A referee report should include the following: • A summary of the research paper • A recommendation to the journal editor as to whether the work should be published, whether it would beneﬁt from revisions, or whether it should be rejected due to a lack of substantive intellectual contribution • A discussion of the research’s contribution to the ﬁeld’s current understanding of the topic • Analysis of the methodological approach, especially the identiﬁcation of shortcomings or areas lacking clear explanation The cover letter is essentially a synopsis of the referee report and is a great exercise in the concise presentation of your thoughts.Corrective tax design in oligopoly
Martin O’Connell†∗ and Kate Smith∗
†
Job Market Paper
This version: January, 2020. Most recent version available here.
Correspondence: martin o@ifs.org.uk.
Abstract
We study the design of taxes aimed at limiting externalities in markets
characterized by differentiated products and imperfect competition. In such
settings policy must balance distortions from externalities with those associated with the exercise of market power; the optimal tax rate depends on
the nature of external harms, how the degree of market power among externality generating products compares with nontaxed alternatives, and how
consumers switch across these products. We apply the framework to the topical question of taxes on sugar sweetened beverages. We use detailed data
on the UK market for drinks to estimate a model of consumer demand and
oligopoly pricing for the differentiated products in the market. We show the
welfare maximizing tax rate leads to welfare improvements over 2.5 times as
large as that associated with policy that ignores distortions associated with
the exercise of market power.
Keywords: externality, corrective tax, oligopoly
JEL classification: D12, D43, D62, H21, H23, L13
Acknowledgements: The authors would like to gratefully acknowledge financial support from the European Research Council (ERC) under ERC2015AdG694822, the Economic and Social Research Council (ESRC) under
the Centre for the Microeconomic Analysis of Public Policy (CPP), grant
number RES544280001, and the British Academy under pf160093. Data
supplied by TNS UK Limited. The use of TNS UK Ltd. data in this work
does not imply the endorsement of TNS UK Ltd. in relation to the interpretation or analysis of the data. All errors and omissions remain the responsibility
of the authors.
∗
Institute for Fiscal Studies and University College London.
1
Introduction
Onefifth of all consumer spending is undertaken in markets subject to taxes, at least
in part, aimed at altering behavior to limit externalities.1 Many of these markets
are characterized by the presence of large multiproduct firms that are likely to
exercise substantial market power. For instance, soft drink markets, the subject
of new taxes in several jurisdictions, are dominated by Coca Cola Enterprises and
PepsiCo. Distortions associated with the exercise of market power have important
implications for corrective tax design. Buchanan (1969) points out that efforts
to fully correct for externalities are only justified in conditions of competition; in
imperfectly competitive environments price is already in excess of marginal cost and
externality correcting policy that fails to take account of this can reduce welfare.
However, the bulk of the long literature on the design of corrective taxes, dating
back to Pigou (1920), assumes a perfectly competitive environment.
Our contribution in this paper is to study the design of taxes levied on externality generating products in markets characterized by product differentiation,
strategic firms and imperfect competition, and to undertake a substantive empirical
application to the taxation of sugar sweetened beverages. We write down a simple
optimal tax model that shows how patterns of consumer substitution, positive pricecost margins and strategic price reoptimization affect the optimal corrective tax
prescription. In our empirical application we estimate a detailed model of consumer
demand and oligopoly price competition in the market for nonalcoholic drinks, and
compute the optimal sugar sweetened beverage tax. We show that despite substantial pricecost margins on these products, there is nonetheless a case for levying a
positive tax rate, in part, because in equilibrium consumers switch to other imperfectly competitive products. Nevertheless, the optimal rate lies below the rate a
planner that ignores distortions associated with the exercise of market power and
aims at full internalization of externalities would set, and results in substantially
larger welfare gains.
We consider a setting in which there are many differentiated products available
to consumers. The consumption of one set of products generates an externality (in
proportion to some specific product attribute), while the remaining set generate no
external costs. The products are supplied by a set of (potentially multiproduct)
firms that derive market power from the imperfectly substitutable nature of the
products in the market. A social planner sets a linear tax on the externality gen1
Spending on alcohol, tobacco, soft drinks, fuel, and motoring (all of which are subject to
some kind of excise duty in the UK – Levell et al. (2016)) accounts for 24% of spending recorded
in the UK’s consumer expenditure survey (Living Costs and Food Survey (2017)).
1
erating product attribute, with the aim of improving welfare. To focus on the
interaction between externality correction and imperfect competition we assume
the planner sets the tax rate to maximize economic efficiency in the market; the
planner does not have a redistributive motive, nor a revenue raising constraint.2
If the market was perfectly competitive, the optimal rate would be equal to the
marginal external cost (if homogeneous across consumers, as in Pigou (1920)) or,
when there is heterogeneity in marginal externalities, the optimal rate would be
equal to a weighted average of marginal external costs (as in Diamond (1973)).
Under imperfect competition the optimal tax rate equals the traditional corrective component minus an adjustment for the distortion associated with the exercise
of market power. In a market with just one product supplied by a monopolist, the
optimal rate is equal to the marginal externality minus the equilibrium pricecost
margin on the product. In a two product market (where one product is associated with externalities and one is not), the planner cares both about achieving an
efficient level of total consumption, and achieving allocative efficiency across the
two products. A higher equilibrium pricecost margin on the externality generating
product acts to reduce the optimal rate, while a higher margin on the substitute
(untaxed) product acts to increase it. The extent to which the margin on the nonexternality generating product raises the optimal rate depends on how strongly
the tax shifts consumption towards it from the taxed product; in the limit, if consumption switches oneforone between the products, the optimal tax rate equals
the marginal externality minus the difference in equilibrium pricecost margins between the two products. With many differentiated products, switching within the
set of taxed products, as well as the specific alternative products that consumers
switch most strongly towards, also influences the optimal rate.
We use the framework to study the taxation of sugar sweetened beverages. Consumption of these products is strongly linked to diet related disease, which creates
externalities through increased societal costs of funding both public and insurance
based health care.3 In recent years, motivated by public health concerns, a number of countries and localities have introduced taxes on these products; as of May
2019, 41 countries and 7 US cities had some form of sugar sweetened beverage tax
2
Sandmo (1975) shows that in the face of a revenue raising constraint, an efficiency maximizing planner that can set a linear tax on each product in the economy will set a tax rate on
an externality generating good that entails a Pigovian component plus a distortionary Ramsey
component. Kopczuk (2003) shows this additivity property holds under much more general conditions, including when there are redistributive motives. See Bovenberg and Goulder (2002) for a
thorough review of work on how the interaction between corrective taxes and other distortionary
taxes changes the Pigovian tax prescription and can limit the effectiveness of externality correcting
taxation.
3
For a survey of the evidence see Allcott et al. (2019b).
2
in place (GFRP (2019)). The market for these products is characterized by large
multiproduct firms that offer strongly branded products and are likely to enjoy
significant market power. To implement our optimal tax framework requires estimating own and crossprice demand elasticities between products in the market,
and the equilibrium pricecost margins on these products (both for products subject
to the tax and for substitutes).
We use longitudinal data on purchases of nonalcoholic drinks that households
bring into the home and that individuals consume while onthego. Most empirical
studies of sugar sweetened beverage taxes do not cover purchases made onthego,
yet they are an important part of the market.4 We obtain demand elasticities by
estimating a model of consumer choice among the differentiated products in the
drinks market (in the broad spirit of Berry et al. (1995)). We model preferences
over key product attributes as random coefficients, allowing the coefficient distributions to depend on consumer age, income and a measure of total dietary sugar.
The overall preference distribution takes the flexible form of a mixture of normal
distributions, relaxing functional form restrictions otherwise imposed on product
demand curves.5,6
Following a long tradition in the empirical industrial organization literature
we treat pricecost margins as unobservable (see Bresnahan (1989)), using our demand estimates and the equilibrium conditions of an oligopoly pricing game to infer
marginal costs (as, for instance, in Nevo (2001)). Our estimates suggest that, on
average, prices are around double marginal costs, though there is considerable variation in pricecost margins across products. In particular, small pack sizes typically
have larger pricecost margins (per liter) than bigger sizes. Our demand estimates
suggest consumers switch more strongly away from large sizes in response to a tax,
meaning a higher tax rate drives up the average margin among taxed products,
which plays an important role in determining the optimal rate. The empirical demand and supply model allows us to simulate, in equilibrium, consumer substitution
patterns and product level margins, and serves as an important input into solving
for the optimal tax rate.
4
An exception is Dubois et al. (2019), who focus on modeling onthego demand for drinks.
In particular, the flexible preference distribution helps relax curvature restrictions on demands. As highlighted by Weyl and Fabinger (2013), demand curvature is one important determinant of how equilibrium prices respond to tax changes.
6
A potential threat to the validity of our demand estimates is the presence of neglected dynamics. In particular there is evidence in the US that consumers stockpile soft drinks (Hendel
and Nevo (2013), Wang (2015)). We provide evidence that stockpiling is much less relevant in the
UK context; when consumers purchase on sale they tend to switch brands or pack type, with no
evidence of significant changes in the timing of purchase.
5
3
We find, for reasonable levels of the externality from sugar consumption, that the
optimal tax on the sugar in sweetened beverages is positive . However, the optimal
rate lies below the Pigovian rate that would be optimal under perfect competition.
It also lies below the rate a planner that ignores distortions associated with the
exercise of market power and aims at full internalization of externalities would set.
The optimal tax rate lies below the rate aimed at full internalization of externalities
due to the existence of substantial pricecost margins for sugar sweetened beverages.
The weighted average margin for these products is actually increased with the tax,
as people switch to smaller sizes with higher margins, and firms raise margins by
increasing prices by more than the tax. However, the optimal rate is positive in
part because consumers switch towards alternative drinks products also supplied
noncompetitively.
We use an estimate of the public health costs from sugar sweetened beverage
consumption to calibrate the marginal externality, however, there is considerable
uncertainty over the size of this parameter. We show how varying the externality affects the optimal tax rate; at all positive levels of the externality, ignoring
distortions associated with the exercise of market power when setting tax leads
to substantially lower welfare than under optimal policy. If externalities are also
generated by substitute goods that contain sugar, a tax on the sugar in sweetened
beverages will be less effective at combating externalities. We show that the existence of untaxed externalities leads to a reduction in the optimal rate of around
20%. We also show that the optimal rate increases modestly in the extent to which
externalities are concentrated among those with high overall dietary sugar.
To show how the degree of market power exercised by firms influences the potential welfare gains from levying a tax on externality generating products, we
simulate the optimally set tax under counterfactual firm ownership structures. A
more competitive market structure leads to welfare gains (in the absence of tax), as
increases in consumer surplus swamp reductions in firm profitability and increased
externalities. In addition, a tax on externality generating goods leads to larger
welfare gains under more competitive market structures, suggesting that there is
complementarity between competition and corrective tax policy.
