Shrinkage Estimation of High-Dimensional Factor Models with Structural Instabilities

In high-dimensional factor models, both the factor loadings and the number of factors may change over time. This paper proposes a shrinkage estimator that detects and disentangles these instabilities. The new method simultaneously and consistently estimates the number of pre- and post-break factors, which liberates researchers from sequential testing and achieves uniform control of the family-wise model selection errors over an increasing number of variables. The shrinkage estimator only requires the calculation of principal components and the solution of a convex optimization problem, which makes its computation efficient and accurate. The finite sample performance of the new method is investigated in Monte Carlo simulations. In an empirical application, we study the change in factor loadings and emergence of new factors during the Great Recession.