Efficient Calculation of All Steady States in Large-Scale Overlapping Generations Models

In this paper, we address the problem of analyzing and computing the steady states of an overlapping generation (OLG) model with production and many generations. The characterization of steady states coincides with a geometrical representation of the algebraic variety of a polynomial ideal and, in principle, one can apply computational algebraic geometry methods to solve the problem. However, it is infeasible for standard methods to solve problems with a large number of variables, parameters and constraints. Instead we use the specific structure of the economic problem to develop a new algorithm that does not employ the usual steps for the computation of Gröbner basis such as the computation of successive S-polynomial and expensive division. All of the described algorithms are also implemented as a computational package in Maple software