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Nonparametric methods for inference in the presence of instrumental variables

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  • Peter Hall
  • Joel L. Horowitz
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    Abstract

    We suggest two nonparametric approaches, based on kernel methods and orthogonal series, respectively, to estimating regression functions in the presence of instrumental variables. For the first time in this class of problems we derive optimal convergence rates, and show that they are attained by particular estimators. In the presence of instrumental variables the relation that identifies the regression function also defines an ill-posed inverse problem, the "difficulty" of which depends on eigenvalues of a certain integral operator which is determined by the joint density of endogenous and instrumental variables. We delineate the role played by problem difficulty in determining both the optimal convergence rate and the appropriate choice of smoothing parameter.

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    File URL: http://cemmap.ifs.org.uk/wps/cwp0302.pdf
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    Bibliographic Info

    Paper provided by Centre for Microdata Methods and Practice, Institute for Fiscal Studies in its series CeMMAP working papers with number CWP02/03.

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    Length: 22 pp.
    Date of creation: Apr 2003
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    Handle: RePEc:ifs:cemmap:02/03

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    Cited by:
    1. Woocheol Kim, 2004. "Identification And Estimation Of Nonparametric Structural," Econometric Society 2004 Far Eastern Meetings 733, Econometric Society.
    2. Oliver Linton & Enno Mammen, 2003. "Estimating Semiparametric ARCH (8) Models by Kernel Smoothing Methods," STICERD - Econometrics Paper Series /2003/453, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    3. Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, edition 1, volume 1, number 8355.
    4. S. Darolles & Y. Fan & J. P. Florens & E. Renault, 2011. "Nonparametric Instrumental Regression," Econometrica, Econometric Society, vol. 79(5), pages 1541-1565, 09.
    5. Richard Blundell & Xiaohong Chen & Dennis Kristensen, 2003. "Nonparametric IV estimation of shape-invariant Engel curves," CeMMAP working papers CWP15/03, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    6. Richard Blundell & Joel Horowitz, 2004. "A nonparametric test of exogeneity," CeMMAP working papers CWP15/04, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    7. Chernozhukov, Victor & Imbens, Guido W. & Newey, Whitney K., 2007. "Instrumental variable estimation of nonseparable models," Journal of Econometrics, Elsevier, vol. 139(1), pages 4-14, July.
    8. Thomas A. Severini & Gautam Tripathi, 2005. "Some Identification Issues in Nonparametric Linear Models with Endogenous Regressors," Working papers 2005-12, University of Connecticut, Department of Economics.
    9. Joel Horowitz, 2004. "Testing a parametric model against a nonparametric alternative with identification through instrumental variables," CeMMAP working papers CWP14/04, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.

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