Attending to inattention: Identification of deadweight loss under nonsalient taxes

• Published date: 01 February 2020
• DOI: http://doi.org/10.1111/jpet.12401
• Date: 01 February 2020
• Author: Benjamin Glass,Giacomo Brusco

J Public Econ Theory. 2020;22:5–24. wileyonlinelibrary.com/journal/jpet © 2019 Wiley Periodicals, Inc.

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Received: 6 May 2019

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Accepted: 16 August 2019

DOI: 10.1111/jpet.12401

ORIGINAL ARTICLE

Attending to inattention: Identification of

deadweight loss under nonsalient taxes

Giacomo Brusco

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Benjamin Glass

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Department of Economics, University of

Michigan, Ann Arbor, Michigan

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Department of Economics, Pennsylvania

State University, University Park,

Pennsylvania

Correspondence

Giacomo Brusco, Department of

Economics, University of Michigan, Ann

Arbor, MI 48109.

Email: giacomo.brusco@gmail.com

Abstract

Recent developments in behavioral public economics

have shown that heterogeneous biases prevent point

identification of deadweight loss. We replicate this result

for an arbitrary (closed) consumption set, whereas

previous results on heterogeneous attention focused on

binary choice. We find that one can bound the efficiency

costs of taxation based on aggregate features of demand.

When individuals have linear demand functions, the

bounds for deadweight loss are easy to calculate from

linear regressions.

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INTRODUCTION

Taxing a good results in a loss of economic efficiency whenever it distorts equilibrium behavior

away from the Pareto optimum. To the extent that agents do not notice a tax, the burden of the

tax is exacerbated by the fact that agents cannot adjust the behavior to protect themselves from

the tax. However, the burden of the tax in excess of government revenue, or deadweight loss, is

mitigated when agents do not pay attention to the tax: if consumers pay the tax without noticing

it, they are effectively transferring some of their income to the government in a lump sum.

Chetty, Looney, and Kroft (2009; henceforth CLK) were the first to make these points. In

addition to their theoretical contributions, they also showed that consumers in the United

States, where sales tax is applied at the register rather than included on the prices displayed on

shelves (or “sticker prices”), tend to under‐react to sales taxes.

While CLK (2009) focuses on the case of homogeneous attention, recent work by Taubinsky

and Rees‐Jones (2018; henceforth TRJ) has noted that introducing the possibility of

heterogeneous attention may prevent the computation of deadweight loss from aggregate data.

If each person faced a different tax rate when buying a certain good, understanding welfare

effects would require us to study not only aggregate demand, but the demand of every

individual. Imposing a high tax on low elasticity individuals and a low tax on high elasticity

individuals would have a very different effect on welfare than doing the opposite. A similar

reasoning applies when all agents face the same tax rate, but perceive different tax rates. TRJ

(2018) find that allowing for heterogeneous attention introduces an issue of allocative

inefficiency that is normally absent from the study of the welfare effects of taxation. In a world

of heterogeneous attention, there is no guarantee that the individuals who end up consuming

the good are the ones who value it the most.

TRJ (2018) make these points in a binary choice model. This is well‐suited to their

experiment, in which people are choosing whether or not to buy a certain object, but their proof

does not generalize trivially. Given the predominance of continuous choice settings in much of

the literature on tax salience, including CLK’s seminal paper, this motivates us to study the

issue further.

We begin by developing a model of choice under misperceived prices with an arbitrary

closed consumption set, and develop our welfare measure: compensating variation due to the

tax, net of tax revenue. Bernheim and Rangel (2009) laid the foundations of welfare analysis

with behavioral agents. Our model is similar to the models of CLK (2007, 2009) and TRJ (2018),

but we slightly modify the treatment of income effects, along the lines of Gabaix’s (2014) model

of rational inattention. In the absence of income effects, our model of choice for an individual

agent is essentially equivalent to the model in CLK (2009), except that we allow for arbitrary

consumption sets. Our model is also similar to the model of Chetty (2009), but for the fact that

we specify a particular way in which behavioral agents maximize utility. While this does not

impose severe restrictions on behavior, it offers a useful framework when we move on to

identification. We confirm that some of the major results in CLK (2009) and TRJ (2018) hold

quite broadly: inattention to taxes increases the size of the loss in consumer surplus, but

decreases the size of deadweight loss; attention heterogeneity amplifies deadweight loss, and

invalidates CLK’s sufficient statistic approach.

The main contribution of this paper is to generalize TRJ’s nonidentification result to an

arbitrary closed choice set. We show that an econometrician who only observes aggregate

consumption data can only determine the true value of aggregate deadweight loss to lie on an

interval. These bounds were first noted by TRJ (2018) in their proposition A.2. We find these

bounds hold generally and propose to use them as a novel empirical tool.

The lower bound for deadweight loss is the calculation one would perform in the case of a

representative consumer. Since the loss in efficiency is a convex function of the perceived tax

rate, the calculation of deadweight loss from one perceived tax‐inclusive price consistent with

aggregate demand will generically underestimate deadweight loss. Heterogeneity in tax salience

creates heterogeneity in perceived net‐of‐tax prices, which creates an allocative inefficiency

across consumers. As the calculation with a representative consumer only accounts for

inefficiency from aggregate foregone consumption due to the tax, it will underestimate excess

burden. However, in the case in which all agents pay the same amount of attention to the tax,

there is no allocative inefficiency between consumers, and so performing the calculation as with

a representative consumer yields the correct value for deadweight loss. The formula for this

lower bound to deadweight loss is an extension of formulas provided by CLK (2009) and TRJ

(2018).

Following TRJ (2018), we obtain an upper bound for deadweight loss by letting the

econometrician assume that tax salience has support on a known bounded nonnegative

interval. The upper bound comes from maximizing perceived price heterogeneity, again

exploiting the convexity of deadweight loss with respect to the perceived tax. This is achieved by

positing that agents have either zero or maximal salience. Generalizing introduces two

additional considerations in calculating the upper bound for deadweight loss. One, a

distribution yielding the upper bound for deadweight loss assigns high tax salience precisely

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BRUSCO AND GLASS