An Examination of the Validity of Wagner’s Public Expenditure Growth and Economic Growth in Nigeria (1990 – 2010)

AN EXAMINATION OF THE VALIDITY OF WAGNER’S PUBLIC EXPENDITURE GROWTH AND ECONOMIC GROWTH IN NIGERIA (1990 – 2010).

Introduction In the nineteenth century, public expenditure under the influence of the classical economists, played a limited role in economic activity. There was neither any sound classification of government expenditure nor any standard laid on which all such expenditures should be based. However, in the latter part of the nineteenth century, Wagner (1883) observed that there exists a relationship between economic growth and public spending. This observation was later formulated as ‘Wagner’s Law of Increasing State Activities’. The fundamental idea behind this relationship is that the growth in public expenditure is a natural consequence of economic growth. In other words, the percentage share of public expenditure increases with an increase in gross domestic product. That is, the growth elasticity of public expenditure is greater than one. According to Wagner, the reason behind the expansion of state activities is a practical approach and is not based upon any formula. Rowley and Tollison (1994) in their study compared the Wagner’s law with the principle of comparative advantage. In their opinion, ‘Wagner’s law explains the complementarity between the growth of the industrial economy and the associated growth in demand for public services of an economic character (such as transport and communication networks, waste disposal, etc.) undertaken ordinarily by the government agencies. When the comparative advantage of government declines, the share of public expenditure in total GDP also declines (quoted in Peacock and Scott, 2000). Nigeria as a country is blessed with an abundance of resources – human and material. Over the years, these resources have been put to use leading to economic growth. In the same vein, government expenditure has also increased tremendously. The researcher thus asks: Is there a long-run equilibrium between economic growth and government expenditure in Nigeria within the period 1990 and 2010? To this end, the null hypothesis is: Ho: µ: There is no long-run equilibrium between government expenditure and economic growth in Nigeria. This work intends to examine these growths and see if they comply with the Wagner’s law of expanding State spending.
Theoretical Framework Wagner (1883) in his law of increasing state activities states that there is a persistent tendency both towards an ‘extensive’ and an ‘intensive’ increase in the functions of the state. New functions are continually being undertaken and old ones are being performed more efficiently and on an extended scale that increases the spending of the Government. Hence, more and more public expenditure is resorted for performing these activities. Thus, social progress brought an increase in state activity which in turn meant more government expenditure (Henrekson, 1993). Wagner had given three main reasons of increasing government expenditure with economic growth. Firstly, with economic growth, industrialization and modernization would take place which will diminish the role of public sector for private one. This continuous diminishing share of the public sector in economic activity leads to more government expenditure for regulating the private sector. For example, saving the labor class from exploitation (in the private sector) would require additional expenditure on contractual enforcement as well as on law and order which will lead to increase in public expenditure. Secondly, the rise in real income would lead to more demand for basic infrastructure particularly education and health facilities and, as Wagner asserts, it is the government that provides these facilities more efficiently than the private sector. Finally, to remove monopolistic tendencies in a country and to enhance economic efficiency in that sector where lumpy investment is required (such as railways), government should come forward and invest. Such action by the government will again increase government spending (Bird, 1971). As noted by Dutt and Ghosh (1997), Wagner did not present his law in mathematical form. Wagner also was not explicit in the formulation of his hypothesis. Hence, over the years, different authors used different mathematical forms for testing this law. There are at least six versions of this law (see Appendix 1) which have been empirically investigated by different economists. The earliest and simplest version of this law was given by Peacock and Wiseman in 1961 by using the following double log equation from which the elasticity estimates were derived:
LNGE = a + bLNGDP (1) This mathematical version, however, did not take into account the effect of increase in population. To account for this increase, Gupta (1967) made use of the following relation for empirically testing the validity of Wagner’s law:
LN(GE / P) = a + bLN(GDP / P) (2) According to him, Wagner’s law may be interpreted as the one wherein growth in real per capita government expenditure (GE/P) is dependent upon the growth in real GDP per capita (GDP/P). In addition, Goffman (1968) gave the following mathematical form, known as the absolute version of the law:
LN(GE) = a + bLN(GDP / P) (3)
In all models stated above, Wagner’s law holds true in case the value of slope coefficient (b) i.e., elasticity, is more than unity. Pryor (1969) gave an explanation of this law similar to the one postulated by Peacock and Wiseman (1961). This he did by using government consumption expenditure (GCE) instead of total government expenditure (GE) as a dependent variable.
LNGCE = a + bLNGDP (4) While reviewing Wagner’s law, Timm (1961) concluded that Wagner had relative growth in mind. Therefore, the law should be interpreted in a relative sense as one of predicting an increasing relative share of public expenditure as per capita real income grows (Henrekson, 1993). Thus, Musgrave (1969) has explained the growth in public expenditure in the relative sense by using the following relation:
LN (NGE / NGDP) = a + bLN (GDP / P) (5) According to him, the growth in the share of nominal government expenditures in nominal GDP (NGE/NGDP) depends upon the real GDP per capita (GDP/P). Mann (1980) also interpreted the law in relative sense. He used the real GDP instead of real GDP per capita as an independent variable. The relation was:
LN (NGE / NGDP) = a + bLNGDP (6) Thus, in the case of both versions (Musgrave and Mann Versions), Wagner’s law holds true; the value of slope coefficient (b) exceeds zero i.e., the elasticity is greater than zero (Henrekson, 1993). It should be noted, however, that there is no objective criterion to decide which of the six versions is the most appropriate. Therefore, following Peacock and Wiseman (1961), the earliest and simplest of the six versions of Wagner’s law was used to test the validity of the law in Nigeria. The regression form of all six versions of Wagner’s law is presented in Appendix 1.
Empirical Literature However, a number of studies have empirically examined the Wagner’s law and have given conflicting results that differ from country to country. In the case of Turkey, either tested for an earlier period (i.e. 1950-1990) by Demirbas (1999), or for a later period (i.e. 1965 - 2000) by Bagdigen and Centinas (2003), no empirical support for Wagner’s law was found. In case of Nigeria, for the period 1970-2001, Olomola (2004) confirms the Wagner’s hypothesis both in short as well as in the long-run. But a study by Babatunde (2008) on a group of four countries including Nigeria for the period 1970-2005 did not find any empirical support for this law. In the case of United Kingdom, Chrystal and Alt (1979) and Yuk (2005) found no empirical support for Wagner’s law. But Mann (1980), in case of Mexico, using time series data for the period 1925-1976 found strong support for this law. Likewise, whereas the studies by Gupta (1967), Goffman and Mahar (1971) and Bird (1971) supported the Wagner hypothesis, the studies by Wagner and Weber (1977) and Ram (1986) refuted the validity of Wagner’s inference. Among the few studies that endeavored to examine the validity of Wagner’s law in the case of Indian economy, some supported the existence of Wagner’s law [Singh and Sahni (1984), Lalvani (1995), Singh (1997), Sahoo (2001)] while some refuted its existence [Bhat et al. (1991) and Mohsin et al. (1995)]. As Henrekson (1992) pointed out, the test of Wagner’s law should focus on time series behavior of public expenditure in a country for as long the time period as possible rather than on a cross-section of countries at different income levels. Therefore, the present study attempts to test the validity of Wagner’s law in the case of Nigeria using time series data spanning over the period 1990 – 2010.

Data and Methodology The data for this work was culled from CBN Statistical Bulletin (Vol. 21) of 2011. Government expenditure is probably the most significant and practical measure of the State’s activity, while Gross Domestic Product (GDP) is the most significant measure of economic growth. Furthermore, the dependent variable (government expenditure) was decomposed into Government Capital Expenditure (GCE) and Government Recurrent Expenditure (GRE). This was done to isolate the specific relationship between each of these components of government expenditure and economic growth. We now have the following set of equations:
LnGCE = α + βLnGDP + Ut (7a)
LnGRE = α + βLnGDP + Ut (7b) where α = constant; β = coefficient of parameter; GDP = Gross Domestic Product; GCE = Government Capital Expenditure; and, GRE = Government Recurrent Expenditure. The first step in our empirical work is to determine the degree of integration of each variable using the Augmented Dickey Fuller (ADF) unit root tests. However, because the ADF has its shortcomings that are remedied by the Philip-Peron (PP) test, we also conduct the PP unit root test alongside the ADF. The second step is to test for a cointegration relationship between/among the relevant variables. The existence of cointegration will lead to the application of an Error Correction Mechanism (ECM) to tie the short-run behaviors of government expenditure to its long-run pattern. All econometric techniques were carried out using econometric package E-Views 4.1 version.
Findings and Analyses Having employed the ADF and PP unit root tests, the following results were obtained:

Table 1: Summary of ADF Unit Root Test with Trend and Intercept
|Series |ADF Test Statistic |5% Critical Values |10% Critical Values |Order |Remarks |
|GDP |-4.809276 |-3.6746 |-3.2762 |1(1) |Stationary |
|GCE |-3.938888 |-3.6746 |-3.2762 |1(1) |Stationary |
|GRE |-3.925596 |-3.6746 |-3.2762 |1(1) |Stationary |

