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On the distribution of estimated technical efficiency in stochastic frontier models

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  • Wang, Wei Siang
  • Schmidt, Peter

Abstract

We consider a stochastic frontier model with error [epsilon]=v-u, where v is normal and u is half normal. We derive the distribution of the usual estimate of u,E(u[epsilon]). We show that as the variance of v approaches zero, E(u[epsilon])-u converges to zero, while as the variance of v approaches infinity, E(u[epsilon]) converges to E(u). We graph the density of E(u[epsilon]) for intermediate cases. To show that E(u[epsilon]) is a shrinkage of u towards its mean, we derive and graph the distribution of E(u[epsilon]) conditional on u. We also consider the distribution of estimated inefficiency in the fixed-effects panel data setting.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 148 (2009)
Issue (Month): 1 (January)
Pages: 36-45

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Handle: RePEc:eee:econom:v:148:y:2009:i:1:p:36-45

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Web page: http://www.elsevier.com/locate/jeconom

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Keywords: Stochastic frontier Technical inefficiency Estimated inefficiency;

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References

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  1. Greene, William H., 1990. "A Gamma-distributed stochastic frontier model," Journal of Econometrics, Elsevier, vol. 46(1-2), pages 141-163.
  2. Waldman, Donald M., 1984. "Properties of technical efficiency estimators in the stochastic frontier model," Journal of Econometrics, Elsevier, vol. 25(3), pages 353-364, July.
  3. Greene, William H., 1980. "Maximum likelihood estimation of econometric frontier functions," Journal of Econometrics, Elsevier, vol. 13(1), pages 27-56, May.
  4. Battese, George E. & Coelli, Tim J., 1988. "Prediction of firm-level technical efficiencies with a generalized frontier production function and panel data," Journal of Econometrics, Elsevier, vol. 38(3), pages 387-399, July.
  5. Stevenson, Rodney E., 1980. "Likelihood functions for generalized stochastic frontier estimation," Journal of Econometrics, Elsevier, vol. 13(1), pages 57-66, May.
  6. Greene, William H., 1980. "On the estimation of a flexible frontier production model," Journal of Econometrics, Elsevier, vol. 13(1), pages 101-115, May.
  7. Pitt, Mark M. & Lee, Lung-Fei, 1981. "The measurement and sources of technical inefficiency in the Indonesian weaving industry," Journal of Development Economics, Elsevier, vol. 9(1), pages 43-64, August.
  8. 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.
  9. 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.
  10. Schmidt, Peter & Sickles, Robin C, 1984. "Production Frontiers and Panel Data," Journal of Business & Economic Statistics, American Statistical Association, vol. 2(4), pages 367-74, October.
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Citations

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Cited by:
  1. Federico Belotti & Giuseppe Ilardi, 2012. "Consistent Estimation of the “True” Fixed-effects Stochastic Frontier Model," CEIS Research Paper 231, Tor Vergata University, CEIS, revised 18 Apr 2012.
  2. Qu Feng & William Horrace & Guiying Laura Wu, 2013. "Wrong Skewness and Finite Sample Correction in Parametric Stochastic Frontier Models," Center for Policy Research Working Papers 154, Center for Policy Research, Maxwell School, Syracuse University.
  3. Eduardo Fé-Rodríguez & Richard Hofler, 2009. "Count Data Stochastic Frontier Models, with an application to the patents-R&D Relationship," The School of Economics Discussion Paper Series 0916, Economics, The University of Manchester.
  4. Shinji Yane & Sanford Berg, 2013. "Sensitivity analysis of efficiency rankings to distributional assumptions: applications to Japanese water utilities," Applied Economics, Taylor & Francis Journals, vol. 45(17), pages 2337-2348, June.
  5. Bellio, Ruggero & Grassetti, Luca, 2011. "Semiparametric stochastic frontier models for clustered data," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 71-83, January.
  6. Wei Wang & Christine Amsler & Peter Schmidt, 2011. "Goodness of fit tests in stochastic frontier models," Journal of Productivity Analysis, Springer, vol. 35(2), pages 95-118, April.
  7. William C. Horrace & Christopher F. Parmeter, 2008. "Semiparametric Deconvolution with Unknown Error Variance," Center for Policy Research Working Papers 104, Center for Policy Research, Maxwell School, Syracuse University.
  8. Gómez-Gallego, Juan Cándido & Gómez-García, Juan & Pérez-Cárceles, María Concepción, 2012. "Appropriate Distribution of Cost Inefficiency Estimates as Predictor of Financial Instability /La distribución de la ineficiencia estimada como predictor de inestabilidad financiera," Estudios de Economía Aplicada, Estudios de Economía Aplicada, vol. 30, pages 1071 (12 pa, Diciembre.
  9. Anup Bhandari & Pradip Maiti, 2012. "Efficiency of the Indian leather firms: some results obtained using the two conventional methods," Journal of Productivity Analysis, Springer, vol. 37(1), pages 73-93, February.

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