Econometrica, Vol. 79, No. 3 (May, 2011), 651–692
UNWILLING OR UNABLE TO CHEAT? EVIDENCE FROM A TAX
AUDIT EXPERIMENT IN DENMARK
B
Y HENRIK JACOBSEN KLEVEN,MARTIN B. KNUDSEN,CLAUS THUSTRUP
KREINER,SØREN PEDERSEN, AND EMMANUEL SAEZ
1
This paper analyzes a tax enforcement field experiment in Denmark. In the base
year, a stratified and representative sample of over 40,000 individual income tax filers
was selected for the experiment. Half of the tax filers were randomly selected to be
thoroughly audited, while the rest were deliberately not audited. The following year,
threat-of-audit letters were randomly assigned and sent to tax filers in both groups. We
present three main empirical findings. First, using baseline audit data, we find that the
tax evasion rate is close to zero for income subject to third-party reporting, but substan-
tial for self-reported income. Since most income is subject to third-party reporting, the
overall evasion rate is modest. Second, using quasi-experimental variation created by
large kinks in the income tax schedule, we find that marginal tax rates have a positive
impact on tax evasion for self-reported income, but that this effect is small in compar-
ison to legal avoidance and behavioral responses. Third, using the randomization of
enforcement, we find that prior audits and threat-of-audit letters have significant ef-
fects on self-reported income, but no effect on third-party reported income. All these
empirical results can be explained by extending the standard model of (rational) tax
evasion to allow for the key distinction between self-reported and third-party reported
income.
K
EYWORDS: Tax evasion, field experiment, tax enforcement.
1. INTRODUCTION
AN EXTENSIVE LITERATURE has studied tax evasion and tax enforcement from
both the theoretical and empirical perspective. The theoretical literature builds
on the Allingham and Sandmo (1972) model in which taxpayers report income
to the tax authorities to maximize expected utility taking into account a prob-
ability of audit and a penalty for cheating. Under low audit probabilities and
low penalties, the expected return to evasion is high and the model predicts
substantial noncompliance. This prediction is in stark contrast with the obser-
vation that compliance levels are high in modern tax systems despite low audit
rates and fairly modest penalties.
2
This suggests that the standard economic
1
We thank a co-editor, Alan Auerbach, Oriana Bandiera, Richard Blundell, Raj Chetty, John
Friedman, William Gentry, Kåre P. Hagen, Wojciech Kopczuk, Monica Singhal, Joel Slemrod,
four anonymous referees, and numerous seminar and conference participants for construc-
tive comments and discussions. We are also thankful to Jakob Egholt Søgaard for outstanding
research assistance. Financial support from ESRC Grant RES-000-22-3241, NSF Grant SES-
0850631, and a grant from the Economic Policy Research Network (EPRN) is gratefully acknowl-
edged. The responsibility for all interpretations and conclusions expressed in this paper lies solely
with the authors and does not necessarily represent the views of the Danish tax administration
(SKAT) or the Danish government.
2
For example, Andreoni, Erard, and Feinstein (1998) concluded at the end of their influential
survey that “the most significant discrepancy that has been documented between the standard
© 2011 The Econometric Society DOI: 10.3982/ECTA9113
652 KLEVEN ET AL.
model misses important aspects of the real-world reporting environment. In
particular, many have argued that observed compliance levels can only be ex-
plained by psychological or cultural aspects of tax compliance such as social
norms, tax morale, patriotism, guilt, and shame (e.g., Andreoni, Erard, and
Feinstein (1998)). In other words, taxpayers, despite being able to cheat, are
unwilling to do so for noneconomic reasons.
While psychology and culture may be important in the decision to evade
taxes, the standard economic model deviates from the real world in another
potentially important aspect: it focuses on a situation with pure self-reporting.
By contrast, all advanced economies make extensive use of third-party infor-
mation reporting whereby institutions such as employers, banks, investment
funds, and pension funds report taxable income earned by individuals (em-
ployees or clients) directly to the government. Under third-party reporting,
the observed audit rate is a poor proxy for the probability of detection faced by
a taxpayer contemplating to engage in tax evasion, because systematic match-
ing of information reports to income tax returns will uncover any discrepancy
between the two (Sandmo (2005); Slemrod (2007)). Thus, taxpayers with only
third-party reported income may be unable to cheat on their taxes. Indeed, the
U.S. Taxpayer Compliance Measurement Program (TCMP) has documented
that aggregate compliance is much higher for income categories with substan-
tial information reporting than for income categories with little or no informa-
tion reporting (Internal Revenue Service (1996, 2006)).
