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 restrictive because it concerns an unobserved component of the model, for which a particular functional form is rarely justified. By contrast, linearity in the observable regressors can often be motivated by economic theory or empirical convention. Linearity in the factors has mainly persisted because it is convenient and improves on standard fixed effects. This paper relaxes that assumption by combining the common correlated effects (CCE) approach with sieve methods. The resulting estimator -- abbreviated ``SCCE'' -- preserves key advantages of CCE, including computational simplicity and good small-sample and asymptotic properties, while allowing for a broader class of factor structures that nests the linear case. This makes it suitable for a wide range of empirical applications.