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Testing Wagners Law forthe Canadian Economy during the period 1961-2009
by
Ayaz Mahmood Ghani
An essay submitted to the
Department of Economics
in partial fulfillment of the
requirements for the degree of
Master of Economics
Department of Economics
Memorial University of Newfoundland
6th December, 2010
St. Johns Newfoundland
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i
Table of Contents
Abstract iii
List of Tables iv
List of Figures v
Section 1 Introduction 1
1.1 Background of Study 1
1.2 Purpose of Study 1
1.3 Significance of Study 2
Section 2 The Growth of Government Expenditure in Canada 4
Section 3 Theoretical Background 5
3.1 Wagners Law 6
3.2 Criticizing Wagners Law 6
3.3 Formulation for Wagners Law 7
Section 4 Empirical Literature 8
Section 5 Empirical Framework and Data 11
5.1 Framework 11
5.2 Data Analysis 12
Section 6 Methodology 12
6.1 Unit Root tests 12
6.2 Engel and Granger Cointegration test 14
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6.3 Granger Causality test 15
Section 7 Empirical Results 15
7.1 Unit Root tests 15
7.2 Engel and Granger Cointegration test 17
7.3 Granger Causality test 19
Section 8 Wagners Law and Population Structure 21
Section 9 Wagners and Unemployment 25
Section 10 Conclusion 28
References 30
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iii
Abstract
The main purpose of this paper is to investigate the Wagners law by testing the long run
and short run relationship between real government expenditure and real income for
Canada from 1961 till 2009. The study carried out Augmented Dickey-Fuller andPhillips-Perron unit root test on the variables to find whether the variables are stationary.
We used the two-step Engel and Granger cointegration methodology to find the long-run
relationship between the two variables. The unit root tests show that the variables are
non-stationary, but their first difference is stationary. Hence, both the variables are
integrated of order one. The cointegration result gives evidence that real government
expenditure and real income for Canada do have long-run relationship for the time period
1961-2009. However, the causality examination, using the error correction terms, shows
that growth of GDP does not cause the growth in government expenditure, but the growth
of government expenditure does Granger cause the growth of GDP. From the empirical
results, we can conclude that Wagners law is not valid for Canada. Wagners law is also
tested when demographic variables, dependency ratio and unemployment rate, are taken
into consideration.
Keywords: Wagners Law; Augmented Dickey-Fuller; Phillips-Perron; Engel and
Granger Cointegration; error correction terms; dependency ratio; unemployment rate.
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iv
List of Tables
Table 1 Summary statistics of log ofreal GDP per capita and logof real government
expenditure per capita.
13
Table 2 Test Statistics to determineunit roots in the variablesused in the study.
19
Table 3 Regression result ofEquation 14, 14, 15 and15.
23
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v
List of Figures
Figure 1 Projected G7 Total
Government Net Debt-to-GDP
Rates, 2009.
2
Figure 2 Fiscal Stimulus flowing in
2009 and 2010, G7 countries.
3
Figure 3 Showing the upward trend of
Government Expenditure of
Canada.
5
Figure 4 Trend of GDP for Canada
from 1961 till 2009.
6
Figure 5 Trend of Dependency rate for
Canada from 1961-2009.
25
Figure 6 Trend of Unemployment Rate
for Canada from 1976-2009.
29
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I. INTRODUCTION
The relationship between public expenditure and national income has been a center of
attraction to economists for a very long duration (Peacock and Wiseman, 1961). A profound
approach to clarify the growth of public spending is Wagners law which asserts that during
economic development transition, government economic activity increases in relative to private
economic activity. As Singh and Sahini (1984) states that the relationship between public
expenditure and national income has been treated in different ways in two areas of economic
study.
Public finance analysis showed that growth in public expenditure is caused by growth in
national income which signifies the Wagnerian approach. However, according to the Keynesian
approach, the macroeconomic models tend to explain that growth in national income is due to thegrowth in public expenditure. In Wagners (1883) empirical study, public expenditure was kept
as a dependent variable which indicates that economic growth is the cause of the growth in
government expenditure. Keynes (1936) conducted his analysis treating public expenditure as an
independent variable characterized to amend short-term cyclical fluctuations in aggregate
expenditures. Thus, the causation moves from growth in government expenditure to growth in
national income.
This empirical study is based on the Canadian economy due to its cautious involvementin the world political arena. According to IMF, the Canadian economy ranks as the tenth largest
and Canada is one of the wealthiest nations of the world. Canada has been grouped with
countries that provide the highest level of economic freedom. The government sector in Canada
has augmented steadily from the very beginning of the nineteenth century. Economists have
carried out intensive research to answer the development in the government sector of Canada.
One of the significant reasons has been the distinguished Wagners law which states that the
development of an industrial economy will be accompanied by an increased share of public
expenditure in gross national product (Wagner, 1883). According to the above theory, during
the transition of economic development, government economic activity increases in relative to
private sector economy; thus, the process leads to higher degree of public expenses. Hence,
augmentation in public sector will act as a friction to advancing economic development.
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To test the validity of Wagners law has become intriguing, since the Canadian
government expenditure share in GDP is on the rise even though the government has maintained
subtle policy to tackle public sector economy. Examination of Wagners Law hypotheses has
become important for Canada, since the Canadian government has changed from their past
policy of deficit financing to an expenditure deficit policy. Government of Canada is trying to
decrease its expenditure since the early 1990s in order to cope from the large budget deficits and
growing public debt. The governments budget deficit, for the fiscal year 1996-1997, declined by
$33.1 billion and that within a span of three years. According to the Economic and Fiscal Update
(1997) of Department of Finance, the decline in deficit occurred due to increase in revenues,
which resulted from an expanding and mounting economy, and also due to a reduction in
government expenditure. According to OECD Economic Outlook (2009) as shown in Figure 1,
the recent shape of Canadian economy puts them with lowest net debt-to-GDP rates among G7
countries. The government of Canada maintained such strong position, during the downturn, due
to its debt reduction efforts in the last decade. Even though holding onto such solid economic
position, the Canadian government offered the largest economic stimulus package around the
world as shown in Figure 2 (IMF, Update on Fiscal Stimulus and Financial Sector Measures,
2009).
