will a fat tax work? romana khan , kanishka misra , vishal...
TRANSCRIPT
1
Will a Fat Tax Work?
Romana Khan1, Kanishka Misra
2, Vishal Singh
34
Abstract:
Of the many proposals to counter the obesity epidemic, the most contentious is the use of
the so-called “fat tax” to discourage consumption of unhealthy products. Using milk sales
data from a quasi-experimental field setting, we conduct a large scale empirical
investigation of the potential for price incentives to alter consumption behavior. We find
that even small price differences are effective in inducing consumers to switch to low fat
milk, particularly amongst lower income groups who are most vulnerable to obesity. Our
results provide empirical evidence and guidelines on how price incentives, via taxes or
subsidies, can shift consumer's choices and serve as an effective mechanism against
obesity.
1 McCombs School of Business, University of Texas at Austin, Austin, TX. 2 London Business School, London, England. Misra thanks the Center for Marketing, at the London
Business School for providing research support for this project. 3 Stern School of Business, New York University, New York, NY. 4 To whom correspondence should be addressed: [email protected]
2
When next at the grocery store, linger a moment longer in front of the milk cooler to
compare the prices for milk across fat content. You may be surprised to learn that
relative prices vary depending on which store you happen to patronize. At some stores,
prices are uniform across all fat content, whilst in others, they are non-uniform -
generally decreasing with fat content. The key issue here is whether and how these price
differences impact people's choices. To put it simply, do people switch to lower fat milk
when it is the cheaper option? This question is of interest because milk is among the top
three leading sources of saturated fat in the American diet (1). More importantly, it
relates to the larger hotly debated issue of whether price incentives (via a tax or subsidy)
can influence people's choices and serve as an effective mechanism to curb obesity.
Obesity in the US has reached epidemic proportions, two-third of adults and one in three
children are overweight or obese (2) (3). Obesity has been linked with increased an risk
of conditions such as heart disease and diabetes (4), and is estimated to cause 112,000
deaths every year (5). Moreover, it imposes significant externalities through productivity
losses and healthcare costs. Recent estimates put obesity-related medical expenditures as
high as $168 billion per year, half of which are paid by taxpayers in the form of Medicare
and Medicaid (6).
Given the individual and societal costs associated with obesity, the issue has received
attention from healthcare professionals, social scientists, and public officials.
Recommendations range from modification of food labels to educational programs
promoting healthier lifestyles (4) (7) (8). Among these interventions, the most
contentious is the use of the so-called “fat tax” to discourage consumption of unhealthy
products (9) (10). Proponents of the measure point to successes achieved in combating
tobacco use, and the potential to use tax revenues to offset other obesity-related costs.
Ideological opposition has come on the grounds of personal responsibility and the role of
government (11), as well as the potentially regressive nature of the policy (12).
Policymakers and researchers are also skeptical about the effectiveness of taxes in
generating additional revenue and/or changing consumption behavior (13) (14).
A major obstacle to evaluating the potential efficacy of a tax policy is the lack of
sufficient evidence on how it may impact consumption behavior. Although lessons from
tobacco taxes can be helpful, the food industry is significantly more diverse and not
3
limited to a subset of the population. There have been two general approaches to provide
guidelines on the likely impact of a fat tax. The first involves manipulating prices in a
controlled experimental setting to create incentives to switch to healthier options. Results
from both lab (15) and field experiments (16) (17) show that relative price reductions on
healthier options are highly effective in shifting demand toward them. The second
approach involves using price elasticity estimates for a class of products (e.g. sugared
beverages) to simulate changes in demand under hypothetical taxes (18) (19)5. Given that
at the category level most food items tend to be relatively price inelastic (20), the general
conclusion from this approach is that low taxes (such as those in place on carbonated
drinks in several states) will not alter behavior (21). Not surprisingly, recent studies
linking state level soda taxes to health outcomes have found limited evidence of any
association (22) (23) (24). To understand the apparent discrepancy in findings between
the two approaches, two aspects of current tax policies on soft drinks and snacks merit
mention. First, they are levied on the entire product class rather than on specific items,
giving consumers limited incentives to substitute within the category (e.g. regular to diet
soda). Second, taxes are usually in the form of sales taxes, rather than reflected in shelf
prices. Evidence suggests that a majority of consumers do not take sales taxes into
account when making purchase decisions (25).
This article provides a large-scale empirical field study on the impact of price differences
across fat content on consumer demand for milk. We use scanner data from 2001 to 2006
on UPC-level sales and prices from a nationwide sample of 1,567 grocery stores,
provided by IRI (26). The demographic profiles of each store's customer base show
significant heterogeneity in characteristics such as age, income, household size, race and
employment status (SOM text, table S1).
