persistence of the
impact can be explained by the relatively higher prices of healthy foods. Counterfactual4

analysis shows that a modest post-program subsidy might be a sustainable way to lengthen
the program’s impact and lead to long-term healthier purchases.
While the paper studies a specific program, many settings have similar concerns. For
example, aid programs in developing countries provide free essential health products, whichhouseholds should continue to obtain indefinitely, but programs’ budget constraints preventthe perpetual supply of free goods. Combining temporarily free products with long-term
subsidies might be a more sustainable way to lengthen the impact of the programs. Overall,
the results imply that when a planner designs a public health policy or a firm chooses a
product line, the trade-off between short-term and long-term effects should be considered.
The paper contributes to the literature in economics that studies nutritional choices. The
literature has shown that prices matter (Dubois et al., 2014; Khan et al., 2016), but alsothat nutritional choices are persistent and difficult to change (Atkin, 2013, 2016; Ma et al.,2013; Oster, 2018; Allcott et al., 2019a).1,2 The current paper contributes to the literature byanalyzing the role of prices and the persistence of nutritional choices together when studying
the impact of public policy.
The paper also adds a new finding to the literature on the long-term effects of temporaryinterventions. The evidence of long-term effects on health behaviors includes alcohol consumption (Kueng and Yakovlev, 2021), exercising (Charness and Gneezy, 2009; Royer et al.,2015), and smoking cessation (Giné et al., 2010). The growing experimental literature on the1

The finding of large persistence of nutritional choices is somewhat in contrast to the evidence from otherchoices, such as brand preferences and alcohol purchases. The past matters also for those (Eizenberg andSalvo, 2015; Sudhir and Tewari, 2015; Kueng and Yakovlev, 2021). But the extent is different, and there isevidence of forgetting (Mehta et al., 2004) and large adjustments to the new circumstances (Bronnenberg
et al., 2012; Hinnosaar and Liu, 2021).
2
There is also a large and growing literature on the impact of soda, sugar, and fat taxes including, among
others, Fletcher et al. (2010); Wang (2015); Harding and Lovenheim (2017); Muller et al. (2017); Bollinger
and Sexton (2018); Allcott et al. (2019b); Cawley et al. (2019); Dubois et al. (2020); Seiler et al. (2021). Other
topics the nutritional choices literature has studied include the role of restaurants (Anderson and Matsa,
2011; Currie et al., 2010), nutritional information (Bollinger et al., 2011; Moorman et al., 2012; Puranam
et al., 2017), bans on advertising (Dhar and Baylis, 2011; Dubois et al., 2018), and weight loss programs(Uetake and Yang, 2020).

5

long-term impacts of temporary incentives on nutritional choices has mixed results (including
List and Samek, 2015; Belot et al., 2016; Loewenstein et al., 2016; Belot et al., 2018). The
results in the paper are consistent with the work on informational treatments that has also
found evidence of depreciation of the effects (e.g., Bronnenberg et al. (2020)). The current
paper adds to the literature by illustrating the importance of prices in the persistence oftemporary interventions.
The paper also contributes to the literature on the impact of the WIC program. Literaturein economics studying the program has concentrated mostly on birth outcomes (Figlio et al.,2009; Hoynes et al., 2011), participation (Rossin-Slater, 2013), and the impact of WIC on
market outcomes (Meckel, 2020).3 Literature in nutrition science has studied the short-term
effects of the 2009 change in the WIC food package on WIC participants’ food consumption.4
Griffith et al. (2018) provide evidence based on a similar program in the UK. Only a coupleof studies address the persistence of WIC’s impact on purchases. In particular, Khan et al.
(2018) analyze the persistent impact focusing on brand loyalty in the breakfast cereals
category. The current paper extends the analysis to food healthiness, which the literature
has shown is more difficult to change than brand loyalty.5 Frisvold et al. (2020) also use
difference-in-differences analysis and the change in the WIC policy to estimate the impactof the WIC vouchers on purchases. In contrast to these papers, the identification in myanalysis takes advantage of a longer sample period combined with a policy reform, whichallows analysis of the same household before, while, and after receiving the WIC subsidies,comparing the changes in purchases of households receiving the subsidies before and after thepolicy reform. Furthermore, I provide evidence that the persistence of the program’s impact
depends on prices.
3

Hoynes and Schanzenbach (2015) provide an overview of the literature on WIC.
For overviews, see Schultz et al. (2015) and a report by the National Academies of Sciences, Engineering,and Medicine (NASEM, 2017).
5
For example, Allcott et al. (2019a) find only small adjustments in food healthiness when people move,
while Bronnenberg et al. (2012) find sizable adjustments in brand choices.
4

6

The rest of the paper is organized as follows. Section 2 describes the WIC program anddata. Section 3 estimates the impact of healthy food subsidies and its persistence. Section 4analyzes the role of prices. Section 5 concludes.

2

Background on WIC and data

2.1

Background on WIC

WIC is a U.S. in-kind food and nutrition assistance program targeted at mothers and children
0–4 years old. In 2016, eight million people participated in WIC per month, accounting forsix percent of U.S. food and nutrition assistance expenditures (Oliveira, 2017). The averagemonthly WIC program cost for food per participant was 43 dollars (Oliveira, 2017).
The following categories of people are eligible to participate in WIC: pregnant, breastfeeding (up to the child’s first birthday), and postpartum women (up to six months after birth);and children up to their fifth birthday.6 The income eligibility requirement to participate
in WIC is income not exceeding 185 percent of the federal poverty guidelines.7 The income
eligibility requirement is automatically satisfied if the individual or a family member is eligible
for SNAP, Medicaid, or Temporary Assistance for Needy Families benefits (for more, see
Oliveira, 2017). A large share of families with small children participate in WIC. According
to the USDA report (Oliveira and Frazao, 2015), in 2012, 51 percent of infants (up to theirfirst birthday) and almost 30 percent of pregnant and postpartum women and children aged
1–4 participated in WIC. Not everyone eligible participates in WIC. According to the USDA
report (Johnson et al., 2014), in 2011, the rate at which eligible individuals participated in
WIC was highest among infants (83%) and postpartum non-breastfeeding women (81%), and
6
USDA. Food and Nutrition Service. “WIC Eligibility Requirements.” Last published: August 3, 2016.
https://www.fns.usda.gov/wic/wic-eligibility-requirements.
7
States are allowed to decrease the eligible income cutoff, but in practice, in all states, it equals 185 percentof the federal poverty guidelines (Oliveira and Frazao, 2015).

7lowest among children aged 1–4 (54%). Those who participate tend to have lower incomes.8
WIC provides quantity vouchers for specific food items (except for fruits and vegetables,
which is a cash voucher). The set of foods in the WIC food package is small. Children aged
1–4 and women receive regular food items, which until 2009 included mainly milk, juice,cereal, eggs, legumes, and peanut butter. Infants, until their first birthday, receive infant
formula, infant cereal, and infant juice.
In 2009, there was a major change in the types of foods provided by WIC. The goal of
the change was to make WIC food packages consistent with new dietary guidelines. While
WIC was established to fight malnutrition in low-income families, over time, obesity becamea problem, and concerns were raised that WIC may contribute to child obesity (Oliveira andFrazao, 2009). The change added new foods: whole grain products, fruits, and vegetables.
Specifically, it added whole wheat bread. The change also introduced restrictions on the fat
percentage of milk. Specifically, whole milk was no longer allowed, except for one-year-old
children. Altogether, the 2009 reform was cost neutral, as it reduced the quantities of somefoods, in particular milk, juice, and eggs.9 The WIC food packages, with the changes over
the years, are shown in online appendix A.
The most controversial of the 2009 changes to the WIC food package was probably the
restriction on the fat percentage of milk. For the past several decades, dietary guidelines haverecommended decreasing dietary fat. But the medical and nutritional science literature has
no consensus on whether that is beneficial (for examples of recent overviews of the debate,
see Wang and Hu (2017); Ludwig et al. (2018)). However, the change in the WIC vouchers
8

More than two-thirds of WIC participants have incomes below the federal poverty level (Oliveira andFrazao, 2015). Less than three percent of participants have incomes above the upper limit. Income can beabove the limit because of automatic eligibility through other programs, which have higher income limits insome states.
9
Additional small modifications to the food package were made by the 2014 change in the regulations.
These changes further reduced milk fat percentage, allowing only low-fat (1%) or non-fat milk for children
2–4 years of age and women, and increased the cash voucher for fruits and vegetables. It also allowed states
to authorize whole wheat macaroni (pasta) products as substitutes for whole wheat bread and allowed partial
substitution of milk with yogurt.

8was made based on the report commissioned from the Institute of Medicine (2006). Thechange was consistent with the recommendations by the American Academy of Pediatrics:
whole milk for one-year-old children and 1% or non-fat for older children (Gidding et al.,2006). Therefore, despite the above-mentioned controversy, in this paper, to be consistent
with the goal of the WIC reform, I call the restrictions to the milk fat percentage healthy.

2.2

Data

In the paper, the main data source is the NielsenIQ Consumer Panel. To compute the productprices, I also use the NielsenIQ Retail Scanner Data.10 I use data that covers 11 years,
2006–2016. Nutritional information is obtained from the U.S. Department of Agriculture
databases (USDA, 2018a,b).
The Consumer Panel is representative of the U.S. population. The participating households
are asked to scan all their grocery purchases bought for personal at-home consumption. The
dataset includes UPC-level information of the purchased quantities and expenditures. The
reliability of the data was analyzed by Einav et al. (2010). In addition to purchases, thedataset has information on household demographic characteristics. Since 2006, the dataset
has provided yearly information on households’ self-reported WIC status.
I focus attention on categories that are in the standard WIC food packages for bothmothers and children. These are milk, bread, fruits and vegetables, juice, eggs, and cereals.11
The 2009 policy reform affected all these categories except cereals.12 Specifically, the new
10

Both datasets are from Nielsen Consumer LLC and marketing databases provided through theNielsenIQ Datasets at the Kilts Center for Marketing Data Center at The University of Chicago
Booth School of Business.
Information on availability and access to the data is available athttps://www.chicagobooth.edu/research/kilts/datasets/nielsenIQ-nielsen.
11
I don’t analyze the impact on dry beans and peanut butter, which are also included in the food vouchers,
but where a substitution is allowed between the products either by the household or in the state-level
regulation.
12
The 2009 policy reform included a minor change for cereals, which changed the choice set of available
products. It required that at least half of the cereal brands available to WIC households must be whole grain.
The reform did not require WIC households to purchase whole grain cereals.

9WIC food packages added bread and fruits and vegetables and decreased the quantity of milk,
juice, and eggs. Therefore, I will analyze the impact on the aggregate quantity of purchases inthese categories (aggregating across brands, package sizes, and other product characteristics).
Additionally, the reform required milk to be low-fat (except for one-year-old children) andbread to be whole wheat. Therefore, in the case of bread and milk, I also study the impact
on the type of product purchased (fat percentage for milk and whether bread is whole wheat).
Specifically, the analysis focuses on white dairy milk, loaves of bread, fruits and vegetables(including fresh, frozen, and canned), and juice (including concentrate and frozen). Milk ismeasured in gallons, bread in pounds, cereals in ounces, and eggs by count. To aggregate
together the more heterogeneous products, different fruits and vegetables, and different typesof juice (including concentrated), I measure the quantities of these categories in calories.13
Next, I outline the choices made in the construction of the datasets used in the estimation.
Further details are in online appendix B.

Dataset for reduced form analysis. In section 3, the reduced form analysis focuses onhouseholds that report receiving WIC assistance and that were in the Consumer Panel thelast year before, during, and the first and the second year after receiving the WIC vouchers.
This restriction allows analysis of within-household changes when a household starts andstops receiving the WIC vouchers.
In 2006–2016, in the Consumer Panel, 3414 households self-reported currently receiving
the WIC vouchers. In order to analyze within-household changes when households start
receiving the vouchers and two years after they have stopped receiving the vouchers, one
needs to observe the households for a minimum of four years (because WIC status in the
13

In the analysis, I include only products with UPCs (barcodes). The products without UPCs are nonpackaged items such as fruit, vegetables, meat, and baked goods. In the Nielsen dataset, only a small subsetof households are asked to record products without UPCs. To use a bigger sample of households and makepurchases of all households comparable, I exclude products without UPCs. Therefore, the measured quantityof fruits and vegetables is smaller than all fruit and vegetable purchases.

10

dataset is reported with yearly frequency). However, only 1336 of the households have been in
the dataset for that long. Moreover, only 571 households are observed before, while, and after
receiving the vouchers. Requiring that each household be observed the last year before andthe first and second years after receiving the vouchers reduces the sample to 347 households.
Table B1 in the online appendix summarizes how much each restriction decreases the sample.
How representative is the final sample of the WIC households in the Consumer Paneland the overall WIC population? Table B2 in the online appendix shows that the sample
and the excluded households are similar regarding education, race, and marital status. But
the households in the sample have a higher income (by 27%) and smaller size (by 13%), areless likely to be of Hispanic ethnicity (by 69%), and are less likely not to work full time (by12%). It also shows that, while the Consumer Panel matches the administrative data of the
WIC population rather well in terms of household size and race, it misses a large share of
low-income and a majority of Hispanic households. As has been already noted in the literature(Khan et al., 2016), the average income of WIC households in the Consumer Panel is morethan twice as high as in the administrative data. Also, over 40% of the WIC population is of
Hispanic ethnicity, while the percentage of Hispanic households in the Consumer Panel is only
about 12 and in the final sample only about four. Therefore, the results might not generalize
to the whole WIC population, especially low-income and Hispanic households. However, thefocus of the study isn’t only on the WIC population but, more generally, learning about the
impact of temporary incentives. The sample used in the analysis is somewhat more similar
to the overall U.S. population than is a typical WIC participant.
Table 1 presents the demographic characteristics of the households in the sample, theirregional locations, and summary statistics of their purchases. It compares the treatmentgroup, that is, those that receive WIC assistance after the policy change (column 1), to thosereceiving it earlier (column 2), and to an additional control group of other households with11

children or lower income or both (column 3).14 Specifically, the households in the additional
control group, for at least one year, had a child (up to 17 years old) or had income notexceeding 200% of the federal poverty guidelines, or both. In the first year in the sample,
52% of households in the additional control group had children, 54% had lower income,and 20% had both children and lower income. As the reform coincides with the end of
the recession, the question arises whether WIC households post-reform (treatment group)
differ from households pre-reform (the control group in column 2). While the households are
similar in income, household size, and marital status, the treatment group households are
more likely to be college-educated (by 20%), white (by 13%), and not employed full time(by 25%). However, none of the differences are statistically significant at the 1% level in
the Wilcoxon rank test.15 In the analysis, the differences will be absorbed by household
fixed effects. Figures B3–B6 in the online appendix present the distribution of purchases andchanges over time.
Not all households purchase all the food products in WIC vouchers each quarter. Whenthe outcome variable is the healthy bread or milk fat percentage, then the sample includes
only households for whom the quarterly variable is defined (who purchase bread or milk,
respectively) at least once per year and in total in at least two quarters. This restriction
is imposed because we cannot use the household in the analysis if the percentage is notdefined. When the outcome variable measures the quantity, then the sample includes all
households that buy any food products with UPCs in a given year. The restriction excludes
104 household years by 57 households from the additional control group of households withchildren or lower income or both.16 This restriction is imposed because when households don’t
14

Online appendix C shows that results remain similar if the non-WIC households are excluded.
Also, none of the differences in demographic characteristics in table 1 between the treatment (column 1)
and the second control group (column 3) are significant at the 1% level in the Wilcoxon rank test, except forhousehold size.
16
Sixteen of the 57 households never buy food products with UPCs. They are excluded from all the analysis,
including table 1.
15

12

Table 1: Summary statistics
Treatment group
Control groups
WIC
WIC
Children or
post-reform
pre-reform
low-income
(1)
(2)
(3)
Panel A: Demographic characteristics
Household income (thousands)
52.9
53.3
54.1
Household size
3.4
3.5
3.0
Race: white
0.755
0.670
0.815
Ethnicity: Hispanic
0.046
0.047
0.073
College
0.407
0.340
0.474
Married
0.730
0.717
0.652
Not employed full time
0.705
0.566
0.701
Panel B: Region
Northeast
10.8
17.9
16.5
Midwest
29.0
27.4
26.4
South
39.4
41.5
37.9
West
20.7
13.2
19.2
Panel C: Purchases (per household/quarter)
Bread (lb)
10.53
10.79
8.10
Bread healthy %
9.25
6.86
9.99
Milk (gallons)
9.30
9.03
6.61
Milk fat %
1.99
2.02
1.83
Fruits & vegetables (kcal)
8207.027936.33
7328.92
Juice (kcal)
5323.154827.27
3713.31
Eggs (count)
66.11
63.89
50.92
Cereals (oz)161.97159.00130.00
Number of households
241
106
96290
Note: Panel A presents the sample average demographic characteristics. Panel B shows the regional
distribution of households. Panel C presents households’ quarterly averages of purchases. All variables aremeasured during each household’s first year in the sample. An observation is a household. Sample consistsof households in the panel data fixed effects regressions. Column 1 includes households who received WIC
assistance after the 2009 policy change. Column 2 includes households who received WIC assistance only
before the 2009 policy change. Column 3 includes households who have children or lower income (income
below 200 percent of the federal poverty guidelines) or both. Income is deflated to 2015 dollars using theconsumer price index for urban consumers. Not employed full time indicates whether at least one household
head is not employed full time. Purchases do not include Nielsen random weight products. Bread healthy %is the percentage of whole wheat bread in all bread purchases.

report any food purchases with UPCs, they are not suitable for studying the changes in WIC
product purchases. These households either purchase only the food products without UPCs
(such as unpackaged fruits and vegetables, meat, or baked goods), only eat in restaurants, or
don’t report food purchases.
Figures B7–B8 in the online appendix provide a preview of the findings in the next section.

13

The cohorts entering the program pre- versus post-reform are rather similar regarding thelevels of purchases before receiving the vouchers. While receiving WIC post-reform vouchers,
healthy bread share increased and milk fat percentage decreased, but the effect reversed whenhouseholds stopped receiving the vouchers.

Dataset to estimate the demand model. In section 4, to keep the demand model
estimation manageable, I restrict attention to the sample of households that all have reported
receiving WIC assistance (households in columns 1–2 of table 1). The demand model isestimated using only the time periods before and after receiving WIC vouchers.17 I exclude
households that don’t have a sufficient number of bread purchases before and after receiving
the vouchers.
The demand model is estimated using data only on the bread category (for reasons thatwill be discussed in section 4). I aggregate all types of bread into four products. White
bread is a non-whole-grain bread made from white refined flour. Following WIC regulation, Iclassify bread as whole wheat bread if it contains 100% whole wheat flour. I classify breadthat is only partially made with whole wheat flour or that contains any other type of wholegrain flour or rye flour whole grain bread. Finally, other bread aggregates together all othernon-whole-grain bread types (like Cinnamon Raisin, Cinnamon Swirl, etc.).
Bread prices are constructed from the Retail Scanner Data for shopping trips to retailchains in the Retail Scanner dataset. To do that, prices are aggregated to the bread type,week, market (Nielsen scantrack market), and chain level. But more than half of the WIC
households’ bread purchases are at retailers (grocery stores and mass merchandisers) that are
not in the Retail Scanner Data. For those shopping trips, the prices are constructed fromthe Consumer Panel data and prices are aggregated to the bread type, week, and market
17

While households received WIC vouchers, it is unknown whether they paid with a voucher or cash on agiven shopping trip. As such, the prices paid on a given shopping trip are unknown—whether these were theregular prices, or a price of zero because of the voucher.

14

(Nielsen scantrack market) level. In both cases, prices are deflated to 2015 dollars using theconsumer price index for urban consumers. How different are the prices constructed fromthe two alternative datasets? We can analyze this for the subset of retailers that overlap
in these datasets. Online appendix B.3 presents this comparison. For these overlapping
retailers, bread prices constructed based on the two datasets line up rather closely; prices
based on the Consumer Panel are about 10% lower for all four product types (column 5 intable B3). The magnitude of the difference is similar to what has been shown for aggregate
grocery price indexes constructed based on the two datasets (for example, Seo (2019)). The
mismeasurement of prices is unlikely to be a substantial concern because the difference issmall, and importantly, in any given choice occasion (shopping trip), consumers face prices
constructed in the same way. To alleviate the potential concerns, I analyze the robustness of
results to the alternative price measures later in section 4, and the main estimates are similar
to those obtained when using only prices from the Retail Scanner data.
Table 2 presents summary statistics of the prices of each product. The cheapest productis white bread, while whole wheat bread is about 60 cents more expensive.
Table 2: Summary statistics of bread prices

Other bread
Whole grain bread
Whole wheat bread
White bread

Mean
(1)
1.76
2.03
1.95
1.36

SD
(2)
0.33
0.30
0.34
0.28

Perc. 25
(3)
1.53
1.83
1.70
1.17

Median
(4)
1.67
1.95
1.88
1.30

Perc. 75
(5)
1.95
2.21
2.17
1.49

N
(6)
28042
28042
28042
28042

Note: The price of bread is measured in dollars per pound, deflated to 2015 dollars using the consumer priceindex for urban consumers. Observations are at the week, market, bread type, and (aggregate) retailer level.

