Impacts of public disclosure on tax compliance using agent-based modeling

Abstract

This study examines the impact of public disclosure of tax information on tax compliance using simulation experiments utilizing agent-based modeling. We investigate two scenarios: (i) partial disclosure, in which tax returns and audit results are made public without taxpayer identities, and (ii) full disclosure, in which this information is publicized with taxpayer identities. Our simulation results reveal that in the partial disclosure scenario, the effect on tax compliance is contingent upon the social state of individual moral values regarding tax payment. Specifically, partial disclosure has a positive impact on tax compliance when taxpayers exhibit a relatively strong moral consciousness and a negative impact when their moral consciousness is weak. In the full disclosure scenario, when the moral consciousness of the population is sufficiently weak, the average reported income decreases despite the positive effect of the naming-and-shaming policy on tax compliance.

1 Introduction

To enhance tax compliance, audits are undoubtedly a useful policy measure for tax authorities, although the associated administrative costs tend to increase with higher audit frequency. The pioneering work by Allingham and Sandmo (1972) on taxpayer compliance behaviors predicts that an increase in the audit rate unambiguously leads to a higher level of individual income reporting. This theoretical prediction aligns with the results of numerous laboratory experiments employing tax evasion games (e.g., Alm et al. 1992a; Fortin et al. 2007) and the results of some empirical research (e.g., Dubin et al. 1990). However, evidence suggests that audit rates in real societies are often estimated to be much lower than 10% (see Andreoni et al. 1998). These limited rates imply that tax audits may not be cost-effective in deterring taxpayers from evading taxes due to the relatively high administrative costs associated with examining tax returns.

As an alternative or complementary measure with lower administrative costs, researchers in tax compliance have explored the impact of publicizing audit results on individual tax compliance behaviors. Gordon (1989) proposes a model where individual taxpayers face non-pecuniary or psychic costs in addition to the expected pecuniary utility described in Allingham and Sandmo (1972). In Gordon's (1989) model, the psychic components of individual utility include an intrinsic moral cost and a reputation or stigma cost for taxpayers engaged in tax evasion. The stigma cost arises from observing the proportion of compliant taxpayers among others in the previous period. It is assumed that the stigma cost for tax evaders increases as the proportion of compliant taxpayers rises, as they believe that a larger portion of society considers tax evasion morally wrong and blames them for their actions. Myles and Naylor (1996) propose a utility function that incorporates the benefit of conforming to a group of tax compliers in addition to the expected pecuniary utility. In their model, taxpayers derive additional utility from complying with their tax obligations, and this utility increases with the proportion of compliers. Therefore, in both models, public disclosure of audit results, including the proportion of compliers or evaders among audited taxpayers, can serve as a mechanism to enhance tax compliance. By making the audit results public, taxpayers are motivated to avoid incurring the stigma cost associated with tax evasion or to obtain the benefits associated with conformity. Although these studies do not explicitly discuss a public disclosure policy, the findings suggest that such a policy can positively influence taxpayer behavior.

In this paper, we investigate the impact of public disclosure of tax information on tax compliance using an agent-based tax evasion model with heterogeneous agents. Our simulation experiment comprises two primary scenarios: one where tax information is publicly disclosed with the identities of detected evaders (full disclosure), and one without disclosing identities (partial disclosure).¹ Publicly disclosing the identities of detected tax evaders is sufficient to stigmatize those individuals as part of the naming-and-shaming policy, as shown in laboratory experiments by Coricelli et al. (2010) and Coricelli et al. (2014). Bø et al. (2015) conducted an empirical study on the impacts of increased public disclosure after 2001, when individual tax information became accessible on the Internet in Norway. Their findings suggest that the average reported income increased by 3.1% due to the increased Internet exposure.² However, most countries keep individual taxpayer information confidential or restrict public access, likely to protect privacy. Empirical evidence from Japan in Hasegawa et al. (2013) suggests privacy costs for taxpayers whose identities are made public, regardless of their compliance with tax obligations.³ Therefore, public disclosure of taxpayers’ identities could be a subject of dispute among individuals concerned about invasion of privacy, even though the disclosure is limited to tax evaders under the naming-and-shaming policy.

Partial disclosure, whereby individual tax returns and audit results are made public without revealing taxpayers’ identities, referred to as partial disclosure, has the potential to activate reciprocal motives among taxpayers by observing compliance behaviors of their peers. Bazart and Bonein (2014) propose a model in which taxpayers adjust their reported income in a reciprocal manner to mitigate perceived inequity in tax burdens among taxpayers with the same tax liability, based on their observation of the average reported income of their peers. In both scenarios of our simulation, we assume that taxpayers’ reciprocal motives arise due to public disclosure in a similar manner as Bazart and Bonein's (2014) model.

However, when we consider that individual taxpayers use the average reported income of their peers from the previous year as a reference point, it can induce both positive and negative reciprocity. In other words, taxpayers are inclined to increase (or decrease) their reported income to address a perceived advantageous (or disadvantageous) inequity if their own reported income in the previous year fell below (exceeded) the reference point. Consequently, due to the existence of heterogeneous taxpayers within society, theoretical analyses cannot provide definitive conclusions about the impact of partial disclosure on average reported income. To address this limitation and gain a deeper understanding of the effects of public disclosure, we conduct several simulation experiments using agent-based modeling, which allows us to consider the extended heterogeneity of taxpayers.

The simulation model utilized in this study incorporates heterogeneous preferences among taxpayers, as well as varying levels of income endowments assigned to these individuals. These preferences are represented through a utility function, which subtracts psychic costs from the expected pecuniary utility based on the formulations proposed by Allingham and Sandmo (1972) and Yitzhaki (1974). The psychic components of the utility function encompass three key aspects: the moral cost associated with violating private norms, the reciprocity cost triggered by observing the behaviors of peers, and the stigma cost arising from the diffusion of deceptive behaviors among peers (which is not present in the partial disclosure setting). Consequently, we assume that taxpayers have different preferences in terms of risk attitudes that influence their pecuniary utility, as well as parameters related to these psychic components. In our simulation experiment, we consider five different distributions of unit moral costs or constant marginal moral costs associated with the amount of unreported income. This allows us to examine how the impact of public disclosure on the average reported income is contingent upon the social state of individual moral values concerning tax payment.