The analysis is motivated by extensive variation across stores in market shares and
pricing across fat content (SOM text, figure S4, table S3). As noted above, retail prices of
milk in the US are either uniform or (weakly) decreasing with fat content. The price
structure at a particular retailer is determined by chain policy at the state level (SOM text,
table S2), rather than by local demand conditions or demographics. This exogenous
5 Note that conclusions from research with secondary field data may be highly dependent on the type of
econometric model used by the researcher.
4
variation in pricing structure provides a natural quasi-experiment where we can observe
differences in purchase patterns directly from the data as opposed to simulating the
impact via an econometric model. The most prevalent structure, in approximately one-
third of stores, is strictly uniform - where prices across all fat content are equal. The
remaining stores span an array of non-uniform structures which share two key features:
whole milk is the most or one of the most expensive types and prices decrease with fat
content. As a preliminary analysis, figure 1 plots average prices and market shares under
uniform and non-uniform prices. When prices are uniform, whole milk has the highest
market share at 36.4%. Under non-uniform prices, where 2% milk is on average 14 cents
cheaper than whole milk, the market share of whole milk falls to 29.7%. The majority of
movement in market share is to 2% milk, which has the highest market share under non-
uniform prices.
While aggregate differences in market share indicate a high level of responsiveness to
price, they do not control for factors such as demographics. Table 1 shows the results
from a regression of whole milk market share on the average price of whole milk and its
substitutes: 2%, 1% and skim milk, and demographic characteristics surrounding each
store (see table S4 for full results). The dependent variable is the logit transformation of
the average market share of whole milk in each store in each year (SOM text). As
expected, the price coefficients indicate that an increase in the price of whole milk
decreases the share of whole milk, while increases in the prices of its lower fat substitutes
result in higher shares for whole milk. Evaluated at the mean, the price elasticity for
whole milk is -2.73, indicating elastic demand. This is higher in magnitude compared to
category-level elasticity measures reported in the literature for milk (14) and food
products in general (20). Note however that we are estimating within category elasticity,
and choice elasticity (i.e. substitution of products within category) tends to be high for
food products (27). This is important because the conclusion that a fat tax will have
limited impact on shifting consumer demand is driven by low price elasticity estimates at
the category level. While overall category elasticity may be low, our results indicate that
within-category demand is highly elastic, and price incentives can be used to shift
demand toward healthier options within a category. The closest substitute for whole milk
5
is 2% milk, with a cross-price elasticity of 1.86, while 1% and skim milk are weaker
substitutes, with cross price elasticities of 0.74 and 0.70, respectively6.
While the price elasticity indicates that demand for whole milk is highly responsive to
price, there may be nonlinearities in this relationship. To address this issue, we estimate a
regression of whole milk market share on the price ratio of whole milk to 2% milk (since
the majority of movement in market share is between whole and 2%). To account for
potential nonlinearities, we discretize the price ratio with a sequence of dummy variables
defined relative to the base of uniform prices: whole milk prices higher than 2% by 1-5%,
5-10%, 10-15%, 15-20%, and greater than 20% (table S5). Figure 2 plots the regression-
based market shares of whole milk at different levels of the price premium. Under
uniform prices, the market share of whole milk is 35%. A 1-5% premium of whole milk
over its 2% substitute reduces whole milk share by 5%. When the premium increases to
5-10%, whole milk share falls an additional 6%. Further increases lead to additional
reductions in whole milk share, but the marginal impact is lower. The key finding here is
that influencing choice through price mechanisms can be achieved with relatively small
price differences, with the majority of shifts in demand achieved with premiums of just 5-
10%.
Our results also reveal differences in demand across demographic groups (SOM text).
Given the higher prevalence of obesity among lower income groups (28), it is important
to assess whether the price incentive is equally effective across income levels. Figure 3
shows the regression-based (table S6) market shares for the lowest and highest income
quartiles at different levels of the whole milk premium. Under uniform prices, the
discrepancy between income groups is large - whole milk share for lower income exceeds
the higher income group by 17%. As the whole milk premium increases, the share for
both income groups falls, but the response is stronger for lower income, driven by higher
price sensitivity for this group. At a premium of 5-10%, the market share for low income
falls from 43% to 29%, while for high income it falls from 26% to 18%. The discrepancy
between income groups continues to fall as the premium increases, and disappears with a
premium of 15-20%. These results provide strong evidence that policies based on price
6 Our results are also robust when we instrument for price (table S4) to alleviate concerns about price
endogeneity.
6
incentives can be particularly useful in shifting the purchases of lower income
consumers, who are most vulnerable to obesity.
