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Abstract ： This paper investigates the relationship between government expenditure and fixed capital investment in private sector using a panel data comprising of 30 provinces economies in China. Using the OLS estimation method， Wald coefficient test and series correlation test to justify a regression model based on panel data. The paper finds that in China， government expenditure has a positive effect on private fixed capital investment， which is an opposite conclusion to the theoretical hypothesis of a crowding-out effect between government spending and fixed capital investment in private sector. However the conclusion is highly confined with the China-Growth-Pattern.
Keywords ： Government spending Panel data Serial correlation First difference model
Introduction
Does government spending have a positive or negative effect on fixed asset investment in private sector？ The majority studies examine the issue introducing "Wagner's Law" with times-series techniques such as unit-root and co-integration test. Another popular approach is Granger causality test. Studies apply Granger causality tests to justify the causal relationship between government spending and the crowding-out effect existed in private investment. Arguments pointing toward a positive effect include the points that valuation of government expenditure， government expenditure is part of GDP and the income effect investment. Arguments pointing towards a negative effect include effect of taxation， crowding out of private investment， crowding out of private production and institutional sclerosis and rent-seeking.
In our hypothesis， we consider that the government spending is not the only factor that has significant effect on the private fixed investment. Employment rate in three industries， foreign capital utilized in different provinces in China， consumption directly controlled by the government and GDP have complicated effects on the fixed asset investment.
Theoretical Analysis
Traditionally， government spending has a dampening effect on the private sector which is coined as a term---crowding out effect. The mechanism works as follows：
Government spending is one of the main components of total output which is represented by GDP， and as government spending increase， output increases. According to Keynesian school of economics， money demand increases with the output. However， in the short term， money supply is held constant， in order to reach the equilibrium in the money market， interest rate has to increase to reduce money demand. Interest rate increases until money demand equals money supply again. With interest rate going up， the private sector may find it "expensive" to borrow money from financial intermediaries thus the fixed capital investment is reduced， dampening total output. However in China， this theory may prove less handy since a large portion of the business enterprises are state-owned or related to the "state". Let's first define private sector here judging by the particular situation in China. Private sector in this article refers to all business enterprises in China including those that are state-owned and those some shares of which are owned by Central Huijin Investment. This definition only works in countries in China but is also consistent with the private sector in western countries in the sense that they all need to borrow money from financial intermediaries for fixed capital investment， the key of the crowding-out effect transmission.
It is expected by us that crowding out effect appears less severe in China or may even reverse.
Model and Data
1.The basic model structure
fiit=β1log（gsit）+β2gdpit+β3log（consit）+β4foreignit
（+） （+） （+）
+β5ipit+β6iipit+β7iiipit+αi+λt +uit
（-） （+）
2.Denotation Form
3.Variable explanation：
Result， Analysis and Conclusions
1.Result
（1）Regression results
△fi=0.5875+0.0496△（foreign）+0.3979△（gdp）
（2.0481） （0.026*） （0.0632***）
+0.6225△log（gs）-3.3287△（ip）+12.8048△（iip）
（4.535） （1.9489*） （4.6412***）
n=234 R2=0.73 ■2=0.716 SER=11.732 F=49.83
As illustrated in the diagram above， the variables：△（foreign），△log（gs），△（ip） are not significant at the 95% confidence level， for their p-value are larger than 0.05 and their absolute T value are smaller than 1.96. But△（foreign）and △（ip）are significant at the 90% confidence level， for their T value are all larger than 1.64.
△（gdp）and△（iip）are both significant at the 99% confidence level for their T value are larger than 2.58.
（2）F-test
As△（foreign），△log（gs），△（ip） are not significant at the 95% confidence level， we take Wald coefficient test to see whether we should eliminate these variables. The F-test result is shown in the diagram：
（The progress is shown in the appendix.）
We cannot eliminate all the variables， and we cannot eliminate△（foreign） and△（ip）at the same time. It seems that we should eliminate，△log（gs）. However， government spending indeed has prominent effect on fixed capital investment according to both the economic theory and common logic. Besides， the model eliminated variable△log（gs）is still not very robust. Based on these reasons， we decide to maintain these three variables in our final model.
