Several causal parameters in short panel data models are scalar summaries of a function called a nested nonparametric instrumental variable regression (nested NPIV). Examples include long term, mediated, and time varying treatment effects identified using proxy variables. However, it appears that no prior estimators or guarantees for nested NPIV exist, preventing flexible estimation and inference for these causal parameters. A major challenge is compounding ill posedness due to the nested inverse problems. We analyze adversarial estimators of nested NPIV, and provide sufficient conditions for efficient inference on the causal parameter. Our nonasymptotic analysis has three salient features: (i) introducing techniques that limit how ill posedness compounds; (ii) accommodating neural networks, random forests, and reproducing kernel Hilbert spaces; and (iii) extending to causal functions, e.g. long term heterogeneous treatment effects. We measure long term heterogeneous treatment effects of Project STAR and mediated proximal treatment effects of the Job Corps.

翻译：短期面板数据模型中的若干因果参数是称为嵌套非参数工具变量回归（嵌套NPIV）函数的标量概括。这些参数包括通过代理变量识别的长期效应、中介效应及时变处理效应。然而，目前似乎不存在针对嵌套NPIV的现有估计量或理论保证，阻碍了这些因果参数的灵活估计与推断。嵌套逆问题导致的复合病态性是主要挑战。我们分析了嵌套NPIV的对抗估计量，并给出了有效推断因果参数的充分条件。本非渐近分析具有三个显著特征：（i）引入限制病态性复合的技术；（ii）兼容神经网络、随机森林及再生核希尔伯特空间；（iii）扩展至因果函数，如长期异质性处理效应。我们测定了"STAR计划"的长期异质性处理效应及"职业训练团"的中介近端处理效应。