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 two-step procedures. Our method yields economically sensible results when used to estimate Engel curves.

翻译：我们将非参数回归平滑样条扩展至存在内生性且具备工具变量的情境中。与现有流行估计量不同，所提出的估计量采用一步法，并仅依赖单一正则化参数。我们推导出该估计量及其一阶导数的均匀收敛速率，同时解决了估计中单调性约束的施加问题。模拟实验证实，与两步法相比，该估计量具有良好性能。当用于估计恩格尔曲线时，该方法获得了具有经济合理性的结果。