In the partial disclosure scenario, we will demonstrate that in a society where taxpayers exhibit a relatively strong (or weak) moral consciousness regarding tax payment, partial disclosure has a positive (or negative) effect on tax compliance. In other words, the impacts of partial disclosure are strongly contingent upon the social state of individual moral values regarding tax payment. In the full disclosure scenario, if a society exhibits a stronger moral consciousness, full disclosure increases the number of taxpayers who fully comply with their tax obligations, thereby enhancing tax compliance on average. Conversely, if the moral consciousness of the population in the society is sufficiently weak, the average reported income is reduced, as the positive effects of the naming-and-shaming policy are outweighed by negative reciprocity effects in full disclosure. Additionally, we observe that the positive effect of increasing the audit rate is significantly reinforced by the naming-and-shaming policy in a society with a stronger moral consciousness, as the cost-effectiveness of auditing can be substantially improved.

The remainder of this paper is organized as follows: Sect. 2 provides background information by reviewing the related literature. Section 3 presents the baseline model without interdependence among taxpayers and introduces theoretical models that incorporate public disclosure of tax information, forming the framework for the simulation experiments. Section 4 outlines the simulation design and presents the results of the experiments. Finally, Sect. 5 concludes the paper.

2 Background

Several experimental studies on tax compliance have investigated whether taxpayers experience any stigma cost when they underreport their income and, if so, how these costs affect tax compliance. These studies involve informing participants about individuals who have evaded taxes with identification in their experimental treatment. The laboratory experiments conducted by Coricelli et al. (2010, 2014) indicate that showing photographs of detected evaders to participants reduces the proportion of evaders and the amount of evaded taxes relative to the tax liability. This effect is attributed to public emotions, such as shame, which subsequently leads to stigmatization. In other experimental studies with a similar naming-and-shaming policy, such as Casagrande et al. (2015) and Casal and Mittone (2016), the treatment in which the identities of tax evaders are made public significantly decreases the average unreported income as well as the likelihood of evasion, compared to the treatment with confidentiality.

The effects of partial disclosure, in which the income amounts reported by individual taxpayers are made public in an anonymous manner, have also been investigated in several experimental studies. Laury and Wallace (2005) report that their experiment found no significant difference in the average reported income between the partial disclosure treatment and the full confidentiality treatment. In their experiment, the access to tax information about other taxpayers in the partial disclosure treatment may have been too restricted to influence the reporting behaviors of individual taxpayers. Fortin et al. (2007) examine the existence of a social conformity effect by providing participants with information on the average reported income and the number of evaders in their reference group from the previous period. Their econometric analysis using data from the experiment concludes that no social conformity effect exists, indicating that the reported income of each taxpayer is not significantly influenced by the average reported income in their reference group. Blaufus et al. (2017), in their laboratory experiment, find that the average compliance rate in the partial disclosure treatment is slightly lower than in the confidentiality treatment, which they refer to as a contagion effect on tax compliance. Furthermore, in the full disclosure treatment, where the reported incomes of peers are publicized along with their photographs, they observe that the shame effect, which enhances tax compliance, outweighs the contagion effect in the average of all experimental rounds.

The fact that the effect of partial disclosure on the average reported income is insignificant or negative does not necessarily mean that individual reported incomes do not change or decrease in response to partial disclosure. Data from the laboratory experiment conducted by Bazart and Bonein (2014) show that providing information about the average reported income among their peers has both significant positive and negative impacts on individual reported income, even though the average reported income does not differ significantly from the treatment in which no tax information is provided.

In the laboratory experiments conducted in the aforementioned studies, it was difficult to observe any significant impact on the average reported income, as the positive and negative reciprocity effects likely offset each other. However, it is worth considering whether the level of taxpayer heterogeneity captured in these experiments is sufficient to represent the real world, given that the majority of subjects are university students recruited from European and North American countries. Alm et al. (2015), who aim to investigate the external validity of tax compliance experiments, suggest that the behaviors observed in laboratory experiments largely parallel behaviors in the real world, and little difference between the behaviors of students and non-students within the same experimental setting exists. However, Choo et al. (2016) indicate that notable differences in behavior between students and non-students are present, which may be attributed to norms of tax compliance. Moreover, participants from different countries may exhibit varying compliance behaviors due to cultural and institutional differences, as demonstrated by Gërxhani and Shram (2006), Alm and Torgler (2006), and Alm et al. (2017).

3 Theoretical framework

Consider a society with N taxpayers and a tax authority. Each taxpayer i ($=1,\ldots , N$) has a gross income $w_{i}$ and reports an income $x_i$ within $[0,w_{i}]$. Taxes are levied on the reported income $x_i$ at a flat rate $\tau$ if $w_i-x_i$ remains undisclosed. After tax payment, taxpayer i has a disposable income $y_{i}^{n}=w_{i}-\tau x_{i}=(1-\tau )w_{i}+\tau (w_{i}-x_{i})$. The tax authority audits each taxpayer with probability p, detecting any unreported income. Audits occur randomly with an audit rate of p, known to all taxpayers before filing returns.⁴ If caught cheating, the taxpayer pays taxes on the unreported income $\tau (w_{i}-x_{i})$ and incurs a fine $f\tau (w_{i}-x_{i})$, resulting in a disposable income $y_{i}^{c}=(1-\tau )w_{i}-f\tau (w_{i}-x_{i})$.

Each taxpayer spends their entire disposable income on private consumption, denoted by $y_i$. Their pecuniary utility is $u_{i}(y_{i})=u(y_{i};\alpha _{i})$, where $\alpha _{i}$ reflects individual risk preferences. We assume that the utility function is increasing, strictly concave with respect to $y_{i}$, and $\lim _{y_{i}\rightarrow 0}u'_i(y_i)=\infty$. Hence, the expected pecuniary utility is $\text {EU}_{i}(x_{i})=pu_{i}(y_{i}^{c})+(1-p)u_{i}(y_{i}^{n})$, where $y_i^c$ and $y_i^n$ are realized with probabilities p and $1-p$, respectively.

3.1 A baseline model

This section introduces a baseline model for comparative analysis. Our focus is on assessing the impact of tax information disclosure on taxpayer compliance. In this baseline model, taxpayer data confidentiality is ensured. Following Gordon (1989), each taxpayer aims to maximize expected pecuniary utility net of a moral cost associated with tax evasion. Formally, the objective function for taxpayer i is

$$\begin{aligned} V_{i}(x_{i})=EU_{i}(x_{i})-\gamma _{i}(w_{i}-x_{i}), \end{aligned}$$

(1)

where $\gamma _{i}\ge 0$ represents the intrinsic moral cost incurred by an additional increase in the taxpayer’s unreported income. This aligns with Gordon's (1989) model.⁵ In the canonical tax evasion model by Allingham and Sandmo (1972) and Yitzhaki (1974) (the ASY model), taxpayers maximize their expected pecuniary utility $EU_i(x_i)$ without bearing any moral cost ($\gamma _i=0$ for all i).⁶

