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Cointegration Analysis and ECM of Industrial Economy and Direct Foreign Investments of China
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less than the critical value of 5%, which means these
variables are significant at the 5% level, reject unit root
hypothesis, ΔLGDPI and ΔLDFI are stable.
3. Cointegration Test Between the Variables
The first difference series rejects unit root hypothesis,
which sho ws a stable li near combinatio n may exis t in the
time series LGDPI and LDF I. The linear combination
reflects the relationship in the proportion of long-term
stability of variab le s, which is c ointegratio n re la tionship.
There are two cointegration test methods among the
variablesone is Engle-Granger two-step test for coin-
tegration test between two variables. Another method is
Johansen test for cointegration test among multiple va-
riables. Since this pap e r studies co integration relationship
between GDPI and DFI, so we would like to use EG
two-step method to te st the cointe gra tion relationship.
Suppose LGDPI and LDFI are cointegrated, use soft-
ware EViews6.0 to estimate the regression equation
model, shown as Tab l e 2.
The cointegratio n equation is obtained:
^
1.138355 0.810262
(2.843) (17.875)
tt
LGDPI LDFI= +
(1)
In the EViews6.0: Series resid01= resid, apply ADF
test to the resid01. Shown as Table 3.
Table 1. The stable test of e ach var iabl e .
Variabl e Inspection
Type (c, t, k) Statistics
ADF Threshold
of 5% Stablity
LGDPI (c, t, 6) -1.0703 -3.5875 Unst able
LDFI (c, t, 6) -2.6446 -3.5875 Unstable
ΔLGDPI (c, 0, 6) -4.0821 -2.9810 Stable
ΔLDFI (c, 0, 6) -4.1636 -2.9810 Stable
Note: (c, t, k) denote the uni t root test equation in cluding the const ant t erm
and time trend and the ord er of lag, 0 d oes not inc lude c or t, adding lags are
intended to make the residuals white noise.
Table 2. Regression equatio n of L DF I with LGDPI
Dependent Variable: LGDPI Method: Least S q uar es
Samp le (adjust ed): 1983 201 0
Variabl e Coeffi cient Std. Error t-Statistic Prob.
C 1.138355 0.400428 2.842843 0.0086
LDF I 0.8 10262 0.045330 17.87474 0.0000
R-squared 0.924748 Mean dep en dent var 8.2367
Adjusted R-squared
0.921854 S.D. dependent var 0.97310
S.E. of r egress ion 0.272026 Aka ike info criterion 0.30291
Sum squared resid 1.923949 Schwarz criterion 0.39807
Log likelih ood -2.240734 F-statistic 319.506
Durbin-Watson stat
0.525614 Prob(F-statistic) 0.00000
From Table 3, the Augmented Dickey-Fuller test sta-
tistic value o f -2.1466 is greater than the 5% critical val-
ue of -2.9763, resid01 can not reject unit root test, series
resid uals resid01 is a non-stable.
Suppose ΔLGDPI and ΔLDFI are cointegrateduse
softwore EViews6.0 to estimate cointegration equation of
ΔLGDPI and ΔLDFI. Shown as Table 4.
The cointegratio n Equation is:
^0.157832-0.265429
(4.638) (1.588)
tt
LGDPI LDFI∆= ∆
(2)
DW statistic is about 1.727 near to 2. In Eviews6.0: se-
ries resid02= resid, resid02 is the random interference
terms, to test for a unit root on the resid 0 2.
Shown as Table 5. the Augmented Dickey-Fuller test
statistic value of -4.2161 is l ess tha n t he 1 % critical value
of -3.7115, we can strongly reject the unit root hypothe-
sis, resid02 residuals is a stable sequence.
Table 3. The Unit Root Test Results of resid01.
Null Hypothesis: RES ID02 has a unit root
t-Statistic Prob.*
Augmented Di ckey-Fuller test statistic -2.1466
Test critical values: 1% level -3.6999
5% lev el -2.9763
Table 4. Cointegration Eq uation of ΔLGDPI with ΔLDFI.
Dependent Variable: ΔLGDPI Method: Least S q ua r es
Samp le (adjust ed): 1983 201 0
Variabl e Coeffi cient Std. Error t-Statistic Prob.
