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Measuring the efficiency of banks: the bootstrapped I-distance GAR DEA approach

    Milan Radojicic Affiliation
    ; Gordana Savic Affiliation
    ; Veljko Jeremic Affiliation

Abstract

The efficiency of the banking sector, particularly in developing countries, has captivated the attention of various researchers. Contributing to this issue, we present the results of in-depth analysis of the efficiency of Serbian banks during the period 2005–2016. Unlike previous papers evaluating the efficiency of South-Eastern European banks, we emphasize the importance of applying weight restrictions in Data Envelopment Analysis (DEA). The aim is to incorporate every aspect of a decision-making unit’s performance to avoid misevaluation of a bank’s efficiency. As a possible remedy to the issue, a bootstrapped I-distance is suggested as a statistically sound framework for determining weight bounds in the Global Assurance Region (GAR) DEA model. In terms of average efficiency, the banking sector of Serbia exhibits an improving trend over the period analyzed. The results show how banks can be evaluated when the impact of all the operating inputs and outputs are properly factored into the study.

Keyword : efficiency evaluation, data envelopment analysis, weight restriction, bootstrap, I-distance, banking, multivariate statistical methods

How to Cite
Radojicic, M., Savic, G., & Jeremic, V. (2018). Measuring the efficiency of banks: the bootstrapped I-distance GAR DEA approach. Technological and Economic Development of Economy, 24(4), 1581-1605. https://doi.org/10.3846/tede.2018.3699
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Aug 14, 2018
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References

Aiello, F., & Bonanno, G. (2017). On the sources of heterogeneity in banking efficiency literature. Journal of Economic Surveys, 32(1), 194-225. https://doi.org/10.1111/joes.12193

Alhassan, A. L., & Tetteh, M. L. (2017). Non-Interest Income and Bank Efficiency in Ghana: a two-stage DEA bootstrapping approach. Journal of African Business, 18(1), 124-142. https://doi.org/10.1080/15228916.2016.1227668

Allen, R., Athanassopoulos, A., Dyson, R. G., & Thanassoulis, E. (1997). Weights restrictions and value judgements in data envelopment analysis: evolution, development and future directions. Annals of Operations Research, 73, 13-34. https://doi.org/10.1023/A:1018968909638

Andersen, P., & Petersen, N. C. (1993). A procedure for ranking efficient units in data envelopment analysis. Management science, 39(10), 1261-1264. https://doi.org/10.1287/mnsc.39.10.1261

Asmild, M., & Matthews, K. (2012). Multi-directional efficiency analysis of efficiency patterns in Chinese banks 1997–2008. European Journal of Operational Research, 219(2), 434-441. https://doi.org/10.1016/j.ejor.2012.01.001

Avkiran, N. K. (1999). An application reference for data envelopment analysis in branch banking: helping the novice researcher. International Journal of Bank Marketing, 17(5), 206-220. https://doi.org/10.1108/02652329910292675

Avkiran, N. K. (2006). Developing foreign bank efficiency models for DEA grounded in finance theory. Socio-Economic planning sciences, 40(4), 275-296. https://doi.org/10.1016/j.seps.2004.10.006

Avkiran, N. K. (2009). Opening the black box of efficiency analysis: an illustration with UAE banks, Omega, 37(4), 930-941. https://doi.org/10.1016/j.omega.2008.08.001

Avkiran, N. K. (2015). An illustration of dynamic network DEA in commercial banking including robustness tests. Omega, 55, 141-150. https://doi.org/10.1016/j.omega.2014.07.002

Bal, H., Örkcü, H. H., & Çelebioğlu, S. (2010). Improving the discrimination power and weights dispersion in the data envelopment analysis. Computers & Operations Research, 37(1), 99-107. https://doi.org/10.1016/j.cor.2009.03.028

