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On the Failure of the Bootstrap for Matching Estimators

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  • Alberto Abadie
  • Guido W. Imbens

Abstract

Matching estimators are widely used for the evaluation of programs or treatments. Often researchers use bootstrapping methods for inference. However, no formal justification for the use of the bootstrap has been provided. Here we show that the bootstrap is in general not valid, even in the simple case with a single continuous covariate when the estimator is root-N consistent and asymptotically normally distributed with zero asymptotic bias. Due to the extreme non-smoothness of nearest neighbor matching, the standard conditions for the bootstrap are not satisfied, leading the bootstrap variance to diverge from the actual variance. Simulations confirm the difference between actual and nominal coverage rates for bootstrap confidence intervals predicted by the theoretical calculations. To our knowledge, this is the first example of a root-N consistent and asymptotically normal estimator for which the bootstrap fails to work.

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Bibliographic Info

Paper provided by National Bureau of Economic Research, Inc in its series NBER Technical Working Papers with number 0325.

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Date of creation: Jun 2006
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Publication status: published as -Abadie, Alberto and Guido W. Imbens. "On the Failure of the Bootstrap for Matching Estimators." Econometrica 76, 6 (2008): 1537-1557.
Handle: RePEc:nbr:nberte:0325

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  1. Michael Lechner, 2002. "Some practical issues in the evaluation of heterogeneous labour market programmes by matching methods," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 165(1), pages 59-82.
  2. Rajeev H. Dehejia & Sadek Wahba, 1998. "Propensity Score Matching Methods for Non-experimental Causal Studies," NBER Working Papers 6829, National Bureau of Economic Research, Inc.
  3. Heckman, James J & Ichimura, Hidehiko & Todd, Petra E, 1997. "Matching as an Econometric Evaluation Estimator: Evidence from Evaluating a Job Training Programme," Review of Economic Studies, Wiley Blackwell, vol. 64(4), pages 605-54, October.
  4. Roberto Agodini & Mark Dynarski, 2004. "Are Experiments the Only Option? A Look at Dropout Prevention Programs," The Review of Economics and Statistics, MIT Press, vol. 86(1), pages 180-194, February.
  5. A. Smith, Jeffrey & E. Todd, Petra, 2005. "Does matching overcome LaLonde's critique of nonexperimental estimators?," Journal of Econometrics, Elsevier, vol. 125(1-2), pages 305-353.
  6. Jalan, Jyotsna & Ravallion, Martin, 1999. "Income gains to the poor from workfare - estimates for Argentina's TRABAJAR Program," Policy Research Working Paper Series 2149, The World Bank.
  7. Alberto Abadie & Guido W. Imbens, 2002. "Simple and Bias-Corrected Matching Estimators for Average Treatment Effects," NBER Technical Working Papers 0283, National Bureau of Economic Research, Inc.
  8. repec:cup:cbooks:9780521496032 is not listed on IDEAS
  9. Emanuela Galasso & Martin Ravallion, 2004. "Social Protection in a Crisis: Argentina's Plan Jefes y Jefas," World Bank Economic Review, World Bank Group, vol. 18(3), pages 367-399.
  10. Patrick A . Puhani, 2002. "Advantage through Training in Poland? A Microeconometric Evaluation of the Employment Effects of Training and Job Subsidy Programmes," LABOUR, CEIS, vol. 16(3), pages 569-608, 09.
  11. Rajeev H. Dehejia & Sadek Wahba, 1998. "Causal Effects in Non-Experimental Studies: Re-Evaluating the Evaluation of Training Programs," NBER Working Papers 6586, National Bureau of Economic Research, Inc.
  12. Alberto Abadie & David Drukker & Jane Leber Herr & Guido W. Imbens, 2004. "Implementing matching estimators for average treatment effects in Stata," Stata Journal, StataCorp LP, vol. 4(3), pages 290-311, September.
  13. Sascha O. Becker & Andrea Ichino, 2002. "Estimation of average treatment effects based on propensity scores," Stata Journal, StataCorp LP, vol. 2(4), pages 358-377, November.
  14. Menno Pradhan & Laura B. Rawlings, 2002. "The Impact and Targeting of Social Infrastructure Investments: Lessons from the Nicaraguan Social Fund," World Bank Economic Review, World Bank Group, vol. 16(2), pages 275-295, August.
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  16. Whitney Newey & Frank Windmeijer, 2005. "GMM with many weak moment conditions," CeMMAP working papers CWP18/05, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
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