Geoscience Reference
In-Depth Information
¼ ˃
kl
ln
þ ˃
kl
ln
w
r
ln
K
L
1
α
kl
α
kl
ð
10
25
Þ
:
Where Q is the composite goods of capital and labor,
w
and
r
represent wage and
rental rates, respectively.
α
kl
are the substitution elasticity and distribution
parameter of K and L. The equation can be simplified to a linear regression statement:
˃
kl
and
lny ¼ ʲ
0
þ ʲ
1
lnx þ ʵ
ð
10
:
26
Þ
where y is the capital-labor ratio, x is the wage-rental ratio, and
is the independent
and identically distributed (iid) error. The elasticity of substitution between capital
and labor is represented by
ʵ
ʲ
1
.
A panel data includes the 48 states and the District of Columbia for 15 years from
1997 to 2011and are constructed following Balistreri et al. (
2003
)'s approach, which
collected similar data from Bureau of Economic Analysis (BEA) but used it only at
an aggregate level of analysis. Four data series are collected to operationalize
equation 26: employment, total employee compensation, private fixed asset and
property income. In the non-spatial assessment, the elasticity of factor substitution
for different sectors is estimated using OLS. Panel regressions including both fixed
effects and random effects estimations are also implemented. However, since some
substitution elasticities have negative estimates that have no economic meanings, the
estimates of panel regressions are not adopted for CGE integration.
10.5.3 Step 3 Spatial Econometric Analysis
The third step is to estimate the elasticity of factor substitution for different sectors
using spatial econometric estimation to control for spatial dependence. Given the
potential complexity of this issue, a generalized spatial model, “Spatial Durbin
Model” (SDM) is adopted as the initial model for the assessment. The general form
of substitution elasticity under SDM is written as:
i
,
t
¼ ˁW
K
i
,
t
þ ʲ
i
,
t
þ ʵ
i
,
t
K
L
w
r
i
,
t
þ ʸW
w
ð
10
27
Þ
:
L
r
ʵ
i
,
t
e
N
0,
2
˃
i
,
t
I
n
where
L
and
r
denote capital-labor ratio variable and wage-rental ratio variable, and
W
L
i
,
t
and
W
r
i
,
t
denote the spatial lag terms of capital-labor ratio variable and
wage-rental ratio variable, respectively.
i
and
t
represent different regions and time
periods.
denote coefficients that need estimation. The analysis is
conducted based on the same panel data as used in step 2.
To help identify the appropriate spatial panel model in a systematic way, Elhorst
(
2012
) developed a spatial panel model selection routine, which can be executed in
Matlab. The key process is illustrated in Fig.
10.3
:
ˁ
,
ʲ
and
ʸ
