On a Generalization of the World Bank Model of Retirement Savings : A Taxonomy of Systems with Two Cross-Subsidized Tiers

We develop a generalization of the World Bank (1994) model of forced saving for retirement. This broader model consists of two tiers of second pillar savings --- mandated and non-mandated (voluntary). Furthermore, the government can set two types of guarantees on the first (mandated) tier --- investment returns and annuity prices --- leading to possible cross-subsidization between the tiers. This has the potential to induce social redistribution, foster a liquid private market for life annuities, as well as obviate some of the investment risk and annuity price risk that retirees face. We formulate a quantitative model of financial flows within such a system, which explains the mechanism by which cross-subsidization occurs. Based on this analysis, a taxonomy of two-tiered retirement systems is presented, that is based on the choices that the government makes. Our modelling is inspired by the Swiss second pillar model, which serves as a motivation and illustration. The Swiss system features unique properties and remarkable outcomes. These include both high levels of savings and (unforced) annuitization, as well as a non-trivial level of internal cross-subsidies between the two tiers of the system. The analysis allows us to shed some light on some of the issues the Swiss system is currently facing