Partial Identification from Bunching at Kinks and Notches

Abstract

This paper proposes a partial identification approach to using choices around a kink or notch as a means to overcome endogeneity in a general nonparametric choice model. I show that observed choices are informative about the joint distribution of two counterfactual choices, which leads naturally to analyzing bunching using tools from causal inference. I define as the parameter of interest an average treatment effect among bunchers, which nests the traditional elasticity parameter while allowing for heterogeneity in responsiveness. Identification of the buncher ATE (and hence the elasticity) requires the researcher to extrapolate the distribution of each counterfactual choice beyond where it is observed. I introduce a flexible family of nonparametric shape restrictions to obtain partial identification, and propose a method for empirical validation of this approach using changes in the location of the kink/notch or using the distribution from another comparison group. I find that a log-concavity version of the distributional assumption is widely---though not universally---supported across the empirical literature, and leads to informative bounds in a canonical tax kink application. The approach accommodates diffuse bunching, at the expense of wider bounds.