American Economic Association
Tax Compliance and Loss Aversion
Author(s): Per Engström, Katarina Nordblom, Henry Ohlsson and Annika Persson
Source: American Economic Journal: Economic Policy, Vol. 7, No. 4 (November 2015), pp.
132-164
Published by: American Economic Association
Stable URL: https://www.jstor.org/stable/24739159
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American Economie Journal: Economie Policy 2015, 7(4): 132-164
http://dx.doi. org/10.1257/pol.20130134
Tax Compliance and Loss Aversion1
By Per Engström, Katarina Nordblom,
Henry Ohlsson, and Annika Persson*
We study if taxpayers are loss averse when filing returns. Preliminary
deficits might be viewed as losses assuming zero preliminary bal
ances as reference points. Swedish taxpayers can to try to escape
such losses by claiming deductions after receiving information about
the preliminary balance. Using a regression kink and discontinu
ity approach, we study data for 3.6 million Swedish taxpayers for
2006. There are strong causal effects of preliminary tax deficits on
the probability of claiming deductions. Compliance will increase and
auditing costs will be reduced if preliminary taxes are calibrated so
that most taxpayers receive refunds.
[J EL H24, H26j
Two same
taxpayers,
A according
and B, are
about
to filethey
their
tax from
returns.
They
both have the
income and
to the
information
receive
the Tax
Agency
they are both supposed to pay $30,000 in total taxes. However, their employers have
already withheld taxes at source during the year; A's employer $29,000 and B's
$31,000. Hence, A has a preliminary balance of $ 1,000 due, while B will get a refund
of the same amount. According to standard neoclassical theory, both would behave
in the same manner since they both end up with the same tax liability of $30,000. We
find, however, that they behave significantly different: A is much more likely than B
to claim deductions in order to reduce his tax liability. This finding is not consistent
with neoclassical theory. On the other hand, reference dependence and loss aver
sion—as defined in Prospect Theory by Kahneman and Tversky (1979) and Tversky
* Engström: Department of Economics, Uppsala University, P.O. Box 513, SE-751 20 Uppsala, Sweden
and Uppsala Center for Fiscal Studies (UCFS) (e-mail: per.engstrom@nek.uu.se); Nordblom: Department
of Economics, University of Gothenburg, P.O. Box 640, SE-405 30 Gothenburg, Sweden, and UCFS (e-mail:
katarina.nordblom@economics.gu.se); Ohlsson: Department of Economics, Uppsala University, P.O. Box 513,
SE-751 20 Uppsala, Sweden, and UCFS (e-mail: henry.ohlsson@nek.uu.se); Persson: The Swedish Tax Agency,
SE-171 94 Solna, Sweden (e-mail: annika.persson@skatteverket.se). We would like to thank Spencer Bastani,
Fredrik Carlsson, Edoardo Di Porto, Martin Dufwenberg, Olof Johansson-Stenman, Martin Kocher, David Lee,
Mikael Lindahl, Oskar Nordstrom Skans, Matthias Sutter, Mäns Söderbom, Benno Torgler, Clive Werdt, Magnus
Wikström, seminar participants in Aarhus, Deakin; Melbourne, Gothenburg, Växjö, University of New South Wales
(UNSW); Sydney, VATT; Helsinki, UCFS, the UCFS Scientific Advisory Board, the European Commission, the
Finnish and the Swedish Tax Agencies as well as conference participants at the International Institute of Public
Finance (IIPF) 2013 Taormina conference, the Shadow 2011 Münster conference, and the 2011 Swedish Economics
Meeting in Uppsala for their valuable comments and suggestions. We are also grateful to three anonymous referees
for their helpful comments. Financial support to UCFS from Riksbankens Jubileumsfond (RJ), the Swedish Council
for Working Life and Social Research (FAS), and the Swedish Tax Agency is gratefully acknowledged. Nordblom
also acknowledges financial support from the Swedish Research Council, project no. 421-2010-1420, and from RJ.
Some of the work was done as Ohlsson enjoyed the hospitality of the School of Economics, UNSW, Sydney and
the Department of Economics, University of Melbourne during his sabbatical. Financial support for the sabbatical
from the Wenner-Gren Foundations is gratefully acknowledged.
TGo to http://dx.doi.org/10.1257/pol.20130134 to visit the article page for additional materials and author
disclosure statement(s) or to comment in the online discussion forum.
132
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VOL. 7 NO. 4 ENGSTROM ETAL.: TAX COMPLIANCE AND LOSS AVERSION 133
0.08
o
|
■o
0.06-1
co
O)
c
o
ffi
o
-O
0
02-1
,
,
,
0.00-1
.
,
,
-3,000 -2,000 -1,000 0 1,000 2,000 3,000
Preliminary deficit, SEK
Figure 1. Share Claiming a Deduction as a Function of the Preliminary Deficit
and Kahneman (1992)—predict such outcomes. Loss averse individuals value losses
(in comparison to a reference point) more than gains by the same amount. In ou
particular application it is likely that a zero balance in preliminary tax payments
such a reference point. An individual with a preliminary deficit (A) will, therefo
perceive a higher marginal value of extra income than someone with a preliminar
surplus of the same amount (B). Those with a deficit would consequently be mor
inclined to take (legal or illegal) actions in order to reduce their tax liability. Th
line of reasoning is put forward in some theoretical studies in the area of prospe
theory and tax compliance.1 Recent empirical evidence by Rees-Jones (2014) poin
in the same direction.
We study the entire population of Swedish taxpayers of working age and their
behavior when filing their income tax returns. The high quality tax return data concern
the income year 2006 and the tax assessment year is 2007. The Tax Agency reports
a preliminary balance in taxes due to the taxpayer before the income tax return has
to be filed. The specific action we study is whether and how much taxpayers claim
deductions for "other expenses for earning employment income." Such deductions
may be accurate, but may also express noncompliance: The Swedish Tax Agency
reports that almost all audited claimed deductions for "other expenses for earning
employment income" were rejected.2
Figure 1 shows that the probability of claiming a deduction is indeed higher for
taxpayers with a preliminary deficit than for those with a preliminary surplus. Each
data point in the figure represents the share for taxpayers with a preliminary deficit
in SEK 300 intervals.3
1 See, e.g., Yaniv (1999), Bernasconi and Zanardi (2004), and Dhami and al-Nowaihi (2007).
2See Riksskatteverket (RSV) (2001). A more recent follow-up in 2006 drew a random sample of claimed
deductions. There were mistakes in 93 percent of the cases.
3 The average SEK/USD exchange rate was SEK 7.38 per USD in 2006.
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134 AMERICAN ECONOMIC JOURNAL: ECONOMIC POUCY NOVEMBER 2015
We design a quasi-experiment using a regression kink and discontinu
to analyze whether the pattern in Figure 1 really is a causal one. This
technique allows us to eliminate potential problems of endogeneity an
in ways that most previous empirical studies have not been able to
behavior to be consistent with loss aversion in the following sense: ta
have a preliminary deficit (taxes due) are more likely to claim deductio
expenses" than those who have a preliminary surplus (tax refund). Th
larger unconditional amounts, on average. None of the covariates exh
evolution around zero preliminary balance. Hence, selection is unlikely
that we have found evidence of a clear departure from neoclassical as
Furthermore, we argue that loss aversion is the most likely candidate
the result. To further strengthen the causal interpretation of our find
use an alternative instrumental variable (IV) approach. The difference
actual and preliminary tax rates is used as an instrument when estimat
ity models for claiming a deduction. The results are confirmed using t
Our conclusion is, therefore, that there is evidence of loss aversion.
We also estimate the coefficient of loss aversion in our empirical an
estimate, A = 2.17 for the full sample, is very close to the estimate r
Tversky and Kahneman (1992), Â = 2.25.
We thus find a causal link from loss aversion to tax filing behavior
some other previous empirical studies also suggesting that people who
too little in advance preliminary taxes are less likely to comply than th
paid too much. These studies do not, however, establish causality.4 To
edge there is only one other study which also has established causality
aversion and tax filing behavior. Rees-Jones (2014) studies tax shelter
US taxpayers. While we study a specific reaction to exogenous ex ante
about taxes due, he uses ex post data to conclude that loss averse taxp
avoid ending up with taxes due.
The major contribution of the paper is thus that we find tax filing
be consistent with loss aversion, which in turn has important policy
Tax authorities could withhold a little bit too much in order to keep
surplus side. This could increase tax payments and reduce the need for
deductions are signs of noncompliance, it could also enhance tax mora
in the long run (Nordblom and Zantac 2012). However, overwithholdin
be used too ambitiously, as that itself could cause credibility problems.
