Sampling risk evaluations in tax audits: Some modelling issues

Abstract The context of this article is the use of sample data to support claims of tax evasion at eateries, where the possibilities are overreporting of take-away sales and underreporting of cash payments. Ratios of sales amounts of alternative types are computed from the sample and used as estimates of the true yearly ratios. Decisions are made by comparison with the reported ratios in the taxpayer’s yearly income statement, allowing for sampling risk. To this end, a ‘risk distribution’ is established and its quantiles used as decision limits. There are different ways of doing the calculation and to establish the accompanying risk distribution, among them models based on Gamma-assumptions, as detailed in Lillestøl (2019, Sample Statistics as Convincing Evidence: A Tax Fraud Case. Law, Probability and Risk, 10, 149–176). They may lead to different results, more or less favourable to the taxpayer. The chosen method must therefore be fair and defensible. In this connection, the question of conditioning turns out to be relevant. The objective of this article is to explore these issues and provide some recommendations on the choice of method.