In summary, we find strong field evidence that price incentives can serve as an effective
mechanism to shift people's choices toward healthier options. Our results suggest that
relatively small price differences (5-10% in the case of milk) can induce substantial shifts
in demand, particularly amongst lower income consumers. These results provide
important guidelines to the hotly debated issue of fat taxes, such as those in consideration
for sugared beverages in several states and cities. The beverage industry has spent
millions of dollars on lobbying and advertising against the proposed taxes (29). Our
results suggest that such taxes, if reflected in shelf prices and strategically implemented
to encourage substitution to healthier options within a category, can be quite effective in
altering behavior. Our findings also lend credence to the potential effectiveness of
Walmart's recent announcement to join Michelle Obama's anti-obesity program, by
making healthy choices more affordable and eliminating the price premium for 'better-
for-you' products (items containing less sodium, sugar, and fats) (30). Based on our
findings, the effects of this policy might be more pronounced if instead of simply
eliminating the price premium on 'better-for-you' products, it were shifted to the 'worse-
for-you' products.
7
Table 1: Response of whole milk market share to price. OLS estimates with standard
errors.
Parameter Std. Error
Intercept -1.695 0.047
Whole milk price -1.352 0.046 -2.73 0.093
2% milk price 0.959 0.085 1.86 0.166
1% price 0.382 0.060 0.74 0.117
Skim price 0.372 0.052 0.70 0.098
Demographic controls: Income, Age, Race, and Population Density
Adjusted r-square 0.534
Number of observations 6835
Dependent variable: ln(Whole milk share/1-Whole milk share)
Elasticity of Whole
Milk wrt price of:
8
Figure 1: Market share and price by milk type, under uniform and non-uniform price
structures.
36.4%
29.7%
16.2%17.7%
29.6%
36.3%
15.5%
18.6%
$2.91 $2.91 $2.91 $2.90
$2.87
$2.73$2.71
$2.60
$2.00
$2.10
$2.20
$2.30
$2.40
$2.50
$2.60
$2.70
$2.80
$2.90
$3.00
10%
15%
20%
25%
30%
35%
40%
45%
50%
Whole milk 2% milk 1% milk Skim milk
Pri
ce p
er
ga
llo
n
Ave
rag
e M
ark
et
Sha
re
Uniform Share NonUniform ShareUniform Price Non-Uniform Price
9
Figure 2: Whole milk market share, by level of whole milk price premium over 2% milk.
Estimates are based on regression results in table S5. Vertical bars show 95% confidence
intervals.
35%
30%
24%
23%
19%
18%
14%
19%
24%
29%
34%
0-1% (Uniform) 1-5% 5-10% 10-15% 15-20% >20%
Wh
ole
m
ilk
mar
ket
sh
are
Percentage price premium of whole milk over 2% milk
10
Figure 3: Whole milk market share by income group, by level of whole milk price
premium over 2% milk. Estimates are based on regression results in table S6. Vertical
bars show 95% confidence intervals.
43%
37%
29%
27%
21%
17%
26%
23%
18%
20%21%
19%
10%
15%
20%
25%
30%
35%
40%
45%
0-1% (Uniform) 1-5% 5-10% 10-15% 15-20% >20%
Wh
ole
mil
k m
ark
et s
har
e
Percentage price premium of whole milk over 2% milk
Low Income
High Income
11
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Supporting Online Material for
Will a Fat Tax Work?
Romana Khan, Kanishka Misra, Vishal Singh
Correspondence to: [email protected]
This file includes:
Materials and Methods
SOM Text
Figs. S1 to S5
Tables S1 to S6
14
1. Materials and Methods
1.1 Store Level Data
Our analysis uses store level sales data provided by IRI (26). Store sales, price and
promotion information is recorded weekly at the UPC level. The data covers a period of
six years, from 2001 to 2006. There are a total of 1,567 reporting stores from 101 chains,
operating in 47 markets across 39 states. There are 416 counties represented in the data;
the population of these 416 counties accounts for 47% of the total US population.
Demographic Information
The customer base of each store is profiled with an extensive set of demographic
variables. Summary statistics are reported in Table S1. The variables fall under four
categories: (1) Age: percent of households with children under age 17, percent of
population under age 5, percent of population over age 55, percent of households with
more than 5 members (large households); (2) Income: per capita income, median income,
percent of population below the poverty level, percent of population unemployed, percent
of population employed in blue collar jobs; (3) Urban/Suburban: population density; (4)
Ethnicity: percent of population that is white. The summary statistics demonstrate the
broad spectrum of demographic profiles served by the stores reporting in the database.
This is a key factor as it allows us to also relate observed variation in demand across
stores to the underlying demographic characteristics of customers served.
