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Two-Step Extremum Estimation with Estimated Single-Indices

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  • Kyungchul Song

    ()
    (Department of Economics, University of Pennsylvania)

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    Abstract

    This paper studies two-step extremum estimation that involves the first step estimation of nonparametric functions of single-indices. First, this paper finds that under certain regularity conditions for conditional measures, linear functionals of conditional expectations are insensitive to the first order perturbation of the parameters in the conditioning variable. Applying this result to symmetrized nearest neighborhood estimation of the nonparametric functions, this paper shows that the influence of the estimated single-indices on the estimator of main interest is asymptotically negligible even when the estimated single-indices follow cube root asymptotics. As a practical use of this finding, this paper proposes a bootstrap method for conditional moment restrictions that are asymptotically valid in the presence of cube root-converging single-index estimators. Some results from Monte Carlo simulations are presented and discussed.

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    File URL: http://economics.sas.upenn.edu/system/files/working-papers/09-012.pdf
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    Bibliographic Info

    Paper provided by Penn Institute for Economic Research, Department of Economics, University of Pennsylvania in its series PIER Working Paper Archive with number 09-012.

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    Length: 45 pages
    Date of creation: 16 Feb 2009
    Date of revision:
    Handle: RePEc:pen:papers:09-012

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    Related research

    Keywords: two-step extremum estimation; single-index restrictions; cube root asymptotics bootstrap;

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    References

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    2. repec:cup:cbooks:9780521496032 is not listed on IDEAS
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    13. Keisuke Hirano & Guido W. Imbens & Geert Ridder, 2000. "Efficient Estimation of Average Treatment Effects Using the Estimated Propensity Score," NBER Technical Working Papers 0251, National Bureau of Economic Research, Inc.
    14. Escanciano, Juan Carlos & Song, Kyungchul, 2010. "Testing single-index restrictions with a focus on average derivatives," Journal of Econometrics, Elsevier, vol. 156(2), pages 377-391, June.
    15. Stoker, Thomas M, 1986. "Consistent Estimation of Scaled Coefficients," Econometrica, Econometric Society, vol. 54(6), pages 1461-81, November.
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    Cited by:
    1. Kyungchul Song, 2009. "Efficient Estimation of Average Treatment Effects under Treatment-Based Sampling," PIER Working Paper Archive 09-011, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.

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