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Journal of Zhejiang University SCIENCE A 2008 Vol.9 No.10 P.1426~1436


A comparative analysis of multi-output frontier models

Author(s):  Tao ZHANG, Eoghan GARVEY

Affiliation(s):  Department of Economics, National University of Ireland, Galway, Ireland

Corresponding email(s):   taozhang7608@hotmail.com

Key Words:  Efficiency, Multi-output, Stochastic distance function frontier, Stochastic ray frontier, Data envelopment analysis (DEA), Correlation

Tao ZHANG, Eoghan GARVEY. A comparative analysis of multi-output frontier models[J]. Journal of Zhejiang University Science A, 2008, 9(10): 1426~1436.

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%A Eoghan GARVEY
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%I Zhejiang University Press & Springer
%DOI 10.1631/jzus.A0820121

T1 - A comparative analysis of multi-output frontier models
A1 - Tao ZHANG
A1 - Eoghan GARVEY
J0 - Journal of Zhejiang University Science A
VL - 9
IS - 10
SP - 1426
EP - 1436
%@ 1673-565X
Y1 - 2008
PB - Zhejiang University Press & Springer
ER -
DOI - 10.1631/jzus.A0820121

Recently, there have been more debates on the methods of measuring efficiency. The main objective of this paper is to make a sensitivity analysis for different frontier models and compare the results obtained from the different methods of estimating multi-output frontier for a specific application. The methods include stochastic distance function frontier, stochastic ray frontier, and data envelopment analysis. The stochastic frontier regressions with and without the inefficiency effects model are also compared and tested. The results indicate that there are significant correlations between the results obtained from the alternative estimation methods.

Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article


[1] Aigner, D.J., Chu, S.F., 1968. On estimating the industry production function. Am. Econ. Rev., 58(4):826-839.

[2] Aigner, D., Lovell, K., Schmidt, P., 1977. Formulation and estimation of stochastic frontier models. J. Econ., 6(1):21-37.

[3] Battese, G., Coelli, T., 1995. A model for technical efficiency effects in a stochastic frontier production function for panel data. Emp. Econ., 20(2):325-332.

[4] Charnes, A., Cooper, W.W., Rhodes, E., 1978. Measuring the efficiency of decision making units. Eur. J. Oper. Res., 2(6):429-444.

[5] Charnes, A., Cooper, W.W., Lewin, A.Y., Seiford, L.M. (Eds.), 1994. Categorical Inputs and Outputs, Section 3.3. In: Data Envelopment Analysis: Theory, Methodology, and Applications. Kluwer Academic Publishers, Boston/ Dordrecht/London, p.52-54.

[6] Coelli, T., Perelman, S., 1996. Efficiency Measurement, Multiple-output Technologies and Distance Functions: With Application to European Railways. CREPP Working Paper, University of Liege, Liege, Wallonia, Belgium.

[7] Coelli, T., Perelman, S., 1999. A comparison of parametric and non-parametric distance functions: with application to European railways. Eur. J. Oper. Res., 117(2):326-339.

[8] Coelli, T., Perelman, S., 2000. Technical efficiency of European railways: a distance function approach. Appl. Econ., 32(15):1967-1976.

[9] Daraio, C., Simar, L., 2005. Introducing environmental variables in nonparametric frontier models: a probabilistic approach. J. Prod. Anal., 24(1):93-121.

[10] Daraio, C., Simar, L., 2007. Conditional nonparametric frontier models for convex and nonconvex technologies: a unifying approach. J. Prod. Anal., 28(1-2):13-32.

[11] Fare, R., Grosskopf, S., Lovell, C.A.K., Yaisawarng, S., 1993. Derivation of shadow prices for undesirable outputs: a distance function approach. Rev. Econ. Stat., 75(2):374-380.

[12] Fecher, F., Kessler, D., Perelman, S., Pestieau, P., 1993. Productive performance of the French insurance industry. J. Prod. Anal., 4(1-2):77-93.

[13] Ferrier, G.D., Lovell, C.A.K., 1990. Measuring cost efficiency in banking: econometric and linear programming evidence. J. Econ., 46(1-2):229-245.

[14] Grosskopf, S., Hayes, K., Taylor, L., Weber, W., 1997. Budget constrained frontier measurement of fiscal equality and efficiency in schooling. Rev. Econ. Stat., 79(1):116-124.

[15] Huang, T.H., Wang, M.H., 2002. Comparison of economic efficiency estimation methods: parametric and non-parametric techniques. The Manchester School, 70(5):682-709.

[16] Kopp, R., Smith, V., 1980. Frontier production function estimates for steam electric generation: a comparative analysis. South. Econ. J., 46(4):1049-1059.

[17] Lothgren, M., 1997. Generalized stochastic frontier production models. Econ. Lett., 57(3):255-259.

[18] Lothgren, M., 2000. Specification and estimation of stochastic multiple-output production and technical inefficiency. Appl. Econ., 32(12):1533-1540.

[19] Lovell, C.A.K., Richardson, S., Travers, P., Wood, L.L., 1994. Resources and Functionings: A New View of Inequality in Australia. In: Eichhorn, W. (Ed.), Models and Measurement of Welfare and Inequality. Springer-Verlag, Berlin, p.787-807.

[20] Ruggiero, J., 2007. A comparison of DEA and the stochastic frontier model using panel data. Int. Trans. Oper. Res., 14(3):259-266.

[21] Sharma, K.R., Leung, P., Zaleski, H.M., 1997. Productive efficiency of the swine industry in Hawaii: stochastic frontier vs. data envelopment analysis. J. Prod. Anal., 8(4):447-459.

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