Competition Information
We collected additional data to characterize local competition and cost factors. This
includes the median hourly wage, the total number of grocery retailers located within 5
miles of each store, and the number of discount grocery retailers (e.g. Wal-Mart
Supercenter) located within 10 miles of each store. We use a larger radius to measure
competition from discount stores since they typically have a larger trading area than
regular supermarkets. The competitive data is used to understand the underlying factors
impacting the retailer's pricing decision.
15
1.2 The Milk Category: Products used in the analysis
The category of plain milk contains a large number of UPCs representing various brands,
sizes, packaging, and fat content. The volume-based market shares are:
by fat content: whole - 31.5%, 2% - 34.4%, 1% - 15.7%; skim - 18.3%;
by brand: private label - 80.5%, national brands - 19.5%;
by size: 128oz - 79.3%, 64oz - 20.7%;
by packaging: plastic jug - 94.3%, carton - 5.7%.
Our analysis uses the store level sales and price data of private label plain milk in the 128
oz plastic jug at the four major fat content levels (whole, 2 %, 1% , and skim). These four
products represent 67% of the total volume share of plain milk. The ubiquity and high
market penetration of private label plain milk facilitates comparison across a large
number of stores and demographic profiles. We do not include organic, lactose free, and
other variants as they are a small share of the market.
An important feature of the data is that the relative prices of milk across fat content vary
extensively across stores. In approximately one-third of stores, prices are uniform across
all fat. Prices at the remaining stores span an array of non-uniform structures which share
two key features: (1) Whole milk is either the most or one of the most expensive types
(this fails to hold in only 3.2% of observations) and (2) Prices are generally decreasing
with fat content. Incidentally, decreasing prices with fat content reflect the actual
underlying costs of milk production - since butterfat is the more expensive component,
the cost of milk increases with its fat content. 7
Before analyzing the impact of these
7 This relates to the process by which milk is produced. The fat content of unprocessed
raw milk varies with factors such as the breed of cow, the weather, and the cow's feed.
After raw milk from different sources is combined, the milk fat is separated from the milk
liquid. The components are then reconstituted to produce the standardized milk found at
grocery stores. Whole milk has 3.25% fat, the fat content of 2% and 1% milk are revealed
in their names, and skim milk has between 0 and 0.5% fat. The cost of whole milk is
highest because the value of butterfat exceeds the value of the liquid component.
Although not reported, we have access to monthly city-specific Cooperative wholesale
prices for milk that are obtained from the USDA's Agricultural Marketing Services
(AMS). These data show that the wholesale prices for milk are strictly declining with fat
content.
16
pricing structures on market shares, we first conduct analyses to understand what drives
the retailer's choice between uniform and non-uniform prices.
2. SOM Text
2.1 Factors Accounting for Variation in Price Structure Across Stores
Given the differences in relative prices across retailers, a question to address is what
drives the retailer's decision to offer uniform versus non-uniform prices. The observed
choices could potentially be driven by factors such as underlying demand characteristics,
competition, actions of downstream processors, state regulations, and chain policy. Note
that it will be problematic to directly compare outcomes under uniform and non-uniform
pricing structures if this decision is based on the underlying demand characteristics at the
store level. For example, if stores tend to choose uniform prices where demand for whole
milk is already high, then a comparison between uniform and non-uniform stores will
yield biased inferences. It will attribute differences in demand to the price structure, when
it is the price structure that is determined by underlying demand. If however the
observed price structure is driven by factors exogenous to local conditions, an analysis of
the impact of the prices on demand for whole milk is valid.
We investigate this issue with a series of analyses reported in Table S2. Column (1)
shows the results of a regression of the price ratio of whole to 2% milk on an extensive
set of explanatory variables. The first set of factors are demographics - median income,
percent of households with kids under 17, population density, and percent of population
that is white - which serve as measures of local demand characteristics. We also include
measures of the competitive environment that may impact the pricing decision - median
hourly wage, number of retailers within 5 miles, and number of discount retailers within
10 miles of the store. The impact of state regulations, milk cooperatives or processors,
and chain level policy are captured with state and chain fixed effects. The demographic
and competitive variables are standardized. While the effects of median income and
percent households with kids are statistically significant, they are negligible in the size of
their impact. For example, a price ratio increase by 1%, from 1.00 to 1.01, is associated
with a median income decrease by three standard deviations, or $47,268. Column (2)
reports the results of a variance decomposition to understand the explanatory power of
17
the included variables. Chain fixed effects account for 80% of the explained variation,
with state fixed effects accounting for 19%. The analysis suggests that the included
demographic and competitive measures have a limited role in the pricing decision. In
column (3) we report the results of a logit regression where the dependent variable is a
dummy for when prices are uniform. For the included demographics, the coefficients of
median income and percent of population that is white are significant. However, the
marginal effects for a one standard deviation increase in each are relatively small at 3.5%
and 4.3%. The marginal effects of wage and number of retailers within 5 miles are
smaller, -1.86% and 0.6% respectively. The analysis indicates that chain and state level
factors are the key determinants of the observed pricing policy.
