## Panel Paper: The Simple Analytics of Sustainable Pension Underfunding, 80 Percent or Otherwise

*Names in bold indicate Presenter

The problem can be stripped to its fundamentals using a two-period model of overlapping generations (OLG) with risk-free investment. The notion of “sustainability” – a term that is often used without precise definition – is logically defined in the context of such a model as stability of a steady state, with a constant funded ratio and constant contribution rates. The simple two-period OLG model shows that there is a continuum of steady-state funded ratios, with lower funded ratios corresponding to higher steady-state contribution rates, and greater generational inequity. This formalizes a result that has previously been put forth informally, but also allows us to go further. The model shows that if a system targets an x-percent funded ratio (below full funding) the steady-state funded ratio will be lower yet, since contributions at the x-percent target will be insufficient to sustain that target. As a result, there is a positive lower bound to the target funded ratio, below which there is no solvent steady state. That floor for the target funded ratio might be identified as an x-percent rule, and we can examine its determinants, although it is worth emphasizing that the corresponding steady state is zero funded. More pertinently, there is a near-isomorphism between a system with an x-percent target funded ratio and the more common case of an assumed rate of return that is arguable too high. The model can be generalized to n periods.