Mean Group Estimation for Large Panel Data models with Localized Parameter Heterogeneity and Cross-sectional Dependence

This paper builds on the common correlated effects mean group estimator (CCEMG) introduced by Pesaran (2006) for a heterogeneous large-panel model with substantial cross-sectional dependence and negligible within-group heterogeneity. The standard asymptotic theory for this method is established under the assumption that the heterogeneous coefficients follow a random coefficient model. This assumption introduces a large variability to the CCEMG estimator, resulting in an asymptotic distribution that depends solely on the distribution of the model, rather than incorporating the observation error distribution as one might typically expect. In the current study, we modify the random coefficient model assumption and re-establish the asymptotic theory for the CCEMG estimator. We demonstrate that, under the new assumption, the asymptotic distribution depends on the error distribution as well. Moreover, we show that the asymptotic normality is achieved at a faster rate than the standard rate; however, this improvement introduces a bias in the estimator. We then subsequently propose a consistent estimator for the new asymptotic covariance structure. Monte Carlo simulations show that the proposed method is more accurate and efficient than the standard method under various conditions. In an application to examine the impact of weather on wheat yields across five Australian states, our findings reveal that the new method provides stronger statistical evidence consistent with the farmers' expectations.