Principal components estimation and identification of static factors

It is known that the principal component estimates of the factors and the loadings are rotations of the underlying latent factors and loadings. We study conditions under which the latent factors can be estimated asymptotically without rotation. We derive the limiting distributions for the estimated factors and factor loadings when N and T are large and make precise how identification of the factors affects inference based on factor augmented regressions. We also consider factor models with additive individual and time effects. The asymptotic analysis can be modified to analyze identification schemes not considered in this analysis.