Cointegration Analysis and ECM of Industrial Economy and Direct Foreign Investments of China

Copyright © 2013 SciRes. IB

36

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

variables：one 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 cointegrated，use

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 LGDPI”is

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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