Discrete Heterogeneity Patterns in Panel Data∗

We propose a panel data estimator that leaves the relationship between observables and unobservables unrestricted, while allowing for flexible time-varying patterns of heterogeneity. Our approach restricts the support of unobserved heterogeneity, effectively assuming that individual units belong to a small number of groups. The “grouped fixed-effects” estimator that this paper introduces is shown to be higher-order unbiased as N and T tend to infinity, under conditions that we characterize. As a result, inference is not affected by the fact that group membership is estimated. We apply our approach to study the link between income and democracy, while allowing for permanent and time-varying country-specific heterogeneity. The results differ significantly from approaches that assume that country heterogeneity does not vary over time. JEL codes: C23.