The McGraw-Hill Series Economics essentials of economics brue, McConnell, and Flynn Essentials of Economics

TABLE 9.7
Indian Wage Earners, 1990
WI
AGE
DE
2
DE
3
DE
4
DPT
D
SEX
WI
AGE
DE
2
DE
3
DE
4
DPT
D
SEX
120
57
0
0
0
0
0
120
21
0
0
0
0
0
224
48
0
0
1
1
0
25
18
0
0
0
0
1
132
38
0
0
0
0
0
25
11
0
0
0
0
1
75
27
0
1
0
0
0
30
38
0
0
0
1
1
111
23
0
1
0
0
1
30
17
0
0
0
1
1
127
22
0
1
0
0
0
122
20
0
0
0
0
0
30
18
0
0
0
0
0
288
50
0
1
0
1
0
24
12
0
0
0
0
0
75
45
0
0
0
0
1
119
38
0
0
0
1
0
79
60
0
0
0
0
0
75
55
0
0
0
0
0
85.3
26
1
0
0
0
1
324
26
0
1
0
0
0
350
42
0
1
0
1
0
42
18
0
0
0
0
0
54
62
0
0
0
1
0
100
32
0
0
0
0
0
110
23
0
0
0
0
0
136
41
0
0
0
0
0
342
56
0
0
0
1
0
107
48
0
0
0
0
0
77.5
19
0
0
0
1
0
50
16
1
0
0
0
1
370
46
0
0
0
0
0
90
45
0
0
0
0
0
156
26
0
0
0
1
0
377
46
0
0
0
1
0
261
23
0
0
0
0
0
150
30
0
1
0
0
0
54
16
0
1
0
0
0
162
40
0
0
0
0
0
130
33
0
0
0
0
0
18
19
1
0
0
0
0
112
27
1
0
0
0
0
128
25
1
0
0
0
0
82
22
1
0
0
0
0
47.5
46
0
0
0
0
1
385
30
0
1
0
1
0
135
25
0
1
0
0
0
94.3
22
0
0
1
1
1
400
57
0
0
0
1
0
350
57
0
0
0
1
0
91.8
35
0
0
1
1
0
108
26
0
0
0
0
0
140
44
0
0
0
1
0
20
14
0
0
0
0
0
49.2
22
0
0
0
0
0
53.8
14
0
0
0
0
1
30
19
1
0
0
0
0
427
55
0
0
0
1
0
40.5
37
0
0
0
0
1
18
12
0
0
0
0
0
81
20
0
0
0
0
0
120
38
0
0
0
0
0
105
40
0
0
0
0
0
40.5
17
0
0
0
0
0
200
30
0
0
0
0
0
375
42
1
0
0
1
0
140
30
0
0
0
1
0
120
34
0
0
0
0
0
80
26
0
0
0
0
0
175
33
1
0
0
1
0
47
41
0
0
0
0
1
50
26
0
0
0
0
1
125
22
0
0
0
0
0
100
33
1
0
0
1
0
500
21
0
0
0
0
0
25
22
0
0
0
1
1
100
19
0
0
0
0
0
40
15
0
0
0
1
0
105
35
0
0
0
0
0
65
14
0
0
0
1
0
300
35
0
1
0
1
0
47.5
25
0
0
0
1
1
115
33
0
1
0
1
1
163
25
0
0
0
1
0
103
27
0
0
1
1
1
175
50
0
0
0
1
1
190
62
1
0
0
0
0
150
24
0
0
0
1
1
62.5
18
0
1
0
0
0
163
28
0
0
0
1
0
50
25
1
0
0
0
0
163
30
1
0
0
1
0
273
43
0
0
1
1
1
50
25
0
0
0
1
1
175
40
0
1
0
1
0
395
45
0
1
0
1
0
117
26
1
0
0
1
0
175
40
0
0
0
1
1
950
47
0
0
1
0
0
87.5
25
1
0
0
0
0
100
30
0
0
0
0
0
75
18
0
0
0
0
0
140
30
0
0
0
0
0
163
24
0
0
0
1
0
97
25
0
1
0
0
0
325
55
0
0
0
1
0
150
36
0
0
0
0
0
121
27
0
1
0
0
0
25
28
0
0
0
0
1
600
35
1
0
0
0
0
15
13
0
0
0
0
1
52
19
0
0
0
0
0
131
55
0
0
0
0
0
117
28
1
0
0
0
0 
301
guj75772_ch09.qxd 12/08/2008 04:19 PM Page 301