15

3

The short- and long-term impacts of healthy food subsidies

3.1

Main empirical strategy

The goal of the empirical strategy is to identify the impact of the healthy food subsidies on
WIC households, both in the short-term (while receiving the subsidies) and long-term (1–2
years after receiving the subsidies). The empirical strategy exploits the 2009 reform of the
WIC program that changed the content of food vouchers. The analysis compares changes inpurchases associated with starting and ending receipt of WIC vouchers in the two groupsof households—those receiving the vouchers from the old program and those from the newprogram. These two groups of households are otherwise similar, but the vouchers are different.
The new policy introduced healthy food subsidies—vouchers for whole wheat bread, low-fat
milk, and fruits and vegetables. It reduced the subsidized quantity of milk, juice, and eggs
while keeping the subsidized quantity of cereals unchanged.
In the main analysis, using household-level quarterly data, I estimate the following
difference-in-differences regression:18

Yit = α1 W ICit + α2 Af terW ICY ears1, 2it+ β1 Ref ormedW ICit + β2 Af terRef ormedW ICY ears1, 2it++ α3 Af terW ICY ear3+
it + β3 Af terRef ormedW ICY ear3it+ σ · P ostRef ormit + Xit ζ + δi + γt + εit .

(1)

The outcome variable Yit is a measure of purchases (e.g., average fat percentage of milk)
18

To address concerns raised by the recent econometrics literature regarding staggered adoption differencein-differences designs, I also calculate the heterogeneity-robust difference-in-differences estimators proposedby de Chaisemartin and D’Haultfœuille (2020a,b). As a robustness check, I also provide the propensity scorematching estimator.

16

of household i in time period t. Variable W ICit is an indicator for household i receiving
WIC vouchers in period t. Variable Af terW ICY ears1, 2it indicates that household i finishedreceiving WIC vouchers 1–2 years earlier. Variable P ostRef ormit is an indicator for time
periods after the WIC reform. The variable is not collinear with time period fixed effects
because the 2009 reform took place in different months in different states. Therefore, thevariable is also indexed by i.
The first variable of interest Ref ormedW ICit is an indicator of receiving the vouchers post
reform and therefore equals Ref ormedW ICit = P ostRef ormit ×W ICit . The second variableof interest Af terRef ormedW ICY ear1, 2it indicates that household i finished receiving
reformed WIC vouchers 1–2 years earlier.19
The coefficients of interest β1 and β2 measure the short- and long-term effects of healthy
food subsidies (introduced by the policy change) on WIC households. Therefore, the coefficients measure the average treatment effect on treated of the policy change.
In the balanced panel (up to two years after vouchers) of WIC households, only a few
remain in the Nielsen panel for more than two years after finishing receiving the vouchers. As
is standard in the literature, to increase statistical power, I don’t drop the observations threeor more years after receiving the vouchers. Instead, I include separate dummies for these+
periods. As such, Af terW ICY ears3+
it and Af terRef ormedW ICY ear3it indicate receiving

WIC and reformed WIC vouchers three or more years earlier. I don’t report the coefficientestimates because the sample is balanced only up to two years after receiving the vouchers.
Therefore, these are biased estimates for these effects and cannot be interpreted.
The regressions include time-varying household characteristics Xit : logarithm of income,household size, and indicator variables for the year before the child is born, and children
aged 0, 1, ..., 5, 6–12, and 13–17. For milk, the regression also includes interaction terms for
19

The first two years after receiving the vouchers are combined to increase statistical power. However,
online appendix C.1 shows that the results remain qualitatively similar when the years are separated.

17

one-year-old child and WIC and reformed WIC to take into account that, for one-year-old
children, the reformed WIC food vouchers make an exception and provide whole milk.20 The
regression also includes household fixed effects δi and time period fixed effects γt .
Each WIC household in the analysis is observed before, while, and the first and second
years after receiving WIC vouchers. In the main analysis, I also include an additional control
group that don’t receive WIC vouchers (households in column 3 of table 1) to control forpossible changes in preferences over time. However, the results remain similar when restricting
the sample to households that receive pre- or post-reform vouchers.

Identification. The identification assumption in the difference-in-differences analysis isthat the purchases of the households who received post-reform WIC subsidies would haveotherwise followed the same trend as the purchases of the households in the control group (whoeither received the pre-reform subsidies or did not receive any subsidies). Due to household
fixed effects, the specification allows the levels of purchases of the households receiving
post-reform subsidies to differ systematically from those in the control group, although figures
B7–B8 show that the levels are rather similar for most products for households receiving preand post-reform vouchers.
A possible concern with the identification strategy is that the selection in and out of the
WIC program could be correlated with the demand for healthy food products. The largest
incentive to enroll in the WIC program is provided by infant formula, as infant formula is themost expensive item in the WIC food vouchers, resulting in the retail price of food vouchers
for infants to be $123 per month compared to only $39 for older children (Kline et al., 2018).
This is also reflected in the WIC enrollment rates: enrollment among the eligible population
is highest among infants (Johnson et al., 2014). Therefore, when enrolling in the program,
20

Because the data provide only yearly information about age, I generate two interaction terms: one withthe last two quarters of the calendar year when the child becomes one year old, and the other with the firsttwo quarters of the calendar year when the child becomes two years old.

18

the selection based on food products is unlikely. However, we might be more worried thatparticipants dropped out of the program because they did not like the healthy products inthe new vouchers. To address the concern, after presenting the main estimates, I analyzechanges in purchases when households become ineligible for the vouchers, and the conclusions
remain the same.
To provide additional support for the identifying assumption, I use summary statistics
to examine the differential trends before treatment (online appendix C.2). There are slightdifferences in changes between treatment and control groups for healthy bread purchases andmilk fat percentage from two to one years before treatment. However, the magnitudes ofthe differential changes before treatment are much smaller than the change in the treatmentgroup at the time of treatment (from a year before treatment to the year of treatment).
Considering the differences in the magnitude of the effects, it is unlikely that the small
differential trends before treatment considerably bias the estimates. While for the quantityof bread and cereals, the changes before treatment for treatment and control groups arerather similar, there are slight differential trends also for the quantity of milk, fruits andvegetables, juice, and eggs. I will re-examine the concern about time-varying factors specificto post-reform WIC households after presenting the main estimates: allowing for separate
trends and testing the parallel trends assumption when calculating the heterogeneity-robust
difference-in-differences estimators.

3.2

Results: Impact of healthy food subsidies

Table 3 presents the main results of the short- and long-term impacts of healthy food subsidies
introduced by the policy reform. The estimate of β1 measures the short-term effect (while
receiving the subsidies), and β2 measures the long-term effect (1–2 years after receiving thesubsidies).
Table 3 shows that the change in the WIC program in the short term increases the healthy19

Table 3: The impact of healthy food subsidies introduced by the policy reform
Breadhealthy %

Milk
fat %

Bread
Milk Fruits&veg. Juice
Eggs Cereals
log.
log.
log.
log.
log.
log.
quantity quantity quantity quantity quantity quantity
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
β1 : Reformed WIC
6.922*** -0.135*** -0.013 0.022-0.0020.275 -0.064 0.036(2.213) (0.050) (0.053) (0.054)(0.087)(0.206) (0.095) (0.085)
β2 : After Reformed WIC Years 1-2 1.380-0.0630.002
0.004-0.0440.158 -0.116 0.189(1.944) (0.066) (0.070) (0.064)(0.112)(0.269) (0.116) (0.118)
α1 : WIC-1.799
0.003
0.040
0.051
0.037
0.457*** 0.073 0.132*(1.333) (0.036) (0.041) (0.046)(0.066)(0.166) (0.079) (0.069)
α2 : After WIC Years 1-2
1.696-0.009
0.008
0.031
0.037
0.221
0.021 -0.113(1.483) (0.059) (0.057) (0.052)(0.093)(0.235) (0.098) (0.102)
σ: Post-Reform
0.207-0.014** -0.001 0.008
0.002
0.111*** 0.021 -0.032*(0.270) (0.007) (0.009) (0.008)(0.018)(0.037) (0.015) (0.017)
Year-quarter FE
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Household FE
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Wald test, β1 = β2 , p-value
0.006
0.256
0.822
0.784
0.713
0.660
0.664
0.191
WIC households
301
301
347
347
347
347
347
347
Households
85421
80721
96637 96637
96637
96637 96637 96637
Household-quarters
1244237 1192570 1602252 1602252 1602252 1602252 1602252 1602252
Note: Each column presents estimates of a separate panel data fixed effects regression (equation (1)). A unitof observation is a household-quarter pair. Bread healthy (whole wheat) % and milk fat % are in the range
of 0–100; quantity is measured in pounds for bread, gallons for milk, kilocalories for fruits and vegetables
and juice, count for eggs, and ounces for cereals. All regressions include household size, logarithm of income,dummies for the year before the child is born, and children aged 0, 1, . . . , 5, 6–12, and 13–17. In column 2,
regressions include interaction terms for WIC (and Reformed WIC) and the last two quarters of the calendar
year when the child turns one year old, and the other with the first two quarters of the calendar year when thechild turns two years old. Regressions include household and time period fixed effects. The sample includes
households in columns 1–3 in table 1. In columns 1 and 2, the sample includes only households for whom thequarterly variable is defined (who purchase bread or milk, respectively) at least once per year and in total
at least two quarters. In columns 3–8, the sample includes all households that buy any food products with
UPCs in a given year. Standard errors (in parentheses) are clustered at the household level. *** Indicatessignificance at the 1 percent level, ** 5 percent level, * 10 percent level.

(whole wheat) bread purchases (as a share from all bread purchases) and decreases milk
fat percentage. For bread, the magnitude of the seven-percentage-point increase is large,
corresponding to an increase of about 75% compared to healthy bread share of nine percent in
the first year in the sample (table 1). For milk, the magnitude of the change is much smaller,
corresponding to a change of only about seven percent. For bread, the effect decreases alreadyin the first two years after the end of receiving the subsidies. For milk, the estimates are
imprecise and don’t allow ruling out large long-term effects. Note that healthy products are
20

typically more expensive than unhealthy alternatives, making healthy products less affordable
for low-income households. But in the case of milk, in some regions, it is the opposite; low-fat
milk is cheaper than whole milk. This makes it more affordable to continue consuming thehealthy product when the program ends. I will explore the role of prices in later parts of thepaper.
The reform of the WIC program has no statistically significant short- or long-term effects
on the total quantities purchased (columns 3–8). But for several products, the estimates are
imprecise and don’t allow rejection of sizable positive or negative effects. While the reformchanged the quantities in food vouchers, this doesn’t necessarily have to affect purchases.
Economic theory suggests that vouchers increase consumption (beyond income effect) only if
one consumes less without vouchers. But table 1 shows that before receiving the vouchers,
for several products, including fruits and vegetables, the typical consumption is larger thanwhat is provided by vouchers (described in table A1).21
The estimates regarding the short-term impact of the healthy food subsidies are largely
consistent with the previous literature. The literature has found that the change in the foodvouchers increased whole wheat bread consumption and lowered milk fat percentage while
receiving the vouchers (Schultz et al., 2015; NASEM, 2017). Previous results regarding fruits
and vegetables have been mixed (Zhang et al., 2020).

Robustness. Below, I summarize the analysis meant to explore the sensitivity of the results;
more details are presented in online appendix C.3. The results are robust to restricting
the sample only to the WIC households. Also, results remain similar for the healthy breadshare and milk fat percentage when allowing separate trends for the treatment group. The
key results remain the same when using the heterogeneity-robust difference-in-differences
21

To alleviate the concern that the WIC fruits and vegetables voucher is too small compared to therecommended fruits and vegetables intakes, in 2021, the size of the voucher was more than tripled. Source:
WIC Policy Memorandum, 2021-3, FNS-GD-2021-0029.

21

estimates proposed by de Chaisemartin and D’Haultfœuille (2020a,b) to correct for the
possible bias of the two-way fixed effects estimator when treatment effects are heterogeneous.
The conclusions regarding the healthy bread share and milk fat percentage remain unchanged
when using the propensity score estimates. To address the concern that households choose
to drop out of the new WIC program because they don’t like the healthy foods, I analyzechanges in purchases when households become ineligible for the vouchers when the childbecomes five years old. I find that households who received the post-reform vouchers when
their youngest child was four, in the following years (with the child aged five and six), changed
their behavior in similar ways as those who stopped receiving the vouchers in table 3.
To account for the possible unobservable changes when households receive WIC vouchers,in this paper, the analysis compares households participating in the old and new WIC
programs. As a result, the estimates measure the incremental effect of the new WIC program
relative to the old. If, instead, we were to exclude from the sample the households in the old
WIC program, the estimates would be slightly different, as these would measure the combined
effect of the new vouchers and everything else that changes when households receive thevouchers (online appendix C.4).

Prices and the program’s impact. Khan et al. (2016) show that there are exogenous
regional differences in milk pricing: states where milk prices increase along with fat percentage and others where milk prices are flat. I use these regional differences to analyze theheterogeneity in the program’s impact. Specifically, I calculate state-level median milk pricedifferences of different fat percentages (whole milk, 2%, 1%, and skim milk) across stores andtime periods using data on private label one-gallon milk.22 Based on these price differences, I
categorize states as those with flat prices where the price of whole milk is not higher thanothers, those where whole milk is more expensive than others, and those with mixed price22

Private label accounts for about 80% of the milk sold, and 1 gallon is the most popular package size.

22

rankings. Figure C6 in the online appendix presents a map describing the regional differencesin prices. Table 4 presents estimates of the short- and long-term impacts of the post-reform
WIC subsidies estimated separately in states where prices are flat and in those where prices
increase along with the fat percentage.23 In states where prices are flat (healthy product is
not cheaper), the long-term effect is not as large as the short-term effect. The Wald test incolumn 1 shows that with 95% probability, the estimates allow rejection of the long-term
impact (β2 ) of the same size as the short-term effect (β1 ).
Table 4: The short- and long-term impact and prices. Dependent variable: milk fat percentage
PricesPricesflat
increasing(1)(2)
β1 : Reformed WIC-0.262** -0.281***(0.105)(0.092)β2 : After Reformed WIC Years 1-2 -0.009-0.301(0.111)(0.198)
α1 : WIC
0.058
0.151**(0.071)(0.060)α2 : After WIC Years 1-2-0.0170.193(0.098)(0.183)σ: Post-Reform-0.013** -0.010**(0.005)(0.005)
Year FE
Yes
Yes
Quarter FE
Yes
YesHousehold FE
Yes
Yes
Wald test, β1 = β2 , p-value
0.031
0.906
WIC households
94
60
Households
27769
18707
Household-quarters
404521278787
Note: The table presents results from re-estimating the regression in column 2 of table 3. In column 1, thesample is restricted to households in states where milk prices are flat (whole milk is not more expensive
than other types of milk). In column 2, the sample is restricted to households in states where milk prices
increase along with fat percentage (whole milk is more expensive than other types of milk). Standard errors(in parentheses) are clustered at the household level. *** Indicates significance at the 1 percent level, ** 5percent level, * 10 percent level.

Externalities to other product categories. While the WIC vouchers include only asmall set of products, there could be nutritional externalities to other purchases. The 200923

Similar estimates using only the WIC sample are in the online appendix (table C10).

23

changes in WIC vouchers aimed to increase fiber consumption in bread and reduce saturated
fat consumption in milk. Consumers could compensate in other product categories, forexample, consume more saturated fat in other dairy products. Alternatively, there could
be positive externalities if consumers learn from the WIC program and increase fiber andreduce saturated fat consumption in other product categories. Online appendix C.7 analyzes
the externalities. The results show that the reform decreased saturated fat consumption inmilk and increased fiber consumption in bread. For non-WIC product categories, the point
estimates are small, and although the estimates are imprecise, they allow ruling out large
externalities.

Discussion and possible limitations. The analysis might raise the question of whether
the impact of the new WIC program is driven by the income effect. The answer is no. While
indeed the WIC vouchers increase income, which might lead the households to switch tohealthier foods, but the change in WIC vouchers kept the value of the vouchers the same.
Therefore, in the above regressions, controlling for receiving WIC vouchers (α1 and α2 inequation 1) captures the WIC-related effects, including the income effect. Therefore, theparameters of interest (β1 and β2 in equation 1) measure only the incremental effect of the
new WIC program, identifying the impact of the food vouchers being restricted to healthy
foods, separating it from the overall impact of the vouchers (including the income effect).
The above analysis focuses on measuring the impact of the new WIC vouchers; it does
not address the mechanism of why purchases changed in some categories while receiving the
new WIC vouchers. It does not measure the importance of the substitution effect (change
in relative prices) and the information effect (learning about recommended foods), andbehavioral heuristics such as mental budgeting (Hastings and Shapiro, 2018). The limited
persistence in the case of healthy bread is more consistent with substitution effect and mental
budgeting than with learning.

24Finally, as is always the case with scanner data, it includes information only on purchases,
not consumption or food waste. If households were more likely to discard food that theyreceived for free, then the short-run impact of the program would be overestimated.

4

The role of prices

In this section, I estimate a demand model to examine the long-term impact of healthy foodsubsidies on preferences and separate it from the role of prices. I focus only on bread for two
reasons. First, bread was a product category with a high short-term impact of the subsidy.
Second, it is a typical product category in terms of the pricing of healthy and unhealthy
products—the healthy version is more expensive than the unhealthy alternative (as opposed
to milk). In this way, it provides a good example of typical choices between healthy andunhealthy foods. I use the demand model estimates for counterfactual analysis, which answers
the question of how long does it take for the purchases to return to the pre-WIC level withdifferent prices.

4.1

Demand model

I model demand using a standard discrete choice multinomial logit model with randomcoefficients. Households choose between four bread products: white, whole grain, whole
wheat, and other. The last option, other, is the composite of all other bread products.
Household i, in shopping trip t, chooses a product with the highest indirect utility, where theindirect utility from product j ∈ {W hite, W G, W W, Other} equals:

uijt = αi pjt + γi · 1[si,t−1 = j] + (βκW W,it + θi ) · W Wj + δi W Gj + λi W hitej + εijt

25

(2)

where pjt is price and coefficient αi measures the household’s price sensitivity. Variable
si,t−1 ∈ {W hite, W G, W W, Other} indicates the product purchased on the previous trip.
The corresponding coefficient (γi ) measures the consumer’s short-term state dependence.
The indicator variables W hitej , W Gj , and W Wj indicate whether the alternative j is whitebread, whole grain, or whole wheat, respectively. The corresponding coefficients (θi , δi , λi )measure time-invariant tastes for those products.24
I model consumer heterogeneity with a multivariate normal distribution across price,
tastes for products, and short-term state dependence coefficients (αi , γi , θi , δi , λi ). I estimate
the parameters of the distribution of the random coefficients, specifically, means (ᾱ, γ̄, θ̄, δ̄, λ̄),standard deviations (σp , σs , σW W , σW G , σW hite ), and the corresponding covariances ρ, allowing
correlation in preferences across these attributes.
The variable κW W,it equals the last year’s (last 52 weeks’) share of whole wheat bread inbread purchases. The corresponding coefficient β measures long-term taste inertia. One could
think of κW W,it as a stock of taste for whole wheat bread, analogous to the taste stock definedin Atkin (2013). The inclusion of long-term state dependence in the model is motivated bynutrition literature, which provides evidence that repeated exposure is required to change
nutritional preferences (Sullivan and Birch, 1990; Birch, 1999; Maier et al., 2007; Lakkakula
et al., 2010; Anzman-Frasca et al., 2012; Hausner et al., 2012).
Finally, the taste shock εijt is assumed to be independent across households, products,
and shopping trips, distributed according to a type 1 extreme value distribution. Let’s denotethe first five terms on the right-hand side of equation (2) by vijt = αi pjt + γi · 1[si,t−1 =j] + (βκW W,it + θi ) · W Wj + δi W Gj + λi W hitej . Then, the probability that household i buys
product j on trip t equals:
exp(vijt )P robijt = PJ
k=1 exp(vikt )24(3)

I don’t include advertising because advertising typically varies by brand and not by product characteristics(by the type of bread).

26

Identification. While the formal proof of identification is beyond the scope of this paper,
let us discuss the intuition of how the available data variation identifies the parameters ofthe model.
Let us first look at the data variation that allows us to pin down the long-term state
dependence parameter β (assumed to be the same across households), separating it fromthe household-specific constant-over-time preference for whole wheat bread θi . We observe
every household making purchases both before and after receiving the WIC vouchers. The
post-reform vouchers generated an exogeneous jump in the state variable: the last year’s
share of whole wheat bread κW W,it . The within-household change in the state variable frombefore to after receiving the vouchers allows us to pin down the long-term state dependence
parameter because, both before and after vouchers, a household is characterized by the sametime-invariant taste for whole wheat θi .25 Figure 1 describes this jump in the state variable.
It presents the within-household comparison of whole wheat bread share before versus after
receiving the vouchers; it is shown separately for households receiving pre- versus post-reform
WIC vouchers. The first grey bar is the whole wheat share’s average across post-reform
WIC households before receiving the vouchers. The first blue bar is the average across thesame households after receiving the vouchers. The comparison of the first grey and blue bars
describes the within-household increase (statistically significant at the 1% level) in whole
wheat bread share due to the post-reform WIC vouchers.
Next, let us look at the data variation that helps pin down the household-specific shortterm state dependence γi . The setting allows to identify short-term state dependence because
bread is often bought, and even more importantly, households often switch between different
types of bread. In the sample, the median household buys bread 100 times, and all households
switch at least once. As noted by Simonov et al. (2020), these switches help to identify theshort-term state dependence because they allow observing each household in both states:
25

Using a major change in conditions to identify inertia is analogous to Handel (2013).

