Omitted-variable bias: education and wages

Question

You regress workers' wages on their years of schooling and find a positive coefficient, the apparent return to education. You omitted innate ability, which raises wages and is positively correlated with years of schooling.

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

Accepted Answer

The coefficient is biased upward. This is the classic "ability bias." The rule. With true model Y = \beta1 X + \beta2 Z + \varepsilon and Z omitted, the estimated slope on X is \hat\beta1 \approx \beta1 + \beta2 \delta, where \delta has the sign of \operatorname{Cov}(X, Z). The bias sign is \operatorname{sign}(\beta2)	imes\operatorname{sign}(\delta). Apply it. X is years of schooling, Z is ability. - \beta2 0: higher ability raises wages. - \delta 0: abler people get more schooling, so ability and schooling are positively correlated. Product positive, so the bias is positive: the schooling c…

Omitted-variable bias: education and wages

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