A comparison of the accuracy of coherent mortality forecasts for subpopulations defined by sex and state – which matters most?

When mortality forecasts for subpopulations are treated as independent, historic relationships among subpopulations may not be reflected in the forecasts. The product-ratio method of coherent forecasting (Hyndman, Booth and Yasmeen, Demography, online 2012) takes account of the relationships among subpopulations based on a single criterion such as sex or state. The coherent forecasts have been shown to improve overall accuracy and to equalise accuracy across subpopulations. The aim of this paper is to compare the accuracy of mortality forecasts when the subpopulations are based on sex and state (or country). The product-ratio method is applied to male and female populations of a group of n states, producing mortality forecasts for 2n subpopulations defined by sex and state. Two forecasts per subpopulation are made: the first set are sex-coherent forecasts for each country, while the second set are country-coherent forecasts for each sex. The accuracy of the two sets of forecasts are compared. Examples include four Nordic countries (Norway, Sweden, Denmark and Finland), three constituents of the UK (England & Wales, Scotland, Northern Ireland) and four states of Australia.