C 0.157832 0.034027 4.638443 0 .0001
ΔLDFI -0.265429 0.167203 -1.587466 0.1 250
R-squared 0.0915 71 Mean dep en dent var 0.11915
Adjusted R-squared
0.055234 S.D. dependent var 0.12697
S.E. of r egress ion 0.1234 17 Aka ike info criterion -1.27531
Sum squared resid 0.380793 Schwarz criteri on -1.17932
Log likelih ood 19.21670 F-statistic 2.52005
Durbin-Watson stat 1.7271 73 Prob(F-statistic) 0.12498
Table 5. The unit root test results resid02.
Null Hypothesis: RES ID02 has a unit root
t-Statistic Prob.*
Augmented Di ckey-Fuller test statistic -4.2161 0.0030
Test critical values: 1% level -3.7115
5% lev el -2.9810
Cointegration Analysis and ECM of Industrial Economy and Direct Foreign Investments of China
opyright © 2013 SciRes. IB
37
There is stable linear co mbination bet ween the ΔLGDPI
and ΔLDFI, that is total direct foreign investments and
gross do mestic industrial production are cointegrated.
4. Estimated Error Correction Model
4.1. Fi rst-Order Error Correction Model
According to the Granger theorem, a set of variables with
cointegration error correction model has the form of
ECM expression. Therefore, based on the cointegration
test, we can establish ECM that includes error correction
term, in order to study the model of short-term dynamic
and long-term cointegration features. It is known by
cointegration test, there is cointegration relationship be-
tween gross domestic production of industry and direct
foreign investments, although DW statistic was signifi-
cantly near to 2, indicating that there is not residual au-
tocorrelation in the series. Therefore, we may re-establish
regr essio n equati on o f LDFI and LGDPI, and add lagged
variables, and establish a single ECM equation using
EViews6.0:
The regressive equation is obtained:
0.1436420.1935260 157976
(4.1827) (-1.1443) (-1.5533)
t tt
GDPILDFI.ECM =−−
(3)
DW statistic is about 1.623 near to 2, there is not resi-
dual autocorrelation in resid. In Eviews6.0: series re-
sid03= resid, resid03 is the random interference terms, to
test for a unit root on the re si d03.
Sho wn a s Table 7. The Augmented Dickey-Fuller test
statistic value of 0.1312 is greater than the 5% critical
value of -2.998, resid03 can not reject unit root test, se-
ries residuals resid03 is a no n-stable .
Table 6. First-or der ECM equation.
Dependent Variable: D(LGDPI)
Met hod: Least S q ua r es
Variabl e Coeffi cient Std. Error t-Statistic Prob.
C 0.143642 0.034342 4.182747 0.0003
D(LDFI) -0.193526 0.169128 -1.144259 0.2638
ECM( -1) -0.157976 0.101703 -1.553306 0.1334
R-squared 0.174555 Mea n dep en dent var 0.119152
Adjusted R-squared 0.105768 S.D. dependent var 0.126973
S.E. of regression 0.120071 Akaike info crit eri on -1.29703
Sum squared resid 0.346008 Schwarz criteri on -1.15305
Log likelih ood 20.50991 F-statistic 2.53761
Durbin-Watson stat 1.622968 Prob(F-statistic) 0.10006
4.2. Second-Order Error C orrec tion Mod e l
Because ΔLDFI and ΔLGDP is cointegration, residuals
autocorrelation exists in first order ECM, so the second
order ECM could be estimated using EViews6.0.
The t statistic o f all varible s ar e o ver nine. DW statistic
is 1.6256 near to 2, there is no residual serial autocorrela-
tion. resid04 is the random interference terms, to test for
a unit root on the resid04.
Shown as Table 9. the Augmented Dickey-Fuller test
statistic value o f -3.750 7 is less than the 1% critic al value
of -3.7241, we can strongly reject the unit root hypothe-
sis, resid04 residuals is a stable sequence.
Table 7. The unit root test results resid03 .
Null Hypothesis: RES ID03 has a unit root
t-Statistic Prob.*
Augmented Di ckey-Fuller test statistic 0.1312 0.9612
Test critical values: 1% level -3.7530
5% lev el -2.9980
Table 8. Second-order ECM equation.