The remainder of the paper is organized as follows: We discuss pros
and its application to tax compliance in Section I. Section II describes
the institutional setting. We then present a simple theoretical model in
which the taxpayers' decisions are studied. The model provides predic
empirical analysis. Some descriptive results are presented in Section IV
presents the empirical results using the regression kink and discontinu
4See, e.g., Chang and Schultz, Jr. (1990) and Persson (2003). There are also experimental stu
that advance payments actually matter for compliance, e.g., Robben et al. (1990), Schepanski a
and Copeland and Cuccia (2002).
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VOL 7 NO. 4 ENGSTROM ET AL: TAX COMPUANCE AND LOSS AVERSION 135
A robustness check using an IV approach and our estimates of the coef
aversion are found in Section VI. Section VII concludes the paper.
I. Prospect Theory
A. Theory and Evidence
Kahneman and Tversky (1979) defined prospect theory. The eleme
marily use are reference dependence and loss aversion. Hence, people
comes as gains and losses compared to some reference point and c
as more salient than gains. This implies that the utility function is
reference point. Although the concept of loss aversion was first intro
settings (and has been proposed to explain parts of observed risk aver
and Kahneman (1991) show that it can also explain behavior in the abs
Many experimental studies have followed the famous mug exp
Kahneman, Knetsch, and Thaler ( 1990),5 showing evidence of an endow
Tversky and Kahneman (1992); Schmidt and Traub (2002); Gächter, J
Herrmann (2007); Abdellaoui, Bleichrodt, and Paraschiv (2007); an
Bleichrodt, and L'Haridon (2008) are some studies finding evidence o
to various extent in within-subject comparisons. They let the subjects
rather few university students) make several choices and conclude t
individual makes different choices depending on gains or losses. Cam
and DellaVigna (2009) discuss several field experiments that have fou
to be consistent with loss aversion and other components of prospec
(2003, 2004) finds in his field experiments that there is a pronounce
effect (like the one found by Kahneman, Knetsch, and Thaler 1990)
perienced subjects, but that experienced subjects behave in line with
theory. However, Pope and Schweitzer (2011) find that even highly
professional golfers exhibit loss aversion. Crawford and Meng (2011) f
dependence among New York cab drivers in a study where they con
tion in an elegant way. Fehr and Goette (2007) study bicycle messen
that a majority are loss averse, which explains their behavioral resp
increase. Genesove and Mayer (2001), who study sellers of residentia
find loss aversion where the purchase price seems to be the relevant r
B. Tax Compliance and Prospect Theory
Some theoretical studies in the area of prospect theory that focus o
ance suggest the following line of reasoning: Loss aversion implies t
vidual values losses compared with the reference point more than gai
amount. An individual with a preliminary tax deficit (more taxes du
fore, perceive a higher marginal value of extra income than an indi
5 Half of the subjects were given a mug for which they were then asked to give a selling p
asked for their willingness to pay for a mug. The price mentioned by the former group widel
mentioned by the latter.
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136 AMERICAN ECONOMIC JOURNAL: ECONOMIC POUCY NOVEMBER 2015
preliminary tax surplus (some taxes will be refunded) of the s
with a preliminary tax deficit would consequently be more inc
chance of noncompliance.6 Although Elffers and Hessing (1997
payments promote compliance, they also point to the fact that w
may make people feel wrongly treated, which has an opposing e
Experimental studies find that advance tax payments actually
ance in a fashion consistent with loss aversion.7 Previous studi
data suggest that people who have paid too little in preliminar
less likely to comply than those who have paid too much.8 Non
studies can, however, establish a causal relationship.9
Rees-Jones (2014) is a recent contribution that is relevant to o
lishes a causal relationship between loss aversion and tax shelte
to reduce tax liability, and concludes that taxpayers behave in a
when filing their tax returns. His approach is different from o
ing system is different from the Swedish. He considers measu
by the taxpayer and studies the resulting balance due. The con
implied sheltering is higher in the loss domain although he cann
specific actions. In our study, we concentrate on one specific tax
which we can observe, namely claiming a deduction for other ex
employment income. We study how this is affected by fully ex
from the Swedish Tax Agency before tax returns are to be file
reveals whether you initially are in the loss domain or in the g
how much. We drop taxpayers who we suspect might have taken
measures from our dataset to get the mechanisms as clean as po
below. Hence, our analysis is more direct than the approach in
II. Data and Institutional Setting
Our entire dataset covers all 4.7 million Swedes 16-67 year
ment income and without any business income, filing their tax
the income year 2006. We have access to a limited number o
employment income, marginal tax rate, gender, age, claimed d
expenses for earning employment income," and the preliminar
due.
Taxable employment income includes salaries, social insur
fits (such as sickness benefits and parental benefits), and unem
reduced by the basic exemption.10 It also includes pensions, bu
6See, e.g., Elffers and Hessing (1997), Yaniv (1999), Dhami and al-Nowaihi (20
Zanardi (2004).
7See, e.g., Kirchler and Maciejovsky (2001), Schepanski and Shearer (1995), R
Copeland and Cuccia (2002).
See, e.g., Cox and Plumley (1988), Chang and Schultz, Jr. (1990), and Persson (200
9 That receiving a refund or having taxes due affects people's behavior has previously
ing other issues than compliance. Feenberg and Skinner (1989) find that owing a balance
prompts greater contributions to individual retirement accounts. Feldman (2010), howev
tax withholding while marginal tax rates were preserved, instead leads to reduced IRA c
10We do not have information on employment status, such as unemployment or sick
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VOL. 7 NO. 4 ENGSTRÖM ET AL.: TAX COMPLIANCE AND LOSS AVERSION 137
expected to have salary income and, therefore, any other expenses tor earnin
employment income. This explains the upper age limit in our sample.
The decision we study in this paper is whether or not the taxpayer claims
deduction for "other expenses for earning employment income" when filing their
tax return. Filing the tax return is one event in the annual sequence of taxpaying:1
employers withdraw preliminary taxes before the salary is paid to the employees
The Tax Agency decides on tax tables specifying employee tax withholdings, i.e.,
the amount that should be submitted directly to the Tax Agency.12 Hence, taxpayin
is typically perceived as automatic for Swedish taxpayers, i.e., there is no need to
take any action of their own.
In April the following year, the Tax Agency sends a preliminary income tax return
to the taxpayer. This tax return is based on the statements of income that the Tax
Agency has received from employers, banks, etc. Virtually all incomes are speci
fied on the tax return form, based on information reported through the legislated
reporting system. Moreover, the Tax Agency calculates a preliminary balance in
taxes due (actual tax liability—preliminary payments made), which is also written
on the tax return. Since preliminary income tax is withheld at source according to
the Tax Agency's tables, the preliminary balance is close to zero for most taxpayers
The preliminary balance may, however, show a deficit (more taxes due) or a surplu
(there will be a tax refund). When filing a tax return, the taxpayer may add missin
information. Because of the extensive reporting by employers etc., the taxpayer doe
not usually have much information to add, but could for instance claim deductions
for "other expenses for earning employment income."
The filing deadline is May 2. After this date, the Tax Agency calculates the fina
tax for the taxpayer, which depending on the preliminary tax payments may be
either a surplus or a deficit. Surpluses are refunded to the taxpayer's bank account i
June or August. If there is a deficit, the taxpayer has to pay the balance in November
or December.13 For the taxpayer there is almost no administrative cost in either case.
In case of a deficit, the taxpayer receives a payment slip from the Tax Agency.
The Swedish income tax system is dual in nature. Capital income is taxed at a flat
national rate of 30 percent, while employment income is taxed progressively and
by both the local governments (municipalities and county councils) and the central
government. Moreover, income taxes are based on individual, and not on household
income. Most Swedes only pay the local employment income tax, which in 2006
ranged from 28.80 to 34.24 percent. The local government employment income
tax consists of two parts—the municipality employment income tax and the county
council employment income tax. High-income earners pay an additional 20 percent
in central government employment income tax on the part of their taxable emplo
ment income that exceeds a threshold that was SEK 306,000 in 2006 and another
11 See also the information from the Tax Agency reproduced in online Appendix A.
12Analogous principles apply for capital income taxation (interest received and paid, dividends, etc.). As
Sweden has a dual income tax system, all capital incomes are taxed at source with 30 percent.
13 The interest paid on surpluses and the interest levied on deficits are independent of the filing date. However
for deficits smaller than SEK 20.000, no interest has to be paid if the taxes due are paid by May 4th at the latest.
deficit is an interest-free loan for quite some time whereas a surplus yields interest from quite early on during th
year. Online Appendix A presents the details that applied during the assessment year 2007. Therefore, the issues
that Slemrod et al. (1997) and Jones (2012) discuss for the United States do not arise in the same way in Sweden.
