Before revision:  No restrictions are imposed on the way these covariates enter the model, such as separability or monotonicity. Further, after the order condition is fulfilled, I provide a new sufficient condition that is weaker than the existing results for the global uniqueness of the solution to the nonlinear system of equations.
After revision:  The structural outcome function must be continuous and monotonic in a scalar disturbance, but it can be nonseparable. The selection model allows for unrestricted heterogeneity. Global identification is obtained under weak conditions. The paper also provides estimators of the structural outcome function. Two empirical examples of the return to education and selection into Head Start illustrate the value and limitations of the nonlinear system of equations.