Heterogeneous coefficients, control variables and identification of multiple treatment effects

Summary Multi-dimensional heterogeneity and endogeneity are important features of models with multiple treatments. We consider a heterogeneous coefficients model where the outcome is linear combination dummy treatment variables, each variable representing different kind treatment. use control variables to give necessary sufficient conditions for identification average effects. With mutually exclusive treatments we find that, provided mean independent from given controls, simple condition that generalized propensity scores (Imbens, 2000) be bounded away zero their sum one, probability one. Our analysis extends distributional quantile effects, as well corresponding effects on treated. These results generalize classical result Rosenbaum & Rubin (1983) binary