Pooling mortality risk in Eurozone state pension liabilities: An application of a Bayesian coherent multi-population cohort-based mortality model

We design a coherent cohort-based multi-population mortality model, calibrate it to national mortality rates in the Eurozone using Human Mortality Database data, and use it to project developments in national mortality across the Eurozone. Combining this model with a stylized model of social security pensions in each country allows us to calculate the pension mortality risk in these systems and estimate the benefits of pooling it across the Eurozone. We examine three risk pools, which are all actuarially fair, but differ in how undiversifiable risk is allocated across countries. The first naïve approach allocates undiversifiable risk in proportion to GDP, a second according to a CAPM-based measure of the undiversifiable risk each country contributes to the pool and a third ensures that the aggregate benefits of diversification are shared equitably across countries using a measure we adopt. In all cases, the benefits of risk pooling increase over time as mortality uncertainty accumulates, but fall over time as cross-country correlation increases due to the long-term dominance of the mortality trend, which by assumption is shared between countries. The peak benefit occurs around 2050, with an aggregate reduction in the standard deviation of pension expenditures of around 0.11% of GDP, or 3% of pension expenditure at the 99th percentile. We find that allocating undiversifiable risk proportional to GDP does not ensure an efficient allocation of undiversifiable risk across countries, given that different countries have markedly different pension mortality risk due to different pension system generosities as well as different mortality correlation with the Eurozone. Based on our results we propose a contract design that surmounts most of the moral hazard risks created by the pool, and suggest directions for future research.