One of your friends is writing a dissertation that uses linear regression to analyze the relationship between log wages and education, log(wage) = α + βeduc + ε. While discussing the interpretation of βˆ, you start debating whether the exogeneity assumption, Cov(educ, ε) = 0, holds in this case. Your friend then claims: "actually it’s easy to test whether exogeneity holds. Even though the error term ε is unobservable, we can estimate it using the regression residuals ˆε = log(wage)−αˆ −βeduc ˆ , and calculate the sample covariance between educ and ˆε. If this sample covariance between educ and ˆε is zero or close to zero, exogeneity holds". Does your friend’s suggestion make sense? If your friend’s argument is correct, describe in detail how you would conduct this test of exogeneity, indicating the null and alternative hypotheses, the test statistic and the critical values you would use. If your friend’s argument is flawed, explain in detail why it is. In either case, use formulas in your answer.