Banker, R. D., Charnes, A., & Cooper, W. W. (1984). Some models for estimating technical and scale inefficiencies in data envelopment analysis. Management Science, 30(9), 1078-1092. https://doi.org/10.1287/mnsc.30.9.1078

Barros, C. P., Chen, Z., Liang, Q. B., & Peypoch, N. (2011). Technical efficiency in the Chinese banking sector. Economic Modelling, 28(5), 2083-2089. https://doi.org/10.1016/j.econmod.2011.04.003

Berger, A. N. (2007). International comparisons of banking efficiency. Financial Markets, Institutions & Instruments, 16(3), 119-144. https://doi.org/10.1111/j.1468-0416.2007.00121.x

Berger, A. N., & Humphrey, D. B. (1997). Efficiency of financial institutions: International survey and directions for future research. European Journal of Operational Research, 98(2), 175-212. https://doi.org/10.1016/S0377-2217(96)00342-6

Bulajic, M., Jeremic, V., Knezevic, S., & Zarkic-Joksimovic, N. (2013). A statistical approach to evaluating efficiency of banks. Economic Research-Ekonomska Istraživanja, 26(4), 91-100. https://doi.org/10.1080/1331677X.2013.11517632

Casu, B., Girardone, C., & Molyneux, P. (2004). Productivity change in European banking: a comparison of parametric and non-parametric approaches. Journal of Banking & Finance, 28(10), 2521-2540. https://doi.org/10.1016/j.jbankfin.2003.10.014

Charnes, A., Cooper, W. W., & Rhodes, E. (1978). Measuring the efficiency of decision making units. European Journal of Operational Research, 2(6), 429-444. https://doi.org/10.1016/0377-2217(78)90138-8

Chiu, C. R., Chiu, Y. H., Fang, C. L., & Pang, R. Z. (2014). The performance of commercial banks based on a context – dependent range – adjusted measure model, International Transactions in Operational Research, 21(5), 761-775. https://doi.org/10.1111/itor.12069

Cook, W. D., & Zhu, J. (2008). CAR-DEA: context-dependent assurance regions in DEA. Operations Research, 56(1), 69-78. https://doi.org/10.1287/opre.1070.0500

Cooper, W. W., Seiford, L. M., & Tone, K. (2006). Introduction to data envelopment analysis and its uses: with DEA-solver software and references. Springer Science & Business Media.

Cvetkoska, V., & Savić, G. (2017). Efficiency of bank branches: empirical evidence from a two-phase research approach. Economic Research-Ekonomska Istraživanja, 30(1), 318-333. https://doi.org/10.1080/1331677X.2017.1305775

Davison, A. C., & Hinkley, D. V. (1997). Bootstrap methods and their application (Vol. 1). Cambridge university press. https://doi.org/10.1017/CBO9780511802843

Davutyan, N., & Yildirim, C. (2017). Efficiency in Turkish banking: post-restructuring evidence. The European Journal of Finance, 23(2), 170-191. https://doi.org/10.1080/1351847X.2015.1049282

Delis, M., Iosifidi, M., & Tsionas, M. G. (2017). Endogenous bank risk and efficiency. European Journal of Operational Research, 260(1), 376-387. https://doi.org/10.1016/j.ejor.2016.12.024

Devaney, M., & Weber, W. L. (2002). Small-business lending and profit efficiency in commercial banking. Journal of Financial Services Research, 22(3), 225-246. https://doi.org/10.1023/A:1019733226515

Dobrota, M., Bulajic, M., Bornmann, L., & Jeremic, V. (2016). A new approach to the QS university ranking using the composite I‐distance indicator: uncertainty and sensitivity analyses. Journal of the Association for Information Science and Technology, 67(1), 200-211. https://doi.org/10.1002/asi.23355

Dobrota, M., Martic, M., Bulajic, M., & Jeremic, V. (2015). Two-phased composite I-distance indicator approach for evaluation of countries’ information development. Telecommunications Policy, 39(5), 406-420. https://doi.org/10.1016/j.telpol.2015.03.003

