
JOURNAL OF RESEARCH IN NATIONAL DEVELOPMENT VOLUME 7 NO 2, DECEMBER, 2009
TESTING WAGNER’S LAW OF GOVERNMENT SIZE FOR SOUTH AFRICA, 19502008
BigBen Chukwuma Ogbonna
Department of Economics, Ebonyi State University, Abakaliki, Nigeria
Email: bigbenogbonna@yahoo.com
Abstract
This paper presents an empirical analysis of Wagner’s law in the case of South Africa over the period 1950–2008. The paper uses modern timeseries econometric techniques, bordering on cointegration analysis to test the law’s proposition that in the course of economic development, government size in the GDP increases. The results of this study support the empirical validity of Wagner’s law for South Africa. In effect, the validity of Wagner’s law, which states that the growth of public expenditure is a function of increase in economic activity, is therefore verified for the South African economy. In addition, the long data sample ensures the reliability of the results in terms of economic significance and statistical inference. Absence of structural break and the stability of the time series data employed are verified by the results of the CUSUM conducted. Policywise, the results imply that development plans of South Africa must incorporate such fiscal policy measures that would guarantee commensurate growth in government revenue.
Keywords: Wagner’s law; cointegration; causality; government size; growth, OLS.
Introduction
Wagner’s law has been the subject of intensive and extensive investigations, in particular during the post second world war era, when public consumption declined in favour of the private activities development. The above law is of the notion that there is a longrun tendency for government activities to grow relative to economic activity (Wagner, 1890).More specifically; the law states that, during the process of economic development, government economic activities relative to private sector economic activities increase. Thus, higher levels of economic growth require higher levels of public expenditure. Wagner stated that during the industrialization process, as real income per capita of a nation increases, the share of public expenditures in total expenditure increases. According by him, three main reasons support this hypothesis: (1) during industrialization, the administrative and regulatory functions of the state would substitute public for private activity; (2) economic growth would result in increased need for cultural and welfare services, which are assumed to be income elastic; (3) state participation would be inevitable to provide the capital funds to finance largescale projects made to satisfy the technological needs of an industrialized society, where private sector lacks the capacity. In other words, Wagner’s law states that government grows because there is an increasing demand for public goods and for the control of externalities. In effect, the law also suggests that causality runs from national income to public consumption, indicating that public expenditure is considered as endogenous to the growth of national income.
Wagner’s law is predicated on a simple positive correlation between a nation’s gross domestic product (GDP) and government expenditure (G). This has generated different interpretations leading to introduction and empirical examination of several versions of the law since the 1960s (FERDA, 2003). Several commentators on Wagner's Law (see e.g. Musgrave, 1969) have claimed that it is unclear whether the law of expanding scale relates to the share of government in national income or just to the absolute level of government. To Timm (1961), this alleged ambiguity is unjustified as thorough assessment of Wagner's writings, convincingly demonstrates that Wagner had the relative growth in mind. In effect,
there seems to be a reasonable consensus in the literature that Wagner's Law should be interpreted as predicting an increasing relative share for the public sector in the total economy as per capita real income grows.. If G/GDP increases as GDP/N increases, the elasticity value for the relationship exceeds zero. Wagner’s law in functional forms, however, seems to be more controversial. See Peacock–Wiseman (1961), Musgrave (1969), Goffman and Mahar
(1971), Pryor (1968), Mann (1980), Goffman (1968), Gupta (1967) and Michas (1975). The final functional form is a Musgrave (1969) version, which expresses the share of government expenditure in gross domestic product (GE/GDP) as a function of income per capita (GDP/N) as follows:
GE/GDP= f (GDP/N)  (1)
