Sharp Bounds on the Distribution of the Treatment Effect in Switching Regimes Models∗

In this paper, we establish sharp bounds on the distribution of the treatment effect in switching regimes models or generalized sample selection models in Heckman (1990). These bounds depend on the identified model parameters only and hence are themselves identified. Their estimation is straightforward once the identified model parameters are estimated. We compare our bounds when the identified bivariate marginal distributions are either both normal or both Student’s t with those assuming trivariate normal or trivariate Student’s t distribution, where the latter bounds follow from existing sharp bounds on the correlation between the outcome errors. To illustrate the usefulness of the distribution bounds established in this paper, we apply them to a wage earnings model for child laborers in the early 1900s, where regimes are governed according to literacy.