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Bootstrap inference for K-nearest neighbour matching estimators

Author

Listed:
  • de Luna, Xavier

    () (Umeå University)

  • Johansson, Per

    () (IFAU - Institute for Labour Market Policy Evaluation)

  • Sjöstedt-de Luna, Sara

    () (Umeå University)

Abstract

Abadie and Imbens (2008, Econometrica) showed that classical bootstrap schemes fail to provide correct inference for K-nearest neighbour (KNN) matching estimators of average causal effects. This is an interesting result showing that bootstrap should not be applied without theoretical justification. In this paper, we present two resampling schemes, which we show provide valid inference for KNN matching estimators. We resample "estimated individual causal effects" (EICE), i.e. the difference in outcome between matched pairs, instead of the original data. Moreover, by taking differences in EICEs ordered with respect to the matching covariate, we obtain a bootstrap scheme valid also with heterogeneous causal effects where mild assumptions on the heterogeneity are imposed. We provide proofs of the validity of the proposed resampling based inferences. A simulation study illustrates finite sample properties.

Suggested Citation

  • de Luna, Xavier & Johansson, Per & Sjöstedt-de Luna, Sara, 2010. "Bootstrap inference for K-nearest neighbour matching estimators," Working Paper Series 2010:13, IFAU - Institute for Evaluation of Labour Market and Education Policy.
  • Handle: RePEc:hhs:ifauwp:2010_013
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    References listed on IDEAS

    as
    1. Ekstrom, Magnus & Luna, Sara Sjostedt-De, 2004. "Subsampling Methods to Estimate the Variance of Sample Means Based on Nonstationary Spatial Data With Varying Expected Values," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 82-95, January.
    2. Burda, Martin & Harding, Matthew & Hausman, Jerry, 2008. "A Bayesian mixed logit-probit model for multinomial choice," Journal of Econometrics, Elsevier, pages 232-246.
    3. Alberto Abadie & Guido W. Imbens, 2008. "On the Failure of the Bootstrap for Matching Estimators," Econometrica, Econometric Society, vol. 76(6), pages 1537-1557, November.
    4. Guido W. Imbens, 2004. "Nonparametric Estimation of Average Treatment Effects Under Exogeneity: A Review," The Review of Economics and Statistics, MIT Press, pages 4-29.
    5. Guido W. Imbens & Jeffrey M. Wooldridge, 2009. "Recent Developments in the Econometrics of Program Evaluation," Journal of Economic Literature, American Economic Association, pages 5-86.
    6. Sjöstedt-de Luna, 2005. "Some properties of weakly approaching sequences of distributions," Statistics & Probability Letters, Elsevier, pages 119-126.
    7. Guido W. Imbens & Jeffrey M. Wooldridge, 2009. "Recent Developments in the Econometrics of Program Evaluation," Journal of Economic Literature, American Economic Association, pages 5-86.
    8. Ben B. Hansen, 2008. "The prognostic analogue of the propensity score," Biometrika, Biometrika Trust, vol. 95(2), pages 481-488.
    9. Alberto Abadie & Guido W. Imbens, 2006. "Large Sample Properties of Matching Estimators for Average Treatment Effects," Econometrica, Econometric Society, vol. 74(1), pages 235-267, January.
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    Cited by:

    1. Juan Díaz & Tomás Rau & Jorge Rivera, 2015. "A Matching Estimator Based on a Bilevel Optimization Problem," The Review of Economics and Statistics, MIT Press, pages 803-812.
    2. de Luna, Xavier & Johansson, Per, 2012. "Testing for Nonparametric Identification of Causal Effects in the Presence of a Quasi-Instrument," IZA Discussion Papers 6692, Institute for the Study of Labor (IZA).

    More about this item

    Keywords

    Block bootstrap; subsampling; average causal/treatment effect;

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models

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