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.
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