On CCE estimation of factor-augmented models when regressors are not linear in the factors

In empirical research it is often of interest to include non-linear functions of the explanatory variables, such as squares or interactions, in the specification. A popular technique to estimate such models in the presence of common factors is the Common Correlated Effects (CCE) methodology. However, this approach assumes that the regressors are linear in the factors, which is not the case if variables enter non-linearly. In this note we show how CCE should be implemented when some regressors violate the linear factor model assumption.