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Bandwidth Selection and the Estimation of Treatment Effects with Unbalanced Data

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Author Info

  • Galdo, Jose C.

    ()
    (Carleton University)

  • Smith, Jeffrey A.

    ()
    (University of Michigan)

  • Black, Dan A.

    ()
    (University of Chicago)

Abstract

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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Bibliographic Info

Paper provided by Institute for the Study of Labor (IZA) in its series IZA Discussion Papers with number 3095.

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Length: 46 pages
Date of creation: Oct 2007
Date of revision:
Publication status: published in: Annales d'Economie et Statistique, 2008, 91-92, 189-216
Handle: RePEc:iza:izadps:dp3095

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Keywords: matching; Monte Carlo simulation; cross-validation; kernel regression;

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References

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  1. Bergemann, Annette & Fitzenberger, Bernd & Speckesser, Stefan, 2005. "Evaluating the Dynamic Employment Effects of Training Programs in East Germany Using Conditional Difference-in-Differences," IZA Discussion Papers, Institute for the Study of Labor (IZA) 1848, Institute for the Study of Labor (IZA).
  2. James Heckman & Hidehiko Ichimura & Jeffrey Smith & Petra Todd, 1998. "Characterizing Selection Bias Using Experimental Data," Econometrica, Econometric Society, Econometric Society, vol. 66(5), pages 1017-1098, September.
  3. 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, Springer, vol. 49(1), pages 79-99, March.
  4. Guido W. Imbens, 2004. "Nonparametric Estimation of Average Treatment Effects Under Exogeneity: A Review," The Review of Economics and Statistics, MIT Press, MIT Press, vol. 86(1), pages 4-29, February.
  5. Jeffrey Smith & Petra Todd, 2003. "Does Matching Overcome Lalonde's Critique of Nonexperimental Estimators?," University of Western Ontario, CIBC Centre for Human Capital and Productivity Working Papers, University of Western Ontario, CIBC Centre for Human Capital and Productivity 20035, University of Western Ontario, CIBC Centre for Human Capital and Productivity.
  6. 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, American Statistical Association, vol. 99, pages 1015-1026, December.
  7. Rajeev H. Dehejia & Sadek Wahba, 2002. "Propensity Score-Matching Methods For Nonexperimental Causal Studies," The Review of Economics and Statistics, MIT Press, MIT Press, vol. 84(1), pages 151-161, February.
  8. Smith, Jeffrey & Todd, Petra, 2005. "Rejoinder," Journal of Econometrics, Elsevier, Elsevier, vol. 125(1-2), pages 365-375.
  9. Black, Dan A. & Smith, J.A.Jeffrey A., 2004. "How robust is the evidence on the effects of college quality? Evidence from matching," Journal of Econometrics, Elsevier, Elsevier, vol. 121(1-2), pages 99-124.
  10. Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, Princeton University Press, edition 1, volume 1, number 8355.
  11. 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, Wiley Blackwell, vol. 64(4), pages 605-54, October.
  12. Rajeev H. Dehejia & Sadek Wahba, 1998. "Causal Effects in Non-Experimental Studies: Re-Evaluating the Evaluation of Training Programs," NBER Working Papers, National Bureau of Economic Research, Inc 6586, National Bureau of Economic Research, Inc.
  13. Hidehiko Ichimura & Oliver Linton, 2003. "Asymptotic expansions for some semiparametric program evaluation estimators," LSE Research Online Documents on Economics, London School of Economics and Political Science, LSE Library 2098, London School of Economics and Political Science, LSE Library.
  14. 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, Chicago - Economics Research Center 88-12, Chicago - Economics Research Center.
  15. Heckman, James J & Ichimura, Hidehiko & Todd, Petra, 1998. "Matching as an Econometric Evaluation Estimator," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 65(2), pages 261-94, April.
  16. LaLonde, Robert J, 1986. "Evaluating the Econometric Evaluations of Training Programs with Experimental Data," American Economic Review, American Economic Association, American Economic Association, vol. 76(4), pages 604-20, September.
  17. Steven Lehrer & Gregory Kordas, 2004. "Matching using Semiparametric Propensity Scores," Econometric Society 2004 North American Summer Meetings, Econometric Society 441, Econometric Society.
  18. Heckman, James, 2013. "Sample selection bias as a specification error," Applied Econometrics, Publishing House "SINERGIA PRESS", Publishing House "SINERGIA PRESS", vol. 31(3), pages 129-137.
  19. Guido Imbens, 2000. "Efficient Estimation of Average Treatment Effects Using the Estimated Propensity Score," Econometric Society World Congress 2000 Contributed Papers, Econometric Society 1166, Econometric Society.
  20. Wang-Sheng Lee, 2013. "Propensity score matching and variations on the balancing test," Empirical Economics, Springer, Springer, vol. 44(1), pages 47-80, February.
  21. Markus Frölich, 2004. "Finite-Sample Properties of Propensity-Score Matching and Weighting Estimators," The Review of Economics and Statistics, MIT Press, MIT Press, vol. 86(1), pages 77-90, February.
  22. Dehejia, Rajeev, 2005. "Practical propensity score matching: a reply to Smith and Todd," Journal of Econometrics, Elsevier, Elsevier, vol. 125(1-2), pages 355-364.
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