On structurally grouped approximate factor models

This article explores the group structure in large-dimensional approximate factor models, which portrays homogeneous effects of the common factors on the individuals that fall into the same group. With the initial principal component estimates, we identify the unknown group structure using a combination of the agglomerative hierarchical clustering algorithm and an information criterion. The loadings and factors are then re-estimated conditional on the identified groups. Under some regularity conditions, we establish the consistency of the membership estimator as well as that of the group number estimator obtained from the information criterion. The new estimators for the loadings and factors under the group structure are shown to achieve improved convergence rates compared to those obtained without this information. Numerical simulations suggest that the proposed estimators enjoy satisfactory finite sample performance. Empirical applications to the U.S. macroeconomic and financial market datasets demonstrate the practical merits of our methodology in capturing meaningful economic relationships among macroeconomic indicators and asset portfolios and in improving return prediction accuracy relative to the semiparametric factor model.