In this work, we analyze the performance of production units using the directionaldistance function which allows to measure the distance to the frontier of the production set along any direction in the inputs/outputs space. We show that this distance can be expressed as a simple transformation of radial or hyperbolic distance. This formulation allows to define robustdirectionaldistances in the lines of α-quantile or order-m partial frontiers and also conditional directionaldistance functions, conditional to environmental factors. We propose simple methods of estimation and derive the asymptotic properties of our estimators.
University of Toulouse, FranceToulouse Business School and Toulouse School of Economics
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Simar, L., & Vanhems, A. (2012). Probabilistic characterization of directionaldistances and their robustversions. Journal of Econometrics, 166(2), 342-354. https://doi.org/10.1016/j.jeconom.2011.10.002 (Original work published 2012)