توزیع درآمد و تعدد تعادل در مدل مبتنی بر ترس از فرار مالیاتی

This paper incorporates continuous income distribution into the stigma-based model of tax compliance. The paper investigates the effect of income distribution on the existence of multiple equilibria, and characterizes the conditions under which multiple equilibria emerge. Precisely, multiple equilibria exist if taxpayer incomes are sufficiently homogeneous, because the ‘social coordination effect’ dominates the ‘individual characteristics effect’. Numerical simulations show that the main proposition is robust to allowing two-step audit policies on the part of the tax agency, under the presumption that the best (or good) equilibrium is selected whenever there are multiple equilibria. As a byproduct, the effect of various forms of tax reforms on the optimal two-step audit policy, the equilibrium compliance, and fiscal revenue is analyzed.

Tax evasion is as old as taxes themselves. In economic models of tax evasion, taxpayers decide how much income to report by solving a standard expected uitility maximization problem that trades off the tax savings from fraud against the risks of penalties for detected cheating. This view, the so-called portfolio approach, was the main idea of the seminal work by Allingham and Sandmo (1972). The portfolio approach has been extended in various directions (see Cowell, 1990; Andreoni et al., 1998, for comprehensive surveys). Nevertheless, close empirical scrutiny has revealed important inconsistencies between theory and evidence. A couple of facts and findings motivate this paper. First, the rate of tax compliance is paradoxically high, relative to the expected punishment. Empirical studies, such as Graetz and Wilde (1985) and Skinner and Slemrod (1985), have documented the high rate of tax compliance in most countries. It seems puzzling that so many households behave honestly and that cheaters do not cheat more, considering that most taxpayers face a low probability of detection and expect a small penalty when caught.1 The experimental evidence (Baldry, 1986; Alm et al., 1992a) also suggests that some people never evade, even when the tax evasion gamble is clearly better than fair. To explain the apparent paradox, researchers have appealed to ethical norms (Bordignon, 1993), moral sentiments and misperceived audit probabilities (Erard and Feinstein, 1994a), and the orders of risk aversion (Benasconi, 1998). This study incorporates social stigma directly into the specification of taxpayer utility, hypothesizing that people may fear social stigma or damage to their reputation if they are to be disclosed as cheaters.2 An important feature of the model is the interdependence of individual behavior. That is, the larger the population share of taxpayers who evade tax, the smaller is the social stigma felt by an individual who attempts to cheat. Second, it is known from experience that there are close relationships among income, tax policy, and evasion. Clotfelter (1983) and Poterba (1987) report that evasion increases with the tax rate. Experimental studies (e.g. Alm et al., 1992b) typically find that higher tax rates are associated with greater evasion. Most empirical findings suggest that the affluent are much more responsive to structural changes in the tax scheme and thus are suspected of more evasion. In statistical analyses of the historical impact of U.S. tax reforms, Feenberg and Poterba (1993) and Auerbach and Slemrod (1997) suggest that higher marginal tax rates lead the rich to underreport enough income to cause a decline in the taxes paid by this class.3 This study explicitly introduces a continuous income distribution. It is a departure from the existing literature, in which evasion is an independent decision-making problem with an equal income. Whether individuals choose to evade tax or not, and how much tax to evade, if any, depend on the before-tax income, the tax policy, and the population share of honest citizens. A social equilibrium is defined to be an endogenously determined population share of honest taxpayers together with the distribution of concealed incomes based on individual optimizations. This paper characterizes the social equilibrium and investigates the effects of pretax income distribution on the multiplicity of equilibrium. This paper also explores the effects of income, the marginal tax rate, and various forms of tax reform on individual evasion behavior and social corruption. This paper elucidates the main points as follows. Equilibrium exists in multiplicity, if taxpayers become sufficiently homogeneous. Since taxpayers care about social stigma, the proportion of individuals who are expected to evade tax plays an important role in individual evasion decisions. If a majority (minority) of people are going to evade, then individual taxpayers will have a greater (smaller) incentive to evade taxes. This force is known as the ‘social coordination effect’. On the other hand, individuals are endowed with different levels of income. Hence, even if all taxpayers have the same preference and face the same tax policy, the marginal utilities of income concealed and the optimal evasion may be different. This second force is called the ‘individual characteristics effect.’ Note that the homogeneity of taxpayers increases as income inequality decreases, since taxpayers may differ only in pretax income. If taxpayers are sufficiently homogenous, the social coordination effect dominates the individual characteristics effect. This leads to the emergence of multiple equilibria. In the limit as all taxpayers become endowed with an exactly equal income, the individual characteristics effect disappears while only the social coordination effect comes into play. In such a society, equilibrium population shares always exist in multiplicity, including two extreme states of complete corruption and complete honesty. One might ask whether this result is an artifact of the assumption that the audit rate is constant over all reported incomes. In particular, how robust is the result to allowing possibilities that the government adopts an optimal two-step audit policy? I shall show that the answer to this question is conditionally positive. What I mean by ‘conditionally’ depends on the nature of the selected equilibrium in the presence of multiple equilibria. Given a particular audit rule, multiple equilibria may exist. But when there are multiple equilibria, which one is realized determines the optimality of the original audit policy. This paper shows by numerical methods that sufficient homogeneity gives rise to equilibrium multiplicity, provided that the best equilibrium is selected in the presence of multiple equilibria. As a byproduct, this paper also analyzes the effect of tax reforms on compliance and tax revenue. In the first type of tax reform examined, marginal tax rates are reduced for all income groups. This study will show that such a tax reform reduces corruption, regardless of the nature of the underlying tax policies. In the second type of reform, a decline in tax rates for high-income groups accompanies a simultaneous increase in tax rates for lower groups to keep the target revenue unchanged. This paper shows by simulations that the effect of such a reform is largely ambiguous. However, the forms of the optimal audit rule look intuitive. If the tax burden is relatively heavier for poor people, it is optimal to concentrate audit resources on the lower and middle class while giving up the investigation of large reports. On the contrary, if tax is very progressive so as for the rich to have more incentive to cheat, the tax agency should audit the rich as well as the poor with less discriminatory probabilities. The paper is most closely related to previous work by Gordon (1989), Besley and Coate (1992), and Lindbeck et al. (1999). Gordon was the first to modify the standard tax evasion model by introducing taxpayers’ social stigma, in order to explain some empirical inconsistencies. Our analysis differs from Gordon in two respects. First, the present treatment generalizes Gordon by allowing broader classes of tax policies and stigma functions. Second, while Gordon focuses on the case of fixed income, we consider the continuous income distribution and its effect on evasion. From the viewpoint of the modeling technique, the paper resembles Lindbeck et al. and its predecessor, Besley and Coate. However, they focus on the welfare stigma while taxation is simply a means of financing welfare payments, so the problem of tax compliance does not arise. In Gordon and Besley–Coate, the source of individual heterogeneity is preferences, such as the private psychic cost of evasion and a personal degree of sympathy for the needy poor, given that the income level is fixed. On the contrary, individuals in this paper have completely identical preferences and may only differ in their endowed income levels. Moreover, individuals not only decide whether to evade or not, but also how much income to conceal, unlike Lindbeck et al.’s binary choice problem. In this paper, tax policy is assumed to be exogenously given as the product of a political process which is not modeled here. On the other hand, some research is focused on the determination of progressive taxation. The normative theory of optimal taxation, which originated with Mirrless (1971), attempts to explain why certain tax schemes may or may not be socially desirable. Some literature on political economy analyzes why a progressive tax policy wins the election as an outcome of the political process. Roemer (1999) deserves special mention. In Roemer, a non-degenerate income distribution plays an important role in explaining why both leftist and rightist political parties typically propose progressive income taxation. Roemer characterizes a Nash equilibrium in a political voting game between a leftist party and a rightist party. He utilizes a crucial assumption on income distribution, which states that more than half the voters have incomes that are less than the mean. Another line of research on tax evasion and corruption deterrence is based on repeated game reasoning or on other dynamics. Examples are Greenberg (1984), Lui (1986), and Tirole (1996). In Lui’s overlapping-generations framework, a multiplicity of steady state equilibria stems from the crucial assumption that when corruption becomes more prevalent in the economy, it is harder to audit a corrupt official effectively. Tirole provides a dynamic model of collective reputations, in which a member’s incentives are affected by his past behavior, and because of partial observability of his track record, by the group’s past behavior as well. Tirole shows that multiple steady states exist when parameters satisfy several conditions for a strong enough dynamic complementarity between past and future reputations. My paper derives the conditions for the emergence of multiple equilibria, which stems only from distributional characteristics of taxpayer income. The remainder of this paper is organized as follows. Section 2 presents the environment, the individual taxpayer’s optimization problem, and the notion of social equilibrium. Section 3 contains an analysis of the relationship between income distribution and equilibrium characterization, especially for the multiplicity of equilibrium. Section 4 studies the robustness of the main result to more general audit policies. Section 5 provides formal definitions of tax reform and analyzes the effect of various forms of tax reform on evasion and actual revenue. Section 6 presents the concluding remarks.

