Testing the Existence of Wagner Law and Government Expenditure Volatility in Indonesia Post-Reformation Era

Aim of this study is to identify the existence of Wagner’s Law in Indonesia economy during post-reformation era. This study takes period sample of five regimes during 1999-2011, which are following: a) Development Reformation Regime; b) National Unity Regime; c) Mutual Cooperation Regime; d) Indonesia Unite I Regime; e) Indonesia Unite II Regime. In order to test the existence of Wagner’s Law, we also elaborate exogenous variable (tax revenue and population) as variable control. We find the result that Wagner Law did occur in post-reformation era by performing an ARDL co-integration model, yet volatility of government expenditure has to be captured. Hence, we run a GARCH model to estimate the volatility of government expenditure by elaborating the regime variable. The ARDL approach, causality test and co-integration test also support the existing of Wagner Law in this study.

economic growth and government expenditure, yet to be known as Wagner Law later. He assumed that economic growth would boost the government expenditure relatively.
The Wagner Law then had become a debatable theory in economics after Keynesian emerged in 1930s. 3 Both theories give a different explanation of the relationship between government expenditure and economic growth. Nevertheless, it is totally understandable since every country has its own behavior on the implementation of fiscal policy and dominant factor for economic growth (Peacock and Wiseman, 1961). It is also considerably because of no convention against causality of those factors (Wijayanti, 2008).
Specifically, Wagner Law explains three main reasons of the national income to raise the government expenditure. Those reasons are: (i) when the country is on the industrialized period; (ii) when the economic growth causes an increasing demand of public services; and (iii) government contribution for a capital accumulation in which private sector would not satisfy. Rowley and Tollison (1994) argued that Wagner Law would exist by comparing it with comparative advantage industries of the country which are under government authority. Hence, it can be said that the decreasing of comparative advantage will trigger the public expenditure -GDP ratio to be decreased (Peacock and Scott, 2000).
We will elaborate the testing of Wagner Law in this study with other exogenous variables, such as population, total tax collected in post-reformation era for a deeper analysis. As Thomas Malthus has explained, population could be a problem for a country by comparing it with a food security. In the recent days, population growth problem correlates with the public services that government has to provide through government expenditure. Yet, this problem occurs in the developing countries oftentimes and burdening the government for the allocation of government expenditure. 4 On the other side, total tax collected is one of government considerations on the determination of the government expenditure. While the people demand a higher public service level, government 3 Keynesian shows that government expenditure is one of endogenous factor on economic growth through Keynesian Cross explanation (Mankiw, 2002). On the other hand, Wagner Law had proposed the opposite (economic growth raises the government expenditure) according to the fact that in industrialized period, public sector will actively play a key role which is driven by government expenditure (Mangkoesoebroto, 2001;Hussein, et al., 2010). 4 Nevertheless, population is still considered as the agent of economy for economic growth. Kelly and Schmidt (1994) argued that a lower population growth will be more beneficial in the economy. will satisfy it with a collected tax from the people. In this case, collecting tax is affected by politics and jurisdiction system of the country, yet to mention the institutional system (Hussain, 2005). It can be totally understood since the government expenditure is also utilized for the public service obligation which cannot be provided by private sectors as the consequences of the market failure . Hence, regimes can bring a different impact to the government expenditure oftentimes, depend on the respective needs and allocations of the regime period (Kohler-Toglhofer and Gnan, 2004;Carter and Palmer, 2010;Bonan and Lukkezen, 2013).
Indonesia is the fourth for the total population of the world and the determination of the government expenditure would always be a problem in the past (Population Reference Bureau, 2012). The population is predicted to increase from 241 millions in 2012 to be 309 millions in 2050, and burdening government expenditure therefore. Table 1 shows the GDP, tax collected, government expenditure and total population of Indonesia. Moreover, regime variable will be used to identify whether volatility on the government expenditure is affected by regime transition or not.

