Which of three candidate controls belongs in the regression?

Question

You want the total effect of a manager's experience (treatment) on fund returns (outcome). You are deciding whether to control for three candidate variables:

A: the firm's overall resources, which make a firm both hire experienced managers and earn higher returns.
B: the manager's average position size, which experience influences and which in turn affects returns.
C: whether the fund won an industry award, which both experience and returns push upward.

Classify A, B, and C as confounder, mediator, or collider, and say which to control for.

Accepted Answer

Classify each by its causal role. - A (firm resources): a confounder. It is a common cause of both the treatment (experience) and the outcome (returns), and it is determined before the treatment. Leaving it out creates omitted variable bias, because experienced managers would look better partly due to their well-resourced firms. Control for it. - B (average position size): a mediator. Experience causes it, and it causes returns, so it lies on the causal path from treatment to outcome. Controlling for it blocks part of experience's total effect, biasing the estimate. Do not control for it (if …

Which of three candidate controls belongs in the regression?

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