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138 AMERICAN ECONOMIC JOURNAL: ECONOMIC POUCY NOVEMBER 2015
5 percent on the taxable employment income that exceeds
was SEK 460,600 in 2006.14 Hence, the Swedish employm
gressive with three brackets. Threshold incomes are the sam
whereas the local employment income tax varies across the c
About 75 percent of the taxpayers in the 4.7 million
employment income lower than SEK 306,000 and therefore
ment income tax, which on average is 32.8 percent. The sh
have a taxable employment income in the interval SEK 3
18 percent. These taxpayers pay the local income tax plus a
their taxable employment income in excess of SEK 306,0
The marginal tax rate in this second tax bracket is 52.8 per
remaining 6 percent of the taxpayers have a taxable emplo
than SEK 460,600. These taxpayers pay the local governmen
central government income tax of 20 percent of taxable emp
SEK 306,000 and an additional 5 percent on taxable emp
SEK 460,600. The average marginal tax rate in this third tax
Final taxes on employment income are determined by the
earned during the full year. However, preliminary taxes on
paid monthly by employers and are estimated assuming the
employment income every month throughout the year. Dev
nary and final taxes are in most cases small and exogenous t
So why may preliminary tax balances deviate from zero at
government part of the employment income tax is levied is a
actual tax rates are set with two decimals of a percentage (fo
or 31.12 percent). The tables for preliminary taxes are, h
ing integer percentages tax rates at source (for example, 31
municipalities for which the tabled tax rates at source are ab
tend to pay too much in preliminary taxes. The opposite ap
municipalities with actual rates higher than the rates used a
that a higher share of those having the preliminary tax rat
preliminary surpluses than those having the preliminary t
wards. The difference is 3.1 percentage points.
The local tax rate is the result of decisions in two separate
ipality and the county council (covering several municipaliti
290 municipalities in 20 counties. Thus, it would be extreme
municipality to set the local tax rate strategically trying to
ples for taxation at source. This would require correctly pre
response of the county council. It would be even more diffic
cil to act strategically in this respect, since it would involve
of several municipalities. It would, consequently, also be very
to predict where to move to take advantage of a lower preli
it should be reasonable to assume that the actual tax rate is
individual taxpayer.
1 In 2006, it corresponded to US$41,460 and US$62,410, respectively.
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VOL. 7 NO. 4 ENGSTROM ETAL. : TAX COMPLIANCE AND LOSS AVERSION 139
0.02:
Preliminary tax rate above actual tax rate
0.005
-6
-4-2
0
2
Preliminary
Figure 2. Relative Frequency Distributions for Taxpayers with
Preliminary Tax Rates Rounded Upwards and Downwards
From Figure 2 it is also apparent that the rounding error is hardly the only
of deviation between preliminary taxes and final taxes. The progressive centra
ernment part of the employment income tax is another possible reason why t
ance may deviate from zero. Employers withhold preliminary taxes according t
Tax Agency's tax tables, which assume that the income stays the same every m
If income varies a lot during the year, the tax withholdings may be misjudged
preliminary taxes may be higher or lower than final taxes. For taxpayers cl
the thresholds between the tax brackets, unanticipated events may create a no
balance. Benefits from the social insurance systems are included in employm
income, but the replacement rates are below 100 percent. Absenteeism may
fore affect the preliminary balance and so may overtime work. A taxpayer
varying employment income over the year will tend not to pay the same amo
preliminary taxes as a taxpayer with the same annual employment income e
distributed over the year. Flaving several employers might also result in insuf
withholdings at source. If every employer withdraws taxes as if they were th
employer, progressivity may result in not enough preliminary taxes being paid
Deviations from a zero preliminary balance may also arise from capital inc
taxation. Interest on loans is deductible at the 30 percent capital income tax
which is not automatically taken into account in the preliminary taxes. Taxp
who pay deductible interest may therefore have preliminary surpluses. Unfortunat
we do not know the taxpayers' deductible interest payments, so we cannot dir
control for this in our analysis.15 This is probably an important source of he
neity in the preliminary balances and may explain why a majority have a prelim
15 On a macro level during 2006, however, 4.7 million of the total Swedish population had deductible in
payments, i.e., a majority of the taxpayers.
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140 AMERICAN ECONOMIC JOURNAL: ECONOMIC POLICY NOVEMBER 2015
Table 1—Construction of the Sample
N
AN
Original sample 4,674,003
Advance payments - 310,094
Missing values for preliminary deficit —281
Taxable employment income < SEK 100,000 —735,952
Taxable employment income > SEK 1,000,000 —16,704
Full sample 3,610,972
surplus.
for
the
the
total
Since
most
taxpayer
tax
taxpayer
to
precisely
liability.
Our objective is to study th
fore want to exclude individ
This is an important differe
means to affect the balance
Agency to be exogenous to
exclude some taxpayers from
Our
original
sample
consi
ment income and without a
taxpayers as they can affec
then exclude taxpayers who
the Tax Agency at their ow
The reason is that these adva
deductions. The preliminary
ers. We exclude them from t
analysis.
Finally, only taxpayers with "normal" annual taxable employment incomes are
included in our sample. We interpret normal annual taxable employment income to
be in the interval SEK 100,000-1,000,000.17 These selection criteria leave us with
a full sample of 3.6 million taxpayers. Descriptive statistics for the full sample are
presented in Table 2.
These 3.6 million taxpayers are studied with respect to deduction behavior.
Taxable employment income could be reduced through approved deductions for
"other expenses for earning employment income" exceeding SEK 1,000 during the
income year 2006. The expenses thus did not have to be large and the specifications
16 There are incentives for taxpayers with preliminary deficits larger than SEK 20,000 to make advance tax
payments before mid-February to avoid having to pay extra interest. See online Appendix A for more information
on interest rates, etc.
17This corresponds to an annual income of US$13,550-$135,000 in 2006. Less than 0.5 percent of our sample
had incomes exceeding SEK 1,000,000. On the other hand, about one-sixth had an income lower than SEK 100,000.
However, we need to exclude those with the lowest incomes since there will be a nontrivial share that bunch at
exactly zero preliminary balance simply because they have zero tax liability. Where the exact cutoff should be is,
however, not easily determined. We therefore made robustness checks based on a SEK 50,000 cutoff instead and
the results remained almost the same.
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VOL. 7 NO. 4 ENGSTRÖM ETAL. : TAX COMPLIANCE AND LOSS AVERSION 141
Table 2—Descriptive Statistics
Full sample Maximum bandwidth sample*
Preliminary
deficit
Preliminary
surplus
Preliminary
All
deficit
Preliminary
surplus
All
810,690
2,800,282
370,929
822,686
Deducting, fraction
0.062
0.044
0.048
0.061
0.042
Deduction, SEK
1,000, conditional
4.72
3.56
3.89
4.21
3.71
3.91
(4.32)
(3.34)
(3.69)
(3.81)
(3.40)
(3.58)
Number of observations
Preliminary balance,
SEK 1,000
Taxable employment
income, SEK 1,000
-10.76
(51.23)
280.1
(136.1)
0.48
Men, fraction
Age, years
Marginal tax rate,
percent
Municipal tax rate,
percent
3,610,972
6.55
2.67
(6.76)
(26.02)
269.1
(115.1)
272.1
(120.1)
0.49
0.49
-1.29
(1.14)
278.1
(131.1)
0.49
1,193,615
0.048
1.61
0.71
(1.15)
(1.77)
277.1
(119.1)
0.50
277.1
(123.1)
0.49
46.8
42.0
43.1
44.9
43.1
43.7
(12.5)
(12.1)
(12.3)
(12.5)
(12.3)
(12.4
39.6
37.5
38.0
38.7
37.9
38.1
(8.8)
(9.1)
(9.6)
(9.1)
(9.3)
32.8
32.8
32.8
32.8
32.8
32.8
(1.0)
(1.0)
(1.0)
(1.0)
(1.0)
(1.0)
(10.0)
Note: Mean (standard deviation).
*Sample selection criterion: weighted preliminary balance in the interval ± SEK 3,000.
were quite vague.18 Hence, there was room for (small scale) tax noncompliance by
means of this deduction.
There are some studies of randomly audited claimed deductions for "other expens
es."19 The overall finding is that 90-95 percent of the claims were not approved. In
some cases, the taxpayer may simply not understand the rules and believe that he
is entitled to the deduction. The taxpayer may knowingly take a chance in other
cases. We cannot, therefore, know whether certain deductions are due to tax evasion,
tax avoidance, or something else. Some claimed deductions are, however, clearly
not due to noncompliance. This is likely to be true especially for large claimed
deductions. Large deductions are more often accurate than small (Persson 2003).
This is an important reason for only including relatively small deductions for "other
expenses." Hence, we concentrate on deductions smaller than SEK 20,000.
