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On the Failure of the Bootstrap for Matching Estimators

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Author Info
Alberto Abadie
Guido W. Imbens

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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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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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Handle: RePEc:nbr:nberte:0325

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Find related papers by JEL classification:
C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Semiparametric and Nonparametric Methods
C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation and Testing

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Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Michael Lechner, 2005. "Some practical issues in the evaluation of heterogeneous labour market programmes by matching methods," Labor and Demography 0505006, EconWPA. [Downloadable!]
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  2. Rajeev H. Dehejia & Sadek Wahba, 2002. "Propensity Score-Matching Methods For Nonexperimental Causal Studies," The Review of Economics and Statistics, MIT Press, vol. 84(1), pages 151-161, February. [Downloadable!] (restricted)
    Other versions:
  3. 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. [Downloadable!]
  4. 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. [Downloadable!]
  5. Menno Pradhan & Laura B. Rawlings, 2002. "The Impact and Targeting of Social Infrastructure Investments: Lessons from the Nicaraguan Social Fund," World Bank Economic Review, Oxford University Press, vol. 16(2), pages 275-295, August.
  6. L.Guarcello & F.Mealli & F.Rosati, 2002. "Household Vulnerability and Child Labour: the Effect of Shocks, Credit Rationing and Insurance," UCW Working Paper 3, Understanding Children's Work (UCW Project). [Downloadable!]
  7. 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, Blackwell Publishing, vol. 64(4), pages 605-54, October. [Downloadable!] (restricted)
  8. 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. [Downloadable!] (restricted)
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  9. 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. [Downloadable!] (restricted)
  10. 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, 01. [Downloadable!] (restricted)
  11. 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. [Downloadable!]
  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. [Downloadable!]
  13. 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. [Downloadable!] (restricted)
  14. 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, 09. [Downloadable!] (restricted)
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