  In this paper, we develop a unified regression approach to model
unconditional quantiles, M-quantiles and expectiles of multivariate dependent
variables exploiting the multidimensional Huber's function. To assess the
impact of changes in the covariates across the entire unconditional
distribution of the responses, we extend the work of Firpo et al. (2009) by
running a mean regression of the recentered influence function on the
explanatory variables. We discuss the estimation procedure and establish the
asymptotic properties of the derived estimators. A data-driven procedure is
also presented to select the tuning constant of the Huber's function. The
validity of the proposed methodology is explored with simulation studies and
through an application using the Survey of Household Income and Wealth 2016
conducted by the Bank of Italy.
