Cross Sectional Regression with Cluster Dependence: Inference based on Averaging

2024/08/24 by Dey, Subhodeep, Basak, Gopal K., Das, Samarjit
#FOS: Computer and information sciences #Methodology (stat.ME)

paper · doi:10.48550/arxiv.2408.13514

Abstract

We re-investigate the asymptotic properties of the traditional OLS (pooled) estimator, β _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 β_P could be inconsistent in many realistic situations. We propose a simple estimator, β_A based on data averaging. The asymptotic properties of β_A are studied. It is shown that β_A is consistent even when β_P is inconsistent. It is further shown that the proposed estimator β_A is more efficient than β_P in many practical scenarios. As a consequence of averaging, we show that β_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 β_A. It is also seen that β_A yields better goodness of fit.

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