Given the analysis above, we conclude that the choice of uniform and non-uniform
pricing structure is primarily driven by chain policy rather than a store level reaction to
local demand conditions. Our empirical findings were corroborated by interviews with
the dairy managers of 3 retail chains (one nationwide chain, one regional chain, one local
chain). They referred to the practice of pricing similar products uniformly as 'line
pricing', and indicated that the practice is a means of simplifying the price decision when
the products in question are very similar.
2.2 Impact of Price Structure on Whole Milk Market Share
Summary Analysis
As noted above, in approximately one-third of stores in the data we observe uniform
prices for all fat content. Table S3 reports the summary statistics for market shares and
prices at each fat content level under uniform and non-uniform price structures. It is
evident that under uniform pricing the market share of whole milk is significantly higher,
and that under non-uniform pricing the majority of substitution from whole milk is to 2%
milk.
Before discussing the regression analyses, we consider a descriptive 'model free' measure
of the impact of price structure based on store matching. In particular, we match (or pair)
every store that charges uniform prices to the (geographically) closest store that charges
non-uniform prices. The key variable of interest is the difference in whole milk share
18
( ) between the store that charges Uniform prices and the store that charges non-
Uniform prices (
).
We consider two store matching criteria. First, we match stores based on their whole milk
prices; therefore every uniform pricing store is matched with the geographically closest
non-uniform pricing store that charges the same whole milk price. For example, a
uniform pricing store A that charges $3 for both whole milk and 2% milk is matched with
the geographically closest non-uniform pricing store that charges $3 for whole milk and a
price less that $3 (say $2.80) for 2% milk. By construction, the measure (
) provides a model free estimate for the impact of a price “subsidy” for 2%
milk. Second, we repeat this matching based on 2% milk prices. For example, here a
uniform pricing store A that charges $3 for both whole and 2% milk is matched with the
closest non-uniform pricing store that charges $3 for 2% milk and a price greater that $3
(say $3.20) for whole milk. Here, the measure (
) provides a
model free estimate for the impact of a “tax” on whole milk. The results of these two
matching methods are shown in figure S1. The dark bars represent the results from
matching based on whole milk prices, an estimate of the impact of a 'fat subsidy' for 2%
milk. The light bars show the results from the matching based on 2% milk prices, an
estimate of the impact of a 'fat tax' for whole milk. The graphs show that both price
incentives, either a subsidy for 2% milk or a tax on whole milk, result in a lower market
share for whole milk. This reduction is increasing with the price difference in non-
uniform pricing stores.
We extend this matching by adding a criterion that the matched stores must serve the
same income group. Therefore a uniform pricing store serving a low (high) income
community that charges $3 for full fat milk and 2% milk is matched with the closest non-
uniform pricing store also serving a low (high) income community that charges $3 for
full fat milk and a price less that $3 (say $2.80) for 2% milk. The results are shown in
figure S2. Here we find that low income consumers respond more to the price incentives
than high income consumers. Finally, we repeat the store matching with limiting the
allowed distance between stores. Therefore we only consider store matches (pairs) where
the distance between the uniform pricing store and the non-uniform pricing store is less
than some threshold. Figure S3 shows that our results are robust to limiting the distance
19
between stores. These summary statistics provide a preview of the results from the main
regression model discussed below.
Regression Results
Dependent Variable: Logit transformation of whole milk market share
Our focal outcome variable is the market share of whole milk in each store-year. The
average market share of whole milk across all years and stores is 31.5%. Figure S4 plots
the distribution of whole milk market share, and demonstrates the variation in share
across stores. An overall goal is to understand the impact of price in explaining this
variation in market share. In our regressions analysis below, we use the logit
transformation of whole milk share ( ) as the dependent variable:
. This
rescales the market share from the (0,1) interval to the real line, and facilitates the use of
linear regression as the main analysis method.
Demand Model
In table S4 column (1), we report the full results of the model in Table 1 of the main text,
with a complete listing of the demographic controls. The dependent variable is the logit
transformation of whole milk market share. The key explanatory variables are the prices
of whole, 2%, 1% and skim milk. Discussions of the price parameters as well as the
resulting own and cross price elasticity estimates are provided in the main text. The
demographic controls include Median Income, Percent of population under age 5, Percent
of population over age 55, Population Density, and Percent of Population that is White.
