大部分无害的机器学习：在线性IV模型中学习最优工具
Mostly Harmless Machine Learning: Learning Optimal Instruments in Linear IV Models
摘要：
我们提供了直接的理论结果，证明将机器学习纳入标准的线性工具变量设置。其核心思想是使用机器学习，结合样本分割，从工具和任何外生协变量预测治疗变量，然后使用预测的治疗和协变量作为技术工具，在第二阶段恢复系数。这允许研究人员提取治疗和仪器之间的非线性协变，这可以通过提高仪器强度来显著提高估计精度和鲁棒性。重要的是，我们将机器学习的预测约束为外生协变量的线性，从而避免治疗和协变量之间的非线性关系引起的虚假识别。我们证明了这种方法在弱条件下提供了一致的和渐近正态的估计，并且它可以被修改为半参数有效的（Chamberlain，1992）。我们的方法保留了标准的直觉和线性工具变量方法的解释，包括在弱识别，并提供了一个简单的，用户友好的升级应用经济学工具箱。我们说明我们的方法在法律和刑事司法的一个例子，检查上诉法院推翻地区法院的判决的因果关系。
英文摘要：
We offer straightforward theoretical results that justify incorporating machine learning in the standard linear instrumental variable setting. The key idea is to use machine learning, combined with sample-splitting, to predict the treatment variable from the instrument and any exogenous covariates, and then use this predicted treatment and the covariates as technical instruments to recover the coefficients in the second-stage. This allows the researcher to extract non-linear co-variation between the treatment and instrument that may dramatically improve estimation precision and robustness by boosting instrument strength. Importantly, we constrain the machine-learned predictions to be linear in the exogenous covariates, thus avoiding spurious identification arising from non-linear relationships between the treatment and the covariates. We show that this approach delivers consistent and asymptotically normal estimates under weak conditions and that it may be adapted to be semiparametrically efficient (Chamberlain, 1992). Our method preserves standard intuitions and interpretations of linear instrumental variable methods, including under weak identification, and provides a simple, user-friendly upgrade to the applied economics toolbox. We illustrate our method with an example in law and criminal justice, examining the causal effect of appellate court reversals on district court sentencing decisions.
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