Endogeneity corrections in binary outcome models with nonlinear transformations: identification and inference

For binary outcome models, an endogeneity correction based on nonlinear rank-based transformations is proposed. Identification without external instruments is achieved under one of two assumptions: Either the endogenous regressor is a nonlinear function of one component of the error term conditionally on exogenous regressors. Or the dependence between endogenous regressor and exogenous regressor is nonlinear. Under these conditions, we prove consistency and asymptotic normality. Monte Carlo simulations and an application on German insolvency data illustrate the usefulness of the method.