IDEAS home Printed from
   My bibliography  Save this paper

Matching on the Estimated Propensity Score


  • Alberto Abadie
  • Guido W. Imbens


Propensity score matching estimators (Rosenbaum and Rubin, 1983) are widely used in evaluation research to estimate average treatment effects. In this article, we derive the large sample distribution of propensity score matching estimators. Our derivations take into account that the propensity score is itself estimated in a first step, prior to matching. We prove that first step estimation of the propensity score affects the large sample distribution of propensity score matching estimators. Moreover, we derive an adjustment to the large sample variance of propensity score matching estimators that corrects for first step estimation of the propensity score. In spite of the great popularity of propensity score matching estimators, these results were previously unavailable in the literature.

Suggested Citation

  • Alberto Abadie & Guido W. Imbens, 2009. "Matching on the Estimated Propensity Score," NBER Working Papers 15301, National Bureau of Economic Research, Inc.
  • Handle: RePEc:nbr:nberwo:15301
    Note: LS

    Download full text from publisher

    File URL:
    Download Restriction: no

    Other versions of this item:

    References listed on IDEAS

    1. Andreou, E. & Werker, B.J.M., 2004. "An Alternative Asymptotic Analysis of Residual-Based Statistics," Discussion Paper 2004-56, Tilburg University, Center for Economic Research.
    2. 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.
    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. 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.
    Full references (including those not matched with items on IDEAS)


    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.

    Cited by:

    1. Daniel L. Millimet & Rusty Tchernis, 2013. "Estimation Of Treatment Effects Without An Exclusion Restriction: With An Application To The Analysis Of The School Breakfast Program," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 28(6), pages 982-1017, September.
    2. David Kaplan & Jianshen Chen, 2012. "A Two-Step Bayesian Approach for Propensity Score Analysis: Simulations and Case Study," Psychometrika, Springer;The Psychometric Society, vol. 77(3), pages 581-609, July.
    3. Wang, Jian & Wang, Xiao, 2015. "Benefits of foreign ownership: Evidence from foreign direct investment in China," Journal of International Economics, Elsevier, vol. 97(2), pages 325-338.
    4. Radice Rosalba & Ramsahai Roland & Grieve Richard & Kreif Noemi & Sadique Zia & Sekhon Jasjeet S., 2012. "Evaluating treatment effectiveness in patient subgroups: a comparison of propensity score methods with an automated matching approach," The International Journal of Biostatistics, De Gruyter, vol. 8(1), pages 1-45, August.
    5. repec:eee:tefoso:v:125:y:2017:i:c:p:178-187 is not listed on IDEAS
    6. Kibriya, Shahriar & Savio, Graham & Price, Edwin & King, Joseph, 2016. "The Role of Conflict in Farmers’ Crop Choices in North Kivu, Democratic Republic of the Congo," International Food and Agribusiness Management Review, International Food and Agribusiness Management Association (IFAMA), vol. 19(3).
    7. repec:sae:envira:v:49:y:2017:i:12:p:2718-2738 is not listed on IDEAS
    8. Nam, Jaehyun & Ansong, David, 2015. "The effects of a dedicated education savings account on children's college graduation," Economics of Education Review, Elsevier, vol. 48(C), pages 198-207.
    9. 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.
    10. Huber, Martin & Camponovo, Lorenzo & Bodory, Hugo & Lechner, Michael, 2016. "A wild bootstrap algorithm for propensity score matching estimators," FSES Working Papers 470, Faculty of Economics and Social Sciences, University of Freiburg/Fribourg Switzerland.
    11. Toffolutti, Veronica & Reeves, Aaron & McKee, Martin & Stuckler, David, 2017. "Outsourcing cleaning services increases MRSA incidence: Evidence from 126 english acute trusts," Social Science & Medicine, Elsevier, vol. 174(C), pages 64-69.
    12. Brown, Zachary, 2016. "Voluntary programs to encourage compliance with refuge regulations for pesticide resistance management: results from a quasi-experiment," 2016 Annual Meeting, July 31-August 2, 2016, Boston, Massachusetts 237333, Agricultural and Applied Economics Association.
    13. Joshua C. Hall & Brad R. Humphreys & Jane E. Ruseski, 2015. "Economic Freedom, Race, and Health Disparities: Evidence from US States," Working Papers 15-43, Department of Economics, West Virginia University.
    14. repec:kap:sbusec:v:50:y:2018:i:1:d:10.1007_s11187-017-9877-3 is not listed on IDEAS
    15. Kibriya, Shahriar & Xu, Zhicheng P. & Zhang, Yu, 2015. "The impact of bullying on educational performance in Ghana: A Bias-reducing Matching Approach," 2015 AAEA & WAEA Joint Annual Meeting, July 26-28, San Francisco, California 205409, Agricultural and Applied Economics Association;Western Agricultural Economics Association.
    16. Delgado, Michael S. & Guilfoos, Todd & Boslett, Andrew, 2016. "The cost of unconventional gas extraction: A hedonic analysis," Resource and Energy Economics, Elsevier, vol. 46(C), pages 1-22.
    17. Anton-Erxleben, Katharina & Kibriya, Shahriar & Zhang, Yu, 2016. "Bullying as the main driver of low performance in schools: Evidence from Botswana, Ghana, and South Africa," MPRA Paper 75555, University Library of Munich, Germany.
    18. 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).
    19. repec:eee:transa:v:100:y:2017:i:c:p:105-120 is not listed on IDEAS
    20. Mark A. C. Kattenberg & Wolter H. J. Hassink, 2017. "Who Moves Out of Social Housing? The Effect of Rent Control on Housing Tenure Choice," De Economist, Springer, vol. 165(1), pages 43-66, March.
    21. Heng Chen & Geoffrey R. Dunbar & Rallye Shen, 2017. "The Mode is the Message: Using Predata as Exclusion Restrictions to Evaluate Survey Design," Staff Working Papers 17-43, Bank of Canada.
    22. Kautonen, Teemu & Kibler, Ewald & Minniti, Maria, 2017. "Late-career entrepreneurship, income and quality of life," Journal of Business Venturing, Elsevier, vol. 32(3), pages 318-333.
    23. Prennushi, G. & Gupta, A., 2014. "Women's empowerment and socio-economic outcomes : impacts of the Andhra Pradesh rural poverty reduction program," Policy Research Working Paper Series 6841, The World Bank.

    More about this item

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

    NEP fields

    This paper has been announced in the following NEP Reports:


    Access and download statistics


    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:nbr:nberwo:15301. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (). General contact details of provider: .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.