One-step nonparametric instrumental regression using smoothing splines

We extend nonparametric regression smoothing splines to a context where there is endogeneity and instrumental variables are available. Unlike popular existing estimators, the resulting estimator is one-step and relies on a unique regularization parameter. We derive uniform rates of the convergence for the estimator and its first derivative. We also address the issue of imposing monotonicity in estimation. Simulations confirm the good performances of our estimator compared to some popular two-step procedures. Our method yields economically sensible results when used to estimate Engel curves.