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The asymptotic variance of semi-parametric estimators with generated regressors

Author

Listed:
  • Jinyong Hahn

    (Institute for Fiscal Studies)

  • Geert Ridder

    (Institute for Fiscal Studies and University of Southern California)

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.

Suggested Citation

  • Jinyong Hahn & Geert Ridder, 2010. "The asymptotic variance of semi-parametric estimators with generated regressors," CeMMAP working papers CWP23/10, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    • Handle: RePEc:ifs:cemmap:23/10
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    File URL: http://cemmap.ifs.org.uk/wps/cwp2310.pdf
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    JEL classification:

    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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