Audits or Distortions: The Optimal Scheme to Enforce Self‐Employment Income Taxes

• Date: 01 August 2016
• Author: EDUARDO ZILBERMAN
• DOI: http://doi.org/10.1111/jpet.12193
• Published date: 01 August 2016

AUDITS OR DISTORTIONS:THE OPTIMAL SCHEME TO ENFORCE

SELF-EMPLOYMENT INCOME TAXES

EDUARDO ZILBERMAN

PUC-Rio

Abstract

I investigate the optimal auditing scheme for a revenue-maximizing

tax collection agency that observes not only reported profits, but also

a single factor of production at each firm. Each firm is owned by a

single entrepreneur whose managerial ability is random. The optimal

auditing scheme is discontinuous and nonmonotone in ability. In inter-

mediate audit costs, less productive entrepreneurs face auditing proba-

bilities that increase in ability, whereas the ablest ones are not audited.

Finally, the effective tax rate is higher in the middle of the manage-

rial ability distribution; thus, the overall regressive (or progressive) bias

that arises from evasion is unknown.

1. Introduction

The literature on optimal income tax enforcement has focused mainly on taxpayers

whose income is exogenous or salaried workers.1However, taxes on wages and salaries

are usually subject to employer withholding and, thus, almost perfectly enforced. In

contrast, self-employment income, which is mostly self-reported, is considerably under-

reported to the tax collection agency (henceforth the IRS). Indeed, in the United States,

1The seminal paper is Reinganum and Wilde (1985), inspired by the costly state verification model of

Townsend (1979). Notable contributions include Border and Sobel (1987), Melumad and Mookherjee

(1989), Mookherjee and Png (1989), Cremer, Marchand, and Pestieau (1990), S´

anchez and Sobel

(1993), Cremer and Gahvari (1996), Macho-Stadler and P´

erez-Castrillo (1997), Chander and Wilde

(1998), Bassetto and Phelan (2008), and Ravikumar and Zhang (2012). The first theoretical work on

tax noncompliance was Allingham and Sandmo (1972), which built on Becker (1968)’s work on the

economics of crime. Recent surveys are Andreoni, Erard, and Feinstein (1998), Slemrod and Yitzhaki

(2002), and Sandmo (2005).

Eduardo Zilberman, Department of Economics, PUC-Rio, Rio de Janeiro, Brazil (zilberman@econ.

puc-rio.br).

I thank Ennio Stacchetti for insightful guidance. I also thank Juliano Assunc¸˜

ao, Tiago Berriel, Ryan

Booth, Vinicius Carrasco, John P. Conley, Bernardo da Silveira, Edoardo di Porto, Bruno Ferman,

Raquel Fern´

andez, Vivian Figer, Nicolas Figueroa, Sean Flynn, Renato Gomes, Pedro Hemsley, Boyan

Jovanovic, Alessandro Lizzeri, Thomas Mertens, Daniel Monte, Giri Parameswaran, Nicola Persico,

Leonardo Rezende, Nikita Roketskiy, Tomasz Sadzik, Daniel Xu, Gianluca Violante, Joyce Wong, two

anonymous referees, and participants at conferences and seminars for helpful comments and discus-

sions. I am especially indebted to Saki Bigio, whose comments and discussions were invaluable. All

errors are mine.

Received September 9, 2013; Accepted June 12, 2015.

C2016 Wiley Periodicals, Inc.

Journal of Public Economic Theory, 18 (4), 2016, pp. 511–544.

511

512 Journal of Public Economic Theory

Slemrod (2007) documents that only 1% of wages and salaries is not reported to the IRS,

whereas 43% of business income is not reported.2In Italy, at the end of the 1980s, for

instance, Galbiati and Zanella (2012) document that 46.4% of self-employed income

is not reported. Kleven et al. (2011) define tax evasion rate as the share of reported

income that is underreported and calculate it for Denmark. They find the tax evasion

rate is 14.9% for self-employment income, but only 1.1% for personal income. This ev-

idence suggests that, in order to enforce income taxes, the IRS should concentrate on

developing a better strategy to monitor business proprietors.

This paper asks the following question: Given that reported income and a single fac-

tor of production are observable, how should a revenue-maximizing IRS monitor het-

erogeneous entrepreneurs? The source of heterogeneity is a random managerial ability,

which is private information. Once the monitoring strategy is conditioned on a single

input, the IRS can indirectly distort production in order to provide incentives, which

enriches its set of tools to enforce self-employment income taxes. This single input can

be any easily observable factor of production, such as electricity bills or intermediate

goods bought from a formal firm. In particular, I interpret it as labor input. Indeed,

since wage taxes are almost perfectly enforced, at least in some sectors, the number of

workers at each firm seems to be easily observable by the IRS.

