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

TL;DR

This paper critically examines the limitations of traditional 2SLS estimators with weak instruments, introduces alternative estimators, and compares their performance through simulations and real-world application to returns on schooling.

Contribution

It provides a theoretical analysis of 2SLS limitations, proposes two new estimators, and evaluates their effectiveness via simulations and empirical data.

Findings

Traditional 2SLS performs poorly with weak instruments

Alternative estimators show improved finite-sample properties

Empirical application demonstrates differences in estimated returns

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.