Should We Go One Step Further? An Accurate Comparison of One-Step and Two-Step Procedures in a Generalized Method of Moments Framework

Abstract

According to the conventional asymptotic theory, the two-step Generalized Method of Moments (GMM) estimator and test perform as least as well as the one-step estimator and test in large samples. The conventional asymptotic theory, as elegant and convenient as it is, completely ignores the estimation uncertainty in the weighting matrix, and as a result it may not reflect finite sample situations well. In this paper, we employ the fixed-smoothing asymptotic theory that accounts for the estimation uncertainty, and compare the performance of the one-step and two-step procedures in this more accurate asymptotic framework. We show the two-step procedure outperforms the one-step procedure only when the benefit of using the optimal weighting matrix outweighs the cost of estimating it. This qualitative message applies to both the asymptotic variance comparison and power comparison of the associated tests. A Monte Carlo study lends support to our asymptotic results.