Tax compliance with strategic auditors:
An experimental study
Abstract
The objective of this research is to experimentally verify a theoretical model of tax
compliance, assuming a game-theory situation between a taxpayer and an auditor.
Specifically, the verification is carried out using experimental data to answer thefollowing three questions: (1) how do the changes of the tax rate affect taxpayers’
behavior? (2) What results are brought about by different expectations about the
behavior of the other player? (3) What influence does personality have on the tax
compliance of taxpayers?
The main findings are shown below. First, with regards to changes to the tax rate andthe behavior of each economic agent, contrary to the forecasts of the theoretical model,
it was found that if the tax rate is lowered, the extent of the taxpayer’s tax complianceincreases. This suggests that the more the model forecast, the less the taxpayer is able toanticipate the behavior of the auditor, and thus the taxpayer behaves in a shortsighted
manner. Second, regarding the relationship between the different expectations about the
behavior of the other player and the taxpayer’s tax compliance, it was found that theextent of the taxpayer’s tax compliance is higher for the “strategic condition,” in which
it is reported to that the other party is an actual human being, compared to the “single
condition,” in which it is reported that the other party is a computer. This suggests that asituation in which the other player is considered an agent who possesses limited
rationality and whose actions may deviate from balanced behavior results in
tax-declaration behavior with higher compliance.
Keywords:
tax compliance; experiment; strategic condition; single condition

1

Tax compliance with strategic auditors:
An experimental study
1. Introduction
	  The objective of this research is to experimentally verify a theoretical model of tax
compliance, assuming a game-theory situation between a taxpayer and an auditor.
Specifically, the verification is carried out using experimental data to answer thefollowing three questions: (1) how do the changes of the tax rate affect taxpayers’
behavior? (2) What results are brought about by different expectations about the
behavior of the other player? (3) What influence does personality have on the tax
compliance of taxpayers?
	  To date, a large amount of research on tax compliance has been conducted. However,first, it cannot be said that the analytical studies as a whole have presented consistentfindings; for example, different conclusions have been derived from the single person
decision making model and the game theory model. As a result, the task of collecting
the appropriate empirical evidence of the models’ forecasts becomes vital. Second,
many of the experimental studies have simply been an exploration of the facts based on
ad hoc settings without any theory-based predictions. In other words, within this priorresearch, the analytical studies and the experimental studies have not been integrated
particularly well, and it can be said that the points under discussion for tax compliance
have not yet been sufficiently verified.
	  Therefore, in this research, we integrate the analytical studies and the experimental
studies. Specifically, assuming an analytical model of tax compliance, we constructedwithin the laboratory a pseudo-society that faithfully expresses the assumptions of themodel, and through observing within it the judgments and the decision making of the
taxpayer and the auditor, we verified the balance of the theory. In other words, theobjective of this research is to conduct a theory-verification and balance-verification
experiment in order to present constant experimental evidence for the various points
under discussion that as yet remain unresolved.
	  In this research, the following three questions are considered as the specific points
under discussion requiring verification.
	  First is the question of the effects that changes to the tax rate will have on the2behaviors of each of the economic agents. Currently, various discussions are taking
place in Japan about the corporation tax rate, but when a tax rate of a certain level isadopted, it is extremely important to understand what types of behavior each economic
agent will engage in as a consequence. In particular, even though the prior research
includes many experimental studies that deal with changes to the tax rate, the current
situation is that, in actuality, there are still no established findings. Assuming ananalytical model concerning this point, we verify the types of effects that changes to thetax rate have on the behavior of taxpayers and auditors.
	  Second is the question of what kind of effects differences in expectations regarding
the behavior of the other player will have on the tax compliance of the taxpayer.
Specifically, assuming the theory of the mind and the social brain hypothesis, which are
currently hot issues in the field of experimental social sciences, for this question, thedifferences generated between a “single condition,” in which it is reported to the playerthat the other party is a computer, and a “strategic condition,” in which it is reported tothe player that the other party is an actual human being, were verified.
	  Third is the question of the relationship between the personalities of taxpayers andthe extent of their tax compliance. While this relationship has been found to exist fromthe results of studies targeting overseas subjects, no research has been conducted withthe prerequisite that the test subjects be Japanese; therefore, in this research, this point
was also verified.
	  The main findings are shown below. First, with regards to changes to the tax rate andthe behavior of each economic agent, contrary to the forecasts of the theoretical model,
it was found that if the tax rate is lowered, the extent of the taxpayer’s tax complianceincreases. This suggests that the more the model forecast, the less the taxpayer is able toanticipate the behavior of the auditor, and thus the taxpayer behaves in a shortsighted
manner. Second, regarding the relationship between the different expectations about the
behavior of the other player and the taxpayer’s tax compliance, it was found that theextent of the taxpayer’s tax compliance is higher for the “strategic condition,” in which
it is reported to that the other party is an actual human being, compared to the “single
condition,” in which it is reported that the other party is a computer. This suggests that asituation in which the other player is considered an agent who possesses limited
rationality and whose actions may deviate from balanced behavior results in
tax-declaration behavior with higher compliance.
3

The remainder of the paper is organized as follows. Section 2 discusses related literature.
Sections 3 develops the model and section 4 explain our hypotheses and theexperimental design. Section 5 presents the experimental results. Section 6 shows ourconclusion.

2.

