The Geneva Risk and Insurance Review

, Volume 44, Issue 1, pp 87–135 | Cite as

Insurer commitment and dynamic pricing pattern

  • Ruo Jia
  • Zenan WuEmail author
Original Article


A central issue in dynamic contracting is the type of inter-temporal pricing pattern. Some insurance products exhibit a highballing (front-loaded) pattern and others a lowballing (back-loaded) pattern, while still others are flat. We develop a unified competitive dynamic insurance model with asymmetric learning to investigate the impact of insurer commitment on the equilibrium inter-temporal pricing pattern. The model predicts that the equilibrium contract exhibits highballing under one-sided commitment and lowballing under no commitment. We then use a unique empirical setting of two products from one insurer, eliminating heterogeneity in firm, market, time horizon, and learning environment, to isolate the role of insurer commitment in determining the pricing pattern. Consistent with our theoretical predictions, we find that (i) the dynamic contracts exhibit a highballing pattern in loaner’s personal accident insurance, a one-sided commitment scenario, and (ii) a lowballing pattern in group critical illness insurance, a no-commitment scenario.


Dynamic contract Commitment Asymmetric learning Information asymmetry Inter-temporal pricing 

JEL Classification

D86 G22 



The authors thank Christian Biener, Alexander Braun, Martin Brown, Richard Butler, Martin Eling, Roland Füss, Felix Irresberger, Andreas Landmann, Tore Nilssen, Joan Schmit, Ruilin Tian, and Wei Zheng, as well as participants in the 2016 ARIA and APRIA conferences, and the 2017 Risk Theory Society Annual Seminar for useful comments and discussions. We thank Shuyan Liu and Linsheng Zhuang for their assistance. We thank the financial support from National Natural Science Foundation of China (Nos. 71703003 and 71803003), and the seeds fund of School of Economics, Peking University. All remaining errors are our own.


