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.

翻译：我们将非参数回归光滑样条扩展至存在内生性且具备工具变量的情景。与现有主流估计量不同，该估计量采用一步估计法，仅依赖单一正则化参数。我们推导了该估计量及其一阶导数的均匀收敛速率，并探讨了在估计中施加单调性约束的问题。仿真结果表明，与若干主流两步估计法相比，本方法具有良好的性能。将本方法应用于恩格尔曲线估计时，可获得具有经济学合理性的结果。