A Review of Previous Research

2-1 Analytical model
Allingham and Sandmo (1972) and Yitzhaki (1974) are examples of pioneering researchin this field. These studies employed a model of decision-making by an individual basedon the probability of a tax audit and the existence of penalties. They confirmed that
increases in these variables have positive effects on tax compliance (tax evasion is
reduced).
Furthermore, Pencavel (1979), Cowell (1981) and Sandmo (1981) made income
endogenous by adding labor supply to the model. They found that with thismodification, variables related to tax enforcement—that is, the probability of a tax audit
and penalties—no longer necessarily resulted in an increase in tax compliance. Whilethese analyses distinguished among a few forms of tax evasion, they did not explicitly
analyze whether these forms could be used to manage the risk of tax evasion bytaxpayers. As an exception, Klepper and Nagin (1989) verified compliance by line item
and found that substitute relationships existed among various items.
Additionally, Landskroner et al. (1990) analyzed tax evasion under uncertainty using aportfolio approach. In other words, with the understanding that whether to evade tax ispart of an individual’s portfolio decision making, the model considered not only theuncertainty of a tax audit but also asset risk. Furthermore, Cremer and Gahvari (1994)
analyzed tax evasion from the point of view of the most suitable income tax anddemonstrated that tax evasion may strengthen or weaken the degree of progressivity ofthe tax system.
The use of equilibrium-solution benchmarks for reference in this study is drawn fromprevious studies based on game theory. Graetz et al. (1986) found that modeling a gamebetween a strategic taxpayer and a tax auditor led to different conclusions than whenmodeling the taxpayer as a sole decision maker. Reinganum and Wilde (1986) modeled4

taxpayer type (by actual income) in a continuous distribution and found that, inequilibrium, high-income taxpayers evaded taxes less. Finally, Erard and Feinstein(1994) used a model of continuously distributed income to show that honest taxpayers
played an important role.
2-2. experimental research
Next, in this subsection, we survey experimental researches that have been carried out
on tax compliance, of which there are many. By referring to Fonseca and Myles (2012),
a survey that collated previous research experiments on tax compliance, we see threemajor characteristics, which provide an overall picture of this body of work.
First, rather than being based on economics, many of the experiments were based on
psychology. In particular, a major characteristic is the large number of “fact finding”
experiments. In other words, currently, experiments are conducted based not on some
sort of theoretical expectation, but rather on ad hoc settings. However, even thoughthese fact finding experiments are being carried out in these sorts of ad hoc settings,
there are major doubts about whether they will result in the discovery of systematic
facts. Therefore, it seems that what is required is to conduct experiments that verify
theories and hypotheses to construct a balanced model.
The second characteristic is that a large number of experiments focus on the
personalities of individuals. Specifically, there is an extremely large number of researchexperiments that collect data on personality via questionnaire, such as the individual’s
age and gender, and then aim to verify if there is some sort of correlation between the
degree of tax compliance and the data on personality. The reason for this focus is that
previous research primarily asked “which kinds of people evade taxes and which donot?” and assumed elements such as actual tax evasion behavior. In particular, this bodyof research has clarified that the older the individual and the higher their years of work
experience, the more honestly they report their taxes. As this research targeted overseas
subjects, there is a need to verify whether the same results would apply to Japanese
subjects. However, the relationship between personality and tax compliance is nothing
more than an analysis based on individuals and, ultimately, ought merely to be a
supplementary issue. This is because, in the final analysis, the important point is notwhich type of person evades tax, but what kind of system and regulations increase tax
compliance. Therefore, even if we consider personality, what is ultimately required is an5

analysis of its relationship to the system.
The third characteristic is that there are no established views on the relationshipbetween changes to the tax rate and tax compliance. Changes to the tax rate are an
important issue for policymakers and such changes are expected to significantly change
the behavior of economic actors as well. However, in the research experiments, noparticular agreement has been reached on the relationship between changes to the tax
rate and changes to the behavior of economic actors. One reason for this is that, as noted
above in the first point, it is thought that research experiments tend to be carried out inad hoc form. Whatever the reason, the effects that the important policy variable of tax
rate has on the behavior of economic actors require an analysis that provides some sortof robust experimental evidence.
3. The model
3-1 The modelThis section describes the model in Reinganum and Wilde (1986) that is used as abenchmark in this research. This game comprises a risk-neutral taxpayer and a similarly
risk-neutral tax examiner.
The taxpayer’s actual income is his or her private information that cannot be observedby the examiner. Based on actual income, the taxpayer reports income to the examiner.
As the examiner does not know the actual income, he or she estimates it from thereported income and decides on a level of effort to employ for the tax examination. The
examiner’s level of effort determines the probability of discovering the actual income
through the tax examination; the higher the level of effort, the greater is the probability
that the actual income will be discovered.
The taxpayer’s actual income I is a random variable and, in the range of 𝐼 ∈ [𝐼, 𝐼](𝐼 <𝐼 < ∞). It is distributed by the distribution function 𝐹(∙). In the game, after observing
his or her actual income, the taxpayer, selects to report an income of x = r (I). If the
taxpayer is not audited, he or she will pay a tax of tx based on a proportionate tax rate oft. If the taxpayer is audited and the actual income is discovered, the tax is levied on theactual income and, in addition, the taxpayer is subject to a fixed penalty according to thedifference between their actual income and reported income. Therefore, the amount paidby the taxpayer in this instance becomes tI + tπ(I-x). According to Yitzhaki (1974),
assumptions about these penalties are considered to conform to the tax laws of both the6United States and Japan.
After observing the taxpayer’s reported income x, the auditor chooses the level of effort.
Costs are incurred for this effort, and in reality, even if the taxpayer’s under-reporting is
discovered, it is assumed that these costs will still be incurred. In other words, forexample, even for reported income 𝐼 that is clearly a case of under-reporting, in theevent that the tax auditing costs are high, it is possible that the effort for the auditing
will not be made. When the probability of discovery through the auditing (subsequently,
the auditing cost) is set as 𝜌, it is assumed that the auditor multiplies the auditing
probability by the cost and then selects what to do. The auditor’s strategy is as follows.
𝜌 = 𝑝 𝑥 , 𝑝: −∞, ∞ → [0.1]
In this formulation, the auditing probability is unrelated to the size of theunder-reporting. In addition, it assumes that the auditing probability is not aconsequence of whether the examination succeeds or fails (it does not say whether somepartial information will be clarified). For simplification purposes, the auditing cost is
assumed to be 𝑐𝜌. The auditing cost is considered to be an increasing function of theexamination probability1.
The auditor’s utility function 𝑈! is expressed as follows.
𝑈! = 𝜌 𝑡𝐸 𝐼 𝑥 + 𝜋𝑡 𝐸 𝐼 𝑥 − 𝑥+ 1 − 𝜌 𝑡𝑥 − 𝑐𝜌

