Microeconomic theory often yields models with multiple nonlinear equations, nonseparable unobservables, nonlinear cross equation restrictions, and many potentially multicollinear covariates. We show how statistical dimension reduction techniques can be applied in models with these features. In...

This paper introduces average treatment effects conditional on the outcome variable in an endogenous setup where outcome Y, treatment X and instrument Z are continuous. These objects allow to refine well studied treatment effects like ATE and ATT in the case of continuous treatment (see Florens...