Instrumental Variable Identification of Dynamic Variance Decompositions

Macroeconomists increasingly use external sources of exogenous variation for causal inference. However, unless such external instruments (proxies) capture the underlying shock without measurement error, existing methods are silent on the importance of that shock for macroeconomic fluctuations. We show that, in a general moving-average model with external instruments, variance decompositions for the instrumented shock are interval-identified, with informative bounds. Various additional restrictions guarantee point identification of both variance and historical decompositions. Unlike structural vector auto-regression analysis, our methods do not require invertibility. Applied to US data, they give a tight upper bound on the importance of monetary shocks for inflation dynamics.