II. Literature Review
Many studies have shown various results in testing the validity of Wagner Law. This theory was considered as a controversial after Keynesian Theory had released, so that many economists remodeled other version of Wagner Law since 1960 (Demirbas, 1999;Halicioglu, 2003).
According to Mangkoesoebroto (2001), Wagner Law is presumable as the 'organic theory of the state', of which government is considered as an independent individual to the others.
Furthermore, Wagner Law can be formulated as: where P k PP is government expenditure per capita and PPK is national income per capita (GDP/total population). Peacock and Wiseman (1961) proposed a theory for government expenditure according to tax collecting. That observation refers to the funding needs for the government on the war period.
Those funding needs, mostly from tax, for war will reduce the investment and consumption of private sector (displacement effect). 5 Moreover, the government still needs an additional funding by issuing both debt and obligation, yet to be paid in the future, which is known as inspection effect. Both effects (displacement effect and inspection effect) cause a shifting of the private's activities to be government activities, also known as concentration effect. Those three effects encourage the government activities to increase gradually and also increasing the government expenditure. Arpaia and Turin (2008) concluded that Wagner Law will occur if economy activity has an elastic demand toward government expenditure, and the growth of government expenditure will be higher than economic growth. According to Ram (1987), Wagner Law can be tested by estimating the government expenditure to GDP without lagged variable. Hence, it can be said that Wagner Law is a long-run equilibrium in the economy as whole, even though it is still possible to have an adjustment in the short-run. This fact is explained further by Kolluri, et al. (2000) who showed the short-run adjustment in the case of Wagner Law in the G-7 countries for the period of 1960 -1993.
Test of the existing of Wagner Law in an economy can be performed by adding exogenous variables (Cheng and Lai, 1997;Ahsan, et al., 1992;Hussain, et al., 2010). Nevertheless, the 5 The displacement effect causes the tax collected by government is shifted for allocation of war rather than for allocation of private sector needs (investment and consumption). model should have a co-integration test among variables used. For example, Demirbas (1999) tested the six models of Wagner Law in Turkey, taking period of 1950 -1990, by performing causality test of Granger (1969) and co-integration model of Engle-Granger. 6 Demirbas (1999) got the result as Wagner Law did not matter in Turkey for the period taken, in which Bagdigen and Centitas (2004)  But, the case of second structural break, the more intensive liberalization phase, showed a longrun equilibrium to prove the existing of Wagner Law. Also, Sideris (2006)  The exogenous variables that significantly affect government expenditure are population and tax collected (Peacock and Wiseman, 1961;Mangkoesoebroto, 2001). According to Auerbach (2010), the government is highly possible to satisfy their target by optimizing its allocation of tax financing. It is also related to the population of which a country has to responsible for their welfare from the tax financing. Thus, many programs of the government, which is allocated on the government expenditure, will always depend on the total population of a country (Mehmood and Sadiq, 10`0;Bryant, et al., 2004;Fan, et al., 1998). Primarily, those programs concerns on the people's welfare, such as poverty alleviation and health care.
The theory of government expenditure is regarded not to be apart from institutional role, despite non-institutional role has played its part as mentioned above. Since government activities keep raised, related to allocation of development planning, cause in volatility of government expenditure (Lamartina and Zaghini, 2008;Carmignani, et al., 2007;Priesmeier and Koester, 2012;Akitoby, et al., 2006). For example, external factors, such as exchange rate volatility, global oil price, and etc., can increase a vulnerability of domestic economy that has to be solved, either in short-run and long-run. Borcherding and Lee (2004) mentioned that institutional role on the government expenditure is related to the policy of the regime's period, such as political appointments. The government expenditure tends to be increased as the consequence of political needs. 7 Alm and Embaye (2011) supported that statement as it was also happened in South Africa. The transition of post-Apartheid government had a significant difference on the government expenditure than pre-Apartheid government has had. 8

III.1. Model Specification
Aim of this study, as mentioned before, is to identify the existing of Wagner Law in Indonesia by adding exogenous factors, such as total population and tax collected. Those variables will be elaborated with regime variable, generated by regimes in Indonesia post-reformation era. There are five regimes in the post-reformation era as we have explained above. This study takes period of 1999:Q1 -2011:Q4 which is considered as transition era after the falling of new-order era. In addition, the regime variable will play role as ordered variable in the analysis and counted as 0 to 4 for the respective regime.
Firstly, we will specify an ARDL co-integration by performing Bound test for analysis of cointegration before identifying volatility on the government expenditure. This specification is regarded to be fit for the estimation since all variables are purely I(0) or I(1), to see whether there is a long-run relationship among variables used in this study. Pesaran, et al. (2001) and Pesaran and Pesaran (1997) suggested the ARDL co-integration test by performing F-statistic for the respective joint significance in the long-run estimation of ARDL model. The ARDL Bound test for this study is also considered as the first stage model according to Wesseh and Niu (2012) in order to ensure the absence of serial correlation in the residual. The first stage model is following as: Where Govt stands as government expenditure, Growth stands as economic growth, Tax  At the same time, this co-integration model can also have an ARCH/GARCH component (Mantalos, et al., 2007;Wong, et al., 2005;Franses, et al., 1994). This process can be analyzed by performing both heteroskedasticity test and ARCH-LM test for Equation 1. In addition, regime variable will be elaborated as a variance regressor to see whether regime transition affects the volatility on the government expenditure. The GARCH (p, q) model, following Haider and Khan (2008), can be written as: Where is residual variance of Equation

