Analyzing business and financial cycles using multi-level factor models

This paper compares alternative estimation procedures for multi-level factor models which imply blocks of zero restrictions on the associated matrix of factor loadings. We suggest a sequential least squares algorithm for minimizing the total sum of squared residuals and a two-step approach based on canonical correlations that are much simpler and faster than Bayesian approaches previously employed in the literature. Monte Carlo simulations suggest that the estimators perform well in typical sample sizes encountered in the factor analysis of macroeconomic data sets. We apply the methodologies to study international co-movements of business and financial cycles as well as asymmetries over the business cycle in the US.