1. INTRODUCTION:

Over the past several years, there has been considerable debate on the issue of the relationship between Government Expenditure and Economic Growth (Peacock and Scott, 2000; Narayan et al., 2008a; Payne and Ewing, 2006; Payne, et al., 2006; Akitoby et al., 2006; Lamartina and Zaghini, 2011; Wahab, 2004 Mohammadi, et al., 2008). The dynamic nature of the possible relationship has been formulated into two hypotheses. The first hypothesis postulated by Adolf Wagner (1890) that public expenditure is an inevitable outcome of economic growth implies that public expenditure increases faster than economic growth.

Wagnerian hypothesis stated that the level of economic development affects the growth of public expenditure where the economic development is an exogenous factor and the public expenditure is an endogenous factor and the causality runs from economic development to government expenditure. The second hypothesis of the relationship between government expenditure and economic growth was postulated by the Keynes (1936). Keynesian hypothesis of the public expenditure stated that public expenditure is an exogenous factor and the economic development is an endogenous factor and the causality runs from government expenditure to economic growth. According to the Wagnerian hypothesis there are three main reason of increasing trend in the public expenditure (Wahab, 2004, Henrekson 1993, Iyare and Lorde, 2004). The first reason is industrialization progresses; there is the trend in the public sector to increases its administrative and protective functions which would leads to a substitution of public activities with private activities. Second reason is that, several public services (like education, cultural activities and health services) and welfare expenditures are income elastic implied that as income increases the demand for these services also increases. Wagner stated that the education and culture are the two areas in which the government could be a better provider than the private sector (Sinha, 1998). The last reason is natural monopolies (such as the railroads services) where the private sector is shy to invest due to the inefficiency of huge finance resources which are needed for the development of these natural monopolies. So the government will take a leading role in financing such large-scale Projects (Oxley, 1994; Iyare and Lorde, 2004; Wahab, 2004). While there are a large number of studies that have tested the wagner law of increasing state acitivties for both developing as well as developed countries. The empirical analysis of these studies found the mixed results for different countries. For example, Gupta (1967), Ansari et al. (1997), Ferda Halicioglu (2002), Chow et al. (2002), Thornton (1999) and Ansari et al. (1997) have found the evidence in support of Wagner’s law whereas Wahab (2004), Chiung- Juhuang (2006), Ram (1986), Afxentiou and Serletis (1996) have not found any evidence in favour of wagner law. There are many other studies such as Weicher (1970), Gonti and Kolluri (1979), Singh and Sahni (1984), Cameron (1984), Lybeck (1986), Reddy K.N. (1988), Oxley (1994), Khalifa H.Ghali (1997), Wagner and Weber (1997), Safa Demirbas (1999), Jackson,Fethi and Fethi (1999), Thornton (1999), Kolluri, Panik and Wahab (2000), Islam (2001), Moalusi (2004), Alfaris (2002), Ali Othman al Hakimi (2002), John Loizides and George Ramvoukas (2004), Hafeez Ur Rehaman et al. (2007), Rafaqet and Mahmood (2012), Aregbeyen and Akpan (2013), Abbas Ali Rezaei (2015) which tested Wagnerian hypothesis for both time series and cross sectional data and found the different results for different countries. But the studies based on the analysis of time series are more reliable and achieved the significant results as compare to the studies based on the analysis of cross section data. According to Bird (1970) there is not any reliable formulation of Wagner law which can states that economy A have the higher expenditure level than the economy B. because the level of per capita income is higher in economy A than in the economy B at a specific point in time. It is interesting to note that some studied utilized the simple regression analysis to investigate the Wagner law where as some studies based on multiple regression analysis and some studies employed time series econometric analysis to find the evidence of Wagner law. The numbers of the explanatory variables are also different in different studies. The objective of this paper is to test the validity of wager law and Keynesian hypothesis in the context of Rajasthan state with the use of data from 1970 to 2014 along with the time series econometrics techniques. The main focus of the study is to analyze the relationship between state government expenditure and net state domestic product in case of Rajasthan state economy. In addition, there are some studies which have attempted the validity of wagner law in india such as Singh & Sahni (1984), Bhat et. al (1991), Ram Kumar (2008), Verma and Arora (2010), Khundrakpam (2013), Srinivasan (2013) etc. but there are only two studies based on state level analysis of relationship between public expenditure and economic growth in India, one for the state of Kerala (Philip, 1998) and another is for the state of Assam (Hussain, 2014).

This paper is structured as follows. Section 2 reviews the theoretical explanations and empirical literature on Wagner’s law. Section 3 presents an overview of public expenditure and economic growth in Rajasthan state. Section 4 provides the sources of data and methodological framework, applied in the study to test Wagner’s law. The Section 5 gives a quantitative Insight on the empirical evidences from time series analysis of the study. The Section 6 summarizes the major findings of the study and suggests some policy implication for the state government of Rajasthan economy.

