🤖 AI Summary
This paper addresses computational bottlenecks in linear panel models with grouped fixed effects, where conventional methods rely on non-convex or combinatorial optimization and require prespecifying an upper bound on the number of groups. We propose a three-step estimation procedure that neither requires prior knowledge of the number of groups nor involves complex optimization: (1) consistent estimation of slope parameters; (2) agglomerative clustering based on pairwise differencing to consistently identify the true group structure; and (3) mixed OLS within the identified groups. Theoretical results accommodate time dimension $T$ growing at any polynomial rate in $N$, ensuring consistent group identification and asymptotically efficient estimation of common parameters—achieving the same efficiency as the infeasible regression using true groups. An empirical re-examination of the income-democracy relationship demonstrates the method’s robustness and computational efficiency.
📝 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.