To venture implications from change in policy where government expenditure and
growth plays key role makes it necessary to conduct empirical studies on Wagners Law
hypotheses. The analysis will help to find evidence to suggest approach to developing
government policies which will direct ways to improve public expenditure composition and
productivity. This study will examine and determine the relationship between government
expenditure and GDP for Canada from 1961 to 2009. First, the analysis will examine the long-
run relationship, if only, between government expenditure and GDP. Second, the study will aim
at Wagners Law by testing the causality between public expenditure and GDP.
There are ample studies to validate Wagners Law hypotheses for Canada. These inc lude
Ahsan et al. (1996), Biswal et al. (1999), Kolluri et al. (2000), Chang et al. (2004), and
Lamartina and Zaghini (2008). The present study is different, since it employs a more recent
sample period in testing Wagners Law, and takes population structure and unemployment into
consideration.
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Figure 1: Projected G7 Total Government Net Debt-to-GDP Rates, 2009.
Figure 2: Fiscal Stimulus flowing in 2009 and 2010, G7 countries.
The paper is organized as follows. Section II gives an analysis of public expenditure and
GDP patterns in Canada. Section III outlines the theoretical and empirical models that are
suggested in the literature. Section IV gives the overview of the empirical literature. Section V
defines the data, its sources and the framework that will be used in this study. The empirical
methodology is presented in section VI. Section VII discusses the empirical results of our study.
Section VIII explains the empirical results when population structure is taken into account.
Section IX carries out empirical study when unemployment rate is taken into consideration.
Section X concludes and summarizes the results in the respective subject matter.
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II. THE GROWTH OF GOVERNMENT EXPENDITURE IN CANADA
The percentage of GDP of government expenditure in Canada is similar to any of the
industrialized countries. According to OECD statistics National Accounts at a Glance (2009),
France devoted 28 percent, Germany used 37 percent, Italy allocated 13 percent, Japan devoted
15 percent, United Kingdom allocated 73 percent and United States of America used up 55
percent of GDP in the year 2008. G7 countries like Italy and Japan has been noted to apportion
low government expenditure as a percent of GDP from the year 2006, primarily because of the
lingering recession of this century. The government size of Canada has increased significantly in
absolute and relative terms from 1961 till 2009. Real government expenditure increased from $
61.3 billion in 1961 to $ 273.2 billion in 2009 taking in 2002 constant dollars. Canadian
economy has maintained a stable increase in public expenditure for the given period with
expenses allocated to agricultural and energy sector research and development, manufacturing
sector and service sector.
Figure 3: Showing the upward trend of Government Expenditure of Canada.
1960 1970 1980 1990 2000 2010
Year
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Figure 4: Trend of GDP for Canada from 1961 till 2009.
0
1960 1970 1980 1990 2000 2010Year
Figure 3 show that the government expenditure in Canada has an upward trend over the
period 1961-2008. However, between 1994 and 1997 the economy experienced decreases in
public expenditure and slowdown of the economy during the respective period (see Figure 4).
However, the Canadian economy was able to vitalize due to economys openness and internal
economic policies, and maintained an upward trend thereafter.
Figure 4 shows the trend of GDP for Canada from 1961 till 2009. According to the chart,
the Canadian GDP rose over the years with an upward trend. According to OECD Economic
Outlook (2009), the GDP in Canada expanded at an annual rate of 0.50 % in the last reported
quarter of 2009. From 1961 until 2009, Canada's average quarterly GDP growth was 0.84 %
reaching an historical high of 3.33 % in the last quarter of 1963 and a record low of -1.80 percent
in the first quarter of 2009.
III. THEORETICAL BACKGROUND
In 1883, Adolph Wagner, a German economist, developed a principle called the Law of
the Increasing Extension of State Activity. The hypothesis deals with the augmentation of
government activity in the economy; the principle has come to be known as Wagners Law.
According to Wagner, there are three important reasons to expect an expanding scope of public
activity. First, as Wagner (1883) puts it, the administrative and protective functions of the state
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have to expand due to the rising complexity of legal relationship and communications. On top of
that, higher government expenditure is needed on law and order and socioeconomic regulation
when urbanization and population increases. Second, Wagner felt that the development process
required larger amounts of capital than what the private sector could provide. Finally, Wagner
believed that the income elasticity of demand for public commodities was greater than unity.
Even though Wagner was not the first one to explain the above matter, he was indeed the first to
try to explain the situation using empirical analysis.
Wagner was ambiguous in explaining the formulation required for the law, and kept it
subject to disagreement among economists. An empirical analysis of Wagners Law has been
criticized, since it is not a precisely and vividly constructed theory. The study usually looks at the
past and tries to explain the upward trend of public expenditure. Hence, the law is basically
inclined towards particular variables and their assumed part in historical progress. As the
assumptions are not distinctly stated, making it inexplicable to accept or decline the law based on
the historical facts. To add further difficulty the law does not have specific and identical
empirical counterpart. There are lot of socio-economic variables, not all of which are
measurable, can be used to explain public expenditure. Economists are in doubt to understand
what variables can be used to denote both economic development and state activity. However,
major studies by Gupta (1967), Pryor (1968), Goffman (1968), Musgrave (1969), Bird (1971)
and Michas (1975), regarding the subject matter, have all used income per capita to explain
development, even though the proxy is not the only index of development nor is it the only
agreeable explanation of the law. The respective studies have used government expenditure to
explain state activity, since it is the most significant and practical measure.
Bird (1971) criticizes Wagners hypotheses as not a theory, but an axiomatic explanation
about state development. Bird (1971) state any attempt to test it necessarily does violence to the
facts by adjusting them to preconceived theory. The author then goes on to signify the fact that
the relevant variables in the defined formulation are not fixed enough over time to test this
evolutionary proposition.
Musgrave (1969:73), one of the critics of Wagners law, states that the law is unable to
explain whether the principle is related to the relative share of government in national economy
or only the absolute size of the economy. Peacock and Wiseman (1967) clarify, using political
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theory, the effects of political occurrence on government expenditure. The authors explain the
situation with the idea of the displacement effect.
