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A New Approach to Dealing With Negative Numbers in Efficiency Analysis: An Application to the Indonesian Banking Sector


  • Muliaman D. Hadad

    (Bank Indonesia, Jakarta, Indonesia)

  • Maximilian J. B. Hall

    () (Dept of Economics, Loughborough University)

  • Wimboh Santoso

    (Bank Indonesia, Jakarta, Indonesia)

  • Karligash Kenjegalieva

    () (Dept of Economics, Loughborough University)

  • Richard Simper

    () (Dept of Economics, Loughborough University)


In one of the first stand-alone studies covering the whole of the Indonesian banking industry, and utilising a unique dataset provided by the Indonesian central bank, this paper analyses the levels of intermediation-based efficiency obtaining during the period 2003-2007. Using a new approach (i.e., semi-oriented radial measure Data Envelopment Analysis, or ‘SORM DEA’) to handling negative numbers (Emrouznejad et al., 2010) and combining it with Tone’s (2001) slacks-based model (SBM) to form an input-oriented, non-parametric SORM SBM model, we firstly estimate the relative average efficiencies of Indonesian banks, both overall, by group, as determined by their ownership structure, and by status (‘listed’/’Islamic’). For robustness, a range-directional (RD) model suggested by Silva Portela et al. (2004) was also employed to handle the negative numbers. In the second part of the analysis, we adopt Simar and Wilson’s (2007) bootstrapping methodology to formally test for the impact of size, ownership structure and status on Indonesian bank efficiency. In addition, we formally test the two models most widely suggested in the literature for controlling for bank risk – namely, those involving the inclusion of provisions for loan losses and equity capital respectively as inputs – to check the robustness of the results to the choice of risk variable. The results demonstrate a high degree of sensitivity of the average bank efficiency scores to the choice of methodology for handling negative numbers – with the RD model consistently delivering efficiency scores some 14% on average above those from the SORM SBM model – and to the choice of risk control variable under the RD model, but only a limited sensitivity to the choice of risk control variable under the SORM SBM model. With respect to group rankings, most model combinations find the ‘state-owned’ group to be the most efficient, with average overall efficiency levels ranging between 64% and 97%; while all model combinations find the ‘regional government-owned’ group to be the least efficient, with average overall efficiency levels ranging between 41% and 64%. As for the impact of bank ‘status’ on the efficiency scores, both the Islamic banks and the listed banks perform better than the industry average in the majority of model combinations. Finally, the results for the impact of scale on the efficiency scores are ambiguous. Under the RD model, and irrespective of the choice of risk control variable, size is very important in determining intermediation-based efficiency. Under the SORM SBM model, however, large banks’ performance is not significantly different from that of the medium-sized banks when equity capital is used as the risk control variable, although the medium-sized banks do out-perform small banks. Moreover, when loan loss provisions are used as the risk control variable, medium-sized banks are shown to significantly out-perform both large and small banks, with the large banks being the least efficient.

Suggested Citation

  • Muliaman D. Hadad & Maximilian J. B. Hall & Wimboh Santoso & Karligash Kenjegalieva & Richard Simper, 2009. "A New Approach to Dealing With Negative Numbers in Efficiency Analysis: An Application to the Indonesian Banking Sector," Discussion Paper Series 2009_20, Department of Economics, Loughborough University, revised Dec 2009.
  • Handle: RePEc:lbo:lbowps:2009_20

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    References listed on IDEAS