(1)

E[I|x] is the examiner’s expected value for the actual income, based on his or her
observation of the reported income. Conversely, the taxpayer’s expected utility function
𝑈! is expressed as follows.
𝑈! = 𝑝(𝑥) 𝐼 − 𝑡𝐼 − 𝜋𝑡(𝐼 − 𝑥 ) + 1 − 𝑝 𝑥 (𝐼 − 𝑡𝑥)(2)

Therefore, if r(I) traces a monotonic increase, the equilibrium that meets the following
requirements becomes the separating equilibrium.
(1) With the forecast of actual income E[I|x] assumed as a given, the examiner selects
the examination probability (verification policy) p (x) that maximizes 𝑈! .
1 As was touched on in Reinganum and Wilde (1986), the cost function, when twice
continuously differentiable, must meet the following requirement. For a linear costfunction, one part of the abovementioned process is not satisfied, but there exists a
unique equilibrium solution.
7

(2) With the examination probability p(x) as a given, the reporting x=r (I) thatmaximizes 𝑈! is selected.
(3) The actual income E[I|x] assumed is consistent with the actual income I.
To calculate the equilibrium, it is solved backwards. When solving the auditor’s
optimization problem, the first order condition is as follows.
!!!
!"=𝑡 1+𝜋 𝐸 𝐼 𝑥 −𝑥 −𝑐(3)	  If this expression is positive, the examiner selects ρ = 1, and if it is negative, he or she
selects ρ = 0. In addition, when the expression is exactly equal to 0, the examiner selects
an arbitrary ρ.
Next, we consider the problem for the taxpayer. With the examination probability as agiven, the taxpayer solves a utility maximization problem, but solving this problem
incorporates the effects that his or her own reported income has on the examination
probability. In other words, the following first order condition is to be obtained.
!!!
!"= 𝑝! 𝑥 −𝑡 1 + 𝜋 𝐼 − 𝑥+ 𝑝 𝑥 𝑡𝜋 − 𝑡(1 − 𝑝(𝑥))(4)Below, we focus on the inner solution. In other words, based on the condition that (3)and (4) equal 0, the first order condition of p and x is solved and the following
equilibrium condition is obtained.
1: The equilibrium examination probability is as follows.
0                                                                                            𝑥 ≥ 𝑥          
!
!! !!!
𝑝 𝑥 = !!!(!!!"#  { ! (!!!)})      𝑥 ∈ [𝑥, 𝑥]1                                                                                              𝑥 < 𝑥(5)

2: The equilibrium reported income is as follows.
𝑥=𝐼−𝑐, 𝑓𝑜𝑟  𝐼 ∈ [𝐼, 𝐼]  𝑡 1+𝜋

3: The equilibrium assumed income by the examiner is as follows.
𝐼                                                                                      𝑥 ≥ 𝑥          𝐸[𝐼 𝑥] = 𝑥 = 𝐼 − 𝑐/𝑡(1 + 𝜋)      𝑥 ∈ [𝑥, 𝑥]𝐼                                                                                            𝑥 < 𝑥(6)8

The interpretation of this equilibrium can be described as follows. First, from actual
income in equilibrium condition 2, we understand that the taxpayer’s reported income I
is smaller than I in the equilibrium. This is because the taxpayer’s reporting
incorporates the fact that costs are incurred for the tax auditing. This reported income
increases with regard to actual income, decreases with regard to the (limit of the) tax
auditing cost c, and increases with regard to the tax rate and penalties.
	  Next, we examine the probability (verification probability) that the equilibrium
examination probability from equilibrium condition 1 is 0 when the reported income
exceeds its upper limit, 1 when the reported income falls below its lower limit, andbetween 0 and 1 when the reported income falls in between.
3-2. Example using numerical values	  The numerical values of the parameters used in this research are assumed to be
𝐼 = 130, 𝐼 = 90, 𝑐 = 8, 𝜋 = 1.5 and t = 0.4, 0.3.
In this instance, the upper and lower limits for the reported income in the model when
the tax rate is 40% becomes 𝑥 = 80, 𝑥 = 40. In addition, when the tax rate is 30%, thelimits become 𝑥 = 63.3, 𝑥 = 23.3.
The equilibrium solutions based on these parameter settings are shown together in thetable 1 and 2.
Insert Table 1 and 2 about here.
First, if we look at taxpayers’ reported income based on the same tax rate, we see thatthe higher the actual income, the higher is the reported income. This is because
taxpayers with high actual incomes obtain a large benefit from the decrease in the tax
auditing probability that results from the increase in reported income. On the other hand,
we can see that the equilibrium auditing probability declines, because the higher theactual income, the higher is the reported income.
	  Next, we consider the effects of changes to the tax rate. By reducing the tax rate from
40% to 30%, the benefit that the auditor obtains from the tax auditing declines, andtherefore, the equilibrium auditing probability also declines. Once this tax rate change
has been incorporated, the taxpayer decides to report a lower level of income. As aresult, we understand that the gains expected by the taxpayer increase when the tax rate9

