Finite sample properties of the efficient method of moments

Abstract

Gallant and Tauchen (1996) describe an estimation technique, known as Efficient Method of Moments (EMM), that uses numerical methods to estimate parameters of a structural model. The technique uses as matching conditions (or moments, in the GMM jargon) the gradients of an auxiliary model that fits a subset of variables that may be simulated from the structural model. This paper presents three Monte Carlo experiments to assess the finite sample properties of EMM. The first one compares it with a fully efficient procedure (Maximum Likelihood) by estimating an invertible moving-average (MA) process. The second and third experiments compare the finite sample properties of the EMM estimators with those of GMM by using stochastic volatility models and consumption-based asset-pricing models. The experiments show that the gains in efficiency are impressive; however, given that both EMM and GMM share the same type of objective function, finite sample inference based on asymptotic theory continues to lead, in some cases, to “over rejections,” even though they are not as significant as in GMM.