用机器学习做2SLS第一阶段，线性方法有效，非线性可能更糟。
Machine learning the first stage in 2SLS: Practical guidance from bias decomposition and simulation
- 将线性机器学习（如后Lasso）用于2SLS第一阶段，可降低偏差。
- 非线性方法（如随机森林、神经网络）会使第二阶段估计偏差剧增。
- 适合做因果推断的学者参考，避免误用非线性模型。
机器学习主要针对预测问题发展而来，而两阶段最小二乘法（2SLS）的第一阶段本质上是预测问题，暗示使用机器学习可能带来收益。然而，目前缺乏关于何时机器学习能提升2SLS、何时反而有害的实用指导。本文通过偏差分解，揭示了将机器学习引入2SLS的三类关键偏差来源。机制上，这类方法同时面临预测与因果推断场景的共性问题及其交互影响。通过模拟实验，发现线性机器学习方法（如后Lasso）表现良好，而非线性方法（如随机森林、神经网络）会导致第二阶段估计产生显著偏差，甚至超过内生性普通最小二乘法（OLS）的偏差。
原文摘要 · Abstract (English)
Machine learning (ML) primarily evolved to solve "prediction problems." The first stage of two-stage least squares (2SLS) is a prediction problem, suggesting potential gains from ML first-stage assistance. However, little guidance exists on when ML helps 2SLS$\unicode{x2014}$or when it hurts. We investigate the implications of inserting ML into 2SLS, decomposing the bias into three informative components. Mechanically, ML-in-2SLS procedures face issues common to prediction and causal-inference settings$\unicode{x2014}$and their interaction. Through simulation, we show linear ML methods (e.g., post-Lasso) work well, while nonlinear methods (e.g., random forests, neural nets) generate substantial bias in second-stage estimates$\unicode{x2014}$potentially exceeding the bias of endogenous OLS.
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