19.4 Instrumental Variables estimator

Two-stage least squares (2SLS)

• 1st stage: instrument to predict treatment
• 2nd stage: predicted treatment to predict outcome
• include controls in both stages
• ratio of effects: \(\frac{Z -> Y}{Z -> X}\)

• pros
  • easy to estimate
  • flexible (add instruments possible)
  • easy to understand (OLS)
• cons
  • doesn’t perform well with small samples
  • doesn’t do well with heteroskedastic errors

Generalized Method of Moments (GMM)

• based on assumptions + theory: construct statistical moments
• IV: assume Z is unrelated to second-stage error term
• overidentification: # instruments > # treatment/endogenous variables
  • GMM more precise than 2SLS (with heteroskedasticity)