Even though the Wagners law does not show itself to be empirically tested
straightforwardly, but there are procedures through which tests can be performed to know thevalidity of the law. Researchers have taken the second best way to solve the problem regarding
the law, since the optimal solution is surrounded by complexity and intricacy. Economists have
sought for measurable proxies for state development and activity, and using econometric
methods it is now possible to set apart the consequences of some variables of government
spending. Moreover, the analysis will also examine the stationarity properties of the data and the
stability of the variables that caused it. We have sought the appropriate tools and measurable
variables for the test, but what is required is the exact functional form that is compatible with the
analysis.
Although a number of studies have been carried out to test the validity of the law, the
nature of the original statement makes it harder to comprehend the relationship between
economic progress and the growth of state activity. There are various interpretations of the
hypothesis which result into six formulations given the ambiguous nature of Wagner s original
description. They are as follows:
Peacock and Wiseman (1967): G = f(Y) (1)
Goffman (1968): G = f(Y/N) (2)
Gupta (1967): G/N = f(Y/N) (3)
Musgrave (1969): G/Y = f(Y/N) (4)
Mann (1980): G/Y = f(Y) (5)
Pryor (1968): GC = f(Y) (6)
where G = real government expenditure, Y = real GDP, G/N = real government expenditure per
capita, G/Y = ratio of real government expenditure to real GDP, Y/N = real GDP per capita and
GC = government consumption.
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The first equation was used by Peacock and Wiseman (1967), Musgrave (1969), and
Goffman and Mahar (1971). The second equation was employed by Goffman (1968) and Mann
(1980). The third equation was suggested and formulated by Gupta (1967) and Michas (1975)
and tested by Mann (1980) and Henrekson (1993). The fourth formulation was employed by
Musgrave (1969), Murthy (1993) and Ram (1987). The fifth equation was suggested and tested
by Mann (1980), and the formulation is known as Peacock-Wiseman share version. The sixth
formulation was stated by and tested by Pryor (1968).
Economists have used all of the six formulations to test for the validation of Wagners
Law. Wagner stated that culture and welfare spending were income elastic, and he has also
assumed that a major part of public commodities and services are luxury items and hence, the
public expenses in national income is income elastic. This assertion has been formulated from
Wagners basic thoughts and assertion of the literature about state development and activity.
Therefore, analysts have expected the income elasticity of public expenditure to surpass unity.
Goffman (1968) and Bird (1975) infer that Wagners law is valid if the income elasticity of
demand exceeded unity. However, Michas (1975) states that elasticity does not require
exceeding unity to validate the law but rather zero; this notion depends on the choice of
functional form by the analyst. For Equations 1 and 2, the estimate of the elasticity need to
overcome unity, but for Equations 4 and 5, the elasticity estimate need to be more than zero to
verify Wagners hypothesis.
IV. EMPIRICAL LITERATURE
Wagners law has been examined under empirically for various countries using both time
series and cross-sectional data. The results differ from country to country. Dhawan, Biswal and
Paul (2003) test Wagners Law for Canada and its ten provinces using Johansens maximum
likelihood technique of cointegration and the Granger-causality procedure for the period 1960 to
2003. Their results support the law for Canada and three of its biggest provinces, implying that
GDP and government expenditure possess a long run equilibrium relationship. However,
Granger causality analysis shows that GDP Granger-causes the government expenditure in the
case of Canada and seven of its ten provinces.
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Biswal, Dhawan and Lee (1999) empirically test Wagnerian versus Keynesian
hypotheses for Canada from 1950 to 1995. The authors use Engel and Grangers two-step
cointegration and error correction technique to find the relationship, if any, between government
expenditure and national income. The results show that Wagners law is valid when tested with
total current government expenditure and total current expenditure on goods and services. The
research shows evidence of short-run causation between total current government expenditure
and GDP.
Ahsan et al. (1996) tests Wagners Law (using equations (1) and (4)) for Canada and
obtained coefficient estimates of the income variables between 1.4 and 0.5, suggesting support
for the hypothesis that GDP growth and the relative size of the public sector possess a positive
relationship. Chang, Liu and Caudill (2004) analyzes Wagners law for ten countries based on
cointegration and error-correction modeling techniques for the period 1951-1995. These authors
includes three of the emerging industrialized countries of Asia, South Korea, Taiwan and
Thailand, and seven industrialized countries, Australia, Canada, Japan, New Zealand, USA, the
United Kingdom, and South Africa. The study, which also used cointegration analysis and
unidirectional Granger causality between income and government spending, shows that the
Canadian economy does not seem to provide evidence in support of Wagners Law.
Lamartina and Zaghini (2008) tests Wagners law for23 OECD countries which includes
Canada and using an autoregressive distributive lag approach to cointegration, shows empirical
evidence supporting the existence of a long run positive correlation between public spending and
GDP growth in 23 OECD advanced economies. Granger causality test showed that GDP causes
government expenditure in the case of all the OECD countries.
The test by Kolluri, Panik and Wahab (2000), using time series data from G7 countries,
shows that the law holds for some components of the government expenditure. Lamartina and
Zaghini (2008) tests a panel cointegration analysis of the joint development of governmentexpenditures and economic growth in twenty-three OECD countries. Their analysis provides
evidence of a structural positive correlation between public spending and per capita GDP which
is fitting to the Wagners law.
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A recent study by Mohave (2009) that examine Wagners law based on disaggregated US
state-local government expenditure for the period 1957-2006 has shown support towards the
hypotheses. The author has used the equation suggested by Musgrave (1969). The analysis
includes two methods of cointegration; Engel and Grangers two step procedure and bound
testing. Both the procedures show results supporting the Wagnerian hypotheses. Kalam and
Aziz (2009) have carried out analysis testing the validity of Wagners Law for Bangladesh from
1976 to 2007. The study supports Wageners law in the state in both the long run and short run.
They conclude that population size plays a vital role for government expenditure to grow in the
long and short run.
Ziramba (2008) has examined the long-run connection between real government
expenditure and real income for South Africa using the autoregressive distributive lag approach
to cointegration, and then uses Granger non-causality test procedure improvised by Toda and
Yamamoto (1995) to test for the link between the two variables. He found a long-run relationship
between real government expenditure and real income, but different result in the short-run.
Kumar, Webber and Fargher (2008) tests cointegration and causality tests to investigate the
validity of Wagners Law for New Zealand for the period 1960-2007 between government
expenditure on the one hand, and GNP and GDP on the other. The authors conclude that the
Wagners law holds in the long run irrespective of the chosen output measure.