Dyson, R. G., & Thanassoulis, E. (1988). Reducing weight flexibility in data envelopment analysis. Journal of the Operational Research Society, 39(6), 563-576. https://doi.org/10.1057/jors.1988.96

Efron, B. (1979). Bootstrap methods: another look at the jackknife. The Annals of Statistics, 7(1), 1-26. https://doi.org/10.1214/aos/1176344552

Emrouznejad, A., Banker, R., Lopes, A. L., de Almeida, M. R. (2014). DEA in the public sector. Socioeconomic Planning Sciences, 48(1), 2-3. https://doi.org/10.1016/j.seps.2013.12.005

Emrouznejad, A., & Yang, G. L. (2018). A survey and analysis of the first 40 years of scholarly literature in DEA: 1978–2016. Socio-Economic Planning Sciences, 61, 4-8. https://doi.org/10.1016/j.seps.2017.01.008

Eskelinen, J. (2017). Comparison of variable selection techniques for data envelopment analysis in a retail bank. European Journal of Operational Research, 259(2), 778-788. https://doi.org/10.1016/j.ejor.2016.11.009

Färe, R., Grosskopf, S., Maudos, J., & Tortosa-Ausina, E. (2015). Revisiting the quiet life hypothesis in banking using nonparametric techniques. Journal of Business Economics and Management, 16(1), 159-187. https://doi.org/10.3846/16111699.2012.726929

Ferrier, G. D., & Hirschberg, J. G. (1997). Bootstrapping confidence intervals for linear programming efficiency scores: with an illustration using Italian banking data. Journal of Productivity Analysis, 8(1), 19-33. https://doi.org/10.1023/A:1007768229846

Fethi, M. D., & Pasiouras, F. (2010). Assessing bank efficiency and performance with operational research and artificial intelligence techniques: a survey. European Journal of Operational Research, 204(2), 189-198. https://doi.org/10.1016/j.ejor.2009.08.003

Fukuyama, H., & Matousek, R. (2017). Modelling bank performance: a network DEA approach. European Journal of Operational Research, 259(2), 721-732. https://doi.org/10.1016/j.ejor.2016.10.044

Fukuyama, H., & Weber, W. L. (2002). Estimating output allocative efficiency and productivity change: application to Japanese banks. European Journal of Operational Research, 137(1), 177-190. https://doi.org/10.1016/S0377-2217(01)00054-6

Fukuyama, H., & Weber, W. L. (2017). Japanese bank productivity, 2007–2012: a dynamic network approach. Pacific Economic Review, 22(4), 649-676. https://doi.org/10.1111/1468-0106.12199

Galagedera, D. U. (2014). Modeling risk concerns and returns preferences in performance appraisal: an application to global equity markets. Journal of International Financial Markets, Institutions and Money, 33, 400-416. https://doi.org/10.1016/j.intfin.2014.09.006

Gofman, M. (2017). Efficiency and stability of a financial architecture with too-interconnected-to-fail institutions. Journal of Financial Economics, 124(1), 113-146. https://doi.org/10.1016/j.jfineco.2016.12.009

Gonçalves, A. C., Almeida, R. M., Lins, M. P. E., & Samanez, C. P. (2013). Canonical correlation analysis in the definition of weight restrictions for data envelopment analysis. Journal of Applied Statistics, 40(5), 1032-1043. https://doi.org/10.1080/02664763.2013.772571

Hou, X., Wang, Q., & Zhang, Q. (2014). Market structure, risk taking, and the efficiency of Chinese commercial banks. Emerging Markets Review, 20, 75-88. https://doi.org/10.1016/j.ememar.2014.06.001

Huang, T. H., Lin, C. I., & Chen, K. C. (2017). Evaluating efficiencies of Chinese commercial banks in the context of stochastic multistage technologies. Pacific-Basin Finance Journal, 41, 93-110. https://doi.org/10.1016/j.pacfin.2016.12.008