In order to answer the question, I adapt the two-stage game developed in Bigio and

Zilberman (2011) to study optimal self-employment income tax enforcement, which is

fully described in Section 2. A self-employed individual is a risk-neutral entrepreneur

who owns and manages a single firm. An entrepreneur experiences a random man-

agerial ability—her privately observed type—that enhances productivity in a plant ex-

hibiting decreasing returns to scale. Production is carried out by a team of workers.

Entrepreneurs can underreport income—that is, the profits generated by their own

firms—in order to evade taxes. If a firm is audited, true income is uncovered, and the

entrepreneur must pay a penalty.

In the first stage, given the distribution of managerial ability, the IRS commits to

a costly monitoring strategy, dependent on both reported income and labor input, in

order to maximize net revenue. In the second stage, entrepreneurs take into account

this monitoring strategy and maximize expected profits by choosing labor input and

reported income. Hence, labor is not only a factor of production, but also a signal of

true income. At a production cost, labor can be strategically distorted to signal a lower

income to the IRS.

To solve this model, I adopt a mechanism-design approach, in which the choice

of labor and reported income are delegated to the IRS, which is the principal. Due

to the revelation principle, it is enough to focus within the class of direct mechanisms

that respect incentive compatibility and individual rationality. That is, an agent reports

her type (i.e., her managerial ability) and is then assigned a labor input to employ,

an amount to declare as profits, and a probability with which she will be audited. The

mechanism is designed such that agents truthfully report their types and derive at least

their reservation values.

The main finding is that the optimal auditing scheme may be nonmonotone in

ability. In intermediate audit costs, less productive entrepreneurs face auditing proba-

bilities that increase in managerial ability, whereas the ablest ones are not audited. At

some threshold level of ability, the optimal auditing scheme discontinuously drops.

2These figures imply a tax gap of 10 and 109 billion dollars, respectively.

Audits or Distortions 513

There are two driving forces behind this nonmonotonicity result. The first is the

reservation value, which is type-dependent. Since an entrepreneur can declare her true

profits and pay the right amount of taxes, her reservation value is the after-tax truth-

fully declared profits, which is increasing in managerial ability. Hence, entrepreneurs

face countervailing incentives. On the one hand, an entrepreneur is willing to un-

derstate her type in order to pay less in taxes. On the other hand, she is willing to

overstate her type in order to be considered an entrepreneur with a higher reserva-

tion value by the principal. Moreover, the incentives to understate (overstate) are rel-

atively stronger for high-ability (low-ability) types. In this environment, a nonmono-

tone monitoring strategy may be optimal as long as incentive compatibility is not

violated.

The second driving force is the joint condition of the monitoring strategy on

both reported income and labor input. If it depends only on reported income, this

model collapses to a variant of S´

anchez and Sobel (1993), in which the optimal

monitoring strategy must be nonincreasing in order to not violate incentive com-

patibility. Every entrepreneur below a certain threshold type is audited with con-

stant probability, whereas those above it are not monitored at all. In contrast, if

the monitoring strategy depends only on labor input, which is solved in Bigio and

Zilberman (2011), the optimal monitoring strategy is nondecreasing. Those types be-

low a certain threshold are not monitored at all, whereas those above it are audited

with constant probability. In Section 3, I discuss the role of each driving force in

detail.

The role of costly audits as a tool to maximize government revenue is twofold: First,

it enforces taxes from those that are audited; second, it provides incentives by prevent-

ing misreport from other types, which allows the IRS to require higher income decla-

rations from them. Similarly, labor distortions can be used to provide incentives, but

only at a production cost that diminishes revenue collection. The optimal mechanism

balances the use of these two tools in a way that preserves incentive compatibility and

maximizes net revenue collection.

The optimal mechanism has the following properties: (1) As in a standard

mechanism-design problem, the top type is not distorted; (2) in the top range of the

type distribution, audits are never used, and labor is distorted downward to provide in-

centives; (3) below some threshold type, in order to be assigned a higher reservation

value, entrepreneurs have stronger incentives to overstate their types, limiting the fur-

ther use of distortions to provide incentives; (4) if the audit cost is too high, only labor

distortions are used to provide incentives; (5) if the audit cost is not too high, audits

and labor distortions are optimally combined to enforce taxes; in the bottom range of

the type distribution, both the optimal monitoring strategy and labor schedule are in-

creasing in ability; and at the threshold type, they drop discontinuously. In Section 3,

I present an example that summarizes the intuition behind these results. In the con-

text of this example, I also argue that (1) every entrepreneur evades taxes; (2) as the

penalty or tax rate increases, the optimal mechanism tends to rely more on audits and

less on distortions; and (3) the effective tax rate is higher in the middle of the type

distribution; thus, the overall regressive (or progressive) bias that arises from evasion is

unknown.

Section 4 and the Appendix derive analytically the properties above. Section 5

concludes.