The other kind of bias: controlling for a mediator

Question

You want the total effect of a new trading signal (the treatment) on portfolio returns (the outcome). Worried about omitted variable bias, you add every control you can think of, including portfolio turnover. But turnover is itself caused by the signal: acting on the signal changes how much you trade. Explain why adding turnover biases your estimate of the total effect, and reconcile this with the usual advice to control for confounders.

Accepted Answer

Two ways to bias a coefficient. Omitted variable bias teaches you to add controls: leaving out a confounder (a common cause of treatment and outcome) biases the estimate. But there is a mirror-image danger, adding the wrong control also biases the estimate. Turnover here is a bad control. Why turnover is a bad control. Turnover sits on the causal path from the signal to returns: signal changes turnover, turnover affects returns. A variable that the treatment causes and that in turn affects the outcome is a mediator. Controlling for a mediator holds it fixed, which blocks the part of the treat…

The other kind of bias: controlling for a mediator

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