Aggregation across countries in stochastic population forecasts

Stochastic methods of multi-state population modeling are less developed than methods for single states for two reasons. First, the structure of a multi-state population is inherently more complex than that of a single state because of state-to-state transitions. Second, estimates of cross-state correlations of the vital processes are a largely uncharted territory. Unlike multi-state lifetable theory, in forecasting applications the role of directed flows from state to state is often less important than the overall coherence of the assumptions concerning the vital processes. This is the case in the context of the European Union. Thus, a simplified approach is feasible, in which migration is represented by state-specific net numbers of migrants. This allows the use of existing single-state software, when simulations are suitably organized, in a multi-state setting. To address the second problem, we provide empirical estimates of cross-country covariances in the forecast uncertainty of fertility, mortality, and net migration. Together with point forecasts of these parameters that are coherent across countries, this produces coherent forecasts for aggregates of countries. The finding is that models for intermediate correlations are necessary for a proper accounting of forecast uncertainty at the aggregate level, in this case the European Union.