What Impulse Response Do Instrumental Variables Identify?

Instrumental variables (IV) are often used to provide exogenous variation in the impulse response analysis but the heterogeneous effects the IV may identify are rarely discussed. In microeconometrics, on the other hand, it is well understood that an IV identifies the local average treatment effect (Imbens and Angrist, 1994). Recognizing that macro shocks are often composites (e.g., the government spending shock is the sum of sectoral spending shocks), we show that the IV estimand can be written as a weighted average of componentwise impulse responses. Negative weights can arise if the correlations between the IV and the components of the macro shock have different signs. This implies that the response of the variable of interest to an IV shock may evolve in an arbitrary way regardless of the true underlying componentwise impulse responses. We provide conditions under which the IV estimand has a structural interpretation. When additional IVs or auxiliary disaggregated data are available, we derive informative bounds on the componentwise impulse responses. With multiple IVs and disaggregated data, the impulse responses can be point-identified. To demonstrate the empirical relevance of our theory, we revisit the IV estimation of the government spending multiplier in the US. We show that the non-defense spending multiplier larger than one can be obtained from the conventional IV estimates of the aggregate spending multiplier, which are smaller than one