The demographics enter as standardized variables and account for differences in
preference for whole milk. We find that the market share of whole milk is lower in areas
with higher income and higher percentage of white population. In terms of age, whole
milk consumption is higher where there are a higher proportion of children under age 5,
and in areas with a higher proportion of people over 55.
Robustness Check: Results Using Instruments for Price
A potential concern often raised in the economics literature is the endogeneity of prices.
This refers to the situation where price levels may be correlated with factors that are
20
unobserved by the analyst, but are known to the retailer in setting the price. If this were
the case, it would bias the price coefficients in our demand model. For example, a local
positive demand shock may cause the retailer to raise prices, which would lead us to
under-estimate the true price sensitivity. To address this concern, we use the farm cost of
milk and chain fixed effects as instruments for price. In Table S4 column(2), we report
the results from estimating the model using a two-stage least squares approach, with
instruments for price. We find that instrumenting for prices increases the own and cross-
price sensitivity parameters. In relative terms, 2% milk continues to be the strongest
substitute for whole milk. There is minimal change in the control demographic parameter
estimates.
Robustness Check: Quantile Regression
There are a few potential concerns with using least squares estimates (LS) from the
analysis presented in Table 1 of the main text. First, least squares estimates can give
additional weight to outliers and these can skew the estimates. Second, LS only provides
estimates in the central location rather than the entire distribution. In other words, a least
squares model assumes a homogeneous response to all independent variables while this
response can be heterogeneous. While our main regression results estimate the average
impact of prices, we cannot claim the effects hold true for the entire distribution. Third,
LS makes parametric assumptions about the error term and the errors could be non-
normal. An alternative to least squares regressions is quantile regression that can account
for each of these (31, 32). The main difference between these two approaches is that LS
estimates parameters at the conditional (conditional on independent variables) mean
whereas quantile regression estimates the parameters at different conditional quantiles
(e.g. median) of the whole milk share distribution. To show our estimates are robust to
these potential problems with a LS model, in figure S5 we plot the estimated coefficients
on whole, 2%, 1% and skim milk prices for all quantiles of the conditional distribution of
whole milk share. There are 4 important takeaways: (1) estimates for the whole milk
price (price elasticity) are negative and significant for the entire distribution, (2) estimates
for 2% milk price are positive (cross price elasticity) and significant for the entire
distribution (3) estimates for 1% milk and skim milk are not significantly different from
21
zero for some parts of the distribution, again suggesting that 2% milk is a closer
substitute to whole milk than 1% or skim milk, (4) the OLS estimates are a good
approximation for the price sensitivity estimates.
Capturing Non-linear Effects
In the analysis above, we evaluated the impact of whole, 2%, 1% and skim milk prices on
the market share of whole milk. However, the response to price differences across the
milk types could be non-linear. In particular, the response to a price premium (or
discount) could vary with the level of discount in a non-linear fashion.
To address this, we estimate a regression of the market share of whole milk on the “price
ratio” of whole to 2% milk. The ratio measures the price premium of whole milk over 2%
milk. We use this ratio since the majority of movement in response to changes in relative
price is between whole and 2% milk (as displayed in the summary analysis and cross
price elasticity). To identify potential non-linearities in response, we create a sequence of
dummy variables to discretize the price ratio. Five dummy variables are defined to
indicate when the price ratio is between: 1.01 and 1.05; 1.05 and 1.10; 1.10 and 1.15;
1.15 and 1.20; and greater than 1.20. The base is where the ratio is between .99 and 1.01,
representing the situation where prices of whole and 2% milk are equal. The model
results are shown in table S5. Figure 2 in the main text plots the model-based market
shares of whole milk as the price ratio between whole milk and 2% milk increases. The
plot shows that as the premium of whole milk increases, the market share of whole milk
falls. The response is non-linear, with a decreasing marginal impact of increases in the
price premium.
In addition to demographic controls, we include demographic interactions with the price
ratio to identify whether response to the price differential between whole and 2% milk
varies with demographic characteristics. In terms of income, as before, consumption of
whole milk is lower in higher income areas. However, the positive coefficient on the
interaction between price ratio and per capita income indicates that as the price ratio
increases, the reduction in market share is higher in lower income areas. This suggests
that lower income groups respond more when the premium of whole milk increases. This
finding motivates the analysis in the following section.
22
Non-Linear Effects by Income Group
Next we investigate how response to the price premium of whole over 2% milk varies
across income levels. To do this, we use interactions between two sets of dummy
variables. The first set is the previously discussed dummy variables based on the price
ratio of whole to 2% milk. The second set of dummy variables indicates the top, middle-
two, and the bottom quartiles of per capita income. The analysis uses interactions
between these two sets of variables to capture how response to the price premium varies
across income groups.