2. LITERATURE REVIEW:

2.1. Wagner’s Law: A Theoretical explanation:

Adolph Wagner propounded the law of increasing public expenditures in 1893 which is popularly known as Wagner’s hypothesis or Wagner’s law in economic literature. According to law the share of public expenditure in the economy rises with the economic growth. Wagner’s law explained that in the process of economic growth the government economic activity increases faster than the private activities. Wagner identified the existence of relationship between public expenditure and economic growth and stated that the growth in public expenditure is a natural consequence of economic growth. Wagnerian hypothesis taken the public expenditure as an endogenous factor and the economic growth as an exogenous factor and the income elasticity was greater than unity and the causality must runs from economic growth to public expenditure. On the contrary side the Keynesian hypothesis states that it’s the public expenditure which causes to increase in the economic growth. The Keynes believed that the public expenditure is the only policy instrument of the government which can balance the long run equilibrium in the economy. The Keynesian view took the public expenditure as exogenous variable and economic growth as an endogenous variable. However Wagner law does not explained the mathematical form of the hypothesis but after the Wagner explanation the various economists explained the Wagner law in different mathematical form. Wagner law has the six versions which has been explained by different economists: Peacock and Wiseman (1961), Gupta (1967), Goffman (1968), Pryor (1969), Musgrave (1969), Goffman and Mahar (1971) and Mann (1980).

2.1.1 Versions of Wagner’s law-

Version 1. Peacock-Wiseman version (1961):

Peacock-Wiseman Version of Wagner law used the double log form function to estimate the impact of economic growth on public expenditure. This version took the real government expenditure as dependent variable and growth rate of real gross domestic product as independent variable and believed the coefficient of real gross domestic product must be greater than.

>1 (1)

Version 2. Gupta (1967) - this version used per capita government expenditure and per capita real gross domestic product in the functional form and considered that the growth in real per capita government expenditure is dependent on the growth of real per capital gross domestic product and the elasticity of real per capita government expenditure with respect to real gross domestic product must be greater than one.

>1 (2)

Version 3. Goffman (1968) - This version is also known as the absolute version of the law, which took real government expenditure as dependent variable and growth in real GDP per capita as independent variable and considered that the coefficient of real per capita gross domestic product will be greater than one.

>1. (3)

Version 4 Pryor (1969)- used the government consumption expenditure as dependent variable instead of government expenditure to explain the Wagner law and ignored the impact of population growth on public expenditure. Pryor version requires output elasticity of government consumption should be greater than one for the explanation of the Wagner law.

>1 . (4)

Version 5. R. A. Musgrave and P. B. Musgrave (1969) - suggested that share of public sector in GDP should increase as per capita GDP increases. It takes growth in the share of nominal government expenditures in nominal GDP) depends upon the real per capita GDP and the elasticity must be greater than zero.

>0(5)

Version 6. Goffman and Mahar (1997) and Mann (1981):

This version is also known as the modified version of Peacock-Wiseman the version represents the share of public expenditure in total output as a function of total output. This approach required the elasticity of share of public expenditure in total output with respect to total output greater than zero to maintain the validity of Wagner hypothesis,

>0 (6)

The present study made an attempt to test the validity of Wagner law with all six versions in case of Rajasthan state during the period of 1970 to 2014.

2.. Empirical Studies:

