1. Introduction
1.2 Literature review
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1.2 Literature review
In order to discuss the government expenditure in production which is related to the public bond, we developed a
dynamic stochastic general equilibrium model for a closed economy. According to discussion above, we had known how government influences production function, but why does government expenditure always play a positive effect on production?
Button (1998) mentioned that the role of public policy is rethought after Aschauer (1988). Besides, Button also discussed the relationship between government in production and infrastructure, and arranged some past paper to explain the reason of positive correlation between productivity and infrastructure. Button summarized Gramlich’s (1994) ideas, which are related to the influence factors of relationship between production and infrastructure. First, the economic performance will make different influences relatively, such as urban and country. Second, the definition of the term infrastructure also makes government capital difficult to measure. Third, the softer infrastructure such as law, education, etc. which makes the macroeconomic growth. In addition to the above discussion, Gramlich and Button also think that public capital also has a positive effect on production, but there are still some studying results different from the above.8
Based on the above discussion about the influence of government expenditure on productivity, we focus on the production elasticity of government expenditure and try to find the optimal value. According to Leeper, Walker, and Yang (2009), pointed out
8 Button (1998), the recent study by Sturm and Haan (1995) employing US and Netherlands data, points that the relation between the effect of public capital(that is government service) are neither stationary nor co-integrated. And according to Leeper, Walker, and Yang (2010), said that Holtz-Eakin (1994 ) find that there is no influence between public-sector capital and private sector productivity.
Evans and Karras (1994) find it is negative relationship. And Kamp (2004) use VARs and find there is no significant influence in the U.S..
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that Nadiri and Mamuneas (1994) use the U.S. data to find the fact, which infrastructure and R&D capital have the significant positive effect on output. And they pointed out that the higher is production elasticity of government expenditure, the higher government expenditure will make the output and employ decline more because of wealth effect. These ideas we can see from Aschauer (1989) and Linnemann and Schabert (2006).
Interestingly, how big is the optimum value about the production elasticity of government expenditure is? Aschauer (1989) used the ordinary least squares method to run the U.S. data from 1949 to 1985, output is dependent variable and government expenditure is independent variable. The result said that output will increase 0.39%
if the government expenditure increases 1% . That is, the production elasticity of government expenditure is 0.39 . Baxter and King (1993) assume the production elasticity of government expenditure value to be 0.05. In this paper, we will test the value from 0 to 0.3 to analyze the different results9.
Macroeconomic theory said that the government expenditure should have the same quantity of revenue. The main government revenue comes from tax, but the government usually expends more than tax revenue, so that the government should finance by other ways, such as monetary financing and debt financing. Which debt financing is the major way for the government to finance, and monetary financing is usually not used since it will disturb the economy.
As we had mentioned above, which Barro had discussed a series of issues about public debt in 1970s, and Aiyagari and McGrattan (1997) also had discussed the optimal debt ratio is two third. The reason is that the government sells public bond, which makes the households more liquidity in their budget constraints.
9 Here, since we use the parameter of Michael Juillard’s paper, so that we set the government capital share is 0.3 which equals to private capital share.
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We can find the same result in Alexandra and Patrick (2009), which proposes an endogenous growth model to compare the welfare between the golden rule of public finance and the balanced budget rule. The balanced budget rule is better in the long run than in the short run, but it is still difficult to judge that the golden rule of public finance is worse than balanced budget rule. When consumption substitution elasticity changed, the optimal debt ratio is also different. For the reason that debt financing makes household increase welfare by transforming the cost to the future even if the cost is higher, the result is the same as Barro (1979).
Greiner (2010) also presents an endogenous growth model to discuss the government expenditure which financed by debt or tax under the balanced budget rule.
The result is that the government takes fiscal policy by debt financing, which will have the higher welfare than pure balance budget rule. With economy growth, the debt to GDP ratio will decrease gradually and convergence to zero10 since the policy under debt financing will have more scopes to enhance the social welfare rather than only tax financing, which is restricted by the limited budget.
Linnemann and Schabert (2006) think that raising the nominal interest rate will decrease the quantity of debt, so that the government will reduce the nominal interest rate to finance by public bonds. Thus, with the higher production elasticity of government expenditure, the government needs more fiscal resource. As a result, to cope with the higher government expenditure, the government will reduce the nominal interest rate more.
Next section of this paper is described as follow. Section 2 is the theoretic structure of our model, and also explains the dynamics relationship of all variables. Section 3 is the analysis of steady states, and the calibration of parameters. Section 4 is the
10 Greiner ( 2010), in deficit policy, the public debt grows in the long run at lower rate rather than another variable, as output. So the debt ratio will decline over time.
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dynamic and impulse response functions which incur a productivity shock, and also explains why the government expenditure level will influence the interest rate, etc.
Section 5 is welfare criterion, which we compare the influence of different debt ratio on welfare. The final section is our conclusion.
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In this section, we refer to Mayer, Moyen and Stahler(2010) and Traum and Yang (2010) to construct a standard New Keynesian DSGE model under closed economy, which incorporated liquidity-constrained consumers and matched frictions in detail.
2.1 The household
Under a closed economy assumption, we consider a representative household who wants to maximize the lifetime utility, which is described as follow: individual household will enhance the utility by increasing consumption, and decline the utility by increasing labor.
The representative household makes a decision from the flow budget constraint as below:
1 (1 )
t t t t t t t t t t
PC B
W L W L r B
(2) Since the market is monopolistically competitive, the consumption goods is acontinuum of differentiated function as:
1 1 1