We compare the performance of the optimal tax on sugar to a number of alternatives. The welfare gains associated with the optimal rate are 2.5 times as large
as tax policy set by a planner that ignores the distortions associated with the exercise of market power. Almost all jurisdictions that have introduced taxes on sugar
sweetened beverages do so on a volumetric basis, rather than in proportion to sugar
content. We find that an optimally set volumetric tax achieves only 60% of the
4
welfare gains achieved by the optimally set sugar tax rate. Some localities, notably
Philadelphia, apply a volumetric tax to both artificially and sugar sweetened beverages as a revenue raising measure; we show that it is much more costly in welfare
terms to raise revenue with this instrument compared to a tax levied only on sugar
sweetened beverages.
We contribute to a small but growing literature that uses empirically rich treatments of markets to evaluate how imperfect competition affects fundamental tax
design questions. Fowlie et al. (2016) use a dynamic oligopoly model of a homogeneous goods market (for concrete) and show that carbon abatement policy aimed at
full internalization of social costs is welfare reducing, whereas policy that explicitly
recognizes distortions associated with the exercise of market power has the potential
to improve welfare. A set of recent papers study optimal commodity taxation in
the differentiated product market for liquor. Miravete et al. (2018a, 2018b) show
the peak and shape of the Laffer curve associated with an ad valorem tax rate depends on the strategic pricing behavior of distillers, and quantify welfare gains that
would be realized if government instead set product specific taxes/prices. Conlon
and Rao (2015) show existing “post and hold” price regulations facilitate collusion
and lead to allocative inefficiencies, and substantial consumer welfare gains would
be realized by replacing them with a higher level of taxation. A number of papers
consider optimal subsidy design in health insurance markets in which providers exercise market power, (see Tebaldi (2017), Polyakova and Ryan (2019) and Einav
et al. (2019)) and show targeted subsidies engender equilibrium pricing responses
and spillovers to nontargeted groups.
Our work also relates to a rapidly growing literature studying sugar sweetened
beverage taxation. One set of papers use data covering the introduction of taxes
to estimate the impact on prices and/or purchases.7 A second set of papers use
estimates of consumer demand to simulate the introduction of taxes similar to
those used in practice.8 Like us, Allcott et al. (2019a) study the optimal design
of a tax on sugar sweetened beverages. They consider a perfectly competitive
environment in which a social planner with a preference for redistribution sets a
tax on sugar sweetened beverages along with a nonlinear labor tax. They find
evidence of larger internalities among low income households, which, all else equal,
7
See, for instance, Bollinger and Sexton (2018) and Rojas and Wang (2017) who study the
Berkeley tax, Seiler et al. (2019) and Roberto et al. (2019) who study the Philadelphian tax, and
Grogger (2017) who study the Mexican tax. For a full survey of the recent literature see Griffith
et al. (2019).
8
These papers include Bonnet and Réquillart (2013), Wang (2015), Harding and Lovenheim
(2017) and Dubois et al. (2019).
5
increases the optimal rate set by a planner with preferences for redistribution.9 Our
work complements theirs by focusing on the impact of imperfect competition on tax
design, while abstracting from issues of redistribution.
The dominant paradigm in modern public economics is the use of sufficient
statistics to assess the welfare consequences of policy reforms (Chetty (2009)). This
is the approach taken by Jacobsen et al. (2018) to quantify the welfare loss associated with the inability to levy productspecific Pigovian taxes. It is also used by
Ganapati et al. (2019) to measure incidence of input taxes in imperfectly competitive markets. In our setting, the welfare effects of changing the tax rate depend on
the switching between, and pricecost margins for, a large set of differentiated products. To estimate these we specify a model of demand and supply in the market.10
This enables us to estimate elasticities and pricecost margins for disaggregate products, and allows us to simulate the effect of nonlocal tax changes, and therefore
recover the optimal tax rate. To provide evidence that our empirical model successfully captures behavior in the market, we use quasiexperimental variation on
price changes resulting from the recent introduction of the UK’s soft drinks tax to
validate our estimated model.
The rest of this paper is structured as follows. In Section 2 we consider the design
of corrective taxes in markets, such as that for drinks products, in which firms set
prices above marginal costs. Section 3 describes the UK market for drinks and the
micro panel data we use on purchase decisions made for consumption outside as well
as in the home. In Section 4 we present our empirical model of consumer demand
and firm pricing competition. Section 5 presents our empirical tax results. A final
section draws together the implications of our results and concludes.
2
Corrective tax design in imperfect competition
Our aim is to highlight how distortions associated with the exercise of market power
influence the efficiency maximizing rate of tax on externality generating products.
We consider a market that comprises a set of differentiated products, a subset of
which have externalities associated with their usage. The products are provided
by firms who set their prices under conditions of imperfect competition. We be9
Gruber and Koszegi (2004) and O’Donoghue and Rabin (2006) also consider the design of
internality correcting taxes.
10
An important difference between our setting and that in Ganapati et al. (2019) is that we
model a market in which asymmetric product differentiation and multiproduct firms are central. This means tax incidence cannot be expressed as a function of a small number of sufficient
statistics.
6
gin by considering a stylized market in which there are just two products, before
generalizing the analysis to a market with many products.
We consider a social planner whose task it is to set a tax rate for the externality
generating goods. The planner’s objective is to maximize efficiency. We abstract
from possible redistributive motives, focusing instead on how imperfect competition
alters the optimal externality correcting tax prescription.11
2.1
A two product market
Setup. Consider a market that comprises two products, j = {1, 2}. Consumer
i, facing prices, p = (p1 , p2 ), chooses how to allocate her income, yi , between the
two products and a numeraire good (which represents expenditure outside of the
market of interest). We assume consumers have preferences that are quasilinear
and can be represented by the indirect utility function Vi (p, yi ) = yi + vi (p), and
denote consumer level demand for product j by qij (p). The quasilinear preference
structure means that a price change for either product does not induce any income
effects. This assumption is reasonable when focusing on a market that accounts for
a small share of total consumer spending,12 and it enables us to focus on a planner
that seeks to maximize economic efficiency.
Each unit of product 1 consumed creates an externality. We initially assume the
externality is homogeneous across individuals and denote it by φ. Product 2 is a
substitute for product 1; its consumption does not create any externalities. A social
planner chooses the rate of tax, τ , to set on product 1. Both products are supplied
imperfectly competitively at constant marginal cost; the equilibrium prices are such
that:
p 1 − τ − c1 = µ 1
p 2 − c2 = µ 2 ,
11
Under perfect competition and when the planner can set a nonlinear labor tax, redistributive
motives do not influence optimal commodity taxes as long as differences in consumption patterns
across the income distribution are driven purely by income differences and consumers are utility
maximizing (Saez (2002)). Jaravel and Olivi (2019) show that this extends to an economy characterized by imperfect competition. Kaplow (2012) shows that accompanying externality correcting
taxes with a distributionneutral adjustment to the income tax system can offset the redistributive
effects of the corrective taxes across the income distribution.
12
In general, the own price effect on demand for good j follows the Slutsky equation ij =
p q
h
ij + jy ij eij , where ij and hij are the Marshallian and Hicksian ownprice elasticities of demand,
p q
and eij is the income elasticity. For a small budget share good jy ij ≈ 0, meaning ij ≈ hij and
preferences are approximately quasilinear.
7
where cj denotes the marginal cost and µj denotes the equilibrium pricecost margin
for product j (per unit, for instance liter, of consumption). The equilibrium prices
and margins depend both on the rate of tax levied on product 1 and the marginal
costs of both products, as well as whether the products are supplied by a monopolist
or duopolists.13 For notational simplicity we suppress this dependence.
We assume that the numeraire is competitively supplied, and its consumption
does not generate any externalities. We relax this assumption when we empirically
implement our results in Section 5.
Optimal policy. We consider a social planner that chooses the rate of tax to
maximize total welfare, which equals the total consumer surplus from participation
in the market, v(p), minus total externalities plus tax inclusive profits. Tax inclusive
profits on product 1 are given by (p1 − c1 )q1 and are equal to the sum of net profits
(p − τ − c1 )q1 and tax revenue, τ q1 . The planner’s problem is:
max v(p) − φq1 + (p1 − c1 )q1 + (p2 − c2 )q2 .
τ
The optimal tax rate, τ ∗ , is implicitly defined by:
dq1
dq2
∗
−
,
τ = φ − µ1 − µ2 ×
dτ
dτ
dq
∂q
(2.1)
(2.2)
∂q
1
2
where dτj = ∂pj1 dp
+ ∂pj2 dp
is the derivative of equilibrium consumption of product
dτ
dτ
1
j with respect to the tax. We expect dq
< 0 and, as the goods are substitutes,
dτ
dq2
dq2
1
> 0. We refer to the expression dτ / − dq
as the switching ratio; it captures
dτ
dτ
the extent to which any reduction in consumption of the externality generating
product induced by a marginal increase in the tax rate is redirected towards the
substitute good (taking account of the equilibrium pricing responses).
When the two products are supplied competitively (so µj = 0 for j = {1, 2}
regardless of the level of τ ) the optimal policy is a Pigovian tax (τ ∗ = φ). Whenever
the products are supplied under imperfect competition, the optimal tax rate is equal
to the Pigovian rate plus an adjustment for noncompetitive pricing.
Under imperfect competition it is instructive to consider two special cases. First,
suppose demands for the two products are independent (i.e. so qj (p1 , p2 ) = qj (pj )
dq1
2
/
−
, is zero, and the
for j = {1, 2}). This implies the switching ratio, dq
dτ
dτ
equilibrium prices of the two goods are independent of one another. In this case the
13
For instance, if the two products are supplied by separate firms that compete in a Bertrand
∂qj (p)
game µj = −qj (p)/ ∂p
. Solving the two optimal pricing equations yields equilibrium prices
j
(p1 (τ ), p2 (τ )) (where we suppress the dependence of prices on marginal cost), and associated
margins (µ1 (τ ), µ2 (τ )).
8
optimal tax rate is (implicitly defined by) τ ∗ = φ − µ1 , product 1 is priced at the
efficient level, p1 = c1 + φ, and the equilibrium price of product 2 is left unaffected
by the tax. Second, suppose instead there is no switching in or out of the market,
so in response to price changes consumers only reallocate their demand between
1
2
/ − dq
= 1. In this case the optimal tax rate
the two products, which implies dq
dτ
dτ
∗
is τ = φ − (µ1 − µ2 ) and the difference in equilibrium prices of the two products
is p1 − p2 = (c1 − c2 ) + φ. The tax achieves an efficient allocation (of the fixed
consumption level) between the two products.
