Partial Identification of the Distribution of Treatment Effects in Switching Regime Models and its Confidence Sets
在参数和半参数转换机制模型中，推导了潜在结果联合分布和处理效应分布的紧界，发现自选择比随机选择收紧这些界，并简要讨论了推断问题。
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 <cross-ref type="bib" refid="R30">Heckman (1990)</cross-ref>. 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 <cross-ref type="bib" refid="R30">Heckman (1990)</cross-ref>. 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.