It was almost without risk to claim small incorrect deductions in 2007 as the
audit probability was very low for small claimed amounts. Moreover, the taxpayer
was only required to pay the increased tax liability if the claimed deduction was
audited and not approved. There were no fines for incorrectly claimed deductions of
small amounts.20 Neither were there any fines for large rejected deductions provided
18 Some examples that could be approved are expenses for safety equipment, safety clothes, tools, and instru
ments related to work not paid for by the employer, expenses for an office if the employer does not provide one (an
office at home is not approved in general), expenses for books and journals related to work for some occupations if
not paid for by the employer, and expenses for phone calls related to work if not paid for by the employer (not the
phone and not fixed costs for phone service). No receipts have to be submitted to the Tax Agency, but they need to
be ready to show in case of an audit.
19See Riksskatteverket (2001) and Persson (2003).
20The tax law has changed since. The threshold value that expenses have to exceed before the tax liability decreases
was increased considerably. It is no longer possible to claim deductions of amounts smaller than SEK 5,000.
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142 AMERICAN ECONOMIC JOURNAL: ECONOMIC POLICY NOVEMBER 2015
0.25
0.20
0.15
0.10
0.05
0.00
6
8
10
12
14
Deducted
amount,
SEK
Figure 3. Frequency Distribution of Deducted Amounts
that the taxpayer could prove having had the expenses for which the deduction was
claimed. The choice to claim a deduction was, therefore, completely without risk.
The 3.6 million taxpayers in our full sample should not have had perfect knowl
edge or control of their preliminary deficit. The closer the preliminary balance is to
zero, the more likely it should be that it is truly random whether one ends up with a
surplus or a deficit. In part of the analysis we, therefore, focus on taxpayers with a
preliminary balance in the interval SEK ± 3,000. There are 1.2 million subjects in
this subsample, which we label the maximum bandwidth sample. Descriptive statis
tics for this sample are also presented in Table 2.21 Our approach is that the deduc
tion behavior of these taxpayers can be viewed as a quasi-experiment.
In Table 2, we note that a larger fraction with a preliminary deficit than with a pre
liminary surplus claim the deduction, in both the full and the maximum bandwidth
sample. We also see that, conditional on claiming a deduction, taxpayers with a
preliminary deficit on average claim larger deductions than those with a preliminary
surplus. Hence, the unconditional deduction is almost twice as large on the deficit
side as on the surplus side. Figure 3 shows the frequency distribution of deductions
in the full sample. Most deductions are fairly small and those in the gain domain
(the dotted line) are more concentrated than those in the loss domain (the solid line).
Suppose that those in deficit had behaved as those in surplus on both the extensive
and intensive margin. The overall tax revenue loss due to the deduction would then
be 17 percent lower (and the one stemming from those with a deficit would be
46 percent lower).
21 This sample is based on the preliminary deficit being weighted by the taxpayer's employment income for
reasons that will be explained in Section IV. Weighting increases the probability of including taxpayers with high
employment income in the sample. Employment income and deduction probability are positively correlated. This is
the reason why the deduction probabilities reported in Table 2 in online Appendix B are slightly higher than those
shown in Figure 1.
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VOL 7 NO. 4 ENGSTRÖM ETAL. : TAX COMPLIANCE AND LOSS AVERSION 143
Just from the descriptives of both samples, we see that among those who ha
a preliminary deficit, the probability of claiming a deduction is about 50 percen
higher than among those who have a preliminary surplus. Due to this and to the f
that they on average claim larger deductions, the average taxpayer on the deficit s
reduces his tax payment by twice as much as the average taxpayer on the surpl
side by means of the deduction.
III. An Illustrative Theoretical Model
The purpose of this section is to provide predictions for our empirical exerci
We apply loss aversion and reference dependence to a simple model of dec
making.
Consider a taxpayer i who is about to file his tax return. He receives information
about his preliminary tax balance on the tax return. Taxpayer i has taxes due if he
has a preliminary deficit, D, > 0, and will receive a refund if he has a preliminary
surplus, D, < 0. He compares the preliminary deficit with his reference point.
There has been a lot of discussion about what the valid reference point should
be.22 Dhami and al-Nowaihi (2007) argue that legal after-tax income should be used
as the reference point. This is related to the idea that the reference point should be
based on rational expectations (Köszegi and Rabin 2006), i.e., how much the tax
payer expects to owe or get refunded. Schepanski and Shearer (1995), however, find
that the current asset position is a more relevant reference point for taxpayers than
the expected asset position. Hence, like in many other areas, status quo seems to be a
natural reference point also when filing tax returns. Also Elffers and Hessing (1997)
and Yaniv (1999) argue for status quo as the reference point when analyzing tax
compliance. Therefore, we assume that a zero balance is the reference point for the
taxpayer when filing their return, an assumption also made by Rees-Jones (2014).23
Hence, if Dt > 0, the taxpayer experiences himself to be in the loss domain. He will
be in the gain domain if D, < 0.
The value function with reference dependence and loss aversion is:
-vD, if D, < 0,
(l)
v(A)
=
-AvD, if D, > 0,
where A > 1 is the coefficient of loss aversion.
We follow, e.g., Benartzi and Thaler (1995), Schmidt and Traub (2002), and
Pope and Schweitzer (2011) and assume a linear value function. This implies con
stant marginal values. We disregard strict concavity in the gain domain and strict
convexity in the loss domain by this assumption. Utility tends, however, to be almost
22 See, e.g., the discussion in Kirchler and Maciejovsky (2001).
23 One could argue that since tax filing is a recurring event, previous preliminary balances may be the relevant
reference point. Since our data does not contain information on previous years and our theoretical model therefore is
a one-period model, we rule out this possibility in the present paper. In Section VB, however, we present sensitivity
analyses allowing the reference point to be endogenous.
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144 AMERICAN ECONOMIC JOURNAL: ECONOMIC POUCY NOVEMBER 2015
linear over very small intervals. A linear approximation sh
since we limit our analysis to a narrow area around zero.
A. Whether to Deduct or Not
A first step is to predict the probability of claiming a deduction to reduce one's
tax liability.
The taxpayer's only choice is whether or not to claim a deduction of a fixed
amount, ö, which is the same for all taxpayers. We analyze what affects the deduc
tion probability. The amount <5 is sufficiently small to ensure that the taxpayer per
ceives to be at no risk of being audited if he claims the deduction.24
Claiming the deduction ö comes at a certain cost, c,-. This cost varies across tax
payers, ct ^ U[0, c]. It may reflect the administrative cost of claiming the deduction
or the moral cost of doing so if the deduction is not legitimate. The deduction is
worth tö, where t is the constant marginal tax rate.
The taxpayer compares the value of his preliminary tax balance, V(—Dt), to the
value if he claims the deduction, V{tô — Dt) — q. He claims the deduction if the
latter exceeds the former. There are three different domains where the taxpayer may
end up depending on the sign and size of Dt. The three conditions for claiming the
deduction S are:
A: q < vtö if Dt < 0,
(2) B: q < v[tö + D,(A - 1)] if A € (0,f<5],
C: c, < XvtS ifD, > tö.
The value of the deduction in the three cases a
The assumption of a uniformly distributed co
conditions (2) to predict the share of taxpayer
preliminary deficits. The share is increasing in
claiming the deduction in the loss domain is lo
A larger share of the taxpayers should, therefo
the gain domain. For those with a positive bala
should be independent of the preliminary bal
The same applies for those with a large prel
still will have a deficit even after the deducti
Di e (0, f<5], that the share of taxpayers claim
liminary deficit:
A = v[fj + A(A - 1)],
(3)
i = v(A-l)>0.
24Contrary to previous studies of tax compliance, we abstract from detection risks in our model. Our main
results, however, remain valid even if we include a risky choice of noncompliance.
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VOL. 7 NO. 4 ENGSTRÖM ETAL. : TAX COMPUANCE AND LOSS AVERSION 145
Figure 4. The Value of Claiming a Deduction in
Three Cases Depending on the Preliminary Deficit
We then predict the pattern for the share of taxpayers claiming the deduction to b
as shown in Figure 5.
The pattern in Figure 5 can be summarized as follows:
PREDICTION 1 : The share of taxpayers who will claim the deduction 6 is larger
among those with a preliminary deficit than among those with a preliminary surplus.
PREDICTION 2: The probability of claiming the deduction S, as a function of the
preliminary deficit, has the shape as in Figure 5 with kinks at D = 0 and at D = td.
How important is loss aversion in terms of magnitude? Loss aversion implies
that the utility (or value) function is steeper for gains than for losses, but how
much steeper? The coefficient of loss aversion, A, should capture this. There is no
overall consensus on how A should be measured. Tversky and Kahneman (1992
originally defined it as the ratio of utilities: A = — U(— 1) / C/( 1). Köbberling and
Wakker (2005) instead propose the following definition, which is independent of
unit of payment: A = U\{0) / t/[(0). This was also informally suggested by Benartz
and Thaler (1995). The two definitions are equivalent when the value function is
linear. Abdellaoui, Bleichrodt, and Paraschiv (2007) summarize and discuss various
methods of measuring A.