Isik, I., & Hassan, M. K. (2002). Technical, scale and allocative efficiencies of Turkish banking industry. Journal of Banking & Finance, 26(4), 719-766. https://doi.org/10.1016/S0378-4266(01)00167-4

Išljamović, S., Jeremić, V., Petrović, N., & Radojičić, Z. (2015). Colouring the socio-economic development into green: I-distance framework for countries’ welfare evaluation. Quality & Quantity, 49(2), 617-629. https://doi.org/10.1007/s11135-014-0012-0

Ivanovic, B. (1977). Classification theory. Institute for Industrial Economic, Belgrade.

Jain, V., Kumar, A., Kumar, S., & Chandra, C. (2015). Weight restrictions in data envelopment analysis: a comprehensive genetic algorithm based approach for incorporating value judgments. Expert Systems with Applications, 42(3), 1503-1512.

Jayaraman, A. R., Srinivasan, M. R., & Jeremic, V. (2013). Empirical analysis of banks in India using DBA and DEA. Management, 18(69), 25-35. https://doi.org/10.7595/management.fon.2013.0029

Jeremic, V., Bulajic, M., Martic, M., Markovic, A., Savic, G., Jeremic, D., & Radojicic, Z. (2012). An evaluation of European countries’ health systems through distance based analysis. Hippokratia, 16(2), 170-174.

Jeremic, V., Bulajic, M., Martic, M., & Radojicic, Z. (2011). A fresh approach to evaluating the academic ranking of world universities. Scientometrics, 87(3), 587-596. https://doi.org/10.1007/s11192-011-0361-6

Johnes, J., Izzeldin, M., & Pappas, V. (2014). A comparison of performance of Islamic and conventional banks 2004–2009. Journal of Economic Behavior & Organization, 103, 93-107. https://doi.org/10.1016/j.jebo.2013.07.016

Kao, C., & Liu, S. T. (2004). Predicting bank performance with financial forecasts: a case of Taiwan commercial banks. Journal of Banking & Finance, 28(10), 2353-2368. https://doi.org/10.1016/j.jbankfin.2003.09.008

Kao, C., & Liu, S. T. (2014). Multi-period efficiency measurement in data envelopment analysis: the case of Taiwanese commercial banks. Omega, 47, 90-98. https://doi.org/10.1016/j.omega.2013.09.001

Kao, C., & Liu, S. T. (2016). A parallel production frontiers approach for intertemporal efficiency analysis: the case of Taiwanese commercial banks. European Journal of Operational Research, 255(2), 411-421. https://doi.org/10.1016/j.ejor.2016.04.047

Kevork, I. S., Pange, J., Tzeremes, P., & Tzeremes, N. G. (2017). Estimating Malmquist productivity indexes using probabilistic directional distances: an application to the European banking sector. European Journal of Operational Research, 261(3), 1125-1140. https://doi.org/10.1016/j.ejor.2017.03.012

Kumar, M., Charles, V., & Mishra, C. S. (2016). Evaluating the performance of indian banking sector using DEA during post-reform and global financial crisis. Journal of Business Economics and Management, 17(1), 156-172. https://doi.org/10.3846/16111699.2013.809785

Kuosmanen, T., & Post, T. (2001). Measuring economic efficiency with incomplete price information: with an application to European commercial banks. European Journal of Operational Research, 134(1), 43-58. https://doi.org/10.1016/S0377-2217(00)00237-X

Le, P. T., Harvie, C., & Arjomandi, A. (2017). Testing for differences in technical efficiency among groups within an industry. Applied Economics Letters, 24(3), 159-162. https://doi.org/10.1080/13504851.2016.1173172

Liu, J. S., Lu, L.Y., & Lu, W. M. (2016). Research fronts in data envelopment analysis. Omega, 58, 33-45. https://doi.org/10.1016/j.omega.2015.04.004

