Empirical (…….) all variables are appear to be

Empirical results

The ADF and ERS-Piont Optimal unit
root has been tested to examine the stationarity order of variables, for time
series and equation (pryor
1969) which revealed in the table (1) in logarithmic form of data in
order of level and first difference, stationarity.

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Table 1. Unit Root Tests

 

Exogenous: Constant, Linear Trend

Lag Length: (Automatic – based on AIC)

LEVELS I(0)

FIRST DIFFERENCE I(1)

COUNTRY

VARIABLE

 

t-Statistic

  Prob.

t-Statistic

  Prob.*

ITALY

LRGC

-2.980335

0.1489

-4.803901**

0.0003

LRGDP

-2.753564

0.2214

-4.850754**

0.0003

CANADA

LRGC

-2.960087

0.1545

-3.147864**

0.0300

LRGDP

-2.300378

0.4251

-4.563567**

0.0006

FRANCE

LRGC

-3.28271

0.0822

-4.92519**

0.0002

LRGDP

-3.096013

0.1196

-4.836165**

0.0003

GERMANY

LRGC

-3.460757

0.0562

-4.698262**

0.0004

LRGDP

-3.096013

0.1196

-4.836165**

0.0003

JAPAN

LRGC

-2.016054

0.5769

-4.723558**

0.0004

LRGDP

-1.701315

0.7343

-4.76733**

0.0003

UNITED KINGDOM

LRGC

-2.769568

0.2156

-4.451348**

0.0009

LRGDP

-3.59637**

0.0414

-4.89532**

0.0003

UNITED STATE

LRGC

-0.214817

 

-3.169386**

 

LRGDP

-1.640828

 

-4.856978**

 

ü  ** Rejection of unit root hypothesis, based on McKinnon’s critical
value, at 5%

ü  The lag selection based on AIC value.

ü  The unit root hypothesis for united stat variables tested under
equation of ERS-Piont Optimal unit root test.

ü  I(0) stationary at the level

ü  I(1) stationary at the firs difference

According to the table (…….) all variables
are appear to be stationary in their first difference I(1).

The lag lengths have been selected
on the basis of AIC value which revealed in the (annx…….) for the further
process of Johnsen maximum likelihood co-integration test, the table (2)
revealed the result for Johansen and Juselius
co-integration.

Table2. Revealed that we couldn’t
reject the null hypothesis (test indicates
no co-integration at the 0.05 level) for
Italy which means the test couldn’t fount long run relationship between general
government consumption and gross domestic product in the case of Italy.

 

Table 2.
Johansen and Juselius co-integration tests and results

NULL

ATRERNATIVE

?-MAX          STATISTIC

95%                
CRITICAL VALUE

Prob

TRACE            
STATISTIC

95%                
CRITICAL VALUE

Prob

ITALY

r = 0

r = 1

11.46592

14.2646

0.1324

14.35874*

15.49471

0.0736

r ? 1

r = 2

2.892822*

3.841466

0.089

2.892822*

3.841466

0.089

CANADA

r = 0

r = 1

15.25191**

14.2646

0.0348

16.46196**

15.49471

0.0357

r ? 1

r = 2

1.210054

3.841466

0.2713

1.210054

3.841466

0.2713

FRANCE

r = 0

r = 1

15.74199**

14.2646

0.029

18.72742**

15.49471

0.0157

r ? 1

r = 2

2.985433*

3.841466

0.084

2.985433*

3.841466

0.084

GERMANY

r = 0

r = 1

21.68438***

14.2646

0.0028

23.49657***

15.49471

0.0025

r ? 1

r = 2

1.812199

3.841466

0.1782

1.812199

3.841466

0.1782

JAPAN

r = 0

r = 1

15.13392**

14.2646

0.0364

18.21303**

15.49471

0.019

r ? 1

r = 2

3.079106

3.841466

0.0793

3.079106*

3.841466

0.0793

UNITED KINGDOM

r = 0

r = 1

29.74447***

14.2646

0.0001

29.75308***

15.49471

0.0002

r ? 1

r = 2

0.00861

3.841466

0.9257

0.00861

3.841466

0.9257

UNITED STATE

r = 0

r = 1

14.90903**

14.2646

0.0395

17.05504**

15.49471

0.0289

r ? 1

r = 2

2.146012m

3.841466

0.1429

2.146012

3.841466

0.1429

ü  ***, ** Rejection of null hypothesis at the levels of  1% 
and  5%

ü  MacKinnon-Haug-Michelis (1999) p-values                                                                        

The finding of Johansen and Juselius
co-integration tests indicate long run relationship between general government
consumption expenditures and gross domestic products for all other countries of
G7.