In this study, we first extend the standard economic model of tax evasion
to account for the fact that the probability of detection is endogenous to the
type of income being underreported (third-party reported versus self-reported
income). The model predicts that evasion will be very low for third-party re-
ported income, but substantial for self-reported income. It also predicts that
the effects of tax enforcement (audits, penalties) and tax policy (marginal tax
rates) on evasion will be larger for self-reported income than for third-party
reported income. Second, we provide a comprehensive empirical test of these
predictions based on a large field experiment carried out in collaboration with
the Danish tax collection agency (SKAT). The experiment imposes different
audit regimes on randomly selected taxpayers, and has been designed to pro-
vide evidence on the size of evasion as well as the response of evasion to tax
enforcement and tax rates under different information environments (third-
party reporting versus self-reporting). Unlike previous work such as the U.S.
TCMP studies, our data allow us to distinguish precisely between income items
subject to third-party reporting and income items subject to self-reporting for
each individual in the sample, and to measure treatment effects on those two
forms of income separately.
economic model of compliance and real-world compliance behavior is that the theoretical model
greatly overpredicts noncompliance.”
UNWILLING OR UNABLE TO CHEAT? 653
The experiment was implemented on a stratified random sample of about
42,800 individual taxpayers during the filing and auditing seasons of 2007 and
2008. In the first stage, taxpayers were randomly selected for unannounced au-
dits of tax returns filed in 2007. These audits were comprehensive and any de-
tected misreporting was corrected and penalized according to Danish law. The
selected taxpayers were not aware that the audits were part of a special study.
For taxpayers not selected for these audits, tax returns were not examined un-
der any circumstances. In the second stage, employees in both the audit and
no-audit groups were randomly selected for pre-announced audits of tax re-
turns filed in 2008. One group of taxpayers received a letter telling them that
their return would certainly be audited, another group received a letter telling
them that half of everyone in their group would be audited, while a third group
received no letter. The second stage therefore provides exogenous variation in
the probability of being audited. The empirical analysis is divided into three
main parts.
The first part studies the anatomy of tax compliance using the baseline audit
data. While the overall tax evasion uncovered by audits constitutes a modest
share of total income, there is considerable variation in tax evasion rates across
income items depending on the information environment. The tax evasion rate
for third-party reported income is close to zero, whereas the tax evasion rate
for self-reported income is substantial. Across different taxpayers, we find that
individuals who earn mostly self-reported income and display substantial non-
compliance overall still do not underreport their third-party reported income,
while individuals who earn mostly third-party reported income and display very
little noncompliance overall often fully evade taxes on their self-reported in-
come. These findings are consistent with the theoretical model and suggest that
the high degree of compliance is driven by the widespread use of information
reporting rather than an intrinsic aversion to cheating. We also study the im-
pact of social and cultural variables on compliance. Although some of these
variables are correlated with tax evasion, their impact is very small in compar-
ison to variables that capture information and incentives, namely the presence
and size of self-reported income or losses. Taken together, our findings sug-
gest that tax evasion is low, not because taxpayers are unwilling to cheat, but
because they are unable to cheat successfully due to the widespread use of
third-party reporting.
The second part estimates the effect of the marginal tax rate on evasion using
quasi-experimental variation in tax rates created by large and salient kinks in
the nonlinear income tax schedule. The effect of marginal tax rates on evasion
is theoretically ambiguous, and existing empirical results have been very sen-
sitive to specification due to data and identification problems. As showed by
Saez (2010), the compensated elasticity of reported income with respect to the
marginal tax rate can be identified from bunching around kinks in progressive
tax schedules. Unlike existing bunching studies, our data allow us to compare
654 KLEVEN ET AL.
bunching in pre-audit and post-audit incomes so as to separately identify com-
pensated elasticities of illegal evasion versus legal avoidance. We find that eva-
sion elasticities for self-reported income are positive but small relative to the
total elasticity. This implies that marginal tax rates have only modest effects
on tax evasion that are dwarfed by the third-party reporting effects obtained in
part one.