Our approach is different. We observe a large number of people in the gain
domain and in the loss domain. It is, therefore, possible to estimate an aggregate
coefficient of loss aversion. We plot the shares claiming the deduction for each leve
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146 AMERICAN ECONOMIC JOURNAL: ECONOMIC POUCY NOVEMBER 2015
p(S>0)
tS
Figure 5. Share of Taxpayers Claiming the Deduction Depending on the Preliminary Deficit
of preliminary deficit as sketched in Figure 5. The share claiming the deduction in
the gain domain is:
(4) /J!S0Ac)dc = x
We observe the actual share, X, in our data. Since the cost is assumed to be
formly distributed, (4) is easily solved to yield:
(5)
The share claiming the deduction in the part of the loss domain where D, > tS is:
(6) £tUc)dc = y
A vtô _ y
Equations (5) and (6) then give A = Y/X. Hence, the coefficient of loss aversi
simply the ratio between the two shares claiming the deduction.
PREDICTION 3: If the cost of claiming the deduction, c, ^ f/[0, c], then the
cient of loss aversion, A, is
X - I
X'
where Y is the share claiming the deduction in the part of the loss domain
Dj > tö and X is the share claiming the deduction in the gain domain.
We will use this prediction to estimate the coefficient of loss aversion, A
Section VIB.
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VOL 7 NO. 4 ENGSTRÖM ETAL.: TAX COMPLIANCE AND LOSS AVERSION 147
B. The Amount Deducted
In this subsection, we derive the empirical predictions from a more general
model. We now drop the assumption of an identical deducted amount and instead let
the deducted amount vary between individuals.
Assume the deduction cost function
Ci = C (Si, Ci),
where c is the individual's cost parameter (independent of D by assumption) and 6
is the size of the deduction. F(c, D) is the conditional distribution function of c. As
above, we make the key assumption that F(c,D) = F(c), i.e., that the distribution
of c is independent of D. In addition, we make the following standard assumptions
(in the following, we suppress subindex i):
(s > 0 (deductions are costly)
(ss > 0 (strictly convex cost function)
C > 0 and (sc > 0 for <5 > 0 (costs and marginal costs of deductions increase in c)
c = Ç(<5, c) is independent of D.
We stick to the same linear value function as in Section IIIA, so the marginal value
of a deduction is MVd = Avt on the deficit side and MVS = vt on the surplus side.
Given A > 1, it follows that MVd > MVS.
The Intensive Margin.—Conditional on claiming a positive deduction, the size (S )
will generally be given by the condition:
(7) MV = (s(S,c).
However, some individuals will bunch at
value of a deduction takes a discontinuou
taxpayer who bunches at zero, the above
effective marginal value MVb e [MVS, MV
Differentiation of equation (7) gives
<8> mv > °
LEMMA 1 : Consider an individual i wh
less of his initial deficit (Dfi Then 8i{D
make a weakly larger deduction on the de
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148 AMERICAN ECONOMIC JOURNAL: ECONOMIC POUCY NOVEMBER 2015
PROOF:
The result follows directly from equation (8) since MV(D, > 0) is either M
MVj,, or MVS (depending on the ex post position), while MV(Dl < 0) - MVS.
The Extensive Margin.—When determining whether a taxpayer will claim a d
tion or not, we need to compare the total value of a deduction with the total cost
total cost is independent of D by assumption, so we only need to focus on the v
The total value (V) of a deduction is simply the integral over marginal values, i.e
(9) V(D, S) = f°_tSMVdx.
LEMMA 2: (/) The value of a deduction will kink upwards at D = 0 when A
(ii) The value of making a deduction is always higher for D > 0 than for D
PROOF:
(i) Equation (9) directly gives
Vd(D, Ö) = OifD < 0
Vd(D,S) = MVd - MVS = (A - l)r > OifD = 0.
(ii) This follows directly from equation (9) and the fact that MVd > MVS. I
Empirical Predictions.—The model renders two empirical predictions that can
be taken directly to data. However, before deriving those, we need one last lemma
LEMMA 3: A taxpayer i with a given cl will make weakly larger deductions when
starting on the deficit side (D, > 0) compared with the surplus side (D, < 0).
PROOF:
Follows directly from Lemma 1 and 2 above. ■
For the extensive margin we get the following empirical prediction, which
analogous to Predictions 1 and 2 above.
PREDICTION 4: (/) The share of individuals who claim a positive deduction
kink upwards at D — 0. (ii) The fraction of individuals who claim a deduction
always be higher on the deficit side.
PROOF:
Follows directly from Lemma 2 when assuming that F(c) has support in the rel
evant domain. I
It is natural that the (negative) kink in deduction we found at D = tô (see
Figure 5) will not prevail in this more general model where different taxpayers make
deductions of different sizes.
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VOL 7 NO. 4 ENGSTRÖM ETAL.: TAX COMPLIANCE AND LOSS AVERSION 149
In addition to this, we find the following empirical prediction concerning th
unconditional average deduction size (Eö(c,D)).
PREDICTION 5: (i) The unconditional average deduction size will kink upwa
at D = 0. (ii) The unconditional average deduction will always be higher on
deficit side.
PROOF:
Follows directly from Lemma 3 and Prediction 4. ■
When turning to the expected size of the conditional deductions (£[<5(c, D)\6 > 0] )
the model does not make any clear predictions. The reason is that there are two c
teracting effects. On the one hand, we know that a given taxpayer (i.e., a given
will make a larger deduction in the deficit domain. But on the other hand, the
age c, among those who claim a positive deduction, will be higher on the deficit
since the incentives to claim deductions are higher. Now, since Qc > 0 (the ma
ginal cost of a deduction increases in c), this will have a counteracting effect on
average size of the conditional deductions on the deficit side. Theoretically, ei
effect could outweigh the other. Consequently, we would expect to find both
largest and the smallest deductions on the deficit side, while the average conditi
deduction size may be both higher or lower on the deficit side.
C. Summarizing Theoretical Predictions
The model demonstrates that the incentives to claim a deduction are stronger
the loss than in the gain domain. The probability of claiming a deduction is hig
in the loss domain and kinks at D = 0. Also the unconditional amount deducted
is higher in the loss than in the gain domain and also kinks at D = 0. Concerning
the conditional amount, however, we do not have any clear theoretical prediction.
Assuming that the costs to claim the deduction are uniformly distributed among the
taxpayers, the coefficient of loss aversion, A could be estimated as the ratio between
the shares of taxpayers claiming the deduction in the loss and in the gain domain.
IV. Descriptives
Theory predicts that the share claiming deductions, under certain assumptions,
could be illustrated as in Figure 5. We note that the actual behavior presented in
Figure 1 is very similar to this. A larger share of those with a preliminary deficit
claims a deduction for "other expenses" than those with a preliminary surplus. The
share claiming a deduction is independent of the preliminary balance for those with
a surplus as predicted by theory. Less than 4.5 percent of those with a preliminary
surplus claim a deduction for "other expenses." The share is, however, increasing in
the preliminary deficit for those with a deficit.25
25 As this kind of deduction was practically riskless, the share of taxpayers claiming the deduction may seem
surprisingly low. However, Swedes have a high degree of tax morale in an international comparison. This might
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ISO AMERICAN ECONOMIC JOURNAL: ECONOMIC POLICY NOVEMBER 2015
120,000
90,000
0
>%
03
CL
X
Z
60,000
30,000
-3,000
-2,000
-1,000
0
1,000
2,000
3,000
Figure 6. Frequency Distribution of Preliminary Deficits
Moreover, theory predicts that more will be deducted in the loss than in the gain
domain and also that the amounts are more spread in the loss than in the gain domain.
From Table 2 and Figure 3, we learned that not only the share claiming deductions,
but also the conditional amount deducted is larger in the loss domain than in the
gain domain. Hence, unconditional deductions in the loss domain exceed those in
the gain domain as predicted by theory.
Although the observed patterns are in line with theory, we cannot be certain that
they are caused by the preliminary balance; there may be an endogeneity problem.
Plotting the distribution of individuals over preliminary deficits is a simple graphi
cal test of this: If the distribution changes dramatically around zero, the individuals
slightly above zero preliminary deficit will not be representative of those slightly
below. Figure 6 shows that the distribution does not seem to kink or jump at zero,
so at first inspection there is no indication of any selection or endogeneity problem.
We could, however, still have problems with selection that do not show up in the
frequency distribution plot. The individuals slightly below zero could be very dif
ferent from the individuals slightly above even if the distribution is smooth around
the reference point. We, therefore, need to look closely at how the covariates evolve
around the reference point. Suppose there is selection based on any of the covariates
or on any unobservable factor that is correlated with the covariates. This would show
up as a kink or discontinuity around zero. The pattern in Figure 1 could then be due
to selection. If, on the other hand, all covariates evolve smoothly around zero, the
deduction pattern is likely to be caused by differences in the preliminary balance.
