Modeling Gender Life Expectancy Ratio in a Multi-population Framework

This paper aims to assess whether the male-to-female ratio in life expectancy is driven by cross-national long-period common trends. If a common trend is detected across a group of countries, then a model taking it into account should provide a more reliable description of the process in scope. We model the gender life expectancy ratio of a set of countries as a multivariate time series. Since our study includes data from 25 countries that are characterized by different longevity patterns, we preliminarily aggregate populations in clusters. Once we verify that all these series are non-stationary, we apply Johansen's cointegration rank test to each cluster. The idea behind this methodology is to detect any stationary linear combination out of nonstationary variables, which implies that the series share some underlying long-period equilibrium relationships. If the cointegration rank test provides evidence for any cointegrating relationship, we further check whether estimated linear combinations of the single series - namely the error correction terms - are stationary. Finally, we measure forecasting errors with respect to the 10-year testing set. At least for two clusters over six, we find enough evidence to outline some cointegrating relationships in the male-to-female life expectancy ratio. This result leads us to assume that an underlying long-period equilibrium in life expectancy gender differentials does exist among the single countries included in these clusters.