Table 2: Summary of PP Unit Root Test with Trend and Intercept
|Series |PP Test Statistic |5% Critical Values |10% Critical Values |Order |Remarks |
|GDP |-4.809276 |-3.6746 |-3.2762 |1(1) |Stationary |
|GCE |-3.938888 |-3.6746 |-3.2762 |1(1) |Stationary |
|GRE |-3.925596 |-3.6746 |-3.2762 |1(1) |Stationary |

The above results show that statistical data on Gross Domestic Product (GDP), Government Capital Expenditure (GCE) and Government Recurrent Expenditure (GRE) are integrated of the same order: 1(1). In other words, the time series data were differenced once to make them stationary, thus ruling out the incidence of a spurious regression. Furthermore, the test statistics in both cases (ADF and PP tests) were found to be greater than the critical values at the 5% and 10% levels of significance. Therefore, we can conclude that the series are stationary at first difference. The Johansen cointegration test carried out on the statistical data for Government Capital Expenditure (GCE) and Gross Domestic Product (GDP) revealed the following result (please refer to equation 7a):
Table 3: Johansen Cointegration Test Result for GCE and GDP
|Hypothesized No. of CE(s) |Eigenvalue |Trace Statistic |5 Percent Critical Value |1 Percent Critical Value |
|None * |0.474200 |18.19656 |15.41 |20.04 |
|At most 1 * |0.270122 |5.982685 |3.76 |6.65 |
| *(**) denotes rejection of the hypothesis at the 5%(1%) level |
| Trace test indicates 2 cointegrating equation(s) at the 5% level |
| Trace test indicates no cointegration at the 1% level |

From the result above, the tested variables are cointegrated at 5% level of significance and not cointegrated at 1% level of significance. This is because in the case of the former, the trace statistics (18.19656 & 5.982685) are greater than the 5% critical values (15.41 & 3.76) in absolute terms; while in the case of the latter, the trace statistic (18.19656 & 5.982685) are less than the 1% critical value (20.04 & 6.65) in absolute terms. The null hypothesis of no cointegration between these variables is rejected. We therefore conclude that there is a long-run equilibrium relationship between economic growth and government capital expenditure in Nigeria. The statistical data for Government Recurrent Expenditure (GRE) and Gross Domestic Product (GDP) revealed the following result when subjected to the Johansen cointegration test (please refer to equation 7b):
Table 4: Johansen Cointegration Test Result for GRE and GDP
|Hypothesized No. of CE(s) |Eigenvalue |Trace Statistic |5 Percent Critical Value |1 Percent Critical Value |
|None ** |0.871191 |41.89135 |15.41 |20.04 |
|At most 1 |0.143912 |2.952265 |3.76 |6.65 |
|*(**) denotes rejection of the hypothesis at the 5%(1%) level |
|Trace test indicates 1 cointegrating equation(s) at both 5% and 1% levels |

The result above indicates that there is, at least, one cointegrating equation at both the 5% and 1% levels of significance. This is because the trace statistic (41.89135) is greater than the 5% critical value (15.41) and 1% critical value (20.04) in absolute terms. In this case too, we reject the null hypothesis of no cointegration between these variables and conclude that there is a long-run equilibrium relationship between government recurrent expenditure and economic growth in Nigeria.
CONCLUSION AND POLICY RECOMMENDATIONS The major objective of this study was to test the validity of Wagner’s law of ‘expanding state spending’ on Nigeria. The test results obtained supports the law and holds that economic growth has led to increased government expenditure in Nigeria (both recurrent and capital). This agrees with the findings of Olomola (2004) but is at variance with the work of Babatunde (2008). As long as such expenditures serve to provide public goods, ensure efficiency in the system and protect the populace from exploitation by the private sector, it is a welcome development. Therefore, government should strengthen her supervisory and regulatory agencies and continue to invest in the provision of public goods.

REFERENCES
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Chrystal, A. and Alt, J. (1979). “Endogenous Government Behaviour: Wagner’s Law of Gotter Dammerung?” in Cook, S.T. and Jackson, P.M. (eds), Current Issues in Fiscal Policy. Oxford: Martin Robertson.
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Goffman, I. J. and Mahar, D. J. (1971). “The Growth of Public Expenditures in Selected Developing Nations: Six Caribbean Countries 1940-65”. Public Finance, Vol. 26, No. 1, pp. 57-74.
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APPENDIX 1
Regression Form of Six Versions of Wagner’s Law
|S/No |Version |Regression Equation |
|Absolute Versions |
|1. |Peacock-Wiseman (1961) |LNGE = a + bLNGDP + ut |
|2. |Gupta (1967) |LN (GE / P) = a + bLN (GDP / P) + ut |
|3. |Goffman (1968) |LNGE = a + bLN (GDP / P) + ut |
|4. |Pryor (1969) |LNGCE = a + bLNGDP + ut |
|Relative Versions |
|5. |Musgrave (1969) |LN (NGE / NGDP) = a + bLN (GDP / P) + ut |
|6. |Mann (1980) |LN (NGE / NGDP) = a + bLNGDP+ut |
|Source: Demirbas (1999) |

APPENDIX 2 DATA FOR ANALYSES
|YEAR |GDP |GCE |GRE |
|1990 |267,549.99 |24,048.60 |36,219.60 |
|1991 |312,139.74 |28,340.90 |38,243.50 |
|1992 |532,613.83 |39,763.30 |53,034.10 |
|1993 |683,869.79 |54,501.80 |136,727.10 |
|1994 |899,863.22 |70,918.30 |89,974.90 |
|1995 |1,933,211.55 |121,138.30 |127,629.80 |
|1996 |2,702,719.13 |212,926.30 |124,491.30 |
|1997 |2,801,972.58 |269,651.70 |158,563.50 |
|1998 |2,708,430.86 |309,015.60 |178,097.80 |
|1999 |3,194,014.97 |498,027.60 |449,662.40 |
|2000 |4,582,127.29 |239,450.90 |461,600.00 |
|2001 |4,725,086.00 |438,696.50 |579,300.00 |
|2002 |6,912,381.25 |321,378.10 |696,800.00 |
|2003 |8,487,031.57 |241,688.30 |984,300.00 |
|2004 |11,411,066.91 |351,300.00 |1,032,700.00 |
|2005 |14,572,239.12 |519,500.00 |1,223,700.00 |
|2006 |18,564,594.73 |552,385.80 |1,290,201.90 |
|2007 |20,657,325.00 |759,323.00 |1,589,270.00 |
|2008 |24,296,329.29 |1,123,458.00 |2,117,362.00 |
|2009 |24,794,238.66 |1,152,796.50 |2,300,194.30 |
|2010 |29,108,020.00 |883,874.50 |3,310,343.38 |

Source: CBN Statistical Bulletin, Vol. 21 (2011)

APPENDIX 3
UNIT ROOT TESTS
ADF UNIT ROOT TEST RESULT ON GDP WITH TREND AND INTERCEPT
|ADF Test Statistic |-4.809276 | 1% Critical Value* |-4.5348 |
| | | 5% Critical Value |-3.6746 |
| | | 10% Critical Value |-3.2762 |
|*MacKinnon critical values for rejection of hypothesis of a unit root. |
| | | | | |
| | | | | |
|Augmented Dickey-Fuller Test Equation |
|Dependent Variable: D(GDP,2) |
|Method: Least Squares |
|Date: 10/17/12 Time: 02:52 |
|Sample(adjusted): 1992 2010 |
|Included observations: 19 after adjusting endpoints |
|Variable |Coefficient |Std. Error |t-Statistic |Prob. |
|D(GDP(-1)) |-1.221722 |0.254034 |-4.809276 |0.0002 |
|C |-736206.5 |540149.1 |-1.362969 |0.1918 |
|@TREND(1990) |230726.8 |60130.83 |3.837080 |0.0015 |
|R-squared |0.594943 | Mean dependent var |224694.3 |
|Adjusted R-squared |0.544310 | S.D. dependent var |1501010. |
|S.E. of regression |1013254. | Akaike info criterion |30.63917 |
|Sum squared resid |1.64E+13 | Schwarz criterion |30.78829 |
|Log likelihood |-288.0721 | F-statistic |11.75028 |
|Durbin-Watson stat |1.843186 | Prob(F-statistic) |0.000725 |

