Sequential Equilibrium Detection and Reporting Policies in a Model of Tax Evasion

Abstract

Noncompliance with tax laws and other forms of criminal activity have typically been treated as equivalent; both have been modeled in decision-theoretic terms, with the same probability of detection applying to all agents. However, noncompliance with tax laws is different from other criminal activities because taxpayers are required to submit a preliminary accounting of their behavior, while potential criminals obviously are not. This preliminary round of information transmission differentiates individuals, and raises the possibility that it may not be optimal to apply the same probability of detection to all taxpayers. We develop a game-theoretic model of income tax compliance in which the taxpayer possesses private information about his own income, while the IRS knows only the probability distribution according to which the taxpayer's income is realized. By investing effort, the IRS can (stochastically) verify a taxpayer's income. We characterize the sequential equilibrium for this game, which consists of a reporting rule for the individual taxpayer, and a verification policy for the IRS. Our equilibrium has the feature that taxpayers with greater true income under-report less than those with lower true income, and efforts at verification are lower the greater is reported income. If individuals can be classified on the basis of some observable characteristic which is related to opportunities for income, we find that classes of taxpayers who enjoy greater opportunities for high income under-report to a greater extent; accordingly, more effort is devoted to their investigation. This is to be distinguished from the former result, which applies to different types of taxpayers within the same class.

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