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Estimation of Input Distance Functions: A System Approach

Author

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  • Tsionas, Efthymios
  • Kumbhakar, Subal C.
  • Malikov, Emir

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 amongst 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

  • Tsionas, Efthymios & Kumbhakar, Subal C. & Malikov, Emir, 2015. "Estimation of Input Distance Functions: A System Approach," MPRA Paper 62329, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:62329
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    File URL: https://mpra.ub.uni-muenchen.de/62329/1/MPRA_paper_62329.pdf
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    References listed on IDEAS

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    1. Giannis Karagiannis & Peter Midmore & Vangelis Tzouvelekas, 2004. "Parametric Decomposition of Output Growth Using A Stochastic Input Distance Function," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 86(4), pages 1044-1057.
    2. David K. Lambert & William W. Wilson, 2003. "Valuing Varieties with Imperfect Output Quality Measurement," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 85(1), pages 95-107.
    3. Hausman, Jerry, 2015. "Specification tests in econometrics," Applied Econometrics, Publishing House "SINERGIA PRESS", vol. 38(2), pages 112-134.
    4. Terza, Joseph V. & Basu, Anirban & Rathouz, Paul J., 2008. "Two-stage residual inclusion estimation: Addressing endogeneity in health econometric modeling," Journal of Health Economics, Elsevier, vol. 27(3), pages 531-543, May.
    5. Abhiman Das & Subal C. Kumbhakar, 2012. "Productivity and efficiency dynamics in Indian banking: An input distance function approach incorporating quality of inputs and outputs," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 27(2), pages 205-234, March.
    6. Jondrow, James & Knox Lovell, C. A. & Materov, Ivan S. & Schmidt, Peter, 1982. "On the estimation of technical inefficiency in the stochastic frontier production function model," Journal of Econometrics, Elsevier, vol. 19(2-3), pages 233-238, August.
    7. Tim Coelli & Gholamreza Hajargasht & C.A. Knox Lovell, 2008. "Econometric Estimation of an Input Distance Function in a System of Equations," CEPA Working Papers Series WP012008, School of Economics, University of Queensland, Australia.
    8. Atkinson, Scott E. & Primont, Daniel, 2002. "Stochastic estimation of firm technology, inefficiency, and productivity growth using shadow cost and distance functions," Journal of Econometrics, Elsevier, vol. 108(2), pages 203-225, June.
    9. COELLI, Tim, 2000. "On the econometric estimation of the distance function representation of a production technology," CORE Discussion Papers 2000042, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    10. Fare, Rolf & Grosskopf, Shawna & Zaim, Osman, 2002. "Hyperbolic efficiency and return to the dollar," European Journal of Operational Research, Elsevier, vol. 136(3), pages 671-679, February.
    11. Caves, Douglas W & Christensen, Laurits R & Swanson, Joseph A, 1981. "Productivity Growth, Scale Economies, and Capacity Utilization in U.S. Railroads, 1955-74," American Economic Review, American Economic Association, vol. 71(5), pages 994-1002, December.
    12. Kumbhakar, Subal C., 2013. "Specification and estimation of multiple output technologies: A primal approach," European Journal of Operational Research, Elsevier, vol. 231(2), pages 465-473.
    13. Daniel Muluwork Atsbeha & Dadi Kristofersson & Kyrre Rickertsen, 2012. "Animal Breeding and Productivity Growth of Dairy Farms," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 94(4), pages 996-1012.
    14. Subal C. Kumbhakar & Gudbrand Lien & Ola Flaten & Ragnar Tveterås, 2008. "Impacts of Norwegian Milk Quotas on Output Growth: A Modified Distance Function Approach," Journal of Agricultural Economics, Wiley Blackwell, vol. 59(2), pages 350-369, June.
    15. Atkinson, Scott E & Cornwell, Christopher & Honerkamp, Olaf, 2003. "Measuring and Decomposing Productivity Change: Stochastic Distance Function Estimation versus Data Envelopment Analysis," Journal of Business & Economic Statistics, American Statistical Association, vol. 21(2), pages 284-294, April.
    16. Cornwell, Christopher & Schmidt, Peter & Sickles, Robin C., 1990. "Production frontiers with cross-sectional and time-series variation in efficiency levels," Journal of Econometrics, Elsevier, vol. 46(1-2), pages 185-200.
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    Cited by:

    1. 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.
    2. 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.
    3. repec:eee:transa:v:120:y:2019:i:c:p:261-276 is not listed on IDEAS
    4. 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.
    5. 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.

    More about this item

    Keywords

    Cost Minimization; Dairy Production; Dairy Quota; Endogeneity; Input Distance Function; Stochastic Frontier;

    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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