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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.
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Suggested Citation

  • Laurens Cherchye & Thomas Demuynck & Bram De Rock & Kristof De Witte, 2014. "Nonparametric analysis of multi-output production with joint inputs," ULB Institutional Repository 2013/252231, ULB -- Universite Libre de Bruxelles.
    • Handle: RePEc:ulb:ulbeco:2013/252231
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    Cited by:

    1. Walheer, Barnabé, 2018. "Disaggregation of the cost Malmquist productivity index with joint and output-specific inputs," Omega, Elsevier, vol. 75(C), pages 1-12.
    2. Laurens Cherchye & Bram Rock & Dieter Saelens & Marijn Verschelde, 2024. "Productive efficiency analysis with incomplete output information," Journal of Productivity Analysis, Springer, vol. 62(3), pages 291-301, December.
    3. Laurens Cherchye & Thomas Demuynck & Bram De Rock & Cédric Duprez & Glenn Magerman & Marijn Verschelde, 2021. "Structural Identification of Productivity under Biased Technological Change∗," Working Papers ECARES 2021-28, ULB -- Universite Libre de Bruxelles.
    4. 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.
    5. Cherchye, Laurens & De Rock, Bram & Kerstens, Pieter Jan, 2018. "Production with storable and durable inputs: Nonparametric analysis of intertemporal efficiency," European Journal of Operational Research, Elsevier, vol. 270(2), pages 498-513.
    6. Cristina M. Campos-Alba & Emilio J. De la Higuera-Molina & Gemma Pérez-López & José L. Zafra-Gómez, 2019. "Measuring the Efficiency of Public and Private Delivery Forms: An Application to the Waste Collection Service Using Order-M Data Panel Frontier Analysis," Sustainability, MDPI, vol. 11(7), pages 1-15, April.
    7. Bertoméu-Sánchez, Salvador & Estache, Antonio, 2017. "Unbundling political and economic rationality: A non-parametric approach tested on transport infrastructure in Spain," Transport Policy, Elsevier, vol. 59(C), pages 181-195.
    8. Aguiar, Victor H. & Kashaev, Nail & Allen, Roy, 2023. "Prices, profits, proxies, and production," Journal of Econometrics, Elsevier, vol. 235(2), pages 666-693.
    9. Laurens Cherchye & Bram De Rock & Veerle Hennebel, 2017. "Coordination efficiency in multi-output settings: a DEA approach," Annals of Operations Research, Springer, vol. 250(1), pages 205-233, March.
    10. Cherchye, Laurens & De Rock, Bram & Hennebel, Veerle, 2014. "The economic meaning of Data Envelopment Analysis: A ‘behavioral’ perspective," Socio-Economic Planning Sciences, Elsevier, vol. 48(1), pages 29-37.
    11. Cherchye, Laurens & De Rock, Bram & Walheer, Barnabé, 2016. "Multi-output profit efficiency and directional distance functions," Omega, Elsevier, vol. 61(C), pages 100-109.
    12. Walheer, Barnabé, 2019. "Aggregating Farrell efficiencies with private and public inputs," European Journal of Operational Research, Elsevier, vol. 276(3), pages 1170-1177.
    13. Laurens Cherchye & Thomas Demuynck & Bram De Rock & Marijn Verschelde, 2018. "Nonparametric identification of unobserved technological heterogeneity in production," Working Paper Research 335, National Bank of Belgium.
    14. Juan Carlos Garrido-Rodríguez & Gemma Pérez-López & José Luis Zafra-Gómez & Diego Prior, 2018. "Estimación de la eficiencia a largo plazo en servicios públicos locales mediante fronteras robustas con datos de panel," Hacienda Pública Española / Review of Public Economics, IEF, vol. 226(3), pages 11-36, September.
    15. Laurens Cherchye & Bram De Rock, 2024. "Nonparametric Analysis of Separable Production Technologies with Intermediate Inputs," Working Papers ECARES 2024-13, ULB -- Universite Libre de Bruxelles.
    16. 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.
    17. 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.
    18. Roets, Bart & Verschelde, Marijn & Christiaens, Johan, 2018. "Multi-output efficiency and operational safety: An analysis of railway traffic control centre performance," European Journal of Operational Research, Elsevier, vol. 271(1), pages 224-237.
    19. Fritz Schiltz & Kristof Witte & Deni Mazrekaj, 2020. "Managerial efficiency and efficiency differentials in adult education: a conditional and bias-corrected efficiency analysis," Annals of Operations Research, Springer, vol. 288(2), pages 529-546, May.
    20. Ding, Jingjing & Dong, Wei & Liang, Liang & Zhu, Joe, 2017. "Goal congruence analysis in multi-Division Organizations with shared resources based on data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 263(3), pages 961-973.
    21. 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.
    22. Laurens Cherchye & Thomas Demuynck & Bram De Rock & Marijn Verschelde, 2018. "Nonparametric Production Analysis with Unobserved Heterogeneity in Productivity," Working Papers ECARES 2018-25, ULB -- Universite Libre de Bruxelles.
    23. Walheer, Barnabe & Hudik, Marek, 2019. "Reallocation of resources in multidivisional firms: A nonparametric approach," International Journal of Production Economics, Elsevier, vol. 214(C), pages 196-205.

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