There are a large number of studies that have been tested the validity of Wagner law. These studies vary from single country to various groups of country and from time series analysis to panel analysis and yielded the mixed results of relationship between public expenditure and economic growth. Laudau (1983) attempted to test the effect of government expenditure on economic growth with the sample of 96 countries. The study found the negative effect of government expenditure on real output. Chang et al. (2004) tested the Wagner’s law in ten countries with the use of Co-integration and the error correction model (ECM) techniques. The study confirmed the Wagner’s law for advanced industrial countries (South Korea, Taiwan, Japan, the United Kingdom (UK) and the United States of America (USA)). The study inferred that there was no co-integration relationship between economic growth and the government expenditure for countries such as New Zealand, South Africa Canada, Australia and Thailand. Ansari et al. (1997) examined the Wagner’s law for three African countries (Ghana, Kenya and South Africa). The study employed both Granger and Holmes-Hutton methodology to test the relationship between government expenditure and economic growth and concluded that all the countries have the evidence in support of Wagner’s law. Omoke (2009) investigated the direction of causality between Government expenditure and National Income for Nigeria. the study used the co-integration and Granger Causality tests for the period 1970-2005. The empirical analyses stated that there was not any evidence of long-run relationship between government expenditure and national income in Nigeria. The results of Granger causality test showed that causality running from government expenditure to national income. Reddy (1972) analyzed the secular trend of public expenditure in India for period of 1872 to 1968. The study concluded that Wagner’s law and displacement effect are valid for Indian economy. Diamond (1991) studied the share of government expenditure to the growth process in both developed and under-developed countries. The study employed the Dennison growth model to analyze the objectives. The outcome of the study reveals that the basic infrastructure investment expenditure is the major contributor to the economic growth. Bhat et. al (1991) examined the causality issue of government spending and national income in Indian states. The study utilized the Sims and Granger causality and multiple rank ‘F’ test with use of annual data from 1969 to 1990. The empirical findings of the study states the Indian states follow the Keynesian view of public expenditure or the causality runs from government expenditure to national income. Sinha (1998) investigated the relationship between government expenditure and economic growth in Malaysia with the use of Penn world table annual data of period 1950-92. The study employs two type of analysis. One for long run relationship between GDP and government expenditure. Second, Augmented Granger Causality test between the growth rates of two sets of variables except the log of government expenditure as a percentage of GDP are stationary in their first difference form. The analysis confirmed that all three pairs of variables are co-integrated and the number of co-integrating vector is equal to one in each case. The outcome of causality test showed that the growth of government expenditure does not cause the growth of GDP. The study concluded that there is no evidence of any reverse. Saiyed (2012) identified the bi-directional causal relationship between economic growth and growth of public expenditure for period of 1992 to 2012. The study employs cross-sectional year-wise analysis to estimate the relationship between national income and public expenditure. The results of the analysis indicate significant bi-directional causal relationship between both the variables. Mayandy (2012) identified the evidence of Wagner’s law for Srilankan Economy. The study concluded that in short run the economy has the evidence of Wagner law but in long run it does not support the Wagner’s law. Singh & Sahni (1984) analyze the pattern of causality between national income and public expenditure in India on both aggregate as well as disaggregate level with the use of three decade data. The results of the study inferred that that there exists feedback relation between both the variable which states that neither the Keynesian nor the Wagner’s hypothesis supported by the Indian economy. Oktayer and Oktayer (2013) employed Trivariate causality analysis to find out the evidence of Wagner’s law in case of Turkey with use of 60 years annual data, inflation ratio is used as the third variable in the study. The study concluded that there is not any relation between non interest real government expenditure and real GNP, this relationship exist if the inflation ratio is introduced in the model. Rauf et al (2012) analysed the applicability of wagner law for Pakistan from period 1979 to 2009. The study utilized the autoregressive distributed leg model and Toda Yamamoto approach to find out the direction of causality between national income and public expenditure. The empirical findings of the study concluded that there is no long run relationship between public expenditure and national income. In addition the findings of the Toda Yamamoto approach inferred that there is no causality in any direction. Ray and Ray (2012) studied the link between government expenditure and economic growth in India utilizing the annual data from period 1961-62 to 2009-10. The objective of the research was to investigate the cointegration and causality between economic growth and development expenditure in India with the use of time series econometrics technique of Granger causality and Error Correction Model. The empirical finding of the cointegration test indicates that economic growth and development expenditure are cointegrated or there is long run equilibrium relationship between both the variables. The results of the Granger Causality test states the absence of any kind of short run causality between both the series.

3. An overview of Public Expenditure and Economic Growth in Rajasthan State:

Rajasthan state is one of the largest states in India among 29 Indian states. The economy of the Rajasthan is based mainly on agriculture and related activity. The Rajasthan state has some distinguishing features. The 60 percent area of the state is desert area (Inhabited by 40 percent of population) in which the cost to provide the basic facilities such as education, drinking water, Medical facilities, power supply etc. are very high. The same condition is in the area of tribal and hilly area of the state. The situation of the drought is common for Rajasthan state due to lake of water resources. The state has only 1 percent of the water resources of national water resources. Some of the study found that in every 10 year there is at least one year with the drought for which the government has to manage the finance resources to provide the basic facilities. The greatest share of the state finances goes to provide the relief operation in such situation. The relief expenditure on drought during 1987-88 was 622 Crore (at current prices). The unstable nature of the state economy has the great impact on the state finances. The state finances play a significant role in the development of state and to increase the welfare of the people. The population of the state was 4.4 crore in 1991 which is about 5.65 crore in 2011. The gross state domestic product of Rajasthan state was 3248568 lakh in 1980-81, 6512340 lakh in 1990-91 and 10126341 lakh in 2000-01 and 21307929 lakh in 2010-11(statistical abstract of Rajasthan). The Gross State Domestic Product (GSDP) of Rajasthan was about € 57 billion (US$ 76.8 billion) and Net state domestic product was € 50 billion (US$ 67.8 billion) in (at current price of 2004-05) in 2011-12(Indian Economic and Industrial Scenario, May 201). The average annual growth rate of GSDP and NSDP was 15.2 percent and 15.3 percent respectively during 2004-12. The per capita GSDP of Rajasthan (at current prices2004-05) was € 830 (US$ 1,122.1) in 2011-12 as compared to € 347 (US$ 468.4) in 2004-05. Where as per capita NSDP was € 733 (US$ 990.9) in 2011-12 as compared to € 306 (US$ 413) in 2004-05(at current prices 2004-05). The total budgetary expenditure of the state was 65372.02 Crore in 2011-12 out of which the capital expenditure was 11778.77 Crore and the revenue expenditure was 53653.31 Crore. The per capita expenditure was 9543.37 rupees during 2011-12. There is increasing trend in the state government expenditure from 1970 to 2014 as shown in the figure 1. The same trend was found in Net State Domestic product. So it’s interesting to know whether there is any long run relationship between the state domestic product of Rajasthan and state government expenditure which will help to provide the policy implication for the state government expenditure as suggested by the Wagner Law and the Keynesian Hypothesis of public expenditure in Economic literature. So the present study analyzes the relationship between Net state domestic product and State government expenditure.

