A Unified Framework for Identification and Inference of Local Treatment Effects in Sharp Regression Kink Designs

Abstract

This paper develops a unified framework for the identification, estimation, and uniform inference of local treatment effects (LTEs) in sharp regression kink designs (RKDs). These LTEs quantify the effect of a marginal change in the treatment at the kink point on various features of the outcome distribution. The identification strategy applies to Hadamard-differentiable functionals of the outcome distribution -- including means, quantiles, and inequality measures -- and encompasses several existing RKD estimands as special cases. For estimation, we categorize the corresponding estimands into two general classes and implement their estimation via local polynomial constrained regression. We establish the asymptotic theory for this framework and provide a valid resampling procedure for uniform inference. The method is applied to examine the effect of unemployment insurance on unemployment durations, focusing on the policy's impact on the distribution and inequality of durations, as a complement to existing empirical evidence.