We provide some simple theoretical results that justify incorporating machine learning in a standard linear instrumental variable setting , prevalent in empirical research in economics. Machine learningtechniques , combined with sample-splitting, extract nonlinear variation in the instrument that may dramatically improve estimation precision and robustness by boosting instrument strength. The analysis is straightforward in the absence of covariates. The presence of linearly included exogenous covariatescomplicates identification, as the researcher would like to prevent nonlinearities in the covariates from providing the identifying variation. Our procedure can be effectively adapted to account for this complication, based on an argument by Chamberlain ( 1992). Our method preserves standard intuitions and interpretations of linear instrumental variable methods 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.
We offer simple theoretical results that justify incorporating machine learning in the standard linear instrumental variable setting that is prevalent in empirical research in economics. 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 rather than from the instrument itself. 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 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.
R
provide some
offer
R
a
the
R
,
that is
R
Machine learningtechniques
The key idea is to use machine learning
R
extract nonlinear variation in the
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
R
The analysis is straightforward in the absence of covariates. The presence of linearly included exogenous covariatescomplicates identification, as the researcher would like to prevent nonlinearities in the covariates from providing the identifying variation. Our procedure can be effectively adapted to account for this complication, based on an argument by Chamberlain (
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 rather than from the instrument itself. 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,