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Asymptotic expansions for some semiparametric program evaluation estimators

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Author Info
Hidehiko Ichimura () (Institute for Fiscal Studies and University of Tokyo)
Oliver Linton () (Institute for Fiscal Studies and London School of Economics)

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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.

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Paper provided by Centre for Microdata Methods and Practice, Institute for Fiscal Studies in its series CeMMAP working papers with number CWP04/01.

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Date of creation: Sep 2001
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Handle: RePEc:ifs:cemmap:04/01

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

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  1. Rothenberg, Thomas J., 1984. "Approximating the distributions of econometric estimators and test statistics," Handbook of Econometrics, in: Z. Griliches† & M. D. Intriligator (ed.), Handbook of Econometrics, edition 1, volume 2, chapter 15, pages 881-935 Elsevier. [Downloadable!] (restricted)
  2. Hall, Peter & Marron, J. S., 1987. "Estimation of integrated squared density derivatives," Statistics & Probability Letters, Elsevier, vol. 6(2), pages 109-115, November. [Downloadable!] (restricted)
  3. Robinson, P M, 1995. "The Normal Approximation for Semiparametric Averaged Derivatives," Econometrica, Econometric Society, vol. 63(3), pages 667-80, May. [Downloadable!] (restricted)
  4. Rothenberg, Thomas J, 1984. "Approximate Normality of Generalized Least Squares Estimates," Econometrica, Econometric Society, vol. 52(4), pages 811-25, July. [Downloadable!] (restricted)
  5. Y. Nishiyama & P. M. Robinson, 2000. "Edgeworth Expansions for Semiparametric Averaged Derivatives," Econometrica, Econometric Society, vol. 68(4), pages 931-980, July.
  6. Oliver Linton, 1996. "Second order approximation in a linear regression with heteroskedasticity of unknown form," Econometric Reviews, Taylor and Francis Journals, vol. 15(1), pages 1-32. [Downloadable!] (restricted)
  7. 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. [Downloadable!] (restricted)
  8. Andrews, Donald W K, 1994. "Asymptotics for Semiparametric Econometric Models via Stochastic Equicontinuity," Econometrica, Econometric Society, vol. 62(1), pages 43-72, January. [Downloadable!] (restricted)
  9. Oliver Linton, 1994. "Edgeworth Approximation for MINPIN Estimators in Semiparametric Regression Models," Cowles Foundation Discussion Papers 1086, Cowles Foundation, Yale University. [Downloadable!]
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  10. 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. [Downloadable!] (restricted)
  11. 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. [Downloadable!] (restricted)
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  12. Linton, Oliver, 2002. "Edgeworth approximations for semiparametric instrumental variable estimators and test statistics," Journal of Econometrics, Elsevier, vol. 106(2), pages 325-368, February. [Downloadable!] (restricted)
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  13. repec:cup:etheor:v:12:y:1996:i:1:p:30-60 is not listed on IDEAS
  14. Srinivasan, T N, 1970. "Approximations to Finite Sample Moments of Estimators Whose Exact Sampling Distributions are Unknown," Econometrica, Econometric Society, vol. 38(3), pages 533-41, May. [Downloadable!] (restricted)
  15. Hardle, Wolfgang & Tsybakov, A. B., 1993. "How sensitive are average derivatives?," Journal of Econometrics, Elsevier, vol. 58(1-2), pages 31-48, July. [Downloadable!] (restricted)
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  16. Rothernberg, Thomas J, 1984. "Hypothesis Testing in Linear Models When the Error Covariance Matrix Is Nonscalar," Econometrica, Econometric Society, vol. 52(4), pages 827-42, July. [Downloadable!] (restricted)
  17. Linton, Oliver, 1995. "Second Order Approximation in the Partially Linear Regression Model," Econometrica, Econometric Society, vol. 63(5), pages 1079-1112, September. [Downloadable!] (restricted)
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(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Martin Biewen & Bernd Fitzenberger & Aderonke Osikominu & Marie Waller, 2007. "Which Program for Whom? Evidence on the Comparative Effectiveness of Public Sponsored Training Programs in Germany," IZA Discussion Papers 2885, Institute for the Study of Labor (IZA). [Downloadable!]
    Other versions:
  2. Daniel Millimet & Rusty Tchernis, 2006. "On the Specification of Propensity Scores: with an Application to the WTO-Environment Debate," Caepr Working Papers 2006-013, Center for Applied Economics and Policy Research, Economics Department, Indiana University Bloomington. [Downloadable!]
  3. Fitzenberger, Bernd & Speckesser, Stefan, 2005. "Employment Effects of the Provision of Specific Professional Skills and Techniques in Germany," ZEW Discussion Papers 05-77, ZEW - Zentrum für Europäische Wirtschaftsforschung / Center for European Economic Research. [Downloadable!]
  4. 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. [Downloadable!] (restricted)
  5. Osikominu, Aderonke & Fitzenberger, Bernd & Völter, Robert, 2006. "Get Training or Wait? Long-Run Employment Effects of Training Programs for the Unemployed in West Germany," ZEW Discussion Papers 06-39, ZEW - Zentrum für Europäische Wirtschaftsforschung / Center for European Economic Research. [Downloadable!]
    Other versions:
  6. Speckesser, Stefan & Fitzenberger, Bernd & Bergemann, Annette, 2004. "Evaluating the Dynamic Employment Effects of Training Programs in East Germany Using Conditional Difference-in-Differences," ZEW Discussion Papers 04-41, ZEW - Zentrum für Europäische Wirtschaftsforschung / Center for European Economic Research. [Downloadable!]
    Other versions:
  7. Jose Galdo & Jeffrey Smith & Dan Black, 2007. "Bandwidth Selection and the Estimation of Treatment Effects with Unbalanced Data," IZA Discussion Papers 3095, Institute for the Study of Labor (IZA). [Downloadable!]
  8. Lechner, Michael, 2004. "Sequential Matching Estimation of Dynamic Causal Models," IZA Discussion Papers 1042, Institute for the Study of Labor (IZA). [Downloadable!]
    Other versions:
  9. Fitzenberger, Bernd & Speckesser, Stefan, 2005. "Employment effects of the provision of specific professional skills and techniques in Germany," IAB Discussion Paper 200521, Institut für Arbeitsmarkt- und Berufsforschung (IAB), Nürnberg [Institute for Employment Research, Nuremberg, Germany]. [Downloadable!]
  10. Guido W. Imbens & Whitney Newey & Geert Ridder, 2005. "Mean-square-error Calculations for Average Treatment Effects," IEPR Working Papers 05.34, Institute of Economic Policy Research (IEPR). [Downloadable!]
  11. Bernd Fitzenberger & Stefan Speckesser, 2005. "Employment Effects of the Provision of Specific Professional Skills and Techniques in Germany," IZA Discussion Papers 1868, Institute for the Study of Labor (IZA). [Downloadable!]
  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. [Downloadable!] (restricted)
  13. Daniel Egel & Bryan S. Graham & Cristine Campos de Xavier Pinto, 2008. "Inverse Probability Tilting and Missing Data Problems," NBER Working Papers 13981, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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