Coase-Sandor Institute for Law & Economics Research Paper Series

Publication Date

2025

Publication Title

Coase-Sandor Working Paper Series in Law and Economics

Abstract

Studies that use tax data to examine income inequality (for example Piketty and Saez, 2003; Piketty et al., 2018a; Auten and Splinter, 2024; Fixler et al., 2020) must confront the issue of tax misreporting (including most prominently tax evasion). To derive an estimate of top true shares of income, researchers must allocate estimates of misreporting to reported income based on limited data. Research groups use di!erent methods of making this allocation, and these di!erences have large e!ects on estimated top shares. To help understand the e!ects of di!erent allocation methods, we lay out a statistical framework for the relationship between true income, reported income, and misreporting, treating the density of reported income as data generated by behavioral primitives: the densities of true income and misreporting. We use this framework to clarify the methodologies and assumptions used by two research groups, Piketty et al. (2018a) and Auten and Splinter (2024), together with the recent comparison by Iselin and Reck (2025).

We show that the approach used by Piketty et al. (2018a) and supported by Iselin and Reck (2025) which assumes that misreporting is proportional to reported income, rules out, by assumption, plausible and central cases for how misreporting can a!ect estimates of true income. If misreporting is heterogeneous (in the sense that people with a given type of income and within and income class misreport at di!erent levels) rather than proportional, misreporting may show up towards the bottom of the reported income distribution even if it originates at the top. Accurately accounting for that misreporting may reduce rather than increase top shares of income. Moreover, an increase in top reported shares need not be accompanied by an increase in top true shares. The approach recommended by PSZ and Iselin and Reck is also not supported by the available data. It is not, therefore, an appropriate method for accounting for misreporting. Instead, researchers should work with the microdata on the pattern of misreporting, focusing on the heterogeneity of miresporting within income groups. We argue further that any approach for imputing true income from reported income and assumptions about misreporting should explicitly take into account the uncertainty in misreporting rather than relying on point estimates.

Number

25-30

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