Published online by Cambridge University Press: 18 April 2017
We consider nonparametric identification and estimation of truncated regression models with unknown conditional heteroskedasticity. The existing methods (e.g., Chen (2010, Review of Economic Studies 77, 127–153)) that ignore heteroskedasticity often result in inconsistent estimators of regression functions. In this paper, we show that both the regression and heteroskedasticity functions are identified in a location-scale setting. Based on our constructive identification 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 finite samples. In particular, we confirm that in the presence of heteroskedasticity, our new estimator of the regression function has a much smaller bias than Chen’s (2010, Review of Economic Studies 77, 127–153) estimator.
We gratefully thank the Co-editor Liangjun Su and three anonymous referees for their many constructive comments. We also thank Arthur Lewbel and the participants of the workshop on “Advances in Microeconometrics” (Hong Kong), the 2014 Asian meeting of the Econometric Society (Taipei), and the seminar at University of Hong Kong for their helpful comments. X. Zhou’s research was supported by the National Natural Science Foundation of China Grant 71371199.