Before revision:  The foundation for this joint regression is a recent result by Fissler and Ziegel (2016), who show that the quantile and the ESare jointly elicitable. This joint elicitability allows for M- and Z-estimation of the joint regression parameters.
After revision:  This regression is based on a strictly consistent loss function for the pair quantile and ES, which allows for M- and Z-estimation of the joint regression parameters.