Mostly Harmless Machine Learning: Learning Optimal Instruments in Linear IV Models
This provides an incremental upgrade to the applied economics toolbox by enhancing standard linear IV methods with machine learning for better instrument strength.
The paper tackles the problem of improving estimation precision and robustness in linear instrumental variable (IV) models by using machine learning to predict treatment from instruments and covariates, then using these predictions as technical instruments. The result is a method that delivers consistent and asymptotically normal estimates under weak conditions, with potential for semiparametric efficiency, as illustrated in a law and criminal justice example.
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.