Diffuse Bunching with Lumpy Incomes : Theory and Estimation

We study the performance of the bunching-based elasticity estimator when income adjustments are lumpy. In our parsimonious model, taxpayers choose their preferred income from random opportunity sets. The model features the standard elasticity of taxable income and a single additional “lumpiness parameter,” which can be jointly estimated using maximum likelihood. This model can match key patterns that are inconsistent with the conventional bunching estimator, including diffuse bunching around kinks and notches in the tax schedule and positive mass above tax notches. When incomes are lumpy, simulations demonstrate that the conventional estimator is biased, underestimating the true elasticity by as much as 50%, and incorrectly sized, with the true parameter lying inside bootstrap 95% confidence intervals with less than 10% probability. We apply this method to administrative tax data on small businesses in South Africa, recovering moderate elasticities at higher incomes and large elasticities at low incomes. Firms with paid tax practitioners exhibit sharper bunching, driven primarily by a lower lumpiness parameter rather than by a different income elasticity