Geoscience Reference
In-Depth Information
X
i
ʱ
i
¼
1,
X
i
0,
X
ʳ
ij
¼
i
ʲ
i
¼
0 adding up
ð
Þ
ð
11
:
9
Þ
X
j
γ
ij
¼
0 homogeneity
ð
Þ
ð
11
:
10
Þ
γ
ij
¼ γ
ji
symmetry
ð
Þ
ð
:
Þ
11
11
Since homogeneity implies
ʳ
ii
¼ʳ
i i
, (Eq.
11.7
) can be re-written as
= P
w
i
¼ α
i
þ ʳ
ii
ln
P
i
=
ð
P
i
Þ ʲ
i
ln
X
ð
11
:
12
Þ
Since the modified AIDS is flexible, it is not guaranteed to satisfy the homoge-
neity and symmetry conditions. So these conditions are introduced as parameter
restrictions in the estimation process. The modified AIDS assumes that the size of
the family affects budget share and
N
, the number of household members, was
introduced as a shift parameter of
α
i
. Then the model can be expressed as:
þ
w
it
¼ α
i
þ
e
i
N
t
þ ʳ
ii
ln
P
it
=
Þ þ ʲ
i
ln
X
t
= P
t
e
i
ð
P
it
ð
11
:
13
Þ
where
e
i
k
is the error term and
i
and
k
refer to ten consumption types and six ages of
reference person.
w
it
¼ α
i
þ
e
i
N
t
þ ʳ
ii
ln
P
it
=
Þ þ ʲ
i
ln
X
t
= P
t
e
i
ð
P
it
þ
ð
11
:
14
Þ
where
e
i
r
is the error term and
i
and
r
refer to ten consumption types and five
quintiles of income.
The empirical results of (Eq.
11.13
) show life cycle changes in consumption
behavior (a sample is provided in Fig.
11.4
). From the estimation results (Eq.
11.13
)
and (Eq.
11.14
), the price elasticity
ʵ
it
j
and expenditure elasticity
ʷ
it
j
are:
it
¼
ʳ
ii
j
w
it
ʵ
w
it
þ
1 for
j
¼
k
age of reference person
ð
Þ
,
r
quintiles of income
ð
Þ
ð
11
:
15
Þ
it
¼
ʲ
i
j
ʷ
w
it
þ
1 for
j
¼
k
age of reference person
ð
Þ
,
r
quintiles of income
ð
Þ
ð
11
:
16
Þ
11.2.2 The AIDS-Type Chicago Region Econometric Input-Output
Model
To predict the demographic changes in the Chicago region up to 2030, this research
extends the Chicago Region Econometric Input-Output Model (CREIM). The
regional econometric input-output model (REIM), initially designed by Conway