Two-step estimation of semiparametric censored regression models

Abstract

Root-n-consistent estimators of the regression coe cients 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. 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 ÿnite-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 ÿnite sample behavior of the proposed methods with their one-step counterparts. ? 2001 Elsevier Science S.A. All rights reserved.

Quantile regression under random censoring

“…Relaxing the traditional parametric restrictions on the form of the distribution of the underlying error terms, a number of consistent estimators have been proposed which require only weak conditions on these distributions, including: constant conditional quantiles (Powell, 1984(Powell, , 1986a An earlier version of this paper was presented at the 2000 World Congress of the Econometric Society. Nawata, 1990;Newey and Powell, 1990;Buchinsky and Hahn, 1998;Chen and Khan, 2001; Khan and Powell, 2001), conditional symmetry (Powell, 1986b;Lee, 1993a, b;Newey, 1991), and independence of the errors and regressors (Duncan, 1986;Fernandez, 1986; Honorà e and Powell, 1994;Horowitz, 1986Horowitz, , 1988aMoon, 1989). These proposed estimators all exploit an assumption that the censoring values for the dependent variable are known for all observations, even those that are not censored; 1 while the typical estimator is constructed under the presumption that the dependent variable is censored to the left at zero, it is generally straightforward to modify it for either right or left censored data (or both) with variable censoring values.…”

Vol. 8, No. 2 (Full Issue)

“…It was shown that all models can be represented in the context of multiple index frameworks (Stoker, 1986) and that it can be estimated by the semi-parametric least squares method if identification conditions are met. Andrews (1991) proposed the establishment of asymptotic series estimators for instant polynomial series, trigonometric series and Gallant's Fourier flexible form estimators, for nonparametric regression models and applied a variety of estimands in the regression model under consideration, including derivatives and integrals of the regression function (see also Klein & Spady, 1993;Gerfin, 1996;Vella, 1998;Martin, 2001;Khan & Powell, 2001;Lee & Vella, 2006). Previous studies in this area concentrated on the sample selection model and used parametric, semi-parametric or nonparametric approaches.…”

Estimated and Analysis of the Relationship Between the Endogenous and Exogenous Variables Using Fuzzy Semi-Parametric Sample Selection Model

“…However, the standard approach of estimating sample selection model shows inconsistent results if the distributional assumptions of the errors terms are made. Hence, an important progress within the last decade in the development of an alternative approach to overcome this problem is through the use of semi-parametric method (Andrews (1991;Cosslett, 1990; Science Publications Gerfin, 1996;Ichimura and Lee, 1991;Khan and Powell, 2001;Klein and Spady, 1993;Lee and Vella, 2006;Martins, 2001;Powell, 1987;Powell et al, 1989).…”