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Two-Step Extremum Estimation with Estimated Single-Indices

  • Kyungchul Song

    ()

    (Department of Economics, University of Pennsylvania)

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    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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    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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    1. Ahn, Hyungtaik & Powell, James L., 1993. "Semiparametric estimation of censored selection models with a nonparametric selection mechanism," Journal of Econometrics, Elsevier, vol. 58(1-2), pages 3-29, July.
    2. Song, Kyungchul, 2008. "Uniform Convergence Of Series Estimators Over Function Spaces," Econometric Theory, Cambridge University Press, vol. 24(06), pages 1463-1499, December.
    3. Jason Abrevaya & Jian Huang, 2005. "On the Bootstrap of the Maximum Score Estimator," Econometrica, Econometric Society, vol. 73(4), pages 1175-1204, 07.
    4. Ahn, Hyungtaik & Manski, Charles F., 1993. "Distribution theory for the analysis of binary choice under uncertainty with nonparametric estimation of expectations," Journal of Econometrics, Elsevier, vol. 56(3), pages 291-321, April.
    5. repec:cup:cbooks:9780521496032 is not listed on IDEAS
    6. Keisuke Hirano & Guido W. Imbens & Geert Ridder, 2003. "Efficient Estimation of Average Treatment Effects Using the Estimated Propensity Score," Econometrica, Econometric Society, vol. 71(4), pages 1161-1189, 07.
    7. Hardle, Wolfgang & Tsybakov, A. B., 1993. "How sensitive are average derivatives?," Journal of Econometrics, Elsevier, vol. 58(1-2), pages 31-48, July.
    8. Klein, Roger W & Spady, Richard H, 1993. "An Efficient Semiparametric Estimator for Binary Response Models," Econometrica, Econometric Society, vol. 61(2), pages 387-421, March.
    9. Manuel A. Domínguez & Ignacio N. Lobato, 2004. "Consistent Estimation of Models Defined by Conditional Moment Restrictions," Econometrica, Econometric Society, vol. 72(5), pages 1601-1615, 09.
    10. Mitali Das & Whitney K. Newey & Francis Vella, 2003. "Nonparametric Estimation of Sample Selection Models," Review of Economic Studies, Oxford University Press, vol. 70(1), pages 33-58.
    11. Newey, Whitney K & Powell, James L & Walker, James R, 1990. "Semiparametric Estimation of Selection Models: Some Empirical Results," American Economic Review, American Economic Association, vol. 80(2), pages 324-28, May.
    12. Moshe Buchinsky & Jinyong Hahn, 1998. "An Alternative Estimator for the Censored Quantile Regression Model," Econometrica, Econometric Society, vol. 66(3), pages 653-672, May.
    13. Heckman, James J, 1990. "Varieties of Selection Bias," American Economic Review, American Economic Association, vol. 80(2), pages 313-18, May.
    14. Stoker, Thomas M, 1986. "Consistent Estimation of Scaled Coefficients," Econometrica, Econometric Society, vol. 54(6), pages 1461-81, November.
    15. Fan, Yanqin & Li, Qi, 1996. "Consistent Model Specification Tests: Omitted Variables and Semiparametric Functional Forms," Econometrica, Econometric Society, vol. 64(4), pages 865-90, July.
    16. Chen, Songnian & Khan, Shakeeb, 2003. "Semiparametric Estimation Of A Heteroskedastic Sample Selection Model," Econometric Theory, Cambridge University Press, vol. 19(06), pages 1040-1064, December.
    17. Heckman, James J & Ichimura, Hidehiko & Todd, Petra, 1998. "Matching as an Econometric Evaluation Estimator," Review of Economic Studies, Wiley Blackwell, vol. 65(2), pages 261-94, April.
    18. 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.
    19. Powell, James L & Stock, James H & Stoker, Thomas M, 1989. "Semiparametric Estimation of Index Coefficients," Econometrica, Econometric Society, vol. 57(6), pages 1403-30, November.
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