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 generation 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 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. In this model our criterion is used to identify the three possible cases: determinacy, and hence, local uniqueness,  and indeterminacy: multiplicity and non-existence of equilibria in the neighbourhood of the baseline.

Joint with A. Gorokhovsky, CU Boulder

Links to the paper and the seminar recording.