Verifying Competitive Equilibria in Dynamic Economies

In this paper, I examine ϵ-equilibria of stationary dynamic economies with heterogeneous agents and possibly incomplete financial markets. I give a simple example to show that even for arbitrarily small ϵ > 0, allocation and prices can be far away from exact equilibrium allocations and prices. That is, errors in market clearing or individuals' optimality conditions do not provide enough information to assess the quality of an approximation. I derive a sufficient condition for an ϵ-equilibrium to be close to an exact equilibrium. If the economic fundamentals are semi-algebraic, one can verify computationally whether this condition holds. The condition can be interpreted economically as a robustness requirement on the set of ϵ-equilibria which form a neighbourhood of the computed approximation. I illustrate the main result and the computational method using an infinite horizon economy with overlapping generations and incomplete financial markets. Copyright 2011, Oxford University Press.