We consider a nonparametric regression model with continuous endogenous independent variables when only discrete instruments are available that are independent of the error term. While this framework is very relevant for applied research, its implementation is cumbersome, as the regression function becomes the solution to a nonlinear integral equation. We propose a simple iterative procedure to estimate such models and showcase some of its asymptotic properties. In a simulation experiment, we discuss the details of its implementation in the case when the instrumental variable is binary. We conclude with an empirical application in which we examine the effect of pollution on house prices in a short panel of U.S. counties.

翻译：本文考虑当仅存在与误差项独立的离散工具变量时，具有连续内生自变量的非参数回归模型。尽管该框架与应用研究高度相关，但其实现过程较为繁琐，因为回归函数需满足非线性积分方程的解。我们提出了一种简单的迭代估计方法，并展示了其部分渐近性质。通过仿真实验，我们详细讨论了当工具变量为二元变量时的实现细节。最后，基于美国县域短期面板数据，我们通过实证应用检验了污染对房价的影响。