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Asymptotic Variance of Semiparametric Estimators With Generated Regressors

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  • Jinyong Hahn
  • Geert Ridder

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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Suggested Citation

  • Jinyong Hahn & Geert Ridder, 2013. "Asymptotic Variance of Semiparametric Estimators With Generated Regressors," Econometrica, Econometric Society, vol. 81(1), pages 315-340, January.
  • Handle: RePEc:ecm:emetrp:v:81:y:2013:i:1:p:315-340
    DOI: ECTA9609
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    File URL: http://hdl.handle.net/10.3982/ECTA9609
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    References listed on IDEAS

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    1. Newey, Whitney K, 1994. "The Asymptotic Variance of Semiparametric Estimators," Econometrica, Econometric Society, vol. 62(6), pages 1349-1382, November.
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    5. James J. Heckman & Hidehiko Ichimura & Petra Todd, 1998. "Matching As An Econometric Evaluation Estimator," Review of Economic Studies, Oxford University Press, vol. 65(2), pages 261-294.
    6. Murphy, Kevin M & Topel, Robert H, 2002. "Estimation and Inference in Two-Step Econometric Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 88-97, January.
    7. Whitney K. Newey, 2009. "Two-step series estimation of sample selection models," Econometrics Journal, Royal Economic Society, vol. 12(s1), pages 217-229, January.
    8. Barro, Robert J, 1977. "Unanticipated Money Growth and Unemployment in the United States," American Economic Review, American Economic Association, vol. 67(2), pages 101-115, March.
    9. Pagan, Adrian, 1984. "Econometric Issues in the Analysis of Regressions with Generated Regressors," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 25(1), pages 221-247, February.
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    More about this item

    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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