Estimation of Cost Efficiency in Non-parametric Frontier Models

  • Galina Besstremyannaya New Economic School and Institute of the Far East Studies of the Russian Academy of Sciences, 45, Skolkovskoe shosse, Moscow, 121353, Russian Federation
  • Jaak Simm Stadius Centre for Dynamical Systems, Signal Processing and Data Analytics, Belgium, B–3001, Heverlee


The paper proposes a bootstrap methodology for estimating cost efficiency in data envelopment analysis. We consider the conventional concept of Fare, Grosskopf and Lovellcost efficiency, for which our algorithm re-samples “naive” input-oriented efficiency scores, rescales original inputs to bring them to the frontier, and then re-estimates cost efficiency scores for the rescaled inputs. Next, we examine Tone cost efficiency, where input prices vary across producers. Here we show that the direct modification on bootstrap algorithms by Simar and Wilson are applicable. We consider cases both with the absence and presence of environmental variables (i.e. input variables not directly controlled by firms). The bootstrap methodology exploits these assumptions: 1) the sample are i.i.d. random variables with the continuous joint probability density function with support over production set; 2) the frontier is smooth; and 3) the probability of observing firms on the frontier approaches unity with an increase in sample. The results of simulations for a multi-input, multi-output Cobb–Douglas production function with correlated outputs, and correlated technical and cost efficiency, show consistency of our proposed algorithm, even for small samples. Finally, we offer real data estimates for the Japanese banking industry in 2013. Our package “rDEA,” developed in the R language, is available from the GitHub and CRAN repository.

Ключевые слова:

bootstrap, price efficiency, border analysis, banking


Данные скачивания пока недоступны.


References in Latin Alphabet

Altunbas Y., Liu M-H., Molyneux P., Seth R. (2000) Effi ciency and Risk in Japanese Banking. Journal of Banking and Finance, vol. 24, iss. 10, pp. 1605–28.

Aly H. Y., Grabowski R., Pasurka C., Rangan N. (1990) Technical, Scale, and Allocative Effi ciencies in U. S. Banking: An Empirical Investigation. Review of Economics and Statistics, no. 72, pp. 211–17.

Badin L., Simar L. (2003) Confi dence Intervals for DEA-Type Effi ciency Scores: How to Avoid the Computational Burden of the Bootstrap. Technical report 0322. Available at: IAP Statistics Network (аccessed: 06.03. 2019).

Banker R., Gadh V. M., Gorr W. L. (1993) A Monte Carlo Comparison of Two Production Frontier Estimation Methods: Corrected Ordinary Least Squares and Data Envelopment Analysis. European Journal of Operational Research, no. 67, pp. 332–43.

Barros C. P., Dieke P. U. C. (2008) Measuring the Economic Effi ciency of Airports: A Simar-Wilson Methodology Analysis. Transportation Research. Part E, no. 44, pp. 1039–51.

Barros C. P., Managi S., Matousek R. (2012) Th e Technical Effi ciency of the Japanese Banks: Non-Radial Directional Performance Measurement with Undesirable Output. Omega, no. 40, pp. 1–8.

Besstremyannaya G. (2013) Th e Impact of Japanese Hospital Financing Reform on Hospital Effi ciency. Japanese Economic Review, vol. 64, iss. 3, pp. 337–362.

Besstremyannaya G. (2017) Heterogeneous Eff ect of the Global Financial Crisis and the Great East Japan Earthquake on Costs of Japanese Banks. Journal of Empirical Finance, no. 42, pp. 66–89.

Borger B. de, Kerstens K., Staat M. (2008) Transit Costs and Cost Effi ciency: Bootstrapping Non-Parametric Frontiers. Research in Transportation Economics, no. 23, pp. 53–64.

Charnes A., Cooper W., Rhodes E. (1978) Measuring the Effi ciency of Decision Making Units. European Journal of Operational Research, no. 2, pp. 429–44.

Coelli T. J., Rao D. S. P., Battese G. E. (1994) An Introduction to Effi ciency and Productivity Analysis. Kluwer Academic Publishers.

Drake L., Hall M. J. B. (2003) Effi ciency in Japanese Banking: An Empirical Analysis. Journal of Banking and Finance, no. 27, pp. 891–917.

Drake L., Hall M. J. B., Simper R. (2009) Bank Modelling Methodologies: A Comparative Non-Parametric Analysis of Effi ciency in the Japanese Banking Sector. Journal of International Financial Markets, Institutions and Money, no. 19, pp. 1–15.

