1. Introduction
1.1 Motivation
army to Iraq. All of those made the U.S. government’s budgetary deficit rose widely.
Furthermore, the subprime mortgage crisis burst in 2008, which exacerbated economic recession and made the U.S. fiscal status to face crisis. The overall U.S.
debt increased almost 2.6 trillion dollar during Bush government period and the debt to GDP ratio increased to almost 30 percent.1 The huge debt made the Obama government to increase the debt ratio, raise the debt ceiling, and cut down the government expenditure. Hence, the U.S. faces a serious debt crisis, which influenced the reputation of the U.S., and the U.S. debt ratio is predicted to exceed 100% in 2013.2
Is it a good policy to increase the debt and reduce the expenditure? Although someone who argued it is good, still someone disagreed. Krugman (2010) suggests that the U.S. government should increase expenditure to stimulate economy growth.3 Hence, the debate arouse our interests in government expenditure influence the U.S.
1 After the Bush government, the Obama government expected that economy can recover by taking quantitative easing monetary policy and selling public debt, and budget can be balanced through economic growth. Unfortunately, what the Obama government did had made fiscal deficit more serious and higher inflation. Then, with the debt maturity dating coming, what the Obama government can do is to just adjust the debt ceiling under the default crisis
2 In 2011 Obama government reached an agreement in the congress. This is, raise the debt ceiling gradually to pay the great debt, reduce government expenditure, and extend the tax cut policy from Bush government time to 2013. But there are existed many argue about the deal. Some economist favor that government reduce the spending debt to GDP ratio.
3 Krugman (2010) in his written ‘’Bad Analysis At The Deficit Commission’’ said that the growth slowly not because the debt(Reinhart and Rogoff, 2010) accumulate but the war. Link:
http://krugman.blogs.nytimes.com/2010/05/27/bad-analysis-at-the-deficit-commission/
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production function first. After that, Ratner (1983) estimated a production function, in which private output is dependent variable, and independent variables include employment, private capital, and government expenditure. Aschauer (1988) also estimated the same equation by the ordinary least squares method, and pointed out the nonmilitary government expenditure, including streets, airports, electricing, highways, gas facilities, water systems, and sewers are more productive to private production.We can see the same way as Fisher and Turnovsky (1998), and Barro (1988).
Barro (1988) also defined a variable
g
as the quantity of public services, and Barro thought that public services only help part of production of final goods.4 In order to discuss the relationship between government expenditure and production function, we need to know how government expenditure influence the production.Finn (1993) mentioned that Aschauer’s work raises many questions about government capital in production.5 So that Finn(1993) analyzed how the government influenced the production function. When discussing the question, Finn (1993) classified the government capital as follow:
First, Highway Capital, which includes highways, streets, bridges, and tunnels, etc.
Government helps private firms to produce public traffic buildings, and highway capital occupies the largest share in government capital, 0.361.6
Second, Government Enterprise Capital, which includes post office, gas and electric utilities, credit and insurance corporations, public transit agencies, etc. The types of government capital as public institution, which directly contribute to private
4 Barro (1988, P.7), Barro assumed that the government purchases included of goods and services. But there are two questions. “First, the flow of public services not corresponds to government purchases.
Second, public services are non-rival for the users.”
5 Finn (1993,P.54),we simplify the question to the three. First, the unique of government capital.
Second, what is the role of government in production. Third, the effect of government capital.
6 Finn (1993) used the U.S. data from 1950 to 1989 to calculate the different of government capital share. That is, production elasticity of government expenditure under different government capital.
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sector output and the share in government capital is 0.25 .
Third, Government Owned and Privately Operated Capital, which includes research and development facilities, atomic energy facilities, nuclear weapon factories, and so on. Those directly help private sector to product as government enterprise capital, and the share in government capital is 0.03.
Fourth, Educational and Hospital Capital, which includes educational building as schools, museums, galleries, gyms, and so on. Those will influence output by promoting labor productivity. The share in government capital is 0.19 .
In addition to above, there are also Administrative, Police, and Research and Development Stocks; and Fire and Natural Resource Stocks. Finn (1993) found that the government expenditure will influence production by those types above. Based on those ideas, we assume that the government expenditure is useful to increase production. To increase the government expenditure also need much tax revenue, even to debt financing. But is debt financing trouble for an economy? Or is the optimal debt ratio zero for a country?
According to Barro discussed the series issue about tax and debt in 1970s. Barro (1974) focused on the different influences of public debt and tax, and Barro thought that debt will influence the net wealth of household. Hence, Barro used a model to explain that there are some factors, which will change the optimal choice between tax and public debt for government department, such as tax-burden to future generations, etc. Next section, we try to discuss the relationship between the quantity of debt and the debt ratio in this paper.
Barro (1979), assumes that
B
t/ (PY as the real debt ratio, where
t t)B denotes the
t nominal public debt, andPY
t t represents the nominal output. Barro use the real debt ratio as a variable to estimate the equation from the U.S. data (1922-76). The result‧ 國
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proved that debt to GDP ratio does not have the optimal value but relies on the government and production shocks,7 which also imply that the government expenditure level will decide the growth rate of debt.
Aiyagari and McGrattan (1997), who pointed out that the optimal debt to GDP ratio is different under different parameter values, and they used the U.S. post-war parameters to obtain the optimal debt to GDP ratio, which is 0.66667 . The result said that debt financing can make the higher welfare when increasing debt ratio. The government debt not only makes the households more liquidity in their budget constraints, but also declines the negative effects that distorts tax causes.
Here, this paper focuses on the optimal debt ratio, which brings the highest welfare under the assumption of government expenditure in production. Besides, we also try to find the optimal debt ratio under different production elasticity of government expenditure.
In this paper, we follow Traum and Yang (2010), who used a New Keynesian model under dynamic stochastic general equilibrium framework. We revise their model to non-capital and introduce the government expenditure in production, that is, government productivity. Moreover, we assume that government controls the debt ratio, hence we can find the optimal debt ratio under different production elasticity of government expenditure.
7 Barro (1979), Government increase expenditure will bring output and price increase, but also the quantity of debt increase. That is, when government spending increased, the inflation expectation increased, too. Hence, even the nominal debt increase, the debt-output ratio still non-change.
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