Tobit models: A survey

This paper studies the bunching identification strategy for an elasticity parameter that summarizes agents’ responses to changes in slope (kink) or intercept (notch) of a schedule of incentives. We show that current bunching methods may be very sensitive to implicit assumptions in the literature about unobserved individual heterogeneity. We overcome this sensitivity concern with new non- and semi-parametric estimators. Our estimators allow researchers to show how bunching elasticities depend on different identifying assumptions and when elasticities are robust to them. We follow the literature and derive our methods in the context of the iso-elastic utility model and an income tax schedule that creates a piece-wise linear budget constraint. We demonstrate bunching behavior provides robust estimates for self-employed and not-married taxpayers in the context of the U.S. Earned Income Tax Credit. In contrast, estimates for self-employed and married taxpayers depend on specific identifying assumptions, which highlight the value of our approach. We provide the Stata package bunching to implement our procedures.