Musgrave (1969) version which was also adopted by Ram (1986), Murthy (1993), Henrekson (1993) and Hsieh and Lai (1994), appears to represent what Wagner had in mind in his proposition and has more or less gained universal acceptance and application. Thus, this paper will follow the same path to investigate the validity of Wagner’s Law for the South African economy.
The remainder of this paper is, structured as follows. Section 2 data, variable definition and econometric methodology; Section 3 presents the econometric results and discussion and Section 4 the concluding remarks.
Synopsis of the literature
One of the frequently quoted stylized facts of public sector economics is that of” Wagner’s Law” about the longrun tendency for public expenditure to grow relative to some national income aggregate such as GDP. This implies that public expenditure can be treated as an outcome, or an endogenous factor, rather than a cause of growth in national income. On the other hand, Keynesian propositions treat public expenditure as an exogenous factor, which could be utilized as a policy instrument. In the former approach, the causality runs from national income to public expenditure whereas in the latter proposition, causality runs from public expenditure via domestic demand to national income (Afonso and Furceri, 2008). Evidence concerning this topic is not conclusive. Additionally, Lucas (1988) argues that public investment in education increases the level of human capital and this can be seen as a main source of longrun economic growth. Moreover, Barro (1990) mentions the importance of government expenditure in public infrastructure for economic growth and Romer (1990) stresses the relevance of research and development expenditure. Therefore, composition of public spending is also a relevant issue, and if the aim is to promote growth, the focus should be put on the more productive items of the budget, even if the balance between the various functional items of the budget can vary in accordance with country specifics.
The basic thrust of Wagner’s law is that the relative size of the public sector in the economy (G/DGP) has an inherent tendency to grow as per capita income (GDP/POP) increases. It is fair to say on balance that most of the time series studies have found the ratioincomeelasticity coefficients to be positive and statistically significant, by using
G/GDP + α + β {GDP/POP} + μi (2).
Thus, Wagner’s law has been validated, particularly for countries in the process of transition from RuralAgricultural to an UrbanIndustrial one (Nagarajan and Spear, 1977)
Wagner’s law has been tested empirically in timeseries and crosssectional frameworks and, with few exceptions, the law has received strong support. In empirical analyses, countryspecific studies are frequently used: for example, Henrekson (1993) for Sweden, Ashworth (1995) for the UK, Hondroyiannis and Papapetrou (1995) for Greece, Nomura (1995) for Japan and Park (1996) for South Korea. Crosscountry studies have also become quite popular, thus, Ram (1987) includes 115 countries, Bohl (1996) investigates the G7 countries and Anwar et al. (1996) analyze 88 countries. In addition to aggregate analyses, disaggregating of data is also noted in empirical studies of Wagner’s law. See, Bairam (1995), Asseery et al. (1999) and Burney (2002).
However, Ziramba (2008) tests Wagner's law by analysing the causal relationships between real government expenditure and real income for South Africa for the period 19602006. The longrun relationship between the two variables is tested using the autoregressive distributive lag approach to cointegration suggested by Pesaran. He went further to use the Granger noncausality test procedure developed by Toda and Yamamoto, which uses a vector autoregression model to test for the causal link between the two. Evidence of cointegration is sufficient to establish a longrun relationship between
government expenditure and income. However, support for Wagner's law would require unidirectional causality from income to government expenditure. The study does find a longrun relationship between real per capita government expenditure and real per capita income and results for the shortrun causality find bidirectional causality. Therefore on the basis of empirical results in this paper, one may tentatively conclude that Wagner's law finds no support in South Africa. The variables employed for this study appear not to be of universal application in testing the validity of Wagner’s Law and the results of Granger causality test may not a sufficient bench mark in determing wether or not Wagner’s Law is satisfied. On these notes, in this work we intend to employ econometric methodologies that has gained reasonable currency to test for the presence of Wagner’s Law in South African economy both for the purpose of providing further empirical literature for South Africa and enquiry into existing results in this direction.
