论文标题
弱仪器，第一阶段异质性，稳健的F检验和GMM估计器，具有基于第一阶段残差的重量矩阵
Weak Instruments, First-Stage Heteroskedasticity, the Robust F-Test and a GMM Estimator with the Weight Matrix Based on First-Stage Residuals
论文作者
论文摘要
本文涉及与安德鲁斯（Andrews）蒙特卡洛分析（Monte Carlo）分析（2018）中与强大的第一阶段F统计有关的发现。这一发现似乎抹黑了强大的F统计量作为对识别未识别的测试。但是，此处显示，强大的F统计量的大量值表示存在第一阶段信息，但是2SLS估计器或标准GMM估计器可能无法很好地利用。对此进行纠正的估计器是一个强大的GMM估计器，表示GMMF，其重量矩阵不是基于结构残差，而是基于第一阶段残差。对于安德鲁斯（Andrews）（2018）的分组数据设置，该GMMF估计器根据组特异性浓度参数的权重以与2SL在同性恋下的方式相同的方式，使用弱仪器渐近仪，正式显示。 GMMF估计器的表现要比Andrews（2018）设计中的2SLS估计量好得多，在相对偏见和WALD-TEST大小扭曲方面的表现良好。我们表明，当误差方差随着时间的推移是异性恋时，动态面板数据模型中可能会发生相同的模式。我们进一步得出了库存和Yogo（2005）弱仪器的临界值适用于与GMMF估计器的行为相关的稳定f统计量的临界值。
This paper is concerned with the findings related to the robust first-stage F-statistic in the Monte Carlo analysis of Andrews (2018), who found in a heteroskedastic grouped-data design that even for very large values of the robust F-statistic, the standard 2SLS confidence intervals had large coverage distortions. This finding appears to discredit the robust F-statistic as a test for underidentification. However, it is shown here that large values of the robust F-statistic do imply that there is first-stage information, but this may not be utilized well by the 2SLS estimator, or the standard GMM estimator. An estimator that corrects for this is a robust GMM estimator, denoted GMMf, with the robust weight matrix not based on the structural residuals, but on the first-stage residuals. For the grouped-data setting of Andrews (2018), this GMMf estimator gives the weights to the group specific estimators according to the group specific concentration parameters in the same way as 2SLS does under homoskedasticity, which is formally shown using weak instrument asymptotics. The GMMf estimator is much better behaved than the 2SLS estimator in the Andrews (2018) design, behaving well in terms of relative bias and Wald-test size distortion at more standard values of the robust F-statistic. We show that the same patterns can occur in a dynamic panel data model when the error variance is heteroskedastic over time. We further derive the conditions under which the Stock and Yogo (2005) weak instruments critical values apply to the robust F-statistic in relation to the behaviour of the GMMf estimator.
