A Survey of the Weak Instruments Problem in Just-Identified Linear IV Regression

The Weak Instruments problem, which characterizes the situation where the endogenous regressor is only weakly correlated with the excluded instrument, is a problem frequently encountered in empirical practice. In this paper, we focus on the most popular setting where there is a single endogenous regressor and single instrument, and try to provide empirical researchers with an accessible guide to the weak instruments literature. The focus is on the nature of weak instruments problem, methods to detect weak instrument, and methods to deal with weak instrument. A distinct feature of this paper is that it also explores the situation where the true first stage regression is nonlinear. This paper also surveys papers published on American Economic Review between 2020 and 2024. The result shows that empirical researchers still have relatively insufficient understanding of the weak instruments problem and the methods available to deal with it.