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.
翻译:我们提供了直接的理论结果,证明将机器学习纳入标准线性工具变量设置是合理的。关键的想法是利用机器学习,加上样本分离,预测仪器和任何外源共变体的治疗变量,然后将这种预测治疗和共变体作为技术工具,以回收第二阶段的系数。这样,研究人员就可以在治疗和工具之间提取非线性共变法,通过提高仪器强度,大大改进估算精确性和稳健性。重要的是,我们限制在外源共变体中进行机器学习预测,从而避免因治疗和共变体之间的非线性关系而出现虚假的识别。我们表明,这种方法在薄弱的条件下提供了一致和无线性正常的估计,并且可以加以调整,使其半成半成效率(Chamberlain,1992年)。我们的方法保留了对线性工具变量方法的标准直观和解释,包括在薄弱识别能力下,并为应用的经济工具箱提供简单、方便用户使用的升级。我们用在法律和刑事司法判决中以实例说明我们的方法。