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

In this paper, we establish sharp bounds on the joint distribution of potential outcomes and the distribution of treatment effects in parametric switching regimes models with generalized hyperbolic errors and in the semiparametric switching regimes models of Heckman (1990). Our results for parametric switching regimes models with generalized hyperbolic errors extend some existing results for Gaussian switching regimes models and our results for semiparametric switching regimes 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. We demonstrate the feasibility of inference on the distribution of treatment effects by constructing an asymptotically uniformly valid and non-conservative confidence set in a semiparametric switching regimes model.