Any tax information is confidential so that taxpayer i attempts to maximize $V_{i}(x_{i})$ in (1) with respect to $x_{i}$. The first-order condition for an interior solution, denoted by $x_{i}^{*}$, is

$$\begin{aligned} V'_i(x_i^*)=EU^{\prime}_i(x_i^*)+\gamma _{i}=0, \end{aligned}$$

(2)

where $EU^{\prime}_i(x^*_i)=pf\tau u'_{i}(y_{i}^{c})-(1-p)\tau u'_{i}(y_{i}^{n})$.⁷ Thus, the optimal amount of income reported, denoted by $x(\gamma _{i},w_{i})$, is

$$\begin{aligned} x(\gamma _{i},w_{i})={\left\{ \begin{array}{ll} w_{i}&{}\quad \text {if }\gamma _{i}\ge -EU'_{i}(w_{i}), \\ x_{i}^{*}\in (0,w_{i})&{}\quad \text {if }-EU'_{i}(w_{i})>\gamma _{i}>-EU'_{i}(0), \\ 0&{}\quad \text {if }\gamma _{i}\le -EU'_{i}(0). \end{array}\right. } \end{aligned}$$

(3)

To avoid a trivial case where all taxpayers comply with their tax obligations even without incurring psychic costs, we assume that $f<(1-p)/p$. From (2), it is evident that the interior solution of reported income $x_{i}^{*}$ increases between 0 and $w_{i}$ as the unit moral cost $\gamma _{i}$ rises.

Applying the implicit function theorem to (2), we can easily see that when the audit rate p or fine rate f increases, the reported income $x^{*}_{i}$ also unambiguously increases, assuming $-EU'_{i}(w_{i})>\gamma _{i}\ge -EU'_{i}(0)$. These effects align with traditional evasion deterrence policies. However, the impact of a change in the income tax rate $\tau$ on $x_{i}^{*}$ is rather complex. If we assume that the Arrow-Pratt measure of absolute risk aversion $\rho _{i}(y_{i})\equiv -u''_{i}(y_{i})/u'_{i}(y_{i})$ is decreasing or constant (DARA or CARA) with respect to $x_{i}$, there exists $\hat{\gamma _i}\in (0,-EU'_i(w_i))$ such that

$$\begin{aligned} \frac{\partial x_{i}^{*}}{\partial \tau }\lesseqgtr 0\text { if }\gamma _{i}\gtreqless \hat{\gamma _{i}}. \end{aligned}$$

(4)

Hence, taxpayers who have any unit moral cost more than their own threshold value of ${\hat{\gamma }}_i$ respond to the higher tax rate by reporting their income less under the assumption of DARA or CARA. (see the proof of Proposition 1 in Gordon 1989).

With heterogeneity among taxpayers, the impact of tax rates on compliance at the societal level depends on the distribution of unit moral costs, that is, in a society where a number of taxpayers have sufficiently large unit moral costs, an increase in the tax rate would decrease the average compliance rate at the intensive margin, where taxpayers determine how much income to report. However, we also need to investigate the impact at the extensive margin-where taxpayers decide whether to engage in tax evasion-in order to obtain a complete understanding of the overall effect on the compliance rate. From (3), we can examine the effect of the tax rate on the number of full compliers. From the assumptions that $f<(1-p)/p$ and $u_i(\cdot )$ is strictly concave, we observe that $-EU'_i(w_i) = (1-p-pf)\tau u'_i[(1-\tau )w_i]$ increases with $\tau$. As a result, the number of taxpayers with $\gamma$ greater than $-EU'_i(w_i)$ decreases. Therefore, an increase in the tax rate changes some taxpayers from being full compliers to becoming evaders. Consequently, an increase in the tax rate unambiguously decreases the compliance rate at the extensive margin.

3.2 Public disclosure with taxpayer interdependence

In many countries, governments maintain strict tax return confidentiality and audit outcomes to respect taxpayers’ privacy. Given the illegality of tax evasion, few willingly disclose their tax information, kee** income reporting clandestine. Consequently, taxpayers’ reported income is not influenced by others, and they do not consider their actions affecting others’ reporting decisions. However, public disclosure by tax authorities could trigger social interactions. Here, we model non-pecuniary utilities from social interactions, exploring the impact of disclosure on compliance behaviors.

3.2.1 Partial disclosure

We assume that taxpayers incur psychic costs perceiving inequity in tax burden distribution. To gauge differences and assess the extent of inequity, they speculate about others’ compliance, forming a reference point based on peers’ total reported income relative to peers’ total income endowment, which can be described as the average compliance rate among the other taxpayers. Deviations from this reference point trigger perceptions of advantageous or disadvantageous inequity. For advantageous inequity, guilt may prompt increased reporting, reducing psychic cost. Conversely, disadvantageous inequity may lead to anger and increased reporting costs. This aligns with the formulation by Fehr and Schmidt (1999) on inequity aversion.

However, the disutility from an inequitable tax burden arises only if the tax authority publicly discloses tax information. Without this information, taxpayers cannot establish their reference point to measure inequity. Thus, public disclosure becomes necessary for this purpose. We assume the tax authority discloses audit results from the previous tax year. Through public disclosure, taxpayers gain access to audited taxpayers’ reported incomes. They also estimate reported incomes of unaudited taxpayers using audit data. As the random audit is conducted and taxpayers receive a distribution of income endowments among audited taxpayers, they can approximate the income distribution among all taxpayers. Additionally, by observing the distribution of reported incomes across different levels of income endowment among the audited taxpayers, taxpayers can make estimations about the overall distribution of reported incomes.

Given that taxpayers rely on the previous tax year’s audit results to make their decision each year, it is essential to consider the dynamics of the process. Since tax years are discrete, indexed as $t=0,1,2,\ldots$, the dynamics proceeds discretely. In year t, the reference point for taxpayer i is determined by the proportion of aggregate income reported by all taxpayers except i relative to their aggregate income in the previous year, denoted as $a_{-i,t-1} \equiv \sum _{j=1, j\ne i}^{N} x_{j,t-1} / \sum _{j=1, j\ne i}^{N} w_{j}$, where $x_{j,t-1}$ represents the reported income of taxpayer j in the previous year. Letting $a_{i,t-1}\equiv x_{i,t-1}/w_{i}$ and ${\textbf{x}}_{t-1}\equiv (x_{1,t-1},\dots ,x_{N,t-1})$, we assume that the public disclosure of audit results induces an additional psychic cost as follows:

$$\begin{aligned} C_{i,t}(x_{i,t},{\textbf{x}}_{t-1}) =\delta _i(a_{-i,t-1}-a_{i,t-1})(w_i-x_{i,t}), \end{aligned}$$

(5)

where $\delta _{i}$ is a positive parameter that is intrinsic to taxpayer i. The psychic cost in (5) captures taxpayer i’s aversion to inequity, where i experiences feelings of guilt (anger) when $a_{i,t-1}<(>)a_{-i,t-1}$, indicating advantageous (disadvantageous) inequity.⁸ Therefore, $\delta _{i}$ can be interpreted as the intensity of taxpayer i’s guilt or anger. Moreover, this psychic cost also stimulates taxpayer i’s reciprocity motives. As $a_{-i,t-1}$ increases, taxpayer i is more inclined to reciprocate the moral behavior of other taxpayers in the previous year through higher tax compliance. Conversely, if $a_{-i,t-1}$ decreases, taxpayer i has a reduced willingness to pay taxes in response to the immoral behavior of other taxpayers in the previous year. As a result, taxpayer i aims to maximize their expected pecuniary utility net of the psychic costs in year $t\ge 1$, represented as $V_{i}(x_{i,t}) -C_{i,t}(x_{i,t},{\textbf{x}}_{t-1})$.