（3）Serial correlation test
After confirming our final model， we take serial correlation test. We make the residual series "r4" of the regression equation， and make regression of "r4" with its first lag "r4（-1）" and other regressors. The result is： Although the p-value of "r4（-1）" is 0.0466， smaller than 0.05， we think we can nearly think there is no obvious serial correlation in the residual series. Compared with all the other possible models in our research， this one performed best in the serial correlation test. We will have a simple comparison analysis later in this paper and the graph of "r4" and "r4（-1）" is shown in the appendix.
2.Analysis
（1）Interpretation of the Meaning of the
Model
An increase in the change of the foreign capital by $1 trillion per province in China can drive the change of the private fixed capital investment to be 0.0469 trillion RMB.
An increase in the change of the provincial GDP by 1 trillion RMB can push the change of the private fixed capital investment to be by 0.3979 trillion RMB.
When the percentage change of the provin-
cial government spending changes 1%， the change of the private fixed capital investment will be 0.006225 trillion RMB.
While the change of the first industry employment rate increases 1%， the change of the private fixed capital investment will be -3.3287 trillion RMB.
When the percent change of the secondary industry employment rate is 1%， the change of the private fixed capital investment will be 12.8048 trillion RMB.
（2）Comparison Analysis
As stated in the previous analysis， initially， we choose a logarithm form of the econometric model shown in the following：
fi=-201.2554+0.105foerign+0.3078gdp
71.3012*** 0.036*** 0.0242***
+20.4904log（gs）-5.312ip+11.8153iip
8.7492*** 0.9997*** 2.7518***
+9.3553log（cons）
4.2261***
n=267 R2=0.9831 ■2=0.9798
SER=12.875 F=293.848
However， when we take the serial correlation test of this logarithm model， we find there is highly serial correlation， which means the model is not correctly built.
Take the first difference of every variable in the logarithm model in order to eliminate the serial correlation. And then eliminate the insignificant variable△log（cons）to get the optimal regression estimate output， which is our final model stated in the previous：
△fi=0.5875+0.0496△（foreign）+0.3979△（gdp）
+0.6225△log（gs）-3.3287△（ip）+12.8048△（iip）
Compare the regression effect of two models：
Logarithm model First difference model
As the graph shown above， we see the first difference model has a better regression effect with dependent variable△f. Besides， take the serial correlation into consideration， the results of serial correlation test are： From this comparison， we choose the first difference model， for it better satisfies the restriction of panel data regression， and has a better regression effect. Besides， the first difference model uses the changes of every independent variable to describe the changes of the dependent variable.
3.Conclusion and direction for future research
Consistent with our theoretical model， the econometric model substantiates the view point that crowing-out effect of the fiscal expansion policy on the private sector is nullified and instead the fiscal expansion policy positively influences the development of private sector enterprises due to the unique "state-owned" background of these enterprises.
This discovery may prove a way to solve the myth of China-Growth-Pattern both in good times and bad times. Traditionally， fiscal policies can influence output in the short term； however， our analysis may suggest the long term influence of fiscal policies on potential output. This is for future research.
Reference
[1]Ahmad Imtiaz and Qayyum， Abdul （2008）， Do Public Expenditures and Macroeconomic.
[2]Uncertainty Matter for Private Invest-
ment？ Evidence from Pakistan， The Pakistan Development Review， Forthcoming issue 2008.
[3]Dhakal， D.， Upadhyaya， K.， & Upadyay， M.（1996）. Foreign aid， economic growth， and causality. Rivista Internazionale di Scienze Economiche e Commerciali， 43（3）， 597-606.