Dependent Variable: D(LGDPI)
Variabl e Coeffi cient Std. Error t-Statistic Prob.
D(LDFI) -0.186079 0.166714 -1.116153 0.2764
D(LGDPI(-1)) 0.938924 0.226459 4.146107 0.0004
D(LDFI(-1)) 0.227451 0.153518 1.481597 0.1526
ECM2(-1) -1.193137 0.398539 -2.993775 0.0067
R-squared 0.162356 Mean dependent var 0.123859
Adjusted R-squared 0.048132 S.D. dependent var 0.1270 63
S.E. of r egress ion 0.123968 Aka ike info criterion -1.196956
Sum squared resid 0.338095 Schwarz criterion -1.003402
Log likelih ood 19.56042 Durbin-Watson stat 1.625600
Table 9. The unit root test results resid04.
Null Hypothesis: RES ID04 has a unit root
t-Statistic Prob.*
Augmented Di ckey-Fuller test statistic -3.7507 0.0094
Test critical values: 1% level -3.7241
5% lev el -2.9862
Cointegration Analysis and ECM of Industrial Economy and Direct Foreign Investments of China
Copyright © 2013 SciRes. IB
38
Table 10. Granger causali ty test variables.
Null Hypothesis: F-Statistic Probability
LGDPI does not Granger Cause LDFI 1.7311 0.2014
LDFI does not Granger Cause LGDPI 4.4247 0.0249
The size of coefficient of the ecm reflects on the devi-
ation from the adjustment of the long-run equilibrium.
From the point of view of estimate coefficient of ecm,
when the short-term fluctuations deviate from the long-
term equilibrium, the adjustment will effects
non-equilibrium state back to equilibrium with 1.193,
which means that the non-equilibrium error rate of pre-
vious year makes amendments of direction on LDF I
with the rate of 119.3%.
5. Test the Granger-causality Between Va-
riables
From the view of the growth effect of variable, when
analysis of Granger-causality between the variables, the
LGDPI and LD F I are cointegrated, we can easily test the
null hypothesis whether LDFI does not Granger cause
LGDPI, or LGDPI does not Granger cause LDFI. Use
software EViews6.0 to test Granger-causality relation-
ship between LGDPI and LDFI [3]. the test results
sho wn as Table 10.
From Table 10, in critical value of 10%, the null hy-
pothe sis of LDFI does not Granger Ca use LGDPIis
rejected; This shows there is one-way Granger causality
between LDFI and LGDPI, that is, the growth of direct
foreign investments impacts industrial economic growth,
direct foreign investments growth is the cause s of indus-
trial econo mic gro wth, while ind ustria l economic growth
is not cau s ality of the dire ct fore ign investments growth.
6. Conclusions and Recommendations
A) Alt ho u gh t he growth o f GDPI and DFI are unstable,
there is long-term stable equilibrium relationship be-
tween GDPI and DFI.
B) The growth of direct foreign investments is the
causality of growth of GDPI. It can be known, the
growth of direct foreign investments plays an important
role of GDPI growth.
C) Foreign d ir e c t invest ment plays an important role in
China 's indu strial ec onomic g rowth in t he short term and
long term. Foreign direct investments keep stable equili-
brium gro wth relationship to China's i ndustrial economic
growth. Foreign direct investment is an important part
and driving force in China 's foreign trade. Foreign direct
investment is an important part and the driving force in
China's foreign trade. Therefore, foreign direct invest-
ment should be encouraged in further to accelerate the
development of China's foreign trade. On the one hand,
China attract foreign investment policy orientation
should be actively adjust, the foreign capital enterprise
with high technology and high added value encouraged
into C hi na . On t he o the r ha nd , t o d e vel op Chi na 's domes-
tic processing trade enterprise's development, which has
not lost comparative advantage industry development
premise, further use of foreign advanced technology and
management level to promote the upgrading of the in-
dustrial str ucture o f Chi na.
7. Acknowledgment
This work was supported by the Planned Science and
Technology Project of China Hunan Provincial Science
& Technology Department under grant No.2012FJ3030,
and The Vocational Education Subject of China Machi-
nery Industry Education Association in 2011 under grant
No. ZJJX11ZZ013.
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