Question

Problem One Suppose the following three equations are estimated: \begin{align} \log(\text{wage}) &= 2.0912 + 0.0691 \text{totcoll} \\ &(0.008) \qquad (0.002) \\ n &= 6,763; R^2 = 0.109; \bar{R}^2 = 0.109 \end{align} and, \begin{align} \log(\text{wage}) &= 2.253 - 0.289 \text{female} + 0.0642 \text{totcoll} \\ &(0.009) \qquad (0.011) \qquad (0.0023) \\ n &= 6,763; R^2 = 0.1964 \end{align} and \begin{align} \log(\text{wage}) &= 2.289 - 0.357 \text{female} + 0.50 \text{totcoll} + 0.030 \text{female} \cdot \text{totcoll} \\ &(0.011) \qquad (0.015) \qquad (0.003) \qquad (0.005) \\ n &= 6,763; R^2 = 0.202 \end{align} where, $\log(\text{wage})$ is natural logarithm of hourly wage; female = 1 for females and zero otherwise; totcoll is total years in college. Standard errors of the estimated coefficients are in parentheses. a. Interpret the coefficient of female in the second regression. Do the coefficients of 'female' in the second and third regressions have the same interpretations? Explain. b. In the third regression, construct the log wage equation for males and females separately and determine the intercept and slope of each equation. Interpret the coefficient on the interaction term. If the effect of education on wage statistically different between males and females? Set up the appropriate test and interpret the test result. c. Is the wage regression different for male and female? Set up the appropriate hypothesis test and explain the result. (Hint: Set up the F test). d. Calculate the adjusted R squared in each of the regressions and briefly explain which regression is preferred.

          Problem One
Suppose the following three equations are estimated:
\begin{align*} \log(\text{wage}) &= 2.0912 + 0.0691 \text{totcoll} \\ &(0.008) \qquad (0.002) \\ n &= 6,763; R^2 = 0.109; \bar{R}^2 = 0.109 \end{align*}
and,
\begin{align*} \log(\text{wage}) &= 2.253 - 0.289 \text{female} + 0.0642 \text{totcoll} \\ &(0.009) \qquad (0.011) \qquad (0.0023) \\ n &= 6,763; R^2 = 0.1964 \end{align*}
and
\begin{align*} \log(\text{wage}) &= 2.289 - 0.357 \text{female} + 0.50 \text{totcoll} + 0.030 \text{female} \cdot \text{totcoll} \\ &(0.011) \qquad (0.015) \qquad (0.003) \qquad (0.005) \\ n &= 6,763; R^2 = 0.202 \end{align*}
where,
$\log(\text{wage})$ is natural logarithm of hourly wage; female = 1 for females and zero otherwise; totcoll is total years in college.
Standard errors of the estimated coefficients are in parentheses.
a. Interpret the coefficient of female in the second regression. Do the coefficients of 'female' in the second and
third regressions have the same interpretations? Explain.
b. In the third regression, construct the log wage equation for males and females separately and determine the
intercept and slope of each equation. Interpret the coefficient on the interaction term. If the effect of education
on wage statistically different between males and females? Set up the appropriate test and interpret the test
result.
c. Is the wage regression different for male and female? Set up the appropriate hypothesis test and explain the
result. (Hint: Set up the F test).
d. Calculate the adjusted R squared in each of the regressions and briefly explain which regression is preferred.

Problem One
Suppose the following three equations are estimated:

log(wage) = 2.0912 + 0.0691 totcoll
(0.008) (0.002)
n = 6,763; R^2 = 0.109; R̅^2 = 0.109

and,

log(wage) = 2.253 - 0.289 female + 0.0642 totcoll
(0.009) (0.011) (0.0023)
n = 6,763; R^2 = 0.1964

and

log(wage) = 2.289 - 0.357 female + 0.50 totcoll + 0.030 female·totcoll
(0.011) (0.015) (0.003) (0.005)
n = 6,763; R^2 = 0.202

where,
log(wage) is natural logarithm of hourly wage; female = 1 for females and zero otherwise; totcoll is total years in college.
Standard errors of the estimated coefficients are in parentheses.
a. Interpret the coefficient of female in the second regression. Do the coefficients of 'female' in the second and
third regressions have the same interpretations? Explain.
b. In the third regression, construct the log wage equation for males and females separately and determine the
intercept and slope of each equation. Interpret the coefficient on the interaction term. If the effect of education
on wage statistically different between males and females? Set up the appropriate test and interpret the test
result.
c. Is the wage regression different for male and female? Set up the appropriate hypothesis test and explain the
result. (Hint: Set up the F test).
d. Calculate the adjusted R squared in each of the regressions and briefly explain which regression is preferred.

Added by Rachel R.

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