From magical thinking to statistical thinking
Summary
The Institute and Faculty of Actuaries in the UK has recently added mortality projection to its syllabus, so this year I have been teaching the subject for the first time to students at Heriot-Watt University. As an exercise, I asked the students to imagine they were an actuary back in 1980, and to first fit a Lee-Carter model to data from the Human Mortality Database for males in England and Wales, 1940–1980. The actuary in 1980 had very limited tools for measuring and managing risk, so outcomes like Figure 1 did transpire, perhaps giving deterministic mortality forecasting a bad name. The results, at age 60, of fitting a Lee-Carter model to England and Wales data, males, 1940–1980, and projecting mortality ahead to 2005, with 95% prediction intervals shown. If we now interpret the projection as an attempt to map out a region within which future mortality may evolve, with stated probability, we have a basis for quantitative risk management.
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