Asymptotic properties of endogeneity corrections using nonlinear transformations

This paper considers a linear regression model with an endogenous regressor which arises from a nonlinear transformation of a latent variable. It is shown that the corresponding coefficient can be consistently estimated without external instruments by adding a rank-based transformation of the regressor to the model and performing standard OLS estimation. In contrast to other approaches, our nonparametric control function approach does not rely on a conformably specified copula. Furthermore, the approach allows for the presence of additional exogenous regressors which may be (linearly) correlated with the endogenous regressor(s). Consistency and asymptotic normality of the estimator are proved and the estimator is compared with copula based approaches by means of Monte Carlo simulations. An empirical application on wage data of the US current population survey demonstrates the usefulness of our method.