Abstract
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 established, 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. JEL Classification: C22
Highlights
This paper is concerned with estimating impulse-response functions (IRFs) when the outcome variable of interest is observed at a lower frequency than the shock of interest
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, (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
One empirical question that can be addressed in this framework, and that is explored in this paper, is the daily pass-through of changes in crude oil price shocks observed at the daily frequency on U.S retail gasoline prices observed only at the weekly frequency
Summary
This paper is concerned with estimating impulse-response functions (IRFs) when the outcome variable of interest is observed at a lower frequency than the shock of interest. One empirical question that can be addressed in this framework, and that is explored in this paper, is the daily pass-through of changes in crude oil price shocks observed at the daily frequency on U.S retail gasoline prices (at the pump) observed only at the weekly frequency. The approaches considered in this literature all assume that the data on the shocks and the outcome variables are observed at the same frequency. Interest has not yet been considered, to the best of our knowledge We borrow from this strand of the literature the idea that the true IRFs can be approximated by a ‡exible function that features a small number of unknown parameters. Extensions, summary of notations and additional supplementary material are provided in the Appendix
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