ADF UNIT ROOT TEST RESULT ON GCE WITH TREND AND INTERCEPT
|ADF Test Statistic |-3.938888 | 1% Critical Value* |-4.5348 |
| | | 5% Critical Value |-3.6746 |
| | | 10% Critical Value |-3.2762 |
|*MacKinnon critical values for rejection of hypothesis of a unit root. |
| | | | | |
| | | | | |
|Augmented Dickey-Fuller Test Equation |
|Dependent Variable: D(GCE,2) |
|Method: Least Squares |
|Date: 10/17/12 Time: 02:53 |
|Sample(adjusted): 1992 2010 |
|Included observations: 19 after adjusting endpoints |
|Variable |Coefficient |Std. Error |t-Statistic |Prob. |
|D(GCE(-1)) |-1.174926 |0.298289 |-3.938888 |0.0012 |
|C |22406.25 |83722.66 |0.267625 |0.7924 |
|@TREND(1990) |3001.257 |7170.255 |0.418570 |0.6811 |
|R-squared |0.505213 | Mean dependent var |-14379.70 |
|Adjusted R-squared |0.443364 | S.D. dependent var |217067.3 |
|S.E. of regression |161949.7 | Akaike info criterion |26.97190 |
|Sum squared resid |4.20E+11 | Schwarz criterion |27.12102 |
|Log likelihood |-253.2330 | F-statistic |8.168560 |
|Durbin-Watson stat |1.782345 | Prob(F-statistic) |0.003592 |

ADF UNIT ROOT TEST RESULT ON GRE WITH TREND AND INTERCEPT
|ADF Test Statistic |-3.925596 | 1% Critical Value* |-4.5348 |
| | | 5% Critical Value |-3.6746 |
| | | 10% Critical Value |-3.2762 |
|*MacKinnon critical values for rejection of hypothesis of a unit root. |
| | | | | |
|Augmented Dickey-Fuller Test Equation |
|Dependent Variable: D(GRE,2) |
|Method: Least Squares |
|Date: 10/17/12 Time: 02:54 |
|Sample(adjusted): 1992 2010 |
|Included observations: 19 after adjusting endpoints |
|Variable |Coefficient |Std. Error |t-Statistic |Prob. |
|D(GRE(-1)) |-1.593515 |0.405930 |-3.925596 |0.0012 |
|C |-187383.7 |98953.74 |-1.893649 |0.0765 |
|@TREND(1990) |39120.06 |10367.61 |3.773297 |0.0017 |
|R-squared |0.526955 | Mean dependent var |53059.22 |
|Adjusted R-squared |0.467824 | S.D. dependent var |253095.5 |
|S.E. of regression |184634.1 | Akaike info criterion |27.23408 |
|Sum squared resid |5.45E+11 | Schwarz criterion |27.38320 |
|Log likelihood |-255.7237 | F-statistic |8.911710 |
|Durbin-Watson stat |1.235280 | Prob(F-statistic) |0.002507 |

PP UNIT ROOT TEST RESULT ON GDP WITH TREND AND INTERCEPT
|PP Test Statistic |-4.809276 | 1% Critical Value* |-4.5348 |
| | | 5% Critical Value |-3.6746 |
| | | 10% Critical Value |-3.2762 |
|*MacKinnon critical values for rejection of hypothesis of a unit root. |
| | | | | |
|Lag truncation for Bartlett kernel: 0 | ( Newey-West suggests: 2 ) |
|Residual variance with no correction |8.65E+11 |
|Residual variance with correction |8.65E+11 |
| | | | | |
| | | | | |
|Phillips-Perron Test Equation |
|Dependent Variable: D(GDP,2) |
|Method: Least Squares |
|Date: 10/17/12 Time: 07:25 |
|Sample(adjusted): 1992 2010 |
|Included observations: 19 after adjusting endpoints |
|Variable |Coefficient |Std. Error |t-Statistic |Prob. |
|D(GDP(-1)) |-1.221722 |0.254034 |-4.809276 |0.0002 |
|C |-736206.5 |540149.1 |-1.362969 |0.1918 |
|@TREND(1990) |230726.8 |60130.83 |3.837080 |0.0015 |
|R-squared |0.594943 | Mean dependent var |224694.3 |
|Adjusted R-squared |0.544310 | S.D. dependent var |1501010. |
|S.E. of regression |1013254. | Akaike info criterion |30.63917 |
|Sum squared resid |1.64E+13 | Schwarz criterion |30.78829 |
|Log likelihood |-288.0721 | F-statistic |11.75028 |
|Durbin-Watson stat |1.843186 | Prob(F-statistic) |0.000725 |

PP UNIT ROOT TEST RESULT ON GCE WITH TREND AND INTERCEPT
|PP Test Statistic |-3.938888 | 1% Critical Value* |-4.5348 |
| | | 5% Critical Value |-3.6746 |
| | | 10% Critical Value |-3.2762 |
|*MacKinnon critical values for rejection of hypothesis of a unit root. |
| | | | | |
|Lag truncation for Bartlett kernel: 0 | ( Newey-West suggests: 2 ) |
|Residual variance with no correction |2.21E+10 |
|Residual variance with correction |2.21E+10 |
| | | | | |
| | | | | |
|Phillips-Perron Test Equation |
|Dependent Variable: D(GCE,2) |
|Method: Least Squares |
|Date: 10/17/12 Time: 07:33 |
|Sample(adjusted): 1992 2010 |
|Included observations: 19 after adjusting endpoints |
|Variable |Coefficient |Std. Error |t-Statistic |Prob. |
|D(GCE(-1)) |-1.174926 |0.298289 |-3.938888 |0.0012 |
|C |22406.25 |83722.66 |0.267625 |0.7924 |
|@TREND(1990) |3001.257 |7170.255 |0.418570 |0.6811 |
|R-squared |0.505213 | Mean dependent var |-14379.70 |
|Adjusted R-squared |0.443364 | S.D. dependent var |217067.3 |
|S.E. of regression |161949.7 | Akaike info criterion |26.97190 |
|Sum squared resid |4.20E+11 | Schwarz criterion |27.12102 |
|Log likelihood |-253.2330 | F-statistic |8.168560 |
|Durbin-Watson stat |1.782345 | Prob(F-statistic) |0.003592 |

PP UNIT ROOT TEST RESULT ON GRE WITH TREND AND INTERCEPT
|PP Test Statistic |-3.925596 | 1% Critical Value* |-4.5348 |
| | | 5% Critical Value |-3.6746 |
| | | 10% Critical Value |-3.2762 |
|*MacKinnon critical values for rejection of hypothesis of a unit root. |
| | | | | |
|Lag truncation for Bartlett kernel: 0 | ( Newey-West suggests: 2 ) |
|Residual variance with no correction |2.87E+10 |
|Residual variance with correction |2.87E+10 |
| | | | | |
| | | | | |
|Phillips-Perron Test Equation |
|Dependent Variable: D(GRE,2) |
|Method: Least Squares |
|Date: 10/17/12 Time: 07:35 |
|Sample(adjusted): 1992 2010 |
|Included observations: 19 after adjusting endpoints |
|Variable |Coefficient |Std. Error |t-Statistic |Prob. |
|D(GRE(-1)) |-1.593515 |0.405930 |-3.925596 |0.0012 |
|C |-187383.7 |98953.74 |-1.893649 |0.0765 |
|@TREND(1990) |39120.06 |10367.61 |3.773297 |0.0017 |
|R-squared |0.526955 | Mean dependent var |53059.22 |
|Adjusted R-squared |0.467824 | S.D. dependent var |253095.5 |
|S.E. of regression |184634.1 | Akaike info criterion |27.23408 |
|Sum squared resid |5.45E+11 | Schwarz criterion |27.38320 |
|Log likelihood |-255.7237 | F-statistic |8.911710 |
|Durbin-Watson stat |1.235280 | Prob(F-statistic) |0.002507 |

APPENDIX 4
COINTEGRATION TESTS
Johansen Cointegration Test on GCE and GDP
|Date: 10/18/12 Time: 06:34 |
|Sample(adjusted): 1992 2010 |
|Included observations: 19 after adjusting endpoints |
|Trend assumption: Linear deterministic trend |
|Series: GCE GDP |
|Lags interval (in first differences): 1 to 1 |
| | | | | |
|Unrestricted Cointegration Rank Test |
|Hypothesized | |Trace |5 Percent |1 Percent |
|No. of CE(s) |Eigenvalue |Statistic |Critical Value |Critical Value |
|None * | 0.474200 | 18.19656 | 15.41 | 20.04 |
|At most 1 * | 0.270122 | 5.982685 | 3.76 | 6.65 |
| *(**) denotes rejection of the hypothesis at the 5%(1%) level |
| Trace test indicates 2 cointegrating equation(s) at the 5% level |
| Trace test indicates no cointegration at the 1% level |
| | | | | |
|Hypothesized | |Max-Eigen |5 Percent |1 Percent |
|No. of CE(s) |Eigenvalue |Statistic |Critical Value |Critical Value |
|None | 0.474200 | 12.21387 | 14.07 | 18.63 |
|At most 1 * | 0.270122 | 5.982685 | 3.76 | 6.65 |
| *(**) denotes rejection of the hypothesis at the 5%(1%) level |
| Max-eigenvalue test indicates no cointegration at both 5% and 1% levels |
| | | | | |
| Unrestricted Cointegrating Coefficients (normalized by b '*S11*b=I): |
|GCE |GDP | | | |
|-8.83E-06 | 4.69E-07 | | | |
| 5.96E-06 |-9.69E-08 | | | |
| | | | | |
| Unrestricted Adjustment Coefficients (alpha): |
|D(GCE) | 45045.85 |-62420.80 | | |
|D(GDP) | 664808.2 | 435746.0 | | |
| | | | | |
|1 Cointegrating Equation(s): |Log likelihood |-539.2233 | |
|Normalized cointegrating coefficients (std.err. in parentheses) |
|GCE |GDP | | | |
| 1.000000 |-0.053150 | | | |
| | (0.00561) | | | |
| | | | | |
|Adjustment coefficients (std.err. in parentheses) |
|D(GCE) |-0.397849 | | | |
| | (0.29447) | | | |
|D(GDP) |-5.871650 | | | |
| | (2.49078) | | | |