27

0

.05

.1

.15

.2

Last year's share of whole wheat.25

Within-household comparison of before versus after WIC

Post-reform households

Pre-reform households

Last before WIC

First after WIC

Figure 1: Within-household comparison of the last year’s share of whole wheat bread: before
WIC versus after WIC; presented separately for pre- versus post-reform WIC households
Note: Each bar presents the average across households, and the capped spikes are the 95% confidence
intervals. The unit of observation is a household. The first two bars are each calculated as the average across
178 households receiving post-reform WIC vouchers. The last two bars each average over 74 households
receiving pre-reform vouchers. Grey bars are averages during the previous trip before receiving the vouchers,
and blue bars during the first trip after receiving the vouchers. According to the t-test, for post-reform
households, the means before versus after vouchers differ at the 1% significance level.

having bought the product or not on the previous trip. For each household, we can compare
the probability of purchasing the product in two different states: one where they bought the
product the last shopping trip and the other where they didn’t. Importantly, the probabilities
are calculated separately for each household. Figure D1 in the online appendix presents theaverage probabilities and 95% confidence intervals by state (whether bought or not on theprevious trip) and product. The figure shows that the average probabilities in the two states
are statistically significantly different from each other, suggesting that, on average, there isshort-term state dependence. We can also calculate the difference between these conditional
probabilities for each household and product pair. Again, as the probabilities are calculated
separately for each household, the difference in probabilities is also household-specific. By
and large, the difference in probabilities in the two states captures the household’s state28

dependence. A household is more state dependent (the difference close to one) if it is very
likely to buy the product when it bought the last trip and not at all likely to buy when it
didn’t buy the last trip. The histogram of the differences between the probabilities (figure
D2 in the online appendix) shows that households are heterogeneous in state dependence. A
few households are variety-seeking (negative difference), but the majority of households are
more likely to buy the same product as last time (positive difference).
Finally, as Simonov et al. (2020) draw attention to, when analyzing state dependence,
the literature (including Keane (1997); Seetharaman et al. (1999); Shum (2004); Dubé et al.
(2010)) has typically relied on assumptions that ignore the initial conditions problem—theissue that the initial observed state is endogeneous. In the main specification of the model,
the current paper follows the literature and assumes that the initial state is exogeneous. In
the current setting, it is likely that the possible bias from the initial conditions problem issmall because the panel is very long, the median household makes exactly 100 purchases,
and all households switch between products. To formally address the concern about theinitial conditions bias, after estimating the demand model, I will use the method proposed by
Simonov et al. (2020) to bound the true short-term state dependence value.
Below, I will discuss the identification of the price coefficient.

Control function. To address the concern of price endogeneity, I also estimate the modelusing a control function. Following Petrin and Train (2010), I assume the pricing function
takes the following form where the price of product j in week26 t in market m in (aggregate)
retailer r equals
pjtmr = z0 jtmr η + ξjtmr(4)

where zjtmr is the vector of exogenous instruments and ξjtmr is the unobserved price shock.
The pricing function is estimated at the week, market, and (aggregate) retailer level because
26With slight abuse of notation, here week, instead of a shopping trip, is indexed by t.

29

price variables are constructed so that these vary only by market and (aggregate) retailer, notby the consumer. Typically, when estimating a demand model, we are concerned that prices
might depend on the unobserved factors that directly affect demand. In the control function
approach, the identifying assumption is that prices and taste shocks, ε, are independentconditional on the unobserved factors, ξ, affecting prices.
For the instrument, I use the average price of the same (aggregate) retailer in othermarkets (following Hausman (1996); Nevo (2001); DellaVigna and Gentzkow (2019)). I also
include product fixed effects and market fixed effects. The instrument has a strong first-stage(table D1 in the online appendix).

Estimation. The demand model is estimated using simulated maximum likelihood. I
estimate the model with the control function in two steps. First, I estimate the reduced
form pricing regression (equation 4) with ordinary least squares to recover the residuals ξjtm .
Then, I include these residuals as an additional regressor (control function) in the indirect
utility (equation 2) and estimate the demand model using simulated maximum likelihood. In
the model with the control function, standard errors are calculated using bootstrap (over two
steps of the estimation, estimating first the control function and then the demand model)
with 100 bootstrap samples.
The demand model is estimated using purchases before and after the household received
the WIC vouchers. The reason why I don’t use time periods when households receive WIC
vouchers is that I don’t have information about whether, on a given shopping trip, they arepaying with the voucher or cash. Therefore, I wouldn’t know the price they faced on a given
shopping trip (zero because of the voucher, or the regular price). In the household’s first year
in the sample, I exclude the first 10 shopping trips to initialize the long-term state dependence
variable κW W,it and use the latest excluded shopping trip to initialize the short-term state
dependence variable si,t−1 .

30

4.2

Estimation results

The estimates of the demand model are in table 5. Specifically, it includes the estimates ofthe means of the random coefficients and estimates of fixed coefficients; estimates of standard
deviations and covariances of the random coefficients are in table D2 in the online appendix.
Columns 1 and 2 present estimates without and with a control function, respectively. As
expected, the estimated coefficient on price is larger in absolute value with the control
function. The estimates show the importance of both the short-term state dependence andlast year’s share of whole wheat bread affecting current purchases. Online appendix D.3
shows that the key results are robust to alternative constructions of prices. Using the method
proposed by Simonov et al. (2020), it also shows that the results are robust to alternative
initial conditions for state dependence.
Table 5: Bread demand model estimatesMeanᾱ: Priceγ̄: Short-term state dependenceβ: Last year’s share of whole wheatθ̄: Whole wheat breadδ̄: Whole grain breadλ̄: White bread
Residual
Log-likelihood
Number of choices
Number of households

No control function(1)
Estim.
SE

Control function(2)
Estim.
SE−1.029∗∗∗0.693∗∗∗
3.872∗∗∗−1.534∗∗∗−0.271∗∗∗−0.403∗∗∗−1.316∗∗∗
0.614∗∗∗
3.784∗∗∗−1.549∗∗∗−0.606∗∗∗−0.809∗∗0.539∗-22821112168252-22843112168252(0.088)(0.025)(0.121)(0.051)(0.059)(0.077)(0.287)(0.067)(0.254)(0.147)(0.195)(0.362)(0.277)

Note: The table presents estimates of two random coefficient logit models. The table presents the estimatesof the means of the random coefficients and estimates of fixed coefficients; estimates of standard deviations
and covariances of the random coefficients are in table D2 in the online appendix. For each model, the firstcolumn presents parameter estimates and the second column standard errors. The base type of bread isother bread. The sample includes households from columns 1–2 in table 1 with a sufficient number of breadpurchases; for each household the sample excludes the years when the household received WIC vouchers.
Standard errors are clustered at the household level. In column 2, standard errors are obtained by bootstrap(over 2 steps of the estimation: estimating first the control function and then the demand model) with 100
bootstrap samples. *** Indicates significance at the 1 percent level, ** 5 percent level, * 10 percent level.

31

Counterfactual analysis. I run a counterfactual analysis to study how long it takes
for purchases to return to the pre-WIC level with alternative prices. Specifically, thecounterfactual policy is a 10-cent subsidy on whole wheat bread; the subsidy is given to thehouseholds after their eligibility for the current WIC program runs out when the child turns
five years old.
This subsidy is easily implementable via coupons that the program could give households
after the current WIC policy ends when the child turns five years old. The WIC program
already works with retailers to ensure that stores accept the WIC vouchers as a payment
method. The contracts with retailers could be extended so that stores would also accept the
WIC coupons for a discount. Nowadays, WIC vouchers are electronic, and so could be thecoupons, which makes the coupons easy to use and limits the paperwork.
The counterfactual analysis uses estimates from column 2 in table 5 and average prices(column 1 in table 2).27 The 10-cent subsidy decreases the price gap with the cheapest (white)bread by less than 20%, but it has a much larger impact on price gaps with more similarly
priced products. The counterfactual analysis is done in the following steps. In step 1, 1000
synthetic households are simulated based on the estimated distribution of preferences. To
focus on the role of preferences, I assume that the households are homogeneous in the shopping
frequency and the length of time spent in the WIC program. For each household, given
the household’s preferences and prices, the pre-WIC equilibrium purchase probabilities andstate variables κW W and st−1 are simulated using 1000 iterations. In step 2, to approximate
receiving the WIC vouchers, I assume that for all households for 36 purchase occasions, theprice of whole wheat bread equals zero on every third shopping occasion. (This reflects that,typically, households buy much more bread than is covered by the voucher.) From step 2,
for each household, we obtain the predicted purchase probabilities, κW W , and st−1 , when27

The counterfactuals are calculated under the assumption that the estimated control function on prices
does not change.

32

the household exits the WIC program (after 36 shopping occasions). In step 3, post-WIC
purchase histories are predicted. I assume all households make 18 shopping trips with breadpurchases per year.28 I predict purchase histories for 20 years (360 purchase occasions)using either the same average prices or the average prices with a 10-cent whole wheat breadprice discount. Then, for each household, it is calculated how many years it takes to returnto the equilibrium whole wheat bread purchase probability calculated in step 1. Online
appendix D.4 presents more details about the counterfactuals. It shows that, as expected, thepurchase probability of whole wheat bread is an increasing function of the state variable κW W .
Receiving the vouchers shifts the distribution upwards, increasing both the state variable
and the purchase probability. It also presents an example of a counterfactual household anddescribes counterfactual households’ heterogeneity.
The results of the counterfactual analysis are in figure 2. With the current prices (figure2a), 70% of the households return to pre-WIC consumption levels in the first two years after
exiting the program. If the price of whole wheat bread were 10 cents lower (figure 2b), thereturn to pre-WIC levels would be considerably slower: only 43% return to pre-WIC levels in
the first two years. The median returning time increases by one year, from two years in thebaseline to three years with the discount.
What do we learn from the counterfactual analysis? The counterfactual analysis showsthat if we would like the program to have a long-term effect beyond the period during whichvouchers are received, then that might be possible via a rather modest subsidy. While thepaper studies a specific program and a specific product, many settings have similar concerns.
For example, aid programs in developing countries provide free essential health products, suchas insecticide-treated bednets, deworming drugs, and home water purification solutions, whichhouseholds should continue to obtain and use indefinitely. But the programs face budget
constraints that limit the ability to support everyone indefinitely. Combining temporarily free28

The median household in the first year post-WIC makes 18 shopping trips with bread purchases.

33

50
0

10

Percent
20
30

40

50
40
Percent
20
30
10
0

1

2

5
Years since WIC

10+1(a) Base

3

5
Years since WIC

10+(b) 10-cent whole wheat bread price discountFigure 2: Number of years it takes to for purchases to return to pre-WIC levels
Note: Each figure presents the histogram of the number of years it takes to return to pre-WIC levels, basedon counterfactual analysis of 1000 randomly drawn households. The red lines show the median number ofyears it takes to return to pre-WIC levels, which is two years in the baseline (figure 2a) and three years in
the counterfactual (figure 2b). The counterfactuals are obtained using the estimates from column 2 in table
5 and average prices (over all households and time periods). In step 1, 1000 households are drawn fromthe estimated distribution, and equilibrium purchase shares (and κW W and st−1 ) for each household are
simulated given the prices. In step 2, to approximate receiving the WIC vouchers for two years, it is assumed
that for 36 purchase occasions, on every third shopping occasion, the price of whole wheat bread equals zero.
This gives for each household the predicted purchase shares, κW W , and st−1 , when the household exits the
WIC program. In step 3, subsequent purchase histories are predicted using either the same average prices(figure 2a) or the average prices with a 10-cent whole wheat bread price discount (figure 2b). Then, for eachhousehold, it is calculated how many years it takes to return to the equilibrium calculated in step 1.

products with long-term subsidies might be a more sustainable way to lengthen the impactof the programs.

5

Conclusion

In this paper, I study the short- and long-term impacts of healthy food subsidies. I findthat the subsidies increase the purchases of subsidized products in the case of whole wheat
bread and low-fat milk. But for bread, the effect decreases already in the first two years
after the end of receiving the subsidies. For milk, the estimates are imprecise and don’t allow
ruling out that the short- and long-term effects are of similar size. Demand model estimates34

show that the program has some long-term impact on preferences. The estimates imply thatprice differences between healthy and unhealthy products play a role in the decrease in the
program’s long-term impact.

References
Allcott, H., R. Diamond, J.-P. Dubé, J. Handbury, I. Rahkovsky, and
M. Schnell (2019a): “Food Deserts and the Causes of Nutritional Inequality,” The
Quarterly Journal of Economics, 134, 1793–1844.
Allcott, H., B. B. Lockwood, and D. Taubinsky (2019b): “Regressive Sin Taxes,
with an Application to the Optimal Soda Tax*,” The Quarterly Journal of Economics, 134,
1557–1626.
Anderson, M. L. and D. A. Matsa (2011): “Are Restaurants Really Supersizing America?”
American Economic Journal: Applied Economics, 3, 152–188.
Anzman-Frasca, S., J. S. Savage, M. E. Marini, J. O. Fisher, and L. L. Birch(2012): “Repeated exposure and associative conditioning promote preschool children’s likingof vegetables,” Appetite, 58, 543–553.
Atkin, D. (2013): “Trade, Tastes, and Nutrition in India,” American Economic Review, 103,
1629–1663.
——— (2016): “The Caloric Costs of Culture: Evidence from Indian Migrants,” American
Economic Review, 106, 1144–1181.
Belot, M., N. Berlin, J. James, and V. Skafida (2018): “The formation and malleabilityof dietary habits: A field experiment with low income families,” Tech. Rep. 11317, Institutefor the Study of Labor (IZA).
35

Belot, M., J. James, and P. Nolen (2016): “Incentives and children’s dietary choices: A
field experiment in primary schools,” Journal of Health Economics, 50, 213–229.
Birch, L. L. (1999): “Development of food preferences,” Annual Review of Nutrition, 19,
41–62.
Bollinger, B., P. Leslie, and A. Sorensen (2011): “Calorie Posting in Chain Restaurants,” American Economic Journal: Economic Policy, 3, 91–128.
Bollinger, B. and S. Sexton (2018): “Local Excise Taxes, Sticky Prices, and Spillovers:
Evidence from Berkeley’s Soda Tax,” SSRN Scholarly Paper ID 3087966, Social Science
Research Network, Rochester, NY.
Bronnenberg, B. J., J.-P. H. Dube, and M. Gentzkow (2012): “The Evolution of
Brand Preferences: Evidence from Consumer Migration,” American Economic Review, 102,2472–2508.
Bronnenberg, B. J., J.-P. Dubé, and R. E. Sanders (2020): “Consumer Misinformationand the Brand Premium: A Private Label Blind Taste Test,” Marketing Science, 39, 382–
406.
Cawley, J. (2015): “An Economy of Scales: A Selective Review of Obesity’s Economic
Causes, Consequences, and Solutions,” Journal of Health Economics, 43, 244–268.
Cawley, J., D. Frisvold, A. Hill, and D. Jones (2019): “The impact of the Philadelphia
beverage tax on purchases and consumption by adults and children,” Journal of Health
Economics, 67, 102225.
Charness, G. and U. Gneezy (2009): “Incentives to Exercise,” Econometrica, 77, 909–931.

36

Currie, J., S. DellaVigna, E. Moretti, and V. Pathania (2010): “The Effect of Fast
Food Restaurants on Obesity and Weight Gain,” American Economic Journal: Economic
Policy, 2, 32–63.
de Chaisemartin, C. and X. D’Haultfœuille (2020a): “Difference-in-Differences Estimators of Intertemporal Treatment Effects,” SSRN Scholarly Paper ID 3731856, Social
Science Research Network, Rochester, NY.
——— (2020b): “Two-Way Fixed Effects Estimators with Heterogeneous Treatment Effects,”
American Economic Review, 110, 2964–2996.
DellaVigna, S. and M. Gentzkow (2019): “Uniform Pricing in U.S. Retail Chains,” The
Quarterly Journal of Economics, 134, 2011–2084.
Dhar, T. and K. Baylis (2011): “Fast-Food Consumption and the Ban on Advertising
Targeting Children: The Quebec Experience,” Journal of Marketing Research, 48, 799–813.
Dubois, P., R. Griffith, and A. Nevo (2014): “Do Prices and Attributes Explain
International Differences in Food Purchases?” American Economic Review, 104, 832–867.
Dubois, P., R. Griffith, and M. O’Connell (2020): “How Well Targeted Are Soda
Taxes?” American Economic Review, 110, 3661–3704.
Dubois, P., R. Griffith, and M. O’Connell (2018): “The Effects of Banning Advertisingin Junk Food Markets,” The Review of Economic Studies, 85, 396–436.
Dubé, J.-P., G. J. Hitsch, and P. E. Rossi (2010): “State Dependence and Alternative
Explanations for Consumer Inertia,” The RAND Journal of Economics, 41, 417–445.
Einav, L., E. Leibtag, and A. Nevo (2010): “Recording discrepancies in Nielsen Homescan
data: Are they present and do they matter?” Quantitative Marketing and Economics, 8,
207–239.
37

Eizenberg, A. and A. Salvo (2015): “The Rise of Fringe Competitors in the Wake of an
Emerging Middle Class: An Empirical Analysis,” American Economic Journal: Applied
Economics, 7, 85–122.
Figlio, D., S. Hamersma, and J. Roth (2009): “Does Prenatal WIC Participation
Improve Birth Outcomes? New Evidence From Florida,” Journal of Public Economics, 93,
235–245.
Fletcher, J. M., D. E. Frisvold, and N. Tefft (2010): “The effects of soft drink taxes
on child and adolescent consumption and weight outcomes,” Journal of Public Economics,
94, 967–974.
Frisvold, D., E. Leslie, and J. P. Price (2020): “Do Targeted Vouchers Instill Habits?
Evidence from Women, Infants, and Children,” Contemporary Economic Policy, 38, 67–80.
Gidding, S. S., B. A. Dennison, L. L. Birch, S. R. Daniels, M. W. Gilman,
A. H. Lichtenstein, K. T. Rattay, J. Steinberger, N. Stettler, and L. V.
Horn (2006): “Dietary Recommendations for Children and Adolescents: A Guide for
Practitioners,” Pediatrics, 117, 544–559.
Giné, X., D. Karlan, and J. Zinman (2010): “Put Your Money Where Your Butt Is:
A Commitment Contract for Smoking Cessation,” American Economic Journal: Applied
Economics, 2, 213–235.
Griffith, R., S. von Hinke, and S. Smith (2018): “Getting a Healthy Start: The
Effectiveness of Targeted Benefits for Improving Dietary Choices,” Journal of Health
Economics, 58, 176–187.
Handel, B. R. (2013): “Adverse Selection and Inertia in Health Insurance Markets: When
Nudging Hurts,” American Economic Review, 103, 2643–2682.
38

Harding, M. and M. Lovenheim (2017): “The effect of prices on nutrition: Comparing theimpact of product- and nutrient-specific taxes,” Journal of Health Economics, 53, 53–71.
Hastings, J. and J. M. Shapiro (2018): “How Are SNAP Benefits Spent? Evidence froma Retail Panel,” American Economic Review, 108, 3493–3540.
Hausman, J. A. (1996): “Valuation of New Goods under Perfect and Imperfect Competition,”in The Economics of New Goods, ed. by T. F. Bresnahan and R. J. Gordon, University of
Chicago Press, 207–248.
Hausner, H., D. L. Hartvig, H. C. Reinbach, K. Wendin, and W. L. P. Bredie(2012): “Effects of repeated exposure on acceptance of initially disliked and liked Nordic
snack bars in 9–11 year-old children,” Clinical Nutrition, 31, 137–143.
Hinnosaar, M. and E. Liu (2021): “Malleability of Alcohol Consumption: Evidence from
Migrants,” SSRN Scholarly Paper ID 3569603.
Hoynes, H., M. Page, and A. H. Stevens (2011): “Can Targeted Transfers Improve
Birth Outcomes?: Evidence From the Introduction of the WIC Program,” Journal of Public
Economics, 95, 813–827.
Hoynes, H. W. and D. W. Schanzenbach (2015): “U.S. Food and Nutrition Programs,”
Working Paper 21057, National Bureau of Economic Research.
Institute of Medicine (2006): WIC Food Packages: Time for a Change, Washington,
D.C.: The National Academies Press.
Johnson, P., L. Giannarelli, E. Huber, and D. Betson (2014): “National andState-Level Estimates of Special Supplemental Nutrition Program for Women, Infants,
and Children (WIC) Eligibles and Program Reach, 2011,” Report WIC-14-ELIG, U.S.
Department of Agriculture, Food and Nutrition Service, Office of Research and Analysis.
39

Keane, M. P. (1997): “Modeling Heterogeneity and State Dependence in Consumer Choice
Behavior,” Journal of Business & Economic Statistics, 15, 310–327.
Khan, R., K. Misra, and V. Singh (2016): “Will a Fat Tax Work?” Marketing Science,
35, 10–26.
Khan, R., T. Zhu, and S. Dhar (2018): “The effect of the WIC program on consumption
patterns in the cereal category,” Quantitative Marketing and Economics, 16, 79–109.
Kline, N., C. Warner-Griffin, E. Wilcox-Cook, and B. Thorn (2018): “Fiscal year
2014 WIC food package costs: Final report,” Tech. rep., U.S. Department of Agriculture,
Food and Nutrition Service, Office of Policy Support, Alexandria, VA.
Kueng, L. and E. Yakovlev (2021): “The Long-Run Effects of a Public Policy on Alcohol
Tastes and Mortality,” American Economic Journal: Economic Policy, 13, 294–328.
Lakkakula, A., J. Geaghan, M. Zanovec, S. Pierce, and G. Tuuri (2010): “Repeatedtaste exposure increases liking for vegetables by low-income elementary school children,”Appetite, 55, 226–231.
List, J. A. and A. S. Samek (2015): “The Behavioralist as Nutritionist: Leveraging
Behavioral Economics to Improve Child Food Choice and Consumption,” Journal of Health
Economics, 39, 135–146.
Loewenstein, G., J. Price, and K. Volpp (2016): “Habit Formation in Children:
Evidence From Incentives for Healthy Eating,” Journal of Health Economics, 45, 47–54.
Ludwig, D. S., W. C. Willett, J. S. Volek, and M. L. Neuhouser (2018): “Dietary
Fat: From Foe to Friend?” Science, 362, 764–770.

