Ambiguity about audit probability, tax compliance, and taxpayer welfare

Economic Inquiry, Oct, 2005 by Arthur Snow, Ronald S. Warren, Jr.

I. INTRODUCTION

To encourage voluntary compliance with the tax code, the U.S. Internal Revenue Service (IRS) relies heavily on a policy of auditing tax returns and levying penalties when undeclared income is detected, with penalties linked to the amount of tax evasion discovered. The selection of returns for auditing is based on both strategic and random procedures. Strategic audits are determined by a closely guarded formula for choosing specific tax returns that exceed certain thresholds for reported income, deductions, and credits. After a decade-long hiatus, the IRS recently revived a program of random audits to measure tax compliance and update the formula for triggering strategic audits. (1)

The IRS has testified to the importance of both the randomness and secrecy of its audit policies as instruments for increasing taxpayer compliance, because auditing all returns is not cost-effective. (2) However, the relatively small penalties levied for detected evasion, combined with the low probability of an audit, would seem to provide taxpayers with a strong incentive to engage in rational evasion behavior. Indeed, the commissioner of the IRS has estimated that the amount of federal tax evaded annually exceeds 10% of the total revenue actually collected. (3)

Experimental analyses of the compliance decision have supported the IRS view that tax evasion is reduced by uncertainty about or upward bias in perceptions of the probability of audit. For example, Spicer and Thomas (1982) report on an experiment showing that the strength of the (negative) correlation between the fraction of taxes evaded and the probability of an audit falls as taxpayer information about the probability of being audited becomes less precise. Aim et al. (1992a) discuss experimental evidence suggesting that uncertainty about the probability of being audited increases compliance when taxpayers believe that their evasion decisions will have no effect on the level of government spending. Clark et al. (2004) compare purely random auditing with two strategic ("conditional") audit rules in an experimental setting in which the subjects faced random assignment to one of two audit pools that differ with respect to audit probability. They find that the purely random audits achieve the highest rate of compliance.

Andreoni et al. (1998, pp. 844-46) survey the empirical literature on taxpayers' subjective beliefs about the probability of audit and conclude that individuals generally make poor predictions about this probability. Aim et al. (1992b) report results from several experiments suggesting that many subjects overestimate the low probability of being audited, leading to less evasion than predicted by the expected utility model. Scholz and Pinney (1995) also provide evidence that taxpayers have upwardly biased subjective estimates of the true audit probability, with the size of the bias negatively correlated with their expected gain from evasion behavior. Sheffrin and Triest (1992) use survey data from a cross-section of taxpayers to estimate a factor-analytic model of tax compliance, allowing for the endogeneity of the perceived probability of evasion detection. They find that taxpayers who perceive a higher probability of detection report significantly less understating of income or overstating of deductions.

The experimental results presented by Spicer and Thomas (1982), Alm et al. (1992a, 1992b), and Clark et al. (2004), as well as the evidence reported by Sheffrin and Triest (1992) and by Scholz and Pinney (1995), point to the importance of imprecise or biased estimates of audit probability in explaining the extent of voluntary tax compliance. The expected utility theory of tax evasion, however, provides an inadequate framework for incorporating these considerations. Because expected utility is linear in the outcome probabilities, increasing uncertainty about the probability of being audited (that is, increasing Knightian uncertainty or ambiguity about the audit probability) has no implications for the evasion decisions of expected utility maximizers, as the expected probability of an audit remains unchanged.

A large number of empirical studies, beginning with Allais (1953) and Ellsberg (1961), have revealed behaviors inconsistent with the expected utility model. Most of these studies have reported apparent violations of the independence axiom, which is responsible for the decision criterion being linear in the outcome probabilities. (4) In response to these anomalies, several alternative theoretical models have been advanced that introduce the potential for nonlinear dependence on the outcome probabilities. These include the rank-dependent expected utility model developed by Quiggin (1982) and Yaari (1987), the decision weighting model of Kahn and Sarin (1988), and cumulative prospect theory advanced by Tversky and Kahneman (1992).

In each of these models, the decision maker may have a systematically biased perception of the probability of a gain or loss caused by a nonlinear transformation of probability through a probability weighting function. We follow this approach, and associate attitudes toward ambiguity with the shape of the probability weighting function. In this manner, we advance the theory of tax evasion by introducing ambiguity preferences that allow taxpayer welfare to depend nonlinearly on the probability of an audit. In our approach, the taxpayer's uncertainty about this probability can be systematically biased in such a way that the perceived probability of an audit differs from the true probability, with the direction of bias depending on whether the taxpayer is ambiguity averse or ambiguity loving.