Choice of function for mortality analysis: Effective forecasting depends on a minimum parameter representation

Abstract

For nearly two centuries actuaries, statisticians and demographers have sought a parameter space in which the mortality pattern of a population could be located, that would be linked to the larger space of age-specific rates by an analytical formula. Gompertz, Makeham, Brillinger, Wolfenden, Pollard and others have made contributions to this end. Model or reference tables perform a similar task, usually with fewer parameters, but are less easily manipulated. A common means of reducing dimensionality is to map the original space of mortality rates in five-year groups on a straight line in which are located the expectations of life at age zero (≐ 0). A small-space representation is advantageous for filling gaps in data. If the only fact known about a country is the fraction of girls who have a living mother, then a one-dimensional set can be indexed on this to provide the full detail of mortality, assuming the unknown mortality is part of that set. For forecasting one would like the succession of life tables for a given population over past times to be representable by points moving in a simple way through a parameter space—ideally in a straight line—over a succession of calendar years. The simpler the curve, the more realistic is likely to be its projection into the future. The Brass relational method provides a trajectory well suited to extrapolation in a space of only two parameters. Some useful extensions of this have recently been devised.