Identification and Wavelet Estimation of Weighted ATE Under Discontinuous and Kink Incentive Assignment Mechanisms

Abstract: This paper studies identification, estimation, and inference of a weighted average treatment effect (W-ATE) parameter in a class of switching regime models, where the agent’s selection of treatment is affected by either a discontinuous or kink incentive assignment mechanism and some unobservable characteristic. For each assignment mechanism, we (i) establish identification and propose a local wavelet estimator of the W-ATE; (ii) establish asymptotic properties of the local wavelet estimator including optimal convergence rate and asymptotic normality; and (iii) investigate the finite sample performance of the local wavelet estimators and compare them with local polynomial estimators via an extensive simulation study. We also propose an identification-robust wavelet estimator of the W-ATE.