I am trying to model the effect of a treatment (x-variable) on an outcome (y-variable), where the treatment is a self-selected, CONTINUOUS variable (e.g., hours of study, dollars spent, etc.), and the outcome is also continuous (performance). I am interested in the effect of the treatment on the outcome in the general population - not just the treatment sample. I observe y for the entire population (i.e., including those studying/spending, and those not). My treatment is either zero, or some positive value (lots of clustering at zero).
This doesn't seem to fit into the self-selection literature - which always focuses on selection on the y-variable, or into the treatment effects literature - which focuses on selection on a binary choice. Any thoughts?