Suppose that you have many observations of the employee level longevity and the wage earned by that employee that year. You run the regression Longevity_i = β₀ + β₁ Wage_i +U_i, and get an estimate of β₁. Now, suppose that a member of the analytics team suggests that education is an omitted variable in your regression and is likely biasing your estimate of β₁. Suppose you knew that, conditional on Wage, more educated employees tended to have shorter stints with the company (lower longevity) and that the error, η_i, in the equation Longevity_i = β₀ + β₁Wage_i + β₂ Education_i + U_i, was uncorrelated with both Wage and Education. How would you sign the bias on your estimate of β₁? A) Argue that education is positively correlated with wage and that your estimate of β₁ is an upper bound. B) Argue that education is negatively correlated with wage and that your estimate of β₁ is a lower bound. C) Argue that education is positively correlated with wage and that your estimate of β₁ is a lower bound. D) Argue that education is positively correlated with longevity and that your estimate of β₁ is an upper bound.

Question

Quizplus · Accepted Answer

If education is positively correlated with wage and negatively correlated with longevity, then including Education in the regression would introduce a negative bias on the estimate of β₁ (since the coefficient on Education would be negative). In other words, the true effect of Wage on Longevity is likely larger than the estimated effect, as some of the relationship between the two variables is being picked up by Education. Therefore, the estimate of β₁ is a lower bound.

Suppose That You Have Many Observations of the Employee Level