Nonparametric Identification And Estimation Of Truncated Regression Models With Heteroskedasticity

We consider nonparametric identi…cation and estimation of truncated regression models with unknown conditional heteroskedasticity. The existing methods (e.g., Chen (2010)) that ignore heteroskedasticity often result in inconsistent estimators of regression functions. In this paper, we show that both the regression and heteroskedasticity functions are identi…ed in a location-scale setting. Based on our constructive identi…cation results, we propose kernel-based estimators of regression and heteroskedasticity functions and show that the estimators are asymptotically normally distributed. Our simulations demonstrate that our new method performs well in …nite samples. In particular, we con…rm that in the presence of heteroskedasticity, our new estimator of the regression function has a much smaller bias than Chen’s (2010) estimator. Key Words: Truncated data; Nonparametric regression; Heteroskedasticity; Kernel estimator. JEL Classi…cation: C14, C24 We would like to thank Arthur Lewbel and Liangjun Su for their helpful comments. Address correspondence to: Songnian Chen, Department of Economics, Hong Kong University of Science and Technology; E-mail: snchen@ust.hk.