Figure-1 Trends in Net State Domestic Product and Government Expenditure in Rajasthan

4. Data and Methodology:

4.1 Data:

The study uses secondary data collected from various issues of statistical abstract of Rajasthan published by Directorate of Economic and Statistics Rajasthan, Jaipur (DIES, Jaipur), Annual publication of Reserve Bank of India of ‘State Finances: A study of Budgets’ and various report of Planning Department of India. The annual time series data covered the period of 44 years from 1970 to 2014. In an attempt to observed the link between economic growth and government expenditure for Rajasthan state we applied the various time series econometric techniques such as unit root test, cointegration test, Engle Granger test of cointegration, Johansen cointegration test and Granger Causality Test etc. The study ascertains the relationship between economic growth and government expenditure so the Net State Domestic Product at constant price (2004-05) is used as proxy variable for economic growth of the state. All the variables has been deflated by the use of Net State Domestic product deflator for the Rajasthan economy from 1970 to 2014. The study used all the six versions of Wagner law mention earlier in the list, to find the validity of Wagner law for Rajasthan State. In addition, all the variables (such as Net State Domestic product (NSDP), State government expenditure and Per capita expenditure and Net State Domestic Product etc.) have been taken in the logarithm form, to avoid the problem of heteroscadasticity, to find the stationarity at lower order of integration and for estimating the elasticity.

4.2 RESEARCH METHODOLOGY:

4.2.1 Unit Root Test (Integration test):

In economic data set most of the time series data are found the non-stationary (has unit root). The standard regression analysis of non-stationary series leads the problem of spurious regression (Granger and Newbold, 1974 and Engle and Granger, 1987). The main reason for spurious regression is the existence of time trend in both the variables. To avoid the problem of spurious regression the variables must be stationary (taking the difference of the variable). Therefore, first step is to test the stationarity of the variables (Noferesti, 2000). Our study used the Augmented Dickey Fuller Test (a test for stochastic non-stationary) to test the stationary property of the time series data (Dickey and Fuller, 1979). The Augmented Dickey Fuller (ADF) test is based on analysis of three different forms of regression analysis.

If the variables are non-stationary at level but stationary t first-difference form, than the variables are said to be 1(1).

4.2.2 Phillips Perron test of Unit Root:

The Phillips Perron test is also widely used for testing the stationary property of the time series data. The Phillips Perron test is differ from ADF Test on the base of heteroscadasticity and serial correlation in the disturbance term. The ADF Test use the parametric autoregression to estimate the ARMA structure of the Error in the regression whereas the Phillips Perron test ignored any serial correlation in test regression. The Phillips Perrion test used the following equation for the estimation-

₍₁₁₎

Where the error tem is integrated of order zero and there may be the problem of heteroscadasticity. The PP test correct for any serial correlation and heteroscadasticity in errors of the test regression by directly modifying the test statistics. DF test is based on the assumption that the errors are independently and identically distributed. The ADF Test adjusts the DF test in terms of the serial correlation in the error terms by adding the lagged difference terms of the regress and term. The PP test used the non-parametric statistical methods for the detection of serial correlation in the error terms without adding difference terms. The null hypothesis under the Phillips Perron test is that the series has unit root or non- stationary. The PP Test is also checked the series with constant, constant and trend and no constant and trend model for unit root property of the series. The study checked the stationary of all the variables al level and first difference with drift, drift and trend and no drift and no trend.

4.2.3. Lag Length Test:

In above ADF Equations each disturbance term is white noise so, the selection of the optimal lag length is very important before the cointegration test. Generally the lags are selected sequentially and with equal values, in related literature lags are determined 1, 2, 3 or 4(Bird, 1971). The present study used the Final Prediction Error (FPE) criterion, Akaike Information Criterion (AIC), Schwarz Infromation Criterion (SIC) and Hannan-Quinn Information Criterion (HQ) for leg length selection in the model.

4.2.4. Cointegration Analysis:

Cointegration is a statistical property of the time series data which is defined by the integration order of the time series variable. Cointegration technique is used to estimate and test stationary linear relations between non-stationary time series variables. Cointegration implies the common stochastic trend between two variables. If two variables are non-stationary it’s possible that any linear combination of those variables may be stationary. If there exists, a stationary linear combination of non stationary random variables the variables combined are said to be cointegrated (Michael P. Murray, 1994). The cointegration sated the long run equilibrium relationship between two variables even there if short run drift between those variable but they mover together in the long run. There are several method to test the cointegration between two time series variables such as Engle - Granger two step method (EGM), Engle Yahoo three step Method (EYM), The Johansen Maximum Likelihood (ML) Vector Autoregressive (VAR) Method, The Saikkonen Method etc. The present study employed the Engle - Granger two step method (EGM) and Johansen Maximum Likelihood (ML) Vector Autoregressive (VAR) Method etc.

4.2.5. Engle-Granger Two Step Technique for Cointegration:

The Engle-Granger two step Technique for cointegration involves the testing of the unit root of residuals. The first step of the Engle-Granger test is to test the stationary property of the variables and if all the variables are integrated of order one or the integration order of all the variables is same but they are not integrated at level (I(0)) then apply the OLS to those variables and found the coefficients. The second step of this procedure is to estimation of the residual of the regression model and testing the unit root properties of the residuals series. If the residual of the OLS model are stationary at level or they have not problem of unit root then the variables are said to be Co integrated or there is long run relationship between those variables. The present study estimated following equations for testing the cointegration between government expenditure and Net State Domestic product for the Rajasthan state economy.

