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ISSN-L: 2223-9553, ISSN: 2223-9944

Academic Research International Vol. 2, No. 2, March 2012




Abdur Rauf Dr. Abdul Qayum Prof Dr. Khair-uz Zaman

Gomal University, D.I.Khan, COMSAT, Wah Cantt. Gomal University, D.I.Khan,


abdur_rauf60@yahoo.com qayyum_72@yahoo.com drkzaman2001@yahoo.com


This study examine the applicability of Wagner’s law (1883)*, national income led growth in public expenditure in the long run, in case of Pakistan for the period of 1979-2009. Moreover the study investigates the direction of causality between public expenditure and national income. To investigate the long run relationship, the ARDL approach to cointegration and for the causality Todo and Yamamoto approach is used in the study. The study concludes that there is no long run relationship between public expenditure and national income at aggregate level. Furthermore, Todo and Yamamoto causality results asserted that there is no causality at all from directions, national income to public expenditure and public expenditure to national income.

Keywords: public expenditures, national income, cointegration and granger causality.


The relationship between public expenditure and national income was first presented by a German Economist Adolph Wagner in a way that tendency of rapid rise in government spending is also due to development in the economy. Wagner’s work is based on empirical observation in a number of industrialized countries. The basic assumption of Wagner’s law is that public expenditure growth continuously linked with growth of output.

Consistent and rapid growth in public expenditures has been seen in both developed and developing countries since the last century, particularly aftermath of World War II. Pakistan has been also experiencing rapid growth in public expenditures, consequently high ratio of government spending to GDP, since its formation. Table 1 is showing trend *Wagner, A (1883), “Three extracts on public finance”, translated and reprinted in R.A.Masgrave and A.T.

Peacock (eds), classics in the theory of public finance, London: McMillan, 1958.

of government spending, GDP, and ratio of government spending to GDP from period 1980-2009.

Table 1:GE = government expenditure (Millions), GDP = Gross Domestic Product (Millions).

Year GE* GDP* GE % of GDP

–  –  –

Above figures shows the increasing trend of government spending along with GDP. Government spending is an important fiscal policy indicator. On the average the ratio of government expenditure to GDP is 20% which is a handsome share. The significance of this study is to check and analyze is there any relationship between important fiscal indicator government spending and output in the long run in case of Pakistan. This study is different and improved from previous studies, ( Afzal M, 2010;

Jamshaid-ur-Rehman 2010, Rehman, Ahamd and Awan, 2007) firstly, in respect that all the previous studies empirically investigate relationship between public expenditure and output along with other control variables in their conventional form, that will work as robustness of previous studies. Secondly most recent time series technique such as ARDL approach to cointegration and Todo Yamamoto causality approach. The advantage of these techniques are easy to apply, no need of prior knowledge of unit root and particularly useful for small sample data such as in our case.

The study is divided in five sections. Section 1 is the introduction of the study. 2 theoretical background and literature review, 3rd methodology and data discussion, 4th empirical results and 5th conclusion.


Wagner’s law of increasing state activities based on historical facts, primarily of Germany, was presented by German economist, Adolph Wagner (1835-1917). According to Wagner there are inherent tendencies between the growth of economy and Gov. Activities with the result that the governmental sector grows faster than the economy. Several reasons given about this inherent long term tendency recorded in history, such as defence became increasingly more expensive over time, the state activities were increasing in their coverage like social securities, subsidies etc., the need to provide and expend the range of public goods received an increasing attention, growing population, increase urbanization, increasing prices etc. however, the vital point of Wagner’s law is only to the unidirectional causal link that is from national income to government expenditure. In contrast, Keynesian hypothesis (1936) emphasis over the unidirectional causal relationship that is from governmental sector is not clear whether Wagner was referring a)- absolute level of expenditures, b)the ratio of governmental expenditures, c)- proportion of the public sector in total economy. However, all the governments had exhibited the same tendency of increasing public expenditures irrespective of their levels and size. Five of the model specifications are predominant in the literature to test the

validity of Wagner’s law. These are as follows:

