Cross Sectional Regression with Cluster Dependence: Inference based on Averaging

We re-investigate the asymptotic properties of the traditional OLS (pooled) estimator, β̂ P, with cluster dependence. The present study considers various scenarios under various restrictions on the cluster sizes and number of clusters. It is shown that β̂P could be inconsistent in many realistic situations. We propose a simple estimator, β̂A based on data averaging. The asymptotic properties of β̂A is studied. It is shown that β̂A is consistent even when β̂P is inconsistent. It is further shown that the proposed estimator β̂A could be more efficient as compared to β̂P in many practical scenarios. As a consequence of averaging, we show that β̂A retains consistency, asymptotic normality under classical measurement error problem circumventing the use of IV. A detailed simulation study shows the efficacy of β̂A. It is also seen that β̂A yields better goodness of fit.