Tuesday, July 15, 2014
Should the IRS warn taxpayers that they are in danger of audit, in the hope of getting them to file accurate amended returns? Here’s how I’d model the situation:
0. The government chooses a policy of an audit probability A(Uhat), where Uhat is the taxpayer’s estimated underpayment. The taxpayers only observe the average audit probability over all incomes and over the taxpayers that are warned in step 4 below and do or do not file amended returns.
1. The taxpayer earns income Y with probability f(Y), unobserved by the IRS.
2. The taxpayer reports income Yrep and income characteristics (salary, tips, mortgage payments, charitable contributions) X1…X9.
3. The government estimates the taxpayer underpayment Uhat = (Y-Yrep) based on Yrep and X1…X9.
4. The government gives the taxpayer a warning if Uhat<Ubar, choosing Ubar, and tells the taxpayer he may file an amended return.
5. The taxpayer files an amended return and reports income Y2 (which can be the same as Yrep, if he doesn’t really file an amended return).
6. The government audits or not. If it audits, it pays P and discovers Y. If the government finds underpayment, it imposes fine F(U), where U = Y2- Y.
That isn’t completely formulated yet, but you’ll get the idea. I don’t know how it would solve out. Anyone who wants to write it up, go ahead. It might make a good PhD exam question for an applied game theory course.