The VECM should be run after the
data co-integrated, in this section the paper has been investigated the short
run causality which known as Wald test, for variables. The table 3, shows the
results of Wald test.

Table.
3Wald Test: causality direction test based on VECM

Null
Hypothesis

 LRGDP does not Granger Cause LRGC

 LRGC does not Granger Cause LRGDP

 

Test
Statistic

Value

df

Probability

Value

df

Probability

ITALY

F-statistic

0.968151

(2,
38)

0.389

1.345279

(2,
38)

0.2726

Chi-square

1.936301

2

0.3798

2.690558

2

0.2605

CANADA

F-statistic

5.730893

(1,
41)

0.0213

0.233149

(1,
41)

0.6318

Chi-square

5.730893**

1

0.0167

0.233149

1

0.6292

FRANCE

F-statistic

2.824994

(9,
19)

0.0271

2.593979

(9,
17)

0.0433

Chi-square

25.42495***

9

0.0025

23.34581***

9

0.0055

GERMANY

F-statistic

2.369844

(9,
17)

0.06

2.665132

(9,
17)

0.0391

Chi-square

21.32859**

9

0.0113

23.98619***

9

0.0043

JAPAN

F-statistic

1.259222

(8,
20)

0.3179

0.361517

(2,
38)

0.699

Chi-square

10.07377

8

0.2599

0.723034

2

0.6966

UNITED KINGDOM

F-statistic

1.940436

(10,
14)

0.1185

1.799983

(10, 14)

0.1527

Chi-square

23.28523**

10

0.0254

17.99983

10

0.055

UNITED STATE

F-statistic

6.164333

(2,
41)

0.0046

2.266169

(2,
38)

0.1175

Chi-square

12.32867***

2

0.0021

4.532338

2

0.1037

ü  ***, ** Revealed rejection of the null hypothesis in the level 1%,
5%

ü  Df shows the lag length which selected based on AIC.

Table3. Revealed existence of
bi-directional causality for France and Germany, uni- directional causality for
Canada, United Kingdom and United State and non-existence of causality for
Italy and Japan.

Table 4. Pairwise
Granger Causality Tests

Country

 Null Hypothesis:

Obs

F-Statistic

Prob.

ITALY

 LRGDP does not Granger Cause LRGC

 

45

0.26229

0.7706

 LRGC does not Granger Cause LRGDP

 

 

0.01933

0.9809

CANADA

 LRGDP does not Granger Cause LRGC

46

9.76236***

0.0032

 LRGC does not Granger Cause LRGDP

 

 

3.69879

0.0611

FRANCE

 LRGDP does not Granger Cause LRGC

38

2.82499**

0.0271

 LRGC does not Granger Cause LRGDP

 

 

3.48154**

0.0106

GERMANY

 LRGDP does not Granger Cause LRGC

38

2.73594**

0.031

 LRGC does not Granger Cause LRGDP

 

 

2.99441**

0.0211

JAPAN

 LRGDP does not Granger Cause LRGC

39

0.68947

0.6966

 LRGC does not Granger Cause LRGDP

 

 

0.88287

0.546

UNITED
KINGDOM

 LRGDP does not Granger Cause LRGC

46

5.47655**

0.024

 LRGC does not Granger Cause LRGDP

 

 

3.45902

0.0698

UNITED
STATE

 LRGDP does not Granger Cause LRGC

45

7.21193***

0.0021

 LRGC does not Granger Cause LRGDP

 

 

0.05103

0.9503

The paper has been used the Angle
Granger pairwise test as well that support the finding of Wald test in the
table 3.The result of pairwise test of Granger appeared in the table 4.

