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, then ivpack::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)