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The asymptotic variance of semi-parametric estimators with generated regressors

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  • Jinyong Hahn
  • Geert Ridder
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    Abstract

    We study the asymptotic distribution of three-step estimators of a finite dimensional parameter vector where the second step consists of one or more nonparametric regressions on a regressor that is estimated in the first step. The first step estimator is either parametric or non-parametric. Using Newey's (1994) path-derivative method we derive the contribution of the first step estimator to the influence function. In this derivation it is important to account for the dual role that the first step estimator plays in the second step non-parametric regression, i.e., that of conditioning variable and that of argument. We consider three examples in more detail: the partial linear regression model estimator with a generated regressor, the Heckman, Ichimura and Todd (1998) estimator of the Average Treatment Effect and a semi-parametric control variable estimator.

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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 CWP23/10.

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    Date of creation: Aug 2010
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    Handle: RePEc:ifs:cemmap:23/10

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    Cited by:
    1. Zhang, Junfu & Zhao, Zhong, 2013. "Measuring the Income-Distance Tradeoff for Rural-Urban Migrants in China," IZA Discussion Papers 7160, Institute for the Study of Labor (IZA).
    2. Song, Kyungchul, 2014. "Semiparametric models with single-index nuisance parameters," Journal of Econometrics, Elsevier, vol. 178(P3), pages 471-483.

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