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This paper studies a cluster robust variance estimator proposed by Chiang,Hansen and Sasaki (2022) for linear panels. First, we show algebraically thatthis variance estimator (CHS estimator, hereafter) is a linear combination ofthree common variance estimators: the one-way individual cluster estimator, the"HAC of averages" estimator, and the "average of HACs" estimator. Based on thisfinding, we obtain a fixed-b asymptotic result for the CHS estimator andcorresponding test statistics as the cross-section and time sample sizesjointly go to infinity. Furthermore, we propose two simple bias-correctedversions of the variance estimator and derive the fixed-b limits. In asimulation study, we find that the two bias-corrected variance estimators alongwith fixed-b critical values provide improvements in finite sample coverageprobabilities. We illustrate the impact of bias-correction and use of thefixed-b critical values on inference in an empirical example from Thompson(2011) on the relationship between industry profitability and marketconcentration.

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