Assignment 7
wage educ age
13
exper marr female
12
41
15
1
0
12.8 14
53
4
0
0
24.33 14
36
18
0
1
6
13
18
9
0
0
8.55 12
29
17
1
0
5.4
11
58
7
1
1
5.25 12
47
4
0
0
6.35 8
40
8
1
1
10.2 11
44
1
0
0
6.2
12
27
30
1
0
5.15 12
29
6
1
1
12
12
46
24
1
0
6
14
23
2
0
0
9
16
30
3
1
1
9.45 13
34
3
1
1
14.33 12
28
3
1
0
6.75 12
24
3
1
1
5.6
12
30
13
1
1
6.5
12
46
8
1
1
45
16
51
8
1
0
15.89 8
48
5
1
0
9
10
50
10
1
1
14.85 13
46
4
1
0
27.97 13
45
4
1
0
8
13
22
3
0
0
6
14
22
6
0
1
10
12
37
11
1
1
7
13
68
4
1
0
6.5
11
36
6
0
1
8.5
14
28
4
1
0
6
8
36
3
0
1
5.5
10
24
1
0
1
7.7
12
41
12
1
1
13.42 13
47
14
1
0
6
12
45
14
1
1
5.4
13
20
2
0
1
8.5
13
28
6
1
0
6.75 13
25
6
0
1
5
12
62
6
0
1
9.72 12
28
7
1
1
6.45 14
27
3
1
1
8.5
13
29
8
1
0
7
12
32
4
0
0
4.5
12
49
5
1
0
7
14
45
2
1
1
9.75 12
44
9
1
1
5.15 10
16
8
0
0
10
11
29
8
1
0
7
11
28
6
1
1
5.5
12
36
6
1
1
11.5 10
33
7
1
0
7
14
53
1
0
1
15.27 12
26
42
1
0
11
12
64
4
1
1
9.5
12
28
4
1
0
15
12
42
2
1
1
10
11
71
4
1
0
7
12
32
4
1
0
8
13
38
8
1
1
11
13
43
6
1
1
6
6
52
11
1
1
7.5
12
26
6
1
0
19.13 16
24
8
1
1
5.25 13
25
1
0
0
9
13
25
13
1
1
12
16
45
6
1
1
12
13
25
7
1
1
7
13
35
1
1
1
9
16
23
8
0
1
20
12
49
1
0
1
26
13
40
3
0
0
9
14
26
3
1
1
11.6 13
26
4
1
0
7.6
13
23
2
0
0
12
12
29
11
1
1
10
12
39
9
1
0
6.5
12
27
10
1
1
11.5 13
36
46
1
1
13.5 13
21
6
0
1
8.5
13
50
2
1
1
5.65 13
27
6
0
1
8
12
22
34
0
1
7.5
12
22
4
0
1
21
13
54
19
1
1
21
13
32
2
1
1
7
13
42
2
1
0
8.5
13
20
3
0
1
8
10
21
8
0
0
14
12
49
21
1
1
10
13
18
2
0
1
15.03 12
47
5
1
1
6.5
12
43
7
1
1
15.54 16
47
6
1
0
12.35 16
45
24
1
1
25.44 13
43
15
1
0
8
13
18
2
0
0
8
11
17
24
0
1
8
11
17
2
0
0
20
13
26
2
0
0
15
13
29
12
0
1
9.5
12
26
18
1
1
19
12
45
2
1
0
30.3 12
36
9
1
0
11.52 12
45
2
1
0
11
12
45
2
1
1
9
13
25
4
0
1
9
9
24
2
0
0
8.5
11
20
2
0
1
10.45 14
28
2
1
1
12.03 12
41
4
0
1
12.45 16
26
6
1
0
18.1 16
24
11
1
1
9
13
51
10
1
0
11.18 11
49
5
1
1
11
16
24
9
0
0
16
16
37
3
1
1
15.2 13
29
6
1
0
8.83 12
31
1
1
1
10.53 12
32
1
1
1
14
49
2
0
1
13
5.3
16
29
3
0
0
19
13
53
5
1
0
9
12
38
5
0
1
23.75 12
42
38
1
1
25.5 12
40
24
1
0
38
13
40
5
1
0
24
14
39
24
1
1
28.28 12
39
4
1
0
18.04 12
22
2
0
1
18
13
23
30
0
1
15
12
24
2
0
1
12.83 14
43
22
1
1
14.75 8
48
12
0
1
5.3
14
30
5
0
0
5.5
18
28
37
0
0
12
16
41
8
0
1
18
13
47
10
1
0
12
12
40
8
1
1
7
12
24
15
1
0
17.41 16
41
4
1
1
12
13
29
12
0
1
12.98 16
29
5
1
1
5
13
47
18
1
1
7.5
8
36
40
1
0
8
9
33
2
0
1
5.25 16
40
5
1
1
7.5
11
67
3
0
1
21.85 13
39
52
0
1
7.5
13
29
4
0
0
18.32 21
43
14
1
1
12.3 16
43
5
1
0
8.77 13
56
6
0
1
18.9 14
51
16
1
1
5.5
13
31
3
1
1
14
12
27
8
1
0
22
12
51
22
1
0
11
13
20
11
0
0
5.5
9
16
2
0
0
6.5
11
25
3
0
1
6.25 12
24
2
0
0
6
6
53
1
1
1
6
13
61
5
1
0
15
12
40
18