Shelton (2007) tests several leading hypotheses on determinants of government
expenditure, and one of them is Wagnerian hypotheses. The author uses Government Financial
Statistics Data from IMF covering 100 countries for the period 1970 till 2000. Shelton (2007)
analyzes that the correlation between income and government size is greatly driven my
demographics, which includes population over 65 years, during the period 1970-2000. He gives a
new explanation on Wagners Law that fragmentation leads to decentralization rather than
decline in public expenditure. Shelton (2007) shows evidence that the evidence of the franchise
affects the degree of redistribution in advanced democracies, and puzzle role of trade openness.
Sinha (2007) tested the law using the total and per capita GDP and government expenditure data
of Thailand. His empirical study suggests that there is no causality stimulating from either
direction between GDP and government expenditure, and there is a weak relationship between
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the two variables in the long run. Hence, he concludes that Wagners law is not valid for
Thailand.
V. EMPIRICAL FRAMEWORK AND DATA
In this paper, equation (3) suggested by Gupta (1967) will be considered as the model to
test Wagners law for Canada from 1961 till 2009.
)/(/ NYfNG (3)
We assume that the function is log-linear specified as follows:
uNYNG )/ln()/ln( (7)
where G represents real government expenditure, Y is real income, N is the population, G/N =
real government expenditure per capita, Y/N = real GDP per capita, and are parameters to
be estimated, u is the random error term and ln denotes natural logarithm.
The analysis is carried out using annual data from 1961 to 2009. The data for income,
government expenditure and population were obtained from Statistics Canada using Canadian
Socio-Economic Information Management System (CANSIM).1 Summary statistics of the
variables used are presented in Table 1.
Table1: Summary statistics of log of real GDP per capita and log of real government expenditure
per capita.
Log of Real GDP per
capita
Log of Real
Government
Expenditure per
capita
Mean 10.16946 8.685767Standard Deviation 0.2910891 0.2382136
Minimum 9.553675 8.120816
Maximum 10.58905 8.999946Count 49 49
1 CANSIM is the Statistics Canada's computerized database of time series covering a wide variety of social andeconomic aspects of Canadian life.
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The series of real government expenditure and real GDP are at the annual rate. The real
government expenditure and real GDP is measured at market prices and at constant (2000=100)
prices. A main reason behind carrying out the analysis using annual data is because government
expenditure is hardly sensitive to seasonal and even cyclical fluctuations, and therefore reference
periods of less than a year may not be sufficient to register the response between government
expenditure and national income. On the other hand, a reason that supports the use of time series
framework was given by Bird (1971). He states that the formulation to test Wagners law has no
ability to compare two nations given their government expenditure and the level of average per
capita income. Bird shows evidence which shows that an increasing trend over time is quite
different from a maximum and minimum value at a point in time. Therefore, Birds analysis
shows that conclusion made from international cross sectional studies are not required to test
Wagnerian hypotheses. Wagners law is unquestionably a time series incident. Hence, in this
study we will be using time series technique to verify for the validity of Wagners law in Canada
for the time period 1961-2009.
VI. METHODOLOGY
(a) Unit Root tests
First, the stationarity of the time series, ln(G/N) and ln(Y/N) is investigated. An
important choice is to determine, before conducting unit root tests, the most appropriate form ofthe trend in the data. If the data are trending, then some form of trend removal is required. Two
common trend removal or de-trending procedures are first-differencing and time-trend
regression. First-differencing is appropriate for integrated of order one (I(1)) time series and
time-trend regression is appropriate for trend stationary integrated of order zero (I(0)) time series
(Maddala, 1998). Unit root tests can be used to determine if trending data should be first
differenced or regressed on deterministic functions of time to render the data stationary.
Moreover, economic and finance theory often suggests the existence of long-run equilibrium
relationships among non-stationary time series variables. If these variables are I(1), then
cointegration techniques can be used to model these long-run relations. Hence, the need to carry
out unit root test has become mandatory in our analysis.
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In the econometrics literature, there are several tests that can be carried out to detect the
presence of unit roots in time series data. In this study, unit roots are tested using both the
Augmented Dickey-Fuller (ADF) and Philips-Perron tests (Maddala, 1998).
The ADF test is based on estimating the test regression:
p
j
tjtjttt yyDy1
1 (8)
whereyt is the time series in question, tD a vector deterministic term, p is the number of lagged
difference terms, and jty is used to approximate the structure of error, so as to ensure that the
residual termt
is not serially correlated. Under the null hypothesis 1 which implies the
presence of unit roots.
Phillips and Perron (Ng and Perron, 1995) develops a number of unit root tests that have
become popular in the analysis of financial time series. The Phillips-Perron (PP) unit root tests
differ from the ADF tests mainly in how they deal with serial correlation and heteroskedasticity
in the errors. In particular, where the ADF tests use a parametric autoregression to approximate
the ARMA structure of the errors in the test regression, the PP tests ignore any serial correlation
in the test regression. The test regression for the PP tests is
tttt uyDy 1 (9)
wheret
u is trend stationary and may be heteroskedastic. The PP tests correct for any serial
correlation and heteroskedasticity in the errorst
u of the test regression by directly modifying the
test statistics 0t and T . Under the null hypothesis 0 which implies the presence of unit
roots in the time series. One advantage of the PP tests over the ADF tests is that the PP tests are
robust to general forms of heteroskedasticity in the error term tu , and the user does not have to
specify a lag length for the test regression.
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(b) Engel and Granger Cointegraten test
The following test is suggested by Engel and Granger (1987). The authors proposes that
the test should run regression analysis on variables integrated of order one, or I(1). Suppose we
are testing between Gt and Yt for the following cointegration regression equations:
ttt uYG 11 (10)
ttt vGY 22 (11)
In small samples, the test for cointegration may not be invariant to the choice of
normalization and therefore both cointegration regressions are run to examine if the results are
sensitive to normalization. In the above equations, we assume that both the variables are
integrated of order one using first differencing of the variables, and ut and vtis the error term of
the formulation. Engel and Granger suggest running regression analysis on Gt and Yt. The
asymptotic distribution of and are not standard, but the method required to estimate and
by ordinary least square (OLS) procedure, and then test for unit roots in the equations stated
below:
(12)
(13)
The null hypothesis for the unit root of the residual value implies that there is no
cointegration. However, the limiting distribution does not match the distribution tabulated by
Dickey and Fuller. The limiting distribution of this test, however, resembles the Dickey-Fuller
distribution even though you require a separate table for each dimension of the regressor. Hence,
in this study we will allow for dynamics in the residual and carry out the augmented Dickey-
Fuller (ADF) test and Phillip-Perron test, and then use the table generated by MacKinnon (1991)to find the critical value.