I conclude the paper with some suggestions for future research. Perhaps the assumption one would most like to weaken is the inelasticity of labor supply. However, this assumption is partly motivated by existing empirical findings (Auerbach and Slemrod, 1997) that much of the movement in the reported income of high-income households represents the shifting of income and not income creation, such as additional labor supply. Another suggestion for future research may be a fusion of two types of stigma-based models, including both tax evasion and welfare transfer. The current paper focuses on taxpayers’ evading decision, while the literature on welfare stigma, such as Moffitt (1983), Besley and Coate (1992), and Lindbeck et al. (1999), assumes away the possibility of evasion. A more concrete suggestion for future research is related to equilibrium selection among multiple equilibria. In order to evaluate the tax reform in the presence of multiple equilibria, it is assumed that, as the structure of the economy changes, the equilibrium moves smoothly by an ad hoc adjustment dynamic process. If one is concerned more about the equilibrium selection problem, an incomplete information approach such as Morris and Shin (2001) can be the proper path to follow. In a possible modification, taxpayers observe their own cost of stigma and the history of the levels of aggregate corruption. The distribution of individual characteristics evolves through a random process. Applying the iterative elimination of strictly dominated strategies, one can characterize the Bayesian Nash equilibrium with a unique cutoff property. Kim (2001) pursues this line of research to explain the ambiguity and uncertainty often observed in tax auditing policies.