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 <i>lower</i> 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.

本文提出了混频分布滞后（mixed-frequency distributed-lag, MFDL）估计量，用于估计如下设定场景下的脉冲响应函数：（1）所关注的冲击可被观测；（2）所关注的被影响变量以较低频率被观测（即作为时间加总或序贯抽样得到的变量）；（3）数据生成过程（data generating process, DGP）由对应于冲击频率的向量自回归（Vector Autoregression, VAR）模型刻画；（4）进入该数据生成过程的全部相关内生变量未知或不可观测。本文证明了所提出的MFDL估计量的一致性与渐近正态性，并通过一系列蒙特卡洛（Monte Carlo）实验验证了其有限样本表现。随后，本文通过三个实证应用说明了MFDL估计量的实用价值：（1）日度观测的原油价格冲击对周度观测的美国汽油消费者价格的传导效应；（2）全球投资者风险偏好冲击对全球资本流动的影响；（3）货币政策冲击对实体经济活动的影响。