Shrinkage Estimation of High-Dimensional Factor Models with Structural Instabilities

In large-scale panel data models with latent factors the number of factors and their loadings may change over time. Treating the break date as unknown, this article proposes an adaptive group-LASSO estimator that consistently determines the numbers of pre- and post-break factors and the stability of factor loadings if the number of factors is constant. We develop a cross-validation procedure to fine-tune the data-dependent LASSO penalties and show that after the number of factors has been determined, a conventional least-squares approach can be used to estimate the break date consistently. The method performs well in Monte Carlo simulations. In an empirical application, we study the change in factor loadings and the emergence of new factors in a panel of U.S. macroeconomic and financial time series during the Great Recession.