Johansen Cointegration Test on GRE and GDP
|Date: 10/18/12 Time: 07:14 |
|Sample(adjusted): 1992 2010 |
|Included observations: 19 after adjusting endpoints |
|Trend assumption: Linear deterministic trend |
|Series: GRE GDP |
|Lags interval (in first differences): 1 to 1 |
| | | | | |
|Unrestricted Cointegration Rank Test |
|Hypothesized | |Trace |5 Percent |1 Percent |
|No. of CE(s) |Eigenvalue |Statistic |Critical Value |Critical Value |
|None ** | 0.871191 | 41.89135 | 15.41 | 20.04 |
|At most 1 | 0.143912 | 2.952265 | 3.76 | 6.65 |
| *(**) denotes rejection of the hypothesis at the 5%(1%) level |
| Trace test indicates 1 cointegrating equation(s) at both 5% and 1% levels |
| | | | | |
|Hypothesized | |Max-Eigen |5 Percent |1 Percent |
|No. of CE(s) |Eigenvalue |Statistic |Critical Value |Critical Value |
|None ** | 0.871191 | 38.93909 | 14.07 | 18.63 |
|At most 1 | 0.143912 | 2.952265 | 3.76 | 6.65 |
| *(**) denotes rejection of the hypothesis at the 5%(1%) level |
| Max-eigenvalue test indicates 1 cointegrating equation(s) at both 5% and 1% levels |
| | | | | |
| Unrestricted Cointegrating Coefficients (normalized by b '*S11*b=I): |
|GRE |GDP | | | |
| 1.66E-06 | 6.59E-08 | | | |
|-9.30E-06 | 7.90E-07 | | | |
| | | | | |
| Unrestricted Adjustment Coefficients (alpha): |
|D(GRE) | 216271.7 | 8130.762 | | |
|D(GDP) | 776387.8 |-357505.8 | | |
| | | | | |
|1 Cointegrating Equation(s): |Log likelihood |-532.0203 | |
|Normalized cointegrating coefficients (std.err. in parentheses) |
|GRE |GDP | | | |
| 1.000000 | 0.039691 | | | |
| | (0.01219) | | | |
| | | | | |
|Adjustment coefficients (std.err. in parentheses) |
|D(GRE) | 0.358861 | | | |
| | (0.03679) | | | |
|D(GDP) | 1.288266 | | | |
| | (0.42353) | | | |
| | | | | |

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WAGNER.pdf
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Wagner’s ‘law’ of expanding state activity, is the proposition that there is a long run propensity for government expenditure to grow relative to national income. This paper presents a discussion of the applicability of this hypothesis to four totally diverse countries. To test the proposition, unit root pre tests and maximum likelihood estimation techniques of cointegrating vectors are employed. The paper concludes that the ‘law’ is more universal than Wagner himself intended it to be. The empirical evidence places this paper among the numerous studies that support Wagner’s ‘law’.

1. INTRODUCTION
Over one hundred years ago a German economist, Adolph Wagner in his classic book,
Grundlegung der Politischen Ökonomie (1863) formulated a ‘law’ of expanding state activity. He asserted that there is a long run propensity for the scope of government to increase with higher levels of economic development.
Wagner’s contribution to public expenditure theories is particularly significant when we consider that before Wagner made his observations, the prevailing view was the notion that as a country grows richer, government activities would have a tendency to decline
(Henrekson, 1993). To a large extent this view is still prevalent in modern economic thought. Indeed, many conservative economists in the debate on the role of government assert that the expansion of government activity in macroeconomic affairs associated with the Keynesian revolution, is an unfortunate aberration.
Since the initial formulation of Wagner’s hypothesis, a considerable amount of effort has gone into testing it. This has given rise to many debates in the Public Finance literature on a wide spectrum of issues. First, the specification of an appropriate functional form for empirical testing and a means by which the results are to be interpreted, is a serious discussion that has not abated. Second, in regression analysis, there is a choice between time series models and cross section models to adequately test the ‘law’. Furthermore, the cointegration revolution in time series analysis indicates that in order for a long run relationship between government activity and economic development to exist, the two
4
variables should cointegrate. In other words, the variables should exhibit a long-run equilibrium. Another issue of note, is whether Wagner’s hypothesis is applicable to developing nations and to a lesser extent to highly mature economies.
This paper argues that Wagner’s ‘law’ is plausible and universal. The stationarity properties of the data are examined and maximum likelihood techniques are used to test for the presence of cointegrating vectors. This study utilises data from four countries at varying stages of development, of different economic and physical size, and with different economic history and experiences of public sector expansion. These countries are, the United States;
Thailand; Barbados and Haiti. Section 2 offers a detailed statement about the ‘law’, while
Section 3 examines the formulation, testing and results of some of the major studies that have tested Wagner’s hypothesis. Section 4 discusses the methodology of this study and the results are presented in section 5. Section 6 concludes the paper.
2. STATEMENT ABOUT THE ‘LAW’
The size and growth of public expenditure are complex societal processes that cannot be explained exclusively by the discipline of economics. In fact, there are many causal factors behind the size and growth of public expenditure.
Wagner’s ‘law’ is not really a theory of public expenditure growth but, rather, a generalisation concerning the secular trend of public spending (Goffman and Mahar, 1971).
5
Bird (1971) states that ‘as per capita income rises in industrialising nations, their public sectors will grow in relative importance.’
Wagner offered three reasons in support of his hypothesis. Firstly, as nations develop they experience increased complexity of legal relationships and communications, as a result of the immense division of labour that accrues with industrialization. Because of this, Wagner envisaged an enlarged role for the state in the form of public, regulatory and protective activity. Further, increased urbanization and population density would lead to greater public expenditure on law and order, and economic regulation due to the associated risk of more conflict in densely populated urban communities. Because of the substitution of private for public activity, the administrative and protective functions of the state would expand. Thus, as nations become more advanced the number and/or magnitude of market failures would force the state to become more regulatory in nature, thereby expanding its role and this would inevitably involve higher public expenditures.
Wagner predicted the expansion of ‘cultural and welfare’ expenditures based on the presumption that as income rises, society would demand more education, entertainment, a more equitable distribution of wealth and income, and generally more public services.
Public Services were seen as normal goods, that is, their income elasticities of demand exceeded unity. Wagner cited education and culture as areas in which collective producers were more efficient than private producers.
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Wagner’s final suggestion was that the dynamic nature of technology and increasing scale of investment required in many activities would bring the development of large private monopolies whose domineering effects on the market would have to be neutralised by the state or alternatively the monopolies would have to be taken over by the state in the interest of economic efficiency. For some economic activities the required scale of capital was so large that the only way these capital projects could be financed was if the state participated in the activity.
Wagner, undoubtedly, was influenced by the historical events that surrounded him. The
‘law’ was formulated in Germany in the late nineteenth century, a period characterised by expansion of the German empire and the fall of the Ottoman empire. At this time, incomes in
Germany were rising as a result of rapid growth in technology.
Richard Bird (1971) supports this notion by postulating that the ‘law’ operates under the following conditions:
(i) Rising per capita incomes;
(ii) Technological and institutional change of a particular sort, and
(iii) At least implicitly, democratization (in the sense of wider political participation of the polity).
7
Before examining some of the underlying conditions and assumptions, that are supposed to limit the existence of the ‘law’ to only a few countries, we evaluate the plausibility of the
‘law’.
At least on the surface Wagner’s proposition appears to be plausible. Wagner simply envisioned increasing social complexity with economic development and with this he saw increased responsibilities of the state. Economic development can be defined as the process of both quantitative and qualitative improvement in the standard of living in a given country.
This includes sustainable increases in the per capita income, reduction in the levels of poverty, and social, political and legal modernisation, resulting in a reduction in inequality and unemployment. It is reasonable to assume, therefore, that economic development will bring about increased labour participation, larger and more diverse markets with more players. As countries develop, they become more efficient and effective in the production of goods and services, so there is reason to believe that complexity will increase. Increased prosperity and complexity require management. The scope of the government will inevitably grow as the demands placed on government services expand.
Bird (1971) concurs with Wagner’s ‘law’ stating that ‘the activities of government are an increasing function of the changing structure of the economy.’ Whether the state decides to combat or to support private sector activity such as private monopolies, with the growth of this sector, it is plausible to assume that public sector activity will increase.
8
We noted earlier that Wagner’s hypothesis was formulated in the context of industrializing economies with rising per capita incomes. While this is so, public expenditures have been observed to rise over time in many developing countries. Is Wagner’s hypothesis applicable to developing nations? The answer lies in one’s conceptualisation of underdevelopment. In the late nineteenth century underdevelopment referred to a static state of nature, where the production function was unchanging. Both production and consumption in those countries were low. However, due to the improvement in technology, developing countries can no longer be considered to exist in a static state of nature. Developing countries have improved access to technology. It is reasonable to assume that developing nations today are fundamentally different now than they were in the late nineteenth century because they possess dynamic technology and many of them experience rapidly rising incomes.
Richard Musgrave (1969) stated that ‘low income countries today do not operate under the same technical, political, and value conditions as prevailed in the past when now developed countries were at similar low levels of income. Attitudes toward growth, changed communication, the demonstration effect of affluence and welfare measures taken abroad, the conflict of political ideologies all make for the basic differences in the historical setting.’
This means that developing nations are more likely to provide public services which approximate current levels in the developed countries than the levels provided by the currently developed nations when they were in the earlier stages of development.
Some economists argue that it is not the level of income that determines a nation’s expenditure, but rather its prevailing conception of the role of the government. They note
9
that developed countries currently spend relatively more on their public services than they had done a hundred years ago, not because they became richer and more prosperous but rather as a result of an evolving conception of the duties of the state. That the state should pay for schooling for every child, that they should pave and light the streets of every village with over a thousand inhabitants was not taken for granted a hundred years ago. They argue that these changes in ideas were not confined to the richer countries; poorer countries went through similar experiences and they too experienced increases in relative public expenditures. Perhaps the evolution of ideas is as much a part of development as rising incomes, since the former induces the latter. Today there are many developing countries that satisfy the three conditions set out by Bird (1971). That is, in the long run per capita incomes are rising, they possess dynamic technology, and increasingly the polity has the opportunity to transmit their demands and/or preferences through a democratic system. Equally, highly mature economies that have already industrialised still satisfy the three conditions, in other words being developed is not a static equilibrium either and so there is every reason to believe that
Wagner’s ‘law’ will operate in those countries as well.
The prevailing conditions of the time have increased the scope of Wagner’s ‘law’ and in its most abstract form, Wagner’s ‘law’, is more universal.
10
3. FORMULATION AND TESTING OF WAGNER’S LAW
Wagner was inexplicit in his own formulation of the hypothesis leaving the precise formulation of the hypothesis subject to disagreement among economists. It can be argued that Wagner’s ‘law’ cannot be adequately tested empirically because it is not a clear and concise theoretical construct; it amounts to looking at the past and trying to explain the upward trend in public spending. It is therefore inherently biased toward certain factors and their assumed role in the historical process. The assumptions are not clearly outlined, rendering it difficult to accept or reject this ‘law’ based on ‘fact’. Moreover, the ‘law’ does not have an explicit empirical counterpart. Whether the relevant variables that determine public spending can be limited is debatable, as public spending is influenced by a number of socio-economic variables not all of which are quantifiable. In fact, it is not clear what variables should be used to measure both economic development and state activity. It is conventional however, to use per capita income as an index of development but this is not the only index of development nor is it the only compatible interpretation of the ‘law’ but it continues to be used by most economists (Michas, 1975; Bird, 1971; Goffman, 1968; Gupta,
1967; Musgrave, 1969; Pryor, 1968).

