Question45 Consider the following regression of the logarithm of wages on age and an IQ score for a sample of US households: The estimated marginal effect of age on wages would suffer from omitted variables bias if there exists an additional excluded variable, say for instance productivity, which has an effect on wages there exists an additional excluded variable, say for instance productivity, which is correlated with age All of the above Any of the above None of the above ResetMaximum marks: 1 Flag question undefined

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BlackTom AI · Accepted Answer

Question content: Consider the regression of the logarithm of wages on age and an IQ score for a sample of US households. The estimated marginal effect of age on wages would suffer from omitted variables bias if
- there exists an additional excluded variable, say for instance productivity, which has an effect on wages
- there exists an additional excluded variable, say for instance productivity, which is correlated with age
- All of the above
- Any of the above
- None of the above

Option 1: there exists an additional excluded variable, say for instance productivity, which has an effect on wages
This statement describes one essential condition for omitted variable bias: an omitted variable must influence the dependent variable (wages). If productivity affects wages but is not included in the regression, the estimated coefficient on age could absorb some of the effect of productivity, leading to biased estimates. So this statement can create bias, but alone it does not specify whether the variable is correlated with age.

Option 2: there exists an additional excluded variable, say for instance productivity, which is correlated with age
This statement captures the second crucial requirement for OVB: the omitted variable must be correlated with one or more of the included regressors (here, age). If productivity is correlated with age and affects wages, omitting it biases the age coefficient. This condition is explicitly necessary for OVB to occur in a regression that uses age as a regressor.

Option 3: All of the above
If both conditions hold simultaneously—that productivity affects wages and is correlated with age—then both criteria for omitted variable bias are satisfied. In that case, stating that “all of the above” would be true, since the two individual statements both contribute to the bias mechanism under standard OVB logic.

Option 4: Any of the above
This option asserts that either of the statements 1 or 2 (or both) could independently cause bias. While it is true that either a relevant omitted variable with an effect on wages could cause bias (statement 1), and that a correlated omitted variable with a regressor could cause bias (statement 2), the more precise topping would be that both conditions together generally produce OVB. Saying “any of the above” is ambiguously inclusive in this context because 1 alone suggests a potential channel for bias, but 2 adds the correlation mechanism essential for OVB when age is the regressor.

Option 5: None of the above
Saying none of the above would mean that none of the listed scenarios could lead to omitted variable bias in this setup. This contradicts the standard OVB framework: if productivity exists as an omitted variable that affects wages and is correlated with age, bias would arise. Therefore this choice is inconsistent with OVB theory.

Summary assessment:
- Under standard omitted variable bias reasoning, both the existence of a relevant omitted variable that affects the dependent variable and its correlation with the included regressor are the core ingredients for bias. Consequently, statements 1 and 2 identify important pieces of the bias mechanism, and statement 3 (All of the above) correctly groups those conditions. Statement 4 (Any of the above) is plausible but requires careful interpretation in the multiple-choice framework, as it can be read as including the conjunction of the two conditions as well as each individually. Statement 5 (None of the above) contradicts the fundamental OVB concept. The exam design may push toward option 3 as the most comprehensive single choice, or toward 4 depending on whether “Any of the above” is intended to mean at least one of 1–4 is sufficient on its own.

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