Bunching estimation of elasticities using Stata

Typical censoring models have mass points at the upper or lower tails, or at both tails, of an otherwise continuous outcome distribution. In contrast, we consider a censoring model with a mass point in the interior of the outcome distribution. We refer to this mass point as “bunching” and use it to estimate model parameters. For example, economic theory suggests that, for increasing marginal income tax rates, many taxpayers will report income exactly at the threshold where the tax rate increases. This translates into a censoring model with bunching at the threshold. The size of this mass point of taxpayers can be used to estimate an elasticity parameter that summarizes taxpayers’ responses to taxes. In this article, we introduce the command bunching, which implements new nonparametric and semiparametric identification methods for estimating elasticities developed by Bertanha, McCallum, and Seegert (2021, Technical Report 2021-002, Board of Governors of the Federal Reserve System). These methods rely on weaker assumptions than what are currently made in the literature and result in meaningfully different estimates of the elasticity.