No it just came up when I was working on something else and had me puzzling about how the OLS estimand relates to the ate in the bivariate continuous case. But clearly this is already long since solved even if not talked about enough
I'm not sure if it's solved fully -- see the ongoing work in continuous treatments in DiD. Offhand, it would seem that you are defining a different estimand than OLS (or maybe that is trivially true). In any case, I have certainly had issues with reviewers when employing continuous treatments.
Yes lots more to do; what’s solved in yitzhaki and later work is how the “ols estimand”—-the quantity targeted by lm(y~x) or the BLP—- relates to different interpretations of ate — eg avg change in Y given changes in X averaged over diff X values.
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