Table S6 presents the results of a regression of whole milk market share on the income
dummies, and the interactions between the income and price ratio dummy variables. Note
that this regression does not have an intercept. The coefficients on the dummies for low,
middle and high income quartiles capture whole milk market share under uniform prices.
The coefficients on the interaction dummies capture how market share for each income
level responds as the price ratio between whole and 2% milk increases. Figure 3 in the
main text plots the regression-based market shares for different levels of income and
price ratio. Under uniform prices, the discrepancy between income groups is large -
whole milk share for lower income exceeds the higher income group by 17%. As the
whole milk premium increases, the share for both income groups falls, but the response is
stronger for lower income, driven by higher price sensitivity for this group. At a premium
of 5-10%, the market share for low income falls from 43% to 29%, while for high income
it falls from 26% to 18%. The discrepancy between income groups continues to fall as the
premium increases, and disappears with a premium of 15-20%. These results provide
strong evidence that policies based on price incentives can be particularly useful in
shifting the purchases of lower income consumers, who are most vulnerable to obesity.
23
Figure S1. The difference whole milk market shares between uniform and non-uniform
stores, by whether there is a subsidy for 2% milk versus a tax on whole milk. Matching-
based estimates are shown for different levels of the tax/subsidy. The dark bars represent
the results from matching stores based on whole milk prices, to estimate the impact of a
'fat subsidy' for 2% milk. The light bars represent the results from matching stores based on 2% milk prices, to estimate the impact of a 'fat tax' on whole milk.
-14%
-12%
-10%
-8%
-6%
-4%
-2%
0%
1%-5% 5%-10% 10%+
Wh
ole
milk
sh
are
in U
NIF
OR
M s
tore
MIN
US
wh
ole
m
ilk s
har
e in
NO
N U
NIF
OR
M s
tore
Difference between whole and 2% milk price in the NON UNIFORM store
UNIFORM and NON UNIFORM have same Whole milk price
UNIFORM and NON UNIFORM have same 2% milk price
24
Figure S2. The difference in whole milk market share between uniform and non-uniform
stores, by income level. Matching-based estimates are shown for stores that serve the
same income group.
-25%
-20%
-15%
-10%
-5%
0%
Low income High income
Wh
ole
milk
sh
are
in U
NIF
OR
M s
tore
MIN
US
wh
ole
m
ilk s
har
e in
NO
N U
NIF
OR
M s
tore
25
Figure S3. The difference in whole milk market share between Uniform and Non-
Uniform stores, by maximum distance between stores. Matching-based estimates are
shown for stores that are no more than 0, 10, 100, and 150 miles apart.
-9%
-8%
-7%
-6%
-5%
-4%
-3%
-2%
-1%
0%
0 (n = 22) 10 (n = 191) 100 (n = 848) 150 (n = 1141)
Wh
ole
milk
sh
are
in U
NIF
OR
M s
tore
MIN
US
wh
ole
milk
sh
are
in N
ON
UN
IFO
RM
sto
re
Distance between (ZIP code centers of) UNIFORM and NON UNIFORM STORES
26
Figure S4. Distribution of whole milk market share across stores.
27
Fig. S5
Response of whole milk market share to price. Using Quantile Regression
Dependent variable is ln(Whole milk market share/1-Whole milk market share)
The black line represents the quantile regression estimates, the grey bars are the 95% confidence
intervals. The solid red line is the OLS estimate and the dotted lines are the 95% confidence
intervals.
28
Table S1.Summary statistics on demographics and competitive environment of stores
Variable Mean Std
Dev
Minimum Maximum
Age:
% households with kids <17 34.8 8.6 1.2 66.4
% population < age 5 6.6 1.3 1.2 12.1
% population > age 55 24.5 5.7 9.4 83.4
%households with >5 members 24.1 8.0 1.1 60.2
Income:
Per capita income 23639 8294 8476 69054
Median income 48140 15756 13971 153259
Poverty rate 10.1 6.4 1.0 45.1
Unemployment rate 5.2 2.8 0.6 30.4
% Blue collar 33.6 10.0 7.8 67.2
% White 71.3 21.4 1.2 99.1
Population density 3406 3938 20 54713
Competitive factors:
All retailers within 5 miles 7.0 5.3 1.0 79.0
Discount retailers within 10
miles
3.6 2.2 0.0 17.0
Hourly wage 18.4 3.6 8.4 29.8
Number of Observations
(stores)
1567
29
Table S2. Factors accounting for the variation in the price ratio of whole to 2% milk.
(1)OLS estimates with standard errors (2) Results of variance decomposition, showing
percentage of explained variance accounted for by each factor. (3) Logit regression.