40

Ma, Y., K. L. Ailawadi, and D. Grewal (2013): “Soda Versus Cereal and Sugar Versus
Fat: Drivers of Healthful Food Intake and the Impact of Diabetes Diagnosis,” Journal ofMarketing, 77, 101–120.
Maier, A., C. Chabanet, B. Schaal, S. Issanchou, and P. Leathwood (2007):“Effects of repeated exposure on acceptance of initially disliked vegetables in 7-month oldinfants,” Food Quality and Preference, 18, 1023–1032.
Meckel, K. (2020): “Is the Cure Worse Than the Disease? Unintended Effects of Payment
Reform in a Quantity-Based Transfer Program,” American Economic Review, 110, 1821–
1865.
Mehta, N., S. Rajiv, and K. Srinivasan (2004): “Role of Forgetting in Memory-Based
Choice Decisions: A Structural Model,” Quantitative Marketing and Economics, 2, 107–140.
Moorman, C., R. Ferraro, and J. Huber (2012): “Unintended Nutrition Consequences:
Firm Responses to the Nutrition Labeling and Education Act,” Marketing Science, 31,
717–737.
Muller, L., A. Lacroix, J. L. Lusk, and B. Ruffieux (2017): “Distributional Impactsof Fat Taxes and Thin Subsidies,” The Economic Journal, 127, 2066–2092.
NASEM (2017): Review of WIC Food Packages: Improving Balance and Choice: Final
Report, Washington, D.C.: National Academies Press.
Nevo, A. (2001): “Measuring Market Power in the Ready-to-Eat Cereal Industry,” Econometrica, 69, 307–342.
Oliveira, V. (2017): “The Food Assistance Landscape: FY 2016 Annual Report,” Economic
Information Bulletin EIB-169, U.S. Department of Agriculture, Economic Research Service.

41

Oliveira, V. and E. Frazao (2009): “The WIC Program: Background, Trends, andEconomic Issues, 2009 Edition,” Economic Research Report 73, United States Departmentof Agriculture, Economic Research Service.
——— (2015): “The WIC Program: Background, Trends, and Economic Issues, 2015 Edition,”
Economic Information Bulletin 134, U.S. Department of Agriculture, Economic ResearchService.
Oster, E. (2018): “Diabetes and Diet: Purchasing Behavior Change in Response to Health
Information,” American Economic Journal: Applied Economics, 10, 308–348.
Petrin, A. and K. Train (2010): “A Control Function Approach to Endogeneity inConsumer Choice Models,” Journal of Marketing Research, 47, 3–13.
Puranam, D., V. Narayan, and V. Kadiyali (2017): “The Effect of Calorie Posting
Regulation on Consumer Opinion: A Flexible Latent Dirichlet Allocation Model with
Informative Priors,” Marketing Science, 36, 726–746.
Rossin-Slater, M. (2013): “WIC in Your Neighborhood: New Evidence on the Impacts ofGeographic Access to Clinics,” Journal of Public Economics, 102, 51–69.
Royer, H., M. Stehr, and J. Sydnor (2015): “Incentives, Commitments, and Habit
Formation in Exercise: Evidence from a Field Experiment with Workers at a Fortune-500
Company,” American Economic Journal: Applied Economics, 7, 51–84.
Schultz, D. J., C. Byker Shanks, and B. Houghtaling (2015): “The Impact of the2009 Special Supplemental Nutrition Program for Women, Infants, and Children Food
Package Revisions on Participants: A Systematic Review,” Journal of the Academy of
Nutrition and Dietetics, 115, 1832–1846.

42

Seetharaman, P., A. Ainslie, and P. K. Chintagunta (1999): “Investigating Household
State Dependence Effects across Categories,” Journal of Marketing Research, 36, 488–500.
Seiler, S., A. Tuchman, and S. Yao (2021): “The Impact of Soda Taxes: Pass-Through,Tax Avoidance, and Nutritional Effects,” Journal of Marketing Research, 58, 22–49, publisher: SAGE Publications Inc.
Seo, B. (2019): “Firm Scope and the Value of One-Stop Shopping in Washington State’s
Deregulated Liquor Market,” SSRN Scholarly Paper ID 2863094.
Shum, M. (2004): “Does Advertising Overcome Brand Loyalty? Evidence from the BreakfastCereals Market,” Journal of Economics & Management Strategy, 13, 241–272.
Simonov, A., J.-P. Dubé, G. Hitsch, and P. Rossi (2020): “State-Dependent Demand
Estimation with Initial Conditions Correction,” Journal of Marketing Research, 57, 789–809,
publisher: SAGE Publications Inc.
Sudhir, K. and I. Tewari (2015): “Long Term Effects of ’Prosperity in Youth’ onConsumption: Evidence from China,” SSRN Scholarly Paper ID 2681182.
Sullivan, S. A. and L. L. Birch (1990): “Pass the sugar, pass the salt: Experience
dictates preference.” Developmental psychology, 26, 546.
Thorn, B., N. Kline, C. Tadler, E. Budge, E. Wilcox-Cook, J. Michaels,
M. Mendelson, K. L. Patlan, and V. Tran (2018): “WIC Participant and Program
Characteristics 2016,” Tech. rep., U.S. Department of Agriculture, Food and Nutrition
Service.
Uetake, K. and N. Yang (2020): “Inspiration from the “Biggest Loser”: Social Interactions
in a Weight Loss Program,” Marketing Science, 39, 487–499.

43

USDA (2018a): USDA Branded Food Products Database, U.S. Department of Agriculture,
Agricultural Research Service, Nutrient Data Laboratory.
——— (2018b): USDA National Nutrient Database for Standard Reference, U.S. Departmentof Agriculture, Agricultural Research Service, Nutrient Data Laboratory.
Wang, D. D. and F. B. Hu (2017): “Dietary Fat and Risk of Cardiovascular Disease:
Recent Controversies and Advances,” Annual Review of Nutrition, 37, 423–446.
Wang, E. Y. (2015): “The impact of soda taxes on consumer welfare: implications ofstorability and taste heterogeneity,” The RAND Journal of Economics, 46, 409–441.
Zhang, Q., M. A. Alsuliman, M. Wright, Y. Wang, and X. Cheng (2020): “Fruitand Vegetable Purchases and Consumption among WIC Participants after the 2009 WIC
Food Package Revision: A Systematic Review,” Advances in Nutrition, 11, 1646–1662.

44Online Appendix: Not For Publication

45

A

Online Appendix: WIC food package
Table A1: WIC food package, per monthChildren
1–4 years

Milk (gallons)2
Whole wheat/grain bread (lb)
Fresh fruits and vegetables ($)
Juice (fluid oz)
Eggs
Breakfast cereal (oz)Canned fish (oz)Carrots (lb)
Cheese (lb)Legumes (lb)And/or peanut butter (oz)Milk (gallons)4
Whole wheat/grain bread (lb)5
Fresh fruits and vegetables ($)6
Juice (gallons)
Eggs
Breakfast cereal (oz)Canned fish (oz)Carrots (lb)
Cheese (lb)Legumes (lb)And/or peanut butter (oz)Pregnant,
partially breastfeeding
Panel A: 2006-20091
6
7
2.25
2.25
24-30
24-30
36
36
1
1
Or 18
Or 18
Panel B: 2009-20163
4
5.5
2
1
6 (8)
8 (10)
1
1.125
12
12
36
36
1
1
Or 18
And 18

Women
Postpartum

Breastfeeding

6
1.5
24-30
36
-

7
2.625
24-30
36
26
2
1
1
And 184
8 (10)
0.75
12
36
1
Or 18

6
1
10
1.125
24
36
30
1
1
And 18Notes: 1: In 2009, the exact date of the introduction of the new food package (described in panel B) varied bystate. 2: Milk is allowed to be partially substituted by cheese. 3. In 2014, federal regulation required small
modifications to the food package, the implementation date (in 2014–2015) of the modifications varied bystate and product. 4: For children 2-4 years of age and women reduced fat (2%), low-fat (1%) or nonfat milk
is the standard until 2014; afterwards only low-fat (1%) or non-fat milk is the standard. Whole milk is thestandard milk for 1-year-old children. Milk is allowed to be partially substituted by cheese, and since 2015,
states are allowed to authorize milk to be partially substituted by yogurt (only low-fat and non-fat yogurts
can be authorized for children over 2 years of age and women). 5: As substitutes to bread, states are allowed
to authorize on an equal weight basis brown rice, bulgur, oatmeal, whole-grain barley, or soft corn or whole
wheat tortillas, and since 2014 also whole wheat macaroni (pasta). 6: Fresh fruits and vegetables allowance isthe larger amount in parenthesis for for children since 2014 and for women since 2009–2010 (depending on astate). Sources: For panel A: Institute of Medicine (2006), pp. 212–215. For panel B: Federal Register, 2007,
Vol. 72, No. 234, pp. 68990–68991. Federal Register, 2009, Vol. 74, No. 250, p 69243. Federal Register, 2014,
Vol. 79, No. 42, p. 12294.

46

B

Online Appendix: Dataset construction and summary
statistics

In this appendix, I describe the construction of the dataset from the NielsenIQ Consumer
Panel and Retail Scanner data from years 2006–2016. The Retail Scanner data is used toconstruct price variables and the Consumer Panel data is used for both purchases and prices.

B.1

Dataset construction

This part describes the construction of the sample and variables, except prices which are
discussed in appendix B.3.

Purchases of subsidized products. In the case of bread, I concentrate on loaves of bread.
I exclude organic products, multi-unit products, and unusual package sizes. That is, I restrict
the sample to four most common package sizes: 16, 20, 22, and 24 oz. Note that in the
majority of states, only 16 oz package bread is allowed as a WIC product, some states also
allow 24 oz packages.
In the case of milk, I concentrate on dairy white fluid refrigerated milk. I exclude goatmilk, lactose free milk, and organic milk. I also drop multi-unit products, and unusual package
sizes. That is, the package sizes which I keep are: one gallon, half a gallon, and a quart (0.25
gallon). Note that in the majority of states, only one gallon package size is allowed as a WIC
product, a few states also allow half a gallon and a quart. I keep only packages which areeither plastic or carton, and drop glass bottles and other unusual packages.
Fruits and vegetables include fresh, frozen, and canned products. Fruits and vegetables
include all products with barcodes (UPCs), except potatoes. Juice includes regular, frozen,
and concentrated juice, but not fruit drinks. Cereals include breakfast cereals, hot cereals(including grits and cream of wheat), and granola.
47

Nutritional characteristics. The information about calories, saturated fat, and fiber
content is obtained from the USDA databases (USDA, 2018a,b). However, the databases
do not include nutritional information for all the products in the Nielsen dataset. I use asequential matching procedure similar to what is used by Dubois et al. (2014) and Oster(2018).
Product definition and aggregation of purchases in reduced form analysis (section
3). In section 3, purchases of each product are summed up to quarterly level. Following
WIC regulations, I classify a bread as whole wheat bread if it is made using 100% whole
wheat flour. A bread that only partially is made using whole wheat flour is classified as
non-whole-wheat. I call the whole wheat bread healthy bread and I don’t include wholegrain bread in healthy bread because majority of whole grain breads don’t satisfy the WIC
requirement of having whole grain as the primary ingredient by weight.
Sample for reduced form analysis (section 3). In section 3, the reduced form analysis
focuses on households that report receiving WIC assistance and who are in the Consumer
Panel data before, during, and at least two years after receiving the WIC vouchers. Households
are not necessarily in the Consumer Panel continuously, for all years in a row. I requirethat each household is in the dataset continuously at least at the time when the householdstarts to receive the vouchers (the last year before receiving the vouchers and the first year
while receiving the vouchers) and when he stops receiving the vouchers (the last year while
receiving the vouchers and the first year after receiving the vouchers). This allows analyzing
within-household changes when a household starts and stops receiving the WIC vouchers.
In 2006–2016, 3414 households report currently receiving WIC vouchers. Figure B1
presents for each year, the total number of households and households that report currently
receiving WIC vouchers. In order to analyze within-household changes when households start
receiving the vouchers and two years after they stop receiving the vouchers, one would need48

to observe the households for a minimum of four years. However, only 1336 of the households
are in the dataset for that long. Moreover, only 571 households are observed before, while,and after receiving the vouchers. Requiring that each household is observed the last year
before and the first and the second year after receiving the vouchers reduces the sample to

2006

0

0

Number of households in WIC
200
400
600

Total number of households
20000
40000
60000

800

347 households. How much each restriction decreases the sample is described in table B1.

2008

2010

2012

2014

2016

2006

2008

2010

2012

2014

2016

Year

Year

(a) Total(b) Reporting receiving WIC voucher

Figure B1: Number of households
Note: The increase in the number of households reporting receiving WIC vouchers from year 2006
to 2007 is partly due to the increase in the NielsenIQ Consumer Panel from about 40,000 to about
60,000 households.

Table B1: Sample construction
Number of households
NielsenIQ Consumer Panel dataset 2006-2016
158004.. report receiving WIC vouchers
3414.. & in the dataset at least 4 years
1336.. & in the dataset before report receiving WIC
695.. & in the dataset after report receiving WIC
571.. & in the dataset in the 1st and 2nd year after report receiving WIC
374.. & in the dataset the latest year before report receiving WIC
347

Table B2 presents the comparison of households included versus excluded from the sample.
It shows that the sample and the excluded households are similar in terms of education,49

race, and marital status, but the households in the sample have higher income (by 27%),
smaller size (by 13%), are less likely to be Hispanic ethnicity (by 69%), and are less likely
not to work full time (by 12%). It also shows that while the consumer panel matches theoverall WIC population rather well in terms of household size and race, it misses a large
share of low-income and a majority of Hispanic households. As has been already noted in
the literature (Khan et al., 2016), the average income of WIC households in the consumer
panel is more than twice as high as in the administrative data. Also, over 40% of the WIC
population is of Hispanic ethnicity, while in the consumer panel only about 12% and in the
final sample only about 4%.
Table B2: Comparison of WIC households in the sample, excluded from the sample WIC
households in the NielsenIQ Consumer Panel, and administrative data
NielsenIQ WIC households Wilcoxon Administrative data
2006-2016
rank test
WIC households
SampleExcludedp-value
2016
(1)
(2)
(3)
(4)
Panel A: Demographic characteristics
Household income (thousands)
52.2
41.2
0.000
18.4
Household size
3.5
4.0
0.000
4.1
Race: white
0.723
0.739
0.517
0.586
Ethnicity: Hispanic
0.040
0.128
0.000
0.418
College
0.395
0.404
0.733
.
Married
0.726
0.741
0.540
.
Not employed full time
0.709
0.805
0.000
.
Panel B: Region
Northeast
13.0
15.7
.
14.3
Midwest
28.8
26.5
.
18.3
South
40.3
39.0
.
41.7
West
17.9
18.8
.
25.7
Number of households
347
3067
Notes: Source for the administrative data in column 4 is the USDA report (Thorn et al., 2018). The average
income in the report is calculated to 2015 dollars using the consumer price index for urban consumers.
Column 1–2 present unweighted data, that is, NielsenIQ household weights are not used.

The characteristics of the households in the sample by treatment and control group are50

presented in columns 1–2 of table 1.
I use other households with children or lower income or both as an additional control
group (column 3 in table 1). Specifically, these households at least for one year had a child up
to 17 years old or had income not exceeding 200% of the federal poverty guidelines or both.
Product definition and aggregation of purchases in demand model estimation(section 4). In section 4, I group bread into four products: white, whole wheat, wholegrain, and other. White bread is a non-whole-grain bread made from white refined flour.
Following WIC regulation, I classify bread as whole wheat bread if it contains 100% whole
wheat flour. I classify bread that is only partially made with whole wheat flour or contains
any other type of whole grain flour or rye flour whole grain bread. Finally, other bread
aggregates together all other non-whole-grain bread types (like Cinnamon Raisin, Cinnamon
Swirl, etc.).
Purchases of each product are aggregated to week and (aggregate) retailer level. The
aggregation is done in the following way. First, I aggregate purchases to week, bread type,and retail chain level. If a household bought more than one type of bread in a retail chain in
a given week, I keep the largest purchase by weight. If a household bought bread in morethan one retail chain per week, then I keep the largest purchase by weight in a chain in the
Retail Scanner Dataset (if any exists) and the largest purchase in a chain not in the Retail
Scanner Dataset (if any exists).
Sample for demand model (section 4). To keep the demand model estimation manageable, I restrict attention to the sample of households who all have reported receiving WIC
assistance (households in columns 1–2 of table 1). The demand model is estimated using
only the time periods before and after receiving WIC vouchers. While households received
WIC vouchers, I don’t know whether they paid with a voucher or cash on a given shopping
trip. Hence, I don’t know the price they faced on a given shopping trip: whether the regular51

price or price zero because of the voucher.
I use only purchases in grocery stores and mass merchandisers (discount stores). Drugstores and others are excluded because those are unlikely to sell all four types of bread.
In the first year of each household in the dataset, I don’t use the first ten shopping trips
in the estimation. But I use these purchases to construct the stock variable of whole wheat
bread past purchases. Ideally, I would exclude the whole first year from the estimation, butthat would result in excluding all the households who are in the dataset only one year before
receiving the WIC vouchers.
I exclude households that don’t have a sufficient number of bread purchases in grocery anddiscount stores. Each purchase should also have enough information about the past purchases
to construct the stock variable of past year’s whole wheat bread purchases. Specifically, I
exclude households who don’t have purchases before receiving the vouchers. I also requirethat a household has purchases in the first and second year after receiving the vouchers, andaltogether at least ten purchases in the first two years after receiving the vouchers. In order
to use the impact of WIC policy reform for identification, I also require that a household
purchased bread in the grocery and discount stores during the last year on WIC.
Construction of demographic variables. I generate income variable as the mid-pointof the reported income interval. Except for the highest income group, for which the mid-point
cannot be calculated as no highest level is reported. For that group I assume that theirhousehold annual income equals 115,000 dollars, which is consistent with the current income
distribution. Income is deflated to 2015 dollars using the consumer price index for urban
consumers.
Underreporting of WIC status. In the survey data, household’s WIC status seems to
be underreported. The information on WIC status is collected via a survey question, whichhouseholds are not required to answer. Therefore, as expected, in the dataset, the reported
52

share of households receiving WIC assistance is lower than in the administrative data. Figure
B2 shows the percentage of income eligible households who report receiving WIC assistance,by the age of the youngest child. The figure illustrates two aspects of the data. First, themagnitude of underreporting. Back-of-the-envelope calculations suggest that about forty
percent of WIC participants report it in the survey.29 Second, the households’ reported WIC
participation mirrors well the pattern in the administrative data. Namely, WIC participationis the highest during the calendar year when the child is born and decreases after that up to
the child’s fifth birthday. In the analysis, I focus on households who report receiving WIC

0

Percentage with WIC
10
20

30

assistance.

-1

0

1

2

3

4

5

Figure B2: Percentage of households reporting receiving WIC assistance, by the years since
the youngest child is born
Note: Sample is restricted to WIC income eligible households. Calculated as an average overhousehold-years and weighted by Nielsen projection weights. Year 0 indicates that the youngest
child is born during the current panel year. Income eligibility is calculated using the mid-point valueof Nielsen reported household income interval.
29

According to the USDA report (Johnson et al., 2014), around 80% of eligible infants (up to their firstbirthday) receive WIC. However, in this dataset, the reported WIC participation of the corresponding
households is slightly above 30%. According to the administrative data, participation of children aged 1–4 isabout 50%, but in this dataset, only around 20%.

53

How could the underreporting bias the analysis? First, if non-WIC households in thecontrol group also received the WIC vouchers, then the short-term effect would be underestimated. It is reassuring that later in the analysis, when non-WIC households are excluded,
the estimates remain similar. Second, if households selectively report the years when theyreceive the WIC vouchers, specifically, if underreporting increases with the number of years
in the sample, then a household would be mistakenly assigned to the post-WIC period while
it is still receiving the vouchers. In that case, the persistence of WIC would be overestimated.
It is somewhat reassuring that in section 3, we will see that the estimated persistence israther low already.

