Analyzing international business and financial cycles using multi-level factor models: A comparison of alternative approaches

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 twostep approach based on canonical correlations that are much simpler and faster than Bayesian approaches previously employed in the literature. An additional advantage is that our approaches can be used to estimate more complex multi-level factor structures where the number of levels is greater than two. 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 comovements of business and financial cycles.