Asymptotic properties of endogeneity corrections using nonlinear transformations

This paper studies the asymptotic properties of endogeneity corrections based on nonlinear transformations without external instruments, which were originally proposed by Park and Gupta (2012) and have become popular in applied research. In contrast to the original copula-based estimator, our approach is based on a nonparametric control function and does not require a conformably specified copula. Moreover, we allow for exogenous regressors, which may be (linearly) correlated with the endogenous regressor(s). We establish consistency, asymptotic normality and validity of the bootstrap for the unknown model parameters. An empirical application on wage data of the US current population survey demonstrates the usefulness of the method.