Environmental Engineering Reference
In-Depth Information
Linear
E
it
5 b
0
1 b
1
y
it
1 e
it
;
E
it
5 b
0
1 b
1
y
it
1 b
2
(
y
it
)
2
1 e
it
;
Quadratic
Log- linear
E
it
5 b
0
1 b
1
ln(
y
it
) 1 e
it
;
E
it
5 b
0
1 b
1
ln(
y
it
) 1 b
2
(ln
y
it
)
2
1 e
it
;
Log- quadratic
where:
E
5 environmental indicator;
y
5 per capita income;
b 5 parameter to be estimated;
t
5 time trend;
e 5 error term.
Other models included population density as another independent
variable, commonly in a log-quadratic form equation (Panayotou, 1993;
Selden and Song, 1994; Cropper and Grii ths, 1994; Roberts and Grimes,
1997; Vincent, 1997; Carson et al., 1997):
E
it
5 b
0
1 b
1
ln(
y
it
) 1 b
2
ln(
P
it
)
+
b
3
(ln
y
it
)
2
Log- quadratic
1 b
4
(ln
P
it
)
2
1 e
it
;
where:
E
5 environmental indicator;
y
5 per capita income;
P
5 population density;
b 5 parameter to be estimated;
t
5 time trend;
e 5 error term.
A third specii cation of models was used that included geographical char-
acteristics as independent variables, in addition to per capita income and
population density, usually using a quadratic form equation (Grossman
and Krueger, 1991, 1995):
E
it
5 b
0
1 b
1
(
y
it
) 1 b
2
(
P
it
)
+
b
3
(
G
it
) 1 b
4
(
y
it
)
2
Quadratic
1 b
5
(
P
it
)
2
1 b
6
(
G
it
)
2
1 e
it
;
where:
E
5 environmental indicator;
y
5 per capita income;
P
5 population density;
G
5 geographic characteristic;
b 5 parameter to be estimated;
t
5 time trend;
e 5 error term.