Fare R., Grosskopf S., Lovell C. A. (1985) Th e Measurement of Effi ciency in Production. Boston: Kluwer Academic Publishers.

Farrell M. J. (1957) Th e Measurement of Productive Effi ciency. Journal of the Royal Statistical Society, Series A (General), no. 3, pp. 253–81.

Fethi M. D., Pasiouras F. (2010) Assessing Bank Effi ciency and Performance with Opeartional Research and Artifi cial Intelligence Techniques: A Survey. European Journal of Operational Research, no. 204, pp. 189– 98.

Fukuyama H. (1993) Technical and Scale Effi ciency of Japanese Commercial Banks: A Non-Parametric Approach. Applied Economics, no. 25, pp. 1101–1112.

Fukuyama H. (1995) Measuring Effi ciency and Pruductivity Growth in Japanese Banking: A Nonparametric Frontier Approach. Applied Financial Economics, no. 5, pp. 95–107.

Fukuyama H., Weber W. L. (2002) Estimating Output Allocative Effi ciency and Productivity Change: Application to Japanese Banks. European Journal of Operation Research, no. 137, pp. 177–90.

Fukuyama H., Weber W. L. (2008) Japanese Banking Ineffi ciency and Shadow Pricing. Mathematical and Computer Modelling, no. 48, pp. 1854–67.

Fukuyama H., Weber W. L. (2010) A Slacks-Based Ineffi ciency Measure for a Two-Stage System with Bad Outputs. Omega, no. 38, pp. 398–409.

Giokas D. (1991) Bank Branch Operating Effi ciency: A Comparative Application of DEA and the Loglinear Model. Omega, vol. 19, iss. 6, pp. 549–57.

Glass J. C., McKillop D. G., Morikawa Y. (1998) Intermedication and Value-Added Models for Estimating Cost Economies in Large Japanese Banks 1977–93. Applied Financial Economics, no. 8, pp. 653–61.

Hori K., Yoshida A. (1996) Nihon-No Ginkougyou-No Hiyou Kouritsusei [Measuring Cost Effi ciency in Japanese Banking]. Japanese Journal of Financial Economics, no. 1, pp. 87–110.

Kasuya M. (1986) Economies of Scope: Th eory and Application to Banking. BOJ Monetary and Economic Studies, no. 4, pp. 59–104.

Kasuya M. (1989) Ginkou-No Kosutokouzou-No Jisshobunseki. Kouritsusei, Gijutsusinpo, YosoukankawaseNi Kansuru Gyoutaibetsu Jisshobunseki [Empirical Analysis of Cost Structure in Banking. Empirical Analysis of Effi ciency, Technological Progress and Input Substitution by Industry].

Kinyuu Kenkyuu, no. 8, pp. 79–118. Kittelsen S. A. C. (1999) Monte Carlo Simulations of DEA Effi ciency Measures and Hypothesis Tests. Memorandum 09. Department of Economics, University of Oslo.

Kneip A., Simar L., Wilson P. W. (2008) Asymptotics and Consistent Bootstraps for DEA Estimators in Nonparametric Frontier Models. Econometric Th eory, no. 24, pp. 1663–97.

Kneip A., Simar L., Wilson P. W. (2011) A Computationally Effi cient, Consistent Bootstrap for Inference with Non-Parametric DEA Estimators. Computational Economics, no. 38, pp. 483–515.

Kumbhakar S. C. (2011) Estimation of Multiple Output Production Functions. 2012 spring seminar series April 17. les/seminars/kumbhakar11.pdf: Georgia Tech (аccessed: 06.03. 2019).

Linna M., Hakkinen U., Peltola M., Magnussen J., Anthun K. S., Kittelsen S., Roed A., Olsen K., Medin E., Rehnberg C. (2010) Measuring Cost Effi ciency in the Nordic Hospitals — a Cross-Sectional Comparison of Public Hospitals in 2002. Health Care Management Science, no. 13, pp. 346–57.

Liu J., Tone K. (2008) A Multistage Method to Measure Effi ciency and Its Application to Japanese Banking Industry. Socio-Economic Planning Sciences, no. 42, pp. 75–91.

Liu L., Ondrich J., Ruggiero J. (2012) Estimating Multiple-Input–multiple-Output Production Functions with an Analysis of Credit Unions. Applied Economics, no. 44, pp. 1583–1589.

