Hello, dear friend, you can consult us at any time if you have any questions, add WeChat: THEend8_
ECON4003 EMPIRICAL EXERCISE
3.1 SOLUTIONS Week 6
(a) There appears to be a positive relationship between wage and education.
The sample covariance and correlation also suggest a positive relationship between wage
and education.
Cov(wage, educ) = 20.029 Corr(wage, educ) = 0.455
(b) The observations for wage are skewed to the right indicating that most of the observations
lie between the hourly wages of 5 to 50, and that there is a smaller proportion of obser-
vations with an hourly wage greater than 50. Half of the sample earns an hourly wage
of more than $19.30 per hour, with the average being $23.64 per hour. The maximum
earned in this sample is $221.10 per hour and the least earned in this sample is $3.94 per
hour.
variable n min 25th pct median mean 75th pct max
wage 1200 3.94 13.00 19.30 23.64 29.80 221.1
1
25% of the people had up to 12 years of education. The spike at 12 years of education
describes those who finished their education at the end of high school. There are a few
observations at less than 12, representing those who did not complete high school. The
spike at 16 years describes those who completed a 4-year college degree, while those
at 18 and 21 years represent a master’s degree, and further education such as a PhD,
respectively. Spikes at 13 and 14 years are people who had one or two years at college.
variable n min 25th qtile median mean 75th qtile max
educ 1200 0 12.0 14.0 14.2 16.0 21.0
2
(c) Estimation results:
ŵage
(se)
= −10.4000
(1.9624)
+ 2.3968
(0.1354)
· educ R2 = 0.2073 SER = 13.553
The slope estimate 2.3968 suggests that an extra year of education is associated with an
increase in hourly wage rate by $2.3968 on average.
The intercept estimate -10.4 represents the estimated average hourly wage rate of a worker
with no years of education. It should not be considered meaningful as it is not possible
to have a negative hourly wage rate.
(d) Estimation results:
̂lnwage
(se)
= 1.5968
(0.070)
+ 0.0988
(0.0048)
· educ R2 = 0.2557 SER = 0.4847
The slope estimate 0.0988 suggests that an extra year of education is associated with an
increase in hourly wage rate by 9.88% on average.
(e) From the results, we can see that the percentage increase in hourly wage associated with
an extra year of education is larger for white workers (9.9% per year) than for black work-
ers (9% per year) on average. And the percentage increase in hourly wage associated with
an extra year of education is larger for female workers (11.4% per year) than for male
3
workers (9.5% per year) on average.
Dependent variable: Log of hourly wage
(1) (2) (3) (4)
Male Female White Black
Years of education 0.095 0.114 0.099 0.090
(0.006) (0.008) (0.005) (0.017)
Constant 1.724 1.272 1.603 1.638
(0.088) (0.113) (0.074) (0.239)
N 672 528 1095 105
R2 0.263 0.297 0.260 0.210
SER 0.481 0.470 0.487 0.452
Note: Standard errors are in parenthesis.
(f) The residuals are plotted against education in the figure below. There is a pattern evident:
as educ increases, the spread of the residuals also increases, suggesting that the error vari-
ance is larger for larger values of educ - a violation of assumption SR.5 homoskedasticity.