We assume that the tax authority makes annual public disclosures starting from year 1. In year 0, taxpayer i aims to maximize their expected pecuniary utility net of the moral cost $\gamma _{i}(w_i-x_{i,0})$, denoted as $V_{i}(x_{i,0})$, since no tax information to induce their reciprocity motives is available. Assuming that every taxpayer is myopic, from year 1 onward, taxpayer i attempts to maximize $V_{i}(x_{i,t}) -C_{i,t}(x_{i,t},{\textbf{x}}_{t-1})$ with respect to $x_{i,t}$ given ${\textbf{x}}_{t-1}$ in any $t\ge 1$. The first-order condition for an interior solution $x_{i,t}^{*}\in (0,w_{i})$ is

$$\begin{aligned} EU'_{i}(x_{i,t}^*)+\gamma _i+\delta _i(a_{-i,t-1}-a_{i,t-1})=0. \end{aligned}$$

(6)

Applying the implicit function theorem to (6), we can derive the relationships of $\text {d}x_{i,t}/\text {d}x_{i,1-t}<0$ and $\text {d}x_{i,t}/\text {d}x_{j,1-t}>0$ for any i and $j\ne i$. The former indicates that a small increase in taxpayer i’s reported income $x_{i,t-1}$ in the previous year $t-1$ reduces their own feelings of guilt (or strengthens their anger) when reporting income in the current year t, as it implies a decrease (or increase) in advantageous (or disadvantageous) inequity. As a result, taxpayer i decreases their reported income $x_{i,t}^*$ in year t. However, if taxpayer $j\ne i$ increases their reported income $x_{j,1-t}$ infinitesimally in the previous year, taxpayer i feels more guilt (or less anger) because the advantageous inequity expands (or the disadvantageous inequity reduces). Consequently, taxpayer i responds to the kind and moral behavior of other taxpayers by increasing their reported income $x_{i,t}^*$ in year t.

3.2.2 Full disclosure

Next, let us consider the scenario in which the tax authority not only discloses the auditing results but also reveals the identities of taxpayers who have been caught evading taxes. We assume that if taxpayer i underreported income and their evasion is detected in year t, they incur a stigma cost $S_{i}$ regardless of the amount of income underreported in that year. According to Gordon (1989), $S_{i}$ is proportional to the proportion of taxpayers whom taxpayer i perceives as considering tax evasion to be morally wrong. This proportion can be positively correlated with the proportion of fully compliant taxpayers. Let us denote the proportion of full compliers, excluding taxpayer i, in year $t-1$ as $\lambda _{i,t-1}$. If the tax authority estimates this proportion and publicly discloses it in year t, we can define the stigma cost for taxpayer i in year t as follows:

$$\begin{aligned} S_{i}(x_{i,t},\lambda _{i,t-1})={\left\{ \begin{array}{ll} \lambda _{i,t-1}s_{i}>0 &{} \quad \text {if }x_{i,t}<w_{i}, \\ 0 &{} \quad \text {if }x_{i,t}=w_{i}. \end{array}\right. } \end{aligned}$$

(7)

Here, $s_{i}$ is a positive fixed parameter that represents the level of aversion of taxpayer i toward being stigmatized. This parameter is assumed to be intrinsic to taxpayer i and unaffected by any information regarding other taxpayers’ compliance behaviors.

In Gordon’s model, the stigma cost incurred by a taxpayer is assumed to be positively correlated with the amount of tax evaded by that taxpayer. In contrast, Alm et al. (2017) present evidence suggesting that the effect of shaming primarily influences the decision to engage in tax evasion rather than the extent of evasion. This evidence is based on their tax compliance experiment, in which they examined the impact of displaying photographs of tax evaders to all participants. Consequently, the stigma cost has a limited effect on the decision of how much to evade, but rather focuses on the decision of whether to evade or not. Our assumption, as described in (7), aligns with the experimental findings reported by Alm et al. (2017).

The stigma cost in (7) leads to income reporting decisions at the extensive margin, that is, at the beginning of year t, taxpayer i chooses whether to evade taking $x_{i,t}^*\in [0,w_i)$ as given. Thus, taxpayer i chooses to be an evader if

$$\begin{aligned}{} & {} EU_{i}(x^{*}_{i,t})-[\gamma _i+\delta _{i}(a_{-i,t-1}-a_{i,t-1})] (w_{i}-x^{*}_{i,t})-p\lambda _{i,t-1}s_{i}\nonumber \\{} & {} \quad >EU_{i}(w_{i})=u_{i}[(1-\tau )w_{i}], \end{aligned}$$

(8)

Otherwise, i chooses not to evade at all.⁹ Since the left-hand side of the inequity (8) decreases with p while the right-hand side is not affected by p, an increase in the audit rate decreases the likelihood of taxpayer i evading taxes.¹⁰

4 Simulation analysis

In this section, we begin by presenting a simulation model along with various scenarios for experimentation. Subsequently, we analyze the outcomes obtained from these experiments. The simulations were conducted using NetLogo (Wilensky 1999).¹¹

4.1 Model description

We utilize a constant relative risk aversion (CRRA) utility function as a pecuniary utility component for each taxpayer:

$$\begin{aligned} u_{i}(x_{i})= {\left\{ \begin{array}{ll} \frac{x_{i}^{1-\alpha _{i}}}{1-\alpha _i} &{} \quad \text {for }\alpha _i\ne 1, \\ \ln x_{i} &{} \quad \text {for }\alpha _i=1, \end{array}\right. } \end{aligned}$$

(9)

where $\alpha _i$ represents the preference parameter for agent i. From (9), the Arrow-Pratt measures of absolute and relative risk aversion are derived, with $\rho _{i}(x_i)=\alpha _{i}/x_{i}$ representing decreasing absolute risk aversion (DARA) and $r_{i}(x_{i})=\alpha _i$ representing constant relative risk aversion (CRRA). Therefore, $\alpha _i$ serves as a CRRA coefficient, and the pecuniary utility function in (9) implies that taxpayer i exhibits behavior that is risk averse for $\alpha _i>0$, risk neutral for $\alpha _i=0$, and risk seeking for $\alpha _i<0$.

