A Simple Method for Computing Equilibria when Asset Markets Are Incomplete

11 December 2014
Author: Wei Ma
Publication Type: Working Paper
JEL Code: C63, C68

The problem of computing equilibria for general equilibrium models with incomplete real asset markets, or GEI models for the sake of brevity, is reconsidered. It is shown here that the rank-dropping behavior of the asset return matrix could be dealt with in rather a simple fashion: We first compute its singular value decomposition, and then, through this decomposition, construct, by the introduction of a homotopy parameter, a new matrix such that it has constant rank before a desired equilibrium is reached. By adjunction of this idea to the homotopy method, a simpler constructive proof is obtained for the generic existence of GEI equilibria. For the purpose of computing these equilibria, from this constructive proof is then derived a path-following algorithm whose performance is finally demonstrated by means of two numerical examples.

Working paper 485
1 December 2014
Journal: Journal of Economic Dynamics & Control
1 March 2015