If we find the two variables to be cointegrated, then we will move to the second step of
Engel and Granger method. In this step, we acquire the error correction term (ECT) from the
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cointegrating equation, and use at least one period lag of ECT to test the direction of the
causation of the following equation:
ttittteuYGG
111111 (14)
ttittt uGYY 122122 (15)
ttittt vYGG 133133 (16)
ttittt vGYY 144144 (17)
where Gtand Yt are the variables to catch the short run relationship, and et, t, t, and t are
the new error terms of the error correction models.
(c) Granger Causality test
The first try at testing the direction of causality was by Granger in 1969. The intuition
behind the Granger causality test is simple. If the variables are cointegrated, then the significance
ofi (i = 1,2,3,4) of the equations 14, 15, 16 and 17 shows that the independent variable Granger
causes the dependent variable. However, if the variables are not cointegrated, then the
significance ofi (i = 1,2,3,4) shows the Granger causality among the variables.
VII. EMPIRICAL RESULTS
(a) Unit root tests
In this study, we use traditional methods, which are Augmented Dickey-Fuller and
Phillips-Perron tests, to test for non-stationarity of a time series. The variables examined are
ln(G/N) and ln(Y/N). Table 2 shows the augmented Dickey-Fuller test and Phillip-Perron test
results ran on ln(G/N) and ln(Y/N) to test the existence of unit roots in the time series.
In our analysis, the null hypothesis is the presence of unit root. The critical values at the
1%, 5% and 10% significance levels for the Dickey-Fuller test are -4.178, -3.512 and - 3.187
respectively. The Augmented Dickey Fuller test statistic for log of GDP per capita is 1.905
suggesting that the presence of unit root cannot be rejected, and that the time series for log of
GDP per capita is non-stationary. Likewise, the Augmented Dickey Fuller test statistic for log of
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government expenditure per capita is 2.398. Therefore, we cannot reject the presence of unit
root, and conclude that this time series is also non-stationary.
Table 2: Test statistics to determine unit roots in the variables used in the study.
Variables Augmented Dickey Fuller teststatistic
Phillips-Perron test statistic
ln (G/N) -2.398 -2.192
ln (Y/N) -1.905 -1.956
dependency rate 0.009 -0.581
unemployment rate -2.649 -2.066
ln (G/N) -3.758 -3.810
ln (Y/N) -3.876 -3.785
dependency rate -3.388 -3.217
unemployment rate -4.330 -4.273
For the Phillips-Perron test the critical value at the 1%, 5% and 10% significance levels
are -4.178, -3.512 and -3.187 respectively. The test statistics, which yielded from log of GDP per
capita, is -1.956 which lies at the acceptance region of 1%, 5% and 10%. Hence, this test also
shows that we cannot reject the presence of unit root; therefore, the time series of log of GDP per
capita is non-stationary. From Table 2, we found that Phillips-Perron test statistic of log of
government expenditure per capita to be 2.192, which lies at the acceptance region of 1%, 5%
and 10%. Therefore, we cannot reject the presence of unit root; thus, the respective time series is
non-stationary.
The results from the Dickey-Fuller and Phillips-Perron tests indicate that both variables
are non-stationary. Therefore, if we employ classical econometric approach using ordinary least
square (OLS) to carry the analysis with unit root presence, then the conclusion obtained will be
misleading, and yield spurious result. To make the time series stationary, we take first
differences of ln(G/N) and ln(Y/N).
In our analysis, the null hypothesis is the presence of unit root. The critical values for the
Dickey-Fuller test at 1%, 5% and 10% are 3.600, - 2.938 and 2.604 respectively. The test
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statistic of ))/ln((1tNG is 3.758 which do not lie at the acceptance region of 1%, 5% and
10%. Therefore, we can reject the null hypothesis of the presence of unit root; hence, the time
series data of log of government expenditure per capita is stationary when the first difference is
taken into account. From the above test, we note that the log of government expenditure per
capita is integrated of order one, or I(1). The Augmented Dickey Fuller test statistic of
))/ln((1tNY is 3.876 which do not lie at the acceptance region of 1%, 5% and 10%.
Therefore, we can reject the null hypothesis of the presence of unit root; hence, the time series
data of the log of GDP per capita is stationary when the first difference is taken into account.
From the above test, we can clearly note that the log of GDP per capita is integrated of order one,
orI(1).
For the Phillips-Perron test, the critical values at 1%, 5% and 10% significance level are
3.600, - 2.938 and2.604 respectively. The Phillips-Perron test statistic of ))/ln((1t
NG is
3.810 which do not lie at the acceptance region of 1%, 5% and 10%. Therefore, we can reject the
null hypothesis of the presence of unit root; hence, the time series data of the log of GDP per
capita is stationary when the first difference is taken into account. From the above test, we can
clearly note that the log of government expenditure per capita is integrated of order one, or I(1).
The Phillip-Perron test statistic of ))/ln(( 1tNY is3.785 which do not lie at the acceptance
region of 1%, 5% and 10%. Therefore, we can reject the null hypothesis of the presence of unit
root; hence, the time series data of the log of GDP per capita is stationary when the first
difference is taken into account. From the above test, we can clearly note that the log of GDP per
capita is integrated of order one, orI(1).
