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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 ,
Xun Lu ,
Xianbo Zhou  and
Yahong Zhou
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: snchen@ust.hk.
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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
Information
Econometric Theory , Volume 34 , Issue 3 , June 2018 , pp. 543 - 573
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

REFERENCES

Akritas, M. & Van Keilegom, I. (2001) Nonparametric estimation of the residual distribution. Scandinavian Journal of Statistics 28, 549–567.CrossRefGoogle Scholar
Amemiya, T. (1985) Advanced Econometrics. Harvard University Press.Google Scholar
Cosslett, S. (2004) Efficient semiparametric estimation of censored and truncated regressions via smoothed self-consistency equation. Econometrica 72, 1277–1293.CrossRefGoogle Scholar
Chen, S. (2010) Nonparametric identification and estimation of truncated regression models. Review of Economic Studies 77, 127–153.CrossRefGoogle Scholar
Chen, S., Dahl, G., & Khan, S. (2005) Nonparametric identification and estimation of a censored location-scale regression model. Journal of the American Statistical Association 100, 212–221.CrossRefGoogle Scholar
Chen, S. & Zhou, X. (2012) Semiparametric estimation of a truncated regression model. Journal of Econometrics 167, 297–304.CrossRefGoogle Scholar
Fan, J. & Gijbels, I. (1994) Censored regression: Local linear approximations and their applications. Journal of the American Statistical Association 89, 560–570.CrossRefGoogle Scholar
Fan, J. & Gijbels, I. (1996) Local Polynomial Modelling and its Applications. Chapman and Hall.Google Scholar
Heuchenne, C. & Van Keilegom, I. (2010) Estimation in nonparametric location-scale regression models with censored data. Annals of the Institute of Statistical Mathematics 62, 439–463.CrossRefGoogle Scholar
Honoré, B.E. & Powell, J.L. (1994) Pairwise difference estimators of censored and truncated regression models. Journal of Econometrics 64, 241–278.CrossRefGoogle Scholar
Khan, S. & Lewbel, A. (2007) Weighted and two stage least squares estimation of semiparametric truncated regression models. Econometric Theory 23, 309–347.CrossRefGoogle Scholar
Lee, L.-F. (1992) Semiparametric nonlinear least-square estimation of truncated regression models. Econometric Theory 8, 52–94.CrossRefGoogle Scholar
Lewbel, A. & Linton, O. (2002) Nonparametric censored and truncated regression. Econometrica 70, 765–779.CrossRefGoogle Scholar
Li, Q. & Racine, J. (2003) Nonparametric estimation of distributions with categorical and continuous data. Journal of Multivariate Analysis 86, 266–292.CrossRefGoogle Scholar
Matzkin, R. (2007) Nonparametric identification. In Heckman, J.J. & Leamer, E.E. (eds.), The Handbook of Econometrics, vol. 6B, pp. 5307–5368. North-Holland.CrossRefGoogle Scholar
Matzkin, R. (2012) Identification in nonparametric limited dependent variable models with simultaneity and unobserved heterogeneity. Journal of Econometrics 166, 106–115.CrossRefGoogle Scholar
Newey, W.K. (1997) Convergence rates and asymptotic normality for series estimators. Journal of Econometrics 79, 147–168.CrossRefGoogle Scholar
Newey, W.K. (2001) Conditional moment restrictions in censored and truncated regression models. Econometric Theory 17, 863–888.CrossRefGoogle Scholar
Newey, W.K. (2004) Efficient semiparametric estimation via moment restrictions. Econometrica 72, 1877–1897.CrossRefGoogle Scholar
Politis, D., Romano, J., & Wolf, M. (1999) Subsampling. Springer-Verlag.CrossRefGoogle Scholar
Pollard, D. (1995) Uniform ratio limit theorems for empirical processes. Scandinavian Journal of Statistics 22, 271–278.Google Scholar
Powell, J.L. (1986) Symmetrically trimmed least squares estimation for Tobit models. Econometrica 54, 1435–1460.CrossRefGoogle Scholar
Silverman, B.W. (1986) Density Estimation for Statistics and Data Analysis. Chapman and Hall.CrossRefGoogle Scholar
Van Keilegom, I. & Akritas, G. (1999) Transfer of tail information in censored regression models. Annals of Statistics 27, 1745–1784.Google Scholar