Necessary and Sufficient Conditions for Determinacy of Asymptotically Stationary Equilibria in OLG Models

26 Pages Posted: 1 Jun 2019 Last revised: 19 Jun 2019

See all articles by Alexander Gorokhovsky

Alexander Gorokhovsky

University of Colorado at Boulder

Anna Rubinchik

Western Galilee College - Department of Economics

Date Written: May 31, 2019

Abstract

We propose a criterion for determining whether a local policy analysis can be made in a given equilibrium in an overlapping generations model. 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 or individuals’ 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.

Keywords: Overlapping generations, Implicit function theorem, Determinacy, Time-invariance, Comparative statics

JEL Classification: C02, C62, D50

Suggested Citation

Gorokhovsky, Alexander and Rubinchik, Anna, Necessary and Sufficient Conditions for Determinacy of Asymptotically Stationary Equilibria in OLG Models (May 31, 2019). Cowles Foundation Discussion Paper No. 2179 (2019), Available at SSRN: https://ssrn.com/abstract=3397100 or http://dx.doi.org/10.2139/ssrn.3397100

Alexander Gorokhovsky

University of Colorado at Boulder ( email )

1070 Edinboro Drive
Boulder, CO 80309
United States

Anna Rubinchik (Contact Author)

Western Galilee College - Department of Economics ( email )

POB 2125
Akko, 24121
Israel

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