The simulation spans 41 tax years. In year 0, taxpayers make their choices under the assumption of confidentiality. From years 1 to 40, certain tax information from the previous year is made public annually. All parameter values and the relevant distributions used in the simulation are described in Table 1. Additionally, the histograms of income endowments and preference parameters are displayed in Fig. 14a–e in the Appendix. The distribution of CRRA coefficient aligns with the experimental findings from Holt and Laury (2002, 2005), Harrison et al. (2005), and Harrison and Ruström (2008).¹² In the field experiment conducted by Harrison et al. (2007) in Denmark, which replicates the Holt-Laury experiment, they report an average CRRA coefficient of 0.67. Furthermore, they found a scarcity of risk-seeking or risk-neutral subjects within the Danish population.

Table 1 Model parameters and values

In our simulation, we conducted two experiments. The first simulation experiment, labeled "Experiment 1," involved 25 runs without the naming-and-shaming policy. The combinations of the audit rate, mean unit moral cost, and mean reciprocal propensity for runs 1–25 are presented in Table 2 in the Appendix. In the second experiment, "Experiment 2," we performed 25 runs with the naming-and-shaming policy, corresponding to runs 1–25 in Table 2. Prior to those two experiments, we conducted a preliminary experiment in which agents choose their decision only in year 0 when any taxpayer interdependence does not occur. In the preliminary experiment, another audit rate $p = 0.2$ and two additional tax rates $\tau = 0.2$ and 0.4 are included in order to confirm the external validity for our model, in comparison with the results of the laboratory experiments.

4.2 Results of simulation experiments

4.2.1 Confidentiality

In tax year 0, taxpayers make their choice under confidentiality. Figure 1 presents the compliance rates obtained from the outcomes of the preliminary experiment. The compliance rate is defined as a proportion of total reported income to total true income (i.e., $\sum _{j=1}^N x_j/\sum _{j=1}^N y_j$).¹³ An individual compliance rate is defined as the proportion of income reported by an individual taxpayer to their true income (i.e., $x_i/y_i$ for $i=1,\dots ,N$). Taxpayers who reported their true income are classified as full compliers, while those who reported zero income are considered full evaders. Taxpayers who reported a positive but lower amount of income than their true income are referred to as partial evaders. Figure 2 shows the proportions of those behavioral types of taxpayers under confidentiality. Furthermore, Fig. 3 illustrates the distribution of individual compliance rates in year 0 when the audit rate is 0.2 along with the other three audit rates.

Fig. 1

Compliance rates with confidentiality

Fig. 2

Proportions of three behavioral types of agents with confidentiality

Fig. 3

Distributions of individual compliance rates

The meta-analysis conducted by Alm and Malézieux (2021) utilizes data from 70 papers on tax compliance laboratory experiments published between 1978 and 2018. According to their findings, the average audit rate is 0.2 (with a standard deviation of 0.15), the average fine rate is 2.01 (1.47), the average tax rate is 0.34 (0.11), and the average compliance rate is $65\%$ ($41\%$).¹⁴ While the fine rate in our simulation is lower on average compared to the meta-analysis results, the fine rate of 1 we adopted is more realistic than the average rate observed in the laboratory experiments. In our simulation, with an audit rate of 0.2 (illustrated by the purple bars in Fig. 1), the compliance rate of $65\%$-consistent with the average rate in the laboratory experiments-falls between $57\%$ and $73\%$ for mean unit moral costs of 0.05 and 0.07, respectively.

Fig. 4

Compliance rates and proportions of behavioral types of agents in the experimental literature

Figure 4 shows the compliance rates and the proportions of full compliers and full evaders obtained in several experimental studies. Out of 11 articles, we extract the results from experimental sessions relevant to the taxpayer’s compliance decision under confidentiality.¹⁵ Considering the eight experimental studies from the fourth column to the last on the horizontal axis in the figure, the audit rates are set at 0.2 or more in their treatments (refer to Table 3 in the Appendix), so the resulting compliance rates in all of those studies except for Laury and Wallace (2005) are around two-thirds. Those results corroborate Alm and Malézieux (2021). However, those audit rates are much higher than the actual rates as these are estimated to be substantially smaller than 0.1 in real societies. Focusing on the first three columns in Fig. 4, the compliance rates in those three studies are around a third in their relevant settings, with more realistic values of audit rates (as shown in the first three rows in Table 3). In particular, Alm et al. (1992a) implement their experimental session in which the audit rate is 0.02, the tax rate is 0.3, and the fine rate is 1 with no public good. They show an average compliance rate of $32.1\%$, which is close to the compliance rate of $34.46\%$ when the audit rate is 0.02 and the mean of unit moral cost is 0.05 as illustrated by the blue bars in Fig. 1. Alm et al. (2015) report that the average compliance rate is 28.6% for $p = 0$ and 36.8% for $p = 0.05$ using data from only baseline scenarios of six experimental studies they selected. In our simulation, the compliance rates for $p = 0.02,0.03$, and 0.04 lie between 28.6% and 36.8% when the mean unit moral cost is 0.05.

As shown in Fig. 3, the individual compliance rates obtained from our simulation exhibit a bimodal distribution with modes appearing at either 1 (representing full compliance) or 0 (representing full evasion), while the frequencies at each of the 19 rates between 0 and 1 are very small. In the case where $p = 0.2$, the proportion of taxpayers who report all-or-none is 79.17%, 79.17%, 83.54%, 89.47%, and 94.64% for ${\bar{\gamma }}$ values of 0.03, 0.05, 0.07, 0.09, and 0.11, respectively (refer to the purple bars in Fig. 3). In comparison, the meta-analysis conducted by Alm and Malézieux (2021) also shows a bimodal distribution with 45% of taxpayers classified as full compliers and 19% as full evaders. Therefore, the proportions of all-or-none behaviors observed in our simulation for $p = 0.2$ are higher than the 64% reported in their meta-analysis which provides an average audit rate of 0.2.¹⁶ Additionally, results from experimental studies in Alm et al. (1992b), Laury and Wallace (2005), and Bazart and Bonein (2014) demonstrate proportions of around two-thirds (refer to Fig. 4). Nevertheless, our simulation experiment successfully replicates the bimodal distribution and prevalence of all-or-none behaviors observed in laboratory experimental studies.