[4]Im， K. S.， Pesaran， M. H.， & Shin， Y. （1997）. Testing for unit roots in heterogeneous panels. Cambridge University.
[5]Quah， D. （1993）. Empirical cross-section dynamics in economic growth. European Economic Review， 37， 326-434.
（作者單位：University of International Business and Economics）
Keywords ： Government spending Panel data Serial correlation First difference model
Introduction
Does government spending have a positive or negative effect on fixed asset investment in private sector？ The majority studies examine the issue introducing "Wagner's Law" with times-series techniques such as unit-root and co-integration test. Another popular approach is Granger causality test. Studies apply Granger causality tests to justify the causal relationship between government spending and the crowding-out effect existed in private investment. Arguments pointing toward a positive effect include the points that valuation of government expenditure， government expenditure is part of GDP and the income effect investment. Arguments pointing towards a negative effect include effect of taxation， crowding out of private investment， crowding out of private production and institutional sclerosis and rent-seeking.
In our hypothesis， we consider that the government spending is not the only factor that has significant effect on the private fixed investment. Employment rate in three industries， foreign capital utilized in different provinces in China， consumption directly controlled by the government and GDP have complicated effects on the fixed asset investment.
Theoretical Analysis
Traditionally， government spending has a dampening effect on the private sector which is coined as a term---crowding out effect. The mechanism works as follows：
Government spending is one of the main components of total output which is represented by GDP， and as government spending increase， output increases. According to Keynesian school of economics， money demand increases with the output. However， in the short term， money supply is held constant， in order to reach the equilibrium in the money market， interest rate has to increase to reduce money demand. Interest rate increases until money demand equals money supply again. With interest rate going up， the private sector may find it "expensive" to borrow money from financial intermediaries thus the fixed capital investment is reduced， dampening total output. However in China， this theory may prove less handy since a large portion of the business enterprises are state-owned or related to the "state". Let's first define private sector here judging by the particular situation in China. Private sector in this article refers to all business enterprises in China including those that are state-owned and those some shares of which are owned by Central Huijin Investment. This definition only works in countries in China but is also consistent with the private sector in western countries in the sense that they all need to borrow money from financial intermediaries for fixed capital investment， the key of the crowding-out effect transmission.
It is expected by us that crowding out effect appears less severe in China or may even reverse.
Model and Data
1.The basic model structure
fiit=β1log（gsit）+β2gdpit+β3log（consit）+β4foreignit
（+） （+） （+）
+β5ipit+β6iipit+β7iiipit+αi+λt +uit
（-） （+）
2.Denotation Form
3.Variable explanation：
Result， Analysis and Conclusions
1.Result
（1）Regression results
△fi=0.5875+0.0496△（foreign）+0.3979△（gdp）
（2.0481） （0.026*） （0.0632***）
+0.6225△log（gs）-3.3287△（ip）+12.8048△（iip）
（4.535） （1.9489*） （4.6412***）
n=234 R2=0.73 ■2=0.716 SER=11.732 F=49.83
As illustrated in the diagram above， the variables：△（foreign），△log（gs），△（ip） are not significant at the 95% confidence level， for their p-value are larger than 0.05 and their absolute T value are smaller than 1.96. But△（foreign）and △（ip）are significant at the 90% confidence level， for their T value are all larger than 1.64.
△（gdp）and△（iip）are both significant at the 99% confidence level for their T value are larger than 2.58.
（2）F-test
As△（foreign），△log（gs），△（ip） are not significant at the 95% confidence level， we take Wald coefficient test to see whether we should eliminate these variables. The F-test result is shown in the diagram：
（The progress is shown in the appendix.）
We cannot eliminate all the variables， and we cannot eliminate△（foreign） and△（ip）at the same time. It seems that we should eliminate，△log（gs）. However， government spending indeed has prominent effect on fixed capital investment according to both the economic theory and common logic. Besides， the model eliminated variable△log（gs）is still not very robust. Based on these reasons， we decide to maintain these three variables in our final model.