2
1
In practice, dq
/ − dq
is likely to lie somewhere between 0 and 1; the imperfect
dτ
dτ
competition adjustment to the Pigovian tax rate partly reflects how policy changes
total consumption in the market and partly how it influences the allocation of consumption across the two products. To see this, note that we can rewrite equation
dq1
2
/
−
. The more
(2.2) as τ ∗ = φ − [(1 − SR) µ1 + SR (µ1 − µ2 )], where SR := dq
dτ
dτ
strongly the reduction in equilibrium quantity of product 1 from a marginal change
dq1
2
in the tax rate is directed to product 2 (i.e. the closer dq
/
−
is to 1), the more
dτ
dτ
weight is placed on the difference in equilibrium margins of the two goods.
2.2
Many differentiated products
In practice, corrective taxes are typically used in markets in which there are many
differentiated products. To the extent that there is variation across the equilibrium
pricecost margins of these products and in whether their consumption generates externalities,14 this will influence the optimal tax prescription. In addition, it matters
whether the tax is levied directly on the product characteristic that is associated
with externalities, or whether the tax is levied on a per unit basis. For instance,
a tax on sugar sweetened beverages can either be levied directly on sugar, or on a
volumetric (i.e. per liter) basis.
Suppose there are many products j = {1, . . . , J}. A subset of products, j ∈ S,
contain an attribute that is associated with an externality, where zj denotes the
amount of the attribute in product j, while for the remaining products, j ∈
/ S
(which we denote by the set j ∈ N ), zj = 0. Consider a tax levied on z. The
products are supplied in an imperfectly competitive environment with equilibrium
prices satisfying:
pj − τ zj − cj = µj ∀j ∈ S
pj − cj = µj ∀j ∈ N .
14
For instance, in the case of sugar sweetened beverages, a given amount of consumption of a
product with 10g of sugar per 100ml, all else equal, is likely to be associated with more externalities
than one with 5g sugar per 100ml.
9
In Appendix A we show that in this case the optimal tax rate can be expressed
as follows:
Proposition 1. Define: (i) the derivative of the total equilibrium quantity of the
P
S
dq
set of externality generating products with respect to the tax as dQ
= j∈S dτj , (ii)
dτ
S
dq
the share that product j ∈ S contributes to this derivative as wjS = dτj / dQ
, (iii)
dτ
the analogous expressions for the set of products that do not generate externalities
P
N
dqj
dqj dQN
N
=
and
w
=
/ dτ ), and (iv) the derivative of the total
(i.e. dQ
j
j∈N
dτ
dτ
dτ
equilibrium quantity of the externality generating attribute with respect to the tax
P
dq
rate as dZ
= j∈S zj dτj . The optimal tax rate is then implicitly defined by:
dτ
1
τ ∗ = φ − dZ dQS
dτ
dτ
X
j∈S
dQN
wjS µj −
wjN µj ×
dτ
j∈N
X
!
dQS
−
.
dτ
(2.3)
This expression generalizes the optimal tax formula in the two good case (equation (2.2)). Now the rate depends on the weighted average pricecost margin among
the sets of externality and nonexternality generating products. As the tax rate
varies, the average margin term may vary for two reasons – (i) firms may reoptimize their prices, changing product level pricecost margins, and (ii) consumers, in
equilibrium, may switch differentially away from/towards products with different
equilibrium margins. The many product optimal tax expression also depends on
the ratio of the marginal change in equilibrium quantity of the externality generating attribute and equilibrium quantity of the externality generating goods with
dQS 15
). This term results from the tax being levied
respect to the tax rate (i.e. dZ
dτ
dτ
on the externality generating product attribute rather than volumetrically on the
externality generating products (see Appendix A for the expression for a volumetric tax). All else equal, the more effective is the tax at lowering consumption of
attribute z relative to consumption of the z containing products, the higher is the
optimal rate.
2.3
Extensions
Heterogeneity in externalities. Marginal externalities may be heterogeneous,
either because externalities depend nonlinearly on an individual’s total intake of
the externality generating attribute, or because, conditional on consumption, some
individuals’ intake is more problematic than others. Let φi denote the marginal ex15
In the case of a tax on the sugar in sweetened beverages, this captures the ratio of the
marginal change in sugar consumption with respect to a small change in the tax over the marginal
change in liters of sugar sweetened beverage consumption with respect to the tax.
10
ternality for individual i.16 Now the planner must tradeoff setting a tax rate that is
too high for those that create relatively small marginal externalities, and one that is
too low for those that generate high externalities. In this case, the externality component in equation (2.3), φ, is replaced by the weighted average (across consumers)
P
marginal externality, i ωi φi , where the weight, ωi , is the contribution of individual
i to the marginal change in the equilibrium quantity of the externality generating
characteristic with respect to a marginal change in the tax rate (see Appendix A
for the full expression). The more strongly those whose marginal consumption is
most socially costly respond to the tax, then the more effective will be the tax in
correcting for externalities and, all else equal, the higher will be the optimal rate.
P
The expression i ωi φi takes a similar form as the optimal externality correcting
tax with heterogeneous externalities in a perfectly competitive market, derived in
Diamond (1973). However, in an imperfectly competitive environment, the weights
ωi incorporate the equilibrium pricing response of firms in the market.
Broader externalities. In some circumstances a policymaker may be restricted
to set a tax on a subset of externality generating products, perhaps due to some
political constraint.17 In this case, the corrective component in equation (2.3), φ,
S
A
A
, where dZdτ denotes the marginal reduction in the
is scaled by the ratio dZdτ dZ
dτ
externality generating characteristic from taxed and untaxed products associated
S
denotes the marginal reduction in the
with an increase in the tax rate, and dZ
dτ
externality generating characteristic from taxed products only (the full expression
is provided in Appendix A). If, in equilibrium, a marginal increase in the tax rate
induces switching from the taxed to untaxed goods that create an externality, then
dZ A dZ S
< 1, and, all else equal, the optimal tax rate is lower.
dτ
dτ
Full externality internalization. A policymaker may choose to ignore the distortions associated with the exercise of market power, aiming instead at full externality internalization. One approach to doing this is to set a Pigovian tax, τ = φ.
Doing this fails to recognize that equilibrium quantities in the market are already
below the competitive level, and, as pointed out by Buchanan (1969), can actually
be welfare reducing. Even if the policymaker is willing to ignore this and aims at full
externality internalization (relative to the zero tax market equilibrium), the pricing
16
When externalities are a nonlinear function of intake of attribute z, the total externality
P
i)
individual i creates is Φ(Zi ), where Zi = j zj qij . In this φi denotes dΦ(Z
dτ .
17
A leading example is when a good can be imported taxfree (see Fowlie et al. (2016) who
study greenhouse gas emissions leakage due to imported concrete). In the case of sugar sweetened
beverage taxes, some legislators have argued for a broadening of the base to cover other sources
of dietary sugars (for instance, see House of Commons Health Committee (2018)).
11
response of firms can undermine the Pigovian policy. For instance, suppose there
is just one product in the market and that equilibrium passthrough of a Pigovian
tax is 150%; the tax leads to a price increase in excess of the marginal externality
and an exacerbation of market power concerns, as the equilibrium pricecost margin
for the taxed good increases. The policymaker can mitigate this issue by adjusting
the Pigovian tax rate by the inverse of the equilibrium passthrough rate – setting
τ so that τ = φρ , where ρ is the passthrough rate defined as the change in the
equilibrium consumer price divided by the tax). In Appendix A we formalize the
problem a planner solves when aiming for full externality internalization, relative
to the zero tax equilibrium quantities, and show that tax policy will depend on
the weighted average passthrough rate across all taxed products, as well as the
equilibrium margin adjustment on nontaxed alternatives.
Internalities. Corrective taxes are sometime justified on the basis of the presence
of internalities – costs consumers impose on themselves by making choices that
fail to maximize their underlying utility. Internalities may arise for many reasons
including consumer selfcontrol problems, incorrect beliefs and inattention. Our
framework accommodates internalities that lead to consumer welfare taking the
P
form vi (p) − ϕi j zj qij , where ϕi can be interpreted as the marginal internality.
We show in Appendix A that if demand is generated from a discrete choice random
utility model and internalities arise from consumers overestimating their underlying
preference for a particular attribute (z) when making consumption decisions, the
expression for consumer welfare will take this form.
2.4
Empirical implementation
We apply our framework to the topical issue of the taxation of sugar sweetened
beverages. We estimate consumer demand and firm competition in the UK market
for nonalcoholic drinks; the model allows us to simulate equilibrium quantities
(allowing for the endogenous response of prices) and pricecost margins for any
given tax policy. We calibrate two key parameters over which there is considerable
uncertainty: the magnitude of externalities from sugar sweetened beverages, and
the degree of market power outside the drinks market.
Our analysis assumes that firms compete in their price setting, but hold fixed
the portfolio of products they offer and nonprice features of these products. A
tax that is levied directly on the sugar content of products potentially incentivises
firms to reduce the sugar content of some of their products to reduce tax liability
(though this will depend on how this changes production costs and the strength of
12
consumer preference for sugar). We return to this point when discussing our results
in Section 6.
3
The drinks market
We model behavior in the UK market for drinks. Our market definition includes all
chilled or ambient nonalcoholic beverages with the exception of water and unsweetened milk. Figure 3.1 shows a classification of drinks that we use to refer to different
sets of products throughout the rest of the paper. We refer to one subset of the
drinks as soft drinks. These include carbonates, fruit concentrates and sports and
energy drinks. Soft drinks can be further divided into sugar sweetened beverages
and diet (or artificially sweetened) beverages. We refer those drinks that are not
soft drinks as sugary alternatives. These include fruit juice and flavored milk; they
are generally exempt from sugar sweetened beverage or soft drinks taxes.
Figure 3.1: Drinks classification
*drinks refers to all nonalcoholic drinks with the exception of water and unsweetened milk.
3.1
Externalities from sugar sweetened beverages
There is considerable evidence that consumption of sugar sweetened beverages increases the risk of developing a number of diseases.18 Sugar sweetened beverages
are high in sugar and the sugar is in liquid form; this means it is digested quickly,
which leads to spikes in insulin and a higher propensity to develop type II diabetes.
Calories consumed in liquid form are also less likely to sate appetites, which means
people are less likely to compensate for their intake with reduced calories from other
sources and thus consumption of these drinks leads to weight gain. Sugar sweetened
beverage intake is also associated with increased blood pressure and a higher risk
of cardiovascular disease, as well as causing tooth decay.
18
Allcott et al. (2019b) provide a useful summary of the evidence. The Scientific Advisory
Committee on Nutrition (2015) provide a thorough review of the medical literature.
