Accuracy of stochastic perturbation methods: The case of asset pricing models

This paper investigates the accuracy of a perturbation method in approximating the solution to stochastic equilibrium models under rational expectations. As a benchmark model, we use a version of asset pricing models proposed by Burnside (1998, Journal of Economic Dynamics and Control 22, 329-340) which admits a closed-form solution while not making the assumption of certainty equivalence. We then check the accuracy of perturbation methods - extended to a stochastic environment - against the closed form solution. Second- and especially fourth-order expansions are then found to be more efficient than standard linear approximation, as they are able to account for higher-order moments of the distribution - which constitutes a major improvement of this stochastic approach to approximation compared to other methods that assume certainty equivalence, (C) 2001 Elsevier Science B.V. All rights reserved.