1
0
10.5 12
45
16
1
1
7.3
12
46
5
0
1
13
12
28
3
0
0
8.3
11
24
2
0
0
14.62 12
41
15
1
1
8.31 12
21
7
0
1
6.5
18
5
0
0
13
6.5
13
18
5
0
0
8.32 12
31
1
0
0
7.5
44
14
0
1
8.31 13
22
1
1
1
7
11
48
4
0
0
12
12
54
4
0
0
6
6
29
7
1
0
4
9
20
3
1
1
12
16
36
3
1
1
21
14
33
5
0
1
9.3
14
32
3
0
1
7.46 12
62
6
0
1
13
10
58
3
1
0
8
8
31
12
0
1
7.5
6
34
18
0
0
15
13
31
8
0
0
10
13
19
3
0
1
6
8
16
3
0
0
5.5
11
18
10
0
0
19.75 12
42
6
1
1
5
12
25
4
1
1
7
10
28
1
1
0
5
12
40
4
1
1
7.25 12
42
5
0
1
7
21
5
1
1
8
13
7.5
10
22
2
0
0
5.5
11
52
2
1
1
5.25 14
59
1
0
1
9.69 13
58
30
1
0
10.69 13
49
28
1
1
7.5
13
47
3
1
0
10
12
44
5
1
1
2.35 12
23
4
0
0
21.9 14
41
9
1
0
8.5
12
35
3
1
0
8.38 13
37
6
1
1
8.63 12
54
6
1
1
10.66 16
29
2
0
1
12
16
22
7
0
1
8.37 12
49
4
0
0
15
12
47
25
1
0
13
14
43
10
1
1
10
13
20
8
0
0
8
13
26
3
0
0
14
11
33
8
1
0
7.75 12
33
24
1
1
13.87 14
35
7
1
0
10
9
52
10
1
0
10
12
40
4
0
0
10
12
30
5
0
1
5.5
9
16
8
0
0
8
13
48
18
1
0
8
13
46
5
1
1
14.62 12
41
18
1
1
7
13
21
2
0
1
6
11
18
5
0
0
6
10
17
2
0
1
8
13
20
5
1
1
10
12
37
15
1
1
5.35 12
21
3
0
1
13
10
57
17
1
0
5
12
44
16
1
1
6
12
21
5
0
0
9.5
9
31
66
1
0
9
12
24
60
1
1
7.41 13
28
2
1
0
5.15 12
36
6
1
1
5.15 10
16
6
0
0
18
21
27
1
0
1
5.25 13
28
7
1
1
5.15 12
25
7
1
1
7.25 12
42
2
0
1
7.43 14
51
6
1
1
7
12
39
10
0
0
6
12
38
1
0
0
7
12
45
4
1
1
7.5
12
30
2
0
1
7.5
12
30
3
0
0
6.7
9
38
3
1
1
7
8
40
3
1
0
6.25 9
28
3
1
0
9
12
55
5
1
0
31
16
52
30
1
1
6.5
13
21
6
0
0
10.5 12
40
14
1
0
8.6
12
44
9
1
1
7.25 13
19
7
0
1
7.25 13
22
3
0
1
5.25 12
25
3
0
0
6
11
17
1
0
0
13
13
29
4
1
1
6
16
22
7
0
1
8.6
12
54
3
0
1
10
13
37
2
1
1
11.35 12
51
2
1
1
19.44 13
36
3
0
1
9.5
26
2
0
0
8.03 8
42
9
1
1
5.15 12
19
3
0
0
7.55 12
33
9
1
0
12
8
8
51
20
1
0
5.15 12
24
3
0
1
6.25 12
30
3
1
0
7.56 12
33
15
0
1
11.7 13
42
14
0
1
15
13
40
10
0
0
5.15 13
29
4
1
1
18
12
70
11
0
0
12
13
33
1
1
0
18
14
34
8
1
0
10.35 13
34
1
1
1
5.95 12
31
1
1
1
12.09 12
35
3
1
0
15
14
48
2
0
0
9
12
23
4
0
1
5.5
12
73
20
0
1
7
13
30
6
1
0
5.15 12
33
12
1
1
8.5
9
22
2
1
0
14
14
37
15
1
1
10
12
53
5
1
1
15
16
58
20
1
0
15
14
41
12
1
1
6.5
13
25
5
0
0
6
12
23
10
1
1
6
12
23
4
1
0
6.37 13
57
9
1
1
13.25 12
34
6
1
0
28
16
30
11
0
1
11
13
28
2
0
0
8.63 13
48
18
1
1
5.5
13
20
18
0
0
24
16
53
15
1
0
16.5 12
57
34
1
1
6
12
22
6
0
0
11.25 16
31
4
0
0
16
16
34
3
0
0
13
13
34
2
0
1
18
13
37
17
1
0
13.47 16
39
18
1
1
26
13
49
41
0
1
10
12
24
1
0
0
9
12
24
2
0
0
21.99 13
46
20
1
0
14.55 12
23
6
0
0
12
13
20
3
1
1
12
10
40
12
0
0
13.5 16
35
4
0
0
5.5
14
22
1
0
0
6.75 13
21
5
0
0
5.75 13
21
8
0
0
5.75 13
21
24
0
0
6.25 12
55
5
1
1
6
12
27
4
0
1
11.52 14
49
6
0
0
8
12
21
2
0
0
16.97 14
42
6
1
0
14.37 14
29
1
1
1
5
12
31
6
1
1
