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.