is low.
4. Hypothesis
4-1. The needs for experimental verification
There are two broad requirements to be met by economic experiments.
First, through the experiment, it is possible to directly verify the model. In other words,
in order to verify an economic model, it is necessary to collect and analyze data on
people’s judgments and decision making based on an information set in accordancewith the model and in an environment in line with the model. However, it is consideredextremely difficult to do so via an empirical analysis using archival data. In contrast,
through an experiment, the experimenters can to a certain degree freely create anenvironment that corresponds to the timeline of the model and the information set. In
addition, they can directly observe people’s behavior within it and collect behavioral
and psychological data. For example, reported income appears in the model. Usingarchival data, it is difficult to accurately ascertain in which situations and to what degree“real income” deviates from reported income, but this becomes possible in theenvironment created by an experiment. Thus, the important point is that, through theexperiment, it becomes possible to directly verify the model.
	  The second requirement is that the experiment possesses the quality of priorverification. For example, in an archival analysis, only data based on the system in
actual existence can be collected. In contrast, in an experiment, a pseudo-environmentthat does not exist in the actual system can be created and the behavior of economic
actors within it can be ascertained. Therefore, before implementing the actual system, it
is possible to verify the economic consequences that would result from such a system
by assessing whether they are in accordance with the model’s predictions, and toascertain in advance the unintended consequences that the model cannot predict.
Through this, it is possible to make various proposals for the design of the system priorto actually creating the system. For the model used in this type of research, comparative
statistics are conducted for the relationship between changes to the tax rate andeconomic actors, and a major strength of an experiment is that it is easily possible to
make tax rates the subject of analysis, even those that have not actually been adopted.

104-2. Three hypotheses
The first hypothesis concerns the relationship between changes to tax rates and taxpayer
behavior. As debates surrounding corporate tax rates are currently taking place in Japan,
it is anticipated that changes to tax rates will affect the behavior of economic actors.
In this study, the following two indicators of tax compliance amongst taxpayers areproposed: (1) the average rate of tax compliance and (2) the degree of safe divergence.
The average rate of compliance is the ratio between each individual’s actual income andhis or her declared income. The higher this figure becomes (i.e., it approaches a value of1), the more the taxpayer’s behavior can be regarded as being highly compliant.
The degree of safe divergence is the difference between the area assumed to be safe by
the taxpayer and their reported income, and it can be assumed that the lower this figure,the higher the rate of compliance.2
Adopting these two indicators, we are able to establish the following hypotheses
conforming to the equilibrium of the model.
Hypothesis 1

Changes in tax rates and economic consequences

Hypothesis 1-1. Taxpayer’s average rate of compliance
When the tax rate is lowered, the average rate of compliance declines.
Hypothesis 1-2. Taxpayer’s degree of safe divergence
When the tax rate is lowered, the taxpayer’s degree of safe divergence declines.
2

In addition to declared income, the reason for using the degree of safe divergence as

an indicator of compliance is as follows. While equilibrium declared income within thecurrent research takes into consideration the behaviour of tax investigators, it is possiblethat individual assumptions about investigator behaviour may vary. In other words, wemight interpret an individual who assumes there is a relatively high probability ofinvestigation as actively trying to lower their tax burden, even if they declare a
relatively high income. Conversely, an individual who assumes there is a relatively low
probability of investigation may be seen as more passive in curtailing their tax burden,
even if they declare a relatively low income. Therefore, taking as given eachindividual’s assumptions about the probability of investigation, the indicator of how
much declared income is relatively lowered by is defined by the degree of safe
divergence.
11Second, the point to be verified here is whether there are differences in taxpayers’
tax-reporting behavior depending on whether the other party is an actual person or not.
Behind this question lies the theory of mind (ToM), which has its origins in the researchof Premack and Woodruff (1978). It is a theoretical schema that considers the functionsof the mind that are perceived for others by people and other animals. In recent years, it
has combined with the problem awareness of understanding society from theperspective of others, as well as the social brain hypothesis, which posits that the humanbrain significantly evolved from the need to understand the minds of others. ToM has
been the subject of considerable attention in the fields of psychology andneuro-economics.
Rilling et al. (2002) is a leading example of research in which ToM and the social brain
hypothesis are understood by integrating game theory and neuroscience. Throughrepeatedly conducting the prisoner’s dilemma game theory experiment, Rilling et al.
(2002) shows there are major differences in the brain’s nerve activity depending onwhether the opponent is a human being or a computer. Specifically, he establishes thatwhen one player chooses “cooperation,” followed by the other player also choosing“cooperation,” the corpus striatum, the anterior cingulate cortex, and the orbitofrontal
cortex are activated. Furthermore, the activation of the corpus striatum and theorbitofrontal cortex, which are responsible for producing feelings of pleasure, results infurther reciprocal cooperative behavior. Moreover, Rilling et al. (2002) uses functional
magnetic resonance imaging (f-MRI) to measure whether brain activity is different
when the opponent is a human being and when it is a computer, and the results of thesemeasurements show that although the parts of the brain that became active are the same
in both instances, the degree of brain activation is greater when the opponent is a humanbeing. In other words, the person feels greater pleasure from reciprocal cooperative
behavior when the other person is an actual human being; moreover, these feelings ofpleasure result in their further cooperative behavior. If we consider these points, we canunderstand them as signifying that for feelings or decision making recalled inrelationships with others, there will be major differences in what is recalled for eachindividual.
	  Fujiwara et al. (2008) also uses f-MRI to measure the brain activity of test subjects
when they take part in a selection problem in which they receive financial rewards or12

