Verifying competitive equilibria in dynamic economies

Abstract

In this paper I derive a sucient condition for a numeri-cally computed -equilibrium of a dynamic stochastic economy with heterogeneous agents 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 -equilibria that form a neighborhood of the computed approximation.

I use this method of 'self-validating computation' to prove that in realistically calibrated stochastic overlapping generation models, competitive equilibria can often be
extremely well approximated by cubic functions, mapping the current shock and the beginning-of-period wealth-distribution to current endogenous variables.