Consider the problem of estimating the wage equation for US workers ln(Wagei) = b0 + b1 Edui+ ui, where Wageiis theith observation onweekly earnings, Eduiis theith observation's years of education, and uiis other factors that affect Wagei, such as ability.

1.In the above model, is Eduipositively or negatively correlated with the regression error ui(ability)?

A. Eduiis not correlated with the regression error.

B. Eduimay be positively or negatively correlated with the regression error, depending on the size of the regression error.

C. Eduiis negatively correlated with the regression error.

D. Eduiis positively correlated with the regression error.

2.We estimate b1 by OLS.The omitted variable ability in the regression error uiis likely to have a positive effect on Wagei.

A. The OLS estimator is likely to be smaller than the true value (biased downward), because Eduiis negatively correlated with the regression error ui(ability).

B. The OLS estimator is likely to be smaller than the true value (biased downward), because Eduiis positively correlated with the regression error ui(ability).

C. None of the options is correct.

D. The OLS estimator is likely to be larger than the true value (biased upward), because Eduiis positively correlated with the regression error ui(ability).

3.In an influential paper, David Card (1995) suggested the following:

(I) If a potential student lives close to a college, this reduces the cost of attendance and thereby raises the likelihood that the student will attend college.

(II) College proximity does not directly affect a student's abilities, so should not have a direct effect on his or her market wage.

Let the instrumental variable Zibe the college proximity that is a binary variable equal to 1 if theith observation grew up in the same county as a 4-year college, and equal to 0 otherwise.

A. (I) implies the relevant condition of the instrumental variable is reasonable.

B. None of the options is correct.

C. (II) implies the relevant condition of the instrumental variable is reasonable.

D. (I) implies that the exogenous condition of the instrumental variable is reasonable.

4.

Your Two Stage Least Squares (2SLS) estimation is: log(Wage;) = 5.48 + 0.08Edui, R2 = 0.35, F - statistics = 9.3. (0.01) (0.035) You also run the two stages for the 2SLS estimation separately and the first stage result is: Edui = 12.89 + 1.45Zi, R2 = 0.51, F - statistics = 12.8. (0.02) (0.45) If a college graduate decided to go to a master's program, that is, Edu; increases from 16 to 18, by how much is Wage; expected to change? (SHOW YOUR WORK!)