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Optimal bandwidth selection for conditional efficiency measures: A data-driven approach

Author

Listed:
  • Badin, Luiza
  • Daraio, Cinzia
  • Simar, Léopold

Abstract

In productivity analysis an important issue is to detect how external (environmental) factors, exogenous to the production process and not under the control of the producer, might influence the production process and the resulting efficiency of the firms. Most of the traditional approaches proposed in the literature have serious drawbacks. An alternative approach is to describe the production process as being conditioned by a given value of the environmental variables (Cazals, C., Florens, J.P., Simar, L., 2002. Nonparametric Frontier estimation: A robust approach. Journal of Econometrics 106, 1-25; Daraio, C., Simar, L., 2005. Introducing environmental variables in nonparametric Frontier models: A probabilistic approach. Journal of Productivity Analysis 24(1), 93-121). This defines conditional efficiency measures where the production set in the input x output space may depend on the value of the external variables. The statistical properties of nonparametric estimators of these conditional measures are now established (Jeong, S.O., Park, B.U., Simar, L., 2008. Nonparametric conditional efficiency measures: Asymptotic properties. Annals of Operations Research doi: 10.1007/s10479-008-0359-5). These involve the estimation of a nonstandard conditional distribution function which requires the specification of a smoothing parameter (a bandwidth). So far, only the asymptotic optimal order of this bandwidth has been established. This is of little interest for the practitioner. In this paper we fill this gap and we propose a data-driven technique for selecting this parameter in practice. The approach, based on a Least Squares Cross Validation procedure (LSCV), provides an optimal bandwidth that minimizes an appropriate (weighted) integrated Squared Error (ISE). The method is carefully described and exemplified with some simulated data with univariate and multivariate environmental factors. An application on real data (performances of Mutual Funds) illustrates how this new optimal method of bandwidth selection works in practice.

Suggested Citation

  • Badin, Luiza & Daraio, Cinzia & Simar, Léopold, 2010. "Optimal bandwidth selection for conditional efficiency measures: A data-driven approach," European Journal of Operational Research, Elsevier, vol. 201(2), pages 633-640, March.
  • Handle: RePEc:eee:ejores:v:201:y:2010:i:2:p:633-640
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    References listed on IDEAS

    as
    1. 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.
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    4. Park, Byeong U. & Simar, Léopold & Zelenyuk, Valentin, 2008. "Local likelihood estimation of truncated regression and its partial derivatives: Theory and application," Journal of Econometrics, Elsevier, vol. 146(1), pages 185-198, September.
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    9. Cinzia Daraio & Léopold Simar, 2007. "Conditional nonparametric frontier models for convex and nonconvex technologies: a unifying approach," Journal of Productivity Analysis, Springer, vol. 28(1), pages 13-32, October.
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    More about this item

    Keywords

    Nonparametric efficiency estimation Conditional efficiency measures Environmental factors Conditional distribution function Bandwidth;

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C40 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - General
    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • D20 - Microeconomics - - Production and Organizations - - - General

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