Dependent Variable: Uniform Dummy (=1)
(2) (3)
Estimate
% of explained variation
accounted for
Intercept 1.10955 6.2322
(0.0186) (21.036)
Median Income -0.00355* 0.52% 0.1583*
(0.0008) (0.061)
% HH Kids 0.00195* 0.22% -0.0854
(0.0007) (0.048)
Pop Density -0.00011 0.00% 0.139
(0.0009) (0.080)
% White -0.00066 0.01% 0.1985*
(0.0009) (0.077)
Wage 0.00128 0.29% -0.0842*
(0.0004) (0.029)
All retailers within 5 miles -0.00013 0.02% 0.0285*
(0.0002) (0.014)
Discount retailers within 10 miles 0.00022 0.01% -0.0375
(0.0003) (0.027)
State Fixed Effects Included 18.69% Included
Chain Fixed Effects Included 80.24% Included
R2 0.541
Number Observations 6835 6835
(1)
Ratio : Price Whole/Price 2%
30
Table S3. Summary statistics of market shares and prices by uniform/non-uniform price structure.
Mean Std Dev Mean Std Dev
Market Share:
Whole 36% 16% 30% 15%
2% 30% 9% 36% 9%
1% 16% 9% 16% 7%
Skim 18% 9% 19% 10%
Price:
Whole $2.91 $0.47 $2.87 $0.40
2% $2.91 $0.47 $2.73 $0.40
1% $2.91 $0.47 $2.71 $0.40
Skim $2.90 $0.47 $2.60 $0.41
No. of Observations 1982 4853
Uniform Non-Uniform
31
Table S4. Response of whole milk market share to price. (1) Shows the Full results for
Table 1 text. (2) Shows the 2SLS parameter estimates using instruments for the prices.
Variables
Parameter Std. Error Parameter Std. Error
Intercept -1.695 0.047 -2.111 0.079
Whole milk price -1.352 0.046 -2.352 0.075
2% milk price 0.959 0.085 1.567 0.148
1% price 0.382 0.060 1.051 0.103
Skim price 0.372 0.052 0.291 0.074
Per capita income -0.249 0.008 -0.245 0.008
% Age<5 0.043 0.010 0.044 0.011
% Age>55 0.123 0.009 0.115 0.010
Population density 0.026 0.008 0.032 0.009
% White -0.412 0.009 -0.384 0.011
Adjusted r-square 0.534 0.572
Number of observations 6835 6835
(1) (2)
Dependent variable: ln(Whole milk share/1-Whole milk share)
32
Table S5. Impact of Price Premium of Whole milk on Whole Milk Share
Dependent variable: ln(Whole milk share/1-Whole milk share)
Parameter Std. Error
Intercept -0.611 0.010
Dummy for price whole milk > price 2% milk by:
1-5% -0.233 0.017
5-10% -0.559 0.018
10-15% -0.626 0.027
15-20% -0.808 0.040
20%+ -0.908 0.052
Per capita income -1.914 0.142
% Age<5 -0.089 0.187
%Age>55 0.788 0.174
Population density 0.765 0.235
% White 0.599 0.181
Demographic Interactions with Price Ratio
Per capita income 1.612 0.136
% Age<5 0.126 0.180
%Age>55 -0.630 0.168
Population density -0.722 0.231
% White -0.997 0.174
Adjusted r-square 0.529
Number of observations 6835
33
Table S6. Impact of Price Premium of Whole Milk on Whole Milk Share, by Income
Dependent variable: ln(Whole milk market share/1-Whole milk market share)
Parameter Std. Error
Low Income (Bottom Quartile PC Income) -0.266 0.020
Middle Income (Middle Quartiles PC Income) -0.617 0.015
High Income (Top Quartile PC Income) -1.044 0.021
Dummy for price whole milk > price 2% milk by: * Low income
1-5% -0.247 0.032
5-10% -0.629 0.034
10-15% -0.749 0.049
15-20% -1.081 0.076
20%+ -1.330 0.091
Dummy for price whole milk > price 2% milk by: * Middle Income
1-5% -0.242 0.025
5-10% -0.555 0.027
10-15% -0.703 0.040
15-20% -0.911 0.055
20%+ -0.975 0.074
Dummy for price whole milk > price 2% milk by: * High Income
1-5% -0.178 0.033
5-10% -0.453 0.037
10-15% -0.338 0.054
15-20% -0.252 0.084
20%+ -0.436 0.120
% Age<5 -0.057 0.189
%Age>55 0.661 0.175
Population density 0.177 0.234
% White 0.334 0.181
Demographic Interactions with Price Ratio
% Age<5 0.077 0.182
%Age>55 -0.531 0.169
Population density -0.175 0.230
% White -0.742 0.175
Adjusted r-square 0.789
Number of observations 6835