Extreme Conditional Quantiles for Panel Data Model with Individual Effects

Panel quantile regression models play an important role in real applications of finance, econometrics, insurance and risk management. However, direct estimates of the extreme conditional quantiles may lead unstable results due to data sparsity on the tail regions. Moreover, the presence of individual effects complicates the inference for extreme quantiles and a study on their theoretical properties is necessary. This paper proposes a two-stage method to estimate/predict the extreme conditional quantiles where an intermediate quantile is first estimated according to panel regression models and the extrapolation of the intermediate quantile to an extreme quantile is carried out in the second stage. Under a set of second-order regular variation conditions of heteroscedastic extremes, we establish the asymptotic theories for the two-stage prediction while its finite sample performance is demonstrated and compared to the direct prediction by simulations. 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 as well as the cross country heterogeneity.