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Asymptotic expansions for some semiparametric program evaluation estimators

  • Hidehiko Ichimura


    (Institute for Fiscal Studies and University of Tokyo)

  • Oliver Linton


    (Institute for Fiscal Studies and University of Cambridge)

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
Date of revision:
Handle: RePEc:ifs:cemmap:04/01
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  1. Y. Nishiyama & P. M. Robinson, 2000. "Edgeworth Expansions for Semiparametric Averaged Derivatives," Econometrica, Econometric Society, vol. 68(4), pages 931-980, July.
  2. Oliver Linton & Zhijie Xiao, 2001. "Second-order approximation for adaptive regression estimators," LSE Research Online Documents on Economics 317, London School of Economics and Political Science, LSE Library.
  3. Oliver Linton, 1993. "Second Order Approximation in the Partially Linear Regression Model," Cowles Foundation Discussion Papers 1065, Cowles Foundation for Research in Economics, Yale University.
  4. Hall, Peter & Marron, J. S., 1987. "Estimation of integrated squared density derivatives," Statistics & Probability Letters, Elsevier, vol. 6(2), pages 109-115, November.
  5. Oliver Linton, 1994. "Edgeworth Approximation for MINPIN Estimators in Semiparametric Regression Models," Cowles Foundation Discussion Papers 1086, Cowles Foundation for Research in Economics, Yale University.
  6. Rothenberg, Thomas J, 1988. "Approximate Power Functions for Some Robust Tests of Regression Coefficients," Econometrica, Econometric Society, vol. 56(5), pages 997-1019, September.
  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 533-41, May.
  8. 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.
  9. Andrews, Donald W K, 1994. "Asymptotics for Semiparametric Econometric Models via Stochastic Equicontinuity," Econometrica, Econometric Society, vol. 62(1), pages 43-72, January.
  10. Robinson, P M, 1995. "The Normal Approximation for Semiparametric Averaged Derivatives," Econometrica, Econometric Society, vol. 63(3), pages 667-80, May.
  11. 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.
  12. 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.
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