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BigBen Chukwuma Ogbonna
Department of Economics, Ebonyi State University, Abakaliki, Nigeria

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 time-series econometric techniques, bordering on co-integration 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. Policy-wise, 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; co-integration; causality; government size; growth, OLS.


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 long-run 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 large-scale 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 long-run 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 long-run 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 ratio-income-elasticity 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 Rural-Agricultural to an Urban-Industrial one (Nagarajan and Spear, 1977)
Wagner’s law has been tested empirically in time-series and cross-sectional frameworks and, with few exceptions, the law has received strong support. In empirical analyses, country-specific 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. Cross-country studies have also become quite popular, thus, Ram (1987) includes 115 countries, Bohl (1996) investigates the G-7 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 1960-2006. The long-run 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 non-causality 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 long-run 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 long-run relationship between real per capita government expenditure and real per capita income and results for the short-run 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 IMF-International financial statistics (IFS) On-line (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 log-linear 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 = z

  (i) Unlike traditional econometric methodology, time-series econometrics methodology requires an analysis of the time-series 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 + gyt-i + a2t +  S bj ∆Yt-i-1 + 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 Dickey-Fuller (ADF) and Phillip-Perron (PP) unit root tests are employed to test the integration level and the possible co-integration among the variables. (Dickey and Fuller, 1981; Phillips and Perron, 1988).



j = 2

  (ii) Next, we employ Engle-Granger’s (1987) co-integration test to determine if the variables in

the system are co-integrated. The Engle-Granger procedure needs an estimation of the co-integrating regression equation. Thus, if there are n series, Yt1 . . . Ytn, the co-integrating 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 co-integrated and hence interrelated with each other in the long-run.

(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 long-run 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 1950-2008 periods are presented in table 1 with their means, standard deviation (SD) and coefficient of variation (CV).

Table 1: Summary statistics of employed variables.
















Std. Dev.









Coef. of variation












Sum Sq. Dev.






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 non-stationary 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 non-stationary at times has important econometric implication. Augmented Dickey-Fuller (ADF) and Phillips-Perron (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 Phillips-Perron tests procedures which compute a residual variance that is robust to auto-correlation are employed as an alternative to the ADF. According to the unit root test results, all the time-series 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 non-stationary and thus quiet suitable for purpose intended.

Co-integration 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 non-stationary, integrated of order one, but not co-integrated, the model cannot be estimated in levels. Instead, the variables in their first-difference 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 time-series. This is implemented using Granger’s causality test, and the null hypothesis, f-statistics and the p-values 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.
Utilizing annual data drawn from South Africa for the period of 1950-2008, 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 Augmented-Dickey 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 co-integration test to the regression model. The hypothesis of a long-run relationship between real income per capita (RYPCAP) and the share of real public expenditure in real gross domestic product (RGCYR) is investigated using Engle-Granger co-integration 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.


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Fig 1: Result of CUSUM test.
Table 2: Results of Augmented Dickey Fuller and Phillips Perron Unit Root Test



































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





Lags interval (in first differences): 1 to 1







Unrestricted Co integration Rank Test (Trace)

















No. of CE(s)



Critical Value

















At most 1















Trace test indicates no co integration at the 0.05 level

 * denotes rejection of the hypothesis at the 0.05 level

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



Unrestricted Co integration Rank Test (Maximum Eigenvalue)
















No. of CE(s)



Critical Value

















At most 1















 Max-eigenvalue 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): 




































Note: The test is performed using E-views 6.0 Econometric Package.


Table 4: Granger Causality Test Results.

Sample: 1950-2008



Lags: 1














Null Hypothesis:















LRYPCAP does not Granger Cause LRGCYR





LRGCYR does not Granger Cause LRYPCAP















Table 5: OLS Estimation Results.

Sample: 1950 2008



Included observations: 59















Std. Error



































    Mean dependent var


Adjusted R-squared


    S.D. dependent var


S.E. of regression


    Akaike info criterion


Sum squared resid


    Schwarz criterion


Log likelihood


    Hannan-Quinn criter.




    Durbin-Watson stat

















Note: The test is performed using E-views 6.0 Econometric package.