12.4 Assumptions

• “A valid instrument induces changes in the explanatory variable but has no independent effect on the dependent variable” (Wikipedia)
• Assumption: IV “must be independent of other causes of the dependent variable, and it must influence exposure to treatment but not influence the outcome, other than through its effect on exposure to treatment [exclusion restriction]” (Dunning 2009, 6–7)
  • The instrument \(Z_{i}\) is correlated with the treatment indicator \(D_{i}\) \((\delta \neq 0)\).
  • There is no other (direct or indirect) relation between the instrument \(Z_{i}\) and the outcome \(Y_{i}\) expect through the treatment \(D_{i}\) (exclusivity) [conditional on covariates]

References

Dunning, Thad. 2009. “Instrumental Variables.” In International Encyclopedia of Political Science.