First Step - estimation of following equitation-

……………….……….(12)

Second Step - testing of unit root property of the residual series

…………………………(13)

After the estimation of these two equations if this is found that the residuals are stationary then it is the sign of the cointegration between two variables and if this condition will not meet there is no long run relationship between the variables and the variables will drift away from each other in the long run. There are a number of problems associated with the Engle Granger cointegration test. Firstly there may be significant small sample biases in OLS estimation of cointegration (Banerjee et al, 1986). Secondly the conventional DF and ADF tests are generally suffer from parameter instability (Hendryand Mizon, 1990). Moreover the limiting distributions for the DF and ADF tests are not well defined, implying that the power of the tests is low (Phillips and Ouliaris,1990). Lastly the there may be the possibility of more than one long run relationship or multiple cointegrating vectors. The OLS estimates of the cointegrating vector cannot identify multiple long run relationship or test for number of co integration vectors. The EG test is not very powerful and robust as compared with the Johansen cointegration test. Thus, it is necessary to complement the Engle-Granger two step procedures (EG) test with the Johansen Maximum Likelihood (ML) Vector Autoregressive (VAR) Method.

4.2.6. Johansen Maximum Likelihood (ML) Vector Autoregressive (VAR) Method:

After knowing the limitations of the Engle-Granger Two step procedure of the cointegration. The present study also employed the Johansen Maximum Likelihood (ML) Vector Autoregressive (VAR) Method for testing the long run relationship. Johensen and Juselius (1990) present a cointegration estimation methodology which overcomes most of the limitations of the two step approach. The Johansen approach is based on maximum likelihood estimates of all the cointegratng vectors. The Johensen approach is based on likelihood ratio (LR) test to determine the number of cointegration vectors in the regression. Three tests statistics are suggested to determine the number of cointegration vectors: the first is Johansen’s “trace” statistic method, the second is “maximum eigenvalue” statistic method, and the third method chooses r to minimize an information criterion. The Johansen and Juselius cointegration technique is based on the following equation:

_{……….(14)}

Where

………………...(15)

…………..…….(16)

The long run relationship can be found on the basis of rank (r) in the matrix ∏. Rank (r) zero shows the absence of cointegration. If the rank(r) ≤(n-1) then there are (n-1) cointegration relationship exists in the model. The ranks are found with Trace and Maximum Eignvalue statistics-

………(17)

……..….………(18)

In multivariate model it may be possible that there may be more than one long run relationship between the variables (Ali and Shah, 2012). After examine the cointegration if there is the sign of cointegration among the variables then the causality can be examined by the vector error correction model. On the opposite side, if there is no cointegaration between the variables then the VAR Model can be applied on the first difference of all the variables.

4.2.7. Vector Error Correction Model:

After testing the Cointegration between the variable, the next step is the test the short run as well as the long run relationship between the variables. The study employed the vector error correction model (adopted by Narayan, et al (2008) and Aregbeyen (2006)) to test the short run and long run equilibrium between the variable under study. A Vector Error Correction Model is a restricted VAR model which is used with the non-stationary series but have cointegration between them.

The Vector Error Correction Model has co integration relation built in it to restrict the long run behavior of the endogenous variables to converge to their co integrating relationship with the short run adjustment dynamics. The study specify the following VECM Model for analysis-

Table 1. Results of Unit root (ADF Test)

Variable	Level		First Difference		Order of Integration
Variables	with intercept	with intercept and trend	With intercept	with intercept and trend
Variables	ADF Stat	ADF Stat	ADF Stat	ADF Stat
lnGCE	2.5995 (1.00)	-0.4681 (0.9814)	-1.632 (0.4572)	-7.8032 (0.000)*	I(1)
lnGE	1.0698 (0.9966)	-1.7023 (0.7330)	-6.3605 (0.000)*	-6.4887 (0.000)*	I (1)
lnGEPC	2.5458 (1.000)	-0.3680 (0.9857)	-9.5144 (0.000)*	-10.8245 (0.000)*	I(1)
lnNSDP	2.7954 (1.000)	-0.1493 (0.9922)	-9.4784 (0.000)*	-10.7517 (0.000)*	I(1)
lnNSDPPC	2.8438 (1.000)	0.0222 (0.9953)	-9.1702 (0.000)*	-10.6327 (0.000)*	I(1)
lnRGETNSDP	0.6804 (0.9903)	-2.1877 (0.48411)	-6.6958 (0.0000)*	-6.689 (0.000)*	I(1)

(*)indicate significant at 5 percent level. Source: Author’s Computation.