Bird (1971) states ‘essentially, this ‘law’ is not really a theory at all but rather a kind of philosophising about history. Any attempt to ‘test’ it necessarily does violence to the facts by adjusting them to preconceived theory.’ He then went on to suggest that even if a
11
narrowly defined formulation of the relevant variables was desired, the variables are probably not stable enough over time to allow testing of this evolutionary proposition.
Perhaps Wagner’s ‘law’ does not readily lend itself to empirical testing but this does not mean it cannot be tested. In the absence of optimal solutions, economists have sought second best solutions to the problem of testing Wagner’s ‘law’. They have reasonable measures of economic development (national income) and state activity (government expenditure) and can, through the employment of econometric estimation, now isolate the effects of a few variables on public spending. In addition to this, the stationarity properties of the data can be assessed and the stability of the variables accounted for. The appropriate tools are available for the testing of such a hypothesis, a few appropriate variables can be defined to express the law explicitly in numerical terms, what is now left to decide upon is the exact functional form and method of testing.
There are in general six different formulations of Wagner’s hypothesis. These are:
1 Peacock-Wiseman “traditional” version G = f (GDP)
2 Pryor version C = f (GDP)
3 Goffman version G = f (GDP/N)
4 Musgrave version G/GDP = f (GDPR/N)
12
5 Gupta/Michas version G/N = f (GDP/N)
6 Peacock-Wiseman “share” version G/GDP = f (GDP) where G is nominal total government expenditure, GDP is nominal Gross Domestic Product,
GDPR is real Gross Domestic Product, N is the total population size, and C is government consumption expenditure.
The first formulation was employed by Peacock and Wiseman (1961), Musgrave (1969), and
Goffman and Mahar (1971). The second functional form was formulated and tested by Pryor
(1968). The third formulation was suggested and formulated by Goffman (1968) and Mann
(1980). The fourth was utilised by Musgrave (1969), Murthy (1993), and Ram (1987).
Gupta (1967) and Michas (1975) considered the fifth formulation and the sixth formulation was suggested and tested by Mann (1980).
All of the above functional forms have been employed to test Wagner’s hypothesis.
According to Wagner, “cultural and welfare” expenditures were income elastic and by extension one of Wagner’s major assumptions was that a large number of public goods and services are luxuries so that public outlay in national income is income elastic. This contention derived from his organic concept of the state. As such, economists expected the income elasticity of public spending to exceed unity. Bird (1971) suggested that Wagner’s
‘law’ would be verified if the income elasticity of demand was in excess of unity. Goffman
13
(1968) employed similar reasoning. Michas (1975) points out that the elasticity does not have to exceed unity but rather zero, depending on the functional form. For formulations, one and three, an elasticity estimate would have to transcend unity to verify the ‘law’, but for functional forms six and four, the elasticity estimate would have to be in excess of zero. The elasticity for formulation four is defined as follows:
[1] η4 =d(G/GNP) ÷ d(GNP/N)
G/GNP GNP/N and it is monotonically related to the elasticity of the fifth functional form (See Appendix):
[2] η4=η5-1
[3] η4= d(G/GNP) ÷ d(GNP/N) = d(G/N) ÷ d(GNP/N) -1
G/GNP GNP/N G/N GNP/N
It has now become the general consensus that Wagner had the relative growth of the public sector in mind (Timm, 1961). In addition to this, GDP per capita is used to measure increases in income, as it is a more accurate index of income advances because it accounts for population growth. A time series framework is used because as Bird (1971) states ‘there is nothing in any conceivable formulation of Wagner’s ‘law’ which tells us country A must have a higher government expenditure ratio than country B simply because the level of average per capita income is higher in A than in B at a particular point in time.’ He then points out that a rising ratio over time is quite different from a higher ratio at a point in time.
Hence, inferences made from international cross sectional studies are irrelevant as tests of
14
Wagner’s ‘law’. Wagner’s hypothesis is undoubtedly a time series phenomenon. Hence, in this study time series techniques are used to test for the ‘law’.
Over time numerous economists have tested for the presence of Wagner’s ‘law’ in both developed and developing countries. They have employed various formulations and estimation techniques and while Wagner’s ‘law’ appears to be supported in some instances, it is negated in others, the evidence seems more to support than to controvert the ‘law’.
Musgrave (1969) and Goffman and Mahar (1971) found strong support for the ‘law’ using ratios of percentage changes in government spending and GDP and interpreting the ratios as elasticities. Mann (1980) used six different formulations to test for the ‘law’. He employed an ordinary least squares bivariate regression on a data set spanning from 1925 to 1976.
From this study he found strong support for different formulations of the ‘law’. Gupta
(1967) tested formulation five for the United States, United Kingdom, Sweden, Canada, and
Germany for different periods between the late nineteenth century and 1960. With the exception of two cases, all elasticity estimates were in excess of unity, thereby supporting the
‘law’.
Ganti and Kolluri (1979) used U.S. data for the period 1929-1971, to test formulation number five. He excluded government expenditure from GDP as opposed to using total
GDP per capita. The income elasticity of demand that was derived was approximately two.
Abizadeh and Gray (1985) used a pooled regression for fifty-five countries for the period
1963-1974. The countries were categorised into three groups according to their levels of
15
development. The ‘law’ appeared to hold for the wealthier groups, but not for the poorest group. Ram (1987) used data for the period 1959-1980 for one hundred and fifteen (115) countries finding mild support for Wagner’s hypothesis.
Many studies have tested for the ‘law’ in specific countries. Gyles (1991) tested the ‘law’ for the UK. Pluta (1979) and Kyzyzaniak (1974) tested the ‘law’ for Taiwan and Turkey respectively. In addition to those aforementioned, Vatter and Walker (1986) tested the ‘law’ on US data. Nagarajan and Spears (1990) and Murthy (1990) tested for the existence of the
‘law’ in Mexico, the results were mixed. Apart from the aforementioned, Bird (1970), Singh and Sahni (1984), and Afxentiou and Serletis (1991) tested the ‘law’ in Canada.
Provopoulos (1981), Courakis et al (1993), and Hondroyiannis and Papapetrou (1995), apart from those previously mentioned, tested the ‘law’ for Greece.
Most of the studies have found strong support for Wagner’s proposition, however, most of the studies have not examined the stationary properties of the data and therefore may be inappropriate as estimation techniques. The next section will present a discussion of the methodology used in this paper.
The operation of Wagner’s ‘law’ is explained from a demand perspective. That is, public spending is responsive to the expansionary demand for more public goods, and state regulatory and protective activity. However, there is a budget constraint that the state must observe. The state cannot and does not behave like an unconstrained economic agent but rather it must maximise some form of welfare function subject to a budget constraint. It is
16
plausible at the same time to associate a relationship between government revenue and national income, so that as economic activity heightens or as a country becomes wealthier, tax revenues should rise as well. Rising revenues increase the government’s ability to spend.
