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Stochastic Frontier Models with Threshold Efficiency

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  • Young Hoon Lee

    ()
    (Department of Economics, Sogang University, Seoul)

  • Sungwon Lee

    (Korea Development Institute)

Abstract

This paper proposes a tail-truncated stochastic frontier model that allows for the truncation of technical efficiency from below. The truncation bound implies the inefficiency threshold for survival and also can be used as a measure of market competition. Specifically, this paper assumes a uniform distribution of technical inefficiency and derives the likelihood function. Even though this distributional assumption imposes a strong restriction that technical inefficiency has a uniform probability density over [0,], where is the threshold parameter, this model has two advantages: (i) the reduction of the number of parameters from the more complicated tail-truncated models allows better performance in numerical optimization; and (ii) the threshold parameter itself represents a degree of competition because the variance of technical inefficiency is dependent solely on the parameter. The Monte Carlo simulation results support the argument that this model approximates the distribution of inefficiency precisely.

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File URL: ftp://163.239.165.41/RePEc/sgo/wpaper/LYH_RIME_2012-5.pdf
File Function: First version, 2011
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Bibliographic Info

Paper provided by Research Institute for Market Economy, Sogang University in its series Working Papers with number 1205.

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Length: 23 pages
Date of creation: 2011
Date of revision:
Handle: RePEc:sgo:wpaper:1205

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Keywords: Stochastic frontier; technical efficiency; threshold inefficiency; uniform distribution; productivity distribution;

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References

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  1. Greene, William H., 1980. "Maximum likelihood estimation of econometric frontier functions," Journal of Econometrics, Elsevier, vol. 13(1), pages 27-56, May.
  2. Chad Syverson, 2001. "Market Structure and Productivity: A Concrete Example," Working Papers 01-06, Center for Economic Studies, U.S. Census Bureau.
  3. Qu Feng & William C. Horrace, 2010. "Alternative Technical Efficiency Measures: Skew, Bias, and Scale," Center for Policy Research Working Papers 121, Center for Policy Research, Maxwell School, Syracuse University.
  4. 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.
  5. Amemiya, Takeshi, 1973. "Regression Analysis when the Dependent Variable is Truncated Normal," Econometrica, Econometric Society, vol. 41(6), pages 997-1016, November.
  6. 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.
  7. Greene, William H., 1990. "A Gamma-distributed stochastic frontier model," Journal of Econometrics, Elsevier, vol. 46(1-2), pages 141-163.
  8. David Good & M. Nadiri & Lars-Hendrik Röller & Robin Sickles, 1993. "Efficiency and productivity growth comparisons of European and U.S. Air carriers: A first look at the data," Journal of Productivity Analysis, Springer, vol. 4(1), pages 115-125, June.
  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.
  11. David A. Matsa, 2011. "Competition and Product Quality in the Supermarket Industry," The Quarterly Journal of Economics, Oxford University Press, vol. 126(3), pages 1539-1591.
  12. Thomas J. Holmes & James A. Schmitz, Jr., 2010. "Competition and productivity: a review of evidence," Staff Report 439, Federal Reserve Bank of Minneapolis.
  13. Stevenson, Rodney E., 1980. "Likelihood functions for generalized stochastic frontier estimation," Journal of Econometrics, Elsevier, vol. 13(1), pages 57-66, May.
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