The empirical distribution of sequential LS factors in multi-level dynamic factor models

Monte Carlo experiments confirm that under general forms of the idiosyncratic covariance matrix, the finite-sample distribution of the sequential Least Squares (SLS) estimator of global and group-specific factors in multi-level dynamic factor models (ML-DFMs) can be well approximated using the asymptotic distribution of Principal Components (PC) factors in dynamic factor models (DFMs). The performance of alternative estimators of the covariance matrix of the SLS factors is also analysed. The estimator that allows for idiosyncratic cross-sectional correlation and accounts for estimation uncertainty in factor loadings performs best. The results are illustrated by constructing confidence bounds for global and group-specific international business cycles.