Multivariate quantile regression

Abstract: This paper introduces a new framework for multivariate quantile regression based on the multivariate distribution function, termed multivariate quantile regression (MQR). In contrast to existing approaches--such as directional quantiles, vector quantile regression, or copula-based methods--MQR defines quantiles through the conditional probability structure of the joint conditional distribution function. The method constructs multivariate quantile curves using sequential univariate quantile regressions derived from conditioning mechanisms, allowing for an intuitive interpretation and flexible estimation of marginal effects. The paper develops theoretical foundations of MQR, including asymptotic properties of the estimators. Through simulation exercises, the estimator demonstrates robust finite sample performance across different dependence structures. As an empirical application, the MQR framework is applied to the analysis of exchange rate pass-through in Argentina from 2004 to 2024.