All simulators
Weak Instruments
As the first stage weakens, 2SLS drifts to OLS and t-intervals under-cover; Anderson–Rubin stays at 95%.
Day 65: Weak Instruments & Robust Inferencemean first-stage F
2.9
median 2SLS
1.123
OLS limit 1.79
t-interval coverage
91.5%
Anderson–Rubin coverage
94.7%
true effect 1OLS probability limit
1,500 simulated studies with 200 observations each; the true effect is 1. As the first stage weakens, the 2SLS distribution shifts towards the OLS limit (orange), grows heavy tails, and the usual t-based interval under-covers. The Anderson–Rubin test keeps its 95% coverage at every strength.