penalties resulting from their decision making, and finds that the subjects experience
absolute profit or loss and relative profit or loss in different parts of the brain.
Specifically, their limbic systems are activated for absolute profit and loss; in contrast,
their prefrontal areas are activated for relative profit and loss. When we consider this,we can see that for economic decision making also, the outcomes will be different when
the subject is a lone individual, compared to when he or she assumes there to be otherpeople, and it is important to comparatively study both.
If we think about the findings described in relation to this research, and we assume thesame type of game theory situation, then it is possible, for example, that the behavior of
taxpayers will change depending on whether the other party is a computer or a humanbeing.
If we consider this from the perspective of tax policy, then we can see it relates to theways in which the behavior of taxpayers might change depending on whether the rules
are applied and managed mechanically and uniformly, or with some degree of flexibility
and uncertainty. In other words, when we expand the abovementioned discussion, it canbe connected to a discussion of whether, in actuality, in order to increase tax
compliance, it is better to manage the rules mechanically and uniformly (when the
taxpayer behaves on the assumption that the other party has a “device” that reflects
behavior in a mechanical and uniform manner on balance) or alternatively, whether it isbetter to manage the rules to some degree flexibly and with an element of uncertainty(when the taxpayer behaves on the assumption that the other party will act flexibly andwith an element of uncertainty and will not reflect behavior in a uniform manner onbalance). It can be argued that this question is an important one in terms ofpolicymaking, and one that requires some analysis.
Hypothesis 2: There is no statistically significant difference in the taxpayer’s tax
reporting behavior in a “single condition,” in which the player is notified that “the otherplayer is a computer,” and in a “strategic condition,” in which the player is notified that“the other player is a human being” (null hypothesis).
Third, there is the matter of whether the personality of the taxpayer results indifferences in their reporting of taxable income, and additionally, what the precise
personality factors are that might bring about differences in the degree of tax
13compliance. With regard to these questions, previous research conducted with overseas
subjects has demonstrated that factors such as age, years of working experience, andgender are significantly correlated to the degree of tax compliance. It is necessary toverify whether these factors also correlate to the degree of tax compliance amongst
Japanese subjects. This leads to the following hypotheses.
Hypothesis 3 : There is a statistically significant correlation between taxpayer
personality and taxpayer behavior.
Hypothesis 3-1. The higher the age of the taxpayer, the higher is the indicator of tax
compliance.
Hypothesis 3-2. Female taxpayers have higher indicators of compliance than maletaxpayers.
Hypothesis 3-3. Individuals with higher confidence in the other players have higher
indicators of compliance.
Hypothesis 3-4. Individuals with lower levels of strategic reciprocal relationships havehigher indicators of compliance.
Hypotheses 3-1 and 3-2 are conclusions partially derived from and verified in priorresearch, which shows that higher rates of tax compliance are associated with higher
ages of taxpayers and being female. Hypothesis 3-3 posits that more trusting individuals
demonstrate higher compliance. This is based on the assumption that more trusting
individuals are likely to envisage larger benefits from paying taxes. Furthermore, withregard to Hypothesis 3-4, strategic reciprocal relationships are not seen to be purely
altruistic, but rather as indicators of a type of “cunning.” They are, thus, assumed towork toward lowering compliance, although it is possible that such relationships will be
purely altruistic, depending on the individual. In order to test these assumptions, in thisresearch, a regression analysis is carried out using the tax compliance indicators, withvarious tax rates as the explained variables.
The average rate of compliance and the degree of safe convergence are used as theindicators of tax compliance. The regression model to be tested is as follows:
𝑌! = 𝛼 + 𝛽! 𝐴𝐺𝐸! + 𝛽! 𝐺𝐸𝑁! + 𝛽! 𝑇𝑅𝑈𝑆𝑇! + 𝛽! 𝑀𝐵! +𝛽! 𝑆𝐼𝑁_𝐷 + 𝜀!

(7)

14

𝑌! is the average rate of compliance (  𝐶𝑜𝑚𝑝! ) or the degree of safe divergence (𝑆𝐴𝐹𝐸! ).
In addition, these explained variables are tested for correspondence with tax rates of
30% and 40%, respectively.
Individual contextual data are used for the explanatory variables. Specifically, AGE
indicates taxpayer age; GEN is a dummy variable in which 1 = female and 0 = male;
TRUST expresses levels of trust derived from the results of a questionnaire in a trust
game; while MB indicates levels of strategic altruism derived from the results of anultimatum game questionnaire. Furthermore, the model recognizes differences between
single and strategic compliance indicators, and introduces a dummy variable to control
for this, where 1 = single condition and 0 = strategic condition.
For signs to be consistent with the hypotheses, positive and negative signs are reversed
for the explained variables. When the explained variable is the average rate ofcompliance (or the degree of safe divergence) then, for the signs to be consistent withthe hypotheses, 𝛽! is positive (or negative), 𝛽! is positive (negative), 𝛽! is positive(negative), 𝛽! is negative (positive), and 𝛽! is negative (positive).
4-3. Experimental design	  In our experiment, the key concepts are type of auditors and tax rate. With regard totype of auditors, the following two sets of conditions are created:“Single condition”: Subjects play only the role of the taxpayer, and the role of theauditor is played by the computer.
“Strategic condition”: Subjects are divided into those who play the role of the taxpayer
and those who play the role of the auditor.
	  The experiment uses tax rates of 40% and 30%. These tax rates are commonly usedin previous studies and were set with current Japanese tax rates in mind.
	  An overview of the experiment is illustrated in the table 3.
Insert table 3 about here.
The experiment sessions were conducted in 2014 at Keio Business School. The subjects
15

of the experiment were all graduate students undergoing an MBA program. There were
42 experimental subjects across all sessions in total and each subject participated in only
one session (Between-subject design). The allocation of subjects to sessions wascompletely random. In each session, decision-making data were collected using a
within-subject design for both the 40% and 30% tax rates based on the two
abovementioned sets of conditions.
	  We collected behavioral data from the subjects using the strategy method. Thismethod involves: 1) having subjects make decisions on all possible situations they could
encounter in their roles (each subject submits a strategy profile for dealing with eachsituation) and 2) randomly matching subjects, randomly selecting certain situations, anddetermining the outcome of the game in one shot based on all strategy profiles
submitted by the subjects (Casari and Cason 2009). By having subjects submit strategy
profiles for dealing with all situations based on their individual roles (as in step 1), thismethod allows large volumes of data to be collected. Unlike experiments that require
subjects to make decisions in sequential play, this method elicits more careful decisions.
In addition, providing compensation based on the outcome from step 2 gives the
subjects financial incentives, which also increases internal validity. In this way, thestrategy method is advantageous as it maintains a certain level of internal validity while
securing a large volume of data and eliciting more careful decisions.
	  The details of the actual experiment conducted are as follows. First, the subjects
gathered in a classroom with an internet connection and computer facilities, wererandomly divided into two groups (“taxpayer” and “auditor”), and were randomly
assigned identity (ID) numbers. No subject was allowed to know the ID number or roleof any other subject. The subjects were also forbidden from communicating with eachother. Then, the experimenter gave the instructions to the subjects and conducted asimple test to assess their level of understanding. The content of the instructions was
kept to a minimum to avoid interfering with subjects’ comprehension. Subsequently,
each subject used a PC to access the website designated to their assigned role andresponded to each situation in the strategy profile on the website within the time limit.
During the task, each subject was able to download an online spreadsheet to assist indecision making. This spreadsheet provided a simple simulation for ascertaining thebenefits, to the subject and the other participant, of making a particular decision at a
specific tax rate. After submitting the strategy profiles, the subjects responded to a16

