19.9 Don’t just test for weakness, fix it
- use method that’s not as strongly affected by weak instruments
- most common: 1 treatment, 1 control variable**
Adjust standard errors
- old (1949): Anderson-Rubin confidence intervals
- not universal practice, but you could always report these SE
- in
R
:AER::ivreg
, thenivpack::anderson.rubin.ci
Limited-information maximum likelihood (LIML)
- estimation that performs better with weak instruments
- scales down prediction with parameter \(\kappa\)
- \(\kappa = 1\) –> no adjustment, 2SLS
- \(\kappa < 1\) –> bring back some of the endogenous variable
- additionally use Fuller’s \(\alpha\)
- \(\kappa = \hat{\kappa} - \frac{\alpha}{N - N_1}\)
- \(N\) # observations, \(N_1\) # instruments
- worse precision, but less reliance on instrument
Use lots of weak instruments
- starting place: Chao and Swanson (2005)