Extrapolating LATE with Weak IVs

TL;DR

This paper develops robust inference methods for treatment effect parameters like LATE and ATE in the presence of weak instruments, ensuring valid confidence intervals even with limited instrument variation.

Contribution

It introduces the first weak instrument robust inference framework for a broad class of treatment effect parameters, including LATE, ATE, and policy effects.

Findings

Provides asymptotically valid confidence sets for treatment effects with weak instruments.

Demonstrates the methods using data on prosecutors' leniency and recidivism.

Addresses limitations of classical tests like the F-test in weak instrument scenarios.

Abstract

To evaluate the effectiveness of a counterfactual policy, it is often necessary to extrapolate treatment effects on compliers to broader populations. This extrapolation relies on exogenous variation in instruments, which is often weak in practice. This limited variation leads to invalid confidence intervals that are typically too short and cannot be accurately detected by classical methods. For instance, the F-test may falsely conclude that the instruments are strong. Consequently, I develop inference results that are valid even with limited variation in the instruments. These results lead to asymptotically valid confidence sets for various linear functionals of marginal treatment effects, including LATE, ATE, ATT, and policy-relevant treatment effects, regardless of identification strength. This is the first paper to provide weak instrument robust inference results for this class of parameters. Finally, I illustrate my results using data from Agan, Doleac, and Harvey (2023) to analyze counterfactual policies of changing prosecutors' leniency and their effects on reducing recidivism.