Estimation and Inference of Quantile Impulse Response Functions by Local Projections: With Applications to VaR Dynamics

This article investigates the estimation and inference of quantile impulse response functions. We propose a new estimation method using the idea of local projections by Jordà (2005). We establish consistency and asymptotic normality of the estimator, thereby enabling asymptotic inference. We also consider the confidence interval construction based on the stationary bootstrap and prove its consistency. Confirmatory simulation results and empirical practices on value-at-risk dynamics are provided.