嵌套非参数工具变量回归
Nested Nonparametric Instrumental Variable Regression
AI总结：
针对短面板数据中嵌套非参数工具变量回归因复合病态性导致收敛速率未知的问题，提出相对良态性与多重稳健性技术，实现了显式均方收敛速率与有效推断，并兼容多种机器学习方法。
摘要：
短面板数据模型中的若干因果参数是嵌套非参数工具变量回归（nested NPIV）的泛函。近期的例子包括使用代理变量识别的中介、时变和长期处理效应。在计量经济学中，这类例子出现在三角联立方程和享乐价格系统中。然而，嵌套 NPIV 的显式均方收敛速率似乎是未知的，这阻碍了使用通用机器学习对其中部分参数进行推断。一个主要挑战是由嵌套逆问题导致的复合病态性。为限制病态性的复合方式，我们引入了两种技术：相对良态性和对病态性的多重稳健性。借助这些技术，我们为嵌套 NPIV 提供了显式均方速率，并对近期识别的因果参数实现了有效推断。我们的非渐近分析适用于神经网络、随机森林和再生核 Hilbert 空间。它还扩展到因果函数，例如异质长期处理效应。
英文摘要：
Several causal parameters in short panel data models are functionals of a nested nonparametric instrumental variable regression (nested NPIV). Recent examples include mediated, time varying, and long term treatment effects identified using proxy variables. In econometrics, examples arise in triangular simultaneous equations and hedonic price systems. However, it appears that explicit mean square convergence rates for nested NPIV are unknown, preventing inference on some of these parameters with generic machine learning. A major challenge is compounding ill posedness due to the nested inverse problems. To limit how ill posedness compounds, we introduce two techniques: relative well posedness, and multiple robustness to ill posedness. With these techniques, we provide explicit mean square rates for nested NPIV and efficient inference for recently identified causal parameters. Our nonasymptotic analysis accommodates neural networks, random forests, and reproducing kernel Hilbert spaces. It extends to causal functions, e.g. heterogeneous long term treatment effects.
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