A Computationally Efficient, Consistent Bootstrap for Inference with Non-parametric DEA Estimators

  • Authors:

  • Alois Kneip;Léopold Simar;Paul W. Wilson

  • Affiliations:

  • Institut für Gessellschafts- und Wirtschaftswissenschaften, Statistische Abteilung, Universität Bonn, Bonn, Germany 53113;Institut de Statistique, Université Catholique de Louvain, Louvain-la-Neuve, Belgium;The John E. Walker Department of Economics, Clemson University, Clemson, USA 29634---1309

  • Venue:
  • Computational Economics
  • Year:
  • 2011

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Abstract

We develop a tractable, consistent bootstrap algorithm for inference about Farrell---Debreu efficiency scores estimated by non-parametric data envelopment analysis (DEA) methods. The algorithm allows for very general situations where the distribution of the inefficiencies in the input-output space may be heterogeneous. Computational efficiency and tractability are achieved by avoiding the complex double-smoothing procedure in the algorithm proposed by Kneip et al. (Econometric Theory 24:1663---1697, 2008). In particular, we avoid technical difficulties in the earlier algorithm associated with smoothed estimates of a density with unknown, nonlinear, multivariate bounded support requiring complicated reflection methods. The new procedure described here is relatively simple and easy to implement: for particular values of a pair of smoothing parameters, the computational complexity is the same as the (inconsistent) naive bootstrap. The resulting computational speed allows the bootstrap to be iterated in order to optimize the smoothing parameters. From a practical viewpoint, only standard packages for computing DEA efficiency estimates, i.e., solving linear problems, are required for implementation. The performance of the method in finite samples is illustrated through some simulated examples.