Control Function Approach for Partly Ordered Endogenous Treatments: Military Rank Premium in Wage

In treatment effect analysis, there are many cases where the treatment of interest is ordered (e.g. general-education years or medicine doses) and the control treatment is not zero, but a different type of treatment (a vocational training or a surgery). We develop an approach to find effects of partly ordered treatments, while correcting for possible treatment endogeneity with nearly parametric control functions. We use this control function approach, along with its supplementary version, to estimate effects of military ranks (ordered treatments) on wage relative to non-veteran status (control treatment) with the Wisconsin Longitudinal Study data. In our empirical analysis, the military rank effects differ much: officer has large positive effects, but enlisted ranks have small or no effects.