Estimation of Impulse Response Functions When Shocks are Observed at a Higher Frequency than Outcome Variables*

This paper proposes mixed-frequency distributed-lag (MFDL) estimators of impulse response functions (IRFs) in a setup where (<i>i</i>) the shock of interest is observed, (<i>ii</i>) the impact variable of interest is observed at a <i>lower</i> frequency (as a temporally aggregated or sequentially sampled variable), (<i>iii</i>) the data generating process (DGP) is given by a VAR model at the frequency of the shock, and (<i>iv</i>) the full set of relevant endogenous variables entering the DGP is unknown or unobserved. Consistency and asymptotic normality of the proposed MFDL estimators is established, and their small-sample performance is documented by a set of Monte Carlo experiments. The usefulness of MFDL estimator is then illustrated in three empirical applications: (<i>i</i>) the daily pass-through of shocks to crude oil prices observed at the daily frequency to U.S. gasoline consumer prices observed at the weekly frequency, (<i>ii</i>) the impact of shocks to global investors’ risk appetite on global capital flows, and (<i>iii</i>) the impact of monetary policy shocks on real activity.