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EFFICIENT SEMIPARAMETRIC SEEMINGLY UNRELATED QUANTILE REGRESSION ESTIMATION

Published online by Cambridge University Press:  01 October 2009

Sung Jae Jun  and
Joris Pinkse
Sung Jae Jun*
Affiliation:
The Pennsylvania State University and The Center for the Study of Auctions, Procurements and Competition Policy
Joris Pinkse
Affiliation:
The Pennsylvania State University and The Center for the Study of Auctions, Procurements and Competition Policy
*
*Address correspondence to Sung Jae Jun, Department of Economics, The Pennsylvania State University, 608 Kern Graduate Building, University Park, PA 16802, U.S.A.; e-mail: [email protected].
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Abstract

We propose an efficient semiparametric estimator for the coefficients of a multivariate linear regression model—with a conditional quantile restriction for each equation—in which the conditional distributions of errors given regressors are unknown. The procedure can be used to estimate multiple conditional quantiles of the same regression relationship. The proposed estimator is asymptotically as efficient as if the true optimal instruments were known. Simulation results suggest that the estimation procedure works well in practice and dominates an equation-by-equation efficiency correction if the errors are dependent conditional on the regressors.

Type
ARTICLES
Information
Econometric Theory , Volume 25 , Issue 5 , October 2009 , pp. 1392 - 1414
Copyright
Copyright © Cambridge University Press 2009

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References

REFERENCES

Aitken, A.C. (1935) On least squares and linear combination of observations. Proceedings of the Royal Society of Edinburgh 55, 42–48.CrossRefGoogle Scholar
Carroll, R.J. (1982) Adapting for heteroscedasticity in linear models. Annals of Statistics 10, 1224–1233.Google Scholar
Chamberlain, G. (1987) Asymptotic efficiency in estimation with conditional moment restrictions. Journal of Econometrics 34, 305–334.CrossRefGoogle Scholar
Davidson, J. (1994) Stochastic Limit Theory. Oxford University Press.CrossRefGoogle Scholar
Delgado, M. (1992) Semiparametric generalized least squares estimation in the multivariate nonlinear regression model. Econometric Theory 8, 203–222.CrossRefGoogle Scholar
Koenker, R. (2005) Quantile Regression. Cambridge University Press.CrossRefGoogle Scholar
Koenker, R. & Bassett, G. (1978) Regression quantile. Econometrica 46, 33–50.CrossRefGoogle Scholar
Komunjer, I. & Vuong, Q. (2006) Efficient Conditional Quantile Estimation: The Time Series Case. Working paper, University of California, San Diego.Google Scholar
Newey, W.K. (1990) Efficient instrumental variables estimation of nonlinear models. Econometrica 58, 809–837.CrossRefGoogle Scholar
Newey, W.K. (1993) Efficient estimation of models with conditional moment restrictions. In Maddala, G.S., Rao, C.R., & Vinod, H.D. (eds.), Handbook of Statistics, Vol. 11. pp. 419–454. North-Holland.Google Scholar
Newey, W.K. & Powell, J.L. (1990) Efficient estimation of linear and type I censored regression models under conditional quantile restrictions. Econometric Theory 6, 295–317.CrossRefGoogle Scholar
Pakes, A. & Pollard, D. (1989) Simulation and the asymptotics of optimization estimators. Econometrica 57, 1027–1057.CrossRefGoogle Scholar
Pinkse, J. (2006) Heteroskedasticity Correction and Dimension reduction. Working paper, Pennsylvania State University.Google Scholar
Robinson, P.M. (1987) Asymptotically efficient estimation in the presence of heteroskedasticity of unknown form. Econometrica 55, 875–891.CrossRefGoogle Scholar
Stone, C.J. (1977) Consistent nonparametric regression. Annals of Statistics 5, 595–645.CrossRefGoogle Scholar
van der Vaart, A. & Wellner, J.A. (1996) Weak Convergence and Empirical Processes: With applications to Statistics. Springer-Verlag.CrossRefGoogle Scholar
Whang, Y. (2006) Smoothed empirical likelihood methods for quantile regression models. Econometric Theory 22, 173–205.CrossRefGoogle Scholar
Zhao, Q. (2001) Asymptotically efficient median regression in the presence of heteroskedasticity of unknown form. Econometric Theory 17, 765–784.CrossRefGoogle Scholar