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Econometric estimation of distance functions and associated measures of productivity and efficiency change

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Abstract

Multi-input multi-output production technologies can be represented using distance functions. Econometric estimation of these functions typically involves factoring out one of the outputs or inputs and estimating the resulting equation using maximum likelihood methods. A problem with this approach is that the outputs or inputs that are not factored out may be correlated with the composite error term. Fernandez et al. (J Econ 98:47–79, 2000 ) show how to solve this so-called ‘endogeneity problem’ using Bayesian methods. In this paper I use the approach to estimate an output distance function and an associated index of total factor productivity (TFP) change. The TFP index is a new index that satisfies most, if not all, economically-relevant axioms from index number theory. It can also be exhaustively decomposed into a measure of technical change and various measures of efficiency change. I illustrate the methodology using state-level data on U.S. agricultural input and output quantities (no prices are needed). Results are summarized in terms of the characteristics (e.g., means) of estimated probability density functions for measures of TFP change, technical change and efficiency change. Copyright Springer Science+Business Media, LLC 2014

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  • C. O’Donnell, 2014. "Econometric estimation of distance functions and associated measures of productivity and efficiency change," Journal of Productivity Analysis, Springer, vol. 41(2), pages 187-200, April.
    • Handle: RePEc:kap:jproda:v:41:y:2014:i:2:p:187-200
    DOI: 10.1007/s11123-012-0311-1
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    1. Fernandez, Carmen & Koop, Gary & Steel, Mark, 2000. "A Bayesian analysis of multiple-output production frontiers," Journal of Econometrics, Elsevier, vol. 98(1), pages 47-79, September.
    2. Christopher J. O’Donnell, 2016. "Nonparametric Estimates of the Components of Productivity and Profitability Change in U.S. Agriculture," International Series in Operations Research & Management Science, in: Joe Zhu (ed.), Data Envelopment Analysis, chapter 0, pages 515-541, Springer.
    3. Caves, Douglas W & Christensen, Laurits R & Diewert, W Erwin, 1982. "The Economic Theory of Index Numbers and the Measurement of Input, Output, and Productivity," Econometrica, Econometric Society, vol. 50(6), pages 1393-1414, November.
    4. V. Eldon Ball & Charles Hallahan & Richard Nehring, 2004. "Convergence of Productivity: An Analysis of the Catch-up Hypothesis within a Panel of States," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 86(5), pages 1315-1321.
    5. 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.
    6. V. Eldon Ball & Jean-Christophe Bureau & Richard Nehring & Agapi Somwaru, 1997. "Agricultural Productivity Revisited," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 79(4), pages 1045-1063.
    7. Christopher J. O'Donnell, 2010. "Measuring and decomposing agricultural productivity and profitability change ," Australian Journal of Agricultural and Resource Economics, Australian Agricultural and Resource Economics Society, vol. 54(4), pages 527-560, October.
    8. O'Donnell, Christopher J., 2007. "Estimating the Characteristics of Polluting Technologies," 2007 Conference (51st), February 13-16, 2007, Queenstown, New Zealand 10413, Australian Agricultural and Resource Economics Society.
    9. Kopp, Raymond J. & Mullahy, John, 1990. "Moment-based estimation and testing of stochastic frontier models," Journal of Econometrics, Elsevier, vol. 46(1-2), pages 165-183.
    10. C.J. O'Donnell, 2008. "An aggregate quantity-price framework for measuring and Decomposing productivity and profitability change," CEPA Working Papers Series WP072008, School of Economics, University of Queensland, Australia.
    11. Fernandez, Carmen & Osiewalski, Jacek & Steel, Mark F. J., 1997. "On the use of panel data in stochastic frontier models with improper priors," Journal of Econometrics, Elsevier, vol. 79(1), pages 169-193, July.
    12. Bjurek, Hans, 1996. " The Malmquist Total Factor Productivity Index," Scandinavian Journal of Economics, Wiley Blackwell, vol. 98(2), pages 303-313, June.
    13. Dale J. Poirier, 1995. "Intermediate Statistics and Econometrics: A Comparative Approach," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262161494, December.
    14. Aigner, Dennis & Lovell, C. A. Knox & Schmidt, Peter, 1977. "Formulation and estimation of stochastic frontier production function models," Journal of Econometrics, Elsevier, vol. 6(1), pages 21-37, July.
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    1. C. O’Donnell & K. Nguyen, 2013. "An econometric approach to estimating support prices and measures of productivity change in public hospitals," Journal of Productivity Analysis, Springer, vol. 40(3), pages 323-335, December.
    2. Diewert, W. Erwin & Fox, Kevin J., 2017. "Decomposing productivity indexes into explanatory factors," European Journal of Operational Research, Elsevier, vol. 256(1), pages 275-291.
    3. R. Todd Jewell, 2017. "Technical efficiency with multi-output, heterogeneous production: a latent class, distance function model of english football," Journal of Productivity Analysis, Springer, vol. 48(1), pages 37-50, August.
    4. Tran, Trung & Thanh, Hai Trinh & Van Le, Dao & Phuong, Thao Trinh Thi & Lan, Phuong Nguyen, 2022. "Does government financial support decrease the inefficiency of public universities? A decomposition approach," Finance Research Letters, Elsevier, vol. 47(PA).
    5. Walker, Nathan L. & Styles, David & Williams, A. Prysor, 2023. "Water sector resilience in the United Kingdom and Ireland: The COVID-19 challenge," Utilities Policy, Elsevier, vol. 82(C).
    6. Mocholi-Arce, Manuel & Sala-Garrido, Ramon & Molinos-Senante, Maria & Maziotis, Alexandros, 2021. "Water company productivity change: A disaggregated approach accounting for changes in inputs and outputs," Utilities Policy, Elsevier, vol. 70(C).
    7. Halkos, George & Tzeremes, Nickolaos, 2012. "Evaluating professional tennis players’ career performance: A Data Envelopment Analysis approach," MPRA Paper 41516, University Library of Munich, Germany.
    8. C.J. O'Donnell, 2011. "The Sources of Productivity Change in the Manufacturing Sectors of the U.S. Economy," CEPA Working Papers Series WP072011, School of Economics, University of Queensland, Australia.

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    More about this item

    Keywords

    Total factor productivity; Transitivity; Färe-Primont index; Solow residual; Endogeneity; Markov Chain Monte Carlo; C11; C43; D24;
    All these keywords.

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C43 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Index Numbers and Aggregation
    • D24 - Microeconomics - - Production and Organizations - - - Production; Cost; Capital; Capital, Total Factor, and Multifactor Productivity; Capacity

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