A demographic model with migration for a PAYG pension system

In the analysis of economic and social issues of a country (or any larger or smaller socio-economic unit) the demographic dynamics of the considered population often plays a crucial role. Actual emergencies in this aspect are e.g. pay-as-you-go pension systems, unemployment and staterun healthcare. Over the last decade migration between EU countries also became an important issue, and in recent years the uncontrolled migration into the EU also is a major concern. Therefore, the analysis and better theoretical understanding of the mechanism of development of the age composition of populations interacting via migration is a timely modelling-methodological task. The present paper is a methodological contribution to the support of socio-economic decision making concerning migration issues. It is known that in the framework of the classical age-specific Leslie model, under simple demographic conditions, a closed population in the long term tends to an equilibrium age distribution. In the paper a similar convergence is proved for a system of several populations with migration between them, and this long-term behaviour (convergence theorem) is extended to system of sex-structured populations. Based on the latter model, medium term projections are also analysed concerning the effect of migration between countries on the development of the old-age dependency ratio (the proportion of pensioners to actives), which is a crucial issue for the sustainability of the pay-as-you-go pension systems in most European countries. Illustrative simulation analysis is carried out with data of three European countries.