| This paper develops the theory of extremal (extreme and near-extreme) conditional quantiles: estimation, inference, and applications in economics. Particularly, the limit laws for extremal quantile statistics are obtained under different conditions reflecting rare nature of the conditional extremal events. Relevant inference framework that facilitates immediate applicability is provided. The obtained results apply to cross-section as well as time series data. Examples, ranging from the decision making under extreme uncertainty to price search models, provide motivation and empirical applications of the theory developed herein. In particular, the use of the new theory is demonstrated in an empirical risk-evaluation example. |