    1. Laeven, Luc & Majnoni, Giovanni, 2003. "Loan loss provisioning and economic slowdowns: too much, too late?," Journal of Financial Intermediation, Elsevier, vol. 12(2), pages 178-197, April.
    2. Tortosa-Ausina, Emili, 2002. "Exploring efficiency differences over time in the Spanish banking industry," European Journal of Operational Research, Elsevier, vol. 139(3), pages 643-664, June.
    3. Leopold Simar & Valentin Zelenyuk, 2006. "On Testing Equality of Distributions of Technical Efficiency Scores," Econometric Reviews, Taylor & Francis Journals, vol. 25(4), pages 497-522.
    4. Drake, Leigh & Hall, Maximilian J.B. & Simper, Richard, 2009. "Bank modelling methodologies: A comparative non-parametric analysis of efficiency in the Japanese banking sector," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 19(1), pages 1-15, February.
    5. Akhigbe, Aigbe & McNulty, James E., 2003. "The profit efficiency of small US commercial banks," Journal of Banking & Finance, Elsevier, vol. 27(2), pages 307-325, February.
    6. repec:pal:jorsoc:v:55:y:2004:i:10:d:10.1057_palgrave.jors.2601768 is not listed on IDEAS
    7. Drake, Leigh & Hall, Maximilian J. B., 2003. "Efficiency in Japanese banking: An empirical analysis," Journal of Banking & Finance, Elsevier, vol. 27(5), pages 891-917, May.
    8. Williams, Jonathan & Nguyen, Nghia, 2005. "Financial liberalisation, crisis, and restructuring: A comparative study of bank performance and bank governance in South East Asia," Journal of Banking & Finance, Elsevier, vol. 29(8-9), pages 2119-2154, August.
    9. Emrouznejad, Ali & Anouze, Abdel Latef & Thanassoulis, Emmanuel, 2010. "A semi-oriented radial measure for measuring the efficiency of decision making units with negative data, using DEA," European Journal of Operational Research, Elsevier, vol. 200(1), pages 297-304, January.
    10. Charnes, A. & Cooper, W. W. & Rhodes, E., 1978. "Measuring the efficiency of decision making units," European Journal of Operational Research, Elsevier, vol. 2(6), pages 429-444, November.
    11. Simar, Leopold & Wilson, Paul W., 2007. "Estimation and inference in two-stage, semi-parametric models of production processes," Journal of Econometrics, Elsevier, vol. 136(1), pages 31-64, January.
    12. Sato, Yuri, 2005. "Bank restructuring and financial institution reform in Indonesia," The Developing Economies, Institute of Developing Economies, Japan External Trade Organization(JETRO), vol. 43(1), pages 91-120, March.
    13. Kenjegalieva, Karligash & Simper, Richard & Weyman-Jones, Tom & Zelenyuk, Valentin, 2009. "Comparative analysis of banking production frameworks in eastern european financial markets," European Journal of Operational Research, Elsevier, vol. 198(1), pages 326-340, October.
    14. Altunbas, Yener & Liu, Ming-Hau & Molyneux, Philip & Seth, Rama, 2000. "Efficiency and risk in Japanese banking," Journal of Banking & Finance, Elsevier, vol. 24(10), pages 1605-1628, October.
    15. R. D. Banker & A. Charnes & W. W. Cooper, 1984. "Some Models for Estimating Technical and Scale Inefficiencies in Data Envelopment Analysis," Management Science, INFORMS, vol. 30(9), pages 1078-1092, September.
    16. Tone, Kaoru, 2001. "A slacks-based measure of efficiency in data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 130(3), pages 498-509, May.
    17. Fethi, Meryem Duygun & Pasiouras, Fotios, 2010. "Assessing bank efficiency and performance with operational research and artificial intelligence techniques: A survey," European Journal of Operational Research, Elsevier, vol. 204(2), pages 189-198, July.
    18. Sealey, Calvin W, Jr & Lindley, James T, 1977. "Inputs, Outputs, and a Theory of Production and Cost at Depository Financial Institutions," Journal of Finance, American Finance Association, vol. 32(4), pages 1251-1266, September.
    19. Scheel, Holger, 2001. "Undesirable outputs in efficiency valuations," European Journal of Operational Research, Elsevier, vol. 132(2), pages 400-410, July.
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    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.

    Cited by:

    1. repec:spt:apfiba:v:7:y:2017:i:5:f:7_5_2 is not listed on IDEAS
    2. Mihăiță-Cosmin M. POPOVICI, 2013. "A Survey On Bank Efficiency Research With Data Envelopment Analysis And Stochastic Frontier Analysis," SEA - Practical Application of Science, Fundația Română pentru Inteligența Afacerii, Editorial Department, issue 1, pages 134-142, June.
    3. Mihăiță-Cosmin M. Popovici, 2013. "Latest Challenges In Efficiency Convergence In Balkan And Baltic Countries," Network Intelligence Studies, Fundația Română pentru Inteligența Afacerii, Editorial Department, issue 2, pages 110-118, October.
    4. Cheng, Gang & Zervopoulos, Panagiotis & Qian, Zhenhua, 2013. "A variant of radial measure capable of dealing with negative inputs and outputs in data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 225(1), pages 100-105.
    5. Wahyoe Soedarmono & Philippe Rous & Amine Tarazi, 2011. "Bank Capital and Self-Interested Managers: Evidence from Indonesia," Working Papers hal-00918584, HAL.
    6. Richard Simper & Maximilian J.B. Hall & Wenbin B. Liu & Valentin Zelenyuk & Zhongbao Zhou, 2014. "How Relevant is the Choice of Risk Management Control Variable to Non-parametric Bank Profit Efficiency Analysis?," CEPA Working Papers Series WP122014, School of Economics, University of Queensland, Australia.
    7. repec:cmj:journl:y:2013:i:27:popovicimc is not listed on IDEAS

    More about this item


    Indonesian Finance and Banking; Efficiency.;

    JEL classification:

    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • G21 - Financial Economics - - Financial Institutions and Services - - - Banks; Other Depository Institutions; Micro Finance Institutions; Mortgages

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