  1. Chan, C.S.C. 2009. Creating a market in the presence of cultural resistance: The case of life insurance in China. Theory and Society 38 (3): 271–305.Google Scholar
  2. Chan, L.F., Y. Huang, and L.Y. Tzeng. 2016. Who obtains greater discounts on automobile insurance premiums? Geneva Risk and Insurance Review 41 (1): 48–72.Google Scholar
  3. Chiappori, P.A., and B. Salanié. 2000. Testing for asymmetric information in insurance markets. Journal of Political Economy 108 (1): 56–78.Google Scholar
  4. Chiappori, P.A., and B. Salanié. 2013. Asymmetric information in insurance markets: Predictions and tests. In Handbook of insurance, ed. G. Dionne, 397–422. New York: Springer.Google Scholar
  5. Cochrane, J.H. 1995. Time-consistent health insurance. Journal of Political Economy 103 (3): 445–473.Google Scholar
  6. Cohen, A. 2012. Asymmetric learning in repeated contracting: An empirical study. Review of Economics and Statistics 94 (2): 419–432.Google Scholar
  7. Conniffe, D. 2007. The flexible three parameter utility function. Annals of Economics and Finance 8 (1): 57–63.Google Scholar
  8. Cooper, R., and B. Hayes. 1987. Multi-period insurance contracts. International Journal of Industrial Organization 5 (2): 211–231.Google Scholar
  9. Cox, L.A., and Y. Ge. 2004. Temporal profitability and pricing of long-term care insurance. Journal of Risk and Insurance 71 (4): 677–705.Google Scholar
  10. Crocker, K.J., and J.R. Moran. 2003. Contracting with limited commitment: Evidence from employment-based health insurance contracts. RAND Journal of Economics 34 (4): 694–718.Google Scholar
  11. D’Arcy, S.P., and N.A. Doherty. 1990. Adverse selection, private information, and lowballing in insurance markets. Journal of Business 63 (2): 145–164.Google Scholar
  12. de Garidel-Thoron, T. 2005. Welfare-improving asymmetric information in dynamic insurance markets. Journal of Political Economy 113 (1): 121–150.Google Scholar
  13. Dionne, G. 1983. Adverse selection and repeated insurance contracts. Geneva Papers on Risk and Insurance—Issues and Practice 8 (4): 316–332.Google Scholar
  14. Dionne, G., and N.A. Doherty. 1994. Adverse selection, commitment, and renegotiation: Extension to and evidence from insurance markets. Journal of Political Economy 102 (2): 209–235.Google Scholar
  15. Dionne, G., and P. Lasserre. 1985. Adverse selection, repeated insurance contracts and announcement strategy. Review of Economic Studies 52 (4): 719–723.Google Scholar
  16. Dionne, G., and P. Lasserre. 1987. Adverse selection and finite-horizon insurance contracts. European Economic Review 31 (4): 843–861.Google Scholar
  17. Dionne, G., and C. Rothschild. 2014. Economic effects of risk classification bans. The Geneva Risk and Insurance Review 39 (2): 184–221.Google Scholar
  18. Eling, M., R. Jia, and Y. Yao. 2017. Between-Group adverse selection: Evidence from group critical illness insurance. Journal of Risk and Insurance 84 (2): 771–809.Google Scholar
  19. Finkelstein, A., K. McGarry, and A. Sufi. 2005. Dynamic inefficiencies in insurance markets: Evidence from long-term care insurance. American Economic Review 95 (2): 224–228.Google Scholar
  20. Harris, M., and B. Holmstrom. 1982. A theory of wage dynamics. Review of Economic Studies 49 (3): 315–333.Google Scholar
  21. Hendel, I. 2016. Dynamic selection and reclassification risk: Theory and empirics. Working paper, Northwestern University.Google Scholar
  22. Hendel, I., and A. Lizzeri. 2003. The role of commitment in dynamic contracts: Evidence from life insurance. Quarterly Journal of Economics 118 (1): 299–328.Google Scholar
  23. Henriet, D., N. Klimenko, and J.C. Rochet. 2016. The dynamics of insurance prices. The Geneva Risk and Insurance Review 41 (1): 2–18.Google Scholar
  24. Herring, B., and M.V. Pauly. 2006. Incentive-compatible guaranteed renewable health insurance premiums. Journal of Health Economics 25 (3): 395–417.Google Scholar
  25. Hofmann, A., and M. Browne. 2013. One-sided commitment in dynamic insurance contracts: Evidence from private health insurance in Germany. Journal of Risk and Uncertainty 46 (1): 81–112.Google Scholar
  26. Hosios, A.J., and M. Peters. 1989. Repeated insurance contracts with adverse selection and limited commitment. Quarterly Journal of Economics 104 (2): 229–253.Google Scholar
  27. Ioannidou, V., and S. Ongena. 2010. “Time for a change”: Loan conditions and bank behavior when firms switch banks. Journal of Finance 65 (5): 1847–1877.Google Scholar