In the preliminary experiment, we conducted the simulation for three different tax rates: $\tau =0.02,0.03$, and 0.04. The result, as shown in Fig. 15 in the Appendix, indicates that the compliance rate decreases as the tax rate increases, regardless of the combination of four audit rates and five distributions of unit moral costs. Clotfelter (1983) demonstrates in his empirical research that higher tax rates tend to induce tax evasion. Similarly, laboratory experiments conducted by Benjamini and Maital (1985) and Alm et al. (1992a) show a significant negative effect of higher tax rates on tax compliance. Moreover, the meta-analysis by Alm and Malézieux (2021) reports a highly significant negative impact of the tax rate on tax compliance at both the intensive and extensive margins within a flat-rate tax system. As discussed in Sect. 3.1, the comparative statics analysis based on the Gordon model suggests that, at the intensive margin, the reported income of an individual taxpayer decreases as the tax rate increases if the taxpayer’s unit moral cost is sufficiently large. Therefore, according to the theoretical model, tax compliance is expected to decrease with higher tax rates in societies where a significant number of taxpayers have high unit moral costs. Our simulation results support this theoretical prediction. Figure 15 in the Appendix presents the findings, indicating that even for a distribution with a mean unit moral cost of 0.03 (the lowest among the five means considered in the simulation), the tax rate has a negative impact on tax compliance. At the extensive margin, the theoretical prediction suggests that higher tax rates lead to a decrease in the proportion of full compliers and an increase in the number of evaders for any distribution of unit moral costs considered in our simulation. Our simulation results align with this prediction, as shown in Fig. 16 in the Appendix, which reports the proportion of full compliers for each tax rate.

4.2.2 Partial disclosure

Figure 5 shows the increases in the total amount of reported incomes resulting from partial disclosure from year 1 to 40. The annual increased amounts in each distribution of unit moral cost are drawn by the color-coded dotted lines. Every year, starting from year 1, taxpayers make their choice after observing the compliance rate among all other taxpayers in the previous year. Therefore, the total reported income tends to fluctuate up and down in a two-year cycle during the 40-year time period. We also draw lines illustrating the 2-period moving mean of the increase in reported income (the solid lines drawn with the same color as the corresponding dotted line) to make it easier to identify trends.

In Fig. 5, the increased amounts of total reported income are displayed for each audit rate of 0.02, 0.03, and 0.04 under the setting of partial disclosure. The total reported incomes show the same qualitative behavior across these three cases. For all scenarios with mean unit moral costs of 0.03, 0.05, and 0.07, the total reported income decreases below the level observed under confidentiality in year 1 when tax information is first made public. Furthermore, the 2-period moving means of the increase in total reported income from year 2 onward consistently show negative values. However, for ${\bar{\gamma }} = 0.07$ and $p = 0.02$, some of the annual increases in reported incomes in even years (represented by the yellow dotted line in Fig. 5a) are slightly above zero. In contrast, when the mean of unit moral cost is 0.09 or 0.11, partial disclosure leads to an increase in total reported income in year 1, and the 2-period moving means of the increase in total reported income remains positive every year from year 2. In many even years, the annual reported income shows negative increments, except for the case in which $p = 0.02$ and ${\bar{\gamma }} = 0.11$, although those values are very close to zero.

Fig. 5

Total reported income increases from partial disclosure

Figure 6 reports the average compliance rates over a span of 40 years, from year 1 to 40. For the three audit rates, the average compliance rate under partial disclosure is significantly lower than the confidentiality level when the mean of unit moral cost is 0.03 or 0.05 (refer to the bottom bar graph in Fig. 6, which represents the difference between the average compliance rate under partial disclosure and the compliance rate in year 0). For ${\bar{\gamma }} = 0.07$, the average compliance rate also decreases although the amount is relatively small compared to the previous cases. Conversely, when the mean unit moral cost is 0.09 or 0.11, the compliance rate shows an average increase as a result of partial disclosure.

Fig. 6

Average compliance rates over 40 years with partial disclosure

Accordingly, the results of the simulation experiment suggest that whether partial disclosure is useful for a society to enhance tax compliance depends on a social state of individual moral consciousness of tax payment. In a society in which a large number of taxpayers are strongly conscious of their responsibility to pay taxes, partial disclosure might have a positive effect on tax compliance. In contrast, if a society includes a large number of taxpayers who have lower consciousness of tax compliance, a backlash against paying taxes may become prominent as a result of the partial disclosure.

In our model, such a backlash is induced by feelings of anger felt by taxpayers who are aware of their disadvantageous inequity due to partial disclosure as explained in Sect. 3.2.1. Taxpayers facing disadvantageous inequity have negative reciprocity motives so that they might have an incentive to lower their reported income to less than the one in the previous year. However, advantageous inequity induces feelings of guilt for taxpayers, leading to positive reciprocity motives. As a result, the positive reciprocity motives might make those taxpayers increase their reported income to greater than in the previous year. From our simulation, we calculated the average numbers of taxpayers who may be positive or negative reciprocators over 40 years (from year 1 to 40) when the audit rate is 0.02. In the cases where ${\bar{\gamma }} = 0.03,0.05$, and 0.07, the majority of the population consists of potential positive reciprocators, while for ${\bar{\gamma }} = 0.09$ or 0.11, the number of potential negative reciprocators surpasses the number of positive reciprocators.¹⁷ However, according to the results of our simulation, partial disclosure diminishes tax compliance for the lower three distributions of unit moral cost, whereas partial disclosure enhances it for the higher two distributions. Therefore, we can infer that a significant number of potential positive reciprocators do not increase their reporting income very much or at all in the former cases. Similarly, in the latter cases, potential negative reciprocators do not have a strong enough incentive to decrease their reporting income.

In year 0, when any tax information is kept confidential, taxpayer i is considered a partial evader if their optimal reported income is given as the interior solution satisfying (2). Therefore, if the tax information provided in year 1 indicates $a_{i,0}<(\text {or}>)a_{-i,0}$, the partial evader i responds to the advantageous (or disadvantageous) inequity by increasing (or decreasing) their reported income to satisfy (6). However, when taxpayer i is a full evader in year 0 such that $V'_i(0)<0$, the full evader reports a part or all of their income in year 1 only if $\delta _i(a_{-i,0}-a_{i,0})>-V'_i(0)$. Put differently, if their marginal reciprocity cost (MRC) $\delta _i(a_{-i,0}-a_{i,0})$ is smaller than or equal to $-V'_i(0)$, taxpayer i, who is a full evader in year 0, keeps reporting no income in year 1. Thus, starting from year 2, the full evader in the previous year does not change their behavior if $\delta _i(a_{-i,t-1}-a_{i,t-1})\le -V'_i(0)$. Similarly, taxpayer i, who is fully compliant in the previous year, reports honestly in every year $t\ge 1$ if $-\delta _i(a_{-i,t-1}-a_{i,t-1})\le V'_i(w_i)$.

