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Testing for covariate balance using quantile regression and resampling methods


  • Martin Huber



Consistency of propensity score matching estimators hinges on the propensity score's ability to balance the distributions of covariates in the pools of treated and nontreated units. Conventional balance tests merely check for differences in covariates' means, but cannot account for differences in higher moments. Specification tests constitute an alternative, but might reject misspecified, but yet balancing propensity score models. This paper proposes balance tests based on (i) quantile regression to check for differences in the distributions of continuous covariates and (ii) resampling methods to estimate the distributions of the proposed Kolmogorov-Smirnov and Cramer-von-Mises-Smirnov test statistics. Simulations suggest that the tests capture imbalances related to higher moments when conventional balance tests fail to do so and correctly keep misspecified, but balancing propensity scores when specification tests reject the null.

Suggested Citation

  • Martin Huber, 2010. "Testing for covariate balance using quantile regression and resampling methods," University of St. Gallen Department of Economics working paper series 2010 2010-18, Department of Economics, University of St. Gallen.
  • Handle: RePEc:usg:dp2010:2010-18

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    References listed on IDEAS

    1. James J. Heckman & Hidehiko Ichimura & Petra E. Todd, 1997. "Matching As An Econometric Evaluation Estimator: Evidence from Evaluating a Job Training Programme," Review of Economic Studies, Oxford University Press, vol. 64(4), pages 605-654.
    2. Andrea Ichino & Fabrizia Mealli & Tommaso Nannicini, 2008. "From temporary help jobs to permanent employment: what can we learn from matching estimators and their sensitivity?," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 23(3), pages 305-327.
    3. Torsten Persson, 2001. "Currency unions and trade: how large is the treatment effect?," Economic Policy, CEPR;CES;MSH, vol. 16(33), pages 433-462, October.
    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.
    5. T. S. Breusch & A. R. Pagan, 1980. "The Lagrange Multiplier Test and its Applications to Model Specification in Econometrics," Review of Economic Studies, Oxford University Press, vol. 47(1), pages 239-253.
    6. Lawrence M. Berger & Jennifer Hill & Jane Waldfogel, 2005. "Maternity leave, early maternal employment and child health and development in the US," Economic Journal, Royal Economic Society, vol. 115(501), pages 29-47, February.
    7. Li, Qi & Maasoumi, Esfandiar & Racine, Jeffrey S., 2009. "A nonparametric test for equality of distributions with mixed categorical and continuous data," Journal of Econometrics, Elsevier, vol. 148(2), pages 186-200, February.
    8. Jalan, Jyotsna & Ravallion, Martin, 2003. "Estimating the Benefit Incidence of an Antipoverty Program by Propensity-Score Matching," Journal of Business & Economic Statistics, American Statistical Association, vol. 21(1), pages 19-30, January.
    9. Richard Blundell & Monica Costa Dias & Costas Meghir & John Van Reenen, 2004. "Evaluating the Employment Impact of a Mandatory Job Search Program," Journal of the European Economic Association, MIT Press, vol. 2(4), pages 569-606, June.
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    11. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January.
    12. Zhao, Zhong, 2008. "Sensitivity of propensity score methods to the specifications," Economics Letters, Elsevier, vol. 98(3), pages 309-319, March.
    13. Shaikh, Azeem M. & Simonsen, Marianne & Vytlacil, Edward J. & Yildiz, Nese, 2009. "A specification test for the propensity score using its distribution conditional on participation," Journal of Econometrics, Elsevier, vol. 151(1), pages 33-46, July.
    14. Petri Böckerman & Pekka Ilmakunnas, 2009. "Unemployment and self-assessed health: evidence from panel data," Health Economics, John Wiley & Sons, Ltd., vol. 18(2), pages 161-179.
    15. Abadie A., 2002. "Bootstrap Tests for Distributional Treatment Effects in Instrumental Variable Models," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 284-292, March.
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    Cited by:

    1. Dehejia, Rajeev, 2013. "The Porous Dialectic: Experimental and Non-Experimental Methods in Development Economics," WIDER Working Paper Series 011, World Institute for Development Economic Research (UNU-WIDER).
    2. Huber, Martin & Lechner, Michael & Wunsch, Conny, 2013. "The performance of estimators based on the propensity score," Journal of Econometrics, Elsevier, vol. 175(1), pages 1-21.
    3. Dehejia Rajeev, 2015. "Experimental and Non-Experimental Methods in Development Economics: A Porous Dialectic," Journal of Globalization and Development, De Gruyter, vol. 6(1), pages 47-69, June.
    4. Huber, Martin & Lechner, Michael & Wunsch, Conny, 2010. "How to Control for Many Covariates? Reliable Estimators Based on the Propensity Score," IZA Discussion Papers 5268, Institute for the Study of Labor (IZA).

    More about this item


    Balancing property; balance test; propensity score matching;

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models

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