  28. Kofman, P., and G.P. Nini. 2013. Do insurance companies possess an informational monopoly? Empirical evidence from auto insurance. Journal of Risk and Insurance 80 (4): 1001–1026.Google Scholar
  29. Kunreuther, H., and E. Michel-Kerjan. 2015. Demand for fixed-price multi-year contracts: Experimental evidence from insurance decisions. Journal of Risk and Uncertainty 51 (2): 171–194.Google Scholar
  30. Kunreuther, H., and M. Pauly. 1985. Market equilibrium with private knowledge: An insurance example. Journal of Public Economics 26 (3): 269–288.Google Scholar
  31. Kysucky, V., and L. Norden. 2014. The benefits of relationship lending in a cross-country context: A meta-analysis. Management Science 62 (1): 90–110.Google Scholar
  32. Laffont, J.J., and J. Tirole. 1990. The regulation of multiproduct firms: Part I: Theory. Journal of Public Economics 43 (1): 1–36.Google Scholar
  33. Lu, W.M., W.K. Wang, and Q.L. Kweh. 2014. Intellectual capital and performance in the Chinese life insurance industry. Omega 42 (1): 65–74.Google Scholar
  34. Miyazaki, H. 1977. The rat race and internal labor markets. Bell Journal of Economics 8 (2): 394–418.Google Scholar
  35. Nilssen, T. 2000. Consumer lock-in with asymmetric information. International Journal of Industrial Organization 18 (4): 641–666.Google Scholar
  36. Palfrey, T.R., and C.S. Spatt. 1985. Repeated insurance contracts and learning. RAND Journal of Economics 16 (3): 356–367.Google Scholar
  37. Pauly, M.V. 2003. Time, risk, precommitment, and adverse selection in competitive insurance markets. Working paper.Google Scholar
  38. Pauly, M.V., H. Kunreuther, and R. Hirth. 1995. Guaranteed renewability in insurance. Journal of Risk and Uncertainty 10 (2): 143–156.Google Scholar
  39. Pauly, M.V., K. Menzel, H. Kunreuther, and R. Hirth. 2011. Guaranteed renewability uniquely prevents adverse selection in individual health insurance. Journal of Risk and Uncertainty 43 (2): 127–139.Google Scholar
  40. Pinquet, J., M. Guillén, and M. Ayuso. 2011. Commitment and lapse behavior in long-term insurance: A case study. Journal of Risk and Insurance 78 (4): 983–1002.Google Scholar
  41. Prendergast, C. 1992. The insurance effect of groups. International Economic Review 33 (3): 567–581.Google Scholar
  42. Rogerson, W.P. 1985. Repeated moral hazard. Econometrica 53 (1): 69–76.Google Scholar
  43. Rothschild, M., and J. Stiglitz. 1976. Equilibrium in competitive insurance markets: An essay on the economics of imperfect information. Quarterly Journal of Economics 90 (4): 629–649.Google Scholar
  44. Rubinstein, A., and M.E. Yaari. 1983. Repeated insurance contracts and moral hazard. Journal of Economic Theory 30 (1): 74–97.Google Scholar
  45. Saha, A. 1993. Expo-power utility: A ‘flexible’ form for absolute and relative risk aversion. American Journal of Agricultural Economics 75 (4): 905–913.Google Scholar
  46. Shaffer, S. 1998. The winner’s curse in banking. Journal of Financial Intermediation 7 (4): 359–392.Google Scholar
  47. Sharpe, S.A. 1990. Asymmetric information, bank lending, and implicit contracts: A stylized model of customer relationships. Journal of Finance 45 (4): 1069–1087.Google Scholar
  48. Shi, P., and W. Zhang. 2016. A test of asymmetric learning in competitive insurance with partial information sharing. Journal of Risk and Insurance 83 (3): 557–578.Google Scholar
  49. Spence, M. 1978. Product differentiation and performance in insurance markets. Journal of Public Economics 10 (3): 427–447.Google Scholar
  50. Villeneuve, B. 2014. Mortgage life insurance: A rationale for a time limit in switching rights. Mathematics and Financial Economics 8 (4): 473–487.Google Scholar
  51. Watt, R., and F.J. Vazquez. 1997. Full insurance, Bayesian updated premiums, and adverse selection. Geneva Papers on Risk and Insurance Theory 22 (2): 135–150.Google Scholar
  52. Wilson, C. 1977. A model of insurance markets with incomplete information. Journal of Economic Theory 16 (2): 167–207.Google Scholar
  53. Xie, D. 2000. Power risk aversion utility functions. Annals of Economics and Finance 1: 265–282.Google Scholar
  54. Zhang, L., and H. Wang. 2008. Dynamic process of adverse selection: Evidence from a subsidized community-based health insurance in rural China. Social Science and Medicine 67 (7): 1173–1182.Google Scholar

Copyright information

© International Association for the Study of Insurance Economics 2018

Authors and Affiliations

  1. 1.Department of Risk Management and Insurance, School of EconomicsPeking UniversityBeijingChina
  2. 2.Department of Economics, School of EconomicsPeking UniversityBeijingChina

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