Tests in Censored Models when the Structural Parameters Are Not Identified

This paper presents tests for the structural parameters of a censored regression model with endogenous explanatory variables. These tests have the correct size even when the identification condition for the structural parameter is invalid. My approach starts from the estimation of the unrestricted parameters, which does not depend on the identification of the structural parameter. Next, I set up the optimal minimum distance objective function, from where I derive the tests. The proposed robust tests are implemented in many statistical software packages since they demand only the Tobit and the ordinary least squares estimation functions. By simulating their power curves, I compare the robust to the Wald and the likelihood ratio tests. A case of the labor supply of married women illustrates the use of the robust tests for the construction of confidence intervals.