The third part studies the effect of tax enforcement on evasion using the ran-
domization of audits and audit threats. First, we estimate the effect of audits
on future reported income by comparing the audit and no-audit groups in the
following year. Past audits may affect reported income by changing the per-
ceived probability of detection. Consistent with our theoretical model, we find
that audits have a strong positive impact on reported income in the follow-
ing year, with the effect driven entirely by self-reported income. Second, we
estimate the effect of the probability of audit on reported income by compar-
ing the threat-of-audit letter and no-letter groups. Because taxpayers received
the letters shortly after receiving a prepopulated return containing third-party
information, we focus on the effect of letters on self-reported adjustments to
the prepopulated return. Consistent with the predictions of the model, we find
that audit threats have a positive impact on self-reported income and that the
effects are stronger for the 100% threat than for the 50% threat.
Our paper contributes to a large body of empirical work studying the size
and determinants of tax evasion, including the effect of tax rates, prior audits,
audit probabilities, penalties, and socioeconomic variables.
3
Most of the litera-
ture relies on observational and nonexperimental data, which is associated with
important measurement and identification problems, or on laboratory experi-
ments that do not capture central aspects of the real-world reporting environ-
ment such as the presence of third-party reporting. An important exception in
the literature is Slemrod, Blumenthal, and Christian (2001), who analyze the
effects of threat-of-audit letters in a small field experiment in Minnesota, and
upon which the last part of our analysis is built.
The paper is organized as follows. Section 2 presents an economic model of
tax evasion with third-party reporting. Section 3 describes the context, exper-
imental design, and data. Section 4 analyzes the anatomy of tax compliance.
Section 5 estimates the effect of the marginal tax rate on evasion. Section 6
estimates the effects of tax enforcement on evasion. Section 7 concludes.
2.
A SIMPLE ECONOMIC MODEL OF TAX EVASION
We consider a version of the Allingham–Sandmo (henceforth AS) model
with risk-neutral taxpayers and an endogenous audit probability that depends
3
Andreoni, Erard, and Feinstein (1998) and Slemrod and Yitzhaki (2002) provided extensive
surveys. An earlier version of this paper (Kleven, Knudsen, Kreiner, Pedersen, and Saez (2010))
also provides a more thorough review of the literature.
UNWILLING OR UNABLE TO CHEAT? 655
on reported income.
4
The basic model is similar to models considered in the
literature, but we present the condition determining tax evasion in a differ-
ent manner to demonstrate that a high degree of tax compliance is potentially
consistent with a low audit probability and a low, or even zero, penalty for
evasion. We then introduce third-party reporting into the model and discuss
its implications for the structure of the (endogenous) audit probability and
tax compliance behavior. Notice that the assumption of risk neutrality, besides
simplifying the analysis, makes our case harder because risk-neutral taxpayers
are more inclined to evade taxes than risk-averse taxpayers.
We consider a taxpayer with true income
¯
y, reported income y,andunde-
clared income e ≡
¯
y − y.Letp be the probability that the government detects
undeclared income. We can think of the detection probability as a product
of the probability of audit and the probability of detection conditional on au-
dit.
5
The distinction between these two probabilities is implicit in the model,
but becomes relevant in the interpretation of the empirical findings from the
randomized experiment. We assume that the probability of detection is an in-
creasing function of undeclared income, p = p(e),wherep
(e) > 0. That is,
the more the individual evades, the more likely is the tax administration to
suspect underreporting and to carry out an audit.
When evasion is detected, the taxpayer is forced to pay the evaded tax plus
a penalty. The tax is proportional to income with rate τ, and the penalty is
proportional to the evaded tax and, is given by θ. The risk-neutral taxpayer
maximizes expected net-of-tax income, that is,
u = (1 − p(e)) ·[
¯
y(1 − τ) + τe]+p(e) ·[
¯
y(1 − τ) − θτe](1)
An interior optimum for e satisfies the first-order condition du/de = 0, which
can be written as
[p(e) + p
(e) · e](1 + θ) = 1(2)
The second-order condition to this problem puts a restriction on the second-
order derivative of p(e).
6
We can define the elasticity of the detection prob-
ability with respect to evasion as ε ≡ p
(e)e/p ≥ 0. The first-order condition
that determinines tax evasion can then be written as
p(e) · (1 + θ) · (1 + ε(e)) = 1(3)
4
A number of previous studies have considered an endogenous audit probability, including the
original paper by Allingham and Sandmo (1972), Yitzhaki (1987), Slemrod and Yitzhaki (2002),
and Sandmo (2005).
5
For expositional simplicity, we make the assumption that a tax audit either uncovers every-
thing or nothing; there is no middle ground where tax evasion is partially uncovered.
6
The second-order condition is given by −2p
(e) − p
(e) · e<0. A sufficient condition for this
to hold is that p(·) is convex so that p
(e) > 0.
