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Some impossibility results for inference with cluster dependence with large clusters
Kojevnikov,Denis Song,Kyungchul
Kojevnikov,Denis
Song,Kyungchul
Abstract
This paper focuses on a setting with observations having a cluster dependence structure and presents two main impossibility results. First, we show that when there is only one large cluster, i.e., the researcher does not have any knowledge on the dependence structure of the observations, it is not possible to consistently discriminate the mean. When within-cluster observations satisfy the uniform central limit theorem, we also show that a sufficient condition for consistent n−−√-discrimination of the mean is that we have at least two large clusters. This result shows some limitations for inference when we lack information on the dependence structure of observations. Our second result provides a necessary and sufficient condition for the cluster structure that the long run variance is consistently estimable. Our result implies that when there is at least one large cluster, the long run variance is not consistently estimable.
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Date
2023-12
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Keywords
Cluster dependence, Consistent discrimination, Consistent estimation of long-run variance, Local dependence, Log likelihood process, Unknown dependence structure
Citation
Kojevnikov, D & Song, K 2023, 'Some impossibility results for inference with cluster dependence with large clusters', Journal of Econometrics, vol. 237, no. 2, 105524. https://doi.org/10.1016/j.jeconom.2023.105524
License
info:eu-repo/semantics/openAccess