6.75 16
52
1
1
1
14.67 13
48
8
0
1
18
12
34
5
0
0
10.45 14
62
9
1
0
12.25 11
39
7
1
0
11.93 12
36
9
1
1
40
21
36
5
1
0
11.69 12
42
18
1
1
7
13
46
10
1
1
5.5
12
29
8
0
1
12
11
32
5
1
1
5.15 6
26
2
1
0
6.5
13
21
36
0
1
6.5
13
19
12
0
0
20.78 13
36
6
1
0
8.65 12
31
3
1
1
7.99 13
47
6
1
1
12
11
20
12
1
0
13.75 13
31
10
1
1
19.16 13
43
27
1
1
7.75 12
28
11
0
0
7
11
48
5
1
1
6
13
21
2
1
1
21.9 12
50
10
0
0
8.52 12
35
4
1
1
12
12
52
8
1
0
6.4
13
47
18
1
1
11.08 14
39
6
1
1
12.11 12
58
15
0
1
20
16
35
3
0
0
13.74 13
41
5
1
1
7.5
12
44
7
1
0
7.5
13
19
1
0
0
10
13
19
3
0
0
15
8
33
12
1
0
16
14
36
3
1
1
10
11
58
4
1
0
5.5
11
17
9
0
1
7
13
43
1
0
1
14
13
45
4
0
0
5
10
16
3
0
1
12.5 13
25
3
0
0
7
13
50
6
1
1
10.81 12
31
3
1
0
12
13
29
3
1
1
5
11
44
2
1
0
33
21
37
7
1
0
15.7 14
44
7
1
0
14
10
47
5
1
1
16.5 16
42
18
0
1
16.5 16
34
10
0
0
37
18
49
4
0
0
28
16
53
3
1
1
8
16
24
1
0
1
40
16
45
8
1
0
7
9
15
1
0
1
20
13
49
30
1
0
18
13
38
3
1
0
17
14
38
10
1
1
7.63 14
24
3
0
0
11
12
63
3
1
0
9
10
31
7
1
0
12
16
30
3
1
0
13
14
28
1
1
1
10
14
30
8
1
0
14
18
37
9
1
1
6
4
32
7
1
0
6
6
31
3
1
0
5.15 11
19
4
0
1
9
32
2
1
0
7.38 11
61
7
0
1
7
23
1
0
1
5.15 8
27
16
1
0
5.15 6
29
18
1
0
7
14
70
3
0
1
7
12
27
2
0
0
8
9
27
2
1
1
8.5
14
58
8
1
0
5.15 13
37
13
1
0
13
16
28
4
0
1
20
16
45
10
0
1
27
13
35
9
1
0
14.33 4
48
13
0
0
9
16
26
4
0
1
5.41 12
18
1
0
1
10
18
36
4
0
1
6.8
13
25
3
0
1
5
6
29
10
1
0
18
12
35
12
1
0
13
16
28
30
1
1
12.25 16
27
6
0
0
6
13
13.5 16
28
8
1
0
10
13
23
1
1
1
8.75 14
24
4
1
0
6
13
23
6
1
1
18.75 12
36
7
0
0
9.5
12
36
2
0
1
6.95 13
24
2
0
0
9.1
13
25
5
0
1
14
9
35
18
0
0
9.75 12
34
6
1
0
25
18
40
10
1
0
23
16
37
10
1
1
26
16
37
10
1
0
6
11
17
8
0
0
22.5 16
38
3
1
1
21.5 13
41
4
1
0
12.5 21
31
1
0
0
6
4
34
1
1
0
9
6
33
13
1
1
7
11
52
5
0
1
5
1
30
3
1
0
5
1
28
2
1
0
5
1
24
3
1
1
5
4
54
4
1
0
5
8
23
6
0
1
6
6
40
5
1
0
8
13
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20.63 13
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15.82 16
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6
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3
1
1
ECN/PUB 480/580
Assignment #7
Due: Friday, April 20th, 2017, 5:30pm
Directions: Completely answer all the questions. You can integrate the Stata output
within the questions using the techniques previously discussed. Please do not print out
or turn in any of the original raw data!! Be sure to clearly indicate the units for all
numbers ($, %, years, etc). Please staple all the pages together (no folders). Due by
Monday, April 24th, either by personal delivery to 220 French Hall or by email of a MS
Word file. Please turn in your assignment by the final deadline, even if it is incomplete