13
The higher disease burden associated with sugar sweetened beverages leads to
costs borne by people other than the person consuming the products (i.e. externalities). A central source of externalities are raised public costs of funding heath
care systems. These can result from higher taxpayer costs of publicly funded systems and from increased premiums in insurance based systems. For instance, in the
UK it is estimated that the costs of treating obesity and related conditions added
£5.8 billion in 200607 to the costs of public health care provision (Scarborough
et al. (2011)). Wang et al. (2012) estimate that a 15% reduction in sugar sweetened beverage consumption in US would lead to a $17.1 billion saving in heath care
costs over 10 years; a portion of this saving would be realized by the consumer
themselves; however, this portion is likely to be small (for instance, Cawley and
Meyerhoefer (2012) estimate 88% of the US medical costs of treating obesity are
borne by third parties). These externalities have led many governments, including
the UK (Scientific Advisory Committee on Nutrition (2015)), to specifically target
reductions in the intake of sugar sweetened beverages.
There is also concern about high levels of added sugar (including from foods) in
diet more broadly. The World Health Organization recommends average intake of
added sugars should not exceed 10% of total dietary energy (World Health Organization (2015)), while the UK has adopted the more stringent target of 5%.19 In our
analysis of a sugar sweetened beverage tax, we allow for the possibility that the nature of externalities from sugar sweetened beverages interact with broader dietary
sugar, and we consider the implications for the optimal tax on these products if
there are externalities created by switching to other markets.
3.2
Purchase data
We use micro data on the grocery purchases of a sample of consumers living in Great
Britain (i.e. the UK excluding Northern Ireland). The data contain information on
household level purchases for home consumption (“athome”), as well as purchases
made by individuals for consumption outside of the home (i.e. “onthego”). Onthego consumption is an important part of soft drink intake – accounting for 30% of
total soft drink consumption and 40% of total sugar consumption from soft drinks.20
Our data are collected by the market research firm Kantar and comprise two parts:
19
These targets are in fact stated in terms of “free sugars”, which are similar to added sugar
but also include naturally occurring sugars in fruit juices and honey.
20
Based on our calculations using the National Diet and Nutrition Survey, an individual level
dietary intake survey representative of the UK population.
14
the Kantar Worldpanel covers the athome segment of the market and the Kantar
OnTheGo Survey covers the onthego segment.
The Kantar Worldpanel contains details of all the grocery purchases (including
food, drink, alcohol, toiletries, cleaning produce and pet foods) that are made
and brought into the home by a representative sample of just over 30,000 British
households from January 2008 to December 2012. Participating households use
a hand held scanner to record all grocery purchases at the UPC level (i.e at the
disaggregate level at which items are barcoded). Households participate in the
survey for several months, and the data contain detailed information on the UPCs
they buy (including brand, flavor, size and nutrient composition), the store where
the transaction took place, and transaction level prices.
The Kantar OnTheGo Survey is based on a random sample of just under
3000 individuals drawn from the Worldpanel households. Using a cell phone app,
individuals record purchases of food and drinks at the UPC level made onthego
from shops and vending machines (the data do not cover bars and restaurants).
The data contain details of the item they purchased, as well as transaction store
and price, from June 2009 to December 2012. Individuals aged 13 and upwards are
included in the sample.
3.3
Consumers
We use the term consumer to refer to households in the athome segment, and individuals in the onthego segment. In our empirical demand model we incorporate
observed and unobserved heterogeneity in consumer preferences. We allow observed
heterogeneity across the athome or onthego segments, as well as allowing preferences to vary depending on consumer age and with a measure of the total sugar in
the consumer’s diet in the preceding year. This allows us to capture any differences
in demand behavior along dimensions over which marginal externalities from sugar
sweetened beverage intake might vary.
Table 3.1 shows the groups into which we place consumers. In the athome
segment we split households based on whether there are any children (people aged
under 18) in the household or not. In the onthego segment we separate individuals
aged 30 and under from those aged above 30. We also differentiate between those
with low, high or very high total dietary sugar. This measure is based on the
household’s (or, for individuals in the onthego sample, the household to which
they belong) share of total calories purchased in the form of added sugar across
all grocery shops in the preceding year. We classify those that purchase less than
10% of their calories from added sugar (corresponding to meeting the World Health
15
Organization’s guideline) as “low dietary sugar”, those that purchase between 10%
and 15% as “high dietary sugar”, and those that purchase more than 15% of their
calories from added sugar as “very high dietary sugar”.
Table 3.1: Consumer groups
No. of
consumers
% of
sample
7499
11930
7291
3561
8382
5185
17
27
17
8
19
12
240
576
381
601
1319
757
6
15
10
16
34
20
Athome segment (households)
No children, low dietary sugar
No children, high dietary sugar
No children, very high dietary sugar
With children, low dietary sugar
With children, high dietary sugar
With children, very high dietary sugar
Onthego segment (individuals)
Under 30, low dietary sugar
Under 30, high dietary sugar
Under 30, very high dietary sugar
Over 30, low dietary sugar
Over 30, high dietary sugar
Over 30, very high dietary sugar
Notes: Columns 2 and 3 show the number and share of consumers (households in the athome
segment, individuals in the onthego segment) in each group, respectively. If consumers move
group over the sample period (200812) they are counted twice, hence the sum of the numbers of
consumers in each group is greater than the total number of consumers. Dietary sugar is calculated
based on the share of total calories from added sugar purchased in the preceding year; “low” is less
than 10%, “high” is 1015% and “very high” is more than 15%. Households with children are
those with at least one household member aged under 18.
3.4
Firms, brands and products
In Table 3.2 we list the main firms that operate in the drinks market and the brands
that they own. We focus on the principal brands in the market; these comprise over
75% of total spending on nonalcoholic drinks in both the athome and the onthego segments.21 The firms Coca Cola Enterprises and Pepsico/Britvic dominate the
market, having a combined market share exceeding 65% in the athome segment
and close to 80% in the onthego segment. Each of these firms owns several well
recognized and long established brands, including some soft drinks and fruit juice
brands. The most popular single brand is Coke (also known as Coca Cola), which
accounts for over 20% of the athome and 36% of the onthego market segment.
21
The brands include all soft drinks brands with more than 1% market share in either segment,
as well as the main fruit juice and flavored milk brands. For some brands, there are only a very
small number of transactions in one of the two segments of the market; we therefore omit these
brands from the choice sets in that segment.
16
In addition to the main branded products, we include store brands in our analysis;
these are popular in the athome segment.
The majority of soft drinks brands are available in sugar sweetened (“regular”)
and artificially sweetened (“diet” and/or “zero”) variants. In Table 3.3 we list the
variants available for each brand. Among the regular variants there is variation in
sugar content across brands – many of the carbonates have around 10g of sugar per
100ml, with some of the fruit flavored soft drinks (such as Oasis and Vimto) having
less sugar per 100ml. This variation in sugar content means a tax levied directly
on sugar will have different implications to one levied volumetrically (i.e. per liter
of product sold).
Brandvariants can be purchased in different sizes for two reasons: (i) the availability of different pack sizes (or UPCs), and (ii) the purchase of multiple units.
For instance, a consumer may choose to purchase one 2l bottle of Diet Coke, or a
pack of 6×330ml cans, or two 2l bottles, and so on. Purchases of multiple units
of the same brandvariant most commonly involve 2, or sometimes 3, units of the
same pack (or UPC) and are typically a consequence of multibuy offers. Multibuy
offers in the UK market are long running, so the set of UPCs for which multiple
units are popular is broadly stable over time.
We incorporate the choice consumers make over size into our model of demand.
Specifically, we define products as brandvariantsize combinations, and we model
the consumer’s choice of product from a discrete set of alternatives. For each brandvariant, the set of possible sizes includes both the available pack sizes (i.e. UPCs)
and the most common multiple unit purchases of UPCs.22 Table 3.3 shows, for
each brandvariant, the number of sizes available to consumers in the athome and
onthego segments. For instance, Diet Coke is available in 10 sizes in the athome
segment, and two sizes in the onthego segment.23 Onthego sizes are always
designed as a single serving, while athome sizes are typically multiportion.
22
Specifically, we include a size option corresponding to multiple units of a single UPC if that
UPCmultiple unit combination accounts for at least 10,000 (around 0.2%) of transactions. This
means that for over 75% of transactions of branded products, we accurately model the choice over
number of units to purchase.
23
These are, in the athome segment, 1.25l and 2l bottles, multipacks of 330ml cans containing
6, 8, 10 and 12 cans, two and three unit purchases of 2l bottles, and twounit purchases of 6pack
and 8packs of cans; and, in the onthego segment, a 500ml bottle and 330ml can.
17
Table 3.2: Firms and brands
Market share (%)
Firm
Brand
Type
Coke
Capri Sun
Innocent fruit juice
Schweppes Lemonade
Fanta
Dr Pepper
Schweppes Tonic
Sprite
Cherry Coke
Oasis
Soft
Soft
Fruit
Soft
Soft
Soft
Soft
Soft
Soft
Soft
Robinsons
Pepsi
Tropicana fruit juice
Robinsons Fruit Shoot
Britvic fruit juice
7 Up
Copella fruit juice
Tango
Soft
Soft
Fruit
Soft
Fruit
Soft
Fruit
Soft
JN Nichols
Ribena
Lucozade
Lucozade Sport
Vimto
Barrs
Price (£/l)
Athome
Onthego
Athome
Onthego
Soft
Soft
Soft
Soft
33.0
20.4
3.1
2.1
1.7
1.7
1.2
1.1
1.0
0.8
–
33.6
10.7
10.1
6.1
2.6
1.6
0.9
0.8
0.8
7.6
3.3
3.1
1.1
1.6
59.1
36.4
–
1.6
–
5.3
3.4
–
2.8
4.0
5.6
20.0
–
11.6
3.8
0.8
–
1.7
–
2.2
12.7
3.4
6.4
2.9
–
0.86
1.08
2.03
0.44
0.79
0.75
1.22
0.77
0.96
–
2.09
–
7.09
–
2.10
2.08
–
2.08
2.17
2.15
1.09
0.64
1.62
1.49
2.17
0.70
1.74
0.66
–
1.93
3.63
2.83
–
1.88
–
1.73
1.69
1.11
1.15
1.06
2.20
2.37
2.22
–
Irn Bru
Soft
0.6
2.6
0.61
1.93
Merrydown
Shloer
Soft
2.0
–
1.79
–
Red Bull
Red Bull
Soft
0.2
3.5
3.67
5.27
Muller
Frijj flavoured milk
Milk
–
1.4
–
1.90
Friesland Campina
Yazoo flavoured milk
Milk
–
0.8
–
1.95
Store brand soft drinks
Store brand fruit juice
Soft
Fruit
21.2
13.1
8.1
0.0
–
–
0.62
1.05
–
–
Coca Cola Enterprises
Pepsico/Britvic
GSK
Store brand
Notes: Type refers to the type of drinks product: “soft” denotes soft drinks, “fruit” denotes fruit
juice, and “milk” denotes flavored milk. The fourth and fifth columns display each firm and brand’s
share of total spending on all listed drinks brands in the athome and onthego segments of the
market; a dash (“–”) denotes that the brand is not available in that segment. The final two columns
display the mean price (£) per liter for each brand.
