Robust Inference in Econometrics

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This research is designed to improve the econometric and statistical methods available for empirical researchers in economics and other fields, including political science, medicine, and the physical sciences. Standard statistical methods rely on certain basic assumptions for their validity. However, these assumptions are not guaranteed to hold in practical applications, and their failure can lead to misleading results. This project contributes to the literature that aims to develop methods that rely on a much weak set of assumptions, which leads to more robust statistical procedures. Emphasis in the research is to make methods robust to weak identification and lack of identification, where "identification" refers to the amount of information available in the data concerning the object of interest. This research has the potential to make empirical research, upon which economic policy is based, more robust.The literature on identification-robust inference has made considerable progress on inference for an unknown parameter vector as a whole. This research focuses on linear and nonlinear functions of the parameter vector, such as subvectors, which typically are of much greater interest in practice than the whole parameter. The investigator develops methods that are completely robust to weak identification and identification failure (in the sense of having correct asymptotic size in a uniform sense), are not asymptotically conservative, and are asymptotically efficient under strong identification. The methods will be of a two-step fashion where the first-step involves a confidence set for the nuisance parameter and the second step involves a C(α)-type test (or confidence set) that employs a data-dependent critical value. The investigator also carries out research on (i) deterministically time-varying autoregressive models that may exhibit (local) nonstationarity or stationarity and smooth transitions between the two, (ii) optimality properties of tests in the widely-used linear instrumental variables model, and (iii) subvector tests with optimality properties under weak and strong identification in the linear instrumental variable model with two endogenous variables.