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.

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)