  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 SVAR analysis, our methods do not require
invertibility. Applied to U.S. data, they give a tight upper bound on the
importance of monetary shocks for inflation dynamics.
