Ambiguity about audit probability, tax compliance, and taxpayer welfare

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

In the next section, we set out a nonexpected utility model of tax evasion in which the taxpayer faces ambiguity about the probability of being audited and may also have biased perceptions concerning this probability. In section III, we show that tax evasion declines (increases) as the probability of being audited becomes more ambiguous when taxpayers are ambiguity averse (loving). In section IV, we discuss the welfare implications for audit policy of heterogeneity among taxpayers with respect to ambiguity preferences. We conclude that the presence in the taxpaying population of individuals who are either ambiguity loving or ambiguity neutral weakens the case for using uncertainty about the probability of being audited as a policy instrument intended to increase taxpayer compliance and enhance the welfare of taxpayers.

II. TAX EVASION WITH AMBIGUITY

We consider an individual taxpayer with a fixed taxable income W facing a certain tax rate t who chooses an amount of undeclared income x to shield from the tax authority. If the taxpayer is not audited, then income is [W.sub.N] [equivalent to] W(1 - t) tx. If the taxpayer is audited, then all evasion is detected and the taxpayer is charged this amount plus a proportional penalty. In this event, income is [W.sub.A] [equivalent to] [W.sub.N] - [theta]tx, where [theta] > 1 is the gross penalty rate, which is known to the taxpayer.

The taxpayer is assumed to have a strictly concave utility function for wealth U(W), reflecting strict risk aversion. The objective probability of being audited is p [member of] (0,1), but the taxpayer is uncertain about this probability and therefore faces ambiguity. Let [pi] denote the taxpayer's subjective probability of being audited, and denote by F([pi]; a,p) the cumulative distribution function describing the taxpayer's uncertainty about [pi], with F(0; a,p) [euqivalent to] 0. This second-order probability (SOP) distribution is parameterized by an index of ambiguity a, discussed shortly, and the objective audit probability p. (5)

We assume that the taxpayer's expectation about [pi] is unbiased in the sense that

(1) [[integral].sup.1.sub.0] [pi]dF([pi]; a,p) = p

for all values of a. The taxpayer's perception of [pi], however, is distorted according to the probability weighting function [phi]([pi], p), which may have a value greater or less than [pi]. However, we assume that [phi]([pi], p) equals p when [pi] equals p. The probability weighting function introduces a systematic bias in the perceived probability of an audit that depends on the concavity of [phi] as a function of n in a manner described next.

The taxpayer chooses an amount of undeclared income [x.sup.*] to maximize the objective function

(2) E[U] [equivalent to] U([W.sub.N]) - [[[integral].sup.1.sub.0] [phi]([pi], p)dF([pi; a,p])] x [U(W.sub.N) - U([W.sub.A])],

where the taxpayer's distorted perceptions of and uncertainty about the probability of being audited determine the perceived probability of an audit,

(3) [[integral].sup.1.sub.0] [phi]([pi], p)dF([pi; a,p])] [member of] (0, 1)

on which the evasion decision is based. We assume that this expected probability is always sufficiently low that [x.sup.*] is positive. (6)

In the absence of ambiguity (a = 0), F is the improper distribution equal to 0 for all [pi] < p and equal to 1 otherwise, so that

(4) [[integral].sup.1.sub.0] [phi]([pi], p)dF([pi; a,p])] = [phi](p,p) = p

In this case, the taxpayer's objective function reduces to the expected utility of wealth with an audit probability of p. We assume that an increase in the index of ambiguity results in a mean preserving spread of the SOP distribution. Hence, in the presence of ambiguity (a > 0), F([pi]; a,p) is a mean preserving spread of the improper distribution with mass at [pi] = p. Because of the probability weighting function [phi]([pi], p), however, the taxpayer's perceived probability of being audited typically differs from p.