Evaluating restricted common factor models for non-stationary data

Abstract

Approximate factor models with restrictions on the loadings may be interesting both for structural analysis (simpler structures are easier to interpret) and forecasting (parsimonious models typically deliver superior forecasting performances). However, the issue is largely unexplored. In particular, no currently available test is entirely suitable for the empirically important case of non-stationary data. Building on the intuition that defactoring the data under a correct set of restrictions will lower the number of factors, we propose a procedure based on the comparison of the number of factors selected for the raw and de-factored data. To control and reduce the risk of rejecting valid constraints we develop a bootstrap procedure, shown analytically to be asymptotically valid and by simulation to have good small sample properties.JEL: C12, C33, C55