Estimators and inference in a censored regression model with endogenous covariates

This paper derives the asymptotic distribution theory for censored regression models with endogenous covariates under no parametric assumptions on the disturbance distribution, extending the modeling framework of Powell (1986). While it is well known that under some restrictions the use of reduced form residuals will lead to consistent estimators of the structural parameters, derivation of the asymptotic distribution theory that is essential for inference and the usual hypothesis testing is not obvious for this model. The problem arises because the structural model generates a set of moment restrictions that are discontinuous in the parameters, making standard methods inapplicable. This paper illustrates that the techniques in Pakes and Pollard (1989) can be adapted to this model by treating the multi-stage problem as simultaneously satisfying the joint vector of population moment restrictions, and partitioning the joint asymptotic covariance matrix appropriately. A Monte Carlo study illustrates the high practical power of the estimators, and shows that they will provide a useful alternative to methods that depend on Gaussian or other specified distributions.