54

B.2

Additional summary statistics of the dataset for reduced form

0

0

.2

.05

.4

.1

.6

DensityDensity

.15

.8

.2

1

analysis

0

20

40

60

80

100

0

1

2

Bread healthy %WIC post-reform
Children or low-income

3

4

Milk fat %WIC pre-reform

WIC post-reform
Children or low-income(b) Milk fat %Density

0

0

.02

.02

.04

.04

Density

.06

.06

.08

.1

.08

(a) Bread healthy %WIC pre-reform

0

50

100

150

200

250

0

Bread (lb)
WIC post-reform
Children or low-income

50

100

150

Milk (gallons)
WIC pre-reform

WIC post-reform
Children or low-income(c) Quantity of bread

WIC pre-reform(d) Quantity of milk

Figure B3: Kernel density estimates of the distribution of purchases of bread and milk
Note: The kernel density estimates of the distribution of quarterly average household purchases
during first year in the sample, separately for the three groups in table 1. Estimates are obtainedusing Epanechnikov kernel and the bandwidth that would minimize the mean integrated squared
error if the data were Gaussian and a Gaussian kernel were used. Except for milk fat percentage
which uses bandwidth 0.1 because with the multimodal distribution the above bandwidth would
oversmooth the density.

55

.00015

Density

0.00005

Density.0001.00002 .00004 .00006 .00008 .0001
0

0

50000

100000150000050000

Fruits and vegetables (kcal)
WIC post-reform
Children or low-income

100000150000

Juice (kcal)

WIC pre-reform

WIC post-reform
Children or low-income

Density

.002
0

0

.005

Density

.01

.004

.006

(b) Quantity of juice.015(a) Quantity of fruits and vegetables

WIC pre-reform

0

500

1000

1500

Eggs (count)
WIC post-reform
Children or low-income

0

500

1000

1500

2000

Cereals (ounces)
WIC pre-reform

WIC post-reform
Children or low-income(c) Quantity of eggs

WIC pre-reform(d) Quantity of cereals

Figure B4: Kernel density estimates of the distribution of purchases of other products
Note: The kernel density estimates of the distribution of quarterly average household purchases
during first year in the sample, separately for the three groups in table 1. Estimates are obtainedusing Epanechnikov kernel and the bandwidth that would minimize the mean integrated squared
error if the data were Gaussian and a Gaussian kernel were used.

56

2.5

20

1

5

1.5

10

Milk fat %2

15

Bread whole wheat %

0

2006

2008

2010

2012

2014

2016

2006

2008

2010

Year
WIC post-reform

2012

2014

2016

Year
Children or low-income

WIC post-reform(b) Milk fat %

0

0

3

3

6

6

Bread (lb)9

Milk (gallons)

9

12

12

(a) Bread healthy %Children or low-income

2006

2008

2010

2012

2014

2016

2006

2008

2010

Year
WIC post-reform

2012

2014

2016

Year
Children or low-income

WIC post-reform(c) Quantity of breadChildren or low-income(d) Quantity of milk

Figure B5: Average quarterly purchases over time, bread and milk
Note: Averages and 95% confidence intervals of households’ yearly average quarterly purchases.
When calculating the average and confidence intervals, for each year, the unit of observation is ahousehold. The blue line presents the average purchases for the WIC post-reform households (column
1 in table 1) and the black line for the additional control group of Children or low-income households(column 3 of table 1). For the WIC post-reform households only years before receiving WIC vouchers
are included. It is not possible to look at the trend for WIC pre-reform households using years
before vouchers, because that would be limited to only the pre-reform years. Depending on a year,
the averages are calculated based 22–139 households for the WIC post-reform and 22,267–38,565
households for the Children or low-income group.

57

15000

0

2000

5000

4000

6000

Juice (kcal)

10000

8000

Fruits and vegetables (kcal)

0

2006

2008

2010

2012

2014

2016

2006

2008

2010

Year
WIC post-reform

2012

2014

2016

Year
Children or low-income

WIC post-reform

0

0

50

30

100

60

150

Eggs (count)

Cereals (ounces)

90

200

250

(b) Quantity of juice

120(a) Quantity of fruits and vegetables

Children or low-income

2006

2008

2010

2012

2014

2016

2006

2008

2010

Year
WIC post-reform

2012

2014

2016

Year
Children or low-income

WIC post-reform(c) Quantity of eggs

Children or low-income(d) Quantity of cereals

Figure B6: Average quarterly purchases over time, other products
Note: Averages and 95% confidence intervals of households’ yearly average quarterly purchases.
When calculating the average and confidence intervals, for each year, the unit of observation is ahousehold. The blue line presents the average purchases for the WIC post-reform households (column
1 in table 1) and the black line for the additional control group of Children or low-income households(column 3 of table 1). For the WIC post-reform households only years before receiving WIC vouchers
are included. It is not possible to look at the trend for WIC pre-reform households using years
before vouchers, because that would be limited to only the pre-reform years. Depending on a year,
the averages are calculated based 22–139 households for the WIC post-reform and 22,267–38,565
households for the Children or low-income group.

58

Milk fat %

2

2.05

20
15

1.95

10

Bread whole wheat %5

Before WIC

During WIC
Pre-reform WIC

After

Before WIC

Post-reform WIC

During WIC
Pre-reform WIC(b) Milk fat %

9

7.5

9.5

8

8.5

Milk quantity

10.5
10

Bread quantity

9

11

9.5

11.5

(a) Bread healthy %After
Post-reform WIC

Before WIC

During WIC
Pre-reform WIC

After
Post-reform WIC

Before WIC

During WIC
Pre-reform WIC(c) Quantity of bread

After
Post-reform WIC(d) Quantity of milk

Figure B7: Comparison of changes in purchases before, while, and after receiving WIC
vouchers, pre-reform WIC versus post-reform WIC households, bread and milk
Note: The sample of Pre-reform WIC includes households in column 2 of table 1 who started toreceive WIC vouchers in 2007–2008. The sample of Post-reform WIC includes households in column
1 of table 1 who started to receive WIC vouchers in 2010–2011. The sample excludes time periods
earlier than four years before receiving the vouchers and later than two years after receiving thevouchers.

59

6000

Juice quantity

4500

5000

5500

8200
8000
7800
7600

During WIC
Pre-reform WIC

After

4000

Fruits and vegetables quantity

7400
7200

Before WIC

Before WIC

Post-reform WIC

During WIC
Pre-reform WIC(b) Quantity of juice

Before WIC

160

Cereals quantity

During WIC
Pre-reform WIC

After
Post-reform WIC

140

55

150

60

Eggs quantity

170

65

180

(a) Quantity of fruits and vegetables

After
Post-reform WIC

Before WIC

During WIC
Pre-reform WIC(c) Quantity of eggs

After
Post-reform WIC(d) Quantity of cereals

Figure B8: Comparison of changes in purchases before, while, and after receiving WIC
vouchers, pre-reform WIC versus post-reform WIC households, other products
Note: The sample of Pre-reform WIC includes households in column 2 of table 1 who started toreceive WIC vouchers in 2007–2008. The sample of Post-reform WIC includes households in column
1 of table 1 who started to receive WIC vouchers in 2010–2011. The sample excludes time periods
earlier than four years before receiving the vouchers and later than two years after receiving thevouchers.

60

B.3

PricesBread prices are constructed from the Retail Scanner Data for shopping trips to retail chainsin the Retail Scanner dataset. To do that, prices are aggregated to the bread type, week,
market (Nielsen scantrack market) and chain level. But more than half of the WIC households’
bread purchases are at retailers (grocery stores and mass merchandisers) that are not in the
Retail Scanner Data. For those shopping trips the prices are constructed from the Consumer
Panel Data and prices are aggregated to the bread type, week, and market (Nielsen scantrackmarket) level. In both cases, prices are deflated to 2015 dollars using the consumer priceindex for urban consumers.
I use data on sales and purchases in grocery stores and mass merchandisers (discountstores). Drug stores and others are excluded.

Retail Scanner Data. Using the Retail Scanner Data, I define a chain by the retailer code.
If a chain is present in only one market, then to be able to calculate instruments (average
price in other markets), I follow DellaVigna and Gentzkow (2019) and split the market. To
do that, I assign stores by 3 digit zip code into one of the two split markets, by first ranking
3 digit zip codes by the number of stores and then using a greedy algorithm to assign zip
codes to split markets with a goal of making the split markets as equal as possible by the
number of stores.
To aggregate UPC level prices to product prices, first I convert these to price per ounce.
Then, for each of the products (white, whole wheat, whole grain, and other bread), I calculate
the weighted average prices. The weight of the UPC is equal to its share of volume of that
product in a market in a given year in a retail chain.

Consumer Panel Data. Using the Consumer Panel Data, I ignore consumers’ possible
use of coupons, and use the price without subtracting the value of coupons. I convert all

61

UPC level prices to price per ounce to be able to aggregate to product level prices. As isstandard in the literature that constructs prices from the Consumer Panel data, I exclude
outliers. Specifically, I exclude UPCs that are bought by less than 25 households in the entire
dataset. I also exclude purchases if the price is more than four times the median price or lessthan one-fourth of the median of all purchases in the entire dataset for that UPC. Finally,for each bread type, market, year, and aggregate retailer combination, I replace prices lower
than the first percentile with the first percentile and similarly, replace prices higher than the
99th percentile with the 99th percentile.
The Consumer Panel Data has price information about a UPC in a given week in a given
market only when there is a household in the sample who buys the product. We don’t observe
the price of a UPC if noone in the sample bought it. I use the following method to fill in the
missing price information. First for each week-market-chain triplet, I calculate UPCs average
price (using the household sample weights included in the Consumer Panel Data). If in agiven week the price of the UPC is missing in a market in a chain, then I use the price of thesame UPC in the same chain in the same market within the previous and following 4 weeks.
If there is still no price information available for the UPC, then I exclude the UPC for thatweek and market and chain.
Using these UPC-chain level prices, I calculate the weighted average product (white, whole
wheat, whole grain, and other bread) prices for two aggregate retailers. The two aggregate
retailers are first, those in the Retail Scanner Data, and second, those not in the Retail
Scanner Data. The weight of the UPC and chain pair is equal to its share of volume of that
product in a market in a given year in an aggregate retailer. I use sample weights provided
in the dataset to calculate the weighted average.

Price comparison. How different are the prices constructed from the two alternative
datasets? We can look at that for the subset of retailers that is overlapping in these datasets.

62

Table B3 presents summary statistics of prices calculated from Consumer Panel and Retail
Scanner data. In columns 2–3 prices are calculated from the Consumer Panel data. These
prices are calculated aggregating across all the retailers in the Retail Scanner data (column
3) or across all the retailers not in the Retail Scanner (column 2). Column 4 presents prices
calculated from the Retail Scanner data, these prices are calculated at the retailer level.
Column 1 combines prices from columns 2 and 4, these are the prices used in demand model
estimation. Column 5 compares prices for the retailers in the Retail Scanner data calculatedusing Consumer Panel (column 3) and Retail Scanner data (column 4). That is, column 5presents the percentage difference (divided by 100) between the prices in columns 4 and 3.
For these overlapping retailers, bread prices constructed based on the two datasets line up
rather closely, prices based on the consumer panel data are on about 10% lower for all four
product types (column 5 in table B3). The magnitude of the difference is very similar to what
has been shown for aggregate grocery price indexes constructed based on the two datasets(for example, Seo (2019)). The mis-measurement of prices is unlikely to be a substantial
concern since the difference is small, and importantly, in any given choice occasion (shoppingtrip), consumers face prices constructed in the same way.
Table 2 presents summary statistics of prices used in the demand model estimation.
Table B4 shows that majority of the households in the sample make bread purchases bothin retailers that are only in the consumer panel and in those in the retail scanner data. The
market shares of different types of bread purchases in those two types of retailers are alsorather similar.

63

Table B3: Summary statistics of bread prices calculated using alternative methods
Consumer
Panel &
Retail Scanner
(1)
Mean
Sd
Min
25th perc.
Median75th perc.
Max
Number of obs.

1.77
0.41
0.61
1.49
1.75
2.03
4.27
112168Mean
Sd
MedianNumber of obs.

1.95
0.34
1.88
28042

Mean
Sd
MedianNumber of obs.

2.03
0.30
1.95
28042

Mean
Sd
MedianNumber of obs.

1.36
0.28
1.30
28042

Mean
Sd
MedianNumber of obs.

1.76
0.33
1.67
28042

Stores only inOverlapping storesConsumer
Consumer
Retail Scanner
Panel
Panel
(2)
(3)
(4)
Panel A: All bread products
1.64
1.79
1.98
0.33
0.35
0.42
0.61
0.84
0.78
1.40
1.51
1.68
1.65
1.82
2.00
1.87
2.05
2.29
2.90
3.03
4.27
68608
43560
43560
Panel B: Whole wheat bread
1.77
2.07
2.23
0.22
0.23
0.30
1.74
2.07
2.22
17152
10890
10890
Panel C: Whole grain bread
1.92
1.97
2.20
0.23
0.28
0.33
1.90
1.99
2.17
17152
10890
10890
Panel D: White bread
1.24
1.38
1.54
0.19
0.19
0.30
1.22
1.35
1.49
17152
10890
10890
Panel E: Other bread
1.62
1.74
1.97
0.22
0.23
0.36
1.58
1.70
1.94
17152
10890
10890

%∆
(5)
-0.10
-0.17
0.07
-0.10
-0.09
-0.10
-0.29
43560
-0.07
-0.25
-0.07
10890
-0.10
-0.16
-0.09
10890
-0.10
-0.37
-0.09
10890
-0.12
-0.35
-0.12
10890

Note: Price of bread is measured in dollars per pound, deflated to 2015 dollars using the consumer priceindex for urban consumers. Observations are at the week, market, bread type, and (aggregate) retailer
level. Columns 2–3 present prices calculated from the Consumer Panel data. These prices are calculated
aggregating across all the retailers in the Retail Scanner data (column 3) or across all the retailers not in the
Retail Scanner (column 2). Column 4 presents prices calculated from the Retail Scanner data, these prices
are calculated at the retailer level. Column 1 combines prices from columns 2 and 4. Column 5 presents thepercentage difference (divided by 100) between the prices in columns 5 and 4.

64

Table B4: Descriptive statistics of bread purchases

Share of households purchasing in retailers
Number of retailers household purchases (median)
Number of households
Other bread
Whole grain bread
Whole wheat bread
White bread
Number of shopping trips

65

Retailers in
Only in
RetailConsumer Panel Scanner
(1)
(2)
0.98
0.87
3
2
252
252
Bread type market shares
0.32
0.33
0.13
0.20
0.12
0.10
0.42
0.37
17152
10890

C

Online Appendix: Additional analysis for the shortand long-term impact of healthy food subsidies

This appendix reports additional analysis that are mentioned in the main text of section 3.

C.1

Long-term effect separately for years 1 and 2

Table C1 presents the estimates of the long-term effect separately for years 1 and 2 after
receiving the WIC vouchers. It estimates the following regression similar to the main
specification (equation (1)):

Yit = α1 W ICit + α2,1 Af terW ICY ear1it + α2,2 Af terW ICY ear2it+ β1 Ref ormedW ICit + β2,1 Af terRef ormedW ICY ear1it + β2,2 Af terRef ormedW ICY ear2it++ α3 Af terW ICY ear3+
it + β3 Af terRef ormedW ICY ear3it+ σ · P ostRef ormit + Xit ζ + δi + γt + εit(5)Compared to the estimates of the long-term effect β2 in the main specification (table 3),
the corresponding estimates β2,1 , β2,2 are similar, but less precise.

66

Table C1: The impact of post-reform WIC on subsidized products; long-term effect separately
for years 1 and 2 after receiving the WIC vouchersBreadhealthy %

Milk
fat %

Bread
Milk Fruits&veg. Juice
Eggs Cereals
log.
log.
log.
log.
log.
log.
quantity quantity quantity quantity quantity quantity
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
β1 : Reformed WIC
6.925*** -0.135*** -0.013 0.022-0.0020.275 -0.064 0.036(2.212) (0.050) (0.053) (0.054)(0.087)(0.206) (0.095) (0.085)
β2,1 : After Reformed WIC Year 1 4.033*-0.046 -0.056 0.030-0.0650.604** -0.026 0.228*(2.074) (0.069) (0.071) (0.071)(0.111)(0.299) (0.120) (0.123)
β2,2 : After Reformed WIC Years 2 -1.255-0.0820.060 -0.022-0.023-0.288 -0.206 0.150(2.157) (0.075) (0.082) (0.076)(0.142)(0.305) (0.133) (0.146)
α1 : WIC-1.799
0.003
0.040
0.051
0.037
0.456*** 0.073 0.132*(1.332) (0.035) (0.041) (0.046)(0.066)(0.166) (0.079) (0.069)
α2,1 : After WIC Year 1
0.672-0.0440.037 -0.003
0.084-0.161 -0.038 -0.126(1.424) (0.059) (0.056) (0.058)(0.089)(0.265) (0.100) (0.105)
α2,2 : After WIC Year 2
2.708
0.028
-0.022 0.064-0.0090.604** 0.079 -0.101(1.758) (0.067) (0.069) (0.065)(0.120)(0.261) (0.112) (0.128)
σ: Post-Reform
0.207-0.014** -0.001 0.008
0.002
0.111*** 0.021 -0.032*(0.270) (0.007) (0.009) (0.008)(0.018)(0.037) (0.015) (0.017)
Year-quarter FE
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Household FE
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Wald test, β1 = β2,1 , p-value
0.136
0.153
0.495
0.893
0.560
0.265
0.746
0.105
Wald test, β1 = β2,2 , p-value
0.001
0.485
0.363
0.590
0.887
0.062
0.317
0.440
WIC households
301
301
347
347
347
347
347
347
Households
85421
80721
96637 96637
96637
96637 96637 96637
Household-quarters
1244237 1192570 1602252 1602252 1602252 1602252 1602252 1602252
Note: Each column presents estimates from a separate panel data fixed effects regression (equation (5)).
A unit of observation is a household-quarter pair. Bread healthy (whole wheat) % and milk fat % are in
the range of 0–100, quantity is measured in pounds for bread, gallons for milk, kilocalories for fruits andvegetables and juice, counted for eggs, and ounces for cereals. All regressions include household size, logarithmof income, dummies for the year before child is born, and children aged 0, 1, . . . , 5, 6-12, and 13-17. Incolumn 2, regressions include an interaction terms for WIC (and Reformed WIC) and the last two quartersof the calendar year when the child gets one years old and the other with the first two quarters of thecalendar year when the child gets two years old. The sample includes households in columns 1–3 in table 1.
Regressions include household and time period fixed effects. Standard errors (in parentheses) are clustered at
the household level. *** Indicates significance at the 1 percent level, ** 5 percent level, * 10 percent level.

67Pre-trends

2
1.8

1.9

Milk fat %

12
11

1.7

10

Healthy bread %

13

14

2.1

C.2

-2

-1

0

-2

Years since WIC
Control

Post-reform WIC

Control0

Post-reform WIC(b) Milk fat %

8
7
6

7

8

9

Milk quantity

9

10

11

10

(a) Bread healthy %Bread quantity-1

Years since WIC

-2

-1

0

-2

Years since WIC
Control-10Years since WIC

Post-reform WIC

Control(c) Quantity of bread

Post-reform WIC(d) Quantity of milk

Figure C1: Pre-trends comparison households in post-reform WIC versus control group ofhouseholds not receiving WIC vouchers, bread and milk
Note: The sample of Post-reform WIC (treatment group) includes households in column 1 of table 1 whoare in the dataset at least two years before starting to receive the post-reform WIC vouchers. The sample ofControl includes households in column 3 of table 1, it does not include households in column 2 because only
very few of those are in the dataset two years before receiving the vouchers. For milk fat percentage, thesample excludes observations in the treatment group, when a household has a one year old child because
for one-year-old children, the reformed WIC food vouchers make an exception and provide whole milk. The
figure presents averages of purchases from two years before receiving the post-reform WIC vouchers (-2)
to the first year of receiving the post-reform WIC vouchers (0), for the treatment group (the households
receiving the post-reform vouchers) and the corresponding control group. The averages are calculated in thefollowing steps. First, each treatment group cohort (households that started receiving post-reform vouchers
in year t) is matched to the corresponding control group: households who are in the dataset continuously for
years t − 2 to t. Second, the cohort averages are calculated of both the treatment and control group. Third,
the weighted average over the cohorts (t = 2009, ..., 2014) is calculated, where the weights are equal to thetreated cohort’s share in all the treated observations.

68

3000

3500

4000

Juice quantity

4500

5000

9000
8500
8000

Fruits and vegetables quantity

7500

-2

-1

0

-2

Years since WIC
Control

Post-reform WIC

Control0

Post-reform WIC(b) Quantity of juice

50

150
140
120

55

130

60

65

Cereals quantity

70

160

75

170

(a) Quantity of fruits and vegetables

Eggs quantity-1

Years since WIC

-2

-1

0

-2

Years since WIC
Control-10Years since WIC

Post-reform WIC

Control(c) Quantity of eggs

Post-reform WIC(d) Quantity of cereals

Figure C2: Pre-trends comparison households in post-reform WIC versus control group ofhouseholds not receiving WIC vouchers, other products
Note: The sample of Post-reform WIC (treatment group) includes households in column 1 of table 1
who are in the dataset at least two years before starting to receive the post-reform WIC vouchers. The
sample of Control includes households in column 3 of table 1, it does not include households in column
2 because only very few of those are in the dataset two years before receiving the vouchers. The figure
presents averages of purchases from two years before receiving the post-reform WIC vouchers (-2) to the firstyear of receiving the post-reform WIC vouchers (0), for the treatment group (the households receiving thepost-reform vouchers) and the corresponding control group. The averages are calculated in the following
steps. First, each treatment group cohort (households that started receiving post-reform vouchers in year t)
is matched to the corresponding control group: households who are in the dataset continuously for yearst − 2 to t. Second, the cohort averages are calculated of both the treatment and control group. Third, theweighted average over the cohorts (t = 2009, ..., 2014) is calculated, where the weights are equal to the treatedcohort’s share in all the treated observations.