We employ the use of formulation four as it stems from the interpretation of the ‘law’ as predicting an increasing relative share for the public sector in the total economy as per capita income grows. It is now generally agreed that Wagner had the relative growth of the public sector in mind (Timm, 1961).
4. METHODOLOGY
Classical methods of estimation are based on the assumption that the means and variances of the variables are well-defined constants, independent of time. In other words standard estimation methods assume that the variables are stationary. The applications of unit root tests have demonstrated that these assumptions are not satisfied by many macroeconomic time series so using classical techniques such as ordinary least squares (OLS) on data with the presence of unit roots can lead to misguided inferences.
Hence, testing Wagner’s ‘law’ on non-stationary variables as most studies hitherto have done could lead to spurious results. This implies that just observing the income elasticity of demand estimates is insufficient. Tests have been developed to determine the degree of stationarity, by Fuller (1976), Dickey and Fuller (1981), Phillips (1987) et cetera. These tests,
17
determine whether the series are integrated of order one I(1) against the alternative that they are integrated of order zero I(0). If the two variables exhibit long run equilibria they can be said to be cointegrated.
The hypothesis that the variables are integrated of order one I(0) plus the significance of deterministic trend can be tested using the Augmented Dickey Fuller (ADF) statistic. The tests are derived from OLS estimation of the following:
[4.1] Δyt =μ+ψT+γyt-1+ δ1Δyt-1+ δ2Δyt-2+ ….+ δ p-1Δyt-p+1+εt
The null hypothesis that the series contains a unit root is tested by H0: γ=0. The hypothesis that the series is non-stationary with a stochastic trend rather than a deterministic time trend is tested by H0: ψ=γ=0, the rejection of which suggests the presence of deterministic trend.
The lag order was determined by the Schwartz criteria.
The unit root test proposed by Phillips (1987), Perron (1988), and Phillips and Perron (1988) is also employed. This test is an extension of the Dickey-Fuller tests that makes semiparametric correction for autocorrelation.
The long run comovement of two variables is examined using the two step test for cointegration proposed in Engle and Granger (1987).
18
The paper then applies the Johansen maximum likelihood approach (Johansen, 1988;
Johansen and Juselius, 1990 and 1992). This cointegration procedure can test hypothesis concerning the number of equilibrium relationships and it is based on the assumption that the introduction of sufficient lags will produce a well-behaved disturbance term.
Many studies using cointegration techniques have used the Engle Granger two step procedure (Murthy, 1993 and Henrekson, 1993) but as Houdroyiannis and Papapetrou (1995) point out there are several advantages that the Johansen and Juselius method has over the
Engle Granger. Firstly, it tests for all the cointegrating vector variables, secondly all variables are treated as endogenous, so that the choice of dependent variable is not arbitrary.
19
5. EMPIRICAL RESULTS
The study examines the United States, Thailand, Barbados, and Haiti for the periods 1948-
1995, 1952-1995, 1966-1995 and 1965-1995 respectively. First we present some graphs so as to get an idea of the relationship. Figure 1 depicts the log of real per capita income (X) and the ratio of government exhaustive expenditure to GDP (EGDP). The prefixes US, T, B, and
H represent the United States, Thailand, Barbados, and Haiti respectively. For the United
States both real per capita income and government share in economic activity have increased over the years. For Thailand and Barbados the same appears to be true though it is less apparent by just looking at the graphs. Haiti is the exception because incomes rose and then started to decline rapidly. Interestingly enough, the share of government activity in the economy moved in tandem with real per capita income. Hence the data appears to lend support to Wagner’s hypothesis.
20
0.00
0.05
0.10
0.15
0.20
0.25
0.30
7.2
7.4
7.6
7.8
8.0
65 70 75 80 85 90 95
HEGDP HX
0.12
0.14
0.16
0.18
0.20
0.22
8.5
9.0
9.5
10.0
10.5
11.0
55 60 65 70 75 80 85 90 95
TEGDP TX
0.12
0.14
0.16
0.18
0.20
0.22
0.24
0.26
9.2
9.4
9.6
9.8
10.0
10.2
50 55 60 65 70 75 80 85 90 95
USEGDP USX
0.26
0.28
0.30
0.32
0.34
0.36
0.38
8.6
8.8
9.0
9.2
9.4
9.6
65 70 75 80 85 90 95
BEGDP BX
FIGURE 1
Evolution of real per capita income in logs (X) and the ratio government exhaustive expenditure to GDP (EGDP).
21
A slightly more objective approach to evaluating data trend would be to test for trend in the data. To do this we employ the Cox and Stuart non-parametric sign test for trend for all the variables. LCAP refers to per capita income (without logs). The results are presented in table
1.
22
TABLE 1
Cox and Stuart Test For Trend
Variable
n* n T t Hypotheses
Decision Rule
Reject Ho If:
Result
USLCAP 34 17 17 6 H0:P(+) ≤ P(-)
Ha:P(+) > P(-)
T ≥ n-t +ve Trend
USEGDP 33 16 16 4 Ho:P(+) ≤ P(-)
Ha:P(+) > P(-)
T ≥ n-t +ve Trend
TLCAP
33 16 16 4 Ho:P(+) ≤ P(-)
Ha:P(+) > P(-)
T ≥ n-t +ve Trend
TEGDP
33 14 11 3 Ho:P(+) ≤ P(-)
Ha:P(+) > P(-)
T ≥ n-t +ve Trend
BLCAP
26 13 13 3 Ho:P(+) ≤ P(-)
Ha:(P(+) > P(-)
T ≥ n-t +ve Trend
BEGDP
21 10 6 2 Ho:P(+) ≤ p(-)
Ha:P(+) > P(-)
T ≥ n-t, T ≤ t No Trend
HLCAP1
17 8 8 1 Ho:P(+)≥ P(-)
Ha:P(+) > P(-)
T ≥ n-t +ve Trend
HLCAP2 17 8 0 1 Ho:P(+) ≥ P(-)
Ha:P(+) < P(-)
T ≤ t -ve Trend
HEGDP1
12 6 6 0 Ho:P(+) ≤ P(-)
Ha:P(+) > P(-)
T ≥ n-t +ve Trend
HEGDP2 17 8 1 1 Ho:P(+) ≥ P(-)
Ha:P(+) < P(-)
T< t -ve Trend n*-sample size, n=n*/2 or (n*-1)/2, T= the number of ‘+’ signs (y>x), t=1/2(n+wα√n) P=0.5, α=0.05
23
The results show that at the 95 per cent confidence level, it is reasonable to conclude that for the United States and Thailand, both real per capita income and the ratio of government expenditure to GDP exhibit positive trend over their respective time periods. For the country of Barbados, although there was a strong growth trend in per capita income, the ratio of government expenditure to GDP exhibited neither upward trend nor downward trend. On the surface it appears as though government involvement in the economy is independent of the level of development (i.e. per capita income), in which case it is not so apparent that the
‘law’ has a presence in Barbados. Finally, Haiti poses the most interesting case because when testing the whole period for both variables the results (not shown) reveal that for both variables there is no trend. We then split the data set into two time series so as to capture the actual relationship and account for any structural breaks. Both variables increased (upward trend), peaked and then declined rapidly (downward trend). Although Wagner did not really envision negative development, there appears to be a positive relationship between per capita income and the ratio of government expenditure to GDP in Haiti.
It is not sufficient to casually observe data trend and conclude that there is a long run relationship between the two variables. Regressions in levels are misleading, as they do not take into account the stationarity properties of the data. As mentioned in the previous section, in a case where most economic time series are non-stationary, regressions on non-stationary variables will produce spurious results. It is against this background that we test for the presence of unit roots in all of the variables in levels and in first differences to determine whether the series are I(0) or I(1). To do this we employ the Augmented Dickey-Fuller test and the Phillips-Perron (PP) test, with and without the assumption of deterministic trend, so
24
as to account for the possibility of stochastic trend in any one of the series. The prefix D refers to a variable that has been differenced and the X and Y notation refer to log per capita income and the log of government expenditure as a proportion of GDP, respectively. The results are shown in table 2 and table 3.
