Omitted-variable bias: advertising spend and profitability

Question

You regress firms' profitability on their advertising spend to gauge whether advertising pays. You omit firm age. In your sample, older firms are more profitable (established brands, loyal customers) but spend less on advertising (age is negatively correlated with ad spend).

Is your estimated coefficient on advertising spend biased upward or downward? State the reasoning.

Accepted Answer

The coefficient is biased downward. 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 advertising spend, Z is firm age. - \beta2 0: older firms are more profitable. - \delta < 0: firm age is negatively correlated with ad spend (older firms advertise less). Positive times negative is negative, so the bias is downward: the advertising coefficient is understated. The highly p…

Omitted-variable bias: advertising spend and profitability

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