Table 2. Results of Unit root (Phillips Perron Test)

Variable	Level		First Difference		Order of Integration
Variables	with intercept	with intercept and trend	With intercept	with intercept and trend
Variables	PP Stat	PP Stat	PP Stat	PP Stat
lnGCE	2.8129 (1.000)	-0.6623 (0.9696)	-6.8118 (0.000)*	-7.6446 (0.000)*	I(1)
lnGE	-1.110 (0.9970)	-2.0224 (0.5728)	-6.3605 (0.000)*	-6.4887 (0.0000)*	I (1)
lnGEPC	1.1491 (0.9973)	-1.7264 (0.7221)	-9.0129 (0.000)*	-10.7524 (0.000)*	I(1)
lnNSDP	2.5001 (1.000)	-1.5823 (0.7836)	-8.9697 (0.000)	-10.6593 (0.000)*	I(1)
lnNSDPPC	1.3718 (0.9986)	-1.3232 (0.8686)	-8.7069 (0.000)*	-10.2061 (0.000)*	I(1)
lnRGETNSDP	0.8060 (0.9930)	-2.4383 (0.3557)	-6.6933 (0.000)*	-6.6869 (0.000)*	I(1)

(*)indicate significant at 5 percent level. Source: Author’s Computation.

Table 3.Results of Engle Granger Test of 6 version of Wagner’s Law (1^st Step)

Version 1. Peacock Version				Version 2. Gupta Version
Peacock Version	Coefficient	t-Stat	Std.Err.	Gupta Version	Coefficient	t-Stat	Std.Err.
lnNSDP	1.2926	27.478	0.0470	lnNSDPPC	0.1015	193.53	0.005
C	-6.0410	-8.190	0.7376	C	1.2845	255.51	0.005
N	44			N	44
R-Square	0.9473			R-Square	0.9988
Adj. R Square	0.9460			Adj. R Square	0.9988
D-W Stat	0.5010			D-W Stat	0.1840
F-Stat	755.0688 (0.0000)			F-Stat	37454.36 (0.0000)
Version 3. Guffman Version				Version 4. Pryor Version
Guffman Version	Coefficient	t-Stat	Std.Err.	Pryor Version	Coefficient	t-Stat	Std.Err.
lnNSDPPC	1.8365	16.858	0.1089	lnNSDP	1.32134	56.25	0.0234
C	-3.3594	-3.220	1.0433	C	-6.8538	-18.61	0.3682
N	44			N	44
R-Square	0.8712			R-Square	0.9869
Adj. R Square	0.8681			Adj. R Square	0.9865
D-W Stat	0.3330			D-W Stat	0.8982
F-Stat	284.2192 (0.0000)			F-Stat	3165.061 (0.0000)
Version 5. Musgrave Version				Version 6. MannVersion
Musgrave Version	Coefficient	t-Stat	Std.Err.	Mann Version	Coefficient	t-Stat	Std.Err.
lnNSDPPC	-0.0145	-14.45	0.001	lnNSDP	-0.010380	-23.50	0.0004
C	0.3029	31.40	0.0096	C	0.3263	47.130	0.00692
N	44			N	44
R-Square	0.8325			R-Square	0.9293
Adj. R Square	0.8285			Adj. R Square	0.9276
D-W Stat	0.35261			D-W Stat	0.5074
F-Stat	208.8100 (0.0000)			F-Stat	(0.0000)

Source: Author’s Computation.

Table 4.Results of Engle Granger Test of 6 Version of Wagner’s Law (2^nd Step)

Version	Distur-bance Term	Level		First Difference		Second Difference		Order of Integration
		with intercept	with intercept and trend	with intercept	with intercept and trend	with intercept	with intercept and trend
		ADF Stat	ADF Stat	ADF Stat	ADF Stat
Peacock Version	µ₁	-2.727 (0.0777)	-2.6336 (0.2683)	-7.0083 (0.0000)*	-6.9718 (0.0000)*			I(1)
Gupta Version	µ₂	-1.7199 (0.4132)	-0.1368 (0.9922)	0.9139 (0.9946)	0.0835 (0.9959)	-7.31108 (0.000)*	-7.85592 (0.000)*	I (2)
Guffman Version	µ₃	-2.6379 (0.0934)	-2.2659 (0.4427)	-7.7608 (0.000)*	-7.9981 (0.000)*			I(1)
Pryor Version	µ₄	-3.5237 (0.0120)*	-3.4907 (0.0531)*	-5.7565 (0.000)*	-5.7495 (0.000)*			I(1)
Musgrave Version	µ₅	-2.6162 (0.0976)	-0.9070 (0.9450)	-8.8632 (0.000)*	-5.9214 (0.000)*			I(1)
Mann Version	µ₆	-2.7734 (0.0705)	-2.5644 (0.2977)	-5.1022 (0.0002)*	-5.9832 (0.0001)*			I(1)

(*)indicate significant at 5 percent level. Source: Author’s Computation.

Table 5. Results of Johansen Cointegration Test

Unrestricted cointegration Rank Test (Trace)
Version	Hypothesized No.of CE(s)	Eignvalue	Trace Statistics	0.05 Critical value	Prob.
Peacock Version	r=0	0.4779	25.3690	15.4947	0.0012*
Peacock Version	r=1	0.3495	1.3163	3.8414	0.2512
Gupta Version	r=0	0.1365	5.2874	15.4947	0.7776
Gupta Version	r=1	2.80	0.0010	3.8414	0.9748
Guffman Version	r=0	0.4822	25.3707	15.4947	0.0012*
Guffman Version	r=1	0.0269	1.0122	3.8414	0.3144
Pryor Version	r=0	1.1977	14.6069	15.4947	0.0677
Pryor Version	r=1	0.1271	5.5734	3.8414	0.1820
Musgrave Version	r=0	0.2068	13.8444	15.4947	0.0873
Musgrave Version	r=1	0.0932	4.1104	3.8414	0.0426*
Mann Version	r=0	0.1061	8.9157	15.4947	0.3732
Mann Version	r=1	0.0998	4.3139	3.8414	0.0378*

(*) Indicate the rejection of the hypothesis. Source: Author’s Computation.