(so I can compute final grades). Assignments that are submitted late (defined as
starting at 5:31pm on April 20th) will be penalized by 10% per day that they are
late.
Read the questions and the directions carefully!!! The material needed to answer the
questions is contained in the course notes. Your notes contain both the underlying
statistical procedures behind the questions, as well as several examples that are very
similar. You may also want to refer back to Assignments 4, 5, and 6 to refresh your
memory on some of the things you will be doing.
_______________________________________________________________________
Go to Blackboard to download the Assignment #7 exam data set.
How to download:
-Go to the “Assignments” section of Blackboard.
-Right-click on the file. Select “Save Target As”.
-Save the file on your computer in an easy-to-find place, such as The Desktop.
-Open Stata. Select “File”, then “Open” and browse for where you stored the data
set.
-Double-click the data set to open it in Stata.
BEFORE ANSWERING EACH QUESTION, MAKE SURE TO READ THE
QUESTION CAREFULLY AND DO WHAT THE QUESTION ASKS!
1
The data set is a Stata data set containing labor market data for 1000 randomly selected
individuals (unit of analysis) from the February, 1998 U.S. Census Current Population
Survey. The data set includes the following variables:
wage: average hourly earnings, in dollars, for each individual
educ: number of years of education for each individual
age: age of each individual, in years
exper: number of years of work experience for each individual
marr: dummy variable taking the value of 1 if the individual is married, 0 otherwise
female: dummy variable taking the value of 1 if the individual is female, 0 otherwise
Start by opening the data set in Stata and generate 5 new variables using the gen
command. To help you out, I give the command you need to use in parentheses.
a) the natural logarithm of wages (gen lwage = log(wage))
b) experience squared (gen expersq = exper^2)
c) a new dummy variable for male, which takes on the value of 1 if the individual is a
male and 0 otherwise (gen male = 1-female)
d) a new interaction dummy variable marrfe taking on the value of 1 if the individual
is a married female, and 0 otherwise (gen marrfe = marr*female)
e) a new interaction dummy variable that will be equal to 1 if the individual is a married
male, and 0 otherwise (gen marrma = marr*male)
The point of this assignment is to conduct a regression analysis to see if the “wage gap”
between male and female workers persists after we start controlling for other variables,
namely education and experience.
1.
