Omitted-variable bias: fund fees and returns

Question

You regress mutual funds' net returns on their expense ratios, expecting a negative coefficient (fees drag on returns). You omit manager skill. In your sample, more skilled managers earn higher gross returns and also charge higher fees (skill is positively correlated with the expense ratio). The true effect of fees on net return is negative.

Is your estimated coefficient on the expense ratio biased upward or downward, and what does the bias hide?

Accepted Answer

The coefficient is biased upward (toward positive). The rule. With true model Y = \beta1 X + \beta2 Z + \varepsilon and Z omitted, \hat\beta1 \approx \beta1 + \beta2 \delta, where \delta shares the sign of \operatorname{Cov}(X, Z). The bias sign is \operatorname{sign}(\beta2)	imes\operatorname{sign}(\delta). Apply it. X is the expense ratio, Z is manager skill. - \beta2 0: more skilled managers earn higher returns. - \delta 0: skill is positively correlated with the expense ratio (good managers charge more). Positive times positive is positive, so the bias is upward. The true coefficient \be…

Omitted-variable bias: fund fees and returns

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