CEF.UP – ECO Webinar

Tuesday – May 11^th, 2021 3:00 p.m.

“Necessary and Sufficient conditions for Determinacy of Asymptotically Stationary Equilibria in OLG Models”

Anna Rubinchik –  Western Galilee College, Israel (joint work with Alexander Gorokhovsky)

Abstract:

We propose a criterion for verifying whether a local policy analysis can be made in an overlapping generations model,  i.e., whether a given equilibrium 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 equilibrium is not necessarily a steady state; for example, demographic- and type-composition of the population and endowments can change over time.

However, asymptotically, the equilibrium should be stationary. The two limiting stationary paths at either end of the timeline do not have to be the same. If they are, conditions for local uniqueness are far more stringent for an economy with a truncated past as compared to its counterpart with an infinite past.

In addition, we illustrate our main result using a text-book model with a single physical good, a two-period life-cycle and a single type of consumer. In this model we show how to calculate a response to a policy change using the implicit function theorem.