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Estimation of Input Distance Functions: A System Approach

Author

Listed:
  • Efthymios G. Tsionas
  • Subal C. Kumbhakar
  • Emir Malikov

Abstract

This article offers a methodology to address the endogeneity of inputs in the input distance function (IDF) formulation of the production processes. We propose to tackle endogenous input ratios appearing in the normalized IDF by considering a flexible (simultaneous) system of the IDF and the first-order conditions from the firm's cost minimization problem. Our model can accommodate both technical and (input) allocative inefficiencies among firms. We also present the algorithm for quantifying the cost of allocative inefficiency. We showcase our cost-system-based model by applying it to study the production of Norwegian dairy farms during the 1991–2008 period. Among other things, we find both an economically and statistically significant improvement in the levels of technical efficiency among dairy farms associated with the 1997 quota scheme change, which a more conventional single-equation stochastic frontier model appears to be unable to detect.

Suggested Citation

  • Efthymios G. Tsionas & Subal C. Kumbhakar & Emir Malikov, 2015. "Estimation of Input Distance Functions: A System Approach," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 97(5), pages 1478-1493.
    • Handle: RePEc:oup:ajagec:v:97:y:2015:i:5:p:1478-1493.
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    File URL: http://hdl.handle.net/10.1093/ajae/aav012
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    Cited by:

    1. Cai, Rong & Ma, Jie & Wang, Shujuan & Cai, Shukai, 2024. "Access to credit and scale efficiency: Evidence from family farms in East China," Economic Analysis and Policy, Elsevier, vol. 84(C), pages 1538-1551.
    2. Emir Malikov & Gudbrand Lien, 2021. "Proxy Variable Estimation of Multiproduct Production Functions," American Journal of Agricultural Economics, John Wiley & Sons, vol. 103(5), pages 1878-1902, October.
    3. Bhattacharyya, Aditi & Kutlu, Levent & Sickles, Robin C., 2018. "Pricing Inputs and Outputs: Market prices versus shadow prices, market power, and welfare analysis," Working Papers 18-009, Rice University, Department of Economics.
    4. Malikov, Emir, 2016. "Estimating Multi-Product Production Functions and Productivity using Control Functions," 2016 Annual Meeting, July 31-August 2, Boston, Massachusetts 235108, Agricultural and Applied Economics Association.
    5. Shabbir Ahmad, 2020. "Estimating input-mix efficiency in a parametric framework: application to state-level agricultural data for the United States," Applied Economics, Taylor & Francis Journals, vol. 52(36), pages 3976-3997, July.
    6. Mike Tsionas & Marwan Izzeldin & Arne Henningsen & Evaggelos Paravalos, 2022. "Addressing endogeneity when estimating stochastic ray production frontiers: a Bayesian approach," Empirical Economics, Springer, vol. 62(3), pages 1345-1363, March.
    7. Li, Hongchang & Yu, Kemei & Wang, Kun & Zhang, Anming, 2019. "Market power and its determinants in the Chinese railway industry," Transportation Research Part A: Policy and Practice, Elsevier, vol. 120(C), pages 261-276.
    8. Cortés-García, J. Salvador & Pérez-Rodríguez, Jorge V., 2024. "Heterogeneity and time-varying efficiency in the Ecuadorian banking sector. An output distance stochastic frontier approach," The Quarterly Review of Economics and Finance, Elsevier, vol. 93(C), pages 164-175.
    9. Roberto Mosheim & Robin C. Sickles, 2021. "Spatial effects of nutrient pollution on drinking water production," Empirical Economics, Springer, vol. 60(6), pages 2741-2764, June.
    10. Ligia Alba Melo-Becerra & Lucas Wilfried Hahn-De-Castro & Dalma Sofía Ariza-Hernández & Cristian Oswaldo Carmona-Sanchez, 2016. "Efficiency of Public Education in a Multiproduct Context: The Case of Colombian Municipalities," Borradores de Economia 979, Banco de la Republica de Colombia.
    11. Melo-Becerra, Ligia Alba & Hahn-De-Castro, Lucas Wilfried & Ariza, Dalma Sofía & Carmona, Cristian Oswaldo, 2020. "Efficiency of local public education in a decentralized context," International Journal of Educational Development, Elsevier, vol. 76(C).
    12. Yongseung Han & Ronald S. Warren, 2025. "The productive efficiency of U.S. blacksmiths in the late nineteenth century: an input-distance-function approach," Cliometrica, Springer;Cliometric Society (Association Francaise de Cliométrie), vol. 19(3), pages 751-774, September.
    13. Mike Tsionas & Marwan Izzeldin & Arne Henningsen & Evaggelos Paravalos, 2019. "Estimating Stochastic Ray Production Frontiers," IFRO Working Paper 2019/06, University of Copenhagen, Department of Food and Resource Economics.
    14. Ioannis Skevas, 2023. "A novel modeling framework for quantifying spatial spillovers on total factor productivity growth and its components," American Journal of Agricultural Economics, John Wiley & Sons, vol. 105(4), pages 1221-1247, August.
    15. Álvarez-SanJaime, Óscar & Cantos-Sánchez, Pedro & Moner-Colonques, Rafael & Sempere-Monerris, Jose J., 2024. "Efficiency versus market power in the rail industry," Research in Transportation Economics, Elsevier, vol. 108(C).
    16. Heshmati, Almas & C. Kumbhakar, Subal & Kim, Jungsuk, 2016. "Persistent and Transient Efficiency of International Airlines," Working Paper Series in Economics and Institutions of Innovation 444, Royal Institute of Technology, CESIS - Centre of Excellence for Science and Innovation Studies.
    17. Yongseung Han & Arthur Snow & Ronald S. Warren, 2021. "Changes in the productive efficiency of U.S. flour mills in the late nineteenth century: an input-distance-function approach," Journal of Productivity Analysis, Springer, vol. 56(2), pages 115-132, December.

    More about this item

    JEL classification:

    • C33 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Models with Panel Data; Spatio-temporal Models
    • D24 - Microeconomics - - Production and Organizations - - - Production; Cost; Capital; Capital, Total Factor, and Multifactor Productivity; Capacity
    • Q12 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Agriculture - - - Micro Analysis of Farm Firms, Farm Households, and Farm Input Markets

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