Association for Public Policy Analysis & Management

Current public pension funding shortfalls have given rise to a wave of benefit cuts and contribution hikes, but have also given circulation to the idea that “full funding” is not necessary for “sustainability.”  A particularly common form of this idea is the “80 percent funding rule,” according to which professional opinion holds that an 80 percent funded ratio (assets/liabilities) is “sustainable.”  The origins of this “rule” are obscure, and possibly mythical.  That said, it does raise the question of whether funded ratios below 100 percent are “sustainable,” and what the determinants of such ratios might be.  The purpose of this paper is to formally analyze an “x-percent policy” using the simple mathematics of ordinary difference equations – an approach that complements the best existing informal literature on this topic. 

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.