Generalized autoregressive Method of Moments

Abstract

We extend the generalized method of moments to a setting where a subset of the parameters may vary over time with unknown dynamics. We approximate the true unknown dynamics by an updating scheme that is driven by the influence function of the conditional criterion function at time t. The updates ensure a local improvement of the conditional criterion function at each time in expectation. In our framework, time-varying parameters are a function of past data; it leads to a computationally efficient method since it does not require simulation-based methods for estimation. The approach can be applied to a wide range of moment conditions that are used in economics and finance. We provide an illustration for a capital asset pricing model with time-varying risk aversion.

Keywords: dynamic models, time-varying parameters, generalized method of moments, non-linearity, equity premium puzzle, CCAPM

JEL Classification: C10, C22, C32, C51