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

TABLE 9.6
Hypothetical Data
on Output and
Total Cost
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Part One
Single-Equation Regression Models
regressor. 
This is only so if the regressor is quantitative. 
What happens if a regressor is a
dummy variable? To be specific, consider the following model:
ln
Y
i
=
β
1
+
β
2
D
i
+
u
i
(9.10.1)
where 
Y
= 
hourly wage rate ($) and 
D
= 
1 for female and 0 for male.
How do we interpret such a model? Assuming 
E
(
u
i
)
=
0, we obtain:
Wage function for male workers:
E
(ln
Y
i
|
D
i
=
0)
=
β
1
(9.10.2)
Wage function for female workers:
E
(ln
Y
i
|
D
i
=
1)
=
β
1
+
β
2
(9.10.3)
Therefore, the intercept 
β
1
gives the 
mean log hourly earnings 
and the “slope” coefficient
gives the difference in the mean log hourly earnings of male and females. This is a rather
awkward way of stating things. But if we take the antilog of 
β
1
, what we obtain is 
not
the
mean hourly wages of male workers, but their 
median 
wages. As you know, 
mean, median,
and 
mode
are the three measures of central tendency of a random variable. And if we take
the antilog of (
β
1
+
β
2
), we obtain the median hourly wages of female workers.