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

a r t i c l e i n f o 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. Pay-as-you-go (PAYG) pension systems, in which the pensions are paid from the actual contribution of the active population, face a serious problem for two main reasons of demographic character: both low birth rates and growing survival rates affect the sustainability of the system negatively. Since the inverse old-age dependency ratio, i.e. is the proportion of the active subpopulation to pensioners is a good indicator of demographic sustainability, it will be called shortly sustainability index. For an analysis of sustainability, also considering the well-known problem of longevity risk, see e.g. Alho [1] and Pitacco [2]. Different European countries try to solve the problem in different ways; recent " country studies " are among others: Fehr and Habermann [3] for Germany, Blake and Mayhew [4] for the UK and Sanchez and Alfonso [5] for Spain. Furthermore, for China, Yang [6] examines the effects of the replacement rates and population growth rate on pension benefits and finds the optimal replacement rate. Since the work by Boyle and Freedman [7], a variety of demographic models have been applied for medium and long term predictions concerning the pension systems; for a recent overview and a methodological criticism of them see in Herce [8] and Booth [9]. While the comprehensive study of Rother et al. [10] is dedicated to the fiscal sustainability of PAYG pension systems, we will concentrate on the demographic background of sustainability. It is known (see Angrisani et al. [11] and Alho and Spencer [12]) that, based on …