Necessary and sufficient conditions for determinacy of asymptotically stationary equilibria in OLG models

We propose a criterion for verifying whether an equilibrium of an overlapping-generations model is amenable to local policy analysis, i.e., is determinate. The criterion is applicable for a generic set of parameters of the model, and in case of indeterminacy, it indicates the nature of the problem: multiplicity of equilibria or their absence for near-by parameters. The criterion can be applied to models with infinite past and future as well as to those with a truncated past. The baseline equilibrium is not required to be a steady state, and economic parameters, for example endowments, can change over time. However, asymptotically, the equilibrium should be stationary, though the two limiting paths at either end of the time-line do not have to be the same. If they are, conditions for local uniqueness of equilibrium are far more stringent for an economy with a truncated past as compared to its counterpart with an infinite past. We illustrate our main result using a text-book model with a single physical good and a two-period life-cycle. There, price growth paths that start at one steady state and end up at another constitute indeterminate equilibria for all parameters.