Identification and Estimation of Partially Linear Censored Regression Models with Unknown Heteroscedasticity
Zhengyu Zhang
Shanghai University of Finance and Economic
10/14/2013 1:06:18 AM
This article introduces a new identification and estimation strategy for partially linear regression models with a general form of unknown heteroscedasticity, i.e., Y=X'β0+m(Z)+U and U=σ(X,Z)ε, where ε is independent of (X,Z), the functional form of both m(.) and σ(.) are left unspecified. We show that in such a model, β0 and m(.) can be exactly identified while the scale function σ(.) can be identified up to scale as long as σ(X,Z) permits sufficient nonlinearity in X. A two-stage estimation procedure motivated by the identification strategy is described and its large sample properties are formally established. Moreover, our strategy is flexible enough to allow for various degrees of censoring in the dependent variable. Simulation results show that the proposed estimator performs reasonably well in finite samples.
Censored regression model; Partially linear regression; Heteroscedasticity; Quantile regression;