The accuracy of numerical solutions for dynamic GEI models ∗

This paper develops theoretical foundations for the computation of competitive equilibria in dynamic stochastic general equilibrium models with heterogeneous agents and incomplete financial markets. While there are several algorithms which compute prices and allocations for which agents’ first order conditions are approximately satisfied (‘approximate equilibria’), there are few results on how to interpret the errors in these candidate solutions and how to relate the computed allocations and prices to exact equilibrium allocations and prices. Following Postlewaite and Schmeidler (1981) we interpret approximate equilibria as equilibria for close-by economies, i.e. for economies with close-by individual endowments and preferences. In order to conduct an error analysis in dynamic stochastic general equilibrium models, we define an -equilibrium to be a set of endogenous variables which consists of the finite support of an approximate equilibrium process. Given an -equilibrium we show how to derive bounds on perturbations in individual endowments and preferences which ensure that the -equilibrium approximates an exact equilibrium for the perturbed economy. We give a detailed discussion of the error analysis for two models which are commonly used in applications, an OLG model with stochastic production and an asset pricing model with infinitely lived agents. We illustrate the analysis with some numerical examples. It is shown that in these examples the derived bounds are not more than one order of magnitude higher than maximal errors in Euler equations. ∗We thank seminar participants at Stanford University, the Illinois Conference in Economic Theory, the European General Equilibrium Conference in Bielefeld, the 2003 SED conference in Paris, the 2003 SAET conference on Rhodes, the 2003 SITE workshop on computational economics and especially Peter Hammond, Martin Hellwig, Ken Judd, Mordecai Kurz, Alvaro Sandroni and Manuel Santos for discussions and very useful comments.