Professor Jungbin Hwang’s paper “Should We Go One Step Further? An Accurate Comparison of One-step and Two-step Procedures in a Generalized Method of Moments Framework”, co-authored with Yixiao Sun, has been accepted for publication in the Journal of Econometrics, one of the top scholarly journals in theoretical econometrics. The paper started as a third-year paper project when Professor Hwang was a graduate student in the University of California, San Diego.
Professor Hwang’s paper provides an assessment of the merits of the first step GMM estimator and test relative to the two-step GMM estimator and test. The article shows the two-step procedure outperforms the one-step method only when the benefit of using the optimal weighting matrix outweighs the cost of estimating it. The qualitative message applies to both the asymptotic variance comparison and power comparison of the associated tests.
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 that 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.