18
Table 3.3: Brands, sugar contents and sizes
Sugar
Number of sizes
Firm
Brand
Variant
(g/100ml)
Athome
Onthego
Coca Cola Enterprises
Coke
Diet
Regular
Zero
Regular
Regular
Diet
Regular
Diet
Regular
Diet
Regular
Diet
Regular
Diet
Regular
Diet
Regular
Diet
Regular
Diet
Regular
Diet
Max
Regular
Regular
Diet
Regular
Regular
Diet
Regular
Diet
Regular
Regular
Diet
Regular
Regular
Diet
Regular
Diet
Regular
Diet
Regular
Regular
Diet
Regular
Regular
Regular
Diet
Regular
Regular
0.0
10.6
0.0
10.9
10.7
0.0
4.2
0.0
7.9
0.0
10.3
0.0
5.1
0.0
10.6
0.0
11.2
0.0
4.2
0.0
3.2
0.0
0.0
11.0
9.6
0.0
10.3
9.9
0.0
10.8
0.0
10.1
3.5
0.0
10.8
11.3
0.0
3.6
0.0
5.9
0.0
8.7
9.1
0.0
10.8
10.8
9.5
0.0
10.3
10.4
10
9
7
3
4
2
2
2
2
2
2
2
2
2
2
2
2
–
–
6
6
5
6
5
4
2
2
2
2
2
1
2
3
2
4
3
1
1
3
4
1
1
3
–
1
–
–
4
2
2
2
2
2
–
1
–
–
1
2
1
2
–
–
–
2
1
2
1
1
–
–
2
2
2
1
1
–
–
1
2
–
–
2
1
2
2
1
1
–
–
2
2
–
1
1
1
1
–
–
–
Capri Sun
Innocent fruit juice
Schweppes Lemonade
Fanta
Dr Pepper
Schweppes Tonic
Sprite
Cherry Coke
Oasis
Pepsico/Britvic
Robinsons
Pepsi
Tropicana fruit juice
Robinsons Fruit Shoot
Britvic fruit juice
7 Up
Copella fruit juice
GSK
Tango
Ribena
Lucozade
Lucozade Sport
JN Nichols
Vimto
Barrs
Irn Bru
Merrydown
Red Bull
Shloer
Red Bull
Muller
Friesland Campina
Store brand
Frijj flavoured milk
Yazoo flavoured milk
Store brand soft drinks
Store brand fruit juice
Notes: The final two columns displays the number of sizes of each brandvariant in the athome
and onthego segments of the market; a dash (“–”) denotes that the brandvariant is not available
in that segment.
19
3.5
Choice sets and price measurement
Table 3.3 summarizes the full set of products available to consumers in each market
segment. However, the set of products available to a consumer on a particular day,
as well as the price vector they face, will depend on the retailer that they visit.
Athome segment
The median household undertakes a grocery shop once a week. We define a “choice
occasion” as any week in which a household purchases groceries, and model what,
if any, drink a household purchases on a choice occasion.24 We observe households
for an average of 36 choice occasions each year, and in total, we have data on 3.3
million athome choice occasions. On around 42% of choice occasions, a household
purchases a drink, with the average time between drink purchases being 12 days.
Households select one brandvariant (as defined by columns 2 and 3 of Table 3.3)
on 60% of choice occasions on which drinks are purchased. On choice occasions in
which a household chooses multiple (typically 2 or 3), we assume that (conditional
on household specific preferences) these purchases are independent (for instance,
because they are bought for different household members).
For each choice occasion we observe the retailer in which the purchase was
made and the exact price paid. Table 3.4 lists retailers and the share of drinks
spending that they account for in each segment. In the athome segment, four
large national supermarket chains account for almost 90% of spending, with the
remaining expenditure mostly being made in smaller national retailers. Each of
these retailers offers all brands, with some variation in the specific sizes available in
each retailer.
We model the decision consumers take over what to purchase from the available
set of products in the retailer they visit, taking their choice over which retailer
to shop with as given. This assumption is common in models of consumer good
choice.25 In our context this assumption is reasonable. On the median choice
occasion a consumer visits one retailer, and expenditure on nonalcoholic drinks
comprises a small share (4%) of total grocery expenditure. Retailer choice is likely
to be driven by proximity of nearby stores and overall preferences for grocery outlet
24
We focus on households that record making regular purchases; this excludes transactions
(accounting for less than 2% of the total number) made by households who record making fewer
than 10 shopping trips a year. We also focus on households who record making at least one
nonalcoholic drink purchase.
25
An exception is Thomassen et al. (2017), who show that switching across supermarkets can
influence pricing incentives for aggregated grocery goods (e.g. meat, dairy etc.).
20
(which we control for in demand). In practice, the majority of consumers’ drinks
expenditure (over 70%) is made in the retailer they more frequently visit.
The four main retailers in the UK implement national pricing policies.26,27 This
means that if we observe a transaction price for a particular UPC in a store belonging to one of the retailers, Tesco say, we know the price that consumers shopping in
other Tesco stores at the same time faced for that UPC. Using the large number of
transactions in our data we can construct the price vector households faced in each
retailer in each week. For the smaller retailers we construct a mean transaction
price for a product as a measure of the price faced by consumers.
Table 3.4: Retailers
Expenditure share (%)
athome
onthego
Large national chains
of which:
Tesco
Sainsbury’s
Asda
Morrisons
87.0
19.9
34.7
16.8
19.8
15.7
–
–
–
–
Small national chains
10.7
16.4
Vending machines
0.0
9.2
Convenience stores
in region:
South
Central
North
2.3
54.6
–
–
–
13.6
15.5
25.5
Notes: Numbers show the share of total nonalcoholic drink expenditure, in the athome and onthego segment, made in each retailer.
Onthego segment
The natural periodicity for onthego purchases is at the daily level.28 In this
segment we define a choice occasion as any day on which the individual buys a
cold beverages (including bottled water). We observe individuals for an average
26
The supermarkets agreed to implement national pricing policies following a Competition
Commission investigation into supermarket behavior (Competition Commission (2000)).
27
Close to uniform pricing within retail chains has been documented in the US, see, for instance,
DellaVigna and Gentzkow (2019) and Hitsch et al. (2017).
28
As in the athome segment, we focus on individuals who record regularly, dropping less than
3% of total transactions that are made by those who record fewer than 5 purchases each year.
21
of 44 choice occasions each year, and in total, we have data on 286,576 onthego
choice occasions. On 60% of choice occasions individuals choose to buy one of the
products listed in Table 3.3, and on 90% of these choice occasions they buy only
one product.29
The large four supermarkets are less prominent in the onthego segment, collectively accounting for less than 20% of onthego spending on drinks (see Table
3.4). This, coupled with the fact that the single portion cans and bottles are similarly priced across the large four supermarkets, motivates their aggregation into
one composite retailer. The majority of transactions in the onthego segment are
in local convenience stores. This means that for these choice occasions, unlike in
the athome segment, we do not observe the price of nonselected products in consumers’ choice sets. Therefore, in the case of convenience stores, for all options in
consumer choice sets we use a mean monthly price, where the price is constructed
using all convenience store transactions in each of three regions (the south, central,
and north regions of the UK).
Dependence across the athome and onthego segments
We model consumer choice for athome consumption and for onthego consumption separately.30 A concern with this is that recent athome household purchases
influence decisions that individuals make onthego (for instance, a recent athome
purchase may make an individual less likely to buy while onthego). We check
for evidence of such nonseparabilities across the athome and onthego segments.
Specifically, for individuals in the onthego sample we test whether recent purchases of drinks by their household in the athome segment influences either their
propensity to purchase drinks or the quantity they buy, finding no evidence of such
dependence. Full details are provided in Appendix B.
3.6
Price variation
The vector of prices that a consumer faces when making a purchase varies across
time and retailers. Here we describe this variation and in Section 4.2 we discuss
how it allows us to identify the key parameters driving consumer demand behavior.
29
On the rare case when they buy multiple products (usually 2 or 3) we treat these as independent purchases.
30
When constructing market level demand we weight each segment such that their share of
total sugar from sugar sweetened beverage matches that in the National Diet and Nutrient Survey
(an individual level dietary intake survey, representative of the UK population).
22
The athome segment is characterized by products that are sold in multiportion
sizes, and it is dominated by retailers that have national pricing policies. An important source of price variation is promotions (i.e. price reductions), which differ
in their timing, duration and depth, both across UPCs and retailers. In the drinks
market promotions are either multibuy offers (for instance, a discount for purchasing 2 of the same UPC), or ticket price reductions (when a UPC has a temporarily
low price). 30% of the transaction in our data are a multibuy offer, 20% a ticket
price reduction.
We provide a graphical example of each promotion type in Figure 3.2, which
shows the price for two specific UPCs over the most recent year of our data for
two different retailers (Tesco and Sainsbury’s). Panel (a) shows price series for a
2l bottle of Coke. In both retailers, (with the exception of one week in Tesco) 1
unit of a 2l bottle is priced at £2. However, over most of the year each retailer
runs a multibuy offer, where 2 bottles can be purchased at a discounted per bottle
price, though the depth of discount varies both over time and between retailers.31
Panel (b) shows price series for a pack of 12×330ml cans of Coke. This UPC does
not have a multibuy offer, but is reasonably frequently subject to a ticket price
reduction.
Figure 3.2: Examples of price variation for Coke options
(b) 12x330ml cans
5
Price per unit (£)
4
4.5
1
3.5
1.2
Price per unit (£)
1.4
1.6
1.8
2
(a) 2l bottle
0
10
20
Tesco: 1 unit
Tesco: 2 units
Week
30
40
50
0
Sainsbury's: 1 unit
Sainsbury's: 2 units
10
20
Week
30
40
50
Tesco: 1 unit
Sainsbury's: 1 unit
Notes: Panel (a) shows the weekly price series for a 2l bottles of Coke in Tesco and Sainsbury’s
when either one unit or two units are purchased. Prices are expressed per unit. Panel (b) shows
the weekly price series for a pack of 12x330ml cans of Coke in Tesco and Sainsbury’s when one
unit is purchased.
In the examples in Figure 3.2 average prices are similar across the two retailers,
but the time path of price changes is different. This is true more generally. To
illustrate this we compute measures of price stability suggested by DellaVigna and
31
In our demand model we treat one 2l bottle and two 2l bottles of Coke as different options.
23
Gentzkow (2019). First, we calculate the yearly absolute log price difference.32 This
entails, for each product, retailer and year, computing average log price (where the
average is taken across weeks), and then computing the deviation in this for each
retailer pair. The median of these deviations is 8 log points, indicating a relatively
low level of crosssectional differences in average prices across retailers. Second, we
calculate the weekly correlation of log prices. To do this we obtain the residuals from
regressing log prices on productyear fixed effects for each retailer. For each product
we compute the correlation in residuals between each retailer pair. The median of
these correlations is 0.13, indicating that the degree of comovement in prices over
time across retailers is low. In addition, no retailer sets systematically low or high
prices – among the big four retailers, across productweeks (for products that are
branded and available in multiple retailers), Asda is the cheapest retailer most (for
27% of productweeks) and the most expensive the least (for 17%) amount of time,
and Sainsbury’s is cheapest the least (for 22%) and most expensive the most (for
31%) amount of time.