25
TABLE 2
Tests for Unit Root in levels
Augmented Dickey-Fuller Statistic Phillips-Perron Statistic
Variables With Trend No Trend With Trend No Trend
USY -4.07** -2.31* -3.61** -2.62*
USX -3.58** -1.59 -2.92 -0.86
TY -3.07 -2.22 -2.50 -2.23
TX -1.44 2.90* -0.61 3.20**
BY -3.91** -3.14** -4.47** -3.73*
BX -2.36 -2.93* -2.38 -4.31**
HY 1.32 -0.09 2.13 -0.45
HX -.22 -0.01 0.08 0.33
Notes: * (**) denotes rejection of the null hypothesis at 10%(5%) significance level
26
TABLE 3
Tests for Unit Root in First Difference
Augmented Dickey-Fuller Statistic
Phillips-Perron Statistic
Variables With Trend No Trend With Trend No Trend
DUSY -6.85** -6.77** -6.58** -6.63**
DUSX -5.50** -5.60** -8.01** -7.51**
DTY -5.15** -5.22** -6.09** -6.17**
DTX -4.36** -3.49** -5.87** -4.44**
DBY -5.64** -5.69** -7.21** -7.35**
DBX -3.37** -3.08** -4.02** -3.44**
DHY -3.70** -2.11 -5.66** -4.06**
DHX -3.56** -2.38 -4.69** -3.79**
Notes: *(**) denotes rejection of the hypothesis at 10%(5%) significance level
27
Table 2 indicates that at the 90 per cent confidence level, some variables appear to reach stationarity in the level of the series. USY and BY appear to be strongly stationary in the levels for both the ADF test and the PP test, with and without trend. TX and BX also appear to be stationary. The PP test reported stationarity in many variables. The fact that it is possible to obtain stationarity in the level of the series suggests that the numerous tests of
Wagner’s ‘law’ most of which confirm its existence, should not be dismissed. The results reported in table 3 are stationarity tests performed on the first difference of the variables, and all the variables were stationary for both tests and nearly all assumptions, indicating strong stationarity. The series are therefore stationary in the first difference.
It is therefore possible to derive consistent estimates by taking the log difference of the variables and recovering the elasticities. Stock and Watson (1989) show that two I(1) series can give consistent estimates if they cointegrate. To test for cointegration we employ the
Engle Granger cointegration test where Xt=α+βtYt+εt is estimated and from this static regression the residuals are tested for stationarity. In the regression equation X refers to the log of real per capita income and Y refers to the log ratio of government expenditure to GDP.
Table 4 reports the results of the stationarity test on the residuals of the static regression just referred to:
28
TABLE 4
Engle-Granger Co-integration Test: Testing for Unit Roots in the Residuals
Augmented Dickey-Fuller Statistic
Phillips-Perron Statistic
Variables With Trend No Trend With Trend No Trend
URESID -4.04* -3.10 -3.31** -3.47*
TRESID -2.23 -2.84** -2.44 -2.48
BRESID -3.68* -4.46* -6.07* -5.88*
HRESID -3.61* -2.25 -1.48 -2.32
Notes: *(**) denotes rejection of the hypothesis at 10%(5%) significance level
29
The results show that for the United States and Barbados, the variables cointegrate, but for
Haiti and Thailand the variables do not cointegrate. The implication of this is that we cannot find a long run relationship between public expenditure and per capita income for Haiti and
Thailand. It must be noted that this does not necessarily mean that there is no long run relationship between the two variables since as Murthy (1994) states “ the absence of cointegration and hence any cointegrating vector might suggest the possibility that the test results are period-specific or sensitive to the implied lag structure and omitted variable bias.”
Next we report the results of the Johansen maximum likelihood cointegration technique, however a multivariate system is utilised so that we can make use of an improved model and the test is not overly subjected to the presence of missing variables. For this purpose we incorporate a degree of urbanisation variable1, URB, to provide a more correct specification of the ‘law’.
Table 5, 6, 7, and 8 summarise the results of the cointegration analysis using the Johansen maximum likelihood procedure for all the countries. The lag order is 1 and was selected using the Schwartz criteria. Three different models are presented, model 1 assumes linear deterministic trend in the data, performing the cointegration regression equation with an intercept and no trend and testing the vector auto regression (VAR). Similarly model 2 assumes linear deterministic trend in the data, but in addition to including an intercept in the cointegration equation it also includes trend though not in the VAR and finally model 3 assumes that there is no deterministic trend in the data, it has an intercept in the cointegrating equation but not in the VAR and it also has a trend in the cointegrating equation. The results are reported in the following tables:
30
TABLE 5
Johansen and Juselius Cointegration Tests
Variables: USY USX LURB
Model 1
Eigenvalue λ 5%critical value 1% critical value # of CE(s)
0.436223 47.48153 29.68 35.65 None**
0.335149 21.11905 15.41 20.04 At most 1**
0.049643 2.342207 3.76 6.65 At most 2
Model 2
Eigenvalue λ 5%critical value 1% critical value # of CE(s)
0.457764 56.48924 42.44 48.45 None**
0.387313 28.33476 25.32 30.45 At most 1*
0.118449 5.79931 12.25 16.26 At most 2
Model 3
Eigenvalue λ 5% critical value 1% critical value # of CE(s)
0.542811 72.96003 34.91 41.07 None**
0.356037 36.95775 19.96 24.6 At most 1**
0.304633 16.71251 9.24 12.97 At most 2**
*(**) denotes rejection of the hypothesis at 5%(1%) significance level
Model 1: L.R. test indicates 2 cointegrating equation(s) at 5% significance level
Model 2: L.R. test indicates 2 cointegrating equation(s) at 5% significance level
Model 3: L.R. test indicates 3 cointegrating equation(s) at 5% significance level
31
TABLE 6
Johansen and Juselius Cointegration Tests
Variables: TY TX LTURB
Model 1
Eigenvalue λ 5% critical value 1% critical value # of CE(s)
0.446337 29.93787 29.68 35.65 None*
0.124608 5.698679 15.41 20.04 At most 1
0.005892 0.242275 3.76 6.65 At most 2
Model 2
Eigenvalue λ 5% critical value 1% critical value # of CE(s)
0.477225 41.82252 42.44 48.45 None
0.212099 15.22975 25.32 30.45 At most 1
0.1246 5.456056 12.25 16.26 At most 2
Model 3
Eigenvalue λ 5% critical value 1% critical value # of CE(s)
0.493178 52.01032 34.91 41.07 None**
0.368109 24.1469 19.96 24.6 At most 1*
0.121826 5.326333 9.24 12.97 At most 2
*(**) denotes rejection of the hypothesis at 5%(1%) significance level
Model 1: L.R. test indicates 1 cointegrating equation(s) at 5% significance level
Model 2: L.R. rejects any cointegrating equation(s) at 5% significance level
Model 3: L.R. test indicates 2 cointegrating equation(s) at 5% significance level
32
TABLE 7
Johansen and Juselius Cointegration Tests
Variables: BY BX LBURB
Model 1
Eigenvalue λ 5% critical value 1% critical value # of CE(s)
0.556069 35.98469 29.68 35.65 None**
0.366869 13.24625 15.41 20.04 At most 1
0.015876 0.448081 3.76 6.65 At most 2
Model 2
Eigenvalue λ 5% critical value 1% critical value # of CE(s)
0.566352 46.12704 42.44 48.45 None*
0.447625 22.7324 25.32 30.45 At most 1
0.196151 6.113633 12.25 16.26 At most 2
Model 3
Eigenvalue λ 5% critical value 1% critical value # of CE(s)
0.630073 54.87147 34.91 41.07 None**
0.478159 27.02691 19.96 24.6 At most 1**
0.270104 8.815905 9.24 12.97 At most 2
*(**) denotes rejection of the hypothesis at 5%(1%) significance level
Model 1: L.R. test indicates 1 cointegrating equation(s) at 5% significance level
Model 2: L.R. test indicates 1 cointegrating equation(s) at 5% significance level
Model 3: L.R. test indicates 2 cointegrating equation(s) at 5% significance level
33
TABLE 8
Johansen and Juselius Cointegration Tests
Variables: HY HX LHURB
Model 1
Eigenvalue λ 5% critical value 1% critical value # of CE(s)
0.563736 38.19711 29.68 35.65 None**
0.384678 14.14139 15.41 20.04 At most 1
.002022 0.05869 3.76 6.65 At most 2
Model 2
Eigenvalue λ 5% critical value 1% critical value # of CE(s)
0.60299 59.85077 42.44 48.45 None**
