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Alternative Technical Efficiency Measures: Skew, Bias, and Scale

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Abstract

In the fixed-effects stochastic frontier model an efficiency measure relative to the best firm in the sample is universally employed. This paper considers a new measure relative to the worst firm in the sample. We find that estimates of this measure have smaller bias than those of the traditional measure when the sample consists of many firms near the efficient frontier. Moreover, a two-sided measure relative to both the best and the worst firms is proposed. Simulations suggest that the new measures may be preferred depending on the skewness of the inefficiency distribution and the scale of efficiency differences.

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  • 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.
    • Handle: RePEc:max:cprwps:121
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    1. 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.
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    4. William C. Horrace & Peter Schmidt, 2000. "Multiple comparisons with the best, with economic applications," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 15(1), pages 1-26.
    5. Feng, Qu & Horrace, William C., 2007. "Fixed-effect estimation of technical efficiency with time-invariant dummies," Economics Letters, Elsevier, vol. 95(2), pages 247-252, May.
    6. William C. Horrace & Peter Schmidt, 2002. "Confidence Statements for Efficiency Estimates from Stochastic Frontier Models," Econometrics 0206006, University Library of Munich, Germany.
    7. Simar, L., 1991. "Estimating efficiencies from frontier models with panel data: a comparison of parametric, non-parametric and semi-parametric methods with boot strapping," LIDAM Discussion Papers CORE 1991026, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    8. Entani, Tomoe & Maeda, Yutaka & Tanaka, Hideo, 2002. "Dual models of interval DEA and its extension to interval data," European Journal of Operational Research, Elsevier, vol. 136(1), pages 32-45, January.
    9. Léopold Simar & Paul W. Wilson, 1998. "Sensitivity Analysis of Efficiency Scores: How to Bootstrap in Nonparametric Frontier Models," Management Science, INFORMS, vol. 44(1), pages 49-61, January.
    10. 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.
    11. Schmidt, Peter & Sickles, Robin C, 1984. "Production Frontiers and Panel Data," Journal of Business & Economic Statistics, American Statistical Association, vol. 2(4), pages 367-374, October.
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    Cited by:

    1. Pawlak, Tomasz P. & Litwiniuk, Bartosz, 2021. "Ellipsoidal one-class constraint acquisition for quadratically constrained programming," European Journal of Operational Research, Elsevier, vol. 293(1), pages 36-49.
    2. William Horrace & Seth Richards-Shubik & Ian Wright, 2015. "Expected efficiency ranks from parametric stochastic frontier models," Empirical Economics, Springer, vol. 48(2), pages 829-848, March.
    3. Tomer Blumkin & Leif Danziger & Eran Yashiv, 2017. "Optimal unemployment benefit policy and the firm productivity distribution," International Tax and Public Finance, Springer;International Institute of Public Finance, vol. 24(1), pages 36-59, February.
    4. Millo, Giovanni, 2014. "Maximum likelihood estimation of spatially and serially correlated panels with random effects," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 914-933.
    5. Qu Feng & William Horrace & Guiying Laura Wu, 2013. "Wrong Skewness and Finite Sample Correction in Parametric Stochastic Frontier Models Abstract: In parametric stochastic frontier models, the composed error is specified as the sum of a two-sided noise," Center for Policy Research Working Papers 154, Center for Policy Research, Maxwell School, Syracuse University.
    6. Feng, Qu & Horrace, William C., 2012. "Estimating technical efficiency in micro panels," Economics Letters, Elsevier, vol. 117(3), pages 730-733.
    7. Sungwon Lee & Young Lee, 2014. "Stochastic frontier models with threshold efficiency," Journal of Productivity Analysis, Springer, vol. 42(1), pages 45-54, August.
    8. Feng, Qu & Wu, Guiying Laura & Yuan, Mengying & Zhou, Shihao, 2022. "Save lives or save livelihoods? A cross-country analysis of COVID-19 pandemic and economic growth," Journal of Economic Behavior & Organization, Elsevier, vol. 197(C), pages 221-256.
    9. William C. Horrace & Christopher F. Parmeter, 2018. "A Laplace stochastic frontier model," Econometric Reviews, Taylor & Francis Journals, vol. 37(3), pages 260-280, March.
    10. Zhang, Hongsong, 2013. "Biased Technology and Contribution of Technological Change to Economic Growth: Firm-Level Evidence," 2013 Annual Meeting, August 4-6, 2013, Washington, D.C. 150225, Agricultural and Applied Economics Association.
    11. Kutlu, Levent, 2017. "A constrained state space approach for estimating firm efficiency," Economics Letters, Elsevier, vol. 152(C), pages 54-56.
    12. Young Hoon Lee & Hayley Jang & Sun Ho Hwang, 2015. "Market Competition and Threshold Efficiency in the Sports Industry," Journal of Sports Economics, , vol. 16(8), pages 853-870, December.

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    More about this item

    Keywords

    stochastic frontier model; relative efficiency measure; two-sided measure; bias; bootstrap confidence intervals;
    All these keywords.

    JEL classification:

    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models
    • D24 - Microeconomics - - Production and Organizations - - - Production; Cost; Capital; Capital, Total Factor, and Multifactor Productivity; Capacity

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