Table 6. Results of Johansen Cointegration Test

Unrestricted cointegration Rank Test (Maximum Eigen value)
Version	Hypothesized No. of CE(s)	Eigen value	Max. Eigen Stat.	0.05 Critical value	Prob.
Peacock Version	r=0	0.4779	24.0526	14.2646	0.0011*
Peacock Version	r=1	0.0349	1.3163	3.8414	0.2512
Gupta Version	r=0	0.1365	5.2864	14.2646	0.7053
Gupta Version	r=1	2.80	0.0010	3.8414	0.9748
Guffman Version	r=0	0.4822	24.3585	14.2646	0.0009*
Guffman Version	r=1	0.0269	1.0122	3.8414	0.3414
Pryor Version	r=0	0.1977	9.0334	14.2646	0.2834
Pryor Version	r=1	0.1271	5.5734	3.8414	0.0182
Musgrave Version	r=0	0.2068	9.7339	14.2646	0.2300
Musgrave Version	r=1	0.0932	4.1104	3.8414	0.0426
Mann Version	r=0	0.1061	4.6017	14.2646	0.7910
Mann Version	r=1	0.0998	4.3139	3.8414	0.0378

*Indicate the rejection of the hypothesis. Source: Author’s Computation.

Table 7. Calculated Elasticity from Johansen Approach

Version	Dependent Variable	Independent Variable	Standard Error
Peacock Version	lnGE	lnNSDP	(0.0625)
	1	-1.1603
Gupta Version	lnGEPC	lnNSDPPC	(0.00054)
	1	-0.107630
Guffman Version	lnGE	lnNSDPPC	(0.14675)
	1	-1.76092
Pryor Version	lnGCE	lnNSDP	(0.06077)
	1	-1.3557
Musgrave Version	lnRGETNSDP	lnNSDPPC	(0.00747)
	1	-0.006973
Mann Version	lnRGETNSDP	lnNSDP	(0.00706)
	1	-0.003085

Source: Author’s Computation.

Table 8. Results of long Run Causality from VECM Model

Version	Direction of the Causality	Error Correction Term	Coefficient	Standard Error	t-Value	P-value
Peacock Version	lnNSDP→lnGE	ECT1	-0.1787	0.1907	-0.9326	0.3585
Peacock Version	LnGE→ lnNSDP	ECT2	-0.4193	0.1294	-3.2405	0.036*
Gupta Version	lnNSDPPC→lnGEPC	ECT1	-13.0975	9.2589	-1.4145	0.1726
Gupta Version	lnGEPC → lnNSDPPC	ECT2	14.3119	9.7971	1.4608	0.1596
Guffman Version	lnNSDPPC → lnGE	ECT1	-0.1171	0.1375	-0.8516	0.4032
Guffman Version	lnGE → lnNSDPPC	ECT2	-0.4770	0.1424	-3.3478	0.0028*
Pryor Version	lnNSDP →lnGCE	ECT1	0.2333	0.1918	-1.2152	0.0002*
Pryor Version	lnGCE → lnNSDP	ECT2	-0.2299	0.2528	-0.9092	0.3694

Source: Author’s Computation.

Table 9. Results of Short Run Causality from VECM Model (Wald Test)-

Version	Direction of the Causality	F-Stat.	Chi-Square Value	P-value
Peacock Version	lnNSDP→lnGE	3.4728	20.8368	0.0028
Peacock Version	LnGE→ lnNSDP	3.8305	22.9835	0.008
Gupta SVersion	lnNSDPPC→lnGEPC	0.6014	4.2103	0.7553
Gupta SVersion	lnGEPC → lnNSDPPC	0.5856	4.0992	0.7683
Guffman Version	lnNSDPPC → lnGE	3.5288	21.1729	0.0017
Guffman Version	lnGE → lnNSDPPC	3.7112	22.2675	0.0011
Pryor Version	lnNSDP →lnGCE	1.6944	3.3889	0.1300
Pryor Version	lnGCE → lnNSDP	0.0036	0.9964	0.9946

Source: Author’s Computation.

The results for Guffman version shows the bidirectional causality between per capita net state domestic product and government expenditure in short run. On the opposite side the results also states that there is no causality between both the variables in Gupta and Pryor Version of the Wagner law.

5.3.2. Results of Diagnostic Tests of the VECM Model-

The results of Model efficiency of the Vector Error correction model are represented in table 10. To test the efficiency of the model study used the Jarque Bera Test (For the Normality of the residuls), ARCH test (Autoregressive Conditional Heteroskedasticity) and Breusch- Godfrey Serial Correlation LM test.

