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NONPARAMETRIC IDENTIFICATION AND ESTIMATION OF TRUNCATED REGRESSION MODELS WITH HETEROSKEDASTICITY

Published online by Cambridge University Press:  18 April 2017

Songnian Chen*
Affiliation:
Hong Kong University of Science and Technology
Xun Lu
Affiliation:
Hong Kong University of Science and Technology
Xianbo Zhou
Affiliation:
Sun Yat-sen University
Yahong Zhou
Affiliation:
Shanghai University of Finance and Economics
*
*Address correspondence to Songnian Chen, Department of Economics, Hong Kong University of Science and Technology, Hong Kong, China; e-mail: [email protected].

Abstract

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.

Type
ARTICLES
Copyright
Copyright © Cambridge University Press 2017 

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Footnotes

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.

References

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