2008/22 | LEM Working Paper Series | |
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Optimal Bandwidth Selection for Conditional Efficiency Measures: a Data-driven Approach |
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Luiza Badin, Cinzia Daraio, Léopold Simar |
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Keywords | ||
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Nonparametric efficiency estimation, conditional efficiency measures, environmental factors, conditional distribution function, bandwidth.
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JEL Classifications | ||
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C14, C40, C60, D20
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Abstract | ||
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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, Florens and Simar, 2002, Daraio and Simar,
2005). This defines conditional efficiency measures where the
production set in the input × 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,
Park and Simar, 2008). 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 integrated Mean Squared Error (MSE). 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 outperforms former methods.
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