IDEAS home Printed from https://ideas.repec.org/p/wvu/wpaper/10-11.html
   My bibliography  Save this paper

Efficient semiparametric instrumental variable estimation

Author

Listed:
  • 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.

Suggested Citation

  • Feng Yao & Junsen Zhang, 2010. "Efficient semiparametric instrumental variable estimation," Working Papers 10-11, Department of Economics, West Virginia University.
  • Handle: RePEc:wvu:wpaper:10-11
    as

    Download full text from publisher

    File URL: http://be.wvu.edu/phd_economics/pdf/10-11.pdf
    File Function: First version, 2010
    Download Restriction: no

    References listed on IDEAS

    as
    1. J. P. Florens & J. J. Heckman & C. Meghir & E. Vytlacil, 2008. "Identification of Treatment Effects Using Control Functions in Models With Continuous, Endogenous Treatment and Heterogeneous Effects," Econometrica, Econometric Society, vol. 76(5), pages 1191-1206, September.
    2. S. Darolles & Y. Fan & J. P. Florens & E. Renault, 2011. "Nonparametric Instrumental Regression," Econometrica, Econometric Society, vol. 79(5), pages 1541-1565, September.
    3. Newey, Whitney K, 1990. "Efficient Instrumental Variables Estimation of Nonlinear Models," Econometrica, Econometric Society, vol. 58(4), pages 809-837, July.
    4. 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.
    5. Heckman, James J, 1978. "Dummy Endogenous Variables in a Simultaneous Equation System," Econometrica, Econometric Society, vol. 46(4), pages 931-959, July.
    6. Germán Aneiros & Alejandro Quintela, 2001. "Asymptotic properties in partial linear models under dependence," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 10(2), pages 333-355, December.
    7. Delgado, Miguel A & Mora, Juan, 1995. "Nonparametric and Semiparametric Estimation with Discrete Regressors," Econometrica, Econometric Society, vol. 63(6), pages 1477-1484, November.
    8. Li, Qi & Stengos, Thanasis, 1996. "Semiparametric estimation of partially linear panel data models," Journal of Econometrics, Elsevier, vol. 71(1-2), pages 389-397.
    9. Rilstone, Paul, 1992. "Semiparametric IV Estimation with Parameter Dependent Instruments," Econometric Theory, Cambridge University Press, vol. 8(03), pages 403-406, September.
    10. 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.
    11. 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.
    12. 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.
    13. Whitney K. Newey & James L. Powell & Francis Vella, 1999. "Nonparametric Estimation of Triangular Simultaneous Equations Models," Econometrica, Econometric Society, vol. 67(3), pages 565-604, May.
    14. Hardle, Wolfgang & LIang, Hua & Gao, Jiti, 2000. "Partially linear models," MPRA Paper 39562, University Library of Munich, Germany, revised 01 Sep 2000.
    15. White, Halbert, 1980. "A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity," Econometrica, Econometric Society, vol. 48(4), pages 817-838, May.
    16. Powell, James L & Stock, James H & Stoker, Thomas M, 1989. "Semiparametric Estimation of Index Coefficients," Econometrica, Econometric Society, vol. 57(6), pages 1403-1430, November.
    17. Das, M., 2005. "Instrumental variables estimators of nonparametric models with discrete endogenous regressors," Journal of Econometrics, Elsevier, vol. 124(2), pages 335-361, February.
    18. 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.
    19. Chamberlain, Gary, 1992. "Efficiency Bounds for Semiparametric Regression," Econometrica, Econometric Society, vol. 60(3), pages 567-596, May.
    Full references (including those not matched with items on IDEAS)

    More about this item

    Keywords

    Instrumental variables; semiparametric regression; efficient estimation.;

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:wvu:wpaper:10-11. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Josh Hall). General contact details of provider: http://edirc.repec.org/data/dewvuus.html .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.