NONPARAMETRIC IDENTIFICATION AND ESTIMATION OF TRUNCATED REGRESSION MODELS WITH HETEROSKEDASTICITY

We consider nonparametric identification and estimation of truncated regression models with unknown conditional heteroskedasticity. The existing methods (e.g., Chen (2010,Review of Economic Studies77, 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 Studies77, 127–153) estimator.