Liu, J. S., Lu, L. Y., Lu, W. M., Lin, B. J. (2013). Data envelopment analysis 1978–2010: a citation-based literature survey. Omega, 41(1), 3-15. https://doi.org/10.1016/j.omega.2010.12.006

Mandic, K., Delibasic, B., Knezevic S., & Benkovic, S. (2017). Analysis of the efficiency of insurance companies in Serbia using the fuzzy AHP and TOPSIS methods. Economic Research-Ekonomska Istraživanja, 30(1), 550-565. https://doi.org/10.1080/1331677X.2017.1305786

Marković, M., Knežević, S., Brown, A., & Dmitrović, V. (2015). Measuring the productivity of Serbian banks using Malmquist index. Management: Journal of Sustainable Business and Management Solutions in Emerging Economies, 20(76), 1-10. https://doi.org/10.7595/management.fon.2015.0022

Mecit, E. D., & Alp, I. (2013). A new proposed model of restricted data envelopment analysis by correlation coefficients. Applied Mathematical Modelling, 37(5), 3407-3425. https://doi.org/10.1016/j.apm.2012.07.010

Mihailović, N., Bulajić M., & Savić, G. (2009). Ranking of banks in Serbia. Yugoslav Journal of Operations Research, 19(2), 323-334. https://doi.org/10.2298/YJOR0902323M

Moradi‐Motlagh, A., & Saleh, A. S. (2014). Re‐examining the technical efficiency of Australian banks: a Bootstrap DEA Approach. Australian Economic Papers, 53(1-2), 112-128. https://doi.org/10.1111/1467-8454.12024

Mukherjee, A., Nath, P., & Nath Pal, M. (2002). Performance benchmarking and strategic homogeneity of Indian banks. International Journal of Bank Marketing, 20(3), 122-139. https://doi.org/10.1108/02652320210430965

Nurboja, B., & Košak, M. (2017). Banking efficiency in South East Europe: evidence for financial crises and the gap between new EU members and candidate countries. Economic Systems, 41(1), 122-138. https://doi.org/10.1016/j.ecosys.2016.05.006

Paradi, J. C., & Zhu, H. (2013). A survey on bank branch efficiency and performance research with data envelopment analysis. Omega, 41(1), 61-79. https://doi.org/10.1016/j.omega.2011.08.010

Paul, S., & Kourouche, K. (2008). Regulatory policy and the efficiency of the banking sector in Australia. Australian Economic Review, 41(3), 260-271. https://doi.org/10.1111/j.1467-8462.2008.00504.x

Podinovski, V. V. (2005). The explicit role of weight bounds in models of data envelopment analysis. Journal of the Operational Research Society, 56(12), 1408-1418. https://doi.org/10.1057/palgrave.jors.2601969

Podinovski, V. V. (2016). Optimal weights in DEA models with weight restrictions. European Journal of Operational Research, 254(3), 916-924. https://doi.org/10.1016/j.ejor.2016.04.035

Psillaki, M., & Mamatzakis, E. (2017). What drives bank performance in transitions economies? The impact of reforms and regulations. Research in International Business and Finance, 39, 578-594. https://doi.org/10.1016/j.ribaf.2016.09.010

Puri, J., & Yadav, S. P. (2013). A concept of fuzzy input mix-efficiency in fuzzy DEA and its application in banking sector. Expert Systems with Applications, 40(5), 1437-1450. https://doi.org/10.1016/j.eswa.2012.08.047

Radojicic, M., Savic, G., Radovanovic, S., & Jeremic, V. (2015, September). A novel bootstrap DBA-DEA approach in evaluating efficiency of banks. 12th Balkan Conference on Operational Research – BALCOR (pp. 375-384), Constanta, Romania.