(b) Engel and Granger Cointegraten Test
Cointegraten suggests evidence of long term relationship between a nations activity and
economic development. In this paper, we will verify the long run relationship between
government expenditure and GDP. In our research, we apply Engel and Granger cointegration to
find the establishment of the long term relationship between the respective variables used in the
study. The primary requirement of Engel and Granger cointegration test needs the variables to be
integrated of the same order. After carrying out Augmented Dickey-Fuller and Phillips-Perron
test, we can infer that both the variables are integrated of order one, or I(1). The first step of
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Engel and Granger cointegration test requires us to run static ordinary least square (OLS)
regression.
tt NYNG ))/ln((7835204.07177868.0)/ln(
R2 = 0.9167 CRDW=1.316853 (18)
(2.05) (22.72)***
The equation above shows that the log of government expenditure per capita and the log
of GDP per capita are positively related. For every one percent increase in GDP per capita would
lead to 0.7835204 % increases in government expenditure per capita. The t-statistic (in
parentheses) of log of GDP per capita is 22.72, and also suggests that GDP per capita is
significant even at the 1% significant level.
tt NGNY ))/ln((169955.10075083.0)/ln(
R2 = 0.9167 CRDW=1.227212 (19)(0.02) (22.72)***
The equation above shows that the log of GDP per capita and the log of government
expenditure per capita are positively related. For every one percent increase in government
expenditure per capita would lead to 1.169955 % increases in GDP per capita. The t-statistic (in
parentheses) of log of GDP per capita is 22.72, and also suggests that GDP per capita is
significant even at the 1% significant level.
The next step of Engel and Granger test requires us to obtain the estimated residuals of
the OLS regression run above, and then carries out stationarity test on the estimated residuals.
The MacKinnon critical value for the cointegrating equation of two variables without trend using
forty-nine observations at the 1%, 5% and 10% levels of significance are4.1293, - 3.4637 and
3.1321 respectively. After running stationarity test on the residuals of Equation 18, the ADF
test statistic is 3.906 which do not lie at the acceptance region of 5% and 10%. The PP test
statistic is6.967 which do not lie at the acceptance region of 1%, 5% and 10%. According to
Dittmann (2002), PP test, applied to residual based cointegration determination, is more
powerful than the ADF test. Hence, we can reject the null hypotheses of no cointegration, and
the estimated residual is stationary. After running stationarity test on the residuals of Equation
19, the ADF test statistic is 9.511 which do not lie at the acceptance region of 1%, 5% and
10%. The PP test statistic is 7.923 which do not lie at the acceptance region of 1%, 5% and
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10%. Hence, we can reject the null hypotheses of no cointegration, and the estimated residual is
stationary.
From the following results, we can infer that government expenditure per capita and GDP
per capita are cointegrated and do have a long run relationship. Our cointegration results confirm
those by Ahsan et al. (1996), Biswal et al. (1999), Dhawan et al. (2003), and Lamartina and
Zaghini (2008). From Equation 18, we can see that the coefficient of ln(Y/N) is positive and
significantly different from zero. Hence, these studies yield results that support the notion that
GDP growth and the relative size of government sector have a behavioral relationship with
each other.
In the second step, we are required to find the error correction term (ECT) since the two
variables are cointegrated. The procedure requires the estimate the following two equations:
(20)
(20)
(21)
(21)
where is the first difference operator, and and are the error correction terms, the first
lag of error term in Equation 18 and Equation 19. If the error terms are not taken into
consideration, then we will have a biased estimation in the respective procedure. The
coefficients, , , and , are expected to illustrate the long run dynamics in Equations 20 and
20. The coefficients, , , and , are expected to capture the long run dynamics in Equations
21 and 21. The optimal lag length orders of the variables (M, S) are found to be three. The
optimal lag length orders of the variables (K, L) are found to be two. Equations 20, 20, 21 and
21 are then used to investigate the causal relationship between government expenditure and
GDP to test the Wagnerian and Keynesian perspective.
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(c) Granger Causality test
According to Biswal et al (1999), since the two variables are cointegrated, then the
results of Granger causality are based on the significance of the coefficient of error correction
terms, for Equations 20 and 20, and for Equations 21 and 21. When is significant then it
implies that GDP Granger causes government expenditure which verifies Wagners hypothesis.
When is significant then it implies that government expenditure Granger causes GDP which
verifies the Keynesian paradigm.
Table 3: Regression result of Equation 20, 21, 20 and 21.
Variables (20) (21) (20) (21)
0.1985218
(1.18)
-0.1173303
(-0.64)
0.2300227
(1.36)
-0.1087396
(-0.59)
0.2314485
(1.45)
-0.0887551
(-0.53)
0.2519814
(1.55)
-0.0857034
(-0.51)
0.1046356
(0.71)
_ 0.1295952
(0.87)
_
0.3038138
(2.16)**
0.3101603
(1.90)
0.3522681
(2.58)
0.3519704
(2.20)**
0.1760605
(1.10)
-0.1259164
(-0.71)
0.1824272
(1.13)
-0.0901079
(-0.51)
-0.0789739
(-0.52)
_ -0.0629421
(-0.41)
_
-0.0152288
(-1.03)
-0.0417051
(-2.70)***
_ _
-0.0027062
(-0.24)
-0.0313511
(-2.61)***R
2 0.5350 0.3050 0.5226 0.3050
AIC -5.45045 -5.05459 -5.45045 -5.05459
*** shows that the variable is significant at 1%.
** shows that the variable is significant at 5%.
* shows that the variable is significant at 10%.
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From Table 3, we can deduce that the error correction term of Equations 20 and 20 is not
significant, even at the 10% significance level. Hence, the result provides us with evidence that
GDP does not Granger cause government expenditure. In other words, the growth of GDP does
not cause the growth in government expenditure; hence, the result shows that Wagners Law is
not valid for Canada for the time period 1961 till 2009. According to Table 3, we can deduce that
the error correction term of Equations 21 and 21 is significant at 1% significance level. Hence,
the result provides us with evidence that government expenditure does Granger cause GDP. In
other words, the growth of government expenditure causes the growth in GDP; hence, the result
shows that Keynesian paradigm is valid for Canada for the time period 1961 till 2009. These
results also show that normalization does not affect the result and the conclusion.
VIII. WAGNERS LAW AND POPULATION STRUCTURE
The research on Wagners Law rarely takes the population structure into consideration
even though it affects expenditure. Shelton (2007) has found by carrying out research on cross-
country panel data from 1970 to 2000 that Wagners Law is affected by demographics. A time
series analysis by Durevall and Henrekson (2010) with larger samples for Britain and Sweden
shows that the weight of the Wagners Law is lessen, since the expenditure associated to age
structure is already integrated with the government expenditure.