ü  ***, ** Revealed rejection of the null hypothesis in the level 1%,
5%

ü  Lag Length: (Automatic – based on AIC)

 

The empirical results of this
research strongly support the validity of Wagner law for Canada, United Kingdom,
United State, Germany and France but do not support the validity of law for
Italy and Japan for period of 1970-2016.

 

 

 

 

 

 

 

Conclusion

The validity if Wagner law has been
tested for G7 Industrial countries in this paper using time- series data and
econometrics modern techniques for the period of 1970-2016.

The paper considered several
specifications which commonly employed in the literature, for empirical
investigating of Wagner law in last dictates. In the empirical section of this
paper the ADF and ERS-Piont Optimal unit root has been tested to examine the
level of stationarity for variables which indicate all variables are stationary
in their first differences.

The lag lengths have been selected
on the basis of AIC value which revealed in the (annx…….) for the further
process of  Johansen  maximum likelihood co integration test,  The finding of Johansen co-integration test
for  G7 industrial counties shows that
except Italy , there is a long run co-integration exist between Government
consumption and Gross domestic product in the period of 1970-2016 for Canada,
Germany, France, United kingdom, United states and Japan which the
normalization of coefficients also supports the finding but by running VECM
(Vector Error Correction Model), the finding of Error correction
coefficient(table:….) and Wald Test does not support the long run and short run
causality for Japans variables ,whereas 
it supports the long run and short run causality for other countries.

The Granger’s causality test
revealed a bi-directional causality for variables of Germany and France and
uni-directional causality for variables of Canada, United Kingdom and United
State and no causality for variables of Italy, but in case of Japan as the finding shows; a
positive  long run relationship has been
founded between government consumptions and gross domestic products  which supported the law but the causality
tests doesn’t support it.

Finally the
paper found a strong support of Wagner law for Canada, Germany, France, United
Kingdom and United States, the finding also shows that the Wagner law does not
hold for Italy and Japan in the period of 1970-2016.

 Econometric Metodology

The  of GCE (Government Consumption
Expenditure), GDP (Gross Domestic Product) and GDP deflator for this paper collected
from World Bank; data bank and used as the real and logarithmic form to achieve
the most reliable results.  

To test or investigate the validity of Wagner law for the industrial
countries (G7), this paper adopts the formulation which was initially used by
Pryor (1968) in which the government consumption expenditure and gross domestic
product have used as variables which formulated as follows:

LNRGCE = a + LNRGDP + u                 (7)

Where a stands for constant term, LNRGCE stands for logarithmic
form of real government consumptions expenditure, LNRGDP stands for logarithmic
form of real gross domestic products and u stands for classical regression
error. For validity of Wagner’s law, a is expected to
be greater than zero.  In order to prevent
any spurious relationship, the time-series properties of
the variables have been analyzed before any estimation.

  In order to test the relationship between government
consumption expenditure and gross domestic product, the Granger co-integration
has been utilized. The most important  condition
in order to test Granger co-integration is the stationarity, which means for
investigation of co-integration the variables should be stationary in their
level or differenced forms (in the level I(0) or in the first difference I(1)).
To check the stationarity of variable a general from of ADF form of regression
formulated as follows:

 

                                             (8)

 

Where  stands for tirst differenced deries of X, T
stands for trend and  is a white noise residual.

The hypothesis of unit root (non-stationary) is
tasted by setting the null  hypothesis .
Mostly variables are not stationary at their level, then we should investigate
the stationarity of the variables in the some order (in their level of first
difference are prefer), but if the data don’t become stationary at the first
difference I(1) the further differences navt longer five a unique long-run solution(asterious
and hall.2017).  Once the data is found
to be stationary in the first difference, we can run a co-integration test.

Basically there are 2 approaches to test the
long run relationship between time series: first one is   Egle
& Granger (1987) and the other one is Johansen & Juselius (1990,1992). The
Johansen approach is based on VECM which is a VAR represented model. the general
VAR model with a lag length (p) formulated as follow:

     (9)

Where  stands for (mx1)
vector of first difference I(1) of variables, stands for (Sx1) vector of level stationary I(0)