Expanding Annuity Markets: A Solution to the Problem of Longevity Risk

University of Nebraska–Lincoln Actuarial Science Program CAE Grant

July 1, 2015 – June 30, 2018

Project Title: Expanding Annuity Markets: A Solution to the Problem of Longevity Risk

Summary of Project Objectives:

The vast majority of annuity products sold in the USA are geared to individuals who expect to experience significantly higher longevity than the general retiree population. As annuities currently sold are priced to reflect the expected high longevity of annuitants, then such annuities will not be “actuarially fair” from the standpoint of individuals with average to below average expected longevity. This type of outcome is commonly called “adverse selection,” and partly explains the overall low demand for annuities in the USA. To expand the annuities market, we will develop annuity products that are uniquely attractive to individuals with average to below average expected longevity. The unique and challenging aspect of our research is the development of annuity products that will be unattractive to individuals with significantly higher expected longevity but yet be attractive to those with average to below average expected longevity. We will use non-linear pricing methods developed by Stiglitz (1977), who proposed the development of so-called self-selecting policies designed for individuals with different characteristics. Stiglitz’s work was extended by Ramsay and Oguledo (2012) and Ramsay, Oguledo, and Pathak (2013).

Description of Proposed Project

It has become increasingly important to make available products that encourage individuals to use their savings in a way that will ensure a secure retirement (Richardson and Spence, 2010). Life annuities are viewed as desirable tools for this purpose because they can eliminate the “longevity risk,” i.e., the risk of individuals out-living their income. In fact, it is well-known that Yaari’s (1965) life-cycle model of savings predicts that risk-averse individuals will annuitize their accumulated wealth at retirement to protect against longevity risk. Yaari's predictions, however, are not borne out in practice, which implies that risk-averse individuals do not find annuity products appealing. Researchers have found this situation puzzling and have termed it the “annuity puzzle” because very few people avail themselves of the private annuities market (Poterba , 2001; Brown, 2001; Mitchell, et al, 1999; Friedman and Warshawsky, 1988, 1990). Poterba (2001), Brown (2001), and Finkelstein and Poterba (2004) point out that the demand for annuities may also be low if the expected annuity payments are low relative to the annuity's premium. Hu and Scott (2007) suggest there may be behavioral factors that account for the relatively small size of the voluntary annuities market.

Regardless of the underlying reasons, the reality is that in practice annuities tend to be more appealing to healthy individuals with longer life expectancy than to those in poorer health, i.e., adverse selection. In response to the preference for annuities by very healthy individuals, insurers tend to use special annuitant mortality tables to calculate the benefits to be paid to annuitants. The net effect of these “conservative” tables is to drive up the cost of annuities, i.e., for a given premium, the annual annuity benefit is reduced because of the mortality assumptions. Thus, a large number of individuals of average to low life expectancy are automatically priced out of annuity markets. How do we get these individuals into the market? By developing products that are uniquely attractive to them.

One approach to solving the problem of adverse selection is via underwriting. However, unlike the case of life insurance, underwriting of life annuities is almost non-existent in the USA. This may be in part due to the fact that the applicants for annuities have an incentive to present themselves in “poor health” (i.e., with low expected longevity) in order to receive higher annuity payments. Instead, our approach is based on the seminal works on adverse selection by Rothschild and Stiglitz (1976) and Stiglitz (1977). In particular, we use the Stiglitz (1977) technique of developing “self-selecting policies” that are designed for each risk group.

Objectives: We will use the theory of non-linear pricing under information asymmetry developed by Stiglitz (1977) and extended by Ramsay and Oguledo (2012) and Ramsay, Oguledo, and Pathak (2013) to develop optimal pairs of annuity products that eliminate adverse selection and longevity risk. The crux of our approach is to induce self-selection on the part of consumers whereby:

• High expected longevity individuals choose policies designed for high expected longevity individuals;
• Low expected longevity individuals choose policies designed for low expected longevity individuals;
• It would be sub-optimal for high expected longevity individuals to choose policies designed for low expected longevity individuals;
• It would be sub-optimal for low expected longevity individuals to choose policies designed for high expected longevity individuals; and
• The insurer would make a profit on the entire portfolio of policies.

