Before revision:  To illustrate the advantage of our approach, we provide several examples of models where our approach can identify parameters of interest whereas existing methods cannot be applied because monotonicity fails. These include models with multiple unobserved disturbance terms such as the Roy model and multinomial choice models with dummy endogenous variables, as well as potential outcome models with endogenous random coefficients.
After revision:  To illustrate the advantage of our approach, we provide several examples of models where our approach can identify parameters of interest whereas existing methods would fail. These examples include models with multiple unobserved disturbance terms such as the Roy model and multinomial choice models with dummy endogenous variables, as well as potential outcome models with endogenous random coefficients.