# Understanding prediction intervals for firm specific inefficiency scores from parametric stochastic frontier models

## Author

Listed:
• Phill Wheat

()

• William Greene
• Andrew Smith

## Abstract

This paper makes two important contributions to the literature on prediction intervals for firm specific inefficiency estimates in cross sectional SFA models. Firstly, the existing intervals in the literature do not correspond to the minimum width intervals and in this paper we discuss how to compute such intervals and how they either include or exclude zero as a lower bound depending on where the probability mass of the distribution of $$u_{i} |\varepsilon_{i}$$ u i | ε i resides. This has useful implications for practitioners and policy makers, with greatest reductions in interval width for the most efficient firms. Secondly, we propose an ‘asymptotic’ approach to incorporating parameter uncertainty into prediction intervals for firm specific inefficiency (given that in practice model parameters have to be estimated) as an alternative to the ‘bagging’ procedure suggested in Simar and Wilson (Econom Rev 29(1):62–98, 2010 ). The approach is computationally much simpler than the bagging approach. Copyright Springer Science+Business Media New York 2014

## Suggested Citation

• Phill Wheat & William Greene & Andrew Smith, 2014. "Understanding prediction intervals for firm specific inefficiency scores from parametric stochastic frontier models," Journal of Productivity Analysis, Springer, vol. 42(1), pages 55-65, August.
• Handle: RePEc:kap:jproda:v:42:y:2014:i:1:p:55-65
DOI: 10.1007/s11123-013-0346-y
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File URL: http://hdl.handle.net/10.1007/s11123-013-0346-y

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## References listed on IDEAS

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1. 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.
2. 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.
3. Horrace, William C., 2005. "On ranking and selection from independent truncated normal distributions," Journal of Econometrics, Elsevier, vol. 126(2), pages 335-354, June.
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 435-444, June.
5. Rafael Cuesta, 2000. "A Production Model With Firm-Specific Temporal Variation in Technical Inefficiency: With Application to Spanish Dairy Farms," Journal of Productivity Analysis, Springer, vol. 13(2), pages 139-158, March.
6. Train,Kenneth E., 2009. "Discrete Choice Methods with Simulation," Cambridge Books, Cambridge University Press, number 9780521766555, June.
7. Kim, Yangseon & Schmidt, Peter, 2008. "Marginal Comparisons With the Best and the Efficiency Measurement Problem," Journal of Business & Economic Statistics, American Statistical Association, vol. 26, pages 253-260, April.
8. Andrew S. J. Smith & Phil Wheat, 2012. "Evaluating Alternative Policy Responses to Franchise Failure: Evidence from the Passenger Rail Sector in Britain," Journal of Transport Economics and Policy, University of Bath, vol. 46(1), pages 25-49, January.
9. Antonio Alvarez & Christine Amsler & Luis Orea & Peter Schmidt, 2006. "Interpreting and Testing the Scaling Property in Models where Inefficiency Depends on Firm Characteristics," Journal of Productivity Analysis, Springer, vol. 25(3), pages 201-212, June.
10. 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.
11. 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.
12. Alfonso Flores-Lagunes & William C. Horrace & Kurt E. Schnier, 2007. "Identifying technically efficient fishing vessels: a non-empty, minimal subset approach," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 22(4), pages 729-745.
13. 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.
14. Leopold Simar & Paul Wilson, 2010. "Inferences from Cross-Sectional, Stochastic Frontier Models," Econometric Reviews, Taylor & Francis Journals, vol. 29(1), pages 62-98.
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## Citations

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Cited by:

1. Subal C. Kumbhakar & Christopher F. Parmeter & Valentin Zelenyuk, 2017. "Stochastic Frontier Analysis: Foundations and Advances," Working Papers 2017-10, University of Miami, Department of Economics.

### Keywords

Stochastic frontier; Prediction intervals; Efficiency; C12; L25; L51; L92;

### JEL classification:

• C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
• L25 - Industrial Organization - - Firm Objectives, Organization, and Behavior - - - Firm Performance
• L51 - Industrial Organization - - Regulation and Industrial Policy - - - Economics of Regulation
• L92 - Industrial Organization - - Industry Studies: Transportation and Utilities - - - Railroads and Other Surface Transportation

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