A researcher is studying the effect of parents' level of education on educational achievement of individuals. Using data on completed years of education (educ), mother's level of education (motheduc), father's level of education (fatheduc), a measure of cognitive ability (abil), and logarithm of family income (l.income), the researcher estimates 4 models. Table (1) shows the OLS estimates for each model, with standard errors in parentheses underneath each coefficient. The dependent variable in all the models is educ. Model 1 Model 2 Model 3 Model 4 Independent variables L.income (0.2) 0.15 motheduc 0.27 0.18 0.17 (0.02) (0.03) 0.11 (0.02) 0.52 (0.03) 0.11 (0.02) 0.39 (0.03) 0.10 (0.02) 0.35 fatheduc abil 0.53 (0.03) (0.03) (0.03) 0.05 (0.03) 0.09 (0.01) 8.74 abil_squared ww (0.01) 8.74 6.94 (0.32) 1230 Intercept 8.4 (0.12) 1230 3899.97 0.38 Table (1) (0.31) 1230 (0.31) 1210 N SSR R-squared 3999.24 3785.24 3541.2 0.35 0.45 0.49 a. How the degrees of freedom in model (3) compare to the degrees of freedom in model (4)? Explain. b. Why did the coefficient of motheduc decrease after adding variable fatheduc to the regression? Discuss and if necessary, incorporate the Gauss-Markov assumptions in your answer.

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A researcher is studying the effect of parents' level of education on educational
achievement of individuals. Using data on completed years of education (educ), mother's
level of education (motheduc), father's level of education (fatheduc), a measure of cognitive
ability (abil), and logarithm of family income (l.income), the researcher estimates 4 models.
Table (1) shows the OLS estimates for each model, with standard errors in parentheses
underneath each coefficient. The dependent variable in all the models is educ.
Model 1
Model 2
Model 3
Model 4
Independent variables
L.income
(0.2)
0.15
motheduc
0.27
0.18
0.17
(0.02)
(0.03)
0.11
(0.02)
0.52
(0.03)
0.11
(0.02)
0.39
(0.03)
0.10
(0.02)
0.35
fatheduc
abil
0.53
(0.03)
0.09
(0.01)
8.74
(0.03)
(0.03)
(0.03)
0.05
abil_squared
ww
(0.01)
8.74
6.94
(0.32)
1230
Intercept
8.4
(0.12)
1230
3899.97
0.38
Table (1)
(0.31)
1230
(0.31)
1210
N
SSR
R-squared
3999.24
3785.24
3541.2
0.35
0.45
0.49
a. How the degrees of freedom in model (3) compare to the degrees of freedom in
model (4)? Explain.
b. Why did the coefficient of motheduc decrease after adding variable fatheduc to the
regression? Discuss and if necessary, incorporate the Gauss-Markov assumptions in
your answer.
Transcribed Image Text:A researcher is studying the effect of parents' level of education on educational achievement of individuals. Using data on completed years of education (educ), mother's level of education (motheduc), father's level of education (fatheduc), a measure of cognitive ability (abil), and logarithm of family income (l.income), the researcher estimates 4 models. Table (1) shows the OLS estimates for each model, with standard errors in parentheses underneath each coefficient. The dependent variable in all the models is educ. Model 1 Model 2 Model 3 Model 4 Independent variables L.income (0.2) 0.15 motheduc 0.27 0.18 0.17 (0.02) (0.03) 0.11 (0.02) 0.52 (0.03) 0.11 (0.02) 0.39 (0.03) 0.10 (0.02) 0.35 fatheduc abil 0.53 (0.03) 0.09 (0.01) 8.74 (0.03) (0.03) (0.03) 0.05 abil_squared ww (0.01) 8.74 6.94 (0.32) 1230 Intercept 8.4 (0.12) 1230 3899.97 0.38 Table (1) (0.31) 1230 (0.31) 1210 N SSR R-squared 3999.24 3785.24 3541.2 0.35 0.45 0.49 a. How the degrees of freedom in model (3) compare to the degrees of freedom in model (4)? Explain. b. Why did the coefficient of motheduc decrease after adding variable fatheduc to the regression? Discuss and if necessary, incorporate the Gauss-Markov assumptions in your answer.
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