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Asymptotic Expansions for Some Semiparametric Program Evaluation Estimators

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  • Hidehiko Ichimura
  • Oliver Linton

Abstract

We investigate the performance of a class of semiparametric estimators of the treatment effect via asymptotic expansions. We derive approximations to the first two moments of the estimator that are valid to 'second order'. We use these approximations to define a method of bandwidth selection. We also propose a degrees- of-freedom like bias correction that improves the second order properties of the estimator but without requiring estimation of higher order derivatives of the unknown propensity score. We provide some numerical calibrations of the results.

Suggested Citation

  • Hidehiko Ichimura & Oliver Linton, 2003. "Asymptotic Expansions for Some Semiparametric Program Evaluation Estimators," STICERD - Econometrics Paper Series 451, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    • Handle: RePEc:cep:stiecm:451
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    References listed on IDEAS

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    1. Powell, James L. & Stoker, Thomas M., 1996. "Optimal bandwidth choice for density-weighted averages," Journal of Econometrics, Elsevier, vol. 75(2), pages 291-316, December.
    2. Andrews, Donald W K, 1994. "Asymptotics for Semiparametric Econometric Models via Stochastic Equicontinuity," Econometrica, Econometric Society, vol. 62(1), pages 43-72, January.
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    4. 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, July.
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    7. Srinivasan, T N, 1970. "Approximations to Finite Sample Moments of Estimators Whose Exact Sampling Distributions are Unknown," Econometrica, Econometric Society, vol. 38(3), pages 533-541, May.
    8. Linton, Oliver, 1996. "Edgeworth Approximation for MINPIN Estimators in Semiparametric Regression Models," Econometric Theory, Cambridge University Press, vol. 12(1), pages 30-60, March.
    9. Hall, Peter & Marron, J. S., 1987. "Estimation of integrated squared density derivatives," Statistics & Probability Letters, Elsevier, vol. 6(2), pages 109-115, November.
    10. Linton, Oliver & Xiao, Zhijie, 2001. "Second-Order Approximation For Adaptive Regression Estimators," Econometric Theory, Cambridge University Press, vol. 17(5), pages 984-1024, October.
    11. Y. Nishiyama & P. M. Robinson, 2000. "Edgeworth Expansions for Semiparametric Averaged Derivatives," Econometrica, Econometric Society, vol. 68(4), pages 931-980, July.
    12. James J. Heckman & Hidehiko Ichimura & Petra Todd, 1998. "Matching As An Econometric Evaluation Estimator," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 65(2), pages 261-294.
    13. Robinson, P M, 1995. "The Normal Approximation for Semiparametric Averaged Derivatives," Econometrica, Econometric Society, vol. 63(3), pages 667-680, May.
    14. Jones, M. C. & Sheather, S. J., 1991. "Using non-stochastic terms to advantage in kernel-based estimation of integrated squared density derivatives," Statistics & Probability Letters, Elsevier, vol. 11(6), pages 511-514, June.
    15. Hardle, Wolfgang & Tsybakov, A. B., 1993. "How sensitive are average derivatives?," Journal of Econometrics, Elsevier, vol. 58(1-2), pages 31-48, July.
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    Citations

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    Cited by:

    1. Bernd Fitzenberger & Aderonke Osikominu & Robert Völter, 2008. "Get Training or Wait? Long-Run Employment Effects of Training Programs for the Unemployed in West Germany," Annals of Economics and Statistics, GENES, issue 91-92, pages 321-355.
    2. Toru Kitagawa & Chris Muris, 2013. "Covariate selection and model averaging in semiparametric estimation of treatment effects," CeMMAP working papers 61/13, Institute for Fiscal Studies.
    3. Dong, Chaohua & Gao, Jiti & Linton, Oliver, 2023. "High dimensional semiparametric moment restriction models," Journal of Econometrics, Elsevier, vol. 232(2), pages 320-345.
    4. Kitagawa, Toru & Muris, Chris, 2016. "Model averaging in semiparametric estimation of treatment effects," Journal of Econometrics, Elsevier, vol. 193(1), pages 271-289.
    5. Michael Lechner, 2004. "Sequential Matching Estimation of Dynamic Causal Models," University of St. Gallen Department of Economics working paper series 2004 2004-06, Department of Economics, University of St. Gallen.
    6. Annette Bergemann & Bernd Fitzenberger & Stefan Speckesser, 2009. "Evaluating the dynamic employment effects of training programs in East Germany using conditional difference-in-differences," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 24(5), pages 797-823.
    7. Millimet, Daniel L. & Tchernis, Rusty, 2009. "On the Specification of Propensity Scores, With Applications to the Analysis of Trade Policies," Journal of Business & Economic Statistics, American Statistical Association, vol. 27(3), pages 397-415.
    8. Bernd Fitzenberger & Stefan Speckesser, 2007. "Employment effects of the provision of specific professional skills and techniques in Germany," Empirical Economics, Springer, vol. 32(2), pages 529-573, May.
    9. Biewen, Martin & Fitzenberger, Bernd & Osikominu, Aderonke & Waller, Marie, 2007. "Which Program for Whom? Evidence on the Comparative Effectiveness of Public Sponsored Training Programs in Germany," ZEW Discussion Papers 07-042, ZEW - Leibniz Centre for European Economic Research.
    10. Chaohua Dong & Jiti Gao & Oliver Linton, 2017. "High dimensional semiparametric moment restriction models," Monash Econometrics and Business Statistics Working Papers 17/17, Monash University, Department of Econometrics and Business Statistics.
    11. Jose C. Galdo & Jeffrey Smith & Dan Black, 2008. "Bandwidth Selection and the Estimation of Treatment Effects with Unbalanced Data," Annals of Economics and Statistics, GENES, issue 91-92, pages 189-216.
    12. Alberto Abadie & Guido W. Imbens, 2002. "Simple and Bias-Corrected Matching Estimators for Average Treatment Effects," NBER Technical Working Papers 0283, National Bureau of Economic Research, Inc.

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    More about this item

    Keywords

    Bandwidth selection; kernel estimation; program evaluation; semiparametric estimation; treatment effect.;
    All these keywords.

    JEL classification:

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

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