Dynamic immigration control improving inverse old-age dependency ratio in a pay-as-you-go pension system

The sustainability of pay-as-you-go pension systems is a major concern in most European countries. Considering the inverse old-age dependency ratio (the proportion of the class of actives to pensioners) as a sustainability index, based on a classical demographic model, a new optimal control model is proposed where the sustainability index grows along a prescribed trajectory, minimizing the annual immigration flow over a given time horizon. In addition to the admission of young immigrants, immigrant females, by having higher birth rates than the residents, can substantially improve the sustainability index. For the efficiency of the immigration policy, the admission of immigrants is also differentiated by age. Within the limits of our model, the social cost of sustainability in terms of immigration can be estimated on beforehand. Therefore, the simulation analysis of our model may give a sound foundation to the corresponding decision of policy makers.