Over-adjustment: controlling for a proxy of the treatment

Question

You estimate the effect of a value signal on returns. To "be safe," you also control for book-to-price ratio, which is essentially the same construct your value signal is built from: the two are nearly the same information.

Explain why adding this near-duplicate control drives the value coefficient toward zero, and why that is a bias, not a discovery.

Accepted Answer

A control that is a stand-in for the treatment. Book-to-price is not a separate confounder here; it is essentially a proxy for the value signal itself. Controlling for it asks: what is the effect of the value signal holding the value construct fixed? That question has almost no room to answer, because moving the signal while holding its near-twin constant leaves almost no independent variation. This is over-adjustment (or over-control) bias. Why the coefficient collapses. Once you condition on a near-duplicate, the value signal's remaining variation, the part not shared with book-to-price, is…

Over-adjustment: controlling for a proxy of the treatment

Your answer

More Statistics questions