（3）Serial correlation test
After confirming our final model， we take serial correlation test. We make the residual series "r4" of the regression equation， and make regression of "r4" with its first lag "r4（-1）" and other regressors. The result is： Although the p-value of "r4（-1）" is 0.0466， smaller than 0.05， we think we can nearly think there is no obvious serial correlation in the residual series. Compared with all the other possible models in our research， this one performed best in the serial correlation test. We will have a simple comparison analysis later in this paper and the graph of "r4" and "r4（-1）" is shown in the appendix.
2.Analysis
（1）Interpretation of the Meaning of the
Model
An increase in the change of the foreign capital by $1 trillion per province in China can drive the change of the private fixed capital investment to be 0.0469 trillion RMB.
An increase in the change of the provincial GDP by 1 trillion RMB can push the change of the private fixed capital investment to be by 0.3979 trillion RMB.
When the percentage change of the provin-
cial government spending changes 1%， the change of the private fixed capital investment will be 0.006225 trillion RMB.
While the change of the first industry employment rate increases 1%， the change of the private fixed capital investment will be -3.3287 trillion RMB.
When the percent change of the secondary industry employment rate is 1%， the change of the private fixed capital investment will be 12.8048 trillion RMB.
（2）Comparison Analysis
As stated in the previous analysis， initially， we choose a logarithm form of the econometric model shown in the following：
fi=-201.2554+0.105foerign+0.3078gdp
71.3012*** 0.036*** 0.0242***
+20.4904log（gs）-5.312ip+11.8153iip
8.7492*** 0.9997*** 2.7518***
+9.3553log（cons）
4.2261***
n=267 R2=0.9831 ■2=0.9798
SER=12.875 F=293.848
However， when we take the serial correlation test of this logarithm model， we find there is highly serial correlation， which means the model is not correctly built.
Take the first difference of every variable in the logarithm model in order to eliminate the serial correlation. And then eliminate the insignificant variable△log（cons）to get the optimal regression estimate output， which is our final model stated in the previous：
△fi=0.5875+0.0496△（foreign）+0.3979△（gdp）
+0.6225△log（gs）-3.3287△（ip）+12.8048△（iip）
Compare the regression effect of two models：
Logarithm model First difference model
As the graph shown above， we see the first difference model has a better regression effect with dependent variable△f. Besides， take the serial correlation into consideration， the results of serial correlation test are： From this comparison， we choose the first difference model， for it better satisfies the restriction of panel data regression， and has a better regression effect. Besides， the first difference model uses the changes of every independent variable to describe the changes of the dependent variable.
3.Conclusion and direction for future research
Consistent with our theoretical model， the econometric model substantiates the view point that crowing-out effect of the fiscal expansion policy on the private sector is nullified and instead the fiscal expansion policy positively influences the development of private sector enterprises due to the unique "state-owned" background of these enterprises.
This discovery may prove a way to solve the myth of China-Growth-Pattern both in good times and bad times. Traditionally， fiscal policies can influence output in the short term； however， our analysis may suggest the long term influence of fiscal policies on potential output. This is for future research.
Reference
[1]Ahmad Imtiaz and Qayyum， Abdul （2008）， Do Public Expenditures and Macroeconomic.
[2]Uncertainty Matter for Private Invest-
ment？ Evidence from Pakistan， The Pakistan Development Review， Forthcoming issue 2008.
[3]Dhakal， D.， Upadhyaya， K.， & Upadyay， M.（1996）. Foreign aid， economic growth， and causality. Rivista Internazionale di Scienze Economiche e Commerciali， 43（3）， 597-606.
[4]Im， K. S.， Pesaran， M. H.， & Shin， Y. （1997）. Testing for unit roots in heterogeneous panels. Cambridge University.
[5]Quah， D. （1993）. Empirical cross-section dynamics in economic growth. European Economic Review， 37， 326-434.
（作者單位：University of International Business and Economics）