Aggregation of Linear Models for Panel Data

We study the impact of individual and temporal aggregation in linear static and dynamic models for panel data in terms of model specification and efficiency of the estimated parameters. Model wise we find that i) individual aggregation does not affect the model structure but temporal aggregation may introduce residual autocorrelation, and ii) individual aggregation entails heteroskedasticity while temporal aggregation does not. Estimation wise we find that i) in the static model, estimation by least squares with the aggregated data entails a decrease in the efficiency of the estimated parameters but we cannot rank different aggregation schemes in terms of efficiency, and ii) in the dynamic model, estimation by GMM does not necessarily entail a decrease in the efficiency of the estimated parameters under individual aggregation and no analytic comparison can be established for temporal aggregation, though simulations suggests that temporal aggregation deteriorates the accuracy of the estimates.