Inference in Group Factor Models with an Application to Mixed Frequency Data

We propose a new class of large approximate factor models which enable us to study the full spectrum of quarterly Industrial Production (IP) sector data combined with annual non-IP sectors of the economy. We derive the large sample properties of the estimators and test statistics for the new class of unobservable factor models involving mixed frequency data and common as well as frequency-specific factors. Despite the growth of service sectors, we find that a single common factor explaining 90% of the variability in IP output growth index also explains 60% of total GDP output growth fluctuations. A single low frequency factor unrelated to manufacturing explains 14% of GDP growth. The picture with a structural factor model featuring technological innovations is quite different. Last but not least, our identification and inference methodology rely on novel results on group factor models that are of general interest beyond the mixed frequency framework and the application of the paper.