An algorithm for quickly finding long-term equilibria in models of overlapping generations[Алгоритм Быстрого Нахождения Долгосрочных Равновесий В Моделях Пересекающихся Поколений]

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.