post-experiment questionnaire. The post-experiment questionnaire asked subjects theirage, years of work experience, and gender as well as their level of risk aversion,
altruism, and reciprocity. While the subjects answered these questions, experimenters
carried out the matching of subjects and conditions to determine each subject’s
compensation. All compensation was paid in cash on the day of the experiment. In order
to increase the incentives for the subjects, a participation payment of 1,000 yen was
supplemented with an amount that varied based on the number of points won in thegame. The variable amount was calculated as 15 yen per point for those who played as
taxpayers and 25 yen per point for those who played as auditors. This was based on the
expected payoff at the equilibrium of the model in order to ensure that there would be
no significant difference in compensation paid for each session.
	  One experiment session lasted for approximately 45 minutes on average, including
instructions.
	  The following outlines details of the data collected from the subjects.
	  With regard to taxpayers, this study collected data on: a) declared income based on
actual income, b) the threshold of declared income when the audit rate is 0%, and c) the
threshold of declared income when the audit rate is 100%. There are two reasons forinvestigating b) and c) along with a). The first reason is to elicit judgments anddecisions that are closer to the equilibrium of the model. In other words, the equilibriumof the model begins with identifying the risk area and safe area, and can then be
defined by these areas where the probability of being audited ranges from 0–100%.
Therefore, it is important for taxpayers to first become aware of the risk area and safearea, predict the likelihood of being audited in between these two areas, and determine
the level of income they would declare. The second reason is to elicit more careful
judgments and decisions from the subjects, with a greater awareness of otherparticipants’ decision making as a secondary factor.
	  On the other hand, regarding auditors, this study collected data on: d) the probabilityof being audited at a given declared income and e) the actual income estimated byauditors in each relevant situation. The reason for collecting data on e) along with d) is,
as with taxpayers, to elicit more careful judgments and decisions based on awareness ofthe equilibrium of the model and increased awareness of the personal information(actual income) of the taxpayers.
The subjects’ basic data for each session are summarized in the table 4.
17Insert table 4 about here.
As the table 4 shows, because the experiment subjects were all graduate MBA students,
their average age and years of work experience were high. The average compensation
given was 2,253 yen under the single condition, 2,069 yen under the strategic condition,
2,317 yen for taxpayers, 1,857 yen for auditors, and 2,137 yen for the overall
experiment.
5. Experimental results and interpretations
5-1. Hypothesis 1: The economic consequences of changes in tax rates
The differences in reporting income in the 40% and 30% tax rates are compiled in thetable 5 and 6.
Insert table 5 and 6 about here.
Table 5 shows the mean value of reporting income for the entire sample, with actual
income from 130 to 90 for each tax rate. The table 6 also shows the data delineated by
the single condition and the strategic condition. These tables indicate that the average
income reported by the taxpayers tends to increase slightly in general when the tax ratedrops from 40% to 30%, even though no statistically significant difference is found.
This is an outcome antithetical to our theoretical prediction. Theoretically, theprobability of being investigated by an auditor diminishes as tax rates fall, andtaxpayers who foresee this lower their declared income. In other words, in theory the
degree of tax compliance is expected to decline when tax rates fall. However, in reality,
we see the degree of tax compliance increasing further when tax rates drop.
Next, this study attempts to confirm the change in the average compliance ratio (theamount of declared income per unit of actual income) based on changes in tax rates.
The differences between average compliance ratios for the 40% tax rate and those forthe 30% tax rate are shown in the table 7, 8 and 9.

18

Insert table 7, 8 and 9 about here.
In addition, an overall trend can be observed from these tables in which the averagecompliance ratio increases slightly when the tax rate drops, even though there is no
statistically significant difference.
In other words, with regard to Hypothesis 1-1 (the relationship between tax rates
and average compliance ratios), although no statistically significant difference is found,as an overall trend, the results contradict the hypothesis. In other words, when tax rates
fall, the test subjects display the behavior of declaring their taxes as if they intended toincrease their degree of tax compliance.
Furthermore, the degree of safe divergence is compiled in the table 10. 3
Insert table 10 about here.
When the tax rate drops from 40% to 30%, the degree of safe divergence as a wholedrops, and a statistically significant drop (the Wilcoxon matched-pairs signed-rank test.
p < 0.05) is found for the entire sample and the strategic condition. Therefore, it is clearthat the degree of taxpayer compliance becomes greater when the tax rate falls. This
trend is an outcome antithetical to the predictions of our theory.
In other words, Hypothesis 1-2 (the relationship between tax rates and the degree ofsafe divergence) is also in opposition to our results, which show that when tax rates fall,
the test subjects display the behavior of reporting their taxes as if they intended toincrease their degree of tax compliance.
As described above, the data collected from the experiment lead to results that
contradict our hypothesis, a reason for which may be the myopic behavior of taxpayers.
Our hypothesis is that, in theory, taxpayers’ degree of tax compliance drops when the
tax rate falls because they foresee that the probability of being investigated by anauditor declines due to the decreased tax rate and then reduce their declared income
accordingly (the degree of tax compliance decreases).