The various Diagnostics tests results of Vector Error correction model (Table 10.) shows that version 1(Peacock Version) and Version 4 (Guffman version) are efficient from the point of econometrics properties of the model. in these two version there as not problem of Normality, Heteroscadasticity and Serial correlation. However the version 2 (Gupta Version) has the problem of Normality and Heteroscadasticity properties of the residuals. The Pryor version has the problem of non-normality, Heteroscadasticity and Serial correlation. The result states that the Pryor version does not fulfill the econometrics properties of the model.

5.3.3 Results of Standard Pair-wise Granger Causality Test:

The results of Standard pair-wise Granger causality test are reported in Table 11. The standard Pair-wise Granger Causality test checked the short run causality between the variables which are not cointegrated. The present study found that the variables of the version 5 and 6 of the Wagner law have no cointegration between them i.e. no long run relationship between the variables (Suggested by Johansen Maximum Likelihood Method test). To test the short run causality between the variables of version 5 and 6 we employed the Standard Pair-wise Granger Causality test. The optimum leg Length for the test is selected from unrestricted VAR model on the basis of FPE, HQ, AIC and LR criterion of the leg length selection at 5 percent level of significance (as adopted by Afxentios and Serletis (1982), Demirbas (1999) and Aregbeyen (2006)).

Table 11. Results of Standard Granger Causality Test

Version	Null Hypothesis	Leg Length	F-Stat.	P-Value
Musgrave Version	D(lnNSDPPC) Does not Cause D(lnRGETNSDP)	4	1.5546	0.2119
Musgrave Version	D(lnRGETNSDP) Does not Cause D(lnNSDPPC)	4	0.5363	0.7101
Mann Version	D(lnNSDP) Does not Cause D(lnRGETNSDP)	4	1.5749	0.2065
Mann Version	D(lnRGETNSDP) Does not Cause D(lnNSDP)	4	0.5456	0.7035

Source: Author’s Computation.

The results of Standard Pair –wise Granger causality test shows that there is no causality between the variable for both the version 5 and 6. The result indicates that the public expenditure and Net State Domestic Product are independent to each other in both the Musgrave and Mann Version of the Wagner Law.

6. CONCLUSION

The present study provides empirical analysis for the validity of Wagner law in case of Rajasthan economy using the annual time series data from 1970-7 to 2013-14. The major objective of the study is to investigate the validity of all the six versions of Wagner law. The study estimated six models for the six versions of wagner law to confirm the growth elasticity of public expenditure. The study used various econometrics techniques to test the long run relationship between government expenditure and net state domestic product of Rajasthan. The study used the unit root test (ADF, PP Test) to determine the order of integration of the variables under study and found that all the variables are integrated of order one. Secondly the study employed the engle granger two step method and johansen test of cointegration to identify the long run relationship between the variables. The study found that out of six version of wagner law only four version (Peacock, Gupta, Guffman and Pryor Version) have the long run relationship and the remaining two version (Musgrave and Mann Version) have not any long run relationship. Finally to find the causality the study applied the Vector Error Correction Model for first four version of the wagner law where the cointegration was found and the Standard Pair –wise Granger Causality test was employed to find the short run causality between the variables for Musgrave and Mann Version. The results of the study indicates that Peacock, Guffman and Pryor version shows the unidirectional causality between the variables whereas no causality was found in Gupta Version of Wagner Law in long run. The result of the short run causality (Wald Test) states the bidirectional causality in Peacock and Guffman Version and absence of the causality in Pryor and Gupta Version. The results of Standard Pair-wise Granger Causality reflected that there is no causality between the variables in Musgrave and Mann Version. The study found the mix results of various versions of the Wager law for Rajasthan Economy. The empirical findings of the study is similar to the findings of the previous study of Akpan,(2011), Omoke (2009), Reddy (1972), Singh & Sahni (2002), Roy & Roy, (2012) etc. the study concluded that Peacock and Guffman Version of Wagner Law is valid for the Rajasthan economy.

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Received on 02.05.2019 Modified on 27.05.2019

Res. J. Humanities and Social Sciences. 2019; 10(4): 1011-1024.

DOI: 10.5958/2321-5828.2019.00166.9

Verson	Direction of Causality	Normality Test		ARCH Test		Serial Correlation LM Test
Verson	Direction of Causality	JB Stat.	P-value	*Obs R²**	P-value	*Obs R²**	P-value
Peacock Version	lnNSDP→lnGE	0.4531	0.7972	0.4480	0.7993	0.0831	0.7730
Peacock Version	LnGE→ lnNSDP	0.9697	0.6164	0.0340	0.8536	3.6555	0.1608
Gupta Version	lnNSDPPC→lnGEPC	5.1004	0.0780	6.4258	0.0112*	4.2223	0.1211
Gupta Version	lnGEPC → lnNSDPPC	6.7829	0.0336*	7.4645	0.0063	4.3763	0.1121
Guffman Version	lnNSDPPC → lnGE	0.4539	0.7969	0.1180	0.7312	0.4416	0.8019
Guffman Version	lnGE → lnNSDPPC	1.3028	0.5213	0.0037	0.9579	5.2094	0.0739
Pryor Version	lnNSDP →lnGCE	6.6033	0.0368*	6.3432	0.0118*	10.962	0.004*
Pryor Version	lnGCE → lnNSDP	1.2021	0.5482	9.8024	0.0017*	7.8446	0.019*