Coherent forecasting of multiple-decrement life tables: a test using Japanese cause of death data

James E Oeppen, Max Planck Institute for Demographic Research

It is attractive to forecast components of mortality, such as causes of death, so that the aggregate of the components is a plausible all-cause forecast, but this has been difficult to achieve. The components usually diverge in the long run in ways that are implausible when compared with the historical record. The relative values of the components fail to behave in a coherent way, leading to an implausible aggregate. This paper abandons the absolute distances of mortality rates and forecasts the relative numbers of deaths in the d(x) columns. Since the d(x) values obey a unit sum constraint for both conventional and multiple-decrement tables they are intrinsically relative rather than absolute values across decrements as well as ages. Death densities are transformed into the real space so that the full range of multivariate statistics can be applied, then back-transformed to positive values so that the unit sum constraint is honoured. The paper will demonstrate that coherent forecasts can be achieved, although their suitability for forecasting remains to be shown. Illustrations of singular value decomposition and regression-based forecasts of d(x) are evaluated for conventional and multiple decrement life tables.