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Nonparametric analysis of multi-output production with joint inputs

Author

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  • Laurens CHERCHYE
  • Thomas DEMUYNCK
  • Bram DE ROCK
  • Kristof DE WITTE

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.

Suggested Citation

  • Laurens CHERCHYE & Thomas DEMUYNCK & Bram DE ROCK & Kristof DE WITTE, 2011. "Nonparametric analysis of multi-output production with joint inputs," Working Papers Department of Economics ces11.35, KU Leuven, Faculty of Economics and Business, Department of Economics.
  • Handle: RePEc:ete:ceswps:ces11.35
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    1. repec:eee:jomega:v:75:y:2018:i:c:p:1-12 is not listed on IDEAS
    2. Gavoille, Nicolas & Verschelde, Marijn, 2017. "Electoral competition and political selection: An analysis of the activity of French deputies, 1958–2012," European Economic Review, Elsevier, vol. 92(C), pages 180-195.
    3. Cherchye, Laurens & Rock, Bram De & Walheer, Barnabé, 2015. "Multi-output efficiency with good and bad outputs," European Journal of Operational Research, Elsevier, vol. 240(3), pages 872-881.
    4. Cherchye, Laurens & De Rock, Bram & Walheer, Barnabé, 2016. "Multi-output profit efficiency and directional distance functions," Omega, Elsevier, vol. 61(C), pages 100-109.
    5. Laurens Cherchye & Bram De Rock & Antonio Estache & Marijn Verschelde, 2015. "Efficiency Measures in Regulated Industries: History, Outstanding Challenges and Emerging Solutions," Working Papers ECARES ECARES 2015-09, ULB -- Universite Libre de Bruxelles.
    6. repec:eee:trapol:v:59:y:2017:i:c:p:181-195 is not listed on IDEAS
    7. repec:eee:ejores:v:263:y:2017:i:3:p:961-973 is not listed on IDEAS
    8. Salvador Bertomeu & Antonio Estache, 2016. "Unbundling Political and Economic Rationality: a Non-Parametric Approach Tested on Spain," Working Papers ECARES ECARES 2016-17, ULB -- Universite Libre de Bruxelles.

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