3

The sign of ‘*’ in the table is the statistical significance at 5 % level by the Wilcoxon
matched-pairs signed-rank test.
19However, instead of modifying their behavior by predicting auditors’ behavior,taxpayers make their decisions myopically, based solely on the changed tax rate andtheir own interest. In other words, if the tax rate falls, the rate of tax obligations for
taxpayers drops. For example, even if their declared income is the same at 100, theamount of tax paid simply decreases if the tax rate falls. Thus, it could be said that there
is no need for taxpayers to reduce their declared income by taking the risk of being
audited. As a result, it could be considered that taxpayers’ degree of tax complianceincreases even further.
When applying these results to policymaking, it may be possible to encourage morehonest taxpayer behavior by lowering the tax rate, which contrasts with our theoreticalpredictions. Certainly, a more thorough analysis is required to understand the extent towhich tax revenue rises as a result of taxpayer behavior due to reduced tax rate.
5-2. Hypothesis 2: Single vs. Strategic condition
The average reported income with different assumed tax rates is summarized in thetable 11 and 12.4
Insert table 11 and 12 about here.
Table 11 shows that, based on a tax rate of 40%, declared reported income in thestrategic condition is on the whole higher than reported income in the single condition.
Moreover, apart from when actual income is 90%, there is a statistically significant
difference in every instance (ANOVA. p < 0.01 and p < 0.05). Table 12 shows that,based on a tax rate of 30%, reported income in the strategic condition is on the whole
higher than reported income in the single condition. Moreover, apart from when actual
income is 90%, there is a statistically significant difference in every instance (ANOVA.
p < 0.01).
From the abovementioned results, the hypothesis is statistically rejected. This suggeststhat when the other player is an actor of bounded rationality who may possibly diverge
from balanced behavior, the taxpayer’s tax reporting behavior will be more compliant.

4

The sign of ‘*’ in the table is the statistical significance at 5 % level and that of ‘**’in the table is the statistical significance at 1% level by the ANOVA.
20

This is extremely interesting from a policy making. In short, if we consider this inrelation to the problem of how to manage the rules, then the two options correspondrespectively to “the single condition,” in which the rules are applied and managed
mechanically and uniformly, and “the strategic condition,” in which the rules aremanaged, to some extent, flexibly and with an element of uncertainty. The findings
obtained from the experiment suggest that, in the case of somewhat flexible anduncertain rules (or at the very least, when tax payers perceive the situation to correspondto somewhat flexible and uncertain rules), taxpayers’ tax reporting behavior will be
more compliant. To state this in its opposite, the findings suggest that it is preferable not
to manage the rules in a mechanical and uniform way from the perspective of inducing ahigher level of tax compliance from taxpayers.
6-3. Testing Hypothesis 3: Personality and Tax Compliance
The table 13, 14 and 15 show the analysis results of Hypothesis 3.
Insert table 13, 14 and 15 about here.
From left to right of the table 15, the following dependent variables are used: (1)compliance rate when the tax rate is 40%, (2) compliance rate when the tax rate is 30%,(3) deviation from the safety zone when the tax rate is 40%, and (4) deviation from thesafety zone when the tax rate is 30%.
(1) shows that, although the parameter estimate of GEN (dummy variable where 1 =female) is positive, the result is not significant. AGE is negative and significant at the
5% level, indicating that the result is contrary to the hypothesis that the compliance rate
becomes lower among older taxpayers. By way of explanation, it is possible that older
individuals earn higher salaries thanks to the seniority-based wage system common
among Japanese companies and are more conscious of the tax burden.
In addition, the coefficients for TRUST (variable for trustworthiness) and MB (variable
for the level of strategic reciprocity) are significant—positive and significant at the 1%
level and negative and significant at the 5% level, respectively—and support the
hypothesis. This indicates that under the tax rate of 40%, the compliance rate increases
among individuals who are younger, more trustworthy, and have a lower level ofstrategic reciprocity.
21

As mentioned in the definitions of the hypotheses, strategic reciprocity has
characteristics of altruism and strategy. We interpret this estimation result to suggest
strong characteristics of individuals who act strategically to maximize ultimate personal
gain rather than acting under altruism.
In addition, estimation (2), which uses the compliance rate under the tax rate of 30% as
the dependent variable, shows almost the same results for all variables except AGE,
although there are slight differences in significance levels. It is interesting that when the
tax rate is lowered, AGE is no longer significant. Applying the previously described
explanation, it is possible that older individuals who are sensitive to the tax burden
under the higher tax rate considerably increase their compliance rate in response to thelower tax rate.
Next, we focus on (3) and (4), which are the analysis results when deviation from thesafety zone is the dependent variable.
In these models, a smaller value for the dependent variable is interpreted as a higher
compliance indicator. According to the estimation results, while not many variables turnout to be significant, GEN is negative and significant at the 5% level under both tax
rates. Therefore, a result consistent with the previous studies stating that the complianceindicator is higher among women is obtained. GEN, which is not significant when thecompliance rate is the dependent variable, becomes significant for the deviation fromthe safety zone. In other words, although no gender difference is observed when only
the compliance rate is evaluated, it is inferred that women are more accurate inestimating the probability of tax audits, and their compliance is higher when theprobability of tax audits is taken into consideration.
As for the other variable, MB is positive and significant at the 5% level under the tax
rate of 40%. This result is consistent with the compliance rate and implies that
individuals with higher strategic reciprocity are more likely to deviate from the safetyzone (i.e., the compliance indicator is lower). However, since there is no significant
difference when the tax rate falls to 30%, the difference in compliance due to individual
attributes is unlikely to occur under relatively low tax rates.
6. Conclusions
The objective of this research is to experimentally verify a theoretical model of tax
22compliance, assuming a game-theory situation between a taxpayer and an auditor.
Specifically, the verification is carried out using experimental data to answer thefollowing three questions: (1) how do the changes of the tax rate affect taxpayers’
behavior? (2) What results are brought about by different expectations about the
behavior of the other player? (3) What influence does personality have on the tax
compliance of taxpayers?
	  The main findings are shown below. First, with regards to changes to the tax rate andthe behavior of each economic agent, contrary to the forecasts of the theoretical model,
it was found that if the tax rate is lowered, the extent of the taxpayer’s tax complianceincreases. This suggests that the more the model forecast, the less the taxpayer is able toanticipate the behavior of the auditor, and thus the taxpayer behaves in a shortsighted
manner. Second, regarding the relationship between the different expectations about the
behavior of the other player and the taxpayer’s tax compliance, it was found that theextent of the taxpayer’s tax compliance is higher for the “strategic condition,” in which
it is reported to that the other party is an actual human being, compared to the “single
condition,” in which it is reported that the other party is a computer. This suggests that asituation in which the other player is considered an agent who possesses limited
rationality and whose actions may deviate from balanced behavior results in
tax-declaration behavior with higher compliance.

