Essays on weak identification - LIM, Dennis Guo Wei (Institutional Knowledge at Singapore Management University, 2024)
This dissertation presents a comprehensive examination of inference techniques for weak instrumental variable (IV) models, crucial in addressing endogeneity and bias in econometric analyses. Comprising two interconnected chapters, the research explores innovative methodologies to enhance the reliability and robustness of IV regression estimations. Chapter 1 is concerned with maximizing the power of tests in the many weak IVs setting. This is done by introducing a novel approach that considers a linear combination of jackknife Anderson-Rubin (AR), jackknife Lagrangian multiplier (LM), and orthogonalized jackknifeLM tests for inference in IV regressions with many weak instruments and heteroskedasticity. Following I. Andrews (2016), weights are adaptively chosen in a linear fashion based on a decision-theoretic rule, ensuring control of asymptotic size under weak and strong identifications. The proposed test exhibits optimal power against local alternatives, confirmed by simulations and empirical applications to Angrist and Krueger’s (1991) dataset. Chapter 2 deals with inference under both fixed and diverging weak IVs simultaneously. In particular, conventional and jackknife Anderson-Rubin (AR) Tests are developed separately to conduct weak-identification-robust inference when the number of IVs is fixed or diverging toinfinity with the sample size, respectively. These two tests compare distinct test statistics with distinct critical values. To implement them, researchers first need to take a stance on the asymptotic behaviour of the number of IVs, which is ambiguous when this number is just moderate. Instead, in this paper, two analytical and two bootstrap-based weakidentification-robust AR tests are introduced, all of which control asymptotic size whether the number of IVs is fixed or diverging - in particular, the number of instruments is allowedbut not required to be greater than the sample size. Power properties of these uniformlyvalid AR tests under both fixed and diverging number of IVs are analysed.