Extremal quantiles of intermediate orders under two-way clustering

Harold D. Chiang, Ryutah Kato and Yuya Sasaki

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Abstract: This paper investigates extremal quantiles under two-way cluster dependence. We demonstrate that the limiting distribution of the unconditional intermediate order quantiles in the tails converges to a Gaussian distribution. This is remarkable as two-way cluster dependence entails potential non-Gaussianity in general, but extremal quantiles do not suffer from this issue. Building upon this result, we extend our analysis to extremal quantile regressions of intermediate order.

Date: 2024-02, Revised 2024-03
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