Empirical methodology
Data and variable definition
The data we have employed for South African economy are annual figures covering the period 1950 – 2008. Following Musgrave (1969) version of Wagner’s law formulation, the variables are measured as follows: real income (RGDP) is proxied by the Gross Domestic Product deflated with the GDP deflector, real government expenditure (RG) IS proxied total annual public consumption deflected with annual GDP deflectors to adjust for inflation. Government size is defined as the ratio of real government expenditure to real gross domestic product (GCYR) and real per capita income, defined as gross economic activities of South Africa divided by the population (YPCAP). Data are obtained from IMFInternational financial statistics (IFS) Online (2009).
Model specification and estimation procedure
To investigate the relationship between government expenditure and economic activity, this paper adopts Musgrave (1969) final version of functional form of Wagner’s law which examines the relationship between government size in GDP and real per capita income. This can be written in linear natural logarithmic regression of the form:
LGCYRt = ao + a1LYPCAPt + ɛ (3)
where ao is the constant term, GCYR is the share of government expenditure in GDP as adjusted for inflation, YPCAP the per capita income, ɛ is the stochastic error representation, t, the time trend and L, the natural logarithm. The variables are expressed in logarithmic form because studies by Khan and Ross (1977) suggest that in modeling an aggregate import/export demand functions, the log linear specification is preferable to the linear formulation. Secondly, slope coefficients of loglinear model measure the elasticity of a dependent variable with respect to explanatory variables (Gujarati, 1995) and this suits exactly what we need for testing the validity of Wagner’s law for South Africa. The decision rule is that for Wagner’s law to hold, a1 is expected to be greater than zero.
The estimation procedure adopted in this study is in three stages
(i) Unlike traditional econometric methodology, timeseries econometrics methodology requires an analysis of the timeseries properties of the economic variables in a regression equation before any estimation for fear of spurious regression. To stem the problem of spurious regression, it is important that the time series properties of the data set employed in estimation of equation 3 is verified. It might seem reasonable to test for the presence of a unit root in the series using the most general of the models as:
∆Yt = a0 + gyti + a2t + S bj ∆Yti1 + et ………………………………… (4)
where y is the series; t is (trend factor); a’ is the constant term, et is the stochastic error term and P is the lag length. The Augmented DickeyFuller (ADF) and PhillipPerron (PP) unit root tests are employed to test the integration level and the possible cointegration among the variables. (Dickey and Fuller, 1981; Phillips and Perron, 1988).
(ii) Next, we employ EngleGranger’s (1987) cointegration test to determine if the variables in
the system are cointegrated. The EngleGranger procedure needs an estimation of the cointegrating regression equation. Thus, if there are n series, Yt1 . . . Ytn, the cointegrating regression is given by:
Yt1 = β0 + ∑ βjYtj + εt…………………………………………………………………. (5)
Residuals from the regression 3 are tested for the presence of a unit root using the ADF test. If the residuals, εt, from the regression are I (0), i.e. stationary, then variables are said to be cointegrated and hence interrelated with each other in the longrun.
(iii) Then we estimate equation 3 using ordinary least square (OLS) technique.
(iv) Finally, we run the Granger causality test to determine the direction of the cause and effect between the dependent and the explanatory variables.
Empirical evidence
In this section, empirical evidence to verify whether or not Wagner’s Law, the proposition that there is a longrun tendency for the public sector to grow relative to national income, holds for the South African economy employing the estimation procedures below.
Summary statistics
Data on all the employed variables for 19502008 periods are presented in table 1 with their means, standard deviation (SD) and coefficient of variation (CV).
Table 1: Summary statistics of employed variables.

