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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. 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.
  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, 07.
  3. 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.
  4. 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.
  5. James J. Heckman, 1989. "Choosing Among Alternative Nonexperimental Methods for Estimating the Impact of Social Programs: The Case of Manpower Training," NBER Working Papers 2861, National Bureau of Economic Research, Inc.
  6. 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.
  7. Dehejia, R.H. & Wahba, S., 1998. "Propensity Score Matching Methods for Non-Experimental Causal Studies," Discussion Papers 1998_02, Columbia University, Department of Economics.
  8. Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, edition 1, volume 1, number 8355.
  9. Hidehiko Ichimura & Oliver Linton, 2003. "Asymptotic Expansions for Some Semiparametric Program Evaluation Estimators," STICERD - Econometrics Paper Series /2003/451, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
  10. 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.
  11. Wang-Sheng Lee, 2013. "Propensity score matching and variations on the balancing test," Empirical Economics, Springer, vol. 44(1), pages 47-80, February.
  12. 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, vol. 121(1-2), pages 99-124.
  13. Heckman, James, 2013. "Sample selection bias as a specification error," Applied Econometrics, Publishing House "SINERGIA PRESS", vol. 31(3), pages 129-137.
  14. 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.
  15. 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.
  16. 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.
  17. 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.
  18. Dehejia, Rajeev, 2005. "Practical propensity score matching: a reply to Smith and Todd," Journal of Econometrics, Elsevier, vol. 125(1-2), pages 355-364.
  19. 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.
  20. Steven Lehrer & Gregory Kordas, 2013. "Matching using semiparametric propensity scores," Empirical Economics, Springer, vol. 44(1), pages 13-45, February.
  21. Smith, Jeffrey & Todd, Petra, 2005. "Rejoinder," Journal of Econometrics, Elsevier, vol. 125(1-2), pages 365-375.
  22. 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.
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Citations

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Cited by:
  1. Osikominu, Aderonke & Orlyanskaya, Olga & Fitzenberger, Bernd & Waller, Marie, 2008. "Déjà Vu? Short-Term Training in Germany 1980-1992 and 2000-2003," ZEW Discussion Papers 08-038, ZEW - Zentrum für Europäische Wirtschaftsforschung / Center for European Economic Research.
  2. Hans J. Baumgartner & Marco Caliendo, 2008. "Turning Unemployment into Self-Employment: Effectiveness of Two Start-Up Programmes," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 70(3), pages 347-373, 06.
  3. Peter R. Mueser & Carolyn J. Heinrich & Kenneth R. Troske & Kyung-Seong Jeon & Daver C. Kahvecioglu, 2010. "New Estimates of Public Employment and Training Program Net Impacts: A Nonexperimental Evaluation of the Workforce Investment Act Program," Working Papers 1003, Department of Economics, University of Missouri.
  4. Dorn, Sabrina & Egger, Peter, 2012. "On the Distribution of Exchange Rate Regime Treatment Effects on International Trade," Annual Conference 2012 (Goettingen): New Approaches and Challenges for the Labor Market of the 21st Century 62054, Verein für Socialpolitik / German Economic Association.
  5. Steven Lehrer & Gregory Kordas, 2004. "Matching using Semiparametric Propensity Scores," Econometric Society 2004 North American Summer Meetings 441, Econometric Society.
  6. 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).
  7. Hans J. Baumgartner & Marco Caliendo, 2007. "Turning Unemployment into Self-Employment: Effectiveness and Efficiency of Two Start-Up Programmes," Discussion Papers of DIW Berlin 671, DIW Berlin, German Institute for Economic Research.
  8. Caliendo, Marco, 2008. "Start-Up Subsidies in East Germany: Finally, a Policy that Works?," IZA Discussion Papers 3360, Institute for the Study of Labor (IZA).
  9. Collins, J. Michael, 2013. "The impacts of mandatory financial education: Evidence from a randomized field study," Journal of Economic Behavior & Organization, Elsevier, vol. 95(C), pages 146-158.
  10. Peter Z. Schochet & Ronald D'Amico & Jillian Berk & Nathan Wozny, 2012. "Methodological Notes Regarding the Impact Analysis," Mathematica Policy Research Reports 7734, Mathematica Policy Research.
  11. Alberto Chong & José Galdo, 2006. "Does the Quality of Training Programs Matter? Evidence from Bidding Processes Data," Research Department Publications 4451, Inter-American Development Bank, Research Department.
  12. 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.
  13. Martin Biewen & Bernd Fitzenberger & Aderonke Osikominu & Marie Paul, 2012. "The effectiveness of public sponsored training revisited: The importance of data and methodological choices," ECON - Working Papers 091, Department of Economics - University of Zurich.
  14. Wang-Sheng Lee, 2013. "Propensity score matching and variations on the balancing test," Empirical Economics, Springer, vol. 44(1), pages 47-80, February.

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