Estimation of Average Effects in Short $T$ Heterogeneous Panels

Abstract

The commonly used two-way fixed effects estimator is biased under correlated heterogeneity and can lead to misleading inference. The mean group estimator proposed by Pesaran and Smith (1995) is robust to correlated heterogeneity but requires the underlying individual estimates to have second-order moments that could fail if the number of estimated coefficients ($k$) is too close to the time dimension ($T$) of the panel. This paper focuses on panels where $k$ is close to $T$ (including $k=T$), and proposes a trimmed mean group (TMG) estimator that shrinks individual estimates most likely to fail the second-order moment condition. The TMG estimator is shown to be $n^{(1-\alpha )/2}$-consistent and asymptotically normally distributed, where $\alpha$ is determined by the degree to which individual estimates might not have moments. The $\sqrt{n}$ convergence rate is achieved only if all individual estimates have second-order moments. Extensions to panels with time effects are provided, and a new Hausman test of correlated heterogeneity is proposed. Small sample properties of the TMG estimator (with and without time effects) are investigated by Monte Carlo experiments and shown to be satisfactory. The proposed test of correlated heterogeneity is also shown to have the correct size and satisfactory power. The utility of the TMG approach is illustrated with an empirical application.