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)