What Impulse Response Do Instrumental Variables Identify?

Abstract

We study what local projection instrumental variable (LP-IV) regressions identify when an instrument is correlated with several structural shocks, such as defense and non-defense spending shocks. LP-IV identifies an instrument-specific affine combination of the component impulse responses, possibly with negative weights. Over-identified 2SLS or GMM yields another such combination, and the over-identification test can reject even with valid instruments. With as many instruments as shocks, the component responses are identified when each shock has a policy variable (e.g., sectoral spending) and its impact on the other policy variables is restricted. We illustrate with government spending and tax multipliers.