  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.
