# Insurer commitment and dynamic pricing pattern

- 83 Downloads

## Abstract

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.

## Keywords

Dynamic contract Commitment Asymmetric learning Information asymmetry Inter-temporal pricing## JEL Classification

D86 G22## Notes

### Acknowledgements

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.

## References

- 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 - 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 - Chiappori, P.A., and B. Salanié. 2000. Testing for asymmetric information in insurance markets.
*Journal of Political Economy*108 (1): 56–78.Google Scholar - 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 - Cochrane, J.H. 1995. Time-consistent health insurance.
*Journal of Political Economy*103 (3): 445–473.Google Scholar - Cohen, A. 2012. Asymmetric learning in repeated contracting: An empirical study.
*Review of Economics and Statistics*94 (2): 419–432.Google Scholar - Conniffe, D. 2007. The flexible three parameter utility function.
*Annals of Economics and Finance*8 (1): 57–63.Google Scholar - Cooper, R., and B. Hayes. 1987. Multi-period insurance contracts.
*International Journal of Industrial Organization*5 (2): 211–231.Google Scholar - 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 - 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 - 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 - de Garidel-Thoron, T. 2005. Welfare-improving asymmetric information in dynamic insurance markets.
*Journal of Political Economy*113 (1): 121–150.Google Scholar - Dionne, G. 1983. Adverse selection and repeated insurance contracts.
*Geneva Papers on Risk and Insurance—Issues and Practice*8 (4): 316–332.Google Scholar - 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 - Dionne, G., and P. Lasserre. 1985. Adverse selection, repeated insurance contracts and announcement strategy.
*Review of Economic Studies*52 (4): 719–723.Google Scholar - Dionne, G., and P. Lasserre. 1987. Adverse selection and finite-horizon insurance contracts.
*European Economic Review*31 (4): 843–861.Google Scholar - Dionne, G., and C. Rothschild. 2014. Economic effects of risk classification bans.
*The Geneva Risk and Insurance Review*39 (2): 184–221.Google Scholar - 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 - 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 - Harris, M., and B. Holmstrom. 1982. A theory of wage dynamics.
*Review of Economic Studies*49 (3): 315–333.Google Scholar - Hendel, I. 2016. Dynamic selection and reclassification risk: Theory and empirics. Working paper, Northwestern University.Google Scholar
- 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 - 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 - Herring, B., and M.V. Pauly. 2006. Incentive-compatible guaranteed renewable health insurance premiums.
*Journal of Health Economics*25 (3): 395–417.Google Scholar - 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 - 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 - 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 - 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 - 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 - Kunreuther, H., and M. Pauly. 1985. Market equilibrium with private knowledge: An insurance example.
*Journal of Public Economics*26 (3): 269–288.Google Scholar - 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 - 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 - 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 - Miyazaki, H. 1977. The rat race and internal labor markets.
*Bell Journal of Economics*8 (2): 394–418.Google Scholar - Nilssen, T. 2000. Consumer lock-in with asymmetric information.
*International Journal of Industrial Organization*18 (4): 641–666.Google Scholar - Palfrey, T.R., and C.S. Spatt. 1985. Repeated insurance contracts and learning.
*RAND Journal of Economics*16 (3): 356–367.Google Scholar - Pauly, M.V. 2003. Time, risk, precommitment, and adverse selection in competitive insurance markets. Working paper.Google Scholar
- Pauly, M.V., H. Kunreuther, and R. Hirth. 1995. Guaranteed renewability in insurance.
*Journal of Risk and Uncertainty*10 (2): 143–156.Google Scholar - 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 - 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 - Prendergast, C. 1992. The insurance effect of groups.
*International Economic Review*33 (3): 567–581.Google Scholar - Rogerson, W.P. 1985. Repeated moral hazard.
*Econometrica*53 (1): 69–76.Google Scholar - 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 - Rubinstein, A., and M.E. Yaari. 1983. Repeated insurance contracts and moral hazard.
*Journal of Economic Theory*30 (1): 74–97.Google Scholar - 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 - Shaffer, S. 1998. The winner’s curse in banking.
*Journal of Financial Intermediation*7 (4): 359–392.Google Scholar - 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 - 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 - Spence, M. 1978. Product differentiation and performance in insurance markets.
*Journal of Public Economics*10 (3): 427–447.Google Scholar - 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 - 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 - Wilson, C. 1977. A model of insurance markets with incomplete information.
*Journal of Economic Theory*16 (2): 167–207.Google Scholar - Xie, D. 2000. Power risk aversion utility functions.
*Annals of Economics and Finance*1: 265–282.Google Scholar - 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