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A matching estimator based on a bi-level optimization problem


  • Juan Díaz
  • Tomás Rau
  • Jorge Rivera


This paper proposes a matching estimator where the size of the weights and the number of neighbors are endogenously determined from the solution of a bi-level optimization problem. The first level problem minimizes the distance between the characteristics of an individual and a convex combination of characteristics of individuals belonging to the corresponding counterfactual set, and with the second level we choose a solution point of the first level that minimizes the sum of the distances between the characteristics of the individual under analysis and those from the counterfactuals employed in the optimal convex combination. We show that this estimator is consistent and asymptotically normal. Finally we study its behavior in finite samples by performing Monte Carlo experiments with designs based on the related literature. In terms of bias, standard deviation and mean square error, we find significant improvements using our estimator in comparison to the simple matching estimator, widely employed in the literature.

Suggested Citation

  • Juan Díaz & Tomás Rau & Jorge Rivera, 2012. "A matching estimator based on a bi-level optimization problem," Working Papers wp351, University of Chile, Department of Economics.
  • Handle: RePEc:udc:wpaper:wp351

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    References listed on IDEAS

    1. de Luna, Xavier & Johansson, Per & Sjöstedt-de Luna, Sara, 2010. "Bootstrap Inference for K-Nearest Neighbour Matching Estimators," IZA Discussion Papers 5361, Institute for the Study of Labor (IZA).
    2. Guido W. Imbens & Jeffrey M. Wooldridge, 2009. "Recent Developments in the Econometrics of Program Evaluation," Journal of Economic Literature, American Economic Association, vol. 47(1), pages 5-86, March.
    3. Alberto Abadie & Guido W. Imbens, 2008. "On the Failure of the Bootstrap for Matching Estimators," Econometrica, Econometric Society, vol. 76(6), pages 1537-1557, November.
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    Cited by:

    1. Ferman, Bruno, 2017. "Matching Estimators with Few Treated and Many Control Observations," MPRA Paper 78940, University Library of Munich, Germany.

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    JEL classification:

    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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