CONSISTENCY OF A METHOD OF MOMENTS ESTIMATOR BASED ON NUMERICAL-SOLUTIONS TO ASSET PRICING-MODELS

This paper considers the properties of estimators based on numerical s olutions to a class of economic models. In particular, the numerical m ethods discussed are those applied in the solution of linear integral equations, specifically Fredholm equations of the second kind. These i ntegral equations arise out of economic models in which endogenous var iables appear linearly in the Euler equations, but for which easily ch aracterized solutions do not exist. Tauchen and Hussey [24] have propo sed the use of these methods in the solution of the consumption-based asset pricing model. In this paper, these methods are used to construc t method of moments estimators where the population moments implied by a model are approximated by the population moments of numerical solut ions. These estimators are shown to be consistent if the accuracy of t he approximation is increased with the sample size. This result depend s on the solution method having the property that the moments of the a pproximate solutions converge uniformly in the model parameters to the moments of the true solutions.