Fig. 7

Marginal reciprocity costs when $p = 0.02$

Figure 7 shows the changes in the mean and median of MRC for all agents, as well as the maximum and minimum MRCs when $p = 0.02$. In Fig. 7a–c, we can observe that from year 1 onward, the median MRC (the red line) is positive and lies above the mean MRC (the blue line), which is very close to zero. This indicates that potential positive reciprocators are in the majority over the 40-year period in each distribution of unit moral cost with ${\bar{\gamma }} = 0.03,0.05$, or 0.07. Additionally, for ${\bar{\gamma }} = 0.03$ and 0.05, respectively, the median of positive MRC (the green line) is about a seventh and a third of the absolute value of the median negative MRC (the light blue line) in every year. Therefore, based on these observations, it can be inferred that many full evaders lack the incentive to increase their reported income despite having positive reciprocity motives, as their MRC is not sufficiently large to prompt such behavior. However, some full compliers, who are potential negative reciprocators, respond to significant disadvantageous inequity by transitioning into evaders. Consequently, the total reported income decreases even though potential positive reciprocators constitute the majority. In the case of ${\bar{\gamma }} = 0.07$, the median positive MRC is approximately two-thirds of the absolute value of the median negative MRC, resulting in a relatively smaller negative impact on the total reported income compared to the cases of ${\bar{\gamma }} = 0.03$ and 0.05. In contrast to the aforementioned three cases, Fig. 7d and e reveals that the majority of taxpayers exhibit negative reciprocal motives for ${\bar{\gamma }} = 0.09$ and 0.11 throughout the 40-year period, as indicated by the negative median MRC values below the mean MRC. Specifically, the median positive MRC is approximately 1.2 times larger for ${\bar{\gamma }} = 0.09$ and about 1.6 times larger for ${\bar{\gamma }} = 0.11$ than the absolute value of the median negative MRC. These observations suggest that while some full evaders transition into reporting a positive income amount, many full compliers continue to adhere to honesty since their negative MRCs are not substantial enough to prompt them to become evaders.

Fig. 8

Average numbers of agents by behavioral type with partial disclosure

In Fig. 8, the top figure shows the average numbers of full compliers, full evaders, and partial evaders for a fixed audit rate of $p = 0.02$, considering five distributions of unit moral cost. Additionally, the bottom figure illustrates the net increase in the number of each behavioral type resulting from partial disclosure. The increased number represents the net effect of changes in the number of individual agents transitioning to that specific behavioral type, taking into account the number of agents who switched from other types to the specified type and subtracting the number of agents who transitioned from that type to any other type. In the case of ${\bar{\gamma }} = 0.03$, the number of full evaders increases significantly, while the number of full compliers decreases substantially due to partial disclosure. The number of partial evaders also decreases, but the reduction is much smaller compared to that of full compliers. It is important to note that any full evader in year $t-1$ has the potential to become a positive reciprocator in year $t\ge 1$. Since full evaders constitute the majority each year, the increase in their number indicates that some full evaders do not respond to advantageous inequity. This lack of response can be attributed to the small positive MRCs for those full evaders, as discussed earlier (refer to Fig. 7a). Consequently, after partial disclosure, some full compliers and partial evaders under confidentiality transition into full evaders, while a significant proportion of full evaders continue to fully evade, resulting in a decrease in the total reported income. In the cases of ${\bar{\gamma }} = 0.05$ and 0.07, the decrease in the total reported income can be attributed to a decline in the number of full compliers and an increase in the number of evaders. However, for the distribution with ${\bar{\gamma }} = 0.07$, the impact of partial disclosure on the total reported income is relatively small, as the increase in the number of evaders is not significant. In the cases of ${\bar{\gamma }} = 0.09$ and 0.11, partial disclosure leads to a decrease in the number of full evaders, while substantially increasing the number of partial evaders. Additionally, the number of full compliers also increases. From these observations, it can be inferred that some full evaders transition into partial evaders or full compliers to reciprocate positively in response to advantageous inequity, resulting in an overall increase in the total reported income.

We also investigate the cases of ${\bar{\delta }} = 0.02$ and 0.04 in addition to 0.03 when $p = 0.02$. The average compliance rates and the increased compliance rates in those three cases are reported in Fig. 17 in the Appendix. We can see that either a small increase or decrease in the mean of reciprocal propensity distribution provides the same characteristics as the case of ${\bar{\delta }} = 0.03$, that is, the average total reported income decreases for ${\bar{\gamma }} = 0.03,0.05$, and 0.07, while it increases for ${\bar{\gamma }} = 0.09$ and 0.11 as a result of partial disclosure when ${\bar{\delta }} = 0.02$ or 0.04.

4.2.3 Full disclosure

In Experiment 2, evaders who are audited and caught with a probability of p incur a stigma cost-as defined in (7)-because their names are made public in the following year. The individual stigma costs are determined by the intrinsic stigma cost parameters specific to each taxpayer, denoted as $s_i$ in (7). In our simulation experiment, these parameters follow a truncated normal distribution (refer to Table 1 and Fig. 14e in the Appendix).

In Fig. 9, the top figure shows the average compliance rates from year 1 to 40 under full disclosure for the 15 simulation runs. The bottom figure illustrates the increased average compliance rates due to full disclosure. In addition to this, Fig. 10 reports the 2-period moving means of increased total reported income due to full disclosure (the solid line) and partial disclosure (the dashed line) from year 1 to 40. In all 15 cases, the naming-and-shaming policy consistently increases the 2-period moving mean of total reported income every year (thus, on average from year 1 to 40) compared to the corresponding case under partial disclosure. For ${\bar{\gamma }} = 0.9$ or 0.11 (see the green and purple lines, respectively), where partial disclosure already increases the total reported income on average, the positive impact of full disclosure on reporting behaviors is even greater than that of partial disclosure for each $p\in \lbrace 0.02,0.03,0.04\rbrace$. As the mean unit moral cost is 0.07 (represented by the yellow line), full disclosure has a positive impact on reporting behaviors for each of the three audit rates, while partial disclosure decreases the total reported income. This indicates that the negative impact caused by partial disclosure is reversed by the threat of shaming under the full disclosure policy.

