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Bandwidth Selection and the Estimation of Treatment Effects with Unbalanced Data

  • Jose C. GALDO
  • Jeffrey SMITH
  • Dan BLACK

This paper addresses the selection of smoothing parameters for estimating the average treatment effect on the treated using matching methods. Because precise estimation of the expected counterfactual is particularly important in regions containing the mass of the treated units, we define and implement weighted cross-validation approaches that improve over conventional methods by considering the location of the treated units in the selection of the smoothing parameters. We also implement a locally varying bandwidth method that uses larger bandwidths in areas where the mass of the treated units is located. A Monte Carlo study compares our proposed methods to the conventional unweighted method and to a related method inspired by BERGEMANN et al. [2005]. The Monte Carlo analysis indicates efficiency gains from all methods that take account of the location of the treated units. We also apply all five methods to bandwidth selection in the context of the data from LALONDE'S [1986] study of the performance of non-experimental estimators using the experimental data from the National Supported Work (NSW) Demonstration program as a benchmark. Overall, both the Monte Carlo analysis and the empirical application show feasible precision gains for the weighted cross-validation and the locally varying bandwidth approaches.

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File URL: http://www.jstor.org/stable/27917245
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Article provided by ENSAE in its journal Annals of Economics and Statistics.

Volume (Year): (2008)
Issue (Month): 91-92 ()
Pages: 189-216

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Handle: RePEc:adr:anecst:y:2008:i:91-92:p:10
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  1. Keisuke Hirano & Guido W. Imbens & Geert Ridder, 2000. "Efficient Estimation of Average Treatment Effects Using the Estimated Propensity Score," NBER Technical Working Papers 0251, National Bureau of Economic Research, Inc.
  2. 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.
  3. Dehejia, Rajeev, 2005. "Practical propensity score matching: a reply to Smith and Todd," Journal of Econometrics, Elsevier, vol. 125(1-2), pages 355-364.
  4. James Heckman & Hidehiko Ichimura & Jeffrey Smith & Petra Todd, 1998. "Characterizing Selection Bias Using Experimental Data," NBER Working Papers 6699, National Bureau of Economic Research, Inc.
  5. Heckman, James J & Ichimura, Hidehiko & Todd, Petra, 1998. "Matching as an Econometric Evaluation Estimator," Review of Economic Studies, Wiley Blackwell, vol. 65(2), pages 261-94, April.
  6. Heckman, J.J. & Hotz, V.J., 1988. "Choosing Among Alternative Nonexperimental Methods For Estimating The Impact Of Social Programs: The Case Of Manpower Training," University of Chicago - Economics Research Center 88-12, Chicago - Economics Research Center.
  7. 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.
  8. Hidehiko Ichimura & Oliver Linton, 2003. "Asymptotic Expansions for Some Semiparametric Program Evaluation Estimators," STICERD - Econometrics Paper Series 451, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
  9. Steven Lehrer & Gregory Kordas, 2004. "Matching using Semiparametric Propensity Scores," Econometric Society 2004 North American Summer Meetings 441, Econometric Society.
  10. Wang-Sheng Lee, 2013. "Propensity score matching and variations on the balancing test," Empirical Economics, Springer, vol. 44(1), pages 47-80, February.
  11. Dan A. Black & Jeffrey Smith, 2003. "How Robust is the Evidence on the Effects of College Quality? Evidence From Matching," University of Western Ontario, CIBC Centre for Human Capital and Productivity Working Papers 20033, University of Western Ontario, CIBC Centre for Human Capital and Productivity.
  12. LaLonde, Robert J, 1986. "Evaluating the Econometric Evaluations of Training Programs with Experimental Data," American Economic Review, American Economic Association, vol. 76(4), pages 604-20, September.
  13. Speckesser, Stefan & Fitzenberger, Bernd & Bergemann, Annette, 2004. "Evaluating the Dynamic Employment Effects of Training Programs in East Germany Using Conditional Difference-in-Differences," ZEW Discussion Papers 04-41, ZEW - Zentrum für Europäische Wirtschaftsforschung / Center for European Economic Research.
  14. Smith, Jeffrey & Todd, Petra, 2005. "Rejoinder," Journal of Econometrics, Elsevier, vol. 125(1-2), pages 365-375.
  15. 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.
  16. 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.
  17. Heckman, James J, 1979. "Sample Selection Bias as a Specification Error," Econometrica, Econometric Society, vol. 47(1), pages 153-61, January.
  18. Markus Frölich, 2004. "Finite-Sample Properties of Propensity-Score Matching and Weighting Estimators," The Review of Economics and Statistics, MIT Press, vol. 86(1), pages 77-90, February.
  19. Peter Hall & Jeff Racine & Qi Li, 2004. "Cross-Validation and the Estimation of Conditional Probability Densities," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 1015-1026, December.
  20. 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.
  21. Jianqing Fan & Theo Gasser & Irène Gijbels & Michael Brockmann & Joachim Engel, 1997. "Local Polynomial Regression: Optimal Kernels and Asymptotic Minimax Efficiency," Annals of the Institute of Statistical Mathematics, Springer, vol. 49(1), pages 79-99, March.
  22. Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, edition 1, volume 1, number 8355.
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