Estimation of Panel Data Models with Nonlinear Factor Structure

Abstract: Panel data models with unobserved heterogeneity in the form of interactive effects standardly assume that the time effects - or "common factors" - enter linearly. This assumption is unnatural in the sense that it pertains to the unobserved component of the model, and there is rarely any reason to believe that this component takes on a particular functional form. This is in stark contrast to the relationship between the observables, which can often be credibly argued to be linear. Linearity in the factors has persevered mainly because it is convenient, and that it is better than standard fixed effects. The present paper relaxes this assumption. It does so by combining the common correlated effects (CCE) approach to standard interactive effects with the method of sieves. The new estimator - abbreviated "SCCE" - retains many of the advantages of CCE, including its computational simplicity, and good small-sample and asymptotic properties, but is applicable under a much broader class of factor structures that includes the linear one as a special case. This makes it well-suited for a wide range of empirical applications.