Probabilistic Characterization of Directional Distances and their Robust Versions

Leopold Simar and Anne Vanhems ()

No 10-195, TSE Working Papers from Toulouse School of Economics (TSE)

Abstract: In productivity analysis, the performance of production units is measured through the distance of the individual decision making units (DMU) to the technology which is defined as the frontier of the production set. Most of the existing methods, Farrell-Debreu and Shephard radial measures (input or output oriented) and hyperbolic distance functions, rely on multiplicative measures of the distance and so require to deal with strictly positive inputs and outputs. This can be critical when the data contain zero or negative values as in financial data bases for the measure of funds performances. Directional distance function is an alternative that can be viewed as an additive measure of efficiency. We show in this paper that using a probabilistic formulation of the production process, the directional distance can be expressed as simple radial or hyperbolic distance up to a simple transformation of the inputs/outputs space. This allows to propose simple methods of estimation but also to transfer easily most of the known properties of the estimators shared by the radial and hyperbolic distances. In addition, the formulation allows to define robust directional distances in the lines of alpha-quantile or order-m partial frontiers. Finally we can also define conditional directional distance functions, conditional to environmental factors. To illustrate the methodology, we show how it can be implemented using a Mutual Funds database.

JEL-codes: C13 C14 (search for similar items in EconPapers)
Date: 2010-09
New Economics Papers: this item is included in nep-ecm and nep-eff
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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Related works:
Journal Article: Probabilistic characterization of directional distances and their robust versions (2012)
Working Paper: Probabilistic characterization of directionaldistances and their robustversions (2012)
Working Paper: Probabilistic characterization of directional distances and their robust versions (2010)
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