Weak Instruments

An instrument is weak when it is only loosely correlated with the endogenous regressor — a weak first stage. Weak instruments break the usual IV asymptotics: the 2SLS estimator is biased toward OLS (severe in finite samples and when many instruments are used), and conventional standard errors and t-tests are badly sized, so inference is unreliable even when the Exclusion-Restriction holds. Diagnosed via the first-stage F-statistic (rule-of-thumb F>10; later work raises the bar) and addressed with weak-instrument-robust inference (e.g. Anderson–Rubin), limited-information methods, or just-identified designs. Relevance is the testable IV requirement, in contrast to the untestable exclusion restriction.

Relied on by

IV / 2SLS estimation (a first-stage relevance condition is part of the IV requirements, alongside instrument independence and the exclusion restriction).

Referenced by

• Murray2006-WeakAndInvalidInstruments, Imbens2014-IVEconometriciansPerspective, AngristKrueger2001-SearchForIdentification

New-papers pass (2026-07-04): FreyaldenhovenEtAl2019-PreEventTrendsPanelEventStudy (the estimator needs the covariate to carry a strong signal of the confound; weak identification degrades it in simulations).