One-step nonparametric instrumental regression using smoothing splines

Résumé

We extend nonparametric regression smoothing splines to a context where there is endogeneity and instrumental variables are available. Unlike popular existing es-timators, 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. Sim-ulations 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.