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We extend nonparametric regression smoothing splines to a context where thereis endogeneity and instrumental variables are available. Unlike popularexisting estimators, the resulting estimator is one-step and relies on a uniqueregularization parameter. We derive uniform rates of the convergence for theestimator and its first derivative. We also address the issue of imposingmonotonicity in estimation. Simulations confirm the good performances of ourestimator compared to some popular two-step procedures. Our method yieldseconomically sensible results when used to estimate Engel curves.

One-step nonparametric instrumental regression using smoothing splines