Network-Assisted High-Dimensional Factor Model Estimation

This is the authors' abstract. We don't add key points for this paper.

This article takes advantage of group-level heterogeneity and network cohesion phenomenon to improve the estimation accuracy of approximate factor models. As large heterogeneous panels become available, a grouped pattern of unobserved heterogeneity in the panel data is highlighted. Clustering of factor loadings provides a solution to model group-level heterogeneity. Moreover, networks are frequently observed in economics and finance, which capture the interconnectivity between large-scale cross-sectional units and thus should aid in learning the latent group structure. Therefore, we propose a maximum likelihood-based method that equips the negative log-likelihood with two novel regularization terms, where a classical K-means penalty is enforced to encourage community structure among the factor loading vectors and a Laplacian penalty is enforced to encourage similarity in the factor loadings corresponding to linked individuals. A computationally efficient algorithm is developed to implement penalized maximum-likelihood estimation. Under mild assumptions, we establish concise convergence rates of the model-based estimators, allowing the number of latent groups to be over-specified. A likelihood-based information criterion is developed to consistently identify the true group number for practical use. Thorough simulation studies support the asymptotic results. Finally, applications to two real datasets demonstrate the practical relevance and superiority of our method.