Response variable at the group level, independent variables at the entity level

I have a dataset of entities which each belong to a particular group (i.e. entity=schools and group=school district). I also have lots of auxiliary variables on each entity.

However, for my response variable I only have information at the group level (i.e. response variable only at the district level, but regressor variables at the school level).

Can someone recommend an algorithm or class of algorithms that might be appropriate here? I’d rather not aggregate all the auxiliary information up to the group level and throw away all info contained in the correlations among the auxiliary variables.