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Nonparametric identification using instrumental variables: sufficient conditions for completeness

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  • Yingyao Hu

    (Institute for Fiscal Studies and Johns Hopkins University)

  • Ji-Liang Shiu

    (Institute for Fiscal Studies)

Abstract

This paper provides sufficient conditions for the nonparametric identification of the regression function m(.) in a regression model with an endogenous regressor x and an instrumental variable z. It has been shown that the identification of the regression function from the conditional expectation of the dependent variable on the instrument relies on the completeness of the distribution of the endogenous regressor conditional on the instrument, i.e., f(x/z). We provide sufficient conditions for the completeness of f(x/z) without imposing a specific functional form, such as the exponential family. We show that if the conditional density f(x/z) coincides with an existing complete density at a limit point in the support of z, then f(x/z) itself is complete, and therefore, the regression function m(.) is nonparametrically identified. We use this general result provide specific sufficient conditions for completeness in three different specifications of the relationship between the endogenous regressor x and the instrumental variable z.

Suggested Citation

  • Yingyao Hu & Ji-Liang Shiu, 2011. "Nonparametric identification using instrumental variables: sufficient conditions for completeness," CeMMAP working papers CWP25/11, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  • Handle: RePEc:ifs:cemmap:25/11
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    File URL: http://cemmap.ifs.org.uk/wps/cwp2511.pdf
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    References listed on IDEAS

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    1. Sandra E. Black & Paul J. Devereux & Kjell G. Salvanes, 2005. "Why the Apple Doesn't Fall Far: Understanding Intergenerational Transmission of Human Capital," American Economic Review, American Economic Association, pages 437-449.
    2. Hu, Yingyao & Shum, Matthew, 2012. "Nonparametric identification of dynamic models with unobserved state variables," Journal of Econometrics, Elsevier, pages 32-44.
    3. S. Darolles & Y. Fan & J. P. Florens & E. Renault, 2011. "Nonparametric Instrumental Regression," Econometrica, Econometric Society, pages 1541-1565.
    4. Yingyao Hu & Susanne M. Schennach, 2008. "Instrumental Variable Treatment of Nonclassical Measurement Error Models," Econometrica, Econometric Society, vol. 76(1), pages 195-216, January.
    5. D’Haultfoeuille, Xavier, 2011. "On The Completeness Condition In Nonparametric Instrumental Problems," Econometric Theory, Cambridge University Press, vol. 27(03), pages 460-471, June.
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    Cited by:

    1. Shiu, Ji-Liang & Hu, Yingyao, 2013. "Identification and estimation of nonlinear dynamic panel data models with unobserved covariates," Journal of Econometrics, Elsevier, vol. 175(2), pages 116-131.
    2. Fève, Frédérique & Florens, Jean-Pierre, 2014. "Non parametric analysis of panel data models with endogenous variables," Journal of Econometrics, Elsevier, vol. 181(2), pages 151-164.
    3. Daniel Wilhelm, 2015. "Identification and estimation of nonparametric panel data regressions with measurement error," CeMMAP working papers CWP34/15, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.

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