The effect of an instantaneous dependency rate on the social equitability of hybrid PAYG public pension schemes

The defined convex combination (DCC) pay-as-you-go public pension systems recently introduced in the literature are a form of hybridization between defined benefit (DB) and defined contribution (DC) designed to maintain intergenerational social equitability by reacting to demographic shocks in an optimal way. In this paper, we augment DCC schemes with the assumption that the dependency ratio between pensioners and workers is driven by an exogenously modelled instantaneous stochastic rate of change. This assumption enjoys support from the empirical data and allows explicit solutions for the contribution and replacement rate processes which make transparent the nature of the dynamic evolution of a DCC system, as well as the role of the variables involved. The analysis of intergenerational social equitability measures under the assumption of an instantaneous dependency rate confirms the view expressed in previous literature that neither DB nor DC achieves social fairness, and that DCC plans have the potential to improve on both. We perform a calibration test, and our findings seem to indicate that in ageing economies the DC system might indeed be superior to the DB one in terms of intergenerational fairness.