0.482809 33.06076 25.32 30.45 At most 1**
0.381639 13.93981 12.25 16.26 At most 2*
Model 3
Eigenvalue λ 5% critical value 1% critical value # of CE(s)
0.587578 48.71727 34.91 41.07 None**
0.384679 23.03176 19.96 24.6 At most 1*
0.265517 8.949053 9.24 12.97 At most 2
*(**) denotes rejection of the hypothesis at 5%(1%) significance level
Model 1: L.R. test indicates 1 cointegrating equation(s) at 5% significance level
Model 2: L.R. test indicates 3 cointegrating equation(s) at 5% significance level
Model 3: L.R. test indicates 2 cointegrating equation(s) at 5% significance level
34
For all the countries examined there is strong evidence in favour of cointegration. For the
United States there are at least two cointegrating vectors, and at most three. In Haiti there is at least one cointegrating vector and at most two. Finally Thailand probably represented the weakest case, with no cointegrating equations found in model two and a maximum of two cointegrating equations in model three. Cointegrating vectors can be seen as constraints that an economic system imposes on the movement of variables in a system in the long run. It therefore follows that more cointegrating vectors ensure greater stability of the system. It is in general more desirable to have a system that is stationary in as may directions as possible.
There is statistical support for the presence of a long run relationship between government expenditure and income as hypothesised by Wagner. In general, strict cointegration tests of
Wagner’s hypothesis require specification of a correct model with an optimal lag structure
(Murthy, 1994).
35
6. CONCLUSION
This paper examines the plausibility of Wagner’s ‘law’ for countries that are diverse in different ways. It presents a discussion of the applicability of the law to countries at various stages of development and with different characteristics. We use the most accepted functional form to test for the existence of the ‘law’. The unit roots test show that some of the variables are integrated of order zero in levels. The Engle Granger cointegration test and the Johansen and Juselius maximum likelihood estimation technique of cointegrating vectors are employed to determine whether there is a long run relationship between government spending and income. While the Engle Granger test supports the existence of Wagner’s ‘law’ for only United States and Barbados, the Johansen procedure with an improved model supports the existence of Wagner’s ‘law’ for all countries under all assumptions. The paper finds empirical support for Wagner’s hypothesis in four diverse countries. The ‘law’ may be applicable to a wider range of countries due to advancements in technology and communications. 36
APPENDIX
Proof that η4= d(G/GNP) ÷ d(GNP/N) = d(G/N) ÷ d(GNP/N) -1
G/GNP GNP/N G/N GNP/N
Let G/GDP=G/N×N/GDP=(G/N)/(GDP/N)
Let Z=G/GDP
X=G/N
Y=GDP/N
Therefore d log Y=1/Y×dY
Z=X/Y
Therefore d log Z=d log X – d log Y
Hence: dZ/Z=dX/X-dY/Y
Divide through out by dY/Y:
⇒ (dZ/Z=dX/X-dY/Y)÷dY/Y
⇒ dZ/Z×Y/dY=d/X/X×Y/dy-1
⇒ d(G/GNP) ÷ d(GNP/N) = d(G/N) ÷ d(GNP/N) –1; QED
G/GNP GNP/N G/N GNP/N
37
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J., (1980), Practical Non-parametric Statistics. Second Edition, Wiley. Dickey, D.A., and W.A. Fuller, (1979), ‘Distribution of the Estimators For Autorregressive Time Series With A Unit Root’, Journal of the American Statistical Association, 74, 427-31. Dickey, D.A., and W.A. Fuller, (1981), ‘The Likelihood Ratio Statistics for Autoregressive Time Series with a Unit Root’, Econometrica, 49, 1057-72. Engle, R.F., and C.W.J. Granger, (1987), ‘Cointegration and Error Correction Representation, Estimation and Testing’, Econometrica, 55, 251-276. Fuller, W.A., (1985), ‘Nonstationary Autoregressive Time Series’, In E.J Hannan et al (Eds), Handbook of Statistics, 5, Elsevier Science Publishers B.V. Ganti, S., and B.R. Kolluri, (1979), ‘Wagner’s Law of Public Expenditures: Some Efficient Results for the United States’, Public Finance/Finance Publiques, 34, 2, 225-33. Goffman, I.J., (1968), ‘On the Empirical Testing of Wagner’s Law: A Technical Note’, Public Finance/ Finance Publiques, 23, 3, 359-64. Goffman, J.J. and D.J. Mahar, (1971), ‘The Growth of Public Expenditures in Selected Developing Nations: Six Caribbean Countries’, Public Finance/Finances Publique, 26, 1, 57-74. Granger, C.W.J., (1988), ‘Some Recent Developments in a concept of Causality’, Journal of Econometrics, 39, 37, 424-38. Gupta, S.P., (1967), ‘Public Expenditure and Economic Growth: A Time Analysis’, Public Finance/Finances Publique, 22, 4, 423-61. Gyles, A.F., (1991), ‘A Time-Domain Transfer Function Model of Wagner’s Law: The Case of the United Kingdom Economy’, Applied Economics, 23, 2, 327-30. Henrekson, Magnus, (1993), ‘Wagner’s Law: A Spurious Relationship?’, Public Finance/Finances Publique, 48, 2, 406-415. Hondroyiannis, G., and E. Papapetrou, (1985), ‘An Examination of Wagner’s Law For Greece: A Cointegration Analysis’, Public Finance/Finances Publique, 50, 1, 67-79. Hornton J., (1994), ‘Financial Deepening and Economic Growth: Evidence from Asian Economies’, Savings and Development, I-XVIII. International Monetary Fund, (1994, 1995), International Financial Statistics. 40 Johansen, S., (1988), ‘Statistical and Hypothesis Testing of Cointegration Vectors’, Journal of Johansen, S., and K. Juselius, (1990), ‘Maximum Likelihood Estimation and Influence on Cointegration- with Applications to the Demand for Money’, Oxford Bulletin of Economics and Johansen, S., and K. Juselius, (1992), ‘Testing Structural Hypothesis in a Multivariate Cointegration Analysis at the Purchasing Power Parity and the Uncovered Interest Parity for the Koop, G., and D J. Poirier, (1995), ‘An Empirical Investigation of Wagner’s Hypothesis by using a Model Occurrence Framework’, J.R Kyzyzaniak, M., (1974), ‘The Case of Turkey: Government Expenditures, The Revenues Constraint, and Wagner’s Law’, Growth and Change, 5, 2, 13-19. Mann, A.J., (1980), ‘Wagner’s Law: An Econometric Test for Mexico 1925-1976’, National Tax Journal, 33, 189-201. Michas, N. A., (1975), ‘Wagner’s Law of Public Expenditures: What is the Appropriate Measurement for a Valid Test’, Public Finance/ Finances Publiques, 30, 1, 77-84. 41 Murthy, N.R.V, (1993), ‘Further Evidence of Wagner’s Law for Mexico: An Application of Murthy, N.R.V, (1994), ‘Wagner’s Law, Spurious in Mexico or Misspecification: A Reply’, Public Finance/ Finances Publiques, 48, 1, 92-96. Musgrave, R.A., (1969), Fiscal Systems. New Haven and London: Yale University Press. Nagarajan, P., and A. Spears, (1990), ‘An Econometric Test of Wagner’s Law for Mexico: A Re-Examination’, Public Finance/ Finances Publiques, 45, 1, 165-68. Peacock, A. T., and J. Wiseman, (1961), The Growth of Public Expenditure in the United Kingdom Perman, R.J., (1991), ‘Cointegration: An Introduction to the Literature’, Journal of Economic Studies, 18, 3-30. Perron, P., (1988), ‘Trends and Random Walks in Macroeconomic Time Series: Further Evidence from a New Approach’, Journal of Dynamics and Control, 12, 297-332. Phillips, P.C.B., (1987), ‘Time Series Regression with a Unit Root’, Econometrica, 55, 335- 46. Pluta, J.E., (1979), ‘Wagner’s Law, Public Sector Patterns, and Growth of Public Enterprises in Taiwan’, Public Finance/ Finances Publiques, 7, 1, 25-46. Provopoulos, G., (1981), The Pattern of Public Expenditures and Economic Activity. The Greek Experience Pryor, F.L., (1968), Public Expenditures in Communist and Capitalist Nations. London: George Allen and Unwin. Ram, R., (1987), ‘Wagner’s Hypothesis in Time Series and Cross Section Perspectives: Evidence from “Real” Data for 115 Countries’, Review of Economics and Statistics, 69, 2, Singh B., and B.S. Sahni, (1984), ‘Causality Between Public Expenditures and National Income’, Review of Economic Statistics, 66, 4, 630-44. Stock, J.H. and Watson, M., (1988), ‘Testing for common Trends’, Journal of the American Statistical Association, 83, 1097-1107.