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Fixed-b Asymptotics for Panel Models with Two-Way Clustering

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  • Kaicheng Chen
  • Timothy J. Vogelsang

Abstract

This paper studies a cluster robust variance estimator proposed by Chiang, Hansen and Sasaki (2024) for linear panels. First, we show algebraically that this variance estimator (CHS estimator, hereafter) is a linear combination of three common variance estimators: the one-way unit cluster estimator, the "HAC of averages" estimator, and the "average of HACs" estimator. Based on this finding, we obtain a fixed-$b$ asymptotic result for the CHS estimator and corresponding test statistics as the cross-section and time sample sizes jointly go to infinity. Furthermore, we propose two simple bias-corrected versions of the variance estimator and derive the fixed-$b$ limits. In a simulation study, we find that the two bias-corrected variance estimators along with fixed-$b$ critical values provide improvements in finite sample coverage probabilities. We illustrate the impact of bias-correction and use of the fixed-$b$ critical values on inference in an empirical example on the relationship between industry profitability and market concentration.

Suggested Citation

  • Kaicheng Chen & Timothy J. Vogelsang, 2023. "Fixed-b Asymptotics for Panel Models with Two-Way Clustering," Papers 2309.08707, arXiv.org, revised Aug 2024.
    • Handle: RePEc:arx:papers:2309.08707
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    References listed on IDEAS

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