## History lessons

In the debate about how fast mortality will improve in the future, sometimes it is useful to remind ourselves how far we have come.  For example, while reading a paper from one of the leading actuarial researchers on mortality, Robert Beard, I came across the following statement:

"About 1% of births survive beyond age 90 or so"

Beard, R. E. (1971) Some aspects of theories of mortality, cause of death analysis, forecasting and stochastic processes, Biological Aspects of Demography (ed. W. Brass), London: Taylor and Francis.

Beard doesn't give a source for this, but using English Life Table No. 12 (which draws on data from 1960-62), the probability of a male life surviving to age 90 was around 3%.  However, the lesson here isn't that one should check claims and give sources (one should), but how far we have come.  Using the interim life tables for Great Britain for 2006-08, the probability of a male reaching age 90 from birth is 17%, while for a female it is 28%.

Regardless of whether you start from 1% or 3%, these survival probabilities represent a huge change within living memory.  Although they refer to survival since birth, and therefore include large changes in infant mortality, they are nevertheless sobering when you consider the long-term mortality projections which are implicit in the reserving for deferred pensions.  It is nearly fifty years since ELT 12 was produced and I suspect few actuaries at that time would have entertained the idea that survival probabilities could have increased as much as they have.  Despite this, their calculations of pension costs used projections of mortality rates over just such a time scale.

I still occasionally hear the argument that mortality improvements in the future will be less dramatic than in the recent past.  I suspect similar arguments were probably common fifty years ago.  This is one reason why we prefer stochastic projection models: they highlight uncertainty and they are immune to persuasion.  The lesson of this particular piece of history is not to rely on appeals to intuition, but to consider the risks.

Assume we have a random variable, $$X$$, with expected value ... Read more