Model: RGE = f(RGDP) Peacock-Wiseman (1967) Model 2: RGE =f (RGDP)/N Goffman (1968) Model 3: RGE/N = f (RGDP/N) Gupta (1967) Michas (1975) Model 4: RGE/ RGDP =f (RGDP)/N Masgrave (1969) Model 5: RGE/RGDP = f(RGDP) Mann(1980) Here, RGE = real government expenditure, RGDP= real gross domestic product, N= population, RGDP/N = real GDP per capita, RGE/N = real expenditure per capita and RGE/RGDP= the ratio of real expenditure to real GDP. All five models are almost the same; the only difference is the size and measurement of the government expenditure and economic growth. Above models will be used in log linear functional form at the time of estimation.

Many empirical studies have been investigated the validity of Wagner’s law both at the single country and cross country level. These studies have different forms and different econometrics techniques to find out the relationship between government expenditures and national income. These findings are mixed and ambiguous about the validity of law.

Haung. Chiung-Ju 2006 (china and Taiwan), found that Wagner’s law does not hold for c china and Taiwan; Peters c. Amos 2007 (USA, Thailand, Barbados, and Haiti), results support the Wagner’s law;

Zaghini, Andera, 2008 (OECD countries), the empirical evidence provides indication of a structural

–  –  –

positive correlation between public spending and per capita GDP which is consistent with the so called Wagner’s law,; Karagianni, Stella 2008 (European Union economies), the results are very ambiguous and suggest that the validity or invalidity of Wagner’s law is very sensitive to the method applied, Ram R, 1987 (115 countries) found 60% support for the Wagner’s law in time series, while in cross sectional results seem to refute the hypothesis; Badigen, Muhlis and Cetintas, Hakan 2007 (turkey), neither Wagner law neither Keynes hypothesis is valid for Turkish case; Babatude, M. Adetunji, 2008 (Nigeria), empirical results suggest that there exist no long run relationship between government expenditure and output in Nigeria; Tang, T.C, 2009 (Malaysia), found empirical support of both Wagner’s law and Keynesian view in Malaysia over 1960-2005; Don, Webber, 2009 (New Zealand), the results suggest that output measures Granger- Cause the share of government expenditure in the long run, Singh B and Sahni, 1984 (India), found neither conformation for Wagner’s law nor for the Keynesian hypothesis; Rehamn, Ahmad and Awan, 2007 (Pakistan), the study found the long run relationship between government expenditure and per-capita income, Jamshidur Rehman, 2010 (Pakistan), the study found that there is a unidirectional causality running from GDP to government expenditure which support the Wagner’s law; Afzal M, 2010 (Pakistan), found o evidence about Wagner’s law and no causality between aggregate government expenditures and national income.


In this study the Bound testing Approach for cointegration (2001) is used to check the long run relationship between government expenditure and national income. Todo Yamamoto approach is used to check the causality between the two. However before going to estimate the data it is necessary to check the unit root presence in the data and for that in this study the ADF and PP test is used in order to know the order of integration of the series. Although, unit root test is not necessary condition for ARDL cointegration approach but if any of the series is I (2), then bound test for cointegration will not hold.

Bound Testing Approach for cointegration There are different approaches to measure the long run relationship between different variables through cointegration such as Engle Granger (1987), Johansen and Juelius (1990) and Gregory and Hansen (1996). ARDL approach which is used in this study was developed by Pesaran and Shin (1995 and 1998). There are few advantages of this approach over the others cointegration approaches like, it is simple as it is estimated through OLS, once the lag order of the model is selected, b- it can be used without knowing the prior order of integration of the variables, c- suitable for small data as compared to the other approaches of integration. Again, this approach will not hold if the order of integration is

