Confidence Regions and Inference in the Presence of Weak Instruments

本研究的目的是为一般的k-内生变量、过度识别工具、模型提供有效的置信区域的构建统计检验和方法。此外，还有几个附属目标。首先，这项工作将扩展到通用GMM框架。测试统计量的分布很可能延续到非线性和非球面模型，但是需要在依赖于第一阶段的重要性的那些细节上进行工作，因为标准GMM方法没有单独确定的第一阶段。其次，在计算“切换- lr”和“切换- lm”统计量的自由度时，需要澄清包含和排除外生变量之间的区别。第三，其他人最近的工作将得到扩展，为发现“弱仪器”提供诊断。“很明显，第一阶段意义的简单测试是不够的。第四，将通过将所开发的方法应用于实际数据来证明其实际意义。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“测试平台”。使用上述方法的推理将与目前使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.