Better Bunching, Nicer Notching

Abstract

We study the bunching identification strategy for an elasticity parameter that summarizes agents' response to changes in slope (kink) or intercept (notch) of a schedule of incentives. A notch identifies the elasticity but a kink does not, when the distribution of agents is fully flexible. We propose new non-parametric and semi-parametric identification assumptions on the distribution of agents that are weaker than assumptions currently made in the literature. We revisit the original empirical application of the bunching estimator and find that our weaker identification assumptions result in meaningfully different estimates. We provide the Stata package bunching to implement our procedures.

Bunching estimation of elasticities using Stata

“…The application of bunching methods used by Bertanha, McCallum, and Seegert (2021) and this article derives from bunching behavior caused by progressive marginal income taxes, as in Saez (2010). Formally, agents maximize an isoelastic quasilinear utility function of total consumption (or disposable income) and labor, which results in a data-generating process (DGP) for optimal reported taxable income as follows:…”

“…We use utility-maximizing agents and income taxes to motivate (1) and for exposition of the command throughout the rest of this article. Nevertheless, the methods developed by Bertanha, McCallum, and Seegert (2021), as well as the bunching package, apply to any dataset generated by (1). We emphasize that any data must be transformed into units that satisfy (1).…”

“…Appendix B of Bertanha, McCallum, and Seegert (2021) provides a general solution to a model with multiple kinks and notches, and section 3, "Identification", of their article discusses inference for multiple kinks.…”

“…The statistical foundations for these commands were developed by Bertanha, McCallum, and Seegert (2021). That article introduces multiple methods to recover elasticities from bunching.…”

“…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.…”