A concern with relying on price variation from promotions to estimate demand
is that households respond to them by intertemporally switching their purchases
(i.e stocking up during sales) and hence failing to model this behavior will result in
an overestimate of ownprice elasticities (Hendel and Nevo (2006a)). A number of
papers have documented evidence of stockpiling in the US market for soft drinks
(see Hendel and Nevo (2006b), Hendel and Nevo (2013), Wang (2015)).
Although we cannot rule out that there may be some stockpiling underlying
transactions in our data, the evidence for it is much less clear than in the US. Specifically, UK households purchase drinks, on average, more than twice as frequently
(every 12 days on average) as those in the US (see Hendel and Nevo (2006b)), and
when a household does purchase on sale there is no meaningful change in the timing of purchases.33 Instead, we find that sales are associated with switching across
pack types (e.g. cans to bottles), brands and sizes. One reason why stockpiling is
less prevalent in the UK, compared with the US, is that the relatively long running
nature of UK price promotions create less incentives to stockpile. For instance, for
each of the soft drinks products summarized in Table 3.3, the average time between
a price change of 25% or more is 10 weeks, whereas in the US prices can fluctuate
by large amounts from week to week (see an archetypical example in Figure 1 of
32
DellaVigna and Gentzkow (2019) instead compute the quarterly absolute log price difference.
Given the relatively long running nature of promotions in the UK we choose instead to do this at
the yearly level.
33
Hendel and Nevo (2006b) find, in the US, buying soft drinks on sale is associated with an
average reduction in the time from previous purchase of 3 days, and an increase to the next
purchase of 2.5 days. We find changes of 0.23 and 0.14 respectively. See Appendix B.
24
Hendel and Nevo (2013)). A second reason is that transport and storage costs in
the UK are likely to be much higher, with the average size of UK homes around
half of those in US, and vehicle ownership rates 25% lower.34
In the onthego segment only 20% of spending is done in the big four supermarkets, with around 55% of expenditure occurring in conveniences stores. Price
promotions are less common in this segment, with price variation driven by regional
differences in price in convenience stores, and differences in convenience store prices
with national retailers and vending machines.
4
Estimating demand and supply
To implement our optimal corrective tax framework, we need to know how consumers switch across disaggregate products in response to price changes and the
level of and how firms, in response to tax, adjust the pricecost margins on these
products. We estimate a model of consumer demand in the drinks market using a
discrete choice framework in which consumer preferences are defined over product
characteristics (Gorman (1980), Lancaster (1971), Berry et al. (1995)). This approach enables us to model demand and substitution patterns over the many differentiated products in the market, while incorporating rich preference heterogeneity
crucial to capturing realistic substitution patterns. We identify firms’ unobserved
marginal costs by coupling our demand estimates with the equilibrium conditions
from an oligopoly pricing game (Berry (1994), Nevo (2001)).
4.1
Consumer demand
We model which, if any, drink product a consumer (indexed i) chooses on a choice
occasion. We treat the decisions that households make in the athome segment and
individuals make in the onthego segment separately, allowing for the possibility
that preferences vary on each type of choice situation, but for notational parsimony
we suppress a market segment index.
We index the drink products by j = {1, . . . , J}. The products vary by brand,
which we index by b = {1, . . . , B}, size, indexed by s = {1, . . . , S}, and whether
or not they contain sugar (for instance, the brand Coke comes in Regular, Diet
and Zero variants). The consumer chooses between the available drinks products,
and choosing not to buy a drink, which we denote by j = 0. The set of products
34
The mean floor space of UK homes in 2008 was 85m2 , while in 2009 in the US it was 152m2
(UK Government (2018)). In 2014 the US had 816 vehicles per capita (U.S. Department of Energy
(2019)), in 2017 the UK had 616 (ACEA (2019)).
25
available to the consumer, as well as the prices they face, depends on which retailer
they visit – we index retailers by r and denote the set of available drink options in
retailer r by Ωr .
Consumer i in period t, with total period income or budget yit , solves the utility
maximization problem:
V (yit , prt , xt , it ; θi ) = max ν(yit − pjrt , xjt ; θi ) + ijt .
j∈{Ωr ∪0}
(4.1)
where prt = (p1rt , . . . , pJrt ) is the price vector faced by the consumer, xjt are (nonprice) characteristics of product j and xt = (x1t , . . . , xJt ) (note p0 = 0 and x0 = 0);
θi is a vector of consumer level preference parameters; and it = ( i0t , i1t , . . . , iJt )
is a vector of idiosyncratic shocks.
The function ν(.) captures the payoff the consumer gets from selecting option
j. Its first argument, yit − pjrt , is spending on the numeraire good – i.e. spending
outside the drinks market. We assume that preferences are quasilinear, so yit − pjrt
enters ν(.) linearly. This means that yit differences out when the consumer compares
different options; we therefore suppress the dependency of ν(.) on yit .
We assume that ijt is distributed i.i.d. type I extreme value. Under this assumption the probability that consumer i selects product j in period t, conditional
on prices, product characteristics and preferences, is given by:
σj (prt , xt ; θi ) =
exp(ν(pjrt , xjt ; θi ))
P
,
1 + j 0 ∈Ωr exp(ν(pj 0 rt , xj 0 t ; θi ))
(4.2)
and the consumer’s expected utility is given by:
v(prt , xt ; θi ) = ln
X
exp{ν(pjrt , xjt ; θi )} + C,
(4.3)
j∈Ωr
where C is a constant of integration.
Specification details
Let d = (1, . . . , D) index the consumer groups shown in Table 3.1. We assume that
the payoff function ν(.) for consumer i belonging to consumer group d(i) and for
product j belonging to brand b(j) and of size s(j) takes the form:
(1)
(2)
ej + γd(i) x
ν(.) = −αi pjrt + βi x
ejt + ζd(i)b(j)s(j)rt ,
where
(1)
(2)
(3)
(4)
(5)
ζd(i)b(j)s(j)rt = ξd(i)b(j)s(j) + ξd(i)b(j)r + ξd(i)b(j)t + ξd(i)s(j)r + ξd(i)s(j)t .
26
We allow for consumer specific preferences for price (i.e. the marginal utility of
e(1)
e(1)
income) and a subset of product characteristics denoted by x
includes a
j ; x
j
constant, which captures a preference for drinks versus not buying them, dummy
variables indicating whether the product has positive sugar content that is less
than 10g or equal to or more than 10g per 100ml, dummy variables indicating if the
product is a cola, lemonade, store brand soft drink or fruit juice, and an indicator
for whether the size is large.35 These individual level preferences play a key role in
(2)
allowing the model to capture realistic substitution patters across products. x
ejt is
a measure of the stock of advertising for the product in the current period;36 we
allow the effect of advertising to vary across consumer groups.
ζd(i)b(j)s(j)rt denotes a set of consumer group specific shocks to utility. These
include: brandsize effects, which control for unobserved consumer preferences that
are timeinvariant; brand and sizeretailer effects, which capture the possibility
that, on average, consumer preferences over brand and size differ across retailers;
and brand and sizetime effects, that control for shocks to demands through time.
We model the consumer specific preferences, (αi , βi ) as random coefficients. We
specify the distribution for αi as lognormal and βi as normal, both conditional
on consumer group d. The overall random coefficient distribution is a mixture
of normal distributions.37 As well as enabling us to capture realistic patterns of
substitution across products, inclusion of rich unobserved heterogeneity also adds
flexibility to the curvature of market demand (see Griffith et al. (2018)), which
is important for recovering realistic patterns of passthrough (Weyl and Fabinger
(2013)).
4.2
Identification
Our key identification assumption is that, conditional on our demand controls (including those for unobserved product attributes), the residual price variation is
exogenous (and, in particular, the shocks to consumer’s payoff functions, ijt , are
i.i.d.). The main form of price variation we exploit is differential time series variation across retailers.
35
Defined as larger than 2l in the athome segment or 500ml in the onthego segment.
We measure monthly TV advertising expenditure in the AC Nielsen Advertising Digest. We
compute product specific stocks based on a monthly depreciation rate of 0.8. This is similar to
the rate used in Dubois et al. (2018) on similar data in the potato chips market.
37
The means (conditional on d) of the constant, cola, lemonade, store brand, fruit juice and
(1)
large random coefficients are collinear with ξd(i)b(j)s(j) . We normalize them to zero. We allow for
correlation (conditional on d) between the preferences for nonalcoholic drinks and sugar.
36
27
(1)
Our demand controls include brandsize effects, ξd(i)b(j)s(j) ; these control for timeinvariant unobserved characteristics that vary across brands and sizes. For instance,
consumers may value one brand over a second for reasons not fully controlled for
by observed product characteristics; failure to control for this would likely result in
correlation between ijt and prices. By interacting brand with size effects we allow
for the possibility that strength of unobserved brand effects vary across product
sizes (and pack types). Numerous brandsizes are available in both sugar sweetened
and diet variants. We control for the amount of sugar per 100ml in a product in
e(1)
the option characteristic vector, x
j . We are therefore able to identify the mean
(as well as standard deviation) of the consumer group specific preferences for sugar
(based on the restriction that the impact of sugar on utility does not vary across
brands).
(3)
The time (quarterly) varying brand effects, ξd(i)b(j)t , control for shocks to national
level demands for each brand. We additionally control for time varying size effects
(5)
ξd(i)s(j)t , which capture any tendency through time for demands for larger versus
small sizes to fluctuate. As discussed in Section 3.2, the large four retailers that
dominate the market have national pricing policies; the time varying effects help
control for national level shocks to demand that could be correlated with these
(2)
prices. In addition, we control (through x
ejt ) for product level advertising, which
will capture the effect on demand of the (overwhelmingly national) advertising in
the UK drinks market.38 For convenience stores we use mean regional prices. We
include regionquarter varying drinks effects in demand to control for the possibility
of regional shocks to demand for drinks.
(2)
(2)
We also control for brandretailer effects, ξd(i)b(j)r , and sizeretailer effects, ξd(i)s(j)r .
These capture the possibility that either the prominence of products belonging to
different brands, or of large versus small sizes, may vary across retailers. They also
capture average differences in consumer brand and size preferences across retailers.
