Better Bunching, Nicer Notching

Abstract

A continuous distribution of agents that face a piecewise linear schedule of incentives results in a distribution of responses with mass points located where the slope (kink) or intercept (notch) of the schedule changes. Bunching methods use these mass points to estimate an elasticity parameter, which summarizes agents' responses to incentives. This paper studies identification of the elasticity. First, a notch identifies the elasticity but a kink does not when the distribution of agents is non-parametric and continuous. Second, we propose new identification assumptions on the distribution of agents that are weaker than assumptions currently made in the literature. Our assumptions include a non-parametric shape condition which partially identifies the elasticity and two alternative semi-parametric conditions that use covariates and censored regressions to point identify the elasticity. Third, we revisit the original empirical application of the bunching estimator, which is in the economics literature that examines the largest means-tested cash transfer program in the United States. Our weaker identification assumptions result in meaningfully different estimates of the elasticity of reported income with respect to tax rates.

Keywords: partial identification, censored regression, bunching, notching, tax kink, earned income tax credit

JEL Classification: C14, H24, J20