Reconciled Estimates of Monthly GDP in the United States

In the United States, income and expenditure-side estimates of gross domestic product (GDP) (GDPI and GDPE) measure “true” GDP with error and are available at a quarterly frequency. Methods exist for using these proxies to produce reconciled quarterly estimates of true GDP. In this paper, we extend these methods to provide reconciled historical true GDP estimates at a monthly frequency. We do this using a Bayesian mixed frequency vector autoregression (MF-VAR) involving GDPE, GDPI, unobserved true GDP, and monthly indicators of short-term economic activity. Our MF-VAR imposes restrictions that reflect a measurement-error perspective (i.e., the two GDP proxies are assumed to equal true GDP plus measurement error). Without further restrictions, our model is unidentified. We consider a range of restrictions that allow for point and set identification of true GDP and show that they lead to informative monthly GDP estimates. We illustrate how these new monthly data contribute to our historical understanding of business cycles and we provide a real-time application nowcasting monthly GDP over the pandemic recession.

在美国，国内生产总值（Gross Domestic Product，GDP）的收入法核算值（GDPI）与支出法核算值（GDPE）均存在测算误差，且均以季度频率发布。现有方法可借助这两类测算代理变量，生成经调和后的季度‘真实’GDP核算值。本文将此类方法进行拓展，以生成月度频率下经调和的历史‘真实’GDP核算值。我们采用贝叶斯混频向量自回归模型（Bayesian Mixed Frequency Vector Autoregression，MF-VAR）实现该目标，该模型纳入了GDPE、GDPI、不可观测的‘真实’GDP，以及短期经济活动的月度指标四类变量。该模型施加了契合测算误差视角的约束条件，即假定两类GDP代理变量均等于‘真实’GDP加上测算误差。若未施加额外约束，本模型无法实现识别。本文考虑了一系列可实现‘真实’GDP点识别与集合识别的约束条件，并证明此类约束可生成具备信息价值的月度GDP核算值。我们通过案例展示了此类新型月度数据如何助力学界深化对经济周期历史演进的认知，并提供了一项实时应用：在新冠疫情衰退期间对月度GDP进行即时预测（nowcasting）。