Forecasting Life Expectancy: A Statistical Look at Model Choice and Use of Auxiliary Series
Demographic Research Monographs
Since mortality has typically declined, we expect that e x (t) c x (t). We note that even if life expectancies e x (t) have considerable descriptive value, they are of limited direct usefulness in population forecasting. Taken together the values of e x (t) do determine the hazards μ(x,t) for a given t, but if only e 0 (t) is known, then infinitely many patterns μ(x,t)'s would produce the same value e 0 (t). In special cases, such as a proportional hazards model with a(x) and b(x) known), a
... to-one correspondence exists (e.g., Alho 1989). In these cases forecasting e 0 (t) leads directly to estimates of age-specific mortality, but the assumption of known multipliers is strong. Given that the multipliers may change over time, it is not clear that this would, in practice, lead to a more accurate forecast of mortality hazards than forecasting the latter directly. On the other hand, e 0 (t) might perform as an "auxiliary measure" if it behaves in a more time-invariant manner (e.g., Törnqvist 1949) than the age-specific series themselves. The recent finding of Oeppen and Vaupel (2002) , in which the so-called best-practice life expectancy, i.e., the life expectancy of the country that is the highest at any given time, was shown to have evolved almost linearly for 160 years, points to this possibility. The first purpose of this paper is to establish the empirical relationship of the best-practice life expectancy to country-specific life expectancies in selected industrialized countries, during the latter part of the 1900's. Simple regression techniques will be used. The second purpose is to examine the statistical underpinnings of using best practice life expectancy as an auxiliary series for the prediction of the country-specific life expectancies.