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) 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 estab- lished, and their small-sample performance is documented by a set of Monte Carlo experiments. The proposed approach is then applied to estimate the daily pass-through of changes in crude oil prices observed at the daily frequency to U.S. gasoline consumer prices observed at the weekly frequency. We find that the pass-through is fast, with about 23% of the crude oil price changes passed through to retail gasoline prices within five working days, representing about 42% of the long-run pass-through.