69

C.3

Robustness analysis of the main reduced form estimates

C.3.1

Analysis based only on households that received the WIC vouchers

To alleviate the concern, that households start receiving post-reform WIC vouchers due to a
shock that changes food purchases, I compare only the pre- and post-reform WIC households
who arguably are all subject to similar shocks (related to child’s birth) when starting toreceive WIC vouchers. Table C2 presents estimates of the main specification (equation (1)),
except that time period fixed effects are excluded, as these would not be identified. The
short-term effects’ estimates, using this sample of only pre- and post-reform WIC households,
are similar to those from the main specification; long-term effects’ estimates are qualitatively
similar. The difference between the short- and long-term effect is statistically significant at
the 1% level for the healthy bread and 5% level for the milk fat percentage.
Table C2: The impact of post-reform WIC on subsidized products; sample restricted to WIC
households
Breadhealthy %

Milk
fat %

Bread
Milk Fruits&veg. Juice
Eggs Cereals
log.
log.
log.
log.
log.
log.
quantity quantity quantity quantity quantity quantity
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
β1 : Reformed WIC
4.583** -0.143*** -0.017 -0.035-0.044-0.132 -0.135 -0.012(2.117) (0.052) (0.053) (0.056)(0.091)(0.211) (0.099) (0.097)
β2 : After Reformed WIC Years 1-2 -0.456-0.015 -0.052 -0.067-0.024-0.183 -0.109 0.064(1.962) (0.067) (0.071) (0.066)(0.112)(0.269) (0.117) (0.120)
α1 : WIC-1.1840.029-0.005 0.010-0.0050.294* 0.053
0.069(1.379) (0.037) (0.042) (0.045)(0.065)(0.167) (0.076) (0.069)
α2 : After WIC Years 1-2
1.464
0.003
-0.084 -0.092*-0.113-0.253 -0.134 -0.218**(1.584) (0.059) (0.060) (0.053)(0.099)(0.246) (0.102) (0.106)
σ: Post-Reform
3.606*** 0.020 -0.098** -0.002
0.004
0.151
0.050 -0.144*(1.156) (0.036) (0.039) (0.036)(0.061)(0.153) (0.070) (0.076)
Household FE
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Wald test, β1 = β2 , p-value
0.006
0.040
0.587
0.604
0.865
0.848
0.827
0.529
WIC households
301
301
347
347
347
347
347
347
Households
301
301
347
347
347
347
347
347
Household-quarters
9133
9064
11224 11224
11224
11224 11224 11224
Note: The table presents estimates from the same regressions as in table 3, but the sample is restricted tohouseholds who received WIC vouchers (households in columns 1–2 in table 1) and the regressions do notinclude time period fixed effects. Standard errors (in parentheses) are clustered at the household level. ***Indicates significance at the 1 percent level, ** 5 percent level, * 10 percent level.

70C.3.2

TrendsI re-estimate the main specification allowing separate trends for the treatment group, and theestimates for the healthy bread and milk fat percentage remain similar. Additional tests forparallel trends are provided using the heterogeneity-robust difference-in-differences estimates,
which are explained below.
Table C3: The impact of post-reform WIC on subsidized products, including trends fortreatment groupBreadhealthy %

Milk
fat %

Bread
Milk Fruits&veg. Juice
Eggs Cereals
log.
log.
log.
log.
log.
log.
quantity quantity quantity quantity quantity quantity
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
β1 : Reformed WIC
6.742*** -0.147*** 0.019 -0.021-0.0840.074 -0.159* 0.002(2.212) (0.050) (0.054) (0.054)(0.087)(0.208) (0.096) (0.086)
β2 : After Reformed WIC Years 1-2 1.007-0.0920.037 -0.079-0.192*-0.286 -0.318*** 0.084(1.944) (0.066) (0.072) (0.064)(0.112)(0.270) (0.116) (0.119)
α1 : WIC-1.872-0.005
0.011
0.042
0.032
0.340** 0.027
0.073(1.332) (0.036) (0.043) (0.046)(0.066)(0.168) (0.080) (0.069)
α2 : After WIC Years 1-2
1.660-0.013 -0.006 0.026
0.036
0.165
-0.001 -0.142(1.482) (0.059) (0.057) (0.053)(0.093)(0.236) (0.098) (0.102)
σ: Post-Reform
0.017
0.000
0.000
0.000
0.003
0.004
0.001
0.001
(0.270) (0.007) (0.009) (0.008)(0.018)(0.037) (0.015) (0.017)
Year-quarter FE
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Household FE
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Wald test, β1 = β2 , p-value
0.004
0.379
0.788
0.365
0.341
0.175
0.184
0.483
WIC households
301
301
347
347
347
347
347
347
Households
85421
80721
96637 96637
96637
96637
96637
96637
Household-quarters
1244237 1192570 1602252 1602252 1602252 1602252 1602252 1602252
Note: The table presents estimates from the same regressions as in table 3, except that it includes trends
separately for the cohorts that start receiving post-reform WIC vouchers in 2009–2011 and those that startin 2012-2014. (There are no cohorts starting later as the sample is restricted to WIC households who are
observed at least 2 years after receiving the vouchers.) Standard errors (in parentheses) are clustered at thehousehold level. *** Indicates significance at the 1 percent level, ** 5 percent level, * 10 percent level.

71C.3.3

Assessing the importance of negative weights in the two-way fixed effects
estimator

Recent econometrics literature has raised concerns about the two-way fixed effects estimatorwhen the timing of treatment is staggered and treatment effects are heterogeneous either
over time within units or across groups of units treated at different times (Goodman-Bacon,2021; de Chaisemartin and D’Haultfœuille, 2020b). The issue is that the two-way fixed
effects estimator is a weighted average of the heterogeneous treatment effects where someweights potentially could be negative, which would lead to a bias in the estimates. Due tothe negative weights, the estimate may, for example, be negative even when all the averagetreatment effects are positive.
To assess the concern, first, I calculate the share of negative weights (table C4).30
Throughout the appendix, I concentrate on analyzing only the short-term effect, because
estimating the long-term effects would require allowing switching back from treatment, which
the considered methods don’t accommodate. Reassuringly, the share of negative weights
is either zero or very small which implies that it is unlikely to lead to a substantial bias.
To further study whether the treatment effect heterogeneity is potentially problematic forβ1 estimate, we can look at the two diagnostic measures at the bottom of table C4. The
first measure σ̂ f e corresponds to the minimum amount of treatment effect heterogeneity (theminimal value of the standard deviation of the treatment effect across the treated groups andtime periods) under which β̂1 and the true average treatment effect on the treated (ATT)
could be of opposite signs. The second measure σ̂ f e corresponds to the minimum amount oftreatment effect heterogeneity (the minimal value of the standard deviation of the treatment
effect across the treated groups and time periods) under which β̂1 could be of a different
sign than the treatment effect in all the treated group and time periods. Note that the30

I use the twowayfeweights Stata package developed by the authors to accompany the work in de Chaisemartin and D’Haultfœuille (2020b), and is available from the STATA repository.

72second measure is defined only if there are any negative weights. It is reassuring that in these
regressions, σ̂ f e -s are larger than β̂1 -s, which implies that to make the estimated β̂1 -s invalid,
we would need large treatment effect heterogeneity.
Table C4: Negative weights
Breadhealthy %

Milk
fat %

Bread
Milk Fruits&veg. Juice
Eggs Cereals
log.
log.
log.
log.
log.
log.
quantity quantity quantity quantity quantity quantity
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
β1 : Reformed WIC
6.848*** -0.139*** -0.019 0.001-0.0400.165 -0.072 0.075(2.196) (0.053) (0.050) (0.054)(0.086)(0.205) (0.094) (0.088)
Year-quarter FE
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Household FE
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
WIC households
301
301
347
347
347
347
347
347
Households
85421
80721
96637 96637
96637
96637 96637 96637
Household-quarters
1241128 1189478 1598440 1598440 1598440 1598440 1598440 1598440
Sum of negative weights.
-0.022.
.
.
.
.
.
σ̂ f e14.504
0.230
0.041
0.003
0.086
0.356
0.154
0.161
σ̂ f e
.
1.403
.
.
.
.
.
.
Note: Table presents the estimates from the same regression as in the main specification (table 3) except thatit excludes time periods when the household that received post-reform vouchers is not receiving WIC vouchers
anymore. Standard errors (in parentheses) are clustered at the household level. *** Indicates significanceat the 1 percent level, ** 5 percent level, * 10 percent level. The bottom part of table presents the sumof negative weights and other diagnostic measures calculated using the twowayfeweights Stata package,developed by the authors to accompany the work in de Chaisemartin and D’Haultfœuille (2020b), and isavailable from the STATA repository.

Second, I calculate the heterogeneity-robust difference-in-differences estimators proposedby de Chaisemartin and D’Haultfœuille (2020a,b) of the short-term effects of the post-reform
subsidies.31 The estimators are valid even when the treatment effect is heterogeneous overtime and across groups. The analysis uses yearly data (instead of quarterly) to make iteasier to bootstrap standard errors. The estimates in table C5 confirm the main resultson the healthy bread and milk fat percentage. Figures C3–C4 allow further assessing theplausibility of the common trends assumption by presenting both the heterogeneity-robust
difference-in-differences estimators and placebo estimators for two years before treatment.
31

I use the did_multiplegt Stata package developed by the authors to accompany the work in de Chaisemartin and D’Haultfœuille (2020b,a), and is available from the STATA repository.

73

For all products, there are no differences in pre-trends, which provides additional support for
the identification strategy.
Table C5: Heterogeneity-robust difference-in-differences estimates
Breadhealthy %Reformed WIC
Treated households
WIC households
Households(1)
6.405***(2.168)
174
301
58573

Milk
fat %

Bread
log.
quantity(2)(3)-0.128**0.078(0.057)(0.058)
176
202
301
347
54830
67124

Milk
log.
quantity(4)
0.020(0.053)
202
347
67124

Fruits&veg.
Juice
log.
log.
quantityquantity
(5)
(6)
0.029
-0.106(0.063)(0.229)
202
202
347
347
67124
67124

Eggs
log.
quantity(7)-0.109(0.090)
202
347
67124

Cerealslog.
quantity(8)0.135*(0.073)
202
347
67124

Note: The reported coefficients are heterogeneity-robust difference-in-differences estimates of average dynamic
treatment effects. The coefficients are estimated using the method developed by de Chaisemartin and
D’Haultfœuille (2020a) and their did_multiplegt Stata package, which is available from the STATA
repository. Observations are at the household and year pair level. The sample includes all WIC households(columns 1–2 in table 1). It also includes households in column 3 in table 1 who are in the sample for at least 2
years. The sample excludes time periods when a household that received post-reform vouchers is not receiving
vouchers anymore. For milk fat percentage, the sample excludes observations in the treatment group, when ahousehold has a one year old child because for one-year-old children, the reformed WIC food vouchers makean exception and provide whole milk. Standard errors (in parentheses) obtained by 50 bootstrap replications
are clustered at the household level. *** Indicates significance at the 1 percent level, ** 5 percent level, * 10
percent level.

74

DID, from period t-1 to t

-5

-.3

-.2

0

-.1

5

0

.1

10

DID, from period t-1 to t

-2

-1

0

-2

Relative time to period where treatment changes (t=0)-10Relative time to period where treatment changes (t=0)(a) Bread healthy %(b) Milk fat %

-.2

-.2

-.1

-.1

0

0

.1

.1

.2

DID, from period t-1 to t

.2

DID, from period t-1 to t

-2

-1

0

-2

Relative time to period where treatment changes (t=0)-10Relative time to period where treatment changes (t=0)(c) Log. quantity of bread(d) Log. quantity of milk

Figure C3: Heterogeneity-robust difference-in-differences estimates and placebo, bread andmilk
Note: Figures present heterogeneity-robust difference-in-differences estimates of the treatment effectand placebos. The coefficients are estimated using the method developed by de Chaisemartin
and D’Haultfœuille (2020b) and their did_multiplegt Stata package, which is available from the
STATA repository. Observations are at the household and year pair level. The sample includes
WIC households (columns 1–2 in table 1) who are in the dataset at least two years before receiving
WIC vouchers. From the households receiving post-reform vouchers (column 1 in table 1), thesample excludes those who started to receive WIC vouchers before 2010. The sample also includes
households in column 3 in table 1 who are in the sample for at least three years. For milk fat
percentage, the sample excludes observations in the treatment group, when a household has a one
year old child because for one-year-old children, the reformed WIC food vouchers make an exception
and provide whole milk. The figures present point estimates and 95% confidence intervals using
standard errors, clustered at the household level, obtained by 50 bootstrap replications.

75DID, from period t-1 to t

-2

-.4

-1

-.2

0

0

1

.2

DID, from period t-1 to t

-2

-1

0

-2

Relative time to period where treatment changes (t=0)-10Relative time to period where treatment changes (t=0)(a) Log. quantity of fruits and vegetables(b) Log. quantity of juice
DID, from period t-1 to t

-.6

-.2

-.4

0

-.2

.2

0

.2

.4

DID, from period t-1 to t

-2

-1

0

-2

Relative time to period where treatment changes (t=0)-10Relative time to period where treatment changes (t=0)(c) Log. quantity of eggs(d) Log. quantity of cereals

Figure C4: Heterogeneity-robust difference-in-differences estimates and placebo, other products
Note: Figures present heterogeneity-robust difference-in-differences estimates of the treatment effectand placebos. The coefficients are estimated using the method developed by de Chaisemartin
and D’Haultfœuille (2020b) and their did_multiplegt Stata package, which is available from the
STATA repository. Observations are at the household and year pair level. The sample includes
WIC households (columns 1–2 in table 1) who are in the dataset at least two years before receiving
WIC vouchers. From the households receiving post-reform vouchers (column 1 in table 1), thesample excludes those who started to receive WIC vouchers before 2010. The sample also includes
households in column 3 in table 1 who are in the sample for at least three years. The figures present
point estimates and 95% confidence intervals using standard errors, clustered at the household level,obtained by 50 bootstrap replications.

76

C.3.4

Propensity score matching estimators

This appendix presents propensity score matching estimators. To obtain the estimators,
first, I collapse the data to two separate cross-sections: one by calculating the differences inpurchases before receiving and while receiving the WIC vouchers, and the other by calculating
the differences in purchases before receiving and in year 1–2 after receiving the WIC vouchers.
For the share of healthy bread and percentage of low-fat milk, it is a simple differencein the averages. For the quantities, it is the difference between the logarithms of averages(log(yt /yt−1 ), where yt is the average quantity purchased while or after receiving WIC vouchers
and yt−1 is the average quantity before receiving WIC vouchers. For each of the households inthe control group who don’t receive WIC vouchers, I draw a random time period when they
started to receive WIC vouchers and another random time period when they end receiving
the vouchers. Table C6 presents the estimates of propensity score from a logit model thatuses household demographic characteristics to predict WIC participation after the policy
reform. The regressions include indicators for children up to four years old at the time whenhouseholds starts to receive the vouchers (in column 1) or after having received the vouchers(in column 2). I don’t use the information on children before starting to receive the vouchers
because it would be less informative as then most households don’t have children. Figure C5
presents the kernel density estimates of the distribution of the propensity scores separately
for the treatment and control group. The sample on the figure is a trimmed sample, which
excludes the households with propensity scores smaller than the 10th percentile and larger
than the 90th percentile of the treatment group. In the second step, I use these predictedprobabilities to estimate the average treatment effect on the treated using propensity-scorematching based on 10 nearest neighbors.
Table C7, columns 2–4 and 5–6 present the propensity score matching estimates of theaverage treatment effect on the treated. For comparison, columns 1 and 4 present estimatesfrom a simple cross-sectional OLS regression. Columns 1–3 present estimates of the impact
77

Table C6: Predicting WIC participation after the policy reform, logit(1)(2)
Household size 0.374*** 0.382***(0.045) (0.043)
Log. income -0.446*** -0.430***(0.102) (0.102)
College-0.442*** -0.416***(0.142) (0.142)
Non-white
0.232
0.217
(0.146) (0.146)
N
41256
41256
Note: A unit of observation is a household. The sample includes households in columns 1–3 in table 1. The
regressions also include indicators for children up to 4 years old. Standard errors are in parentheses. ***Indicates significance at the 1 percent level, ** 5 percent level, * 10 percent level.

100

Density
200

300

400

Kernel density estimate

0

0

100

Density
200

300

400

Kernel density estimate

0

.01

.02
.03
Propensity score

.04

.05

0

.02

.04
Propensity score

Treatment group
Control group

.06

.08

Treatment group
Control group

kernel = epanechnikov, bandwidth = 0.0032

kernel = epanechnikov, bandwidth = 0.0033(a) WIC(b) After WIC

Figure C5: Distribution of propensity scoresof the reformed WIC and columns 4–6 the long-term impact of 1–2 years after the reformed
WIC. In columns 3 and 4, the sample is trimmed by excluding households with small andlarge values of the propensity score (below and above the 10th percentile of the treatmentgroup). The results for the healthy bread share and milk fat percentage are similar to thosein the main analysis. However, for juice and eggs, the estimates imply that in the short-term
the reformed WIC decreases purchases. This reflects the reformed program decreasing thequantity of juice and eggs in the vouchers. The estimates with the trimmed sample imply
that the reformed WIC in the short-term decreases also bread and cereals purchases. In the78main specification, the estimates for the product quantities were noisy and did not allow torule out negative effects of similar size.
Table C7: Robustness of the short- and long-term impact of post-reform WIC, propensity
score matching
Dependent variable

Reformed WIC
After Reformed WIC Years 1-2
OLS
PSM
PSM
PSM
PSM
TrimmedTrimmed
(4)
(5)
(6)
(1)
(2)
(3)
Bread, healthy %5.104*** 5.463*** 4.640*** 4.296*** 4.380***
2.934*(1.324) (1.469)(1.598)(1.116) (1.560) (1.706)
N
34925
34925
24262
34420
34420
26109
Milk, fat %-0.095*** -0.099** -0.076* -0.066*-0.055-0.065(0.027) (0.039) (0.043)(0.037) (0.038)(0.042)
32285
32285
24549
N
32674
32674
22770
Bread, log. quantity-0.058*-0.059-0.082*
0.052
0.067
0.041
(0.044) (0.045)(0.050)(0.034) (0.041) (0.047)
N
41256
41256
27661
41256
41256
30318
Milk, log. quantity
0.020
0.032
0.012
0.081** 0.110**0.067(0.029) (0.041) (0.044)(0.040) (0.047)(0.051)
41256
41256
30318
N
41256
41256
27661
Fruits & veg., log. quantity -0.047-0.030-0.0750.094
0.063
0.160***(0.058) (0.059) (0.071)(0.076) (0.059)(0.062)
N
41256
41256
27661
41256
41256
30318
Juice, log. quantity-0.289* -0.314** -0.438*** 0.020
0.129
0.041
(0.156) (0.136) (0.153)(0.182) (0.126)(0.144)
N
41256
41256
27661
41256
41256
30318
Eggs, log. quantity-0.118** -0.107* -0.153** -0.026-0.0250.055(0.054) (0.061) (0.069)(0.070) (0.065)(0.070)
41256
41256
30318
N
41256
41256
27661
Cereals, log. quantity-0.061-0.067-0.130*
0.102
0.092
0.112
(0.061) (0.064) (0.076)(0.077) (0.063)(0.068)
N
41256
41256
27661
41256
41256
30318
OLS

Note: A unit of observation is a household. Columns 1 and 4 present estimates from OLS regressions, theremaining columns present propensity score matching estimates of the average treatment effect on the treated.
Dependent variable is the difference before and while receiving WIC vouchers in the share of healthy bread,fat percentage of milk or the difference between the logarithms of quantities (log(yt /yt−1 )). Columns 1–3
present estimates of the impact of the reformed WIC and columns 4–6 of 1–2 years after the reformed WIC.
The sample includes households in columns 1–3 in table 1. In columns 3 and 4, the sample is trimmedby excluding households with small and large values of the propensity score (below and above the 10th
percentile of the treatment group). Standard errors (in parentheses) are adjusted to take into account thatthe propensity score is estimated. *** Indicates significance at the 1 percent level, ** 5 percent level, * 10
percent level.

79C.3.5

Switching out of WIC due to becoming ineligible

Here, I focus on the time period when households become ineligible for the WIC vouchers.
Specifically, I focus on households that received WIC vouchers when the child was 4 years
old and become ineligible for the vouchers when the child gets 5 years old. I analyze thechanges in their purchases when the child is 5 and 6 compared to the base period when thechild was 4 and they received the vouchers. Note that here as opposed to the main sample,
the comparison with the time period before receiving WIC vouchers cannot be made because
we simply don’t observe the households for over so many years (especially, the households
who became ineligible after receiving only the pre-reform WIC vouchers).
Again, the empirical strategy exploits the 2009 reform of the WIC program that changed
the content of food vouchers. I compare two groups of households—those that participated in
the program before the policy reform and those who participated after the policy reform. I
compare the changes in their purchases when they become ineligible for the program. These
two groups of households should be otherwise similar, both become ineligible when their childbecomes five years old, but the vouchers were different.
The sample includes only the WIC households that received WIC vouchers when the child
was four and who are in the Nielsen panel both one and two years later when the child is fiveand six years old. It is a balanced panel of households over these three years. I exclude fromthe sample any time periods before receiving the vouchers. I also exclude from the sample
households with a four year old child in 2009, because the reform took place in the middle of2009, and hence, these households only for a short time period received the post-reform WIC
vouchers. As in the main specification, as a control group the households from column 3 intable 1 are also included.

