2018/21 | LEM Working Paper Series | ||||||||||||||||
Fast and Efficient Computation of Directional Distance Estimators |
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Cinzia Daraio, Leopold Simar, Paul W. Wilson |
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Keywords | |||||||||||||||||
directional distances, conditional efficiency, robust frontiers, environmental factors, nonparametric methods
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Abstract | |||||||||||||||||
Directional distances provide useful, flexible measures of technical
efficiency of production units relative to the efficient frontier of
the attainable set in input-output space. In addition, the additive
nature of directional distances permits negative input or outputs
quantities. The choice of the direction allows analysis of different
strate- gies for the units attempting to reach the efficient
frontier. Simar et al. (2012) and Simar and Vanhems (2012) develop
asymptotic properties of full-envelopment, FDH and DEA estimators of
directional distances as well as robust order-m and order-α di-
rectional distance estimators. Extensions of these estimators to
measures conditioned on environmental variables Z are also available
(e.g., see Daraio and Simar, 2014). The resulting estimators have been
shown to share the properties of their corresponding radial
measures. However, to date the algorithms proposed for computing the
directional distance estimates suffer from various numerical drawbacks
(Daraio and Simar, 2014). In particular, for the order-m versions
(conditional and unconditional) only approximations, based on
Monte-Carlo methods, have been suggested, involving additional
computational burden. In this paper we propose a new fast and
efficient method to compute exact values of the directional distance
estimates for all the cases (full and partial frontier cases,
unconditional or conditional to external factors), that overcome all
previous difficulties. This new method is illustrated on simulated and
real data sets. Matlab code for computation is provided in an
appendix.
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