For continuous treatments, residuals-on-residuals regression targets a variance-weighted average of derivatives at unobserved pseudo-treatment values, not the average causal derivative; a coarsened AIPW estimator fixes this.
Aronow and Cyrus Samii
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Estimating Representative Causal Effects with Double Machine Learning
For continuous treatments, residuals-on-residuals regression targets a variance-weighted average of derivatives at unobserved pseudo-treatment values, not the average causal derivative; a coarsened AIPW estimator fixes this.