80

Using a yearly household panel I estimate the following difference-in-differences regression:

Yit = α2,5 Age5it × ReceivedW ICi + α2,6 Age6it × ReceivedW ICi= β2,5 Age5it × ReceivedW ICi × Ref ormedi + β2,6 Age6it × ReceivedW ICi × Ref ormedi++ α0 Age3−
it × ReceivedW ICi + α3 Age7it × ReceivedW ICi++ β0 Age3−
it × ReceivedW ICi × Ref ormedi + β3 Age7it × ReceivedW ICi × Ref ormedi+ Xit ζ + δi + γt + εit(6)where ReceivedW ICi indicates whether household i received WIC vouchers when the child
was four years old and Ref ormedi indicates whether the vouchers received were post-reform
WIC vouchers. Variables Age5it and Age6it are indicators for the child being 5 and 6 years
old.32 The omitted age (the base group) is 4 years old. Variables ReceivedW ICi and
Ref ormedi don’t vary with time, and hence, these are captured by the household fixed effects.
Therefore, we only estimate their interactions with child age.
A few WIC households are in the Nielsen sample also in years before the child is fourand after the child is 6. In order to increase statistical power, I don’t drop the time periods.
Instead, I include separate dummies for these time periods α0 , α3 , β0 , β3 , but I don’t reportthese estimates because due to the unbalanced sample these are biased estimates for theseeffects, and hence cannot be interpreted.
The regressions include time-varying household characteristics Xit : logarithm of income,household size, and indicator variables for the period before the child is born, and children
aged 0, 1, ..., 5, 6-12, and 13-17. The regression also includes household fixed effects δi andyear fixed effects γt .
The coefficients of interest are β2,5 and β2,6 which estimate the impact of the WIC reform
32
The dataset has only yearly information about age. I say that the child is T is years old in the calendar
year of his/her Tth birthday.

81

on the change in purchases when the WIC household becomes ineligible. Note that thehousehold becomes ineligible during the year when the child gets 5 years old. Hence, thehousehold is eligible for only part of the calendar year when the child has the 5th birthday.33
Hence, if the long-term effect of WIC is decreasing over time (as in the main specificationtable 3) we would expect β2,6 to be larger than β2,5 in absolute value.
The results in table C8 show that indeed, for the healthy bread and milk fat percentage,
the long-term effect (β2,5 and β2,6 ) estimates are in the same direction than in the main
specification (β2 in table 3). This shows that the limited persistence of the program’s impact
is not specific to the households in the main specification, where some households mightvoluntarily choose to exit the WIC program. But instead, the limited persistence characterizes
also the households who exit the program when they become ineligible due to the child’s age.
It is somewhat surprising that for the healthy bread and milk fat percentage the magnitudeof β2,6 coefficient estimate in table C8 is much larger than β2 in table 3. If the short-term
effect were similar in both samples, then table C8 would imply that the post-reform WIC
in the long-term has the opposite of the intended effect. But the magnitudes of β2,6 and β2
cannot directly be compared because the samples are different. In table 3, majority of thehouseholds were exiting the program when the child was much younger than five. It is also
likely that they were receiving the vouchers for a shorter period of time. Unfortunately, when
focusing on households exiting the program due to ineligibility as child gets 5 years old, due
to the data limitations we cannot compare the purchases to the time period before receiving
WIC vouchers. Hence, β2,6 in table C8 does not measure the long-term effect of the program,it only measures the change compared to the year when the child was 4 and the household
was receiving the vouchers.

33

The majority of the households that received the vouchers when the child was 4, do not report receiving
vouchers when the child is 5. This could reflect that they report the WIC status in the end of the calendar
year.

82

Table C8: The impact of post-reform WIC on subsidized products; switching out of WIC due
to becoming ineligibile when the child gets 5 years oldBreadhealthy %

Milk
fat %

Bread
Milk Fruits&veg. Juice
Eggs Cereals
log.
log.
log.
log.
log.
log.
quantity quantity quantity quantity quantity quantity
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
β2,5 : Age 5 × Received WIC × Reformed -4.118* 0.137*** -0.076 0.072-0.021-0.062 -0.058 0.154(2.472) (0.052) (0.088) (0.098)(0.086)(0.199) (0.182) (0.123)
β2,6 : Age 6 × Received WIC × Reformed -11.557*** 0.250*** 0.058
0.215-0.0830.162-0.299 -0.014(3.091) (0.075) (0.147) (0.144)(0.104)(0.368) (0.206) (0.159)
α2,5 : Age 5 × Received WIC-0.606-0.035 0.005 -0.019
0.001-0.1310.025 -0.110(1.349) (0.032) (0.075) (0.077)(0.070)(0.102) (0.164) (0.103)
α2,6 : Age 6 × Received WIC
0.381-0.030 -0.085 -0.102
0.041-0.783*** 0.166 -0.085(1.743) (0.045) (0.122) (0.113)(0.081)(0.283) (0.166) (0.118)
Year FE
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Household FE
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
WIC households
159
156
173
173
173
173
173
173
Households
85279
80576 96463 96463
96463
96463
96463 96463
Household-years
339364 316299 398786 398786
398786398786 398786 398786
Note: Each column presents estimates of a separate panel data fixed effects regression (equation (6)) thatmeasure the changes in purchases when the child is 5 and 6 compared to the base period when the childwas 4 and the household was receiving the vouchers. A unit of observation is a household-year pair. Breadhealthy (whole wheat) % and milk fat % are in the range of 0–100, quantity is measured in pounds forbread, gallons for milk, kilocalories for fruits and vegetables and juice, counted for eggs, and ounces forcereals. All regressions include household size, logarithm of income, dummies for the year before child isborn, and children aged 0, 1, . . . , 5, 6-12, and 13-17. Regressions include household and time period fixed
effects. Standard errors (in parentheses) are clustered at the household level. *** Indicates significance at the
1 percent level, ** 5 percent level, * 10 percent level.

83

C.4

Excluding pre-reform WIC households from the sample

When households start to receive WIC vouchers, there are other changes that could affectpurchases. Some of which are observed, such as a new child, but some may be unobservable.
Comparing households that enter into old and new WIC programs allows to account forthese changes. If instead, we were to exclude from the sample the households in the old
WIC program, the estimates would measure the combined effect of the new vouchers andeverything else that changes when households receive the vouchers.
This appendix analyzes the differences from the main specification if the pre-reform WIC
households had been excluded from the control group. Specifically, the sample includes only
the WIC households who started receiving vouchers in 2010 or later; and the control groupfrom column 3 of table 1. Using this sample, I estimate the following difference-in-differences
regression, which is a simplified version of the main specification given by equation (1):Yit = β̃1 W ICit + β̃2 Af terW ICY ears1, 2it + β̃3 Af terW ICY ear3+
it+ Xit ζ + δi + γt + εit(7)

The results in table C9 illustrate that without the pre-reform WIC control group, theestimated effects of the WIC vouchers (β̃) are the combinations of α and β estimates fromtable 3. For example, the estimated short-term effect of subsidies on the healthy bread shareis smaller (equals 4.2) than β1 estimate (which equals 6.9) in table 3, because it captures also
the negative α1 estimate (which equals -1.8). The estimates of β1 and β2 in table 3 measure
the incremental effect of the new voucher program relative to the old. While the estimates intable C9 measure the effect of the new vouchers and anything else that tends to change when
WIC is adopted.

84

Table C9: The impact of post-reform WIC on subsidized products, the sample excludes
households who received pre-reform WIC vouchers
Bread
Milk
healthy % fat %BreadMilk Fruits&veg. Juice
Eggs Cereals
log.
log.
log.
log.
log.
log.
quantity quantity quantity quantity quantity quantity
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
β̃1 : WIC
4.193** -0.103* 0.023
0.040-0.009 0.639*** -0.030 0.127(1.847) (0.053) (0.050) (0.050)(0.078)(0.189) (0.085) (0.080)
β̃2 : After WIC Years 1-2
3.271* -0.064 0.009 -0.001-0.055
0.198 -0.097 0.045(1.762) (0.048) (0.056) (0.053)(0.089)(0.186) (0.084) (0.084)
Year-quarter FE
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Household FE
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Wald test, β̃1 = β̃2 , p-value 0.588
0.338
0.775
0.384
0.610
0.025
0.427
0.278
WIC households
149
154
175
175
175
175
175
175
Households
85269
80574 96465 96465
96465
96465 96465 96465
Household-quarters
1239541 1188115 1596596 1596596 1596596 1596596 1596596 1596596
Note: Each column presents estimates from a separate panel data fixed effects regression (equation (7)).
A unit of observation is a household-quarter pair. Bread healthy (whole wheat) % and milk fat % are in
the range of 0–100, quantity is measured in pounds for bread, gallons for milk, kilocalories for fruits andvegetables and juice, counted for eggs, and ounces for cereals. All regressions include household size, logarithmof income, dummies for period before child is born, and children aged 0, 1, . . . , , 5, 6-12, and 13-17. In column
2, regression includes interaction terms for WIC and the last two quarters of the calendar year when thechild gets one years old and the other with the first two quarters of the calendar year when the child gets two
years old. Regressions include household and time period fixed effects. Standard errors (in parentheses) areclustered at the household level. *** Indicates significance at the 1 percent level, ** 5 percent level, * 10
percent level.

85

C.5

Map describing regional differences in milk prices

Prices flat
Mixed
Whole milk the most expensive

Figure C6: Milk prices
Note: States are categorized to those with flat prices where the price of whole milk is not higher thanothers, those where whole milk is more expensive than others (more than a cent more expensive),and those with mixed price rankings. States are categorized based on state-level median milk pricedifferences of different fat percentages (whole milk, 2%, 1%, and skim milk) across stores and time
periods using data on private label one-gallon milk.

86

C.6

Analysis of prices and persistence based only on WIC households

Table C10: The short- and long-term impact and prices. Sample restricted to WIC households.
Dependent variable: milk fat percentage
PricesPricesflat
increasing(1)(2)
β1 : Reformed WIC-0.288*** -0.315***(0.100) (0.105)
β2 : After Reformed WIC Years 1-2 0.074-0.310(0.115) (0.215)
α1 : WIC
0.099 0.203***(0.073) (0.070)
α2 : After WIC Years 1-2-0.0470.237(0.103) (0.189)
σ: Post-Reform
0.079
0.023
(0.065) (0.093)
Household FE
Yes
Yes
Wald test, β1 = β2 , p-value
0.003
0.976
WIC households
94
60
Households
94
60
Household-quarters
2802
1831
Note: The table presents estimates from the same regressions as in table 4, but the sample is restricted tohouseholds who received WIC vouchers (households in columns 1–2 in table 1) and the regressions do notinclude year and quarter fixed effects. Standard errors (in parentheses) are clustered at the household level.
*** Indicates significance at the 1 percent level, ** 5 percent level, * 10 percent level.

87

C.7

Externalities to other products

The online appendix analyzes the externalities. It estimates regression (1) to measure theimpact of the program on fiber consumption first in bread which is included in WIC vouchers
and then in product categories not included in the WIC vouchers. Similarly, it estimates theimpact on saturated fat consumption first in milk and then in product categories not includedin the WIC vouchers. To increase precision and make the estimates comparable, the outcome
variables are in the form of percentile rank. The estimates have a simple interpretation: howmuch the reform shifted household’s position in the national distribution of the nutrition
measure.
The change in the WIC vouchers in the short-term increased household’s rank of fiber
content in bread by about 4 percentiles (table C11, column 1). It is a meaningful increase
compared to the 41% pre-WIC level of the median household that later received the postreform WIC vouchers. For both non-WIC grain products34 (column 2) and all non-WIC
product categories (column 3), the estimates of the short-term effect are imprecise, but allow
to rule out with 95% probability positive and negative externalities of the same magnitude
as the main effect (column 1).
The change in the WIC vouchers in the short-term decreased household’s rank of saturated
fat content in milk by about 3 percentiles (column 4). This is a meaningful decrease comparedto the 64% pre-WIC level of the median household that later received the post-reform WIC
vouchers. For non-WIC dairy products35 (column 5), the estimates of the short-term effectallow to rule out positive and negative externalities of the same magnitude as the main
effect (column 4). For all non-WIC product categories (column 6), the point estimate of theshort-term effect is small in magnitude and the estimates allow to rule out large externalities.
34

Non-WIC grain products include other bread and baked goods, flour, baking mixes, pasta, crackers, rice,barley, tortillas, rice cakes, and pretzels.
35
Non-WIC dairy products include butter and margarine, cheese, cottage cheese, sour cream, yogurt, dairy
desserts, cream, buttermilk, flavored milk.

88

Table C11: Externalities: The impact of post-reform WIC on fiber consumption in bread,
non-WIC grains, and all non-WIC product categories, and on saturated fat consumption in
milk, non-WIC dairy, and all non-WIC product categories
Fiber
Saturated fat
Non-WIC All non-WIC
Milk
Non-WIC All non-WIC
grainscategories
dairy
categories
(1)
(2)
(3)
(4)
(5)
(6)
β1 : Reformed WIC
3.958**
0.600-0.242-3.330**-0.366-0.675(1.903)(1.481)(1.761)(1.459)(1.451)(1.907)[0.229,7.688] [-2.303,3.503] [-3.693,3.209] [-6.190,-0.469] [-3.210,2.478] [-4.412,3.063]
β2 : After Reformed WIC Years 1-2
2.153
0.924
2.932
-1.483-0.580-0.814(2.089)(1.554)(1.930)(1.922)(1.741)(2.802)[-1.942,6.249] [-2.123,3.971] [-0.851,6.715] [-5.251,2.284] [-3.992,2.833] [-6.306,4.679]
α1 : WIC-0.163-1.7260.830-0.1680.000-0.395(1.357)(1.169)(1.357)(1.030)(1.123)(1.613)[-2.822,2.497] [-4.017,0.565] [-1.830,3.490] [-2.187,1.851] [-2.201,2.201] [-3.557,2.767]
α2 : After WIC Years 1-2
0.937-2.089-1.126-0.4151.759-0.452(1.687)(1.277)(1.531)(1.691)(1.481)(2.571)[-2.370,4.244] [-4.592,0.415] [-4.127,1.875] [-3.729,2.899] [-1.144,4.663] [-5.492,4.588]
σ: Post-Reform-0.486*0.078
1.083***-0.1970.855***
1.070***(0.284)(0.305)(0.295)(0.204)(0.287)(0.345)[-1.042,0.071] [-0.519,0.675] [0.504,1.662] [-0.597,0.203] [0.292,1.418] [0.394,1.746]
Year-quarter FE
Yes
Yes
Yes
Yes
Yes
Yes
Household FE
Yes
Yes
Yes
Yes
Yes
Yes
Wald test, β1 = β2 , p-value
0.394
0.851
0.114
0.345
0.912
0.959
WIC households
301
301
301
301
301
301
Households
85421
85404
85421
80721
80688
80721
Household-quarters
12442371342951
136282211925701245769
1270611
Bread

Note: Each column presents estimates from a separate panel data fixed effects regression (equation (1)). A
unit of observation is a household-quarter pair. Fiber content is measured in grams per thousand calories,and saturated fat content is measured as a percentage of calories from saturated fat. The outcome variable
is household’s percentile rank of fiber in bread (column 1), non-WIC grains (column 2), and all non-WIC
product categories; and households percentile rank of saturated fat in milk (column 4), non-WIC dairy(column 5), and all non-WIC product categories (column 6). To calculate the percentile ranks, in eachtime period, all the households in the Nielsen Consumer Panel are ranked by fiber or saturated fat content.
Household’s percentile rank is defined based on the position in the national distribution of fiber or saturated
fat content purchases relative to all others in a given time period. The sample includes households in columns
1–3 in table 1. Standard errors (in parentheses) are clustered at the household level. 95% confidence intervals
are in the square brackets. *** Indicates significance at the 1 percent level, ** 5 percent level, * 10 percent
level.

89

Online Appendix: Additional analysis for section 4

D.1

Identification of short-term state dependence

.5
.4
.3
.2
.1
0

Probability of purchasing

.6

D

Other

White

Whole grain Whole wheat

When didn't purchase the product last trip
When purchased the product last trip

Figure D1: Within-household comparison of the conditional probability of purchasing the
product when did or did not buy the same product in the previous trip; presented separately
for the four bread types
Note: An observation is a household-product-state combination. Each bar is the average probability overhouseholds and the spiked interval presents the 95% confidence interval. When calculating the averages, only
the households are included for whom for that product the probability in both states is calculated. Whenhousehold never buys the product, then it is not possible to calculate the probability in a state of havingbought the product in the previous trip. For comparison purposes, in that case, the household is excluded
from calculating both conditional probabilities for that product. Therefore, probabilities are calculated for248 households for Other bread, 228 for White bread, 224 for Whole grain, and 202 for Whole wheat.

90

WhiteWhole grain

Whole wheat

0

10

20

Percent
30 0

10

20

30

Other

-1
-.5
0
.5
1 -1
-.5
0
.5
1
Within-household difference in probabilities of buying product j in period t
conditional that bought j versus did not buy j in t-1

Figure D2: Histogram of within-household differences in the conditional probabilities in thetwo states: when did or did not buy the same product last trip; presented separately for thefour bread types
Note: An observation is a household and product pair. The within-household difference in probabilities isonly possible to calculate for households that bought the product in both states (when did or did not buy thesame product in the previous trip). Therefore, the differences are calculated for 248 households for Other
bread, 228 for White bread, 224 for Whole grain, and 202 for Whole wheat.

91

D.2

Demand model estimates: main specification
Table D1: Control function estimation. Dependent variable: price of breadηp : Average price in other markets
Whole grain bread
Whole wheat bread
White bread
Market FE
F-statistic of H0: ηp = 0
R-squared
Number of clusters
Number of observations

Estimate
0.885***
0.031
0.009
-0.042
Yes
401.391
0.848
50
80288

SE
(0.044)(0.022)(0.018)(0.025)

Note: A unit of observation is a bread type (white, whole grain, whole wheat, or other), market, (aggregate)
retailer, and week combination. Prices are measured in dollars per pound, deflated to 2015 dollars. Standard
errors clustered on the market level are included in parenthesis. It should be noted that these are moreconservative standard errors, while clustering at the market and bread type pair level would imply more
precise estimates. *** Indicates significance at the 1 percent level, ** at 5 percent level, * at 10 percent level.

92

Table D2: Bread demand model estimates
No control function Control function(1)(2)
Estim.
SE
Estim.
SEMeanᾱ: Price−1.029∗∗∗ (0.088)
γ̄: Short-term state dependence
0.693∗∗∗ (0.025)
β: Last year’s share of whole wheat
3.872∗∗∗ (0.121)
θ̄: Whole wheat bread−1.534∗∗∗ (0.051)
δ̄: Whole grain bread−0.271∗∗∗ (0.059)
λ̄: White bread−0.403∗∗∗ (0.077)
ResidualStandard deviation
σp : Price
1.903∗∗∗ (0.132)
σs : Short-term state dependence
0.430∗∗∗ (0.031)
σW W : Whole wheat bread
1.007∗∗∗ (0.059)
σW G : Whole grain bread
1.511∗∗∗ (0.093)
σW hite : White bread
2.273∗∗∗ (0.057)
Covariance
Price, short-term state dependence
0.458∗∗∗ (0.079)
Price, whole wheat bread−0.088(0.106)
Price, whole grain bread−0.612∗∗∗ (0.177)
Price, white bread
1.319∗∗∗ (0.286)
Short-term state dependence, whole wheat bread −0.023(0.034)
Short-term state dependence, whole grain bread 0.105(0.065)
Short-term state dependence, white bread
0.158∗∗∗ (0.030)
Whole wheat bread, whole grain bread
1.364∗∗∗ (0.167)
Whole wheat bread, white bread
0.836∗∗∗ (0.095)
Whole grain bread, white bread
1.106∗∗∗ (0.190)
Log-likelihood-22843
Number of choices
112168
Number of households
252−1.316∗∗∗(0.287)
0.614∗∗∗(0.067)
3.784∗∗∗(0.254)−1.549∗∗∗(0.147)−0.606∗∗∗(0.195)−0.809∗∗ (0.362)
0.539∗ (0.277)
0.670(1.248)0.487(0.343)0.875(0.619)1.524∗∗ (0.704)
1.931∗∗∗(0.670)−0.169(0.367)−0.187(0.469)−0.676(1.585)−0.577(0.783)−0.100(0.360)0.164(0.424)−0.373(0.689)0.957(1.405)0.686(1.082)0.760(1.386)-22821112168252

Note: The table presents the estimates from 2 random coefficient logit models. For each model, the firstcolumn presents parameter estimates and the second column standard errors. The base type of bread isother bread. The sample includes households from columns 1–2 in table 1 with a sufficient number of breadpurchases; for each household the sample excludes the years when the household received WIC vouchers.
Standard errors are clustered at the household level. In column 2, standard errors are obtained by bootstrap(over 2 steps of the estimation) with 100 bootstrap samples. *** Indicates significance at the 1 percent level,** 5 percent level, * 10 percent level.