Ray, S. C., & Das, A. (2010). Distribution of cost and profit efficiency: evidence from Indian banking. European Journal of Operational Research, 201(1), 297-307. https://doi.org/10.1016/j.ejor.2009.02.030

Řepková, I. (2014). Efficiency of the Czech banking sector employing the DEA window analysis approach. Procedia Economics and Finance, 12, 587-596. https://doi.org/10.1016/S2212-5671(14)00383-9

Sahoo, B. K., & Tone, K. (2009). Decomposing capacity utilization in data envelopment analysis: an application to banks in India. European Journal of Operational Research, 195(2), 575-594. https://doi.org/10.1016/j.ejor.2008.02.017

Sarrico, C. S., & Dyson, R. G. (2004). Restricting virtual weights in data envelopment analysis. European Journal of Operational Research, 159(1), 17-34. https://doi.org/10.1016/S0377-2217(03)00402-8

Savic, G., Radosavljevic, M., & Ilievski, D. (2012). DEA window analysis approach for measuring the efficiency of Serbian banks based on panel data. Management, 17(65), 5-14. https://doi.org/10.7595/management.fon.2012.0028

Scalzer, R. S., Rodrigues, A., Macedo, M. Á. D. S., & Wanke, P. (2018). Insolvency of Brazilian electricity distributors: a DEA bootstrap approach. Technological and Economic Development of Economy, 24(2), 718-738. https://doi.org/10.3846/20294913.2017.1318312

Seifert, L. M., & Zhu, J. (1998). Identifying excesses and deficits in Chinese industrial productivity (1953–1990): a weighted data envelopment analysis approach. Omega, 26(2), 279-296. https://doi.org/10.1016/S0305-0483(98)00011-5

Shang, J., & Sueyoshi, T. (1995). A unified framework for the selection of a flexible manufacturing system. European Journal of Operational Research, 85(2), 297-315. https://doi.org/10.1016/0377-2217(94)00041-A

Silva, T. C., Tabak, B. M., Cajueiro, D. O., Dias, M. V. B. (2017). A comparison of DEA and SFA using micro-and macro-level perspectives: efficiency of Chinese local banks. Physica A: Statistical Mechanics and its Applications, 469, 216-223. https://doi.org/10.1016/j.physa.2016.11.041

Simar, L. (2007). How to improve the performances of DEA/FDH estimators in the presence of noise?. Journal of Productivity Analysis, 28(3), 183-201. https://doi.org/10.1007/s11123-007-0057-3

Simar, L., & Wilson, P. W. (1998). Sensitivity analysis of efficiency scores: how to bootstrap in nonparametric frontier models. Management Science, 44(1), 49-61. https://doi.org/10.1287/mnsc.44.1.49

Simar, L., & Wilson, P. W. (2007). Estimation and inference in two-stage, semi-parametric models of production processes. Journal of Econometrics, 136(1), 31-64. https://doi.org/10.1016/j.jeconom.2005.07.009

Simar, L., & Zelenyuk, V. (2011). Stochastic FDH/DEA estimators for frontier analysis. Journal of Productivity Analysis, 36(1), 1-20. https://doi.org/10.1007/s11123-010-0170-6

Simper, R., Hall, M. J., Liu, W., Zelenyuk, V., & Zhou, Z. (2017). How relevant is the choice of risk management control variable to non-parametric bank profit efficiency analysis? The case of South Korean banks. Annals of Operations Research, 250(1), 105-127. https://doi.org/10.1007/s10479-015-1946-x

Staub, R. B., Souza, G. D. S., & Tabak, B. M. (2010). Evolution of bank efficiency in Brazil: A DEA approach. European Journal of Operational Research, 202(1), 204-213. https://doi.org/10.1016/j.ejor.2009.04.025

Stewart, C., Matousek, R., & Nguyen, T. N. (2016). Efficiency in the Vietnamese banking system: a DEA double bootstrap approach. Research in International Business and Finance, 36, 96-111. https://doi.org/10.1016/j.ribaf.2015.09.006

