Instrumental variables: A non-asymptotic viewpoint

TL;DR

This paper offers a non-asymptotic analysis of the linear instrumental variable estimator, introducing a new measure of instrument strength and providing valid confidence intervals even for weak instruments, with practical application to pollution health effects.

Contribution

It introduces a novel measure of instrument strength and develops non-asymptotic confidence intervals for IV estimators, applicable to both strong and weak instruments.

Findings

Strong instruments yield intervals matching asymptotic results.

Weak instruments require adaptive adjustments for valid inference.

PM2.5 exposure significantly increases health risks.

Abstract

We provide a non-asymptotic analysis of the linear instrumental variable estimator allowing for the presence of exogeneous covariates. In addition, we introduce a novel measure of the strength of an instrument that can be used to derive non-asymptotic confidence intervals. For strong instruments, these non-asymptotic intervals match the asymptotic ones exactly up to higher order corrections; for weaker instruments, our intervals involve adaptive adjustments to the instrument strength, and thus remain valid even when asymptotic predictions break down. We illustrate our results via an analysis of the effect of PM2.5 pollution on various health conditions, using wildfire smoke exposure as an instrument. Our analysis shows that exposure to PM2.5 pollution leads to statistically significant increases in incidence of health conditions such as asthma, heart disease, and strokes.