A Simple and Computationally Trivial Estimator for Grouped Fixed Effects Models

Abstract: This paper introduces a new fixed effects estimator for linear panel data models with clustered time patterns of unobserved heterogeneity. The method avoids non-convex and combinatorial optimization by combining a preliminary consistent estimator of the slope coefficient, an agglomerative pairwise-differencing clustering of cross-sectional units, and a pooled ordinary least squares regression. Asymptotic guarantees are established in a framework where $T$ can grow at any power of $N$, as both $N$ and $T$ approach infinity. Unlike most existing approaches, the proposed estimator is computationally straightforward and does not require a known upper bound on the number of groups. As existing approaches, this method leads to a consistent estimation of well-separated groups and an estimator of common parameters asymptotically equivalent to the infeasible regression controlling for the true groups. An application revisits the statistical association between income and democracy.