Cross Sectional Regression with Cluster Dependence: Inference based on Averaging

TL;DR

This paper examines the limitations of traditional pooled OLS estimators under cluster dependence and introduces a data averaging estimator that is more consistent and efficient, especially in complex cluster scenarios.

Contribution

The paper proposes a new averaging-based estimator for cross-sectional regression with cluster dependence, demonstrating its consistency and efficiency over traditional methods.

Findings

The averaging estimator is consistent even when pooled OLS is not.

The new estimator outperforms pooled OLS in efficiency and goodness of fit.

Simulation results confirm the estimator's practical advantages.

Abstract

We re-investigate the asymptotic properties of the traditional OLS (pooled) estimator, $\hat{\beta} _P$, in the context of cluster dependence. The present study considers various scenarios under various restrictions on the cluster sizes and number of clusters. It is shown that $\hat{\beta}_P$ could be inconsistent in many realistic situations. We propose a simple estimator, $\hat{\beta}_A$ based on data averaging. The asymptotic properties of $\hat{\beta}_A$ are studied. It is shown that $\hat{\beta}_A$ is consistent even when $\hat{\beta}_P$ is inconsistent. It is further shown that the proposed estimator $\hat{\beta}_A$ is more efficient than $\hat{\beta}_P$ in many practical scenarios. As a consequence of averaging, we show that $\hat{\beta}_A$ retains consistency, asymptotic normality under classical measurement error problem circumventing the use of Instrumental Variables (IV). A detailed simulation study shows the efficacy of $\hat{\beta}_A$. It is also seen that $\hat{\beta}_A$ yields better goodness of fit.