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Some impossibility results for inference with cluster dependence with large clusters

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  • 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.

Suggested Citation

  • Kojevnikov, Denis & Song, Kyungchul, 2023. "Some impossibility results for inference with cluster dependence with large clusters," Journal of Econometrics, Elsevier, vol. 237(2).
    • Handle: RePEc:eee:econom:v:237:y:2023:i:2:s0304407623002403
    DOI: 10.1016/j.jeconom.2023.105524
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    Keywords

    Consistent discrimination; Local dependence; Unknown dependence structure; Consistent estimation of long-run variance; Cluster dependence; Log likelihood process;
    All these keywords.

    JEL classification:

    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General

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