Econometrics at the Extreme: From Quantile Regression to QFAVAR 1

This paper surveys quantile modelling from its theoretical origins to current advances. We organize the literature and present core econometric formulations and estimation methods for: (i) cross‐sectional quantile regression; (ii) quantile time series models and their time series properties; (iii) quantile vector autoregressions for multivariate data; (iv) quantile panel models for longitudinal data; and (v) quantile factor‐augmented models for information compression in data‐rich environments. Each section outlines theoretical foundations and developments, followed by representative empirical applications. Finally, the survey highlights open gaps in quantile modelling. By studying distributional dynamics beyond averages, quantile methods provide policymakers and regulators with tools to design interventions that are robust to risks and effective across the entire spectrum of possible outcomes.