Fixed-Smoothing Asymptotics in a Two-Step Generalized Method of Moments Framework
研究了两步GMM框架下的固定平滑渐近性质，发现Wald统计量等仍渐近枢轴，且可用非中心F分布近似临界值，模拟表明新方法比现有检验更准确。
This paper develops the fixed-smoothing asymptotics in a two-step generalized method of moments (GMM) framework. Under this type of asymptotics, the weighting matrix in the second-step GMM criterion function converges weakly to a random matrix and the two-step GMM estimator is asymptotically mixed normal. Nevertheless, the Wald statistic, the GMM criterion function statistic, and the Lagrange multiplier statistic remain asymptotically pivotal. It is shown that critical values from the fixed-smoothing asymptotic distribution are high order correct under the conventional increasing-smoothing asymptotics. When an orthonormal series covariance estimator is used, the critical values can be approximated very well by the quantiles of a noncentral F distribution. A simulation study shows that statistical tests based on the new fixed-smoothing approximation are much more accurate in size than existing tests.