Confidence Regions and Inference in the Presence of Weak Instruments

本研究的目的是为一般k-内生变量、过度识别工具、模型的置信区域的构建提供统计检验和方法。 此外，还有几个次要目标。 首先，工作将扩展到一般的GMM框架。 检验统计量的分布很可能会延续到非线性和非球形模型中，但是需要对依赖于第一阶段的重要性的细节进行研究，因为标准GMM方法没有单独识别的第一阶段。第二，在计算“切换LR”和“切换LM”统计的自由度时，需要澄清包含和排除的外生变量之间的区别。 第三，将扩大其他人最近的工作，为寻找“薄弱手段”提供诊断。 显然，简单的第一阶段显著性检验是不够的。 第四，所发展的方法的实际意义将通过将其应用于真实的数据来证明。 特别是，在劳动经济学中广泛采用自然实验作为工具的来源，应该提供一个很好的“试验台”。 使用上述方法的推断将与目前采用的传统方法进行比较。

The purpose of this research is to produce statistical tests and methods for the construction of confidence regions that are valid for the general k-endogenous variable, overidentifying instruments, model. In addition there are several subsidiary goals. First, the work will be extended to the general GMM framework. It is very likely that the distribution of test statistics carries over to nonlinear and nonspherical models, but works needs to be done on those details which rely on the significance of the first stage simply because the standard GMM approach doesn't have a separately identified first stage. Second, the distinction between included and excluded exogenous variables needs to be clarified in computing the degrees of freedom for the `switched-LR` and `switched-LM` statistics. Third, recent work by others will be extended which provide diagnostics for finding `weak instruments.` It is clear that simple tests of first-stage significance are inadequate. Fourth, the practical significance of the methods developed will be demonstrated by applying them to real data. In particular, the widespread adoption in labor economics of natural experiments as a source of instruments should provide a good `test bed.` Inference using the above methods will be compared to the traditional methods currently employed.