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A homothetic reference technology in Data Envelopment Analysis

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Abstract

The assumption of a homothetic production function is often maintained in production economics. In this paper we explore the possibility of maintaining homotheticity within a nonparametric DEA framework. The main contribution of this paper is to use the approach suggested by Hanoch and Rothschild in 1972 to define a homothetic reference technology. We focus on the largest subset of data points that is consistent with such a homothetic production function. We use the HR-approach to define a piecewise linear homothetic convex reference technology. We propose this reference technology with the purpose of adding structure to the flexible non-parametric BCC DEA estimator. Motivation for why such additional structure sometimes is warranted is provided. An estimation procedure derived from the BCC-model and from a maintained assumption of homotheticity is proposed. The performance of the estimator is analyzed using simulation.

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  • Olesen, Ole B., 2012. "A homothetic reference technology in Data Envelopment Analysis," Discussion Papers of Business and Economics 14/2012, University of Southern Denmark, Department of Business and Economics.
  • Handle: RePEc:hhs:sdueko:2012_014
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    File URL: https://www.sdu.dk/-/media/files/om_sdu/institutter/ivoe/disc_papers/disc_2012/dpbe14_2012.pdf
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    1. Hanoch, Giora & Rothschild, Michael, 1972. "Testing the Assumptions of Production Theory: A Nonparametric Approach," Journal of Political Economy, University of Chicago Press, vol. 80(2), pages 256-275, March-Apr.
    2. Simar, Leopold & Wilson, Paul W., 2002. "Non-parametric tests of returns to scale," European Journal of Operational Research, Elsevier, vol. 139(1), pages 115-132, May.
    3. Ferrier, Gary D. & Lovell, C. A. Knox, 1990. "Measuring cost efficiency in banking : Econometric and linear programming evidence," Journal of Econometrics, Elsevier, vol. 46(1-2), pages 229-245.
    4. Kneip, Alois & Park, Byeong U. & Simar, L opold, 1998. "A Note On The Convergence Of Nonparametric Dea Estimators For Production Efficiency Scores," Econometric Theory, Cambridge University Press, vol. 14(06), pages 783-793, December.
    5. Primont, Daniel & Primont, Diane, 1994. "Homothetic non-parametric production models," Economics Letters, Elsevier, vol. 45(2), pages 191-195, June.
    6. Olesen, Ole B. & Ruggiero, John, 2012. "Maintaining the Regular Ultra Passum Law in data envelopment analysis," Discussion Papers of Business and Economics 2/2012, University of Southern Denmark, Department of Business and Economics.
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    More about this item

    Keywords

    Data Envelopment Analysis (DEA); DEA based estimation of a homothetic production function; linear programming; convex hull estimation; isoquant estimation; polyhedral sets in intersection and sum form;

    JEL classification:

    • C00 - Mathematical and Quantitative Methods - - General - - - General
    • C40 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - General
    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General

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