Cross Sectional Regression with Cluster Dependence: Inference based on Averaging
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| Format: | Preprint |
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2024
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| author | Dey, Subhodeep Basak, Gopal K. Das, Samarjit |
| author_facet | Dey, Subhodeep Basak, Gopal K. Das, Samarjit |
| contents | We re-investigate the asymptotic properties of the traditional OLS (pooled) estimator, $\hatβ _P$, 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 $\hatβ_P$ could be inconsistent in many realistic situations. We propose a simple estimator, $\hatβ_A$ based on data averaging. The asymptotic properties of $\hatβ_A$ are studied. It is shown that $\hatβ_A$ is consistent even when $\hatβ_P$ is inconsistent. It is further shown that the proposed estimator $\hatβ_A$ is more efficient than $\hatβ_P$ in many practical scenarios. As a consequence of averaging, we show that $\hatβ_A$ retains consistency, asymptotic normality under classical measurement error problem circumventing the use of Instrumental Variables (IV). A detailed simulation study shows the efficacy of $\hatβ_A$. It is also seen that $\hatβ_A$ yields better goodness of fit. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2408_13514 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Cross Sectional Regression with Cluster Dependence: Inference based on Averaging Dey, Subhodeep Basak, Gopal K. Das, Samarjit Methodology We re-investigate the asymptotic properties of the traditional OLS (pooled) estimator, $\hatβ _P$, 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 $\hatβ_P$ could be inconsistent in many realistic situations. We propose a simple estimator, $\hatβ_A$ based on data averaging. The asymptotic properties of $\hatβ_A$ are studied. It is shown that $\hatβ_A$ is consistent even when $\hatβ_P$ is inconsistent. It is further shown that the proposed estimator $\hatβ_A$ is more efficient than $\hatβ_P$ in many practical scenarios. As a consequence of averaging, we show that $\hatβ_A$ retains consistency, asymptotic normality under classical measurement error problem circumventing the use of Instrumental Variables (IV). A detailed simulation study shows the efficacy of $\hatβ_A$. It is also seen that $\hatβ_A$ yields better goodness of fit. |
| title | Cross Sectional Regression with Cluster Dependence: Inference based on Averaging |
| topic | Methodology |
| url | https://arxiv.org/abs/2408.13514 |