[Abstract]
　Factor loading structural change tests proposed by Breitung and Eickmeier (2011) exhibit nonmonotonic power when a portion of the factor loadings have structural changes occuring at common dates. To investigate this phenomenon, we develop spurious factor representations of the factor model with m common breaks. We show that, under a local alternative asymptotic framework in which the magnitudes of breaks shrink at rate max{N,T}^(1/2), the original factor space is consistently estimated and the tests have power. However, if we apply the fixed alternative asymptotic framework in which the break magnitudes are fixed, then the common breaks in the factor loadings are considered as spurious factors with time invariant loadings, hence the tests lose power. Monte Carlo simulations clearly illustrate these findings. This paper casts a new light on the well known nonmonotonic power problem in structural change testing since it now occurs by identification failure between the common factors and the factor loadings. Furthermore, none of the SupWald, the SupLR, and the SupLM structural change tests can avoid this problem.