Evaluating Restricted Common Factor models for non-stationary data

We propose to evaluate restrictions on the loadings of approximate Factor models comparing the estimated number of factors of the unconstrained and constrained models. A di§erence between the two estimates is evidence against the constraints, which should thus be rejected. To take into account possible Önite sample bias of the model selection procedure, we develop a bootstrap algorithm for the estimation of the probability of rejecting correct constraints. For non-stationary factor models we show analytically that the algorithm is asymptotically valid, and by simulation that the evaluation procedure has good small sample properties.