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A Bayesian Approach To Imposing Curvature On Distance Functions

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Author Info
Tim J. Coelli ()
Chris O’Donnell (CEPA - School of Economics, The University of Queensland)

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Abstract

The estimated parameters of output distance functions frequently violate the monotonicity, quasiconvexity and convexity constraints implied by economic theory, leading to estimated elasticities and shadow prices that are incorrectly signed, and ultimately to perverse conclusions concerning the effects of input and output changes on productivity growth and relative efficiency levels. We show how a Bayesian approach can be used to impose these constraints on the parameters of a translog output distance function. Implementing the approach involves the use of a Gibbs sampler with data augmentation. A Metropolis-Hastings algorithm is also used within the Gibbs to simulate observations from truncated pdfs. Our methods are developed for the case where panel data is available and technical inefficiency effects are assumed to be time-invariant. Two models – a fixed effects model and a random effects model – are developed and applied to panel data on 17 European railways. We observe significant changes in estimated elasticities and shadow price ratios when regularity restrictions are imposed

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Paper provided by School of Economics, University of Queensland, Australia in its series CEPA Working Papers Series with number WP032003.

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Date of creation: Aug 2003
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Handle: RePEc:qld:uqcepa:03

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  1. Gary Koop & M. F. J. Steel, 2004. "Bayesian Analysis of Stochastic Frontier Models," ESE Discussion Papers 19, Edinburgh School of Economics, University of Edinburgh.
  2. Grosskopf, S. & Margaritis, D. & Valdmanis, V., 1995. "Estimating output substitutability of hospital services: A distance function approach," European Journal of Operational Research, Elsevier, vol. 80(3), pages 575-587, February. [Downloadable!] (restricted)
  3. Gallant, A. Ronald & Golub, Gene H., 1984. "Imposing curvature restrictions on flexible functional forms," Journal of Econometrics, Elsevier, vol. 26(3), pages 295-321, December. [Downloadable!] (restricted)
  4. Geweke, John, 1986. "Exact Inference in the Inequality Constrained Normal Linear Regression Model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 1(2), pages 127-41, April. [Downloadable!] (restricted)
  5. Terrell, Dek, 1996. "Incorporating Monotonicity and Concavity Conditions in Flexible Functional Forms," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 11(2), pages 179-94, March-Apr. [Downloadable!] (restricted)
  6. Coelli, Tim & Perelman, Sergio, 1999. "A comparison of parametric and non-parametric distance functions: With application to European railways," European Journal of Operational Research, Elsevier, vol. 117(2), pages 326-339, September. [Downloadable!] (restricted)
  7. Ryan, David L. & Wales, Terence J., 2000. "Imposing local concavity in the translog and generalized Leontief cost functions," Economics Letters, Elsevier, vol. 67(3), pages 253-260, June. [Downloadable!] (restricted)
  8. Grosskopf, S. & Hayes, K. & Hirschberg, J., 1995. "Fiscal stress and the production of public safety: A distance function approach," Journal of Public Economics, Elsevier, vol. 57(2), pages 277-296, June. [Downloadable!] (restricted)
  9. Meeusen, Wim & van den Broeck, Julien, 1977. "Efficiency Estimation from Cobb-Douglas Production Functions with Composed Error," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 18(2), pages 435-44, June. [Downloadable!] (restricted)
  10. 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. [Downloadable!] (restricted)
  11. Koop, Gary & Osiewalski, Jacek & Steel, Mark F. J., 1997. "Bayesian efficiency analysis through individual effects: Hospital cost frontiers," Journal of Econometrics, Elsevier, vol. 76(1-2), pages 77-105. [Downloadable!] (restricted)
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  12. Fare, Rolf, et al, 1993. "Derivation of Shadow Prices for Undesirable Outputs: A Distance Function Approach," The Review of Economics and Statistics, MIT Press, vol. 75(2), pages 374-80, May. [Downloadable!] (restricted)
  13. Brummer, Bernhard & Glauben, Thomas & Thijssen, Geert, 2002. " Decomposition of Productivity Growth Using Distance Functions: The Case of Dairy Farms in Three European Countries," American Journal of Agricultural Economics, American Agricultural Economics Association, vol. 84(3), pages 628-44, August. [Downloadable!] (restricted)
  14. Tim Coelli & Sergio Perelman, 2000. "Efficiency measurement, multiple-output technologiess and distance functions : with application to European Railways," CREPP Working Papers 9605, Centre de Recherche en Economie Publique et de la Population (CREPP) (Research Center on Public and Population Economics) HEC-Management School, University of Liège. [Downloadable!]
  15. 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. [Downloadable!] (restricted)
  16. Cowie, Jonathan & Riddington, Geoff, 1996. "Measuring the Efficiency of European Railways," Applied Economics, Taylor and Francis Journals, vol. 28(8), pages 1027-35, August. [Downloadable!] (restricted)
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  1. Kelvin_Balcombe & Dirk_Bezemer & Junior_Davis & Iain_Fraser, 2005. "Livelihoods and Farm Efficiency in Rural Georgia," Development and Comp Systems 0502005, EconWPA. [Downloadable!]
  2. Kelvin Balcombe & Iain Fraser & Jae H. Kim, 2006. "Estimating technical efficiency of Australian dairy farms using alternative frontier methodologies," Applied Economics, Taylor and Francis Journals, vol. 38(19), pages 2221-2236, October. [Downloadable!] (restricted)
  3. Supawat Rungsuriyawiboon & Chris O’Donnell, 2004. "Curvature-Constrained Estimates of Technical Efficiency and Returns to Scale for U.S. Electric Utilities," CEPA Working Papers Series WP072004, School of Economics, University of Queensland, Australia. [Downloadable!]
  4. David Tomberlin & Garth Holloway, 2007. "Trip-Level Analysis of Efficiency Changes in Oregon’s Deepwater Trawl Fishery," Working Papers 2007.86, Fondazione Eni Enrico Mattei. [Downloadable!]
  5. Sergio Perlman & Daniel Santin, 2005. "On the generation of a regular multi-input multi-output technology using parametric output distance functions," CREPP Working Papers 0507, Centre de Recherche en Economie Publique et de la Population (CREPP) (Research Center on Public and Population Economics) HEC-Management School, University of Liège. [Downloadable!]
  6. Gholamreza Hajargasht & Tim Coelli & D. S. Prasada Rao, 2006. "A Dual Measure of Economies of Scope," CEPA Working Papers Series WP032006, School of Economics, University of Queensland, Australia. [Downloadable!]
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  7. Dirk Bezemer & Kelvin Balcombe & Junior Davis & Iain Fraser, 2005. "Livelihoods and farm efficiency in rural Georgia," Applied Economics, Taylor and Francis Journals, vol. 37(15), pages 1737-1745, August. [Downloadable!] (restricted)
  8. Sergio Perlman & Daniel Santin, 2005. "Measuring educational efficiency at student level with parametric stochastic distance functions: An application to Spanish PISA results," CREPP Working Papers 0504, Centre de Recherche en Economie Publique et de la Population (CREPP) (Research Center on Public and Population Economics) HEC-Management School, University of Liège. [Downloadable!]
  9. Bezemer, Dirk & Balcombe, Kelvin & Davis, Junior & Fraser, Iain, 2005. "Is Rural Income Diversity Pro-Growth? Is It Pro-Poor? Evidence from Georgia," Proceedings of the German Development Economics Conference, Kiel 2005 4, Verein für Socialpolitik, Research Committee Development Economics. [Downloadable!]
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