Literature review

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expenditure, we want to investigate how the default rate may vary with different public spending. Particularly, we want to analyze the impacts of procyclical and countercyclical fiscal policies on the default rate. This is useful for the government to consider how to maintain the low sovereign risk while taking the expansionary fiscal policy. It is also useful for the investors to distinguish which country may have a potential risk to default.

Here, we state the results briefly. The fiscal policies do have effects on the default rate. When it is countercyclical fiscal policy, the government default rate will have negative relation with the technical shock. When the government applies weak procyclical fiscal policy, which means the government spending responded to the output is smaller than the income tax rate, the default rate will also be negative relation with the technical shock. But when the government uses strong procyclical fiscal policy, which means the government spending responded to the output is larger than the income tax rate, the default rate will be positive relation with the technical shock. The initial deficits also affect the default rate. A country with higher initial deficits will face a higher default rate.

This paper is organized as follows. The first section is the motivation and the questions that we want to analyze and the literature review. The second section is the model setting which extends the model of Uribe(2006). In the third section, we discuss the results which were derived from the model and the last section is the conclusion.

1.2. Literature review

The government default is not a new topic to economics. People usually think that the government will not crash, but these scenarios never stop happened. From the book “This Time is Different” which states the history of country’s bankruptcy, we

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can see that even the advanced countries such as England, the US, have defaulted several times in the history. But the issue of government default was never discussed until it suddenly happened.

The research about the government default has been studied from different points of view. Caballero and Krishnamurthy (2004) talked about the reasons why countercyclical fiscal policies are fine in some countries during crises but resulted in bankruptcy in other countries. They assume that during an external crisis, the supply of funds is constrained and thus has limited financial depth. Therefore, the crowding-out effect occurred. In other words, with the limit available fund, the more the government borrows the less the private sectors invest. The situation is more severe in emerging countries than that in advanced countries. The reason is that the author sets the available funds is affected by the level of the government credit. When the government is responsible for its debt, the investors will supply more funds. When the government has no fiscal discipline, the investors will reduce the borrowing.

Because of the constrained funds, the crowding-out effect was even large during the crisis than during the normal time. This situation lessens the effects of expansionary fiscal policy and finally runs into crash. However, in the reality, the reduction of the investments may not be entirely caused by the crowding-out effect. During the recession, the firm usually decreases its supply and lowers the investment for the next year. Therefore, the government needs to offset the private investments by the expansionary fiscal policy to maintain the aggregate demand for output. Moreover, this paper sets the government default rate as an exogenous factor. This is not true because the initial debt, the structure of the liabilities and the tax revenue will also affect the government payment ability.

The disaster of default will happen not only during the crisis. Three papers discuss about the government default in the normal times include Romer (2006),

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Uribe (2006) and Bi (2010). In Romer (2006), he sets up a model to characterize the government default rate. The author has two points. First, he thinks that the investors will borrow if the expected return rate equals to the risk-free interest factor. Second, the government will default if the tax revenue is not equal to the matured liability.

There are two equilibriums in this model. The first equilibrium occurs when the interest rate is slightly above the risk-free interest rate and the possibility of default is very small. The second equilibrium occurs when the possibility of default is 1. This means that the investors will not borrow the money at any interest rate. This model illustrates not only the government but also the investors’ behaviors. It clearly tells us that the government default happened for several reasons. On one hand, the government foundations which are described by the distribution function of the tax revenue will affect the probability of default. On the other hand, the exogenous variables can also affect the probability of default. This means that even two countries with the same distribution function of the tax revenue will have different probabilities of default. However, this model does not have government spending and lacks microeconomic foundation to determinant the quantity of available funds in the equilibrium.

Uribe (2006) used another way to describe the issue of government default in the normal times. The author sets a Dynamic Stochastic General Equilibrium model that has micro-foundation for household and government. The household knows that there is the possibility that the government defaults a fraction of its liability if it does not have enough money to pay the interest. In the equilibrium we can derive the default rate endogenously. The formation of the default rate tells us that if the discounted sum of the expected tax revenue equals to the initial debt, then the government will not have to default even it has lots of deficits right now. The result is distinct from Romer (2006). Because in Romer (2006) the government will crash if its tax revenue is

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smaller than its debt when the debt is due. In Uribe (2006), the payment-ability is measured through its life time. This means that the government will not default if the lifetime income is more than the lifetime deficit. The author continues to analyze the default rates under several monetary policies. When the central bank uses the Taylor rule as their monetary policy, the economy will have hyperinflation. When the central bank uses the price level targeting as their monetary policy, the government gives up its ability to inflate away part of the real value of its liabilities in response to the negative fiscal shocks. It turns out that the government can not peg the price without default. But the author lets the output as a constant and assumes no government spending for simplification. Both of the assumptions are not consistent with the reality and the results can be different if these assumptions are relaxed. With the growth of economy, the government could afford more deficits. Hence, the assumption of the output will definitely change the government payment ability.

In the research of Bi (2010), the author considers the model similar to Uribe (2006) that the government may partially default on its liability. In addition, this paper adds exogenous government expenditure, letting the tax rate endogenously determined, and sets a countercyclical lump-sum transfer to households. These assumptions make the model more close to the reality. The results show that the fiscal limits, which means the ability and willingness of the government to service its debt, is affected by the degree of countercyclical policy responses. The more lump-sum transfers level the more dispersed distributed the fiscal limits are. Finally the author finds a relationship between the default risk premium and the government debt, which is also found in Uribe (2006). Although the author has implemented the government spending, he sets it following a form of AR(1) which is not always right. In advanced countries the fiscal policy is usually countercyclical and the fiscal policy is procyclical in emerging countries. This phenomenon was found in Caballero and

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Krishnamurthy (2004). Therefore, if we want to describe the relationship between the default rