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Bootstrap Inference for K-Nearest Neighbour Matching Estimators

Author

Listed:
  • de Luna, Xavier

    (Umeå University)

  • Johansson, Per

    (Uppsala University)

  • 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," IZA Discussion Papers 5361, Institute of Labor Economics (IZA).
    • Handle: RePEc:iza:izadps:dp5361
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    References listed on IDEAS

    as
    1. Guido W. Imbens & Jeffrey M. Wooldridge, 2009. "Recent Developments in the Econometrics of Program Evaluation," Journal of Economic Literature, American Economic Association, vol. 47(1), pages 5-86, March.
    2. Ben B. Hansen, 2008. "The prognostic analogue of the propensity score," Biometrika, Biometrika Trust, vol. 95(2), pages 481-488.
    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. 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.
    5. Guido W. Imbens, 2004. "Nonparametric Estimation of Average Treatment Effects Under Exogeneity: A Review," The Review of Economics and Statistics, MIT Press, vol. 86(1), pages 4-29, February.
    6. Sjöstedt-de Luna, 2005. "Some properties of weakly approaching sequences of distributions," Statistics & Probability Letters, Elsevier, vol. 75(2), pages 119-126, November.
    7. 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, vol. 97(4), pages 803-812, October.
    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 of Labor Economics (IZA).
    3. de Luna Xavier & Johansson Per, 2014. "Testing for the Unconfoundedness Assumption Using an Instrumental Assumption," Journal of Causal Inference, De Gruyter, vol. 2(2), pages 1-13, September.

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    More about this item

    Keywords

    block bootstrap; subsampling; average causal/treatment effect;
    All these keywords.

    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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