Here we will present descriptive tests if the predetermined covariates show kinks
or discontinuities at zero preliminary balance. The formal econometric tests are pre
sented in Section V.
explain why many do not claim a deduction without actually having had any "other expenses" when the potential
gain is only a couple of thousand SEK.
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VOL. 7 NO. 4 ENGSTROM ETAL.: TAX COMPLIANCE AND LOSS AVERSION 151
400,000
[J]
W
-
300,000
--
--
--
-
Weighted
a
Unweighted
200,000
E
>
o
Q.
E
100,000
-3,000 -2,000 -1,000 0 1,000 2,000 3,000
Figure 7. Employment Income as a Function of the Preliminary Deficit
Employment income is a crucial variable. The diamonds in Figure 7 show
relationship between preliminary deficit and employment income. The kink slig
below zero preliminary deficit could be explained as follows. The higher the em
ment income, the more difficult it is to calibrate the tax payments at source correct
the deviations will be scaled up in proportion to the income. Higher employm
income will, therefore, move us further away from zero preliminary balance. Th
exactly the pattern we see in the unweighted version of the relationship.
The unweighted relationship in Figure 7 suggests that we do not have a
rect specification. It could be argued that the marginal utility of claiming a d
tion is higher for a low-income taxpayer. The mechanical kink that is visible
the unweighted relationship should, however, disappear if we instead mea
preliminary deficit in relation to employment income. We therefore define t
weighted preliminary deficit of taxpayer i as:
(10) 4- = (E/E) x D„
where Di is the unweighted preliminary defic
income of taxpayer i, and Ë is average employ
liminary deficit disappears when we measure
employment income; see the squares in Figure
The other conditioning variables do not seem
zero preliminary deficit. Figures 4 and 5 in on
matter whether we use unweighted or weighte
If we weight the preliminary deficit when w
the same when studying the outcome variable
diamonds from Figure 1, squares showing the
similar. Hence, from the graphs we conclude t
a lot at the point of zero deficit, while none of
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152 AMERICAN ECONOMIC JOURNAL: ECONOMIC POLICY NOVEMBER 2015
0.08,
-3,000 -2,000 -1,000 0 1,000 2,000 3,000
Figure 8. The Share Claiming a Deduction as a Function of the Preliminary Deficit
This suggests that it is actually the deficit itself that causes the behavioral d
ence. However, this is not a formal test, so we continue to the next section, w
we use econometric methods to formally test causality.
V. Estimations
A. Baseline Models
In this section we formally test whether the observed relationship between
liminary deficits and deductions is causal and not due to selection. We follow s
of the empirical strategies suggested in previous work on the regression discont
ity design (Lee and Lemieux 2010) and regression kink design (Card, Lee, and Pe
2009). The empirical tests essentially consist of answering two questions:
• Does the relationship between the preliminary balance and deductions have
statistically significant kink or discontinuity around zero preliminary balan
Can we rule out corresponding statistically significant kinks or discontinuiti
for the predetermined covariates?
If the answer is "yes" to both these questions, it is reasonable to interpret t
relationship as causal.
We will study three, closely related outcome variables that were included in th
theoretical section: the probability of claiming a deduction—the extensive mar
the unconditional amount deducted; and the amount deducted, conditional on cla
ing a deduction. Recall that the theoretical model predicted positive kinks at ze
preliminary deficit for the first and second outcomes (the extensive margin and
unconditional size of deductions), while the theoretical predictions for the third
come (the conditional size of deductions) were ambiguous.
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VOL. 7 NO. 4 ENGSTROM ETAL.: TAX COMPUANCEAND LOSS AVERSION 153
Recall that theory does not predict any discontinuities at zero p
ance in the relation between preliminary deficit and any measure of
completeness, however, we also allow for potential discontinuit
metric specification. A positive discontinuity in, e.g., the probabi
a deduction would be consistent with a fixed subjective cost of en
preliminary deficit—a fixed cost of "losing." Even though such m
predicted by ordinary loss aversion, it would still be a clear indicat
dependence.
Formally, we estimate spline models of the following type (the a
ates: age and gender are suppressed):
(11) A,- — "Y^ctkdj -F ^jßklidf + €j,
k=0
where
4
is
A,
the
is
k=0
the
outcome
(weighted)
measures
the
variable,
preliminary
intercept,
ß0
/,
is
def
measures
(zero preliminary deficit), and ß\ m
The polynomial k ranges from 0, w
nuity at zero preliminary balance, t
ification should be appropriate very
flexible specifications, in particular
We iterate the estimation of each o
many bandwidths. Bandwidths go f
most and SEK ± 500 at the least. W
ence point.26 A bandwidth of SEK
with weighted preliminary balance
A large bandwidth gives a larger sam
A smaller bandwidth, on the other h
estimates. There are 1.2 million taxp
±
3,000)
as
previously
mentioned.
200,000 taxpayers with weighted p
The optimal nonzero polynomial m
determined based on minimizing a
mation criterion weighs better good
is
a
modification
freedom
the
data
two
harder.
best;
(zero).
of
only
Based
the
Akaike
Overall,
for
on
the
very
these
info
SBC
large
m
(s
findings,
estimates based on the linear mode
linear model are reported for a rang
Our primary interest is in the ß\ e
tions from Section III. The ßx param
26We use a logarithmic scale when we iterate ov
at lower bandwidths than at higher bandwidths a
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154 AMERICAN ECONOMIC JOURNAL: ECONOMIC POLICY NOVEMBER 2015
2.9 2.5 2.2 1.9 1.6 1.4 1.2 1.1 0.9 0
Bandwidth, SEK thousands
Figure 9. Kink—Estimates of 0t on the Probability of Deducting
the reference point or, in other words, the kink. As mentioned above, we are also
interested in whether there is a discontinuity at the reference point. This is measured
by ß0.
Figures 9, 10, and 11 report our estimates of a possible kink at zero preliminary
balance, for the three separate outcome variables. Starting with the extensive mar
gin—the probability of claiming a deduction—we find the following. The estimated
kink is significant for all bandwidths except around SEK 700. The thick solid line
reports the estimated coefficients while the thin lines provide the limits of 95 percent
confidence intervals. The estimated coefficients remain stable and positive in a wide
range of bandwidths from SEK 2,500 to SEK 800. The estimate starts to fluctuate a
lot for very narrow bandwidths. However, the overall pattern indicates a stable and
significant positive kink in the deduction probability.
Turning to the second outcome variable—the unconditional deduction amount—
we find a very similar pattern. As seen in Figure 10, we estimate a positive and
stable kink throughout the whole range of bandwidths. The optimal model is linear
for bandwidths above SEK 800 and the estimates are significant for bandwidths
above SEK 900. We thus find clear evidence of a positive kink in the unconditional
deducted amounts.
For the third outcome variable—the amount deducted, conditional on deducting—
the results are much less clear, however. From Figure 11 it is apparent that the kink
estimates are generally insignificant and the point estimates fluctuate between pos
itive and negative. It is only for bandwidths above SEK 2,000 we find positive and
significant kink estimates. Furthermore, the zero order model is optimal for band
widths below SEK 1,800.
It is also possible, though our theory does not predict so, that there is a discon
tinuity in the relationship between the preliminary deficit and our three different
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VOL. 7 NO. 4 ENGSTROM ETAL.: TAX COMPLIANCE AND LOSS AVERSION 155
200
150
100
50
— ^ , ,y >✓
2.9 2.5 2.2 1.9 1.6 1.4 1.2
1.1 0.9 \0.8 JQ.7 O.e
* 0.5
-50
-100
Bandwidth, SEK thousands
Figure 10. Kink—Estimates of ß\ on the Unconditional Amount Deducted
600 '
400
- 200
c
0)
o
3=
©
O 2.9 2.5 2.2 1.9 1.6 1_.4^^1.2
TO
CD
ra -200
E
"So
LU
—400
-600
-800 '
Bandwidth, SEK thousands
Figure 11. Kink—Estimates of on the Conditional Amount Deducted
measures of deductions. Figures 1-3 in online Appendix B report our
of these. The empirical evidence of discontinuities at the reference point i
rather weak compared with the evidence of kinks. We find the strongest e
a discontinuity for the extensive margin, i.e., the probability of claimin
tion. Concerning the unconditional amount of deductions, Figure 2 shows
pattern. The discontinuity estimate decreases when the bandwidth decrease
overall level of significance is lower than in Figure 10. Finally, we find no
at all of a discontinuity in the conditional amounts.
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156 AMERICAN ECONOMIC JOURNAL: ECONOMIC POUCY NOVEMBER 2015
We now turn to the corresponding estimates for the three covari
responding to Figures 9-11 and the figures in online Appendix B a
online Appendix C. The results for employment income show that t
is negative and significant for bandwidths between SEK 2,700 and
polynomial order would, in fact, be optimal for smaller bandwidths
ity estimate is only significant for a narrow range of bandwidths be
and SEK 1,000. We continue with the gender indicator. The opti
order is always one. There is a significant negative kink for large
discontinuity estimates are almost always insignificant.
