Statistics, experimentation, causal reasoning · insight-1022
Report the first-stage strength of an instrument and expect a weak one to pull estimates toward the biased answer
- Evidence type
- documented fact
- Difficulty
- hard
- Roles
- Data scientist
- Industries
- aviation, public-sector, banking
Summary: situation, action, reason, boundary
Situation
A weather-disruption indicator (hypothetical) is used to instrument the fare a rebooked passenger paid, and the first-stage F-statistic is about 3.
Action
Report the first-stage F and partial R-squared, the reduced form (instrument on outcome), and weak-instrument-robust intervals. Argue the exclusion restriction in words, and prefer one or two strong instruments over many weak ones.
Reason
When instruments are only weakly correlated with the endogenous variable, the usual asymptotics fail and the estimator is pulled toward OLS.
Boundary
Instrumental-variable analyses of price, exposure or take-up.
Symptom or risk
Two-stage least squares with weak instruments leans toward the confounded OLS estimate and has poor coverage, so the causal estimate repeats the original bias with false comfort.
Exceptions
Randomised encouragement designs, where the instrument is strong by construction.
Trade-offs
Strong instruments are rare, so many questions remain unanswerable.
Pitfalls
Adding many weak instruments to raise the first-stage R-squared; this pushes two-stage least squares further toward OLS.
Lessons and concepts
Claims and their sources
With instruments only weakly correlated with the endogenous regressor, two-stage least squares estimates with many instruments approach the OLS estimate, as illustrated with returns-to-education data.