34.1 Challenges with Instrumental Variables

While IVs can provide a solution to endogeneity, several challenges arise:

• Exclusion Restriction Violations: If $Z$ affects $Y$ through any channel other than $X$, the IV estimate is biased.
• Repeated Use of Instruments: Common instruments, such as weather or policy changes, may be invalid due to their widespread application across studies (Gallen 2020). One needs to test for invalid instruments (Hausman-like test).
  • A notable example is Mellon (2021), who documents that 289 social sciences studies have used weather as an instrument for 195 variables, raising concerns about exclusion violations.
• Heterogeneous Treatment Effects: The Local Average Treatment Effect (LATE) estimated by IV applies only to compliers—units whose treatment status is affected by the instrument.
• Weak Instruments: Too little correlation with the endogenous regressor yields unstable estimates.
• Invalid Instruments: If the instrument violates exogeneity, your results are inconsistent.
• Interpretation Mistakes: The IV identifies only the effect for those “marginal” units whose treatment status is driven by the instrument.

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References

Gallen, Trevor. 2020. “Broken Instruments.” Available at SSRN 3671850.

Mellon, Jonathan. 2021. “Rain, Rain, Go Away: 194 Potential Exclusion-Restriction Violations for Studies Using Weather as an Instrumental Variable.” American Journal of Political Science.