A popular approach to factor-augmented panel regressions is the common correlated effects (CCE) estimator of Pesaran (Estimation and inference in large heterogeneous panels with a multifactor error structure. Econometrica 74, 967–1012, 2006). In fact, the approach is so popular that it has given rise to a separate CCE literature. A common assumption in this literature is that the common factors are stationary, which would seem to rule out many empirically relevant cases. Moreover, deterministic factors are typically treated as known, which raises the issue of model misspecification. In the current paper, we show how the conditions placed on the factors in CCE can be made much more general than was previously thought possible. In fact, save for some mild regulatory moment conditions, the factors are essentially unrestricted. One implication of this result is that there is no need to discriminate between deterministic and stochastic factors, but that one can instead treat them all as unknown. This is very convenient for practitioners, because it means that under certain conditions they are spared of the problem of having to decide on which deterministic terms to include in the model.
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