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

Author:

Kaicheng Chen, Timothy J. Vogelsang

Keyword:

Economics, Econometrics, Econometrics (econ.EM)

journal:

date:

2023-09-14 16:00:00

Abstract

This paper studies a cluster robust variance estimator proposed by Chiang, Hansen and Sasaki (2022) 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 individual 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 from Thompson (2011) on the relationship between industry profitability and market concentration.

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