The corresponding results for age show decreasing kink estimates
lower than SEK 2,500. The estimates become insignificant belo
of about SEK 1,400. The optimal polynomial order is one except
bandwidths. The discontinuity estimates are insignificant for band
SEK 1,900.
Let us compare the results for the two outcomes where our theory
(the extensive margin and the unconditional deduction amounts) w
sponding results for the covariates. The estimated kinks for the cov
more unstable. The results for the deduction probability and uncond
show a stable and significant kink for a wider range of bandwidth
covariates. Hence, these results suggest that we can make a causal i
the pattern we see in the data. However, the kinks for the covariate
about omitted factors. This is one of the motivations for the sensitiv
follows.
B. Sensitivity Analysis—Placebo Kinks and Discontinuities
The above analysis shows that the patterns predicted by prospect theory are sup
ported by data.27 However, we also find evidence of kinks and discontinuities—
albeit unstable over different bandwidths—for the covariates. This could be a sign of
selection. On the other hand, there is a risk that even small and economically insig
nificant estimates become statistically significant when the sample size is very large.
It is thus relevant to ask whether kinks and discontinuities at the zero reference
point are more pronounced than kinks and discontinuities at other reference points.
We, therefore, present estimates of kinks and discontinuities based on a range
of different placebo reference points. We let the reference points vary between
SEK —3,000 and SEK 3,000. The bandwidth—symmetric around the placebo refer
ence points—is fixed at SEK 1,000 in all regressions.
The analysis serves several closely related purposes. The evidence of causal
effects becomes stronger if we find that the kinks and discontinuities in deduc
tion measures (deduction probability and unconditional deduction size) are more
pronounced for the theoretically predicted reference point than elsewhere. We might
also fear that selection is driving the increase in deduction probability around zero
27The main analysis is made on all Swedes of working age, i.e., 16-67, but the results are robust to narrower
age grouping as well, such as 18-64 or 25-59 years. Results are available on request.
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VOL. 7 NO. 4 ENGSTRÖM ETAL. : TAX COMPLIANCE AND LOSS AVERSION 157
if the kinks and discontinuities for the covariates are more pronounced around
than elsewhere.
Figure 12 in online Appendix D shows the estimated kinks in deduction proba
bility for different placebo reference points. The kink-estimates peak slightly below
zero at a reference point of SEK —180, which we interpret as zero.28 When the pla
cebo reference point enters the deficit side, the kink estimates turn negative and sig
nificant for reference points in the range SEK 500-1,000. This is consistent with the
concave increase in the deduction probability for those with a preliminary deficit;
see Figure 1. The information criterion prefers a zero polynomial order for reference
points above SEK 1,700 and below SEK 1,000, and the linear model is preferred
elsewhere. The corresponding discontinuity estimates mirror the kink estimates.
There is a local peak in the discontinuity estimates for reference points close to zero
(see Figure 13 in online Appendix D).
Turning to the placebo estimates for the unconditional amounts, we find a sim
ilar pattern. The kink estimates peak slightly below zero preliminary deficit, just
as theory predicts. There are no significant kinks or discontinuities elsewhere (see
Figures 14 and 15 in online Appendix D). The last outcome variable, the conditional
amounts, shows no significant kinks or discontinuities at all (see Figures 16 and 17
in online Appendix D). This is also in line with the theoretical predictions.
To sum up the placebo estimations for the outcome variables, we can conclude
that the results for the three outcome variables are in line with theory.
We now turn to the corresponding analysis of the covariates (online Appendix D
has the figures). We find that neither kink nor discontinuity estimates are more pro
nounced around the zero reference point than elsewhere for any of the covariates.
We, therefore, conclude that selection is a very unlikely source of the increase in
deduction probability around zero. It would require very strong selection on some
unobservable factor to produce the pattern we see in Figure 1. It is hard to come up
with a candidate for such an unobservable factor. It is even harder provided that it
also needs to be virtually uncorrelated with employment income, gender, and age.
Flence, the deduction pattern is highly consistent with loss aversion where it is a
salient difference to people whether they will get a refund or have to pay more.
VI. Extensions
A. An Alternative IV Approach
The analysis in Section V strongly indicates that taxpayers behave in a loss av
manner when filing their tax returns. We find significant kinks and discontinu
in deductions, while the results for the covariates are less pronounced. Howev
they are not completely absent and although our placebo estimates suggest that
actually have causal effects, we also use an alternative IV strategy to corroborat
results. Using this alternative IV estimation, we are also able to estimate the co
cient of loss aversion, (A).
28 Incomes are rounded down to the nearest SEK 100 and refunds lower than SEK 100 are not paid out
deficits lower than SEK 100 are not claimed), so a preliminary balance e (-200,200) could be regarded as
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158 AMERICAN ECONOMIC JOURNAL: ECONOMIC POUCY NOVEMBER 2015
The IV estimation makes use of the difference between t
ment income tax rate and the local employment income tax r
taxation at source that was discussed in Section II. Actual lo
ment income are set with two decimals (for example 30.83 p
rates at source, on the other hand, are rounded to the clos
31 percent). Taxpayers will tend to pay too much in prelim
in municipalities where tax rates at source are above the ac
the case in 151 of the 290 municipalities in 2006. The prelim
therefore, tend to be in surplus. The opposite applies to taxp
with actual rates above the rates used at source. We use the difference between the
actual and the preliminary rates as an instrument for a preliminary deficit indicator
when estimating probability models for claiming a deduction.29 We use two differ
ent instruments for the preliminary deficit indicator in the IV analysis: the difference
between the preliminary and actual local tax rates; and the interaction between the
first instrument and employment income. The second instrument can be interpreted
as the impact of the rounding on the preliminary balance—theoretically, the round
off error should matter more for high income earners than low income earners. The
IV analysis uses the full sample of 3.6 million taxpayers. The reason for using the
full sample is that sample inclusion should not be endogenous to the instrument.30
The OLS and baseline IV estimate use the standard set of controls, which now also
includes employment income; see the notes to Table 3 for details.31 The models with
interacted treatments also include all relevant interacted controls and instruments.
The upper part of Table 3 reports the estimation results for the probability of
claiming a deduction. The OLS estimate shows that having a preliminary deficit
increases the probability of claiming a deduction by 2.0 percentage points. This
estimate cannot, however, be causally interpreted since preliminary deficit may for
other reasons be correlated with the probability of claiming a deduction.
The causal estimate given by the IV estimation suggests an even stronger effect.
We estimate an impact of 5.0 percentage points. The loss aversion effect is probably
stronger for individuals close to zero (the salient reference point). Individuals fur
ther away from the reference point (both on the positive and negative side) probably
know which side of zero they will end up. When we simply compare the left-hand
side and right-hand side (i.e., OLS), these individuals will attenuate the estimate.
The IV estimate instead identifies the local average treatment effect (LATE), i.e., for
individuals close enough to zero so that the rounding error is pivotal for preliminary
deficit or surplus.
The estimation reported in the third column of Table 3 shows that there is a sig
nificant kink in the relationship between the probability of claiming a deduction
and the value of the preliminary deficit at zero preliminary deficit. The third column
addresses the exclusion restriction by focusing on the relationship above and below
29 In terms of our covariates, the municipalities rounding up and down do not differ statistically from each other.
30Note that the rounding off error affects the preliminary deficit. This means that sample inclusion based on a
bandwidth in the preliminary deficit dimension could make the rounded up sample different from the rounded down
sample in terms of unobservable characteristics.
Employment income was excluded from the Regression Kink and Discontinuity (RKD) models above since
they were based on the preliminary deficit weighted by employment income.
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VOL. 7 NO. 4 ENGSTRÖM ETAL. : TAX COMPLIANCE AND LOSS AVERSION 159
Table 3—The Probability of Claiming a Deduction, IV Approach, Full Sample
OLS IV IV IV, gender IV, age IV, income
(1)
Positive
deficit,
(2)
0.020
0.050
preliminary
/,
indicator
(0.000)
(0.006)
(3)
-0.027
(0.046)
(4)
(5)
(6)
0.048
0.055
0.047
(0.007)
(0.010)
(0.007)
-0.0044
Preliminary deficit, £>,,
(0.0022)
amount
Interaction:
0.023
I x Dh amount
(0.0059)
Interaction indicators
0.009
I x Man, indicator
(0.013)
/ x Old (age >= 40),
-0.005
(0.013)
indicator
0.034
/ x High income
(0.017)
(> SEK 306,000), indicator
F-stat, first stage
3,387
Overidentification test, p-value
Minimum eigenvalue statistic
0.798
(0.01)
A, men/old/high income
A, women/young/low income
1,637
1,356
1,354
0.356
0.708
0.302
4.33
1.43
A
0.449
2.17
(0.18)
1.97
2.00
2.47
(0.21)
(0.21)
(0.38)
(0.40)
(0.38)
(0.51)
2.91
2.66
3.42
Notes: Number of observations is 3,610,972. Heteroscedasticity-corrected standard errors are in parentheses. Baseline
instruments are the difference between actual local tax rate and preliminary local tax rate, and the tax rate difference
times employment income. Baseline covariates are age. age2 employment income, (employment income)2, and gender.
