masters essay final draft

8/2/2019 Masters Essay Final Draft

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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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ii

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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17

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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18

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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19

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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20

(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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21

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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22

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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23

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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24

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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25

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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27

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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28

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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29

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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