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Econometric Estimation of Distance Functions and Associated Measures of Productivity and Efficiency Change

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Abstract

The economically-relevant characteristics of multi-input multi-output production technologies can be represented using distance functions. The econometric approach to estimating 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, Koop and Steel (2000, p. 58) have developed a Bayesian solution to this so-called ‘endogeneity’ problem. O'Donnell (2007) has adapted the approach to the estimation of directional distance functions. This paper shows how the approach can be used to estimate Shephard (1953) distance functions and an associated index of total factor productivity (TFP) change. The TFP index is a new multiplicatively-complete index that satisfies most, if not all, economically-relevant tests and axioms from index number theory. The fact that it is multiplicatively-complete means it can be exhaustively decomposed into a measure of technical change and various measures of efficiency change. The decomposition can be implemented without the use of price data and without making any assumptions concerning either the optimising behaviour of firms or the degree of competition in product markets. The methodology is illustrated using state-level quantity data on U.S. agricultural inputs and outputs over the period 1960-2004. Results are summarised in terms of the characteristics (e.g., means) of estimated probability densities for measures of TFP change, technical change and output-oriented measures of efficiency change.

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  • C.J. O’Donnell, 2011. "Econometric Estimation of Distance Functions and Associated Measures of Productivity and Efficiency Change," CEPA Working Papers Series WP012011, School of Economics, University of Queensland, Australia.
    • Handle: RePEc:qld:uqcepa:61
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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. repec:bla:scandj:v:98:y:1996:i:2:p:303-13 is not listed on IDEAS
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. Dale J. Poirier, 1995. "Intermediate Statistics and Econometrics: A Comparative Approach," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262161494, December.
    11. 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.
    12. 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.
    13. 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.
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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. 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.
    3. 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).
    4. 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).
    5. 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.
    6. 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).
    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

    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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