Before revision:  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).
After revision:  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).