| 讲座简介： | Panel quantile regression models play an essential role in finance, insurance, and risk management applications. However, a direct application of panel regression for the extreme conditional quantiles may suffer from significant estimation errors due to data sparsity on the far tail. We introduce a two-stage method to predict extreme conditional quantiles over cross-sections. First, use panel quantile regression at a selected intermediate level, then extrapolate the intermediate level to an extreme level with extreme value theory. The combination of panel quantile regression at an intermediate level and extreme value theory relies on a set of second-order conditions for heteroscedastic extremes. We also propose a metric called Average Absolute Relative Error to evaluate the prediction performance of both intermediate and extreme conditional quantiles. Individual fixed effects in panel quantile regressions complicate 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, we apply the two-stage method to the macroeconomic and housing price data and find strong evidence of housing bubbles and common economic factors. |