McKillop D. G., Glass J. C., Morikawa Y. (1996) Th e Composite Cost Function and Effi ciency in Giant Japanese Banks. Journal of Banking and Finance, no. 20, pp. 1651–1671.

Medin E., Anthum K. S., Hakkinen U., Kittelsen S. A. C., Linna M., Magnussen J., Olsen K., Rehnberg C. (2011) Cost Effi ciency of University Hospitals in the Nordic Countries: A Cross-Country Analysis. European Journal of Health Economics, vol. 12, iss. 6, pp. 509–519.

Miyakoshi T., Tsukuda Y. (2004) Regional Disparities in Japanese Banking Performance. RURDS, vol. 16, iss. 1, pp. 74–89.

Resti A. (2000) Effi ciency Measurement for Multi-Product Industries: A Comparison of Classic and Recent Techniques Based on Simulated Data. European Journal of Operational Research, no. 121, pp. 559–78.

Shephard R. W. (1981) Cost and Production Functions. Lecture Notes in Economics and Mathematical Systems. Ed. by M. Beckmann, H. P. Kunzi. Berlin, Heidelberg, New York, Springer-Verlag.

Silverman B. W. (1986) Density Estimation for Statistics and Data Analysis. New York: Chapman; Hall.

Simar L., Wilson P. (1998) Sensitivity Analysis of Effi ciency Scores: How to Bootstrap in Nonparametric Frontier Models. Management Science, no. 44, pp. 49–61.

Simar L., Wilson P. (2000a) A General Methodology for Bootstrapping in Non-Parametric Frontier Models. Journal of Applied Statistics, vol. 27, iss. 6, pp. 779–802.

Simar L., Wilson P. (2000b) Performance of the Bootstrap for DEA Estimators and Iterating the Principle. STAT Discussion Papers 0002.

Simar L., Wilson P. (2002) Non-Parametric Tests of Returns to Scale. European Journal of Operational Research, vol. 139, iss. 1, pp. 115–32.

Simar L., Wilson P. (2007) Estimation and Inference in Two-Stage, Semi-Parametric Models of Production Processes. Journal of Econometrics, no. 136, pp. 31–64.

Simar L., Wilson P. (2008) Statistical Inference in Nonparametric Frontier Models: Recent Developments and Perspectives. The Measurement of Productive Effi ciency and Productivity Growth. Eds H. O. Fried, C. A. K. Lovell, S. S. Schmidt, Oxford University Press, pp. 421–521.

Simar L., Wilson P. (2011a) Inference by the M Out of N Bootstrap in Nonparametric Frontier Models. Journal of Productivity Analysis, no. 36, pp. 33–53.

Simar L., Wilson P. (2011b) Two-Stage DEA: Caveat Emptor. Journal of Productivity Analysis, no. 36, pp. 205–18.

Simm J., Besstremyannaya G. (2016) Robust Data Envelopment Analysis (DEA) for R. Available at: https:// Cran.r (аccessed: 06.03.2019).

Takahashi T. (2000) DEA-Wo Motiiteno Hatansaikenshori-Mo Kamishita Ginkou-No Kouritsusei-No Keisoku [Measurement of Bank Effi ciency with DEA and the Analysis of Bad Loans]. Operations Research, no. 479, pp. 598–602.

Thanassoulis E., Portela M. C. S., Despic O. (2008) Banking. The Measurement of Productive Effi ciency and Productivity Growth.

Eds H. O. Fried, C. A. K. Lovell, S. S. Schmidt. Oxford University Press. Tone K. (2002) A Strange Case of the Cost and Allocative Effi ciencies in DEA. Journal of the Operational Research Society, vol. 53, iss. 11, pp. 1225–31.

Tortosa-Austina E. (2002) Bank Cost Effi ciency and Output Specifi cation. Journal of Productivity Analysis, no. 18, pp. 199–222.

Wang J. C. (2003) Productivity and Economies of Scale in the Production of Bank Service Value Added. Working Paper September. Available at: Research Department, Federal Reserve Bank of Boston (аccessed: 06.03. 2019).

Как цитировать
Besstremyannaya, G., & Simm, J. (2019). Estimation of Cost Efficiency in Non-parametric Frontier Models. Вестник Санкт-Петербургского университета. Экономика, 35(1), 3-21.
Макро- и микроэкономические исследования