The presence of unobserved heterogeneity and its detrimental effect on inference has recently motivated the use of interactive effects panel data models. One of the workhorses of this literature is based on iterating between principal components estimation of the unknown factors and OLS estimation of the model parameters. We refer to this as the “PC” approach, the existing asymptotic theory for which is based on the requirement that all the factors and regressors are either stationary or unit root non-stationary. Deterministic factors are typically treated as known and are projected out prior to the application of PC. This is a problem in practice where there is typically great uncertainty over both the order of integration of the stochastic component of the data and the terms needed to capture the deterministic component. This paper relaxes the above mentioned assumptions by considering a model wherein both the factors and regressors are essentially unrestricted, up to mild regulatory conditions. An estimator based on iterating PC is proposed, which is shown to be not only asymptotically normal and oracle efficient, but under certain conditions also free of the otherwise so common asymptotic incidental parameters bias. Interestingly, the conditions required to achieve unbiasedness become weaker the stronger the trends in the factors, and if the trending is strong enough unbiasedness comes at no cost at all. Equally important as these theoretical properties is the ease with which the new approach can be applied. In particular, the approach does not require any knowledge of how many factors there are, or whether they are deterministic/stochastic. The order of integration of the factors is also treated as unknown, as is the order of integration of the regressors, which means that there is no need to pre-test for unit roots, or to decide.

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