Standard-error Correction in Two-stage Optimization Models: A Quasi–maximum Likelihood Estimation Approach

Following Wooldridge (2014, Journal of Econometrics 182: 226–234), we discuss and implement in Stata an efficient maximum-likelihood approach to the estimation of corrected standard errors of two-stage optimization models. Specifically, we compare the robustness and efficiency of the proposed method with routines already implemented in Stata to deal with selection and endogeneity problems. This strategy is an alternative to the use of bootstrap methods and has the advantage that it can be easily applied for the estimation of two-stage optimization models for which already built-in programs are not yet available. It could be of particular use for addressing endogeneity in a nonlinear framework.