Fig. 9

Average compliance rates over 40 years with full disclosure

Fig. 10

Comparison between increased incomes reported under full and partial disclosure

Figure 11 reports the increased numbers of full compliers, full evaders, and partial evaders as a result of full disclosure, along with the average numbers when $p = 0.02$ for each of five mean unit moral costs. We can observe from the bottom figure that the number of partial evaders decreases due to full disclosure for all five mean unit moral costs. In contrast, the bottom figure in Fig. 8 demonstrates that partial disclosure increases the number of partial evaders for all mean unit moral costs except for 0.03. This indicates that a significant portion of evaders who previously chose to evade taxes under confidentiality opt to comply with tax obligations at the extensive margin when faced with the possibility of public exposure. The effect of shaming on compliance decisions reinforces the positive influence of reciprocity on compliance behaviors for ${\bar{\gamma }} = 0.09$ and 0.11, surpassing the negative impact of reciprocity for ${\bar{\gamma }} = 0.07$. However, for ${\bar{\gamma }} = 0.05$, the shaming effect is insufficient to counterbalance the negative impact of reciprocity, as the average increase in the number of full compliers (or equivalently, the decrease in the number of evaders) is only 2.27. It is worth noting that a significant disparity in the average number of full compliers is present between the case of ${\bar{\gamma }} = 0.05$ and the cases of ${\bar{\gamma }} = 0.07$ and higher. This discrepancy plays a crucial role in generating substantial differences in the effectiveness of full disclosure. Specifically, while the impact of full disclosure is more pronounced for ${\bar{\gamma }} = 0.07$ and higher, where the average number of full compliers experiences a significant increase, the effect is comparatively weaker for ${\bar{\gamma }} = 0.05$.

Fig. 11

Average numbers of agents by behavioral type with full disclosure

Fig. 12

Impacts of audit rate on the total reported income

Figure 12 presents the increased amounts of average total reported income resulting from a 1% increase in the audit rate under conditions of confidentiality, partial disclosure, and full disclosure, respectively. The increments in average total reported income due to a 1% increase in the audit rate under partial disclosure (the red line) are consistently larger than those under confidentiality (the blue line), except for the case of ${\bar{\gamma }} = 0.03$ (refer to Fig. 12a). However, these differences are relatively small, as the former values are only around 10% greater than the latter values in most cases. In contrast, the increments under full disclosure (the yellow line) are significantly larger than those under partial disclosure and confidentiality. In the majority of cases, a 1% increase in the audit rate under full disclosure has double or even greater impact compared to the cases under confidentiality and partial disclosure.

Fig. 13

Impacts of audit rate on the numbers of compliers and evaders

It is anticipated that under the full disclosure policy, an increased audit rate may lead to a significant transition of individuals who were previously evading taxes under confidentiality into full compliance. This suggests that an increase in the audit rate could have a notable influence on individual decision-making at the extensive margin when implementing the full disclosure policy. To assess this impact, Fig. 13 shows the incremental changes in the average numbers of full compliers and evaders resulting from a 1% increase in the audit rate. Notably, in most cases, the increased numbers of full compliers under full disclosure are 2.5–4 times greater than under partial disclosure and confidentiality.

5 Conclusions

Our simulation results indicate that the impact of partial disclosure on tax compliance is strongly influenced by the prevailing moral values concerning tax payment within a society. In a society where taxpayers exhibit a relatively strong moral consciousness regarding tax payment, partial disclosure has a positive effect on tax compliance. Conversely, in a society where moral consciousness is weak, the impact of partial disclosure is negative. It is important to note that these results are contingent upon bimodal distributions of individual compliance rates, wherein the proportion of taxpayers engaging in all-or-none reporting exceeds two-thirds. In a society where moral consciousness does not prevail, the majority consists of full evaders who are incentivized to reciprocate positively in response to advantageous inequity. However, most of them continue to evade taxes fully, as partial disclosure does not significantly augment their feelings of guilt. Simultaneously, full compliers experience strong anger, prompting them to respond by evading taxes. As a result, tax compliance is undermined when implementing the partial disclosure policy in a society with weaker moral values regarding tax payment. Conversely, in a society where a stronger moral consciousness is deeply ingrained, the implementation of the partial disclosure policy improves tax compliance. In this scenario, most full compliers-who comprise the majority-remain unchanged in their behavior, while full and partial evaders with compliance rates below the reference point opt to increase their reported income.

We assumed that the stigma cost incurred by taxpayers is independent of the amount of evaded taxes when the naming-and-shaming policy is implemented. Therefore, that policy significantly affects the taxpayer’s decision regarding whether to fully comply with their tax obligations. As shown in our simulation experiment, the proportion of full compliers in the population depends on the social state of moral values surrounding tax payment. In a society where a stronger moral consciousness is exhibited, full disclosure increases the average total reported income by increasing the proportion of full compliers, in addition to the positive effect of reciprocity. Conversely, if the moral consciousness of the population in the society is sufficiently weak, then the naming-and-shaming policy does not significantly improve the proportion of full compliers, and the average reported income is reduced due to the dominating negative reciprocity effects.

Increasing the frequency of auditing has long been recognized as a traditional policy to deter taxpayers from evading taxes, as demonstrated in Allingham and Sandmo (1972). Several empirical pieces of evidence regarding the effectiveness of audit rates as a deterrence policy are presented by Dubin et al. (1990), Alm et al. (1992a), and Fortin et al. (2007). However, the increase in audit frequency entails a non-negligible rise in administrative costs for tax authorities. This implies that it may not be a cost-effective deterrence policy if the marginal effect on tax compliance is relatively small. Our simulation results suggest that, under confidentiality and partial disclosure, a small increase in the audit rate has a moderately limited impact on tax compliance. In contrast, with full disclosure, a small increase in the audit rate can significantly enhance the proportion of full compliers and reduce the number of full evaders. Consequently, it substantially increases the average total reported income. These findings indicate that increasing the frequency of auditing is more effective when combined with the naming-and-shaming policy.

In our agent-based model, we assumed a random selection of taxpayers for audit at a fixed audit rate. However, an alternative approach could be to introduce an endogenous audit rule based on the relative amount of reported income, such as selecting a certain fraction of taxpayers with the lowest reported incomes for audit. If such an endogenous audit rule proves effective in enhancing tax compliance, it may lead to an increase in the average compliance rate and a decrease in the number of full evaders under confidentiality when compared to the random audit rule. Consequently, the implementation of both disclosure policies may yield different results when combined with an endogenous audit rule. However, further research is required to verify these qualitative properties and their impact on enhancing compliance.

Appendix

See Figs. 14, 15, 16, 17 and Tables 2, 3.

Fig. 14

Distributions of exogeneous parameters

Fig. 15

Impacts of tax rates on tax compliance

Fig. 16

Impacts of tax rates at the extensive margin

Fig. 17

Impacts of reciprocal motives on the average compliance rate under partial disclosure

Table 2 Simulation runs

Table 3 The experimental literature and the corresponding policy variables