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by dash2 1495 days ago
It wouldn't be any worse. The question isn't whether the noise is correlated with the outcome. The question is whether the denoised variable would be much more correlated with the outcome (yes), and whether that would change the effect of the focal variable.

In any case, it's a weird thing to control for in a panel study. Why not just use per-person fixed effects? That would eliminate all effects that are constant across individuals.