Investment efficiency of life insurance companies in Germany: application of a two-stage SBM

  • Thomas Krupa University of Kobe
  • Kirils Farbarzevics Hamburger FH University of Applied Sciences
  • Bassam Salame Faculty of Economics, University of Gdansk
Keywords: DEA-SBM, Efficiency, OLS, Investment, Insurance, Tobit


Purpose – To prove the robustness of the efficiency-measuring model against potentially system-relevant disturbances to company variables such as SIZE, ROA, solvency and organizational form.

Methodology – In the first stage, the established model is applied using the SBM to measure insurance efficiency. The underlying data sets are from the twenty biggest life insurance companies (2008-2017) in Germany. In the second stage, the established model is examined for its robustness against disturbance variables. Several disturbance variables are introduced individually to the system and examined for their influence by three econometric methods, Tobit regression, OLS and the fixed-effect model. This approach allows a comparative analysis of the results with respect to the systemic relevance of every added variable. In the end, the accuracy of the second stage is compared through the Spearman test.

Findings – The comparative analysis of all three econometric techniques brought ROA as an efficiency-influencing variable. Furthermore, both proved econometric models Tobit and OLS are SBM-suitable with cross-sectional data. Further evidence for SBM compatibility are found for Tobit and the fixed-effect model with panel data. 

JEL classification: C510, C520


§ 8 (2) VAG Versicherungsaufsichtsgesetz (engl.: Insurance Supervision Law), online:, accessed 20.10.2018.

Abidin, Z., Cabanda, E. (2011). Efficiency of Non-life Insurance in Indonesia. Journal of Economics, Business, & Accountancy, 14 (3), 1-11.

Banker, R. D., Charnes, A., Cooper, W. W. (1984). Some models for the estimation of technical and scale inefficiencies in data envelopment analysis. Management Science, 30(9), 1078 - 1092.

Black, K. Jr., Skipper, H. D. Jr. (2000). Life & Health Insurance. Prentice Hall. Inc., New Jersey.

Breuer, C., Breuer, W., (2003). Versicherungsvereine auf Gegenseitigkeit versus Versicherungsaktiengesellschaften (engl.: Mutual insurance companies versus insurance corporations). Wirtschaftswissenschaftliches Studium - Zeitschrift für Studium und Forschung, 32 (2), 70-75.

Bureau van Dijk (2018). German life insurance companies. Moody’s Analytics InsuranceFocus, available at: international/insurancefocus, accessed 15.07.2018.

Charnes, A., Cooper, W. W., Rhodes, E. (1978). Measuring the efficiency of decision making units. European Journal of Operational Research, 2, 429-444.

Eling, M., Luhnen, M. (2008). Frontier efficiency methodologies to measure performance in the insurance industry: overview and new empirical evidence. Working paper 56, University of St. Gallen, July 2008.

Grmanová, E. (2016). Influence of selected factors on the efficiency of insurance companies. Journal of Management, 29 (2), 71 - 76.

Grmanová, E., Strunz, H. (2017). Efficiency of insurance companies: Application of DEA and Tobit analyses. Journal of International Studies, 10(3), 250-263.

Gujarati, D. N. (2003). Basic econometrics. McGraw Hill, Boston.

Hoff, A. (2007). Second stage DEA: Comparison of approaches for modelling the DEA score. European Journal of Operational Research, 181 (1), 425-435.

Kürn, T. (2001). Die Rechtsform des VVaG als Wettbewerbsnachteil? Die Problematik der Eigenmittelbeschaffung bei den Versicherungsvereinen auf Gegenseitigkeit (engl.: The legal form of the VVaG as a competitive disadvantage? The issue of own funds procurement with the mutual insurance companies. Freie Universität Berlin.

Lu, W.-M., Wang, W.-K., Kweh, Q. L. (2014). Intellectual capital and performance in the Chinese life insurance industry. Omega, 42, 65-74.

Luhnen, M. (2009). Determinants of Efficiency and Productivity in German Property-Liability Insurance: Evidence for 1995–2006. The Geneva Papers on Risk and Insurance – Issues and Practice, 34 (3), 483-505.

Mahlberg, B., Url, T. (2010). Single market effects on productivity in the German insurance industry. Journal of Banking and Finance (34), 1540-1548.

McDonald, J. (2009). Using Least Squares and Tobit in Second Stage DEA Efficiency Analyses. Flinders University, Adelaide.

Tobin, J. (1958). Estimation of Relationships for Limited Dependent Variables. Econometrica, 26, 24-36.

Tone, K. (2001). A slacks-based measure of efficiency in data envelopment analysis. European Journal of Operational Research, 130, 498-509.

Tone, K., Tsutsui, M. (2009). Network DEA: A slacks-based measure approach. European Journal of Operation Research, 197 (2009), 243–252.

Wang, K., Huang, W., Wu, J., Liu, Y.-N. (2013). Efficiency measures oft the Chinese commercial banking system using an additive two-stage DEA. Omega, 44, 5-20.

Wooldridge, J. M. (2012). Introductory Econometrics: A modern approach. 5th Edition, Cengage Learning, South-Western.

Yakob, R., Yusop, Z., Radam, A., Ismael, N. (2014). Two-stage DEA Method in Identifying the Exogenous Factors of Insurers: Risk and Investment Management Efficiency. Sains Malaysiana, 43(9), 1439- 1450.

How to Cite
Krupa, T., Farbarzevics, K., & Salame, B. (2019). Investment efficiency of life insurance companies in Germany: application of a two-stage SBM. Contemporary Economy, 10(1 (32), 79-91.