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Research Studies in Pension

Factor Affecting Retirement Mortality (FARM)

This FARM site consists of

• an Introduction
• an Abstract
• a Bibliography of research papers
• a collection of Summaries of the research papers.

Use the Table of Summaries to link to the summaries either by author or by risk factor.

Abstract | Bibliography | Introduction | Table of Summaries

Issues in the Modeling of Mortality at Advanced Ages

Brown, Robert L., Research Report 97–05, Institute of Insurance and Pension Research, University of Waterloo, Ontario, Canada.

This paper looks at the methods used to estimate mortality rates and to construct life tables in Canada and the United States. It focuses particularly on the methods used to model mortality at advanced ages. Some deficiencies in the construction of the Canadian Life Tables are identified and suggestions are made that could improve the usefulness of the data presented.

This paper considers how mortality rates progress with age. In constructing life tables, the Gompertz or Makeham formulae are often used as their exponential form generally provides a very good approximation to observed mortality in most western populations between the ages of 30 and 85. However, special methods are required for the extreme elderly age groups, i.e. beyond age 85, as at these advanced ages the force of mortality no longer grows exponentially, rather it levels off and becomes almost constant.

In focusing on mortality rates at more advanced ages, the paper discusses the potential problems in modeling mortality rates at these ages and presents the various modifications that may be used.

At advanced ages the size of the population is relatively small and there are also potential errors due to accidental and deliberate misstatements of age in census data. In the U.S. more reliable data for age 85 and over is sought from Medicare records, as Medicare requires proof of age at age 65.

Mortality rates at advanced ages can be modified by choosing a finite life–span such that at some age qx = 1, by choosing an upper bound (which is less than 1) that mortality rates tend to, or by fixing the ratio of qx+1/qx at a constant value. Another alternative is to simply terminate the life table at a particular age, e.g. 110, even though the table would extend to well beyond this age.

The U.S. Life Table terminates mortality rates at age 110; however, the Canadian Life Table uses special formulae beyond age 89 so that there are no 'survivors' at age 107. The paper proceeds to consider the implications of this decision and then suggests an alternative data source, similar to Medicare in the U.S., to overcome these difficulties. The data source suggested is the Canada/Quebec Pension Plans. These plans only have workers as participants. It is commented that there are indications in the data, that at advanced ages, mortality does not vary by previous work history.

Save a short discussion of the two theories regarding the 'rectangularization' of the survivorship curve, the paper does not attempt to explain the relationship between age and mortality. The paper diagrammatically shows that there has been significant improvement in mortality over this century. The theory of 'rectangularization' hypothesizes that there is an upper bound to the human life–span, and that, as life expectancy improves, a larger proportion of the population approaches, but cannot surpass, this upper bound. In contrast, however it is argued that there is no upper bound, since as life expectancy has improved, the variability of life expectancy at the advanced ages has not reduced.

It is difficult to prove mathematically if there is a finite life–span. It appears that either there is no limit, or we are far enough away from the limit so as not yet to experience the impact of such a limit mathematically.