---

302
Part One
Single-Equation Regression Models
The reference category is male workers with no primary education and temporary jobs.
Our interest is in finding out how weekly wages relate to age, sex, level of education, and
job tenure. For this purpose, we estimate the following regression model:
ln WI
i
= 
β
1
+
β
2
AGE
i
+
β
3
D
S
EX
+
β
4
DE
2
+
β
5
DE
3
+
β
6
DE
4
+
β
7
DPT
+
u
i
Following the literature in Labor Economics, we are expressing the (natural) log of wages
as a function of the explanatory variables. As noted in Chapter 6, the size distribution of
variables such as wages tends to be skewed; logarithmic transformations of such variables
reduce both skewness and heteroscedasticity.
Using 
EViews6,
we obtain the following regression results.
These results show that the logarithm of wages is positively related to age, education, and
job permanency but negatively related to gender, an unsurprising finding. Although there
seems to be no practical difference in the weekly wages of workers with primary or less-
than-primary education, the weekly wages are higher for workers with secondary education
and much more so for workers with higher education.
The coefficients of the dummy variables are to be interpreted as differential values from
the reference category. Thus, the coefficient of the 
DPT
variable suggests that those work-
ers who have permanent jobs on average make more money than those workers whose jobs
are temporary.
As we know from Chapter 6, in a log–lin model (dependent variable in the logarithm
form and the explanatory variables in the linear form), the slope coefficient of an
Dependent Variable: Ln(WI)
Method: Least Squares
Sample: 1 261
Included observations: 261
Coefficient
Std. Error
t
-Statistic
Prob.
C
3.706872
0.113845
32.56055
0.0000
AGE
0.026549
0.003117
8.516848
0.0000
D
SEX
-0.656338
0.088796
-7.391529
0.0000
DE
2
0.113862
0.098542
1.155473
0.2490
DE
3
0.412589
0.096383
4.280732
0.0000
DE
4
0.554129
0.155224
3.569862
0.0004
DPT
0.558348
0.079990
6.980248
0.0000
R-squared
0.534969
Mean dependent var.
4.793390
Adjusted R-squared
0.523984
S.D. dependent var.
0.834277
S.E. of regression
0.575600
Akaike info criterion
1.759648
Sum squared resid.
84.15421
Schwarz criterion
1.855248
Log likelihood
-222.6340
Hannan-Quinn criter.
1.798076
F
-statistic
48.70008
Durbin-Watson stat.
1.853361
Prob(
F
-statistic)
0.000000 
guj75772_ch09.qxd 13/08/2008 05:38 PM Page 302

---

Chapter 9
Dummy Variable Regression Models
303
explanatory variable represents semielasticity, that is, it gives the relative or percentage
change in the dependent variable for a unit change in the value of the explanatory variable.
But as noted in the text, when the explanatory variable is a dummy variable, we have to be
very careful. Here we have to take the anti-log of the estimated dummy coefficient, subtract
1 from it, and multiply the result by 100. Thus, to find out the percentage change in weekly
wages for those workers who have permanent jobs versus those who have temporary
jobs, we take the anti-log of the 
DPT
coefficient of 0.558348, subtract 1, and then multiply
the difference by 100. For our example, this turns out to be (
e
0.558348
−
1) 
=
(1.74778 
−
1) 
=
0.74778, or about 75%. The reader is advised to calculate such percentage changes for the
other dummy variables included in the model.
Our results show that gender and education have differential effects on weekly earnings.
Is it possible that there is an interaction between gender and the level of education? Do
male workers with higher education earn higher weekly wages than female workers with
higher education? To examine this possibility, we can extend the above wage regression by
interacting gender with education. The regression results are as follows:
Dependent Variable: Ln(WI)
Method: Least Squares
Sample: 1 261
Included observations: 261
Coefficient
Std. Error
t
-Statistic
Prob.
C
3.717540
0.114536
32.45734
0.0000
AGE
0.027051
0.003133
8.634553
0.0000
D
SEX
-0.758975
0.110410
-6.874148
0.0000
DE
2
0.088923
0.106827
0.832402
0.4060
DE
3
0.350574
0.104309
3.360913
0.0009
DE
4
0.438673
0.186996
2.345898
0.0198
D
SEX
*
DE
2
0.114908
0.275039
0.417788
0.6765
D
SEX
*
DE
3
0.391052
0.259261
1.508337
0.1327
D
SEX
*
DE
4
0.369520
0.313503
1.178681
0.2396
DPT
0.551658
0.080076
6.889198
0.0000
R-squared
0.540810
Mean dependent var.
4.793390
Adjusted R-squared
0.524345
S.D. dependent var.
0.834277
S.E. of regression
0.575382
Akaike info criterion
1.769997
Sum squared resid.
83.09731
Schwarz criterion
1.906569
Log likelihood
-220.9847
Hannan-Quinn criter.
1.824895
F
-statistic
32.84603
Durbin-Watson stat.
1.856488
Prob (
F
-statistic)
0.000000 
Although the interaction dummies show that there is some interaction between gender
and the level of education, the effect is not statistically significant, for all the interaction
coefficients are not individually statistically significant.
guj75772_ch09.qxd 13/08/2008 05:38 PM Page 303

---

It now seems that education dummies by themselves have no effect on weekly wages, but
introduced in an interactive format they seem to. As this exercise shows, one must be care-
ful in the use of dummy variables. It is left as an exercise for the reader to find out if the
education dummies interact with DPT.