Title:Second-Generation Heterogeneous Panel Data Model with Individual and Common Shocks

Abstract:We study estimation of the mean slope in heterogeneous panels that combine cross-sectional dependence from unobserved common factors with unit-specific structural breaks occurring at different dates. We organize the available second-generation Mean Group estimators into a regime map indexed by the cross-section size, the strength of the cross-sectional dependence, and the nature of the structural change, and we examine two estimators for the small-to-moderate-dependence panels common in applied macroeconomics and energy economics. The Fourier SUR Mean Group (F-SURMG) estimator augments a seemingly unrelated regression system with unit-specific Fourier terms. The proposed Fourier Common Correlated Effects Mean Group (F-CCEMG) estimator augments the CCE regression with deterministic Fourier terms, filtering the common factor while absorbing the heterogeneously timed breaks. In a Monte Carlo study with R = 500 replications across weak, moderate, and strong dependence, F-CCEMG attains the lowest root mean squared error in almost every configuration and near-nominal coverage once the cross-section is not minimal, while F-SURMG gives the best-calibrated inference in the small-N, weak-dependence corner; estimators that do not filter the factor lose coverage as dependence rises. An application to the renewable energy-growth nexus in the G7 over 1965-2019 finds no significant aggregate effect of renewable energy consumption on growth.