Where α=a
α , y
-1t
=(y
,…,y
)
,
ε
=(ε
,…,ε
)
.There is a clear linear correlation
between ε
and y
-1t
, so we rewrite (8) as:
=+
*
′y
-1t
+
∗
(9)
Where a * =a ′(IN-1 – cov( ε
, y
-1t
)var( y
-1t
)-1),
ε
∗
=a′ ε
+a ′cov( ε
, y
-1t
)var( y
-1t
)-1 y
-1t
. Now,
there is no longer linear correlation between ε
∗
and
y
-1t
. According to Hsiao et al. (2012), it means
E(ε
−a
ε
|y
-1t
) is a linear function of y
-1t
, and
E( ε
∗
|y
-1t
) =0 can be guaranteed. The OLS
estimation parameters of (9) keep consistent. The
same discussion about this hypothesis can be found
in Bai et al. (2014) and Ouyang and Peng (2015).
Because other provinces economy are not
affected by the Poyang Lake reconstruction, we
use the GDP growth rates y
-1t
of other provinces to
substitute the common factor ft ,throughout T period,
in order to estimate the situation of Jiangxi Province
without the implement Poyang Lake reconstruction
during the time t.
According to (9), we estimate ∆
as the
following steps: First, before time T
, we conduct be
the regression of y
for y
-1t
=
(y
,…,y
)
following (9), to get parameter
estimatesα
and a
∗
.Then, after the timeT
+1, we
use these parameter estimates and y
-1t
=
(y
,…,y
)
following (9) to construct the GDP
growth rate of Jiangxi Province y
=α
+a
∗
y
-1t
(
t≥T
+1)under the counterfactual situation, and
finally we get ∆
=y
−y
(t≥T
+1).Under
normal conditions, ∆
and ∆
keep consistent.
Since there may be serial correlation in ∆
. we
can use Box-Jenkins method to create an ARMA
model:
(
)
∆
=+
()
, (10)
Furthermore, we can use α
(
L
)
μ to express the
long-run effect following Poyang Lake
reconstruction, and use t-test to check whether the
effect is significant.
2.2 Model Selection
Step1: Starting from j=1, select totally j components
from N-1 provinces, C
combinations can be
obtained. Conducting the regression of y
(t≤T
)
for each combination according to (9), so as to select
the combination with the highest R2 and then label it
M(j)
∗
.
Step2: Select a combination from M (1)
∗
,
M(2)
∗
,…,M(N − 1)
∗
that minimizes the AIC or
AICC information criterion1, and label it M(m)
∗
,
where:
p is the number of provinces in the control group and
e is the residual of the OLS regression.
Step3: Using the optimal M(m)
∗
to construct
y
(t≥T
+1), we get the GDP growth rate of
Jiangxi province in the counterfactual situation.
Step4: According to ∆
=y
−y
(t≥T
+1)
, we can get result of the economic effect on Jiangxi
Province following the Poyang Lake reconstruction.
3 EMPIRICAL RESULT
We use 25 other province economy to construct the
counterfactual economic growth rate of Jiangsu
province: Peking, Tientsin, Hebei, Shanxi, Liaoning,
Jilin, Heilongjiang, Shanghai, Jiangsu, Zhejiang,
Anhui, Fujian, Shangdong, Henan, Hubei, Hunan,
Guangdong, Hainan, Chongqing, Sichuan, Guizhou,
Yunnan, Shanxi, Gansu, Qinghai, which are not
influences by the alteration of Poyang Lake. Those
provinces and cities are inextricably linked with
Jiangxi Provinces in the aspect of economy and
geography. The data of quarter nominal GDP and the
CPI is from Ner Statistics Bureau and the period is
from the first quarter(January) in 2005 to the fourth
quarter (December) in 2014.
There are tow ways to calculate the quarter
growth rate of actual GDP, one is on year-on-year
basis the other is on quarter-on-quarter. In this paper,
we adopt the second one. One one hand, it can avoid
the seasonal adjustment. On the other hand ,it is
conducive for us to estimate the long-term effect of
the transformation of Poyang Lake on economy of
Jiangxi Province.
According to the modeling strategy and the
AICC criteria, Shangxi, Hubei, Hunan, Guangdong,
Shanxi, Qinghai, are selected. Then, we can use the
GDP growth rate of these areas to construct the
counterfactual growth rate of GDP in Jiangxi.
The T value in table 1 shows each coefficient is
significant, R2 is 0.97. The coefficient only refers
to the correlation of economic growth determined
by common factors between different countries or
regions, which has no cause and effect significance.
In figure 2, solid line represents the GDP growth
charts of Jiangxi Province from the first quarter in
2006 to the fourth quarter in 2012, the dotted line
represents the GDP growth charts of Jiangxi
Province predicted by regression equation. It can be
seen directly from figure 2, the GDP growth rate
data of selected province and region well fit the
)2(2)ln()(AIC
1
'
1
++= m
T
ee
Tp
2)1(
)3)(2(2
)2(2)ln()(AICC
11
'
1
−+−
++
+++=
mT
mm
m
T
ee
Tp
ISME 2016 - Information Science and Management Engineering IV
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