This paper develops a general causal inference method for treatment effects models with noisily measured confounders. The key feature is that a large set of noisy measurements are linked with the underlying latent confounders through an unknown, possibly nonlinear factor structure. The main building block is a local principal subspace approximation procedure that combines $K$-nearest neighbors matching and principal component analysis. Estimators of many causal parameters, including average treatment effects and counterfactual distributions, are constructed based on doubly-robust score functions. Large-sample properties of these estimators are established, which only require relatively mild conditions on the principal subspace approximation. The results are illustrated with an empirical application studying the effect of political connections on stock returns of financial firms, and a Monte Carlo experiment. The main technical and methodological results regarding the general local principal subspace approximation method may be of independent interest.

翻译：本文为治疗效果模型制定了一种总的因果推断方法,对治疗效果模型进行了认真测量,主要特征是,通过未知的、可能是非线性的因素结构,大量噪音测量与潜在的潜在混淆模型相联系。主要组成部分是当地主要的次空间近似程序,该程序结合了近邻最接近的美元和主要组成部分的匹配分析。许多因果参数,包括平均治疗效果和反事实分布的推算器,都是根据双重紫外线分数函数构建的。这些估计器的大型抽样特性已经建立,只需要主要次空间近差相对比较温和的条件。其结果通过实验应用加以说明,研究政治联系对金融公司股票回报的影响,以及蒙特卡洛实验。关于一般地方主要次空间接近方法的主要技术和方法结果可能具有独立的兴趣。