Model 3 uses additional instruments that consist of three nonlinear transformations of the baseline instruments:
(i) indicator for higher actual local tax rate than preliminary local tax rate; (ii) and (iii) consist of the baseline instru
ments interacted with (i).
zero preliminary deficit. Compared with the kink estimates reported in the main
analysis, the IV kink estimate is somewhat larger and less precisely estimated, but
of the same overall magnitude. The result supports the interpretation that the prob
ability of claiming a deduction increases substantially when an individual exoge
nously locates in the loss region. This model includes three endogenous regressors
and we only have two baseline instruments. We solve this technically by adding
nonlinear transformations of the two baseline instruments (see Table 3 for details).
As a result, the strength of the instruments is substantially reduced; Stock and Yogo
(2005) report a bias of around 30 percent for a minimum eigenvalue statistic of 4.3
in a model with three endogenous regressors and five instruments.
The remaining columns in Table 3 report IV estimations that test for possible dif
ferences between different subgroups in our sample. From the estimation reported in
column 4, we conclude that there are no significant gender differences. Column 5 pres
ents the results from a corresponding estimation where we test whether the response
of those older than 40 years differs from the estimated response of younger taxpay
ers. The results suggest that there are no such differences. We do find, however, that
there is a significant difference in response between those with employment income
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160 AMERICAN ECONOMIC JOURNAL: ECONOMIC POUCY NOVEMBER 2015
higher than SEK 306,000 (the threshold for the central government
those below this threshold. Those above the threshold have a 20 pe
higher marginal tax rate than those below it. The response of those
tax rate is (both economically and statistically) significantly strong
with theory, since the marginal value of the deduction is higher abov
The corresponding IV estimations of unconditional and condit
respectively, are also in line with the primary results in Section V
mate a significant kink at zero concerning the unconditional amou
tional amounts, albeit larger on the deficit side, do not display a sig
the reference point. The results are available upon request.
B. Estimating the Coefficient of Loss Aversion
Ihe coefficient or loss aversion (A) can be expressed in a simple w
to Prediction 3: the share of taxpayers claiming a deduction in the l
sufficiently large preliminary deficits) divided by the share of taxp
deduction in the gain domain. We use the IV estimation reported in T
to calculate these shares.
We estimate the probability of claiming a deduction for a taxpayer with a prelim
inary surplus and average values of the covariates to 4.23 percent in our full sample
of 3.6 million taxpayers. The standard error of this estimate is 0.001. The corre
sponding probability of claiming a deduction for an average taxpayer with a prelimi
nary deficit is 9.19 percent, with a standard error of 0.005. Given these assumptions,
our estimate of loss aversion is:
(!2) Â = I = « 2.17.
We calculate the standard error of this ratio using the delta method. The resultin
estimate of the standard error is 0.184.
The lower part of Table 3 presents our estimates of the coefficient of loss aver
sion, A. We estimate A to be higher for women than for men, 2.91 versus 1.97. This
difference is statistically significant at the 5 percent level according to a t -test. This
test takes potential covariances between the estimated parameters into account. It
is possible to do this as we have estimated the response of men and women in the
same model.
The estimated A is higher for young than for old. This difference is, however, not
statistically significant at the 5 percent level according to the t -test. There is, on the
other hand, a statistically significant difference in the estimated A between those
with an income higher than the central government tax threshold and those with
lower income. The estimated A of taxpayers with lower income is much higher. This
may seem surprising as the estimated effect of preliminary deficit was significantly
higher for the high-income group. But the A estimate is a ratio, so we need to con
sider differences in both the numerator and the denominator. The high A estimate for
the low-income group is because the deduction probability for those with a prelim
inary surplus is only about 1.7 percent.
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VOL. 7 NO. 4 ENGSTRÖM ETAL.: TAX COMPLIANCE AND LOSS AVERSION 161
Our estimates are all in the range in the literature. Different definitions and di
ferent questions and samples have, however, given rise to quite disperse estimate
of A. The most frequently cited estimate is by Tversky and Kahneman (1992). They
report A = 2.25 using experimental data. Each individual was observed in bot
the gain domain and the loss domain. Our overall estimate, A = 2.17, is very close
to this. Abdellaoui, Bleichrodt, and Paraschiv (2007) cite various studies wher
the estimates of A range from 1.4 to 4.8 in risky settings. Gächter, Johnson, an
Herrmann (2007) estimate an average A = 2.6 for the risky setting and A = 2
for the riskless.
Our finding that women are more loss averse than men is similar to that of Schmidt
and Traub (2002). Yet, Gächter, Johnson, and Herrmann (2007) find no significan
gender difference once controlling for other covariates. We have access to very few
covariates, which may partly explain why our results differ.
VII. Concluding Remarks
We study the vast majority of Swedish working age taxpayers' behavior when f
ing their tax returns for the income year 2006. The research method is quasi-expe
imental using a regression kink and discontinuity approach. We find behavior to b
consistent with loss aversion. Taxpayers who have a preliminary tax deficit are mo
likely to claim deductions for "other expenses for earning employment income"
than those who have a preliminary surplus. We find a significant change at zero
preliminary deficit. The same holds true for the unconditional deducted amount
The empirical analysis also makes clear that none of the covariates show a similar
evolution around zero preliminary deficit. We can, therefore, rule out selection. Los
aversion is the obvious candidate for explaining the result.
There are alternative explanations. A first is the existence of liquidity constraint
A liquidity-constrained taxpayer would be more inclined to claim a deduction in
the deficit domain so as to avoid paying the taxes due. There are, however, several
arguments speaking against this explanation. The taxes due in our study are fairly
small. Tax payments are not due until the end of the year, so the taxpayer has abou
six months to come up with the necessary funds. And finally, we find stronger effects
among high-income earners than low-income earners. The former are arguably les
credit constrained.
The existence of transaction costs is a second alternative explanation. It it would
be cumbersome and time consuming to make the payment, taxpayers would try to
avoid ending up with taxes due. However, the administration costs for the taxpayer
are fixed and very small. It is not more complicated than paying an ordinary bill.
Hence, these costs could only explain a discontinuity and not a kink. The same
argument applies to any fixed psychological gain/loss that taxpayers may attribute
to ending up with a tax refund/taxes due. We, however, only find mixed evidence
of a discontinuity, but strong evidence of a kink. This makes transaction costs an
unlikely candidate.
Finally, one could argue that fairness or reciprocity considerations could explain
the deduction pattern if taxpayers feel mistreated by a tax agency that requires more
taxes at the end of the year. The theoretical predictions from fairness-based models
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162 AMERICAN ECONOMIC JOURNAL: ECONOMIC POLICY NOVEMBER 20/5
are not, however, clear-cut. Alternative stories are poss
plus means that the taxpayer has lent money to the go
Taxpayers with a deficit have been granted an interest-f
apparent that individuals with deficits should feel the
treatment. Furthermore, the deduction probability not o
preliminary deficit, the marginal increase also seems to
This pattern is highly consistent with our model of los
at higher deficit levels is not, on the other hand, consi
fairness and reciprocity.
We also use an alternative IV approach to strengthen th
use the difference between the actual and the preliminar
for a preliminary deficit indicator. This indicator is used
els for claiming a deduction. Our previous results are con
We also estimate the coefficient of loss aversion. Our
full sample, is very close to the estimate reported by Tv
A = 2.25. We use a different approach to estimate this c
previous studies. While they typically use experimental
dents, we use real-world data for the vast majority of taxpay
arrive at results very close to those previously reported.
The main contribution is that we have shown that taxp
consistent with neoclassical theory when filing their tax
to be loss averse.
Many (not all, though) claim the studied deduction because of noncompliance.
Restricting the possibility to claim this kind of deduction would therefore be a can
didate for increased tax payments and tax compliance. In Sweden that has actually
been done and it is no longer possible to claim deductions smaller than SEK 5,000,
which would include the vast majority of the deductions in our study.
A more general implication for tax policy of loss aversion is that a slight over
withholding of preliminary taxes would increase tax revenues. Such a policy might
also strengthen tax morale and reduce tax auditing costs. Overwithholding should
not be made to a too large extent, however, since taxpayers could feel wrongly
treated if too much is withheld repeatedly (Elffers and Hessing 1997). A systematic
overwithholding could also shift the reference point from being zero to being a cer
tain positive amount, so that the effect would disappear.
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