Question

4. You sample 1,000 college graduates, and regress their annual salary (in dollars) from 5 years after graduation on their college GPA (on a scale from 1.0 to 4.0). You estimate the following regression model,

salaryi =20,000+12,000GPAi.

e. Suppose there is a dummy variable Private that is equal to 1 if the student graduated from a private college, and 0 if they graduated from a public college. If private is positively correlated with both salary and GPA, is GPA endogenous in either of the above models? If so, does this endogeneity bias the estimate of the coefficient on GPA upwards or downwards? Explain your answer.

Answer 1

Yes, there is omitted variable bias and the regression equation: salaryi =20,000+12,000GPAi. will provide a biased estimate of the coefficient of GPAi. This is because there is a variable, Private whic is correlated with both the independent variable and the dependent variable, and if it is not included in the model, it will become a part of the error term. Thus, the assumption of exogeneity will be violated and we have a biased estimate.

the direction of bias depends on the sig of correlation between Private and salaryi as well as between Private and GPAi. DIrection depends on the product of these two correlations. Since both are positive, the product is positive and the bias is upwards.