Estimation of Impulse Response Functions when Shocks Are Observed at a Higher Frequency Than Outcome Variables

This article proposes mixed-frequency distributed-lag (MFDL) estimators of impulse response functions in a setup where (i) the shock of interest is observed, (ii) the impact variable of interest is observed at a lower frequency (as a temporally aggregated or sequentially sampled variable), (iii) the data generating process (DGP) is given by a VAR model at the frequency of the shock, and (iv) 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) 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, (ii) the impact of shocks to global investors' risk appetite on global capital flows, and (iii) the impact of monetary policy shocks on real activity.