In developing our optimal pairs of annuity products, we consider two specialized products: life care annuities (which are geared to individuals with low expected longevity) and longevity insurance annuities (which are geared to individuals with high expected longevity). Brown and Warshawsky (2013) describe life care annuities as the integration of the life annuity with long-term care insurance coverage. Longevity insurance annuities are deferred annuities commencing at a late post-retirement age such as age 80 or 85. Blake and Turner (2014) point out that the US government encourages use of these annuities to reduce longevity risks.

Finally, our optimal annuity products will be Pareto improving solutions whereby nobody is worse off and some people (i.e., those with standard or substandard mortality) are better off.

References

1. Blake, D. and Turner, J.A. (2014). "Longevity Insurance Annuities: Lessons from the United Kingdom." Benefits Quarterly, First Quarter, pp. 39--47.
2. Brown, J.R. (2001). "Private Pensions, Mortality Risk, and the Decision to Annuitize." Journal of Public Economics, 82(1), pp. 29--62.
3. Brown, J. and Warshawsky, M. (2013). "The Life Care Annuity: A New Empirical Examination of an Insurance Innovation that Addresses Problems on the Markets for Life Annuities and Long-Term Care Insurance." Journal of Risk and Insurance, 80(3), pp. 677--703.
4. Finkelstein, A. and Poterba, J. (2004). "Adverse Selection in Insurance Markets: Policyholder Evidence from the U.K. Annuity Market." Journal of Political Economy, 112, pp. 183--208.
5. Friedman, B. and Warshawsky, M. (1988). "Annuity Prices and Saving Behavior in the United States," in Z. Bodie, J. Shoven, and D. Wise, eds., Pensions in the U.S. Economy. Chicago: University of Chicago Press, pp. 53--77.
6. Friedman, B. and Warshawsky, M. (Feb 1990). "The Cost of Annuities: Implications for Saving Behavior and Bequest." Quarterly Journal of Economics, 105(1), pp. 135--206.
7. Hu, W-Y and Scott, J.S. (2007). "Behavioral Obstacles in the Annuity Market." Financial Analysts Journal, 63(6), pp. 71--82.
8. Mitchell, O.S., Poterba, J.M., Warshawsky, M.J., and Brown, J.R. (Dec 1999). "New Evidence on the Money's Worth of Individual Annuities." American Economic Review, 89(5), pp. 1299--1318.
9. Poterba, J. M. (2001). "Annuity Markets and Retirement Security." Fiscal Studies, 22(3), pp. 249--270.
10. Ramsay, C.M. and Oguledo, V.I. (2012). "Insurance Pricing with Complete Information, State-Dependent Utility, and Production Costs." Insurance: Mathematics and Economics 50(3), pp. 462--469.
11. Ramsay, C.M., Oguledo, V.I., and Pathak, P. (2013). "Pricing High-Risk and Low-Risk Insurance Contracts with Incomplete Information and Production Costs." Insurance: Mathematics and Economics, 2(3), pp. 606--614.
12. Richardson, D.P. and Spence, C.S. (May 2010). "Increased Longevity and the Annuity Solution: How Retirement Policy Reforms Can Reduced Longevity Risk." TIAA-CREF Institute Policy Brief.
13. Rothschild, M. and Stiglitz, J. (Nov 1976). "Equilibrium in Competitive Insurance Markets: An Essay on the Economics of Imperfect Information." Quarterly Journal of Economics, 90(4), pp. 629--649.
14. Stiglitz, J. (1977). "Monopoly, Non-Linerar Pricing and Imperfect Information: The Insurance Market." Review of Economic Studies, 44, pp. 407--430.
15. Yaari, M. (1965). "Uncertain Lifetime, Life Assurance, and the Theory of the Consumer." Review of Economic Studies, 32(2), pp. 137--150.