LRGCYR 
LRYPCAP 
Mean 
0.150891 
272.5427 
Median 
0.154428 
284.9241 
Maximum 
0.203518 
353.8409 
Minimum 
0.093511 
177.5083 
Std. Dev. 
0.039356 
43.41861 
Skewness 
0.149204 
0.679632 
Kurtosis 
1.416361 
2.630583 
Coef. of variation 
0.260824 
0.159309 
JarqueBera 
6.384190 
4.877499 
Probability 
0.041086 
0.087270 
Sum 
8.902555 
16080.02 
Sum Sq. Dev. 
0.089838 
109340.2 
Observations 
59 
59 
Note: The test was performed using Eviews 6.0 econometric package.
Unit root tests
It is pertinent that we establish the time series properties of the employed variables for the period 1950 – 2008. Testing explicitly for the manifestations of nonstationary is of great essence in econometric analysis associated with time series data. In one way, it serves the first step in exploring the status of the data and in the other, because the presence of such nonstationary at times has important econometric implication. Augmented DickeyFuller (ADF) and PhillipsPerron (PP) unit root test procedures are employed in testing the integration level and the possible co integration among the variables (Dickey and Fuller, 1981, Phillips and Perron, 1988). With respect to the ADF test statistics, it is interesting to note that both the Akaike Information and the Schwarz Bayesian criteria for optimal lag length selection yield consistent results about the order of integration of the variables. The PhillipsPerron tests procedures which compute a residual variance that is robust to autocorrelation are employed as an alternative to the ADF. According to the unit root test results, all the timeseries variables appear to be stationary in their first differences rather than in their levels, i.e., they are both I (1). This by implication suggests that all the employed data
series are nonstationary and thus quiet suitable for purpose intended.
Cointegration test
Now, we proceed to test for co integration between the data series. We present this using the Johansen (1991) and Johansen and Juselius (1994) approaches to test for co integration employing Trace Test and Maximal Eigenvalue. The tests are based on the comparison of H0 (r=0) against the alternative H1 (r≠0), where “r” represents the number of co integrating vectors. Table 3 in the appendix reports the results from the co integration tests. Evidence from the results suggest that the null hypothesis of r = 0 between the variables cannot be rejected. The results further reveal that Wagner’s law is supported for South Africa since the normalized coefficient of real per capital income (rypcap) is positive. Since the two variables are nonstationary, integrated of order one, but not cointegrated, the model cannot be estimated in levels. Instead, the variables in their firstdifference form must be used for standard Granger (1969) causality test. Now, we investigate the direction of causality between the variables using Granger causality test. .
Granger causality test
The next step is to examine the direction of flow of response between the timeseries. This is implemented using Granger’s causality test, and the null hypothesis, fstatistics and the pvalues for each of the variables are as presented in table 4 in the appendix. It should be noted that Granger’s test lag selection is based on the AIC and SBC values which have suggested a short lag structure. The results indicate unidirectional significant effect flowing from real income per capita (RYPCAP) to the share of real public expenditure in real gross domestic product (RGCYR) without any long run feedback mechanism. Analysis of the causality further confirms the results of both the OLSEM and the co integration approach that Wagner’s Law holds for South Africa.
RYPCAP → RGCYR at 1 percent significant level.
Estimation of the model 3
Table 4 in the appendix presents the results of the model estimation of equation 3, using ordinary least square estimation method (OLSEM). The coefficient of the real per capital income (a1) is greater than zero. With recourse to the Decision Rule, the results suggest that Wagner’s Law hold’s for South Africa in support of the outcome of the cointegration approach. According to the CUSUM test results (fig.1) in the appendix, the recursive residuals are within the critical 5% significant lines, which indicate the absence of structural change, and that the stability of the parameter estimates is verified.
Conclusion
Utilizing annual data drawn from South Africa for the period of 19502008, this paper has examined the validity of Wagner’s Law based on co integration analysis, Granger causality and OLS estimation tests. For this purpose, empirical investigation of the stationary properties and the order of integration of the employed variables are conducted using AugmentedDickey Fuller (ADF) and Philips Peron tests. The results show that all the variables were non stationary in levels, but stationary in first differences. Since the variables are integrated of 1 (1), we applied cointegration test to the regression model. The hypothesis of a longrun relationship between real income per capita (RYPCAP) and the share of real public expenditure in real gross domestic product (RGCYR) is investigated using EngleGranger cointegration test and found to be false as evidence from the results suggest that the null hypothesis of r = 0 between the variables cannot be rejected. The results further reveal that Wagner’s law is supported for South Africa since the normalized coefficient of real per capital income (rypcap) is positive. The Granger causality test and OLS estimation results both still support the validity of Wagner’s Law for South Africa.
References
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Appendix
Fig 1: Result of CUSUM test.
Table 2: Results of Augmented Dickey Fuller and Phillips Perron Unit Root Test
Variables 
ADF 
PP 


