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A simple closed-form approximation for the cumulative distribution function of the composite error of stochastic frontier models

Author

Listed:
  • Wen-Jen Tsay

    ()

  • Cliff Huang

    ()

  • Tsu-Tan Fu

    ()

  • I.-Lin Ho

    ()

Abstract

This paper derives an analytic closed-form formula for the cumulative distribution function (cdf) of the composite error of the stochastic frontier analysis (SFA) model. Since the presence of a cdf is frequently encountered in the likelihood-based analysis with limited-dependent and qualitative variables as elegantly shown in the classic book of Maddala (Limited-dependent and qualitative variables in econometrics. Cambridge University Press, Cambridge, 1983 ), the proposed methodology is useful in the framework of the stochastic frontier analysis. We apply the formula to the maximum likelihood estimation of the SFA models with a censored dependent variable. The simulations show that the finite sample performance of the maximum likelihood estimator of the censored SFA model is very promising. A simple empirical example on the modeling of reservation wage in Taiwan is illustrated as a potential application of the censored SFA. Copyright Springer Science+Business Media, LLC 2013

Suggested Citation

  • Wen-Jen Tsay & Cliff Huang & Tsu-Tan Fu & I.-Lin Ho, 2013. "A simple closed-form approximation for the cumulative distribution function of the composite error of stochastic frontier models," Journal of Productivity Analysis, Springer, vol. 39(3), pages 259-269, June.
  • Handle: RePEc:kap:jproda:v:39:y:2013:i:3:p:259-269
    DOI: 10.1007/s11123-012-0283-1
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    File URL: http://hdl.handle.net/10.1007/s11123-012-0283-1
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    References listed on IDEAS

    as
    1. William Greene, 2010. "A stochastic frontier model with correction for sample selection," Journal of Productivity Analysis, Springer, vol. 34(1), pages 15-24, August.
    2. Christine Amsler & Artem Prokhorov & Peter Schmidt, 2014. "Using Copulas to Model Time Dependence in Stochastic Frontier Models," Econometric Reviews, Taylor & Francis Journals, vol. 33(5-6), pages 497-522, August.
    3. A. D. Roy, 1951. "Some Thoughts On The Distribution Of Earnings," Oxford Economic Papers, Oxford University Press, vol. 3(2), pages 135-146.
    4. Olson, Jerome A. & Schmidt, Peter & Waldman, Donald M., 1980. "A Monte Carlo study of estimators of stochastic frontier production functions," Journal of Econometrics, Elsevier, vol. 13(1), pages 67-82, May.
    5. Polachek, Solomon W. & Robst, John, 1998. "Employee labor market information: comparing direct world of work measures of workers' knowledge to stochastic frontier estimates," Labour Economics, Elsevier, vol. 5(2), pages 231-242, June.
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Tai-Hsin Huang & Nan-Hung Liu, 2014. "Bank competition in transition countries: Are those markets really in equilibrium?," Empirical Economics, Springer, vol. 47(4), pages 1283-1316, December.
    2. repec:eee:quaeco:v:67:y:2018:i:c:p:51-62 is not listed on IDEAS
    3. Huang, Tai-Hsin & Lin, Chung-I & Chen, Kuan-Chen, 2017. "Evaluating efficiencies of Chinese commercial banks in the context of stochastic multistage technologies," Pacific-Basin Finance Journal, Elsevier, vol. 41(C), pages 93-110.
    4. repec:spr:empeco:v:54:y:2018:i:2:d:10.1007_s00181-016-1216-z is not listed on IDEAS
    5. repec:eee:quaeco:v:67:y:2018:i:c:p:362-375 is not listed on IDEAS
    6. repec:spr:compst:v:33:y:2018:i:2:d:10.1007_s00180-017-0757-8 is not listed on IDEAS
    7. Hung-pin Lai & Cliff Huang, 2013. "Maximum likelihood estimation of seemingly unrelated stochastic frontier regressions," Journal of Productivity Analysis, Springer, vol. 40(1), pages 1-14, August.
    8. repec:eee:quaeco:v:65:y:2017:i:c:p:212-226 is not listed on IDEAS
    9. Huang, Tai-Hsin & Chiang, Dien-Lin & Lin, Chung-I, 2017. "A new approach to estimating a profit frontier using the censored stochastic frontier model," The North American Journal of Economics and Finance, Elsevier, vol. 39(C), pages 68-77.

    More about this item

    Keywords

    Stochastic frontier analysis; Cumulative distribution function; Censored stochastic frontier model; C13; C46;

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions

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