Income Tax Compliance and Evasion: A Graphical Approach

Abstract

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], Aim 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