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Ranking Accuracy of the Efficiency Index in the Stochastic Frontier Model

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A stochastic frontier model is considered – a linear regression model linking the firm activity measure (e.g., the production volume of an enterprise) and the resource inputs. This model is used to determine the efficiency of decision-making units (DMUs). A series of stochastic experiments is run to determine the model’s ability to rank the DMUs by efficiency – a Spearman rank correlation coefficient and the Harrell concordance index are calculated as a function of the variance of the two error components of the regression model: a normally distributed stochastic shock and an inefficiency index with half-normal or exponential distribution.

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References

  1. Australian Competition and Consumer Commission, Benchmarking Opex and Capex in Energy Networks, ACCC/AER Working Paper Series, No. 6 (May 2012).

  2. A. Schweinsberg, M. Stronzik, and M. Wissner, Cost Benchmarking in Energy Regulation in European Countries, WIK-Consult (Final Report) (2011).

  3. E. I. Shchetinin and E. Yu. Nazrullaeva, “The production process in food industry: interrelationship of fixed-asset investment and technical efficiency,” Prikladnaya Ekonometrika, 28, No. 4, 63–84 (2021).

    Google Scholar 

  4. I. B. Ipatova, “Dynamics of total factor productivity and its components: the case of Russia’s plastics industry,” Prikladnaya Ekonometrika, 38, No. 2, 21–40 (2015).

    Google Scholar 

  5. E. Bessonova and A. Tsvetkova, “Productivity convergence trends within Russian industries: Firm-level evidence,” Bank of Russia Working Paper Series wps 51, Bank of Russia (2019).

  6. V. Makarov, S. Aivazyan, M. Afanas’ev, A. Bakhtizin, and A. Nanavyan, “Modeling regional economic growth and efficiency of the innovation space,” Forsait, 10, No. 3, 76–90 (2016).

  7. S. A. Aivazyan, M. Yu, Afanas’ev, and A. V. Kudrov, “Productive potential models and estimates of regional technological efficiency in Russia allowing for production structure,” Ekonomika i Matematicheskie Metody, 52, No. 1, 28–44 (2016).

  8. S. A. Aivazyan, M. Yu, Afanas’ev, and V. A. Rudenko, “Investigating the dependence of random components of the stochastic production function in technical efficiency estimation,” Prikladnaya Ekonometrika, 34, No. 2, 3–18 (2014).

  9. V. A. Rudenko, S. A. Aivazyan, and M. Y. Afanasyev, “Specification of a stochastic production function model in the extended class of stochastic frontier models,” Modeling of Artificial Intelligence, 4, No. 1, 21–28 (2017).

    Google Scholar 

  10. V. A. Rudenko, “Specification scheme of the stochastic production function for assessment of technical efficiency of the regions in the Russian Federation,” Russian Journal of Mathematical Research, Series A, 4, 38–47 (2018).

    Google Scholar 

  11. M. Farrell, “The measurement of productive efficiency,” J. Royal Statistical Society, Series A, General, 120, 253–281 (1957).

    Article  Google Scholar 

  12. D. Aigner, C. A. K. Lovell, and P. Schmidt, “Formulation and estimation of stochastic frontier function models,” J. Econometrics, 6, 21–37 (1977).

    Article  MathSciNet  MATH  Google Scholar 

  13. D. I. Malakhov and N. P. Pil’nik, “Efficiency estimation methods in stochastic production-frontier models,” Ekonomicheskii Zhural Vysshei Shkoly Ekonomiki, 17, No. 4, 660–686 (2013).

  14. S. C. Kumbhakar and C. A. K. Lovell, Stochastic Frontier Analysis, Cambridge University Press (2003).

  15. C. Winsten, “Discussion on Mr. Farrell’s Paper,” J. Royal Statistical Society, Series A, General, 120, 282–284 (1957).

  16. W. C. Horrace, R.-S. Seth, and I. Wright, “Expected efficiency ranks from parametric stochastic frontier models,” Empirical Economics, 48, No. 2, 829–848 (2015).

    Article  Google Scholar 

  17. D. Feng, C. Wang, and X. Zhang, “Estimation of inefficiency in stochastic frontier models: a Bayesian kernel approach,” J. Productivity Analysis, 51, No. 1, 1–19 (2019).

    Article  Google Scholar 

  18. F. E. Harrell Jr., R. M. Califf, D. B. Pryor, K. L. Lee, and R. A. Rosati, “Evaluating the yield of medical tests,” J. American Medical Association, 247, No. 18, 2543–2546 (1982).

    Article  Google Scholar 

  19. R. B. Newson, “Comparing the predictive powers of survival models using Harrell’s C or Somers’ D,” The Stata Journal, 10, No. 3, 339–358 (2010).

    Article  Google Scholar 

  20. E. V. Rumyantseva and K. K. Furmanov, “Using out-of-sample Cox–Snell residuals in time-to-event forecasting,” Business Informatics, 15, No. 1,: 7–18 (2021).

  21. W. H. Greene, Econometric Analysis, 8th edition, Pearson (2018).

  22. www.stata.com.

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Correspondence to I. M. Nikol’skii.

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Translated from Prikladnaya Matematika i Informatika, No. 71, 2022, pp. 81–94.

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Nikol’skii, I.M., Furmanov, K.K. Ranking Accuracy of the Efficiency Index in the Stochastic Frontier Model. Comput Math Model 33, 319–329 (2022). https://doi.org/10.1007/s10598-023-09575-4

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  • DOI: https://doi.org/10.1007/s10598-023-09575-4

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