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25

Table 1. Numerical example of equilibrium at t =0.4
True

Reportingprobability of

Expected payoff

Expected payoff

incomeincomeAuditing

for taxpayers

for auditors

130

80

0

98

32

120

70

0.29

77.7

40

110

60

0.37

67.6

39.4

100

50

0.39

60.5

30.4

90

40

0.4

51.1

32.7

Table 2. Numerical example of equilibrium at t =0.3
True

Reportingprobability of

Expected payoff

Expected payoff

incomeincomeAuditing

for taxpayers

for auditors

130

63.3

0

111

19

120

53.3

0.24

91.8

26.2

110

43.3

0.34

80.1

27.2

100

33.3

0.38

71.2

25.8

90

23.3

0.39

63.5

23.4

Table 3. Summary of our experiments
No

Date

Place

ConditionN

Tax rate

1

February 2014

Keio business school

Single150.3, 0.4

2February 2014

Keio business school

strategic

27

0.3, 0.4

Table 4. Summary of subjects of the experiments
No

Condition

N

Male

FemaleAverage

Average years

Averageageof businessrewards

1

Single

15

11

4

31.9

6.8

2,253

2

strategic

27

22

5

31.2

7.0

2,069

42

33

9

31.5

6.9

2,137

26

Table 5. The changes of tax rate and the average reporting income (all sample)
True

N

Reporting

Reportingat t = 0.4

at t = 0.3

incomedifference

p value

130

28

96.07

97.86

-1.79

0.26

120

28

91.79

94.29

-2.50

0.08

110

28

88.21

89.29

-1.07

0.47

100

28

83.21

85.36

-2.14

0.15

90

28

78.93

78.21

0.71

0.71

87.64

89.60

-1.35

0.33

Total

Table 6. The changes of tax rate and the average reporting income (by condition)
Single condition
True

N

difference

Strategic condition

t=

t=

p

N

income

0.4

0.3

130

15 88.67 90.00

-1.33

0.58

13 104.62 106.92

-2.31

0.25

120

15 84.00 86.67

-2.66

0.15

13 100.77 103.08

-2.31

0.32

110

15 80.67 84.00

-3.33

0.16

13

96.92

95.38

1.54

0.41

100

15 78.67 80.67

-2.00

0.25

13

88.46

90.77

-2.38

0.37

90

15 76.67 76.00

0.67

0.73

13

81.54

80.77

0.77

0.78

Total

81.73 83.47

-1.73

0.43

94.46

95.38

-0.92

0.58

value

t=

t=

0.4

0.3

difference

p
value

Table 7. The changes of tax rate and the rate of compliance (all sample)
TrueincomeNt = 0.4

t = 0.3

difference

P value13028

73.90%

75.27%-1.37%

0.27

120

28

76.49%

78.57%-2.08%

0.17

110

28

80.19%

81.17%-0.97%

0.47

100

28

83.21%

85.36%-2.14%

0.15

90

28

87.70%

86.90%

0.79%

0.78

80.30%

81.46%-1.16%

0.39

total

27

Table 8. The changes of tax rate and the rate of compliance (Single condition)
True incomeN

t = 0.4

t = 0.3

difference

P value

13015

68.21%

69.33%-1.02%

0.66

120

15

70.00%

72.22%

-2.22

0.13

110

15

73.33%

76.36%

-3.03

0.16

100

15

78.67%

80.67%

-2.00

0.25

90

15

85.19%

84.44%

0.74

0.73

75.08%

76.59%

-1.50

0.51

total

Table 9. The changes of tax rate and the rate of compliance (Strategic condition)
True incomeN

t = 0.4

t = 0.3

difference

P value130

1380.47%

82.25%-1.78%

0.25

120

13

83.97%

85.90%-1.92%

0.59

110

13

88.11%

86.71%

1.40%

0.41

100

13

88.46%

90.77%-2.31%

0.36

90

13

90.60%

89.74%

0.85%

0.89

86.32%

87.07%-0.75%

0.72

Total

Table 10. The changes of tax rate and the degree of safe divergence
Total (N=28)
The degree ofSingle (N=15)

Strategic (N=13)t = 0.4

t = 0.3

t = 0.4

t = 0.3

t = 0.4

t = 0.3

12.14

5.71

11.33

7.33

13.08

3.85

safe divergence
Difference

6.43

4.00

9.23

P value

0.017*

0.236

0.021*

28

Table 11. The Average reported income (by condition) at t = 0.4
True income

Single condition

Strategic condition

p value

130

88.13

104.620.011*

120

83.75

100.770.002**

110

80.63

96.92

0.002**

100

78.75

88.46

0.019*

90

76.25

81.54

0.304

Table 12. The Average reported income (by condition) at t = 0.3
True income

Single condition

Strategic condition

p value

130

88.75

106.920.008**

120

85.63

103.080.003**

110

83.13

95.38

0.003**

100

80.00

90.77

0.009**

90

75.63

80.77

0.193

Table 13. Descriptive statistics
Variable

Average

VAR

Min

Max

29

Table 14. Correlation coefficient

Table 15. The result of regression analysis

Constantterm

Justified R230