2. The general form of the approach is ∆Zt =C0 + βt + ΠZt-1 +ΣҐj∆Zt-1 + ei…………… 1 Where Π and Ґj are matrices contain the long run multipliers and short run dynamics respectively. So according to equation 1, our model functional forms are, ∆IRGE = CO + β1IRGEt-1 + βIRGDPt-1 + Σφi∆IRGEt-I + Σφi∆IRGDPt-i + Ut……..2 ∆IRGE = CO + β1IRGEt-1 + βIRGDPt-1 + Σφi∆IRGEt-I + Σφi∆IRGDPt-i + Ut……...3 ∆IRGE = CO + β1IRGEt-1 + βIRGDPt-1 + Σφi∆IPRGEt-I + Σφi∆IRGDPt-i + Ut……...4 ∆IRGE = CO + β1IRGE_RGDPt-1 + βIRGDPt-1 + Σφi∆IRGE_RGDPt-i + Σφi∆IRGDPt-i + Ut……...5 ∆IRGE = CO + β1IRGE_RGDPt-1 + βIRGDPt-1 + Σφi∆IRGE_RGDPt-i + Σφi∆IRGDPt-i + Ut……...6 Bound testing approach: The first step in the ARDL approach is to estimate equation by OLS in order to test the long run relationship among the variables by conducting F- statistics through Wald restriction test.

–  –  –

HN : β1 = β2 = 0 (there is no cointegration) HA : β1 = β2 = 0 (There is cointegration) If the F-statistics value is above the upper bound value, the null hypothesis will be rejected that is there cointegration, irrespective of the order of integration of the variables. If the F-stat value falls below the lower bound value, null hypothesis accepted that there is no cointegration. And if F- stat value lies between upper and lower bound value then the result is inconclusive.

If null hypothesis rejected which mean there is long run relationship between said variables then we must proceed to second step which is to estimate ARDL long run model.

Zt =C0 + ΠZt-1 + ei……………………..7 In the third and final step, we obtain the short run dynamic parameters by estimating an error correction model.

∆Zt =C0 + ΣҐi∆Zt-1 +φecmt-1 + ei………………………….8 Where Ґi are the short run dynamic coefficients of the model convergence to equilibrium and φ is the speed of adjustment?

–  –  –

CONCLUSION In this study we have examined the validity of Wagner’s law for Pakistan over the period of 1979For this purpose we used ARDL approach to cointegration to check the Wagnerian long run relationship between government expenditure and national income. Five different versions of Wagner’s law taken into account. But no cointegration found any of the five versions, which reveals that there is no long run relationship between government expenditure and national income. We also examined causality through Toda and Yamamoto approach and found that there growth does not cause expenditure nor Gov.Expenditure does cause income. The results are very much according to expectations. Although government spending has increasing trend along with output but increasing government spending is not merely due to growth in output in case of Pakistan but there are other important factors such as ever increasing defence expenditure, interest payments, high population growth rate, lack of developed private sectors, political instability etc. we may conclude that there are some other important factors/ variables which cause to rapid increase in government expenditures over the long period of time in case of Pakistan. Finally, neither Wagner’s law nor Keynesian hypothesis holds in case of Pakistan.

Copyright © 2012 SAVAP International www.journals.savap.org.pk www.savap.org.pk 537 ISSN-L: 2223-9553, ISSN: 2223-9944 Academic Research International Vol. 2, No. 2, March 2012 REFERENCES Afzal, M. (2010),.Wagner’s law in Pakistan: Another look, journal of economics and international finance vol.2 (1) pp. 012-019.

Babatunde m. Adetunji (2008). A bound testing analysis of Wagner’s law in Nigeria: 1970-2006, department of economics, university of Ibadan, Nigeria.

Cetintas and Bagdigen (2008). Causality between public expenditure and economic growth: Turkish case, journal of economics and social research 6(1), 53-72.

DemirbasSafa (1999). Cointegration analysis-causality testing and Wagner’s law: the case of Turkey, 1950-1990, annual meeting of the European public choice society, Lisbon (April: 7-10, 1999).

Dicky, D.A. and Fuller, W.A. (1979). “Distribution of the Estimators for Autoregressive time series with a Unit root” journal of the American Statistical Association 74(366): 427-431.

Huang Chiung-Ju (2006). Government Expenditure in China and Taiwan: Do they follow Wagner’s law? Journal of economics development, vol. 31(2), December 2006.

Karagianni Stella (2008). testing Wagner’s Law for the European Union Economies, journal of Applied Business Research vol.18 (4).

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