Avoiding Invalid Instruments and Coping with Weak Instruments
Causal Question / Estimand
The causal effect of an endogenous regressor via IV/2SLS, with the practical question: how to keep that estimate credible when instruments may be invalid (violate exclusion) or weak (poor first stage)?
Identification Strategy
A practitioner’s guide to the two central IV threats. Invalid instruments: an instrument must be uncorrelated with the disturbance (Exclusion-Restriction) and correlated with the endogenous regressor; over-identifying restrictions tests (Sargan/ Hansen) can detect some invalidity but cannot prove validity, which rests on an untestable argument. Weak instruments: even valid instruments, if weakly correlated with the regressor, bias 2SLS toward OLS and wreck inference; the paper surveys diagnostics (first-stage F) and weak-instrument-robust procedures.
Key Assumptions
Exclusion-Restriction (instrument uncorrelated with the error), relevance / adequate first stage (Weak-Instruments), Monotonicity for a LATE reading, SUTVA.
Threats to Validity
The paper is organized around the threats: invalid instruments (correlated with the error, e.g. via omitted channels or measurement) and weak instruments (finite-sample bias and size distortions). Stresses that overidentification tests are necessary but not sufficient checks.
Setting / Data
n/a — methodological/expository, with worked examples (e.g. crime/incarceration).
Key Claims
- Instrument validity cannot be proven; overidentification tests catch only some violations, so the exclusion argument must be substantive.
- Weak instruments are dangerous even when valid — always report and judge the first stage, and use weak-instrument-robust inference when in doubt.
- Just-identified IV is more robust to weak-instrument bias than many-instrument 2SLS.
Connections
- Develops the Weak-Instruments concept; complements the conceptual treatment in AngristKrueger2001-SearchForIdentification and Imbens2014-IVEconometriciansPerspective.
- Echoes the natural-experiment skepticism of RosenzweigWolpin2000-NaturalNaturalExperiments. See also IV
Citation
Murray, M. P. (2006). Avoiding Invalid Instruments and Coping with Weak Instruments. Journal of Economic Perspectives, 20(4), 111–132.