GMM Model Averaging Using Higher Order Approximations

Abstract

Moment conditions model averaging (MA) estimators in the GMM framework are considered. Under finite sample considerations, MA estimators with optimal weights are proposed, in the sense that weights minimize the corresponding higher-order asymptotic mean squared error (AMSE). It is shown that the higher-order AMSE objective function has a closed-form expression, which makes this procedure applicable in practice. In addition, and as an alternative, different averaging schemes based on moment selection criteria are considered, in which weights for averaging across GMM estimates can be obtained by direct smoothing or by numerical minimization of a specific criterion. Asymptotic properties assuming correctly specified models are derived and the performance of the proposed averaging approaches is contrasted with existing model selection alternatives $i)$ analytically, for a simple IV example, and $ii)$ by means of Monte Carlo experiments in a nonlinear setting, showing that MA compares favourably in many relevant setups. The usefulness of MA methods is illustrated by studying the effect of institutions on economic performance.