Income tax compliance and evasion: a graphical approach.

• Author: Linster, Bruce G.

1. Introduction

   Individual income tax compliance has been one of the most significant applications of Becker's [6] economic approach to criminal activity and punishment. This paper considers an approach to optimal audit policies that relies on the dIstribution of risk aversion among taxpayers and is consistent with some stylized facts about the U.S. tax system. Rather than considering the tax evasion situation as a game between the tax collector and identical taxpayers, this model has the tax collector choose an audit probability to maximize expected tax revenues net of audit costs knowing that each taxpayer has a reservation audit probability - the smallest audit probability that would evoke truthful reporting - depending on how averse to risk she is. As the heterogeneity in the population vanishes, this problem becomes the same as the tax compliance problem analyzed in Graetz, Reinganum, and Wilde [9].

   This paper extends earlier contributions by analyzing income tax evasion and compliance with a population that is heterogeneous with respect to risk aversion. How other parameters of the problem influence optimal audit probabilities as well as the equilibrium proportion of tax evaders will be explored. The diversity in preferences over lotteries leads to some interesting comparative static results. For example, the impact of an increase in the penalty for lying is ambiguous in this model. The graphical approach taken here allows us to identify the relevant factors and how they interact. Additionally, this analysis makes it clear why the distribution of risk aversion in the population affects the equilibrium audit probability, but not the proportion of tax evaders.

   This problem has been approached in several different ways.[1] For example, Clotfelter [7], Slemrod [15], Alm and Beck [2], and Witte and Woodbury [16] have studied this phenomenon econometrically, but the dearth of reliable data has made empirical analysis difficult. Other economists - most noteworthy, Alm, McClelland, and Schulze [5] and Alm, Jackson, and McKee [4] - have taken a different tack, employing the methods of experimental economics. While these seminal studies have shed substantial light on taxpayer behavior, a leap of faith is required to extrapolate from the laboratory to actual tax compliance decisions.

   The theoretical tax compliance literature originally focused on the behavior of the taxpayer, as in Allingham and Sandmo [1]. That is, individuals were modeled as expected utility maximizers with exogenously given audit probabilities. More recent contributions to the theoretical literature, Reinganum and Wilde [12; 13], and Graetz, Reinganum, and Wilde [9] for example, have focused on the interaction between taxpayers and the tax collector. The taxpayers are still modeled as expected utility maximizers, and the tax collector is assumed to maximize expected net revenue. The probability an individual taxpayer will be audited is endogenously determined and depends on the amount of income the individual reports. Our understanding of the tax compliance problem has significantly improved because of these studies; however, their approaches to the problem treat all taxpayers as homogeneous with respect to risk aversion, avoiding the issue of heterogeneous taxpayers altogether.

   The equilibria in the game theoretic models described above have properties that may seem implausible. For example, Graetz, Reinganum, and Wilde [9] require that if the tax collector audits with probability [Pi] [element of] (0, 1), then both the tax collector and taxpayers are indifferent between their pure strategy choices - "audit" and "don't audit" for the tax collector and "report truthfully" and "lie" for the taxpayer. The first-order optimization conditions insure that the tax collector will be indifferent as to whether or not he should audit another return. However, it is certainly true that only a very small group of taxpayers will be truly indifferent between lying and being truthful when reporting tax liability.

   An important goal of the research reported here was to develop a model consistent with certain stylized facts about the U.S. tax system. The first observation is that the Internal Revenue Service relies on "voluntary" reporting of the amount of tax owed while having information on each taxpayer's gross income from employers and financial institutions. An audit frequently involves the verification of deductions claimed by the taxpayer. Second, individuals in similar financial situations frequently respond differently on tax returns. This may be due to different feelings of social responsibility, but certainly risk aversion is an important element in tax reporting decisions.(2) Finally, distinct income groups are audited with different probabilities. The model described here conforms to the above observations.

   The next section describes the basic framework of the model. Although similar to the one used by Graetz, Reinganum, and Wilde [9], this model is substantially more general than its predecessors since it allows for populations that are not homogeneous with respect to risk aversion. In the subsequent sections, the equilibrium outcome is discussed, and some comparative static results are explored. Finally, the results are summarized.

2. The Model

   Since this model focuses primarily on income tax compliance and evasion, income levels, tax rates, and fines are exogenously determined. Pencavel [11] and Sandmo [14] have explored the relationship between tax evasion and labor supply, but the issue is assumed away in this paper. Treating tax rates and fines as exogenous is reasonably realistic since they are, after all, usually set by the legislative branch of government and not the tax collection agency. In order to keep the model tractable, this analysis assumes there are two possible levels of tax, [T.sub.H]...