Weak Instrumental Variables: Limitations of Traditional 2SLS and Exploring Alternative Instrumental Variable Estimators

Abstract: Instrumental variables estimation has gained considerable traction in recent decades as a tool for causal inference, particularly amongst empirical researchers. This paper makes three contributions. First, we provide a detailed theoretical discussion on the properties of the standard two-stage least squares estimator in the presence of weak instruments and introduce and derive two alternative estimators. Second, we conduct Monte-Carlo simulations to compare the finite-sample behavior of the different estimators, particularly in the weak-instruments case. Third, we apply the estimators to a real-world context; we employ the different estimators to calculate returns to schooling.