Semi-parametric Estimation of Program Impacts on Dispersion of Potential Wages

Policy evaluations require estimation of program impacts on both mean and dispersion of potential outcomes, even though the previous identication eorts have focused mostly on impacts on the mean. We propose the use of instrumental variables and pairwise matching to identify the average treatment eect on conditional variance in potential outcomes. We show that it is possible to identify and estimate program impact on conditional dispersion of potential outcomes in an endogenous switching model, without using the identification-at-infinity argument, if we impose semi-parametric conditions on the error structure of the outcome equation. In the presence of a multi-valued or continuously distributed instrument, we recommend the pairwise-matching method if the error term and the latent index are symmetrically distributed around zero. Simulation results show that the proposed estimators converge at the regular parametric rate. We apply the new estimators to a well-known empirical study of the eect of education on potential wage inequality.