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Efficient semiparametric instrumental variable estimation

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  • Feng Yao

    (Department of Economics, West Virginia University)

  • Junsen Zhang

    (Department of Economics, The Chinese University of Hong Kong)

Abstract

We consider the estimation of a semiparametric regression model where data is independently and identically distributed. Our primary interest is on the estimation of the parameter vector, where the associated regressors are correlated with the errors and contain both continuous and discrete variables. We propose three estimators by adapting Robinson's (1988) and Li and Stengos' (1996) framework and establish their asymptotic properties. They are asymptotically normally distributed and correctly centered at the true value of the parameter vector. Among a class of semiparametric IV estimators with conditional moment restriction, the first two are efficient under conditional homoskedasticity and the last one is efficient under heteroskedasticity. They allow the reduced form to be nonparametric, are asymptotically equivalent to semiparametric IV estimators that optimally select the instrument and reach the semiparametric efficiency bounds in Chamberlain (1992). A Monte Carlo study is performed to shed light on the finite sample properties of these competing estimators. Its applicability is illustrated with an empirical data set.

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Bibliographic Info

Paper provided by Department of Economics, West Virginia University in its series Working Papers with number 10-11.

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Length: 39 pages
Date of creation: 2010
Date of revision:
Handle: RePEc:wvu:wpaper:10-11

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Keywords: Instrumental variables; semiparametric regression; efficient estimation.;

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  1. Whitney K. Newey & James L. Powell & Francis Vella, 1998. "Nonparametric Estimation of Triangular Simultaneous Equations Models," Working papers 98-6, Massachusetts Institute of Technology (MIT), Department of Economics.
  2. Hardle, Wolfgang & LIang, Hua & Gao, Jiti, 2000. "Partially linear models," MPRA Paper 39562, University Library of Munich, Germany, revised 01 Sep 2000.
  3. Qi Li & Aman Ullha, 1998. "Estimating partially linear panel data models with one-way error components," Econometric Reviews, Taylor & Francis Journals, vol. 17(2), pages 145-166.
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  7. Das, M., 2005. "Instrumental variables estimators of nonparametric models with discrete endogenous regressors," Journal of Econometrics, Elsevier, vol. 124(2), pages 335-361, February.
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  10. White, Halbert, 1980. "A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity," Econometrica, Econometric Society, vol. 48(4), pages 817-38, May.
  11. Delgado, Miguel A & Mora, Juan, 1995. "Nonparametric and Semiparametric Estimation with Discrete Regressors," Econometrica, Econometric Society, vol. 63(6), pages 1477-84, November.
  12. Baltagi, Badi H. & Li, Qi, 2002. "On instrumental variable estimation of semiparametric dynamic panel data models," Economics Letters, Elsevier, vol. 76(1), pages 1-9, June.
  13. Powell, James L & Stock, James H & Stoker, Thomas M, 1989. "Semiparametric Estimation of Index Coefficients," Econometrica, Econometric Society, vol. 57(6), pages 1403-30, November.
  14. Chunrong Ai & Xiaohong Chen, 2003. "Efficient Estimation of Models with Conditional Moment Restrictions Containing Unknown Functions," Econometrica, Econometric Society, vol. 71(6), pages 1795-1843, November.
  15. Chamberlain, Gary, 1992. "Efficiency Bounds for Semiparametric Regression," Econometrica, Econometric Society, vol. 60(3), pages 567-96, May.
  16. Racine, Jeff & Li, Qi, 2004. "Nonparametric estimation of regression functions with both categorical and continuous data," Journal of Econometrics, Elsevier, vol. 119(1), pages 99-130, March.
  17. Li, Qi & Stengos, Thanasis, 1996. "Semiparametric estimation of partially linear panel data models," Journal of Econometrics, Elsevier, vol. 71(1-2), pages 389-397.
  18. Chen, Songnian, 1999. "Distribution-free estimation of the random coefficient dummy endogenous variable model," Journal of Econometrics, Elsevier, vol. 91(1), pages 171-199, July.
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