An algorithm for quickly finding long-term equilibria in models of overlapping generations

Abstract

In this paper, we consider the problem of finding long-term equilibria in models of overlapping generations with a large number of periods. It is often possible to reduce
the solution of a model to finding the roots of a system of equations. Some OLG models, after
the introduction of additional variables, can be reduced to the form of a system of polynomials. Thus, one can represent the set of long-term equilibria as algebraic
diversity. This makes it possible to use computational methods from algebraic geometry in economic problems. In particular, the method using Grebner bases has become popular. However, this approach can be effectively applied only
when there are few variables. We propose an algorithm for finding solutions to the system and use it to investigate the presence of a plurality of solutions in realistically calibrated
models with long-lived agents.

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