Should We Go One Step Further? ? Accurate Comparison of One-step and Two-step Procedures in a GMM Framework

该奖项资助了一个项目，该项目开发了关于方法统计特性的新知识，这些方法被广泛用于检验从经济理论中发展出来的假设。总体目标是为使用这些方法的研究人员提供新的工具，以了解为其特定应用选择哪种方法。使用这些工具可以得出更精确和可靠的结论。该项目通过改进用于数据分析的方法来推进科学。关于估计器和测试的相对效率的问题是计量经济学的基本问题。在流行的广义矩法（GMM）设置中，使用两步程序来提高效率是标准做法。这个两步的过程需要估计一个加权矩阵。标准渐近理论预测，在加权矩阵的估计误差是渐近可忽略的，因此两步过程优于一步过程在大样本。然而，这个渐近的结果虽然简洁方便，但忽略了加权矩阵中可能存在的估计不确定性。这种不确定性可能非常高。PI计划开发一个新的渐近框架，充分考虑估计的不确定性。他将在此框架下比较一步和两步GMM程序以及其他程序的性能。PI计划考虑时间序列和空间设置以及参数、非参数和半参数模型。结果应该有助于应用研究人员为他们的具体问题选择最有效的统计程序。

This award funds a project that develops new knowledge about the statistical properties of methods that are widely used to test hypotheses developed from economic theory. The overall goal is to give researchers who use these methods new tools for understanding which method to choose for their particular application. Employing these tools could lead to more precise and reliable conclusions. The project advances science by improving the methods used for data analysis.Questions about the relative efficiency of estimators and tests are fundamental in econometrics. In the popular Generalized Method of Moments (GMM) setting, it is standard practice to use a two-step procedure to improve efficiency. The two-step procedure requires the estimation of a weighting matrix. Standard asymptotic theory predicts that the estimator error in the weighting matrix is asymptotically negligible, and therefore the two step procedure outperforms the one step procedure in large samples. However, this asymptotic result, while elegant and convenient, ignores possible estimation uncertainty in the weighting matrix. This uncertainty can be very high. The PI plans to develop a new asymptotic framework that fully accounts for estimation uncertainty. He will compare the performance of the one step and two step GMM procedures, as well as other procedures, under this framework. The PI plans to consider both time series and spatial settings as well as parametric, nonparametric, and semiparametric models. The results should help applied researchers choose the most efficient statistical procedures for their specific problems.