Takamura, Y., & Tone, K. (2003). A comparative site evaluation study for relocating Japanese government agencies out of Tokyo. Socio-Economic Planning Sciences, 37(2), 85-102. https://doi.org/10.1016/S0038-0121(02)00049-6

Tan, Y., Floros, C., & Anchor, J. (2017). The profitability of Chinese banks: impacts of risk, competition and efficiency. Review of Accounting and Finance, 16(1), 86-105. https://doi.org/10.1108/RAF-05-2015-0072

Tandon, D., Tandon, K., & Malhotra, N. (2014). An evaluation of the technical, pure technical and scale efficiencies in the Indian banking industry using data envelope analysis. Global Business Review, 15(3), 545-563. https://doi.org/10.1177/0972150914535141

Tanna, S., Luo, Y., & De Vita, G. (2017). What is the net effect of financial liberalization on bank productivity? A decomposition analysis of bank total factor productivity growth. Journal of Financial Stability, 30, 67-78. https://doi.org/10.1016/j.jfs.2017.04.003

Taylor, W. M., Thompson, R. G., Thrall, R. M., & Dharmapala, P. S. (1997). DEA/AR efficiency and profitability of Mexican banks a total income model. European Journal of Operational Research, 98(2), 346-363. https://doi.org/10.1016/S0377-2217(96)00352-9

Thanassoulis, E., Boussofiane, A., & Dyson, R. G. (1995). Exploring output quality targets in the provision of perinatal care in England using data envelopment analysis. European Journal of Operational Research, 80(3), 588-607. https://doi.org/10.1016/0377-2217(94)00139-4

Thompson, R. G., Langemeier, L. N., Lee, C. T., Lee, E., & Thrall, R. M. (1990). The role of multiplier bounds in efficiency analysis with application to Kansas farming. Journal of Econometrics, 46(1-2), 93-108. https://doi.org/10.1016/0304-4076(90)90049-Y

Thompson, R. G., Singleton Jr, F. D., Thrall, R. M., Smith, B. A. (1986). Comparative site evaluations for locating a high-energy physics lab in Texas. Interfaces, 16(6), 35-49. https://doi.org/10.1287/inte.16.6.35

Thoraneenitiyan, N., & Avkiran, N. K. (2009). Measuring the impact of restructuring and countryspecific factors on the efficiency of post-crisis East Asian banking systems: integrating DEA with SFA. Socio-Economic Planning Sciences, 43(4), 240-252. https://doi.org/10.1016/j.seps.2008.12.002

Tortosa-Ausina, E., Grifell-Tatjé, E., Armero, C., & Conesa, D. (2008). Sensitivity analysis of efficiency and Malmquist productivity indices: an application to Spanish savings banks. European Journal of Operational Research, 184(3), 1062-1084. https://doi.org/10.1016/j.ejor.2006.11.035

Tsionas, E. G., & Mamatzakis, E. C. (2017). Adjustment costs in the technical efficiency: an application to global banking. European Journal of Operational Research, 256(2), 640-649. https://doi.org/10.1016/j.ejor.2016.06.037

Wong, Y. H., & Beasley, J. E. (1990). Restricting weight flexibility in data envelopment analysis. Journal of the Operational Research Society, 41(9), 829-835. https://doi.org/10.1057/jors.1990.120

Yu, M. M. (2012). An integration of the multi-component DEA and GAR models to the measurement of hotel performance. Current Issues in Tourism, 15(5), 461-476. https://doi.org/10.1080/13683500.2011.613985

Zelenyuk, N., & Zelenyuk, V. (2014, December). Regional and ownership drivers of bank efficiency. 27th Australasian Finance and Banking Conference. Sydney, Australia.

Zhu, J. (1996). DEA/AR analysis of the 1988–1989 performance of the Nanjing textiles corporation. Annals of Operations Research, 66(5), 311-335. https://doi.org/10.1007/BF02188949