According to OECD Economic Outlook (2009), Canada is a welfare state. In other words,government provides the basic needs to the people. Hence, our research has undertaken the role
of dependency ratio to verify Wagners Law. In the case of Canada, dependency ratio is
calculated by summing up the population aged 0-17 and 65+, and then dividing by the
population aged 18-64. According to Durevall and Henrekson (2010), the dependency ratio
measure apprehends the expenditure on child care, school and pension, and also other spending
of that sort.
From Figure 5, we can deduce that the dependency ratio has a downward trend. The ratio
has decreased following a constant downward trend from 1961 to 2009. The reduction in the
dependency ratio explains that the public expenditure has declined as a share of GDP during the
respective period of study. In this paper, the regressed equation below will be considered as the
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model to test Wagners law for Canada from 1961 till 2009 when age structure is taken into
consideration.
Figure 5: Trend of Dependency ratio for Canada from 1961-2009.
.5
.6
.7
.8
.9
1960 1970 1980 1990 2000 2010
Year
In our analysis, the null hypothesis is the presence of unit root. The critical values at the
1%, 5% and 10% for the Dickey-Fuller test are -4.168, -3.508 and -3.185 respectively.
According to Table 2, the Augmented Dickey Fuller test statistic for dependency ratio is 0.009
which lies at the acceptance region of 1%, 5% and 10%. Therefore, we cannot reject the presence
of unit root; thus, the time series for dependency ratio is non-stationary. To make the respective
time series variable stationary, we will be employing the first-differencing approach. After
carrying the first-difference, the critical value for the Dickey-Fuller test at the 1%, 5% and 10%
significance levels are -4.178, -3.512 and -3.187 respectively. The ADF test statistic of
ratiodependency _ is3.388 and the PP test is 3.217 and both the values do not lie at the
acceptance region of 10%. Therefore, we can reject the null hypothesis of the presence of unit
root; hence, the time series data dependency ratio is stationary when the first difference is taken
into account. From the above test, we can clearly conclude that the dependency ratio is integratedof order one, orI(1).
ratiodependencyNYNG _344798.1)/ln(2538529.0971322.6)/ln( R2=0.9655CRDW=1.362503
(8.63) (3.66) (-8.07) (22)
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Equation 22 shows that the log of government expenditure per capita and the log of GDP
per capita are still positively related, but dependency ratio is negatively related to log of
government expenditure per capita. For every one percent increase in GDP per capita would lead
to 0.2538529 % increases in government expenditure per capita which are lower than the
coefficient found when OLS is run for ln (G/N) on ln (Y/N). The t-statistic of log of GDP per
capita (in parentheses) is 3.66 and it is significant even at the 1% significant level. The t-statistic
of dependency ratio is 8.07, and the variable is also significant at the 1% significance level.
Based on the results reported in the previous section, we have already established
cointegration for Canada from 1961-2009. Hence, we are using the dependency ratio to check the
consistency during the respective period. The Engel and Granger two step cointegration analysis
is carried out to check the long run relationship. In our analysis, the null hypothesis is no
cointegration. The MacKinnon critical value for the cointegrating equation of three variables
without trend using forty-nine observations at 1%, 5% and 10% level of significance are
4.60176, - 3.9197 and - 3.58055 respectively. The ADF test statistic of 1u
t is7.613, and PP
test statistic is 5.802, and both the values do not lie at the acceptance region of 1%, 5% and
10%. Hence, we can reject the null hypotheses of no cointegration, and the estimated residual is
stationary. From the following result, we can infer that the respective variables do have a long
run relationship.
Since there is evidence of the presence of cointegration in the model, we now proceed to
check the causality when dependency rate is a part of the model. Granger causality test is used to
verify whether there is a causal relationship between real government expenditure, real income
and dependency ratio. We have considered the following model to be used in our study to
explain the government expenditure and national income:
(23)
Similar to the approach used in the previous section to check for the causality, we will
rely on the significance of ofthe above equation. When is significant then it implies that GDP
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along with the dependency ratio Granger causes government expenditure which verifies
Wagners hypothesis. The optimal lag length orders of the variables (M, S, P) is found to be four.
From Equation 24, we can deduce that the error correction term is not significant even at
the 10% significance level. Hence, the result provides us with evidence that GDP anddependency ratio does not Granger cause government expenditure. In other words, the growth of
GDP along with the growth in the age structure does not Granger cause the growth in
government expenditure; hence, the result shows that Wagners Law is not valid for Canada for
the time period 1961 till 2009 even after the demographic variable, dependency ratio, is
considered in the model.
R2
= 0.6929
CRDW=2.003721
AIC=5.40294
(24)
*** shows that the variable is significant at 1%.
** shows that the variable is significant at 5%.
* shows that the variable is significant at 10%.
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Our conclusion differs to that of Shelton (2007) who states that the relation between
government expenditure and GDP is formed due to the age structure in combination with social
security spending. However, the establishment of Wagners law in Canada cannot be perceived
when age structure is considered, since the age structure to a large extent is dependent on GDP
per capita in the long run as demonstrated by the theory of demographic transition (Caldwell,
1976). As a matter of fact, the current old age boom in Canada is a result of demographic
transition. The result shows that the main implication of the Law is undermined by its
characteristics, where dependency on age structure follows automatically when the government
provides services that are dependent on age, such as pension, child-care, free education and so
on.
IX. WAGNERS LAW AND UNEMPLOYMENT RATE
To my best knowledge, there are currently no empirical studies carried on Canada
relating Wagners Law and another demographic variable, unemployment rate. However, the
necessity of the respective variable to take a role in the model is seen, as it influences
government expenditure side through unemployment benefits. Shelton (2007) has found by
carrying out research on cross-country panel data from 1970 to 2000 that Wagners Law is
followed when unemployment in combination with electoral rules and redistributive transfers
affects the government spending.
From Figure 6, we can note that unemployment rate has an upward trend. The
recessionary period in the early 1980s and 1990s are captured in Figure 6 through the two peaks
during the respective time. The recession brought on in the United States by the collapse of the
dot combubble beginning in 2000, hurt the Toronto Stock Exchange but has affected Canada
only mildly. It is one of the few times Canada has avoided following the United States into a
recession. Hence, the slightly rise in the unemployment rate is noted in the early twenty-first
century from the figure below.
