Sex Differential Dynamics in Coherent Mortality Models

Abstract

The main purpose of coherent mortality models is to produce plausible, joint forecasts for related populations avoiding, e.g., crossing or diverging mortality trajectories; however, the coherence assumption is very restrictive and it enforces trends that may be at odds with data. In this paper we focus on coherent, two-sex mortality models and we prove, under suitable conditions, that the coherence assumption implies sex gap unimodality, i.e., we prove that the difference in life expectancy between women and men will first increase and then decrease. Moreover, we demonstrate that, in the model, the sex gap typically peaks when female life expectancy is between 30 to 50 years. This explains why coherent mortality models predict narrowing sex gaps for essentially all Western European countries and all jump-off years since the 1950s, despite the fact that the actual sex gap was widening until the 1980s. In light of these findings, we discuss the current role of coherence as the gold standard for multi-population mortality models.