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A Ray-Based Input Distance Function to Model Zero-Valued Output Quantities: Derivation and an Empirical Application

Author

Listed:
  • Juan José Price

    (Business School, Universidad Adolfo Ibáñez)

  • Arne Henningsen

    (Department of Food and Resource Economics, University of Copenhagen)

Abstract

We derive and empirically apply an input-oriented distance function based on the stochastic ray production function suggested by Löthgren (1997, 2000). We show that the derived ray-based input distance function is suitable for modeling production technologies based on logarithmic functional forms (e.g., Cobb-Douglas and Translog) when control over inputs is greater than control over outputs and when some productive entities do not produce the entire set of outputs — two situations that are jointly present in various economic sectors. We also address a weakness of the stochastic ray function, namely its sensitivity to the outputs’ ordering, by using a model-selection approach and a model-averaging approach. We estimate a ray-based Translog input distance function with a data set of Danish museums. These museums have more control over their inputs than over their outputs, and many of them do not produce the entire set of outputs that is considered in our analysis. Given the importance of monotonicity conditions in efficiency analysis, we demonstrate how to impose monotonicity on ray-based input distance functions. As part of the empirical analysis, we estimate technical efficiencies, distance elasticities of the inputs and outputs, and scale elasticities and establish how the production frontier is affected by some environmental variables that are of interest to the museum sector.

Suggested Citation

  • Juan José Price & Arne Henningsen, 2022. "A Ray-Based Input Distance Function to Model Zero-Valued Output Quantities: Derivation and an Empirical Application," IFRO Working Paper 2022/03, University of Copenhagen, Department of Food and Resource Economics.
  • Handle: RePEc:foi:wpaper:2022_03
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    References listed on IDEAS

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    3. Frey, Bruno S. & Meier, Stephan, 2006. "The Economics of Museums," Handbook of the Economics of Art and Culture, in: V.A. Ginsburgh & D. Throsby (ed.), Handbook of the Economics of Art and Culture, edition 1, volume 1, chapter 29, pages 1017-1047, Elsevier.
    4. Martin Feldstein, 1991. "The Economics of Art Museums," NBER Books, National Bureau of Economic Research, Inc, number feld91-1, January.
    5. Yapo Genevier N’guessan & Allen Featherstone & Oluwarotimi Odeh & Sreedhar Upendram, 2017. "Choice of the empirical definition of zero in the translog multiproduct cost functional form," Applied Economics Letters, Taylor & Francis Journals, vol. 24(15), pages 1112-1120, September.
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    More about this item

    Keywords

    Stochastic ray production frontier; distance function; input-oriented efficiency; zero output quantities; model averaging; monotonicity; museums.;
    All these keywords.

    JEL classification:

    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • D22 - Microeconomics - - Production and Organizations - - - Firm Behavior: Empirical Analysis
    • D24 - Microeconomics - - Production and Organizations - - - Production; Cost; Capital; Capital, Total Factor, and Multifactor Productivity; Capacity

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