Statistics and Computing

, Volume 15, Issue 3, pp 197–215 | Cite as

Matching estimators and optimal bandwidth choice

  • Markus Frölich


Optimal bandwidth choice for matching estimators and their finite sample properties are examined. An approximation to their MSE is derived, as a basis for a plug-in bandwidth selector. In small samples, this approximation is not very accurate, though. Alternatively, conventional cross-validation bandwidth selection is considered and performs rather well in simulation studies: Compared to standard pair-matching, kernel and ridge matching achieve reductions in MSE of about 25 to 40%. Local linear matching and weighting perform poorly. Furthermore, the scope for developing better bandwidth selectors seems to be limited for ridge matching, but non-negligible for kernel and local linear matching.


covariate adjustment nonparametric regression propensity score missing data counterfactual treatment effect 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Abadie A. and Imbens G. 2001. Simple and Bias-Corrected Matching Estimators for Average Treatment Effects, mimeo, Harvard University.Google Scholar
  2. Angrist J. 1998. Estimating labour market impact of voluntary military service using social security data. Econometrica 66: 249– 288.Google Scholar
  3. Dehejia R. and Wahba S. 1999. Causal effects in non-experimental studies: Reevaluating the evaluation of training programmes. Journal of American Statistical Association 94: 1053–1062.Google Scholar
  4. Fan J. 1993. Local linear regression smoothers and their minimax efficiency. Annals of Statistics 21: 196–216.Google Scholar
  5. Fan J., Gasser T., Gijbels I., Brockmann M. and Engel J. 1997. Local polynomial regression: Optimal kernels and asymptotic minimax efficiency. Annals of the Institute of Mathematical Statistics 49: 79–99.CrossRefGoogle Scholar
  6. Fan J. and Gijbels I. 1996. Local Polynomial Modeling and its Applications. Chapman and Hall, London.Google Scholar
  7. Frölich M. 2002. Propensity score matching without conditional independence assumption-with an application to the gender wage gap in the UK. mimeo, University of St. Gallen.Google Scholar
  8. Gerfin M. and Lechner M. 2002. Microeconometric evaluation of the active labour market policy in switzerland. Economic Journal 112: 854–893.CrossRefGoogle Scholar
  9. Gu X. and Rosenbaum P. 1993. Comparison of multivariate matching methods: Structures, distance, and algorithms. Journal of Computational and Graphical Statistics 2: 405–420.Google Scholar
  10. Hahn J. 1998. On the role of the propensity score in efficient semiparametric estimation of average treatment effects. Econometrica 66: 315–331.Google Scholar
  11. Heckman J., Ichimura H., Smith J. and Todd P. 1998. Characterizing selection bias using experimental data. Econometrica 66: 1017–1098.Google Scholar
  12. Heckman J., Ichimura H. and Todd P. 1997. Matching as an econometric evaluation estimator: Evidence from evaluating a job training programme. Review of Economic Studies 64: 605–654.Google Scholar
  13. Heckman J., Ichimura H. and Todd P. 1998. Matching as an econometric evaluation estimator. Review of Economic Studies 65: 261– 294.CrossRefMathSciNetGoogle Scholar
  14. Heckman J. and Robb R. 1985. Alternative methods for evaluating the impact of interventions. In: Heckman J. and Singer B. (Eds.) Longitudinal Analysis of Labour Market Data, Cambridge University Press, Cambridge.Google Scholar
  15. Hirano K., Imbens G. and Ridder G. 2003. Efficient estimation of average treatment effects using the estimated propensity score. Econometrica 71: 1161–1189.CrossRefGoogle Scholar
  16. Horvitz D. and D. Thompson 1952. A generalization of sampling without replacement from a finite population. Journal of American Statistical Association 47: 663–685.Google Scholar
  17. Imbens G. 2000. The role of the propensity score in estimating dose-response functions. Biometrika 87: 706–710.CrossRefMathSciNetGoogle Scholar
  18. Lechner M. 1999. Earnings and employment effects of continuous off-the-job training in east germany after unification. Journal of Business and Economic Statistics 17: 74–90.Google Scholar
  19. Little R. and Rubin D. 1987. Statistical Analysis with Missing Data. Wiley, New York.Google Scholar
  20. Loader C. 1999. Bandwidth selection: Classical or plug-in?. Annals of Statistics 27: 415–438.CrossRefGoogle Scholar
  21. Pagan A. and A. Ullah 1999. Nonparametric Econometrics. Cambridge University Press. Cambridge.Google Scholar
  22. Rosenbaum P. and Rubin D. 1983. The central role of the propensity score in observational studies for causal effects. Biometrika 70: 41–55.Google Scholar
  23. Ruppert D. and Wand M. 1994. Multivariate locally weighted least squares regression. Annals of Statistics 22: 1346–1370.Google Scholar
  24. Seifert B. and Gasser T. 1996. Finite-sample variance of local polynomials: Analysis and solutions. Journal of American Statistical Association 91: 267–275.Google Scholar
  25. Seifert B. and Gasser T. 2000. Data adaptive ridging in local polynomial regression. Journal of Computational and Graphical Statistics 9: 338–360.MathSciNetGoogle Scholar

Copyright information

© Springer Science + Business Media, Inc. 2005

Authors and Affiliations

  1. 1.University College London and University of St. GallenSt. GallenSwitzerland

Personalised recommendations