Omitted-variable bias: remote days and productivity

Question

You regress each worker's productivity on their number of remote-work days per month. You omit seniority. In your data, senior workers are more productive (seniority raises productivity) but they take fewer remote days (seniority is negatively correlated with remote days).

Is your estimated coefficient on remote days 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 carries the sign of \operatorname{Cov}(X, Z). The bias sign is \operatorname{sign}(\beta2)	imes\operatorname{sign}(\delta). Apply it. X is remote days, Z is seniority. - \beta2 0: seniority raises productivity. - \delta < 0: seniority is negatively correlated with remote days (senior workers take fewer). Positive times negative is negative, so the bias is downward: the coefficient on remote days is understated. Because the …

Omitted-variable bias: remote days and productivity

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