Estimation of the Technical Efficiency Measure Within the DEA Method

Anna Pajor; Artur Prędki

doi:https://doi.org/10.59139/ps.2009.03-04.1

Anna Pajor Uniwersytet Ekonomiczny w Krakowie , Artur Prędki Uniwersytet Ekonomiczny w Krakowie Przegląd Statystyczny. Statistical Review, vol. 56, 2009, 3-4, pages: 5-25 Published online: 31 December 2009 DOI https://doi.org/10.59139/ps.2009.03-04.1

464 Views 41 Downloads

ARTICLE

(Polish) PDF

ABSTRACT

In the paper we present the proposition of the description of uncertainty related to the technical efficiency measure received using the DEA method. A nonparametric, statistical model functioning within the DEA method is introduced and the DEA estimator of the technical efficiency measure is defined. For a single input – single output variable case, the value of the technical efficiency measure and frontier production function are related. Thus a corresponding DEA frontier estimator for a given point is defined. Next, forms of the asymptotic distributions of the DEA estimators are presented. It allowed us to derive the asymptotic bias and variance of the DEA estimator and to construct asymptotic confidence intervals. In the last part, finite sample performance of the DEA estimator is investigated via a simulation study. We also illustrate the DEA estimation procedure using real data, which come from the Polish Energy Sector.

KEYWORDS

DEA method, technical efficiency, asymptotic distribution, nonparametric Frontier Model

REFERENCES

[1] Banker R.D., Charnes A., Cooper W.W., [1984], Some models for estimating technical and scale inefficiencies in DEA, Management Science, Vol. 30 (No. 9), s. 1078-1091.

[2] Charnes A., Cooper W.W., Rhodes E., [1978], Measuring the efficiency of decision making units, European Journal of Operations Research, Vol. 2, s. 429-444.

[3] Charnes A., Neralić L., [1989], Sensivity analysis in Data Envelopment Analysis – Part 1 i 2, Glasnik Matematički, Vol. 24 (No. 44), s. 211-226 oraz 449-463.

[4] Charnes A., Neralić L., [1992], Sensivity analysis in Data Envelopment Analysis – Part 3, Glasnik Matematički, Vol. 27 (No. 47), s. 191-201.

[5] Gijbels I., Mammen E., Park B.U., Simar L., [1999], On estimation of monotone and concave frontier function, „Journal of the American Statistical Association”, Vol. 94, s. 220-228.

[6] Gospodarowicz M., [2000], Procedury analizy i oceny banków, Materiały i Studia NBP.

[7] Grosskopf S., [1996], Statistical inference and nonparametric efficiency: a selective survey, „Journal of Productivity Analysis”, Vol. 7, s. 161-176.

[8] Kneip A., Park B.U., Simar L., [1998], A Note on the convergence of nonparametric DEA estimators for production efficiency scores, Econometric Theory, Vol. 14, s. 783-793.

[9] Kneip A., Simar L., Wilson P.W., [2008], Asymptotics and consistent bootstraps for DEA estimators in nonparametric Frontier Models, Econometric Theory, Vol. 24, s. 1663-1697.

[10] Korostelev A.P., Simar L., Tsybakov A.B., [1995], Efficient estimation of monotone boundaries, „The Annals of Statistics”, Vol. 23, s. 476-489.

[11] Korostelev A.P., Simar L., Tsybakov A.B., [1995], On estimation of monotone and convex boundaries, Publications de l’Institut de Statistique des Universités de Paris XXXIX, Vol. 1, s. 3-18.

[12] Park B.U., Simar L., Weiner Ch., [2000], The FDH estimator for productivity efficiency scores, Econometric Theory, Vol. 16, s. 855-877.

[13] Prędki A., [2003], Analiza efektywności za pomocą metody DEA: podstawy formalne i ilustracja ekonomiczna, „Przegląd Statystyczny”, Vol. 50 (No. 1), s. 87-100.

[14] Sengupta J.K., [1990], Transformations in stochastic DEA models, „Journal of Econometrics”, Vol. 46, s. 109-123.

[15] Simar L., [1992], Estimating efficiences from Frontier Models with panel data: a comparison of parametric, non-parametric and semi-parametric methods with bootstrapping, „Journal of Productivity Analysis”, Vol. 3, s. 167-203.

[16] Simar L., [1996], Aspects of statistical analysis in DEA-type Frontier Models, „Journal of Productivity Analysis”, Vol. 7, s. 177-185.

[17] Simar L., Wilson P.W., [1998], Sensivity analysis of efficiency scores: how to bootstrap in nonparametric frontier models, Management Science, Vol. 44, s. 49-61.

[18] Simar L., Wilson P.W., [1999], Some Problems with the Ferrier/Hirschberg Bootstrap Idea, „Journal of Productivity Analysis”, Vol. 11, s. 67-80.

[19] Simar L., Wilson P.W., [2000], A general methodology for bootstrapping In nonparametric frontier models, „Journal of Applied Statistics”, Vol. 27, s. 779-802.

[20] Simar L., Wilson P.W., [2000] Statistical Inference in Nonparametric Frontier Models: The State of the Art, „Journal of Productivity Analysis”, Vol. 13, s. 49-78.

[21] Sueyoshi T., [1997], Measuring Efficiences and Returns to Scale of Nippon Telegraph..., Management Science, Vol. 43 (No. 6), s. 779-796.

[22] Varian H.R., [1992], Microeconomic Analysis, W.W. Norton & Company, Inc.