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

additive
as in Eq. (9.6.1) but
multiplicative
as well, as in
the following model.
Y
i
=
α
1
+
α
2
D
2
i
+
α
3
D
3
i
+
α
4
(
D
2
i
D
3
i
)
+
β
X
i
+
u
i
(9.6.2)
where the variables are as defined for model (9.6.1).
From Eq. (9.6.2), we obtain:
E
(
Y
i
|
D
2
i
=
1,
D
3
i
=
1,
X
i
)
=
(
α
1
+
α
2
+
α
3
+
α
4
)
+
β
X
i
(9.6.3)
which is the mean hourly wage function for female nonwhite/non-Hispanic workers.
Observe that
α
2
= 
differential effect of being a female
α
3
= 
differential effect of being a nonwhite/non-Hispanic
α
4
= 
differential effect of being a female nonwhite/non-Hispanic
which shows that the mean hourly wages of female nonwhite/non-Hispanics is different
(by
α
4
) from the mean hourly wages of females or nonwhite/non-Hispanics. If, for instance,
all the three differential dummy coefficients are negative, this would imply that female
nonwhite/non-Hispanic workers earn much lower mean hourly wages than female or
nonwhite/non-Hispanic workers as compared with the base category, which in the present
example is male white or Hispanic.
Now the reader can see how the