An important restriction we make is the absence of retailertime shocks to product demands that correlate with price setting.39 As outlined in Section 3.6 average
prices across retailers are similar, but comovement in prices is low, with, for instance, the use of price promotions not synced across retailers. We assume that
this create randomness in the prices faced by consumers that is not a consequence
of retailers anticipating time varying demand shocks that differ for their consumers
compared to those in other retailers. Given the national nature of much retailing,
38
Note targeted price discounts through use of coupons – common in the US (see Nevo and
Wolfram (2002)) – is not a feature of the UK market.
(2)
(3)
(4)
(5)
39
The (ξd(i)b(j)r , ξd(i)b(j)t , ξd(i)s(j)r , ξd(i)s(j)t ) effects control for all pairwise interactions between
(b, s, r, t) but not higher order interactions.
28
pricing and advertising in the UK drinks market, and the absence of targeted price
offers and coupons, we believe that this assumption is reasonable.
4.3
Supply model
We model price competition among the firms operating in the UK drinks market.
We assume that they simultaneously set prices to maximize profits in a NashBertrand game, abstracting from modeling retailermanufacturer interactions. This
outcome can be achieved by use of nonlinear vertical contracts (see VillasBoas
(2007), Bonnet and Dubois (2010)).40 In Section 5.4 we show how our optimal tax
results are influenced by different supplyside models.
Let pm = (p1m , . . . , pJm ) denote the prices that drinks firms set in market m,
where markets are temporal (and defined as quarters).41 Market demand for product j is given by:
Z
qjm (pm ) =
σj (pm , xm ; θi )dF (θ)Mm ,
where Mm denotes the potential size of the market.42 We denote the marginal cost
of product j in market m as cjm .43
We index the drinks firms by f = (1, . . . , F ) and denote the set of products
owned by firm f by Jf . Firm f ’s total variable profits in market m are
Πf m (pm ) =
X
(pjm − cjm )qjm (pm ).
(4.4)
j∈Jf
We assume firms engage in Bertrand competition and that the prices we observe in
the data are the Nash equilibrium outcome of this game, and thus they satisfy the
40
Nonlinear contracts with side transfers between manufacturers and retailers allow them to
reallocate profits and avoid the double marginalization problem. Bonnet and Dubois (2010) show
evidence of price equilibria in the French bottled water market consistent with use of nonlinear
contracts.
41
In the supply model we average over price variation within a quarter, as this is likely to reflect
random price promotions strategies rather than fundamentals of demand or supply. Specifically,
let M denote the set
P of (r, t) pairs observed in market m, the market price for product j is defined
as pjm = (M)−1 (r,t)∈M pjrt .
42
Mm is the potential number of nonalcoholic drinks transactions in market m, it differs from
the true market size due to inclusion in the demand model of the option to purchase no drinks.
43
Note, in Section 2 we express quantity in terms of units (i.e. liters) and prices and marginal
costs per liter. Here we express quantity as number of transactions and price and marginal cost per
transaction. The difference is one of convenience rather than substance, multiplying qjm by the
size of the product and dividing pjm and cjm by the size of the product transforms the variables
into their analogues in Section 2 without changing the nature of the firms’ problem.
29
set of first order conditions: ∀f and ∀j ∈ Jf
qjm (pm ) +
X
j 0 ∈J
(pj 0 m − cj 0 m )
f
∂qj 0 m (pm )
= 0.
∂pjm
(4.5)
From this system of equations we can solve for the implied marginal cost, cjm , for
each product in each market.
Counterfactual market equilibrium. When solving for the optimal tax rate
we need to solve for the associated counterfactual market equilibrium. Denote the
set of sugar sweetened beverages by S and the total sugar content of option j ∈ S
by zj (noting that for j ∈
/ S zj = 0). If some tax rate τ , levied on the sugar in
sweetened beverages, is in place the set of first order conditions are: ∀f and ∀j ∈ Jf
qjm (p0m ) +
X
(p0j 0 m − τ zj 0 − cj 0 m )
j 0 ∈Jf
∂qj 0 m (p0m )
= 0.
∂pjm
For any τ , we can solve the system of equations to obtain the vector of counterfactual
equilibrium prices, p0m = (p01m , . . . , p0Jm ).44
Solving for the optimal tax rate also requires us to compute the derivative of
0
the equilibrium price vector with respect to the tax rate, dpdτm . To obtain this we
differentiate the first order conditions with respect to the tax rate and solve the
resulting system of equations. For details see Appendix E.
4.4
Demand estimates
We estimate the demand model outlined in Section 4.1 using simulated maximum
likelihood.45 The estimated coefficients exhibit some intuitive patterns; those with
more added sugar in their diets (based on their purchases in the preceding year)
have stronger preferences for high sugar drinks products, and those with below
median income are more sensitive to price, have stronger preferences for soft drinks
and weaker preferences for fruit juice. The variance parameters of the random
coefficients are all significant both statistically and in size, indicating an important
44
Note that for the set of store brand products, we do not model price reoptimization – for
store brand sugar sweetened beverages we assume passthrough of any tax is 100%, and for store
brand diet beverages we assume consumer prices remain unchanged.
45
We allow all parameters to vary by consumer group and estimate the choice model separately
by groups. In the athome segment, for each group, we use a random sample of 1,500 households
and 10 choice occasions per household; in the onthego sample we use data on all individuals
in each group and randomly sample 50 choice occasions per individual, weighting the likelihood
function to account for differences in the frequency of choice occasion across consumers. We
conduct all post demand estimation analysis on the full sample.
30
role for unobserved preference heterogeneity. We report the coefficient estimates in
Appendix C.
The estimated preference parameters jointly determine our demand model predictions of how consumers switch across products as prices change. The model
generates a large matrix of market level own and crossprice demand elasticities;
in Table 4.1 we summarize the market level own and crossprice elasticities. The
mean ownprice elasticity is around 2.5, though with significant variation around
this: 25% of products have ownprice elasticities with magnitude greater than 2.8,
a further 25% of products have ownprice elasticities with magnitude less than 1.8.
The distribution of the crossprice elasticities exhibits a high degree of skewness,
with the mean being equal to the 75th percentile. This reflects consumers being
significantly more willing to switch between products close together in product
characteristic space.
Table 4.1: Summary of own and crossprice elasticities
No. elasticities
Ownprice
Crossprice
Percentile
per market
Mean
25th
50th
75th
175
18757
2.431
0.013
2.795
0.003
2.434
0.007
1.765
0.014
Notes: In each market there are 175 ownprice elasticities (one for each product) and 18757 crossprice elasticities (between product pairs available either in the athome or onthego segment).
Numbers summarize the distribution of market elasticities based on the most recent year covered
by our data (2012).
Table 4.2 illustrates consumers’ tendency to switch between similar products
by showing product level elasticities associated with a price change for the single
portion sizes of Coke Regular and Coke Diet. It shows the impact on demand
for each of the single portion sizes of Coke and Pepsi, and the mean elasticities for
other sugar sweetened and diet beverages, and for fruit juice and flavored milk. The
table illustrates a number of intuitive patterns: (i) consumers are more willing to
switch across cola products of the same variety (sugar vs. nonsugar) than they are
to alternative drinks; (ii) consumers are more willing to switch between products
of the same size than they are to different sizes; (iii) consumer substitution from
sugary varieties of Coke to sugary noncola drinks (both sugar sweetened beverages,
fruit juice and flavored milk) is stronger than it is from Diet Coke. Similar patterns
are present for multiportion products. In Appendix C we report product level
own and crossprice elasticities for popular products in the athome and onthego
segments.
31
Table 4.2: Select elasticities for Coke
Coke
Regular
330
500
Regular
330
500
Diet
330
500
1.66
0.46
0.14
2.24
0.10
0.08
0.02
0.16
Pepsi
Other drinks
Diet
330
500
Zero
330 500
Regular
330 500
Diet
330 500
Max
SSBs
330 500
Diet
Fruit Flav.
juice milk
0.12
0.10
0.04
0.25
0.14
0.10
0.04
0.25
0.44
0.39
0.13
0.86
0.11
0.11
0.04
0.25
0.13
0.11
0.04
0.26
0.07
0.19
0.01
0.06
0.05
0.13
0.07
0.20
1.60 0.10
0.28 2.63
0.37
0.24
0.10
0.56
0.09
0.07
0.02
0.15
0.33
0.30
0.10
0.53
0.31
0.26
0.10
0.53
0.02
0.05
0.05
0.18
0.02
0.04
0.01
0.04
Notes: Numbers show the mean price elasticities of market demand (for products listed in top
row) in the most recent year covered by our data (2012) with respect to price changes for the single
portion sizes of Coke Regular and Coke Diet (shown in first column). “Other drinks” exclude Coke
and Pepsi and are means over products belonging to each set.
In Table 4.3 we summarize the effects of increasing the price of all sugar sweetened beverages by 1%. The resulting reduction in demand (in liters) for sugar
sweetened beverages is 1.48% (i.e. our estimates correspond to an ownprice elasticity for sugar sweetened beverages of 1.48%). The diversion ratio (defined as the
percentage of the reduced sugar sweetened beverage demand that is diverted to
each group of substitute products) is 27.3% for diet drinks and 6.7% for alternative sugary drinks. The percent change in expenditure on nonalcoholic drinks is
0.05% – the price increase leads to a modest increase in drinks expenditure. 95%
confidence intervals are given in brackets.46
Table 4.3: Switching from sugar sweetened beverages
Ownprice elasticity of
Diversion ratio
Elasticity of
sugar sweetened beverages
Diet beverages
Sugary alternatives
drinks expenditure
1.48
27.3%
6.7%
0.05
[1.52, 1.43]
[26.8%, 28.1%]
[6.4%, 7.0%]
[0.04, 0.07]
Notes: We simulate the effect of a 1% price increase for all sugar sweetened beverage products.
Column 1 shows the % reduction in volume demanded of sugar sweetened beverages, columns 2 and
3 shows how much of the volume reduction is diverted to diet beverages and sugary alternatives
and column 4 shows the percent changes in total nonalcoholic drinks expenditure. Numbers are
for the more recent year covered by our data (2012). 95% confidence intervals are given in square
brackets.
The optimal tax formula, given by equation (2.3), partly depends on how much
any reduction in the equilibrium quantity of taxed drinks induced by a marginal
46
To calculate the confidence intervals, we obtain the variancecovariance matrix for the parameter vector estimates using standard asymptotic results. We then take 100 draws of the parameter
vector from the joint normal asymptotic distribution of the parameters and, for each draw, compute the statistic of interest, using the resulting distribution across draws to compute Monte Carlo
confidence intervals (which need not be symmetric).
32
tax increase is shifted to nontaxed substitutes. The diversion ratios suggest a
significant amount of demand for sugar sweetened beverages will be diverted to nontaxed drinks, while the elasticity of total nonalcoholic drinks expenditure indicates
only a modest degree of switching from the numeraire. However, these diversion
ratios and elasticities summarize the demand effects at observed prices. The optimal
tax formula depends on changes in equilibrium quantities (which depend on supply
responses) and are evaluated at the optimal tax rate. We fully incorporate this
when we solve for the optimal tax rate in Section 5.
