Panel quantile regression for extreme risk

Panel quantile regression models play an essential role in finance, insurance, and risk management applications. However, a direct application of panel regression for extreme conditional quantiles may suffer from a significant estimation uncertainty due to data sparsity on the far tail. We introduce a two-stage method to predict extreme conditional quantiles over cross-sections, which uses panel quantile regression at a selected intermediate level and then extrapolates the intermediate level to an extreme level with extreme value theory. This combination of panel quantile regression at an intermediate level and extreme value theory relies on a set of second-order conditions for heteroscedastic extremes. A metric called Average Absolute Relative Error is proposed to evaluate the prediction performance of both intermediate and extreme conditional quantiles. Allowing individual fixed effects in panel quantile regressions challenges the asymptotic analysis of the two-stage method and prediction metric. We demonstrate the finite sample performance of the extreme conditional quantile prediction compared to the direct use of panel quantile regression. Finally, an application of the two-stage method to the macroeconomic and housing price data finds strong evidence of housing bubbles and common economic factors.