Endogeneity in Probit Response Models

We look at conventional methods for removing endogeneity bias in regression models, including the linear model and the probit model. It is known that the usual Heckman twostep procedure should not be used in the probit model: from a theoretical perspective, it is unsatisfactory, and likelihood methods are superior. However, serious numerical problems occur when standard software packages try to maximize the biprobit likelihood function, even if the number of covariates is small. We draw conclusions for statistical practice. Finally, we prove the conditions under which parameters in the model are identifiable. The conditions for identification are delicate; we believe these results are new.