Intercept 
Trend/Intercept 
Interest 
Trend/Intercept 
Decision 
LRGCYR 
067611(0) 
2.04441(0) 
0.58271(0) 
2.03301(0) 
1(0) 
∆LRGCYR 
6.5071(1)* 
6.4531(1)* 
6.6601(1)* 
6.6351(1)* 
1(1) 
LRYPCAP 
1.24081(0) 
1.67951(0) 
1.26571(0) 
1.54651(0) 
1(0) 
∆LRYPCAP 
4.23421(1)* 
4.19351(1)* 
423421(1)* 
4.19361(1)* 
1(1) 
Note: *, **, *** represent 1%, 5% and 10% significant levels respectively.
The test is performed using Eviews 6.0 Econometric Package.
Table 3: Results of Johansen Co integration Test
Sample (adjusted): 1952 2008 


Included observations: 57 after adjustments 

Trend assumption: Linear deterministic trend 

Series: LRGCYR LRYPCAP 


Lags interval (in first differences): 1 to 1 






Unrestricted Co integration Rank Test (Trace) 











Hypothesized 

Trace 
0.05 

No. of CE(s) 
Eigenvalue 
Statistic

Critical Value 
Prob.** 










None 
0.098154 
6.821638 
15.49471 
0.5985 
At most 1 
0.016233 
0.932887 
3.841466 
0.3341 










Trace test indicates no co integration at the 0.05 level 
* denotes rejection of the hypothesis at the 0.05 level 
**MacKinnonHaugMichelis (1999) pvalues 

Unrestricted Co integration Rank Test (Maximum Eigenvalue) 










Hypothesized 

MaxEigen 
0.05 

No. of CE(s) 
Eigenvalue 
Statistic 
Critical Value 
Prob.** 










None 
0.098154 
5.888751 
14.26460 
0.6275 
At most 1 
0.016233 
0.932887 
3.841466 
0.3341 










Maxeigenvalue test indicates no co integration at the 0.05 level 
* denotes rejection of the hypothesis at the 0.05 level
Unrestricted Co integrating Coefficients (normalized by b'*S11*b=I): 












LRGCYR 
LRYPCAP 




35.31778 
0.034273 




17.13312 
0.011107 
















Note: The test is performed using Eviews 6.0 Econometric Package.
Table 4: Granger Causality Test Results.
Sample: 19502008 


Lags: 1 













Null Hypothesis: 
Obs 
FStatistic 
Prob. 











LRYPCAP does not Granger Cause LRGCYR 
58 
8.18490 
0.0060 

LRGCYR does not Granger Cause LRYPCAP 
1.97878 
0.1651 













Table 5: OLS Estimation Results.
Sample: 1950 2008 


Included observations: 59 












Variable 
Coefficient 
Std. Error 
tStatistic 
Prob. 










LRYPCAP 
0.000647 
8.41E05 
7.698298 
0.0000 
C 
0.025488 
0.023196 
1.098851 
0.2765 










Rsquared 
0.509736 
Mean dependent var 
0.150891 
Adjusted Rsquared 
0.501134 
S.D. dependent var 
0.039356 
S.E. of regression 
0.027798 
Akaike info criterion 
4.294421 
Sum squared resid 
0.044044 
Schwarz criterion 
4.223996 
Log likelihood 
128.6854 
HannanQuinn criter. 
4.266930 
Fstatistic 
59.26380 
DurbinWatson stat 
0.092135 
Prob(Fstatistic) 
0.000000 













Note: The test is performed using Eviews 6.0 Econometric package.


