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Estimating international adverse selection in annuities

North American Actuarial Journal, Oct 2002 by Mitchell, Olivia S, McCarthy, David

ABSTRACT

It is well known that purchasers of annuities have lower mortality than the general population. Less widely known is the quantitative extent of this adverse selection and how it varies across countries. This paper proposes and applies several methods for comparing alternative mortality tables and illustrates their impact on annuity valuation for men and women in the U.S. and the U.K. Our results indicate that the relatively lower mortality among older Americans who purchase annuities is equivalent to using a discount rate that is 50-100 basis points below the U.K. rate for compulsory annuitants or 10-20 basis points lower than the U.K. rate for voluntary annuitants. We then draw on the mortality experience of over half a billion lives to estimate mortality differentials due to varying degrees of adverse selection controlling for country, gender, and an allowance for mortality improvements. Results show that adverse selection associated with the purchase of individual annuities reduces mortality rates by at least 25% in the international context. We also find that the system of mortality tables used to value Japanese annuities is quite distinct from international norms.^^

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As life expectancies rise and people anticipate spending longer in retirement, it is becoming increasingly important for aging populations to gain access to financial instruments that can help them insure against the risk of outliving their assets. Life annuities are one product that can help in this regard, in that they help shift mortality risk away from individuals and toward the insurer. In exchange for a fixed sum of money, the insurer pays out a regular flow of income for life and thus guarantees that the survivor will not live so long that he runs out of assets. Inevitably, well-functioning funded retirement systems will require properly functioning annuity markets because annuities play an essential role in converting asset accumulations into a regular flow of retirement income guaranteed for life. The importance of annuity markets and their role in funded retirement systems have been explored by Brown et al. (2000), Diamond (1999), Doyle and Piggott (1999), Feldstein (1998), Finkelstein and Poterba (2000), James and Vittas (1999), Milevsky (1988), Mitchell et al. (1999), and Warshawsky (1988), among others.

Yet, as actuaries well know, it takes a great deal of statistical information on mortality patterns by age and sex to develop the necessary survival forecasts needed for valuing annuity products. In practice, many developing countries lack a vital statistics collection mechanism, so they have few national mortality statistics specific to their own populations. Consequently policymakers and researchers working throughout Latin America, Eastern Europe, Africa, and Asia must often rely on mortality data from other countries in order to value life insurance and annuity products.

In order to properly price such life annuity products, actuaries and financial experts must utilize mortality tables, which are statistical representations of the expected distribution of a population's remaining life span. Devising a mortality table (or life table) is data intensive, of course, because it relies on collecting the incidence of deaths by age and sex occurring in a given population over a specified time.1 Using the raw data, experts then compute the estimated probability that a group member aged x will die in the next year of life, either by fitting a hazard rate model to the empirical distribution of deaths in the population or by applying a smoothing algorithm to the raw maximum likelihood estimates. These smoothed estimates are then used to construct a complete mortality table. For most ages, the results are small numbers, and hence a large number of lives must be observed in order to obtain reliable estimates of small probabilities.

Most developed nations today have their own mortality tables; some are freely available,2 and others are more difficult to obtain. Though actuaries are aware of the international differences in such tables, they differ across countries in ways that are quite striking to the non-actuary. For instance, population mortality pattern differences are substantial enough across the Organization for Economic Co-operation and Development (OECD) countries to imply very different consequences for programs intended to maintain living standards for the older population (Hewitt and Schieber 2000).

In the present paper, we explore alternative measures of these population mortality differences, then we examine mortality differences in annuitant pools. As suggested by prior research using U.S. and U.K. data (Brown et al. 2000; Finkelstein and Poterba 1999), we anticipate that in the large set of countries we examine here, annuitants will also have lighter mortality patterns than the population as a whole because people who opt to buy an annuity in a voluntary purchase market are likely to be self-selected to live longer than average-partly, it may be argued, because they have private information about their own health status and partly because they tend to be wealthier than the general population.

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Estimating international adverse selection in annuities

North American Actuarial Journal, Oct 2002 by Mitchell, Olivia S, McCarthy, David

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