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Nonparametric analysis of multi-output production with joint inputs

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  • Cherchye, Laurens
  • Demuynck, Thomas
  • De Rock, Bram
  • De Witte, Kristof

Abstract

We present a novel framework for analyzing cost minimizing production behavior in multi-output settings. Our specific focus is on dealing with joint inputs, i.e. inputs that are simultaneously used for the production of multiple outputs. Here, we distinguish between two possible approaches. The cooperative approach takes a centralized perspective and assumes cost minimization at the aggregate firm level. By contrast, the noncooperative approach adopts a decentralized view and assumes cost minimization at the level of the individual output departments, which implies the possibility of free riding behavior for the joint inputs. Our framework is non-parametric in nature, which means that it allows for analyzing production behavior while avoiding (nonverifiable) prior functional structure for the production technology. We show that it naturally extends the existing nonparametric framework for analyzing single output production. We establish rationalizability conditions for cooperative as well as noncooperative production behavior. In addition, we introduce goodness-of-fit measures for evaluating the degree of violation of these conditions. An empirical application to the English and Welsh drinking water and sewerage sector shows the practical usefulness of our framework. Specifically, we compare the empirical validity of the cooperative and noncooperative models for describing the observed production behavior.

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Bibliographic Info

Paper provided by Katholieke Universiteit Leuven in its series Open Access publications from Katholieke Universiteit Leuven with number urn:hdl:123456789/331174.

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Date of creation: Dec 2011
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Handle: RePEc:ner:leuven:urn:hdl:123456789/331174

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  1. Laurens Cherchye & Bram De Rock & Frederic Vermeulen, 2011. "The Revealed Preference Approach to Collective Consumption Behaviour: Testing and Sharing Rule Recovery," Review of Economic Studies, Oxford University Press, vol. 78(1), pages 176-198.
  2. Valérie Lechene & Ian Preston, 2008. "Non cooperative household demand," IFS Working Papers W08/14, Institute for Fiscal Studies.
  3. Varian, Hal R, 1982. "The Nonparametric Approach to Demand Analysis," Econometrica, Econometric Society, vol. 50(4), pages 945-73, July.
  4. Laurens CHERCHYE & Bram DE ROCK & Bart DIERYNCK & Filip ROODHOOFT & Jeroen SABBE, 2011. "Opening the 'black box' of efficiency measurement: input allocation in multi-output settings," Center for Economic Studies - Discussion papers ces11.10, Katholieke Universiteit Leuven, Centrum voor Economische Studiën.
  5. Laurens Cherchye & Thomas Demuynck & Bram De Rock, 2011. "Revealed Preference Analysis of Non‐Cooperative Household Consumption," Economic Journal, Royal Economic Society, vol. 121(555), pages 1073-1096, 09.
  6. Laurens Cherchye & Bram De Rock & Frederic Vermeulen, 2007. "The Collective Model of Household Consumption: A Nonparametric Characterization," Econometrica, Econometric Society, vol. 75(2), pages 553-574, 03.
  7. Marques, Rui Cunha & De Witte, Kristof, 2011. "Is big better? On scale and scope economies in the Portuguese water sector," Economic Modelling, Elsevier, vol. 28(3), pages 1009-1016, May.
  8. Varian, Hal R, 1984. "The Nonparametric Approach to Production Analysis," Econometrica, Econometric Society, vol. 52(3), pages 579-97, May.
  9. 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 256-75, March-Apr.
  10. Cherchye, L.J.H. & Demuynck, T. & Rock, B. de, 2011. "Noncooperative Household Consumption with Caring," Discussion Paper 2011-019, Tilburg University, Center for Economic Research.
  11. Cherchye, L.J.H. & Rock, B. de & Vermeulen, F.M.P., 2006. "Analyzing Cost Efficient Production Behavior Under Economies of Scope: A Nonparametric Methodology," Discussion Paper 2006-81, Tilburg University, Center for Economic Research.
  12. Berg, Sanford V & Marques, Rui Cunha, 2010. "Quantitative studies of water and sanitation utilities: a literature survey," MPRA Paper 32891, University Library of Munich, Germany.
  13. Simar, Leopold & Wilson, Paul W., 2007. "Estimation and inference in two-stage, semi-parametric models of production processes," Journal of Econometrics, Elsevier, vol. 136(1), pages 31-64, January.
  14. Laurens Cherchye & Bram De Rock & Frederic Vermeulen, 2011. "The revealed preference approach to collective consumption behavior: nonparametric testing and sharing rule recovery," ULB Institutional Repository 2013/98560, ULB -- Universite Libre de Bruxelles.
  15. Varian, Hal R., 1990. "Goodness-of-fit in optimizing models," Journal of Econometrics, Elsevier, vol. 46(1-2), pages 125-140.
  16. Hunt, Lester C & Lynk, Edward L, 1995. "Privatisation and Efficiency in the UK Water Industry: An Empirical Analysis," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 57(3), pages 371-88, August.
  17. Fare, Rolf & Grosskopf, Shawna, 1995. "Nonparametric tests of regularity, Farrell efficiency, and goodness-of-fit," Journal of Econometrics, Elsevier, vol. 69(2), pages 415-425, October.
  18. David S Saal & David Parker, 2000. "The impact of privatization and regulation on the water and sewerage industry in England and Wales: a translog cost function model," Managerial and Decision Economics, John Wiley & Sons, Ltd., vol. 21(6), pages 253-268.
  19. Léopold Simar & Paul Wilson, 2011. "Two-stage DEA: caveat emptor," Journal of Productivity Analysis, Springer, vol. 36(2), pages 205-218, October.
  20. Cook, Wade D. & Seiford, Larry M., 2009. "Data envelopment analysis (DEA) - Thirty years on," European Journal of Operational Research, Elsevier, vol. 192(1), pages 1-17, January.
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