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Estimating Frontier Cost Models Using Extremiles

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Abstract

In the econometric literature on the estimation of production technologies, there has been considerable interest in estimating so called cost frontier models that relate closely to models for extreme non-standard conditional quantiles (Aragon et al. Econ Theor 21:358–389, 2005) and expected minimum input functions (Cazals et al. J Econometrics 106:1–25, 2002). In this paper, we introduce a class of extremile-based cost frontiers which includes the family of expected minimum input frontiers and parallels the class of quantile-type frontiers. The class is motivated via several angles, which reveals its specific merits and strengths. We discuss nonparametric estimation of the extremile-based costs frontiers and establish asymptotic normality and weak convergence of the associated process. Empirical illustrations are provided.

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Notes

  1. 1.

    The presentation for the output orientation, where we want to estimate the maximal production frontier in the case of univariate outputs, is a straightforward adaptation of what is done here.

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Acknowledgements

This research was supported by the French “Agence Nationale pour la Recherche” under grant ANR-08-BLAN-0106-01/EPI project (Abdelaati Daouia) and the Research Fund KULeuven (GOA/07/04-project) and by the IAP research network P6/03, Federal Science Policy, Belgium (Irène Gijbels).

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Authors and Affiliations

  1. Toulouse School of Economics (GREMAQ), University of Toulouse, Manufacture des Tabacs, Aile J.J. Laffont, 21 Allée de Brienne, 31000, Toulouse, France

    Abdelaati Daouia

  2. Department of Mathematics and Leuven Statistics Research Center, Katholieke Universiteit Leuven, Celestijnenlaan 200B, 2400, 3001, Leuven (Heverlee), Belgium

    Irène Gijbels

Authors
  1. Abdelaati Daouia
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  2. Irène Gijbels
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Correspondence to Irène Gijbels .

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Editors and Affiliations

  1. , Institut de statistique,, Université catholique de Louvain, Voie du Roman Pays 20, Louvain-la-Neuve, 1348, Belgium

    Ingrid Van Keilegom

  2. Dept. Economics, Clemson University, Sirrene Hall 222, Clemson, 29634-1309, South Carolina, USA

    Paul W. Wilson

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Daouia, A., Gijbels, I. (2011). Estimating Frontier Cost Models Using Extremiles. In: Van Keilegom, I., Wilson, P. (eds) Exploring Research Frontiers in Contemporary Statistics and Econometrics. Physica, Heidelberg. https://doi.org/10.1007/978-3-7908-2349-3_4

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