Data Envelopment Analysis with Missing Data: An Application to Life Insurance Industry in Taiwan


  • Yao-Hung Yang Doctor, Department of Business Administration Chung Yuan Christian University, Taiwan 200, Chung Pei Rd. Chung Li, 32023 Taiwan
  • Yueh-Chiang Lee Assistant Professor, Department of Business Administration Vanung University, Taiwan



Financial holding company, Fuzzy data envelopment analysis model, Life insurance, Operational efficiency.


A fuzzy Data Envelopment Analysis model is adopted in this paper to assess the operational efficiency of life insurance companies in Taiwan. The study was conducted from 2008 to 2012 and the data were taken from Taiwan Economic Journal and related financial statements provided by the Taiwan Insurance Institute. The results indicate that the operational efficiency of insurance companies affiliated to financial holding companies appears to be better than that of insurance companies not affiliated with financial holding companies, signifying that the synergy generated after a financial holding company is formed and the cross-selling between its subsidiary groups are highly beneficial to the management of a life insurance company affiliated to such a financial holding company. The chief contribution of this paper is that, in the past, the data envelopment analysis models applied often could not calculate due to missing input and output data. The study adopts the fuzzy linear mathematics to solve the uncertainty.


Barros CP., Nektarios M. Assaf A., 2010. Efficiency in the Greek insurance industry. European Journal of Operational Research, 205(2): 431-436.

Berger AN., Hunter W C., Timme S G., 1993. The efficiency of financial institutions: A review and preview of research past, present and future. Journal of Banking & Finance, 17(2-3): 221-249.

Bonin JP., Hasan, I., Wachtel P., 2005. Bank performance, efficiency and ownership in transition countries. Journal of Banking and Finance, 29: 31-51.

Bowlin W., 1987. Evaluating the efficiency of US Air Force real-property maintenance activities. Journal of the perational Research Society, 38(2): 127-135.

Chen CB., Klein, CM., 1997. A simple approach to ranking a group of aggregated fuzzy utilities. IEEE Transactions on Systems, Man Cybernet. Part B: Cybernet, 27(1): 26-35.

Cummins JD., Tennyson S., Weiss MA., 1999. Consolidation and efficiency in the US life insurance industry. Journal of Banking and Finance, 23(2-4): 325-357.

Diacon SR., 2001. The efficiency of UK general insurance companies. Working Paper, Centre for Risk & Insurance Studies, University of Nottingham.

Donni O., Fecher F., 1997. Efficiency and productivity of the insurance industry in the OECD countries. The Geneva Papers on Risk and Insurance-Issues and Practice, 22(84): 523-535.

Fukuyama H., 1997. Investigating productive efficiency and productivity changes of Japanese life insurance companies. Pacific-Basin Finance Journal, 5 (4): 481-509.

Golany B., Roll Y., 1989. An application procedure for DEA. OMEGA, 17(3): 237-250.

Hsieh LF., Hsu SM., 2009. A new fuzzy DEA ranking model with an application for bank branch performance evaluation. Journal of Management & Systems, 16(3): 469-486.

Hu JL., Yu S., Lin FL., 2012. Efficiency analysis of life insurance companies in Taiwan: A two-stage data envelopment analysis. Insurance Issues and Practices, 11(1): 21-42.

Inuiguchi M., Tanino T., 2000. Data envelopment analysis with fuzzy input-output data. In Y. Y. Haimes and R. E. Steuer (Eds.), Research and Practice in Multiple Criteria Decision Making, Springer-Verlag, Berlin, 296-307.

Isik I., Hassan MK., 2002. Technical, scale and allocative efficiencies of Turkish banking industry. Journal of Banking and Finance, 26(4): 719-766.

Kao C., Liu S T., 2000. Data envelopment analysis with missing data: An application to university libraries in Taiwan. Journal of the Operational Research Society, 51: 897-905.

Kao C., Liu ST., 2004. Predicting bank performance with financial forecasts: A case of Taiwan commercial banks. Journal of Banking and Finance, 28(10): 2353-2368.

Lovell CAK., Pastor JT., 1995. Units invariant and translation invariant DEA models. Operations Research Letters, 18(3): 147-151.

Lu YH., Wang CH., Lee CH., 2011. The differences in technology efficiency of Taiwan's life insurance companies – The application of the Metafrontier DEA model. Journal of Economics and Management, 7(1): 73-100.

Luhnen M., 2009. Determinants of efficiency and productivity in German property-liability insurance: evidence for 1995–2006. The Geneva Papers on Risk and Insurance, 34(3): 483-505.

Norman M., Stocker B., 1991. Data envelopment analysis: The assessment of performance? John Wiley and Sons.

Seiford LM., Zhu J., 1999. Profitability and marketability of the top 55 U.S. commercial banks. Management Science, 45(9): 1270-1288.

Yang Z., 2006. A two-stage DEA model to evaluate the overall performance of Canadian life and health insurance companies. Mathematical and Computer Modeling, 43(7-8): 910-919.