Partial Identification of the Distribution of Treatment Effects in Switching Regime Models and its Confidence Sets

Abstract

In this paper, we establish sharp bounds on the joint distribution of potential outcomes and the distribution of treatment effects in parametric switching regime models with normal mean-variance mixture errors and in the semi-parametric switching regime models of Heckman (1990). Our results for parametric switching regime models with normal mean-variance mixture errors extend some existing results for the Gaussian switching regime model and our results for semi-parametric switching regime models supplement the point identification results of Heckman (1990). Compared with the corresponding sharp bounds when selection is random, we observe that self-selection tightens the bounds on the joint distribution of the potential outcomes and the distribution of treatment effects. These bounds depend on the identified model parameters only and can be easily estimated once the identified model parameters are estimated. The important issue of inference is briefly discussed.