93

D.3

Robustness analysis of demand model estimates

In this appendix, I explore the robustness of demand model estimates first with respect tothe construction of the price variable, and then the initial conditions for state dependence.
First, to address the potential concerns about combining the Retail Scanner and theConsumer Panel data to construct prices, I re-estimate the model restricting the sample to the
shopping trips to the stores in the Retail Scanner data and hence, using only the prices fromthe Retail Scanner data (tables D3–D4). Second, we might be concerned that prices from theConsumer Panel data were constructed based on too few households. Furthermore, for thearea outside the major scantrack markets (which Nielsen aggregates into the remaining U.S.)
prices were calculated by combining all the regions outside the major markets. To address
the concerns about the potential measurement errors introduced in this way, I re-estimate
the model while restricting the sample only to the Nielsen reportable markets and excluding
the remaining US (tables D5–D6).
It is reassuring that the estimates from these models are similar to those from the main
specification. Both the short- and long-term persistence parameter (γ̄ and β) are similar
across the specifications. Also the estimated price coefficients are rather similar, yielding the
average own-price elasticity with control function estimates to equal 1.6 with only Retail
Scanner prices (table D4) and 1.5 with reportable markets and without the remaining U.S.
(table D6) compared to 1.6 in the main specification (table D2).
To address the concern about the initial conditions bias for state dependence, I use themethod proposed by Simonov et al. (2020) to bound the true short-term state dependence
value. The main specification (table 5) assumes that the initial state is exogeneous. HereI re-estimate the model assuming that the first observed purchase occasion has no state
dependence (tables D7–D8). To do that I add to the sample the week that was used to
calculate the first state for short-term state dependence and I assume that there is no shortor long-term state dependence during that week. Simonov et al. (2020) show that the94estimates from these two alternative specifications bound the values of the state dependence.
The estimates show that the possible bias is small as the bound for the short-term state
dependence is tight: the point estimate of the short-term state dependence with alternative
initial conditions is only slightly smaller (0.58 in column 2 table D8) compared to the estimate
in the main specification (0.61 in column 2 of table 5).
Table D3: Control function estimation: prices only from the Retail Scanner dataset. Dependent variable: price of bread.
ηp : Average price in other markets
Whole grain bread
Whole wheat bread
White bread
Market FE
F-statistic of H0: ηp = 0
R-squared
Number of clusters
Number of observations

Estimate
0.884***
0.018
0.016
-0.049**Yes
1324.523
0.869
48
37868

SE
(0.024)(0.022)(0.017)(0.019)Note: A unit of observation is a bread type (white, whole grain, whole wheat, or other), market, aggregate
retailer, and week combination. Prices are measured as dollars per pound, deflated to 2015 dollars. Standard
errors clustered by market are included in parenthesis. *** Indicates significance at the 1 percent level, ** at
5 percent level, * at 10 percent level.

95

Table D4: Robustness of the bread demand model estimates: prices only from the Retail
Scanner dataset
No control function Control function(1)(2)
Estim.
SE
Estim.
SEMeanᾱ: Price−0.852∗∗∗ (0.081)
γ̄: Short-term state dependence
0.729∗∗∗ (0.033)
β: Last year’s share of whole wheat
3.565∗∗∗ (0.197)
θ̄: Whole wheat bread−1.802∗∗∗ (0.094)
δ̄: Whole grain bread−0.905∗∗∗ (0.100)
λ̄: White bread−0.158∗∗ (0.066)
ResidualStandard deviation
σp : Price
0.763∗∗∗ (0.144)
σs : Short-term state dependence
0.445∗∗∗ (0.042)
σW W : Whole wheat bread
1.332∗∗∗ (0.081)
σW G : Whole grain bread
1.593∗∗∗ (0.085)
σW hite : White bread
2.028∗∗∗ (0.084)
Covariance
Price, short-term state dependence
0.334∗∗∗ (0.064)
Price, whole wheat bread−0.635∗∗∗ (0.170)
Price, whole grain bread−0.306∗∗ (0.121)
Price, white bread−0.305∗∗∗ (0.053)
Short-term state dependence, whole wheat bread −0.404∗∗∗ (0.055)
Short-term state dependence, whole grain bread −0.251∗∗∗ (0.053)
Short-term state dependence, white bread−0.076(0.058)Whole wheat bread, whole grain bread
1.432∗∗∗ (0.164)
Whole wheat bread, white bread
0.048(0.120)Whole grain bread, white bread
0.186∗(0.109)Log-likelihood-9211
Number of choices
43560
Number of households
218−1.226∗∗∗(0.306)
0.645∗∗∗(0.077)
4.015∗∗∗(0.409)−1.515∗∗∗(0.256)−0.574∗∗ (0.279)−0.794∗∗ (0.379)
0.463(0.354)0.847(1.231)0.415∗ (0.250)
1.178∗∗∗(0.437)
1.824∗∗∗(0.539)
3.657∗∗∗(0.550)
0.286(0.556)−0.165(0.669)0.225(0.542)0.435(1.079)−0.111(0.293)−0.218(0.481)
0.539(0.484)
1.632(1.280)2.265(1.643)1.376(2.175)
-9229
43560
218

Note: The table presents the estimates from 2 random coefficient logit models. For each model, the firstcolumn presents parameter estimates and the second column standard errors. The base type of bread isother bread. The sample includes households from columns 1–2 in table 1 with a sufficient number of breadpurchases; for each household the sample excludes the years when the household received WIC vouchers.
The sample is restricted to the shopping trips to the stores in the Retail Scanner data. The prices areconstructed only from the Retail Scanner data. Standard errors are clustered at the household level. In
column 2, standard errors are obtained by bootstrap (over 2 steps of the estimation) with 100 bootstrap
samples. *** Indicates significance at the 1 percent level, ** 5 percent level, * 10 percent level.

96

Table D5: Control function estimation: sample includes only the major reportable markets
and excludes the remaining U.S. Dependent variable: price of bread.
ηp : Average price in other markets
Whole grain bread
Whole wheat bread
White bread
Market FE
F-statistic of H0: ηp = 0
R-squared
Number of clusters
Number of observations

Estimate
0.865***
0.047**
0.012-0.050*Yes
301.060
0.842
46
67592

SE
(0.050)(0.022)(0.020)(0.029)Note: A unit of observation is a bread type (white, whole grain, whole wheat, or other), market, (aggregate)
retailer, and week combination. Prices are measured as dollars per pound, deflated to 2015 dollars. Standard
errors clustered by market are included in parenthesis. *** Indicates significance at the 1 percent level, ** at
5 percent level, * at 10 percent level.

97

Table D6: Robustness of the bread demand model estimates: sample includes only the majorreportable markets and excludes the remaining U.S.
No control function Control function(1)(2)
Estim.
SE
Estim.
SEMeanᾱ: Price−1.122∗∗∗ (0.080)
γ̄: Short-term state dependence
0.614∗∗∗ (0.025)
β: Last year’s share of whole wheat
4.132∗∗∗ (0.119)
θ̄: Whole wheat bread−1.296∗∗∗ (0.057)
δ̄: Whole grain bread−0.256∗∗∗ (0.076)
λ̄: White bread−0.287∗∗∗ (0.063)
ResidualStandard deviation
σp : Price
0.463∗∗∗ (0.140)
σs : Short-term state dependence
0.471∗∗∗ (0.027)
σW W : Whole wheat bread
0.848∗∗∗ (0.041)
σW G : Whole grain bread
1.460∗∗∗ (0.053)
σW hite : White bread
1.988∗∗∗ (0.056)
Covariance
Price, short-term state dependence−0.178∗∗∗ (0.055)
Price, whole wheat bread
0.074∗∗∗ (0.026)
Price, whole grain bread−0.081∗(0.046)
Price, white bread−0.058∗∗∗ (0.020)
Short-term state dependence, whole wheat bread −0.115∗∗∗ (0.025)
Short-term state dependence, whole grain bread 0.232∗∗∗ (0.030)
Short-term state dependence, white bread−0.239∗∗∗ (0.047)
Whole wheat bread, whole grain bread
0.827∗∗∗ (0.085)
Whole wheat bread, white bread
0.958∗∗∗ (0.084)
Whole grain bread, white bread
0.263∗∗∗ (0.098)
Log-likelihood-17826
Number of choices
83272
Number of households
198−1.057∗∗∗(0.337)
0.556∗∗∗(0.063)
3.977∗∗∗(0.266)−1.376∗∗∗(0.183)−0.378(0.240)−0.123(0.383)0.621∗∗ (0.299)
1.440(1.555)0.523∗ (0.296)
0.941∗ (0.571)
1.550∗∗ (0.740)
3.370∗∗∗(0.628)
0.099(0.350)−0.387(0.860)−1.416(2.444)2.811(4.019)−0.293(0.368)−0.081(0.403)−0.937(0.837)1.150(1.364)1.110(1.794)−0.911(2.819)-1774883272
198

Note: The table presents the estimates from 2 random coefficient logit models. For each model, the firstcolumn presents parameter estimates and the second column standard errors. The base type of bread isother bread. The sample includes households from columns 1–2 in table 1 with a sufficient number of breadpurchases; for each household the sample excludes the years when the household received WIC vouchers.
The sample is further restricted to include households only in the major reportable markets and exclude theremaining U.S. Also the instruments (prices in other markets) are constructed only based on those markets inthe sample. Standard errors are clustered at the household level. In column 2, standard errors are obtainedby bootstrap (over 2 steps of the estimation) with 100 bootstrap samples. *** Indicates significance at the 1
percent level, ** 5 percent level, * 10 percent level.

98

Table D7: Control function estimation: alternative initial conditions for state dependence.
Dependent variable: price of bread.
ηp : Average price in other markets
Whole grain bread
Whole wheat bread
White bread
Market FE
F-statistic of H0: ηp = 0
R-squared
Number of clusters
Number of observations

Estimate
0.885***
0.032
0.010
-0.042
Yes
402.1
0.848
50
80928

SE
(0.044)(0.022)(0.017)(0.025)

Note: A unit of observation is a bread type (white, whole grain, whole wheat, or other), market, aggregate
retailer, and week combination. Prices are measured as dollars per pound, deflated to 2015 dollars. Standard
errors clustered by market are included in parenthesis. *** Indicates significance at the 1 percent level, ** at
5 percent level, * at 10 percent level.

99

Table D8: Robustness of the bread demand model estimates: alternative initial conditions
for state dependence
No control function Control function(1)(2)
Estim.
SE
Estim.
SEMeanᾱ: Price−1.208∗∗∗ (0.073)
γ̄: Short-term state dependence
0.651∗∗∗ (0.024)
β: Last year’s share of whole wheat
3.900∗∗∗ (0.109)
θ̄: Whole wheat bread−1.683∗∗∗ (0.048)
δ̄: Whole grain bread−0.583∗∗∗ (0.047)
λ̄: White bread−0.841∗∗∗ (0.048)
ResidualStandard deviation
σp : Price
1.260∗∗∗ (0.081)
σs : Short-term state dependence
0.467∗∗∗ (0.035)
σW W : Whole wheat bread
0.830∗∗∗ (0.037)
σW G : Whole grain bread
1.283∗∗∗ (0.040)
σW hite : White bread
2.100∗∗∗ (0.053)
Covariance
Price, short-term state dependence
0.135∗∗ (0.060)
Price, whole wheat bread−0.221∗∗∗ (0.060)
Price, whole grain bread−0.605∗∗∗ (0.075)
Price, white bread
1.141∗∗∗ (0.137)
Short-term state dependence, whole wheat bread −0.221∗∗∗ (0.029)
Short-term state dependence, whole grain bread 0.042(0.031)
Short-term state dependence, white bread−0.085∗(0.045)Whole wheat bread, whole grain bread
0.774∗∗∗ (0.065)
Whole wheat bread, white bread−0.120∗∗ (0.058)
Whole grain bread, white bread−0.719∗∗∗ (0.061)
Log-likelihood-22974
Number of choices
113208
Number of households
252−1.338∗∗∗(0.279)
0.577∗∗∗(0.060)
4.049∗∗∗(0.263)−1.387∗∗∗(0.139)−0.403∗∗ (0.192)−0.407(0.350)0.603∗∗ (0.259)
0.098(1.327)
0.521∗∗ (0.247)
0.968∗ (0.554)
1.340∗ (0.795)
2.184∗∗∗(0.675)−0.051(0.690)0.062(0.828)0.030(0.358)0.126(1.760)−0.345(0.432)−0.189(0.616)−0.680(0.554)1.048(1.408)1.320(1.125)0.998(1.446)-23066113208252

Note: The table presents the estimates from 2 random coefficient logit models. For each model, the firstcolumn presents parameter estimates and the second column standard errors. The base type of bread isother bread. The sample includes households from columns 1–2 in table 1 with a sufficient number of breadpurchases; for each household the sample excludes the years when the household received WIC vouchers.
Standard errors are clustered at the household level. In column 2, standard errors are obtained by bootstrap(over 2 steps of the estimation) with 100 bootstrap samples. *** Indicates significance at the 1 percent level,** 5 percent level, * 10 percent level.

100

D.4

Additional analysis for counterfactuals

To illustrate the role of the state variable κW W that is the share of whole wheat bread in past
year’s bread purchases, figure D3 presents the joint counterfactual distribution of the statevariable and the probability of purchasing whole wheat bread. The figure on the left presents
the distribution in the last period before receiving the vouchers, and on the right, in the first
period after receiving the vouchers. On each figure, the 1000 counterfactual households aregrouped into 11 intervals by the value of the state variable: 0, (0,0.1],(0.1,0.2],...,(0.9,1]. The
size of the circle measures the number of households in the interval. Before receiving the
WIC vouchers (figure D3a), the state variable equalled zero for a large share of households,
while after receiving the vouchers (figure D3b) the number of people in that interval is small.
Overall, after receiving the vouchers the distribution shifts upwards, increasing both in thestate variable and purchase probability. The figures also show that as expected, the purchaseprobability of whole wheat bread is an increasing function of the state variable κW W . Notethat the relationship between the state variable κW W and the purchase probability slightly
differs before and after receiving the vouchers. This is because the probability also depends
on which product was bought last period and that changes with the vouchers.
Figure D4 presents an example of a counterfactual household’s purchase probability as
a function of the state variable κW W and describes the evolution of the state variable overtime. These results are presented for the time period (20 years) after receiving the vouchers.
The black markers indicate the baseline counterfactual and the red markers indicate thecounterfactual with the 10-cent whole wheat bread price discount. Figure D4a presents forthe example counterfactual household the joint distribution of the purchase probability ofwhole wheat bread and the state variable κW W . Note that the state variable κW W takes 19
possible values from zero to one. This is because in the counterfactual, it is assumed that a
year is 18 purchase occasions. Also, note that for a given value of state variable κW W , thepurchase probability is the highest when whole wheat bread was purchased on the last trip
101

1
.8
.6
.4
0

.2

Purchase probability

1
.8
.6
.4
.2

Purchase probability

0

0

.2

.4
.6
State variable.81(a) Before WIC

0

.2

.4
.6
State variable.81(b) After WIC

Figure D3: Counterfactual distribution of purchase probability of whole wheat bread as afunction of state variable κW W before and after receiving the WIC vouchers
Note: The figures present the joint counterfactual distribution of state variable κW W that is the share ofwhole wheat in past year’s bread purchases, and the probability of purchasing whole wheat bread. The figureon the left presents the distribution in the last period before receiving the vouchers, and on the right, in thefirst period after receiving the vouchers. Each figure is calculated using 1000 counterfactual households. The
1000 households are grouped into 11 intervals by the value of the state variable: 0, (0,0.1],(0.1,0.2],...,(0.9,1].
The size of the circle measures the number of households in the interval.

and takes lower values depending on which substitute bread product was bought. Figure D4b
presents for the same example counterfactual household the evolution of the state variable
over time.
Figure D5 presents various characteristics as a function of whole wheat bread purchaseprobability right before receiving WIC vouchers. One thousand counterfactual households aregrouped into quartiles by the value of the purchase probability before receiving the vouchers.
The x-axes displays the mean of the purchase probability before receiving the vouchers ineach quartile. The y-axes shows for the households in each quartile either the average valueof the price parameter αi (figure D5a); the average relative preference for whole wheat bread,calculated as the difference between the preference for whole wheat parameter versus themean of the preference for whole grain, white, and other (the base group) bread, θi − δi +λ3i +0(figure D5b); the average purchase probability after receiving the vouchers (figure D5c); the

102

1
0

.2

State variable
.4
.6
.8

Whole wheat purchase prob.
0
.2
.4
.6
.8
1

0

.2

.4
.6
State variable

.8

1

0

Base
10 cent whole wheat bread price discount10
Years since WIC

20

Base
10 cent whole wheat bread price discount(a) State variable κW W vs purchase probability(b) State variable κW W over time

Figure D4: Counterfactual results for an example household
Note: The figure presents results for an example counterfactual household for the time periods (20 years)
after receiving the vouchers. Figure D4a presents the joint distribution of the purchase probability of whole
wheat bread and the state variable κW W , which is the share of whole wheat bread in past year’s breadpurchases. Figure D4b presents the evolution of the state variable over time. The black markers indicate thebaseline counterfactual and the red markers indicate the counterfactual with the 10-cent whole wheat breadprice discount.

average change in the purchase probabilities from before to after receiving the vouchers (figureD5d); the average difference in the number of years it takes to return to pre-WIC purchaseprobability with a 10-cent discount on whole wheat bread versus the baseline counterfactual(figure D5e). The figure suggests that households that before WIC had lower whole wheatpurchase probability, were more price elastic and had a lower preference for whole wheat
relative to other breads, and for them the counterfactual of the whole wheat bread pricedecrease, has a larger effect.

103Dif. in pref. for WW vs other breads
-1.4
-1.2
-1
-.8

-1.1
Price parameter α-1.5 -1.4 -1.3 -1.2
-1.6

0

.1
.2
.3
Purchase probability before WIC.40(a) Price parameter α

.1
.2
.3
Purchase probability before WIC.4

ΔProbability: after - before WIC
.1
.2
.3
0

0

Purchase probability after WIC
.2
.4
.6

(b) Relative pref. for whole wheat

0

.1
.2
.3
Purchase probability before WIC

.4

0

.1
.2
.3
Purchase probability before WIC.4(d) ∆ purchase prob. during WIC

0

ΔYears: lower price - base4812(c) Purchase probability after WIC

0

.1
.2
.3
Purchase probability before WIC.4(e) Effect of the price decrease

Figure D5: Counterfactual: characteristics as a function of pre-WIC whole wheat breadpurchase probability
Note: One thousand counterfactual households are grouped into quartiles by the value of the whole wheat
bread purchase probability before receiving the vouchers. The x-axes displays the mean of the purchaseprobability before receiving the vouchers in each quartile. The y-axes shows for the households in eachquartile either the average value of the price parameter α (figure D5a); the average relative preference forwhole wheat bread, calculated as the difference between the preference for whole wheat parameter versus
the mean of the preference for whole grain, white, and other (the base group) bread, θi − δi +λ3i +0 (figureD5b); the average purchase probability after receiving the vouchers (figure D5c); the average change in thepurchase probabilities from before to after receiving the vouchers (figure D5d); the average difference in thenumber of years it takes to return to pre-WIC purchase probability with a 10-cent discount on whole wheat
bread versus the baseline counterfactual (figure D5e).

104

References for Online Appendix
de Chaisemartin, C. and X. D’Haultfœuille (2020a): “Difference-in-Differences Estimators of Intertemporal Treatment Effects,” SSRN Scholarly Paper ID 3731856, Social
Science Research Network, Rochester, NY.
——— (2020b): “Two-Way Fixed Effects Estimators with Heterogeneous Treatment Effects,”
American Economic Review, 110, 2964–2996.
DellaVigna, S. and M. Gentzkow (2019): “Uniform Pricing in U.S. Retail Chains,” The
Quarterly Journal of Economics, 134, 2011–2084.
Dubois, P., R. Griffith, and A. Nevo (2014): “Do Prices and Attributes Explain
International Differences in Food Purchases?” American Economic Review, 104, 832–867.
Goodman-Bacon, A. (2021): “Difference-in-differences with variation in treatment timing,”
Journal of Econometrics, 225, 254–277.
Institute of Medicine (2006): WIC Food Packages: Time for a Change, Washington,
D.C.: The National Academies Press.
Johnson, P., L. Giannarelli, E. Huber, and D. Betson (2014): “National andState-Level Estimates of Special Supplemental Nutrition Program for Women, Infants,
and Children (WIC) Eligibles and Program Reach, 2011,” Report WIC-14-ELIG, U.S.
Department of Agriculture, Food and Nutrition Service, Office of Research and Analysis.
Oster, E. (2018): “Diabetes and Diet: Purchasing Behavior Change in Response to Health
Information,” American Economic Journal: Applied Economics, 10, 308–348.
Seo, B. (2019): “Firm Scope and the Value of One-Stop Shopping in Washington State’s
Deregulated Liquor Market,” SSRN Scholarly Paper ID 2863094.

105

USDA (2018a): USDA Branded Food Products Database, U.S. Department of Agriculture,
Agricultural Research Service, Nutrient Data Laboratory.
——— (2018b): USDA National Nutrient Database for Standard Reference, U.S. Departmentof Agriculture, Agricultural Research Service, Nutrient Data Laboratory.

106