Inference in Group Factor Models With an Application to Mixed‐Frequency Data

Abstract

We derive asymptotic properties of estimators and test statistics to determine—in a grouped data setting—common versus group‐specific factors. Despite the fact that our test statistic for the number of common factors, under the null, involves a parameter at the boundary (related to unit canonical correlations), we derive a parameter‐free asymptotic Gaussian distribution. We show how the group factor setting applies to mixed‐frequency data. As an empirical illustration, we address the question whether Industrial Production (IP) is still the dominant factor driving the U.S. economy using a mixed‐frequency data panel of IP and non‐IP sectors. We find that a single common factor explains 89% of IP output growth and 61% of total GDP growth despite the diminishing role of manufacturing.