Probability Statistics Seminars-On Structurally Grouped Approximate Factor Models

Abstract:

This paper 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 principle component estimates, we identify the unknown group structure by 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 under the group structure are shown to achieve efficiency gain compared to those obtained without this information. Numerical simulations and empirical applications demonstrate the nice finite sample performance of our proposed approach when group structure presents.