4.5
Supply estimates
We use the first order conditions of the firms’ profit maximization problem (equation
(4.5)) to solve for the marginal cost of each product. This enables us to compute the
equilibrium pricecost margins (which we express per liter) and pricecost markups
(margin over price) at the observed market equilibrium (where no sugar sweetened
beverage tax is in place). In Table 4.4 we summarize the distribution of (observed)
prices, costs, margins and markups across products. The average markup is 0.55
(price is around double marginal cost), though there is considerable variation around
this.47 In Appendix C we show mean marginal costs, margins and markups by
brand.
Equilibrium pricecost margins play an important role in determining the optimal tax policy. All else equal, the higher (lower) are margins on externality (nonexternality) generating options, the lower (higher) will be the optimal tax rate on
the externality product attribute. At observed prices, the (unweighted) average
margin across sugar sweetened beverages is 0.78, while it is 0.76 across alternative
drinks. How these margins adjust in equilibrium with the tax, and how consumers
switch within the two sets of options and between them is important in determining
the optimal tax rate.
47
This broadly accords with evidence from accounting data, with gross margins in this market
being reported to be around 5070% (see Competition Commission (2013)).
33
Table 4.4: Summary of costs and margins
Percentile
Mean
25th
50th
75th
1.44
0.67
0.77
0.55
0.83
0.31
0.43
0.41
1.16
0.61
0.56
0.50
1.96
0.83
0.98
0.67
Price (£/l)
Marginal cost (£/l)
Pricecost margin (£/l)
Pricecost markup (Margin/Price)
Notes: We recover marginal costs for each product in each market. We report summary statistics
for the most recent year covered by our data (2012). Margins are defined as price minus cost and
expressed in £ per liter; markups are margins over price.
In Figure 4.1 we show how observed prices, marginal costs, and equilibrium
pricecost margins vary with product size. There is strong nonlinear pricing; in
per liter terms smaller products are, on average, more expensive. Average marginal
costs are broadly constant across the size distribution, with the exception of small
single portion sizes (i.e. with sizes no larger than 500ml), which, on average, have
higher costs. Pricecost margins are declining in size – the average margin (per liter)
is more than twice as large for the smallest options compared with the largest. This
turns out to be important in driving the optimal tax rate, as one way consumers
respond to the tax is by shifting their basket of taxed products towards small, high
margin sizes.
0.50
Price, cost, margin (£/l)
1.00
1.50
2.00
2.50
Figure 4.1: Pricecost margins, by product size
(0,0.5]
(0.5,1]
Price (£/l)
(1,2]
(2,3]
Products within size range (l)
Marginal cost (£/l)
(3,4]
(4,∞]
Margin (£/l)
Notes: We group products by size. The figure shows the mean price, cost, and margin (all expressed
in £/l) across products within each size range. Numbers are for the more recent year covered by
our data (2012).
34
4.6
Model validation
We use data on the price changes of nonalcoholic drinks following the introduction
of the UK’s Soft Drinks Industry Levy (SDIL) in 2018 to validate our empirical
model of the market. We use a weekly database of UPC level prices and sugar contents for drinks products, collected from the websites of 6 major UK supermarkets,
that cover the period 12 weeks before and 18 weeks after the introduction of the
tax.48
The UK’s tax is levied per liter of product, with there being a lower rate of
18p/liter for products with sugar contents of 58g/100ml and a higher rate of
24p/liter for products with sugar content > 8g/100ml. We use an event study
approach to estimate the price changes for the sets of products subject to each rate
and for the set of drinks products not subject to the tax – full details are provided
in Appendix D. We find evidence that the tax was slightly overshifted, with price
increases of 26p/liter for products subject to the higher rate and 19p/liter for products subject to the lower rate (implying average passthrough rates of 105108%),
with no change in the price of untaxed products. We simulate the effect of the tax
using our estimated model of supply and demand. Figure 4.2 shows the estimated
price changes in the data (grey markers) for the high and low tax groups (the figure
for untaxed products is shown in the Appendix D), and the predicted price changes
using our model. The predicted price changes from the model are very close to the
observed price changes.
48
The supermarkets are the big four – Tesco, Asda, Sainsbury’s and Morrisons – as well as
smaller national chains Iceland and Ocado. We are grateful to the University of Oxford for
providing us with access to these data, which were collected as part of the foodDB project.
35
Figure 4.2: Comparison of model predictions with event study
Change in price per litre
0
.2
.4
Change in price per litre
0
.2
.4
.6
(b) Lower rate treatment group
.6
(a) Higher rate treatment group
0
10
Tax
Week
Price change (model)
20
Mean effect (data): 0.19
Mean effect (model): 0.20
Tax: 0.18
.2
.2
Mean effect (data): 0.26
Mean effect (model): 0.26
Tax: 0.24
30
0
Price change (data)
10
Tax
Week
Price change (model)
20
30
Price change (data)
Notes: Grey markers show the estimated price changes (relative to the week preceding the introduction of the tax) for the set of products subject to the higher and lower rates. Full details are
given in Appendix D. 95% confidence intervals shown. The blue line shows the value of the tax,
and the red line shows the predicted price changes from our estimated model of the UK drinks
market.
These patterns are broadly consistent with the literature that uses ex post evaluation methods to estimate the effects of sugar sweetened beverage taxes on prices;
for example, the Philadelphian tax was found to be fully passed through to prices
(Seiler et al. (2019), Cawley et al. (2018)), and in Mexico the tax was fully to slightly
more than fully passed through to prices (Grogger (2017), Colchero et al. (2015)).
An exception is Berkeley, where passthrough of the tax is estimated to be statistically insignificant or low (e.g. Bollinger and Sexton (2018)). A likely reason for low
tax passthrough in Berkeley is, given the small geographical area in which the tax
is operation, consumers can readily avoid the tax through crossborder shopping.
5
Corrective tax results
In this section, we embed our estimated empirical model of supply and demand in
the drinks market into the tax design framework set out in Section 2 to solve for
the optimal tax rate on sugar sweetened beverages and its effect on prices, purchases, and welfare. We also consider the tax’s performance relative to alternative
tax instruments, and how its performance is affected by the structure of the market.
We repeat, for reference, the implicit formula for the optimal rate of tax levied on
the externality generating product attribute (the sugar in sweetened beverages),
equation (2.3), with the exception that we split out the effect of switching to the
36
set of untaxed drinks products from the effect of switching to the numeraire good:
∗
τ =
φ̃
{z}
1
− dZ dQS
Externalities
dτ
dτ
X
wjS µj
−
X
j∈N
j∈S
wjN µj
dQN
×
dτ
dQS
−
−
dτ
}

{z
Market power in drinks market
dX
dQS
µ̃ ×
−
.
dτ
dτ

{z
}
(5.1)
Numeraire good market power
Here we denote the externality term by φ̃; the precise form this takes will depend on
whether there is heterogeneity in marginal externalities and whether externalities
arise from consumption of untaxed goods. We use µ̃ to denote the markup on the
to denote the marginal effect of the tax on equilibrium
numeraire good, and dX
dτ
consumption of the numeraire good.49
Our demand and supply model allows us to simulate, for any tax rate, the degree
of switching between drinks products and from drinks to the numeraire, and the
equilibrium pricecost margins on products in the drinks market. However, it does
not provide us with information on the marginal externalities nor on the markup
on the numeraire good. We use existing evidence to calibrate these parameters,
and first describe how the patterns of consumer switching and firms’ endogenous
margin adjustment affect the optimal tax rate. We then show how the optimal rate
and associated components of welfare vary with the calibrated parameters.
Baseline calibration
In Section 3.1 we summarize the wellestablished evidence that relates consumption
of sugar sweetened beverages to nontrivial externalities. However, placing a numerical value on the marginal externality associated with an extra gram of sugar from
these products is challenging. We begin by considering a marginal externality of
£4.00 per kg of sugar that is associated with sweetened beverages (which translates
to approximately 1.3 pence per ounce of sugar sweetened beverage). This value is
similar to what is implied by epidemiological estimates of the impact on health care
costs (e.g. Wang et al. (2012)).50 In this case φ̃ = φ = 4. Below we show how the
P
P
Consumption of the numeraire good is given by X = i yi − j pij qij . See Appendix E
for how the planner’s problem is modified to accommodate the numeraire good.
50
Wang et al. (2012) estimate that a 15% reduction in consumption of sugar sweetened beverages among US adults aged 2465 would result in health care costs savings of $17.1 billion over 10
years. Converting this to savings per person, per kg of sugar and adjusting for differences in the
cost of providing health care in the UK implies an externality of roughly £4 per kg of sugar.
49
37
optimal rate varies with the magnitude, degree of heterogeneity, and source of the
externalities from sugar consumption.
The optimal rate also depends on the degree to which there is market power
associated with the numeraire good (which represents what consumers switch towards when lowering their drinks expenditure),51 and the direction and strength
of consumer switching towards the numeraire good. We calibrate the markup on
the numeraire good using an estimate for the UK economy wide markup from
De Loecker and Eeckhout (2018). Their estimate implies µ̃ = 0.4; the average
markup on drinks products, based on our estimates, is around 30% higher than
this.52 Below we show how the optimal rate depends on the value of the numeraire
markup.
5.1
Optimal tax rate
Under our baseline calibration of the marginal externality function and the pricecost markup on the numeraire good, the optimal rate of tax on the sugar in sweetened beverages is £1.74 per kg of sugar.53 This results in nontrivial price increases
for the taxed products (of 14% on average). However, the optimal tax rate lies well
below the rate that would be optimal under perfect competition (a Pigovian tax
of £4 per kg of sugar). It also lies below the rate that would be set by a planner
that ignores distortions associated with the exercise of market power would set: a
planner that takes the allocation in the absence of tax as a benchmark and aims
for full externality internalization relative to this baseline, would set a tax rate of
£3.64 per kg of sugar.54
The reason why the optimal rate lies below the rate aiming at full internalization
of externalities is the existence of positive pricecost margins for sugar sweetened
beverage products. This is reflected in the optimal tax formula by the weighted
P
S
average margin term,
j∈S wj µj . This expression reflects both the equilibrium
product level pricecost margins set by drinks firms on the taxed products (i.e. µj )
and, through the weights, switching within the set of taxed products. In particular,
51
Note that as we are free to normalize the price of the numeraire to 1, µ̃ can equivalently be
interpreted as the numeraire pricecost margin or markup.
52
De Loecker and Eeckhout (2018) adopt the convention of measuring markups as price over
marginal cost, and estimate that this is 1.68 in the UK economy. This corresponds to a markup defined as margin over price on the numeraire of around 0.4. The average of our estimated
markups on drinks is 0.55.
53
We run the optimal tax analysis using the most recent year covered by our data (2012).
54
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