III.2. Data
This study uses data of government expenditure, economic growth, total population and tax collected for the period of first quarter of 1999 to the fourth quarter of 2011. The government expenditure, economic growth and tax collected are obtained from International Financial Statistic (IFS) and measured as real value using a base year of 2005 (in IDR), whereas the total population is obtained from World Bank Database. In addition, all variables will be turned into natural logarithmic form and counted in million.
Interpolation method will be performed on the total population data in order to obtain the quarterly data. Insukindro (1993) proposed a linear interpolation method to generate the quarterly data from yearly data, which is following as: Where is quarterly data of quarter n th , is a yearly data of year t th and α is a parameter for respective quarter data. 9 This interpolation method will yield a quarterly estimated data for total population.
The regime variable, on post-reformation era, is determined by period of respective regime. The

IV.1. Unit Root Test
We perform the ADF test, in this study, to identify the stationary level of each variable used for the ARDL co-integration model. The determination of optimum lag uses Akaike Information Criterion (AIC), which is test for un-restricted simple model. According to the ADF test, the I (0) variables are economic growth, government expenditure and total population, while tax collected takes on the I(1). According to ADF test in Table 2, variables used in this study are varies in stationary level.
Hence, the appropriate model to estimate the existing of Wagner Law in this study is ARDL cointegration. As we have mentioned before, identifying the long-run equilibrium will be employed firstly before identifying the short-run equilibrium.

IV.2. Result
The main analysis of this study is to identifying the existing of Wagner Law in the long-run for Indonesia economy post-reformation era. Determination of long-run relationship is estimated by performing Bound test for Equation 1 above. Moreover, determination of lag optimum for the ARDL co-integration model will employ 'general to specific' method which can be seen on the Table 3. The ARDL co-integration model will be base on modeling GARCH estimation for the case of volatility on government expenditure. Yet, determination of GARCH order will employ 'specific to general' method and elaborating the regime variable as variance regressor for GARCH estimation. Note: a) dependent variable: Ln ΔGov; b) parentheses on Variable column shows lag of regressors; c) parentheses on Coefficient column show standard error of regressors; (*, **, ***) shows statistically significant for each variable on the respective significant level of 1%, 5% and 10%. Table 3 above shows the estimation of ARDL co-integration model for Equation 1. Cointegration test will be firstly employed to prove the long-run relationship of the ARDL cointegration model. According to F-statistic for Bound test, we find that the long-run relationship of variables used had occurred in Indonesia economy post-reformation era (35.23701). Thus, the existing of Wagner Law is proven in this study as economic growth is statistically significant to affect the government expenditure. In addition, residual of ARDL co-integration model satisfies the normal distribution according to Jarque-Bera test with a critical value of 2.417216. We find that, in this study, Wagner Law had existed in Indonesia economy post reformation era by performing ARDL co-integration model. But, it is little bit different than the pure Wagner Law which only estimates the government expenditure to economic growth (Peacock and Wiseman, 1961). This result is in line with Ismal (2011)  On the other side, the long-run relationship between government expenditure and economic growth can be estimated by performing ARDL model. The estimation result is provided on the   Peacock and Wiseman (1961) of that the government will consider tax collected, which is considered as government revenue, to determine the government expenditure and its appropriate allocation.

V. Conclusion
This study provides analysis of long-relationship between government expenditure and economic growth in Indonesia post-reformation era, which is popularly known as Wagner Law.
Nevertheless, we modify the pure Wagner Law by adding exogenous variables to the model, those are total population and tax collected. Many previous studies used the modified model in estimating Wagner Law in order to provide the best explanation of Wagner Law in an economy (Hussain, et al., 2010;Alkitoby, et al., 2006;Ismal, 2011;Wijayanti, 2008).
Estimation results in this study show that Wagner Law had occurred in Indonesia for the period of 1999:Q1 -2011:Q4, concerning volatility problem on the government expenditure. It is generated by two estimation models, ARDL co-integration and ARDL, which prove the long-run relationship between the government expenditure and economic growth by performing Bound test. On the other hand, the regime transition did not affect to volatility on the government expenditure. This result is based on the estimation of GARCH (1, 2) that accommodating regime variable bas variance regressor.
In addition, ARDL model is employed in order to test the both existing of Wagner Law and lag on the determination of government expenditure. We find that Wagner Law had also occurred in Indonesia economy post-reformation era as ARDL co-integration model states above. Lag of the government expenditure shows that the current government expenditure is based on the previous year. It is in line with Mangkoesoebroto (2001) in which the determination of the government expenditure is always based on how it had been the previous year. In addition, this study is in line with Peacock and Wiseman (1961) as the lag of economic growth is statistically significant to affect the government expenditure. The lag of economic growth could be base of economy capacity and the development stage of a country in order to determine the effective allocation of funding.
Another necessary concern on this study is the possibility of existing of the Keynesian theory.
According to Granger causality test and Johansen test, it is known that there are two possibilities of estimation for the long-run relationship between government expenditure and economic growth. Ismal (2011) showed the similar result and concluded that the application of both theory, Wagner Law and Keynesian, will depend on the discretion of fiscal policy. Since the discretion of fiscal policy should consider the economy condition, both in domestic and global, those two theories are likely to exist at the same time.