Comparing the Bias of Dynamic Panel Estimators in Multilevel Panels: Individual versus Grouped Data

We propose the Grouped Coefficients estimator to reduce the bias of dynamic panels that have a multilevel structure to the coefficient and factor loading heterogeneity. If groups are chosen such that the within-group heterogeneity is small, then the grouped coefficients estimator can lead to a substantial bias reduction compared to fixed effects and Arellano-Bond estimators. We also compare the magnitude of the bias of panel estimators with individual versus aggregate data and show that the magnitude of the bias also depends on the proportion of the heterogeneity that is within groups. In an application to estimating corn acreage response to price, we find that the grouped coefficients estimator gives reasonable results. Fixed effects and Arellano-Bond estimates of the coefficient on the lagged dependent variable appear to be severely biased with county-level data. In contrast, if we randomly assign the fields to groups and aggregate within the random groups, then pooled OLS of the randomly aggregated data gives a reasonable estimate of the coefficient on the lagged dependent variable.