VAR for VaR: Measuring Tail Dependence Using Multivariate Regression Quantiles∗

This paper proposes methods for estimation and inference in multivariate, multi-quantile models. The theory can simultaneously accommodate models with multiple random variables, multiple confidence levels, and multiple lags of the associated quantiles. The proposed framework can be conveniently thought of as a vector autoregressive (VAR) extension to quantile models. We estimate a simple version of the model using market equity returns data to analyse spillovers in the values at risk (VaR) between a market index and financial institutions. We construct impulse-response functions for the quantiles of a sample of 230 financial institutions around the world and study how financial institution-specific and system-wide shocks are absorbed by the system. We show how our methodology can successfully identify both in-sample and out-of-sample the set of financial institutions whose risk is most sentitive to market wide shocks in situations of financial distress, and can prove a valuable addition to the traditional toolkit of policy makers and supervisors.