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.