Two-step estimation of semiparametric censored regression models

Root-n-consistent estimators of the regression coefficients in the linear censored regression model under conditional quantile restrictions on the error terms were proposed by Powell (Journal of Econometrics 25 (1984) 303–325, 32 (1986a) 143–155). While those estimators have desirable asymptotic properties under weak regularity conditions, simulation studies have shown these estimators to exhibit a small sample bias in the opposite direction of the least squares bias for censored data. This paper introduces two-step estimators for these models which minimize convex objective functions, and are designed to overcome this finite-sample bias. The paper gives regularity conditions under which the proposed two-step estimators are consistent and asymptotically normal; a Monte Carlo study compares the finite sample behavior of the proposed methods with their one-step counterparts.