Create a table in MS Word (with a title and description) that summarizes the data
by gender. That is, give the average wage, average education, average
experience, and average age separately for men and women. You can use the
sum command along with an if statement to do this (no commas). For example,
if female == 1 means only females. Use proper units for the variables in
your summary statistics and round to two places past the decimal. Do NOT use
the Stata output as your table! (4 points)
2.
Calculate difference-of-means tests and report the t-statistics for the null
hypothesis that the average wage for male workers is the same as the average
wage for female workers. Use a 5% level of significance. Since you have a large
sample, you can use the z-critical value.
Either do the calculations by hand (show your work), or you can do the test in
Stata using the ttest command. Hint: Refer to Assignment 4 to refresh
your memory of this test. If you want to do the test in Stata, refer to the example
handed out in class regarding the Stata command for the test (example is also
2
available on Blackboard, in case you lost it). If you choose to do the test in Stata,
you still have to indicate whether you are accepting or rejecting the null
hypothesis by comparing the test statistic to the critical value. In other words,
simply copying-and-pasting the Stata output is not sufficient. What does the
difference-of-means test tell you regarding average male and female wages?
(4 points)
3.
Consider the following two regressions:
Regression A: wage 0 1educ 2exper 3expersq 4 female ui
Regression B: lwage 0 1educ 2exper 3expersq 4 female ui
Regression A is just your typical linear multiple regression. Regression B is a log-linear
regression. Refer to the course notes and handout (also available on Blackboard)
regarding log-linear regressions. Estimate both equations using Stata’s reg command.
Include your output along with the command used to generate it.
4.
a.
Interpret the coefficients β1 and β2 from each equation. Based on the
coefficients, how is the independent variable related to the dependent
variable? In particular, how will the dependent variable change if the
independent variable increases by 1 unit? Be specific and use specific
units!! (6 points)
b.
Explain the signs on the coefficients β2 and β3 for Regression A. What do
the signs indicate about the relationship between the independent and
dependent variables? Hint: refer to the section on quadratics in your
notes or the handout on quadratics. Is the relationship between wage and
experience a straight linear relationship or does the relationship taper over
time? Why do you think this is the case? (3 points)
c.
For each regression, interpret β4, which is the estimated coefficient on the
female dummy variable. Recall that the estimated coefficients on dummy
variables have an “if-then” interpretation. In other words, if the dummy
variable equals 1, then the dependent variable changes by the associated β.
β4 would thus be the “wage gap,” since it says how much more or less
someone earns if that particular person is female. (3 points)
a.
In both regressions, which of the estimated coefficients (that is, the βs) are
significant and why? Explain your answer referring to the t-statistics,
critical values, and use a 5% level of significance. You can either use the
t-statistics in the Stata output or calculate them yourself. You can ignore
the constant (β0). Use a two-tailed test. (6 points)
b.
Explain what the R2 and F-statistics mean for these specific equations.
That is, for the F-statistic, do you accept or reject the H0 for the F-test?
(4 points)
3
5.
Estimate Regressions A and B for only single people. Do this by including the
statement if marr == 0 at the end of the reg command (no commas). Is the
wage gap (as given by the coefficient on the variable female) statistically
significant? Compare the estimated coefficient for female in this case to that in
question 3. Is the “wage gap” for single women more or less than for women
in general? How much more or less? Why do you think this is? Hint: compare
the size and significance on the β associated with female in this case compared to
what you found in question 3. (5 points)
6.
Estimate regressions A and B for only people who are single and less than 30
years old. Do this by including the statement if marr == 0 & age < 30
at the end of the reg command (no commas). Given how young this subsample
is, do not include the variable expersq. Include the variable female in both
equations and interpret the results as you did in question 5. Is the wage gap
statistically significant in this case? Is the “wage gap” for single women more or
less than for single women in general? For women in general? How much more
or less? Why do you think this is? Hint: Compare the size and significance of β
in this case to what you found in questions #3 and #5. Why do you think they are
different? (5 points)
1 point extra credit: Refer to the statement “Given how young this subsample
is, do not include the variable expersq” from question 11. What do I mean by this
statement? That is, why would including the square of experience be
inappropriate here? You can answer this in just one or two sentences.
7.
Summarize your results. What do your results suggest regarding the “wage gap”
between male and female workers? Compare your results for the difference of
means tests, Regressions A and B for all workers, for single workers, and for
single young workers. Can we say anything about where the wage-gap is coming
from? (5 points)
You are done!!! Have a good summer! ☺
4
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