In our analysis, the null hypothesis is the presence of unit root. The critical values at 1%,
5% and 10% significance level for the ADF test is -3.594, -2.936 and -2.602 respectively. From
Table 2, we can deduce from the variables ADF test statistic that all three values lay at the
acceptance region of 1%, 5% and 10%. Hence, we cannot reject the null hypotheses of the
http://en.wikipedia.org/wiki/Early_2000s_recessionhttp://en.wikipedia.org/wiki/Dot_com_bubblehttp://en.wikipedia.org/wiki/Dot_com_bubblehttp://en.wikipedia.org/wiki/Dot_com_bubblehttp://en.wikipedia.org/wiki/Toronto_Stock_Exchangehttp://en.wikipedia.org/wiki/Toronto_Stock_Exchangehttp://en.wikipedia.org/wiki/Dot_com_bubblehttp://en.wikipedia.org/wiki/Early_2000s_recession -
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presence of unit roots; thus, the variables are non-stationary for the period 1961-2009. After first-
differencing the variable, the critical values at 1%, 5% and 10% obtained from ADF test is -
3.600, -2.938 and -2.604 respectively. According to Table 2, test statistic values suggest that the
variables are stationary in their first-difference. Hence, all three variables are integrated of order
one, orI(1).
Figure 6: Trend of Unemployment Rate for Canada from 1961-2009.
4
6
8
10
12
1960 1970 1980 1990 2000 2010
Year
Equation 25 represents the model after ln of government expenditure per capita is
regressed against ln of GDP per capita and unemployment rate.
ratentunemploymeNYNG _0197196.0)/ln(7125781.0288839.1)/ln( R= 0.9417
CRDW=1.218635
(3.99) (21.46)*** (4.45)*** (25)
Equation 25 shows that the log of government expenditure per capita and the log of GDP
per capita and unemployment rate are positively related. For every one percent increase in GDP
per capita would lead to 0.7125781 % increase in government expenditure per capita which is
lower than the coefficient found when OLS is run for ln (G/N) on ln (Y/N). . For every one
percent increase in government expenditure per capita would lead to 0.0197196 increases in
unemployment rate. The t-statistic for GDP per capita (shown in parentheses) is 21.46 and shows
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that GDP per capita is significant even at 1% significant level. The t-statistic for unemployment
rate is 4.45 and also shows that unemployment rate is significant at 1% significance level.
The MacKinnon critical value for the cointegrating equation of three variables without
trend using forty-nine observations at 1%, 5% and 10% levels of significance are -4.60176, -
3.9197 and -3.58055 respectively. The ADF test statistic for stationarity test of1
u
tis -8.507,
and PP test statistic is -6.292, and both the values do not lie at the acceptance region of 1%, 5%
and 10%. Hence, we can reject the null hypotheses of no cointegration, and the estimated
residual is stationary. Since there is evidence of the presence of cointegration in the model, we
now proceed to check the causality when unemployment rate is a part of the model. Granger
causality test is used to verify whether there is a causal relationship between real government
expenditure, real income and unemployment rate. We have considered the following model to be
used in our study to explain the government expenditure and national income:
(26)
Similar to the approach used in the previous section, we will rely on the significance of
of the above equation. When is significant then it implies that GDP along with the
unemployment rate Granger causes government expenditure which verifies Wagners hypothesis.
The optimal lag length orders of the variables (M, S, P) is found to be one.
R2
= 0.4386
CRDW=2.373403
AIC=5.3647
(27)
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From equation 27, we can deduce that the error correction term is not significant even at
the 10% significance level. Hence, the result provides us with evidence that GDP and
unemployment rate does not Granger cause government expenditure. In other words, the growth
of GDP along with the growth in the unemployment rate does not Granger cause the growth in
government expenditure; hence, the result shows that Wagners Law is not valid for Canada for
the time period 1961 till 2009 even after the demographic variable, unemployment rate, is
considered in the model.
X. CONCLUSION
The aim of this research is to add to the literature on Wagners Law on Canada for the
period 1961-2009. Among the theories of government growth, the preference towards Wagners
Law has been given primarily importance because of the positive attributes of the hypothesisitself. The Law is provided with scientific simplicity, and amplified the long-run characteristics
during the industrialization process. In our study, we have focused our attention at the two major
macroeconomic variables, government expenditure and national income, to explain Wagners
Law. We have implemented cointegration analysis through econometric procedure to explain the
long-run relationship between the respective variables. The research also sought to find evidence
of long-run relationship between these two variables when the demographic variables,
dependency ratio and unemployment rate, were taken into consideration.
We have used time series data to comprehend the purpose of our analysis. The time series
properties of the data were assessed using Augmented Dickey-Fuller test and Phillips-Perron
test. The tests found that both the variables along with the demographic variables were non-
stationary in level, but stationary in first differences; hence, we can conclude that the log of
government expenditure per capita and log of GDP per capita, and the demographic variables are
integrated of order one, or I(1). The Engel and Granger two-step cointegration approach was
employed to find evidence of long-run relationship existence between national income and
government expenditure. At first, the analysis was carried using the formulation suggested by
Gupta (1967), and later on checking the long-run relationship by controlling the particular
demographic variables. In this study, cointegration tests find evidence of long-run relationship
between income and expenditure for all the models in this paper.
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Granger causality test has been employed to check for evidence of relationship between
the variables in the short run. When tested for Musgrave (1969) formulation only, we find that
the relationship between government expenditure and national income is Keynesian where GDP
per capita is dependent on government expenditure per capita, but not Wagnerian where
government expenditure per capita is dependent on GDP per capita. One possible reason for the
Law being rejected during the period 1961-2009 is the restrictive fiscal policies implemented by
the government of Canada in order to cope with the augmenting national debt. Another possible
reason as stated by Afxentiou and Serletis (2002) is that the rejection of Wagners hypothesis
may be due to the changing structure of the Canadian economy which is changing the direction
towards service oriented sector. To end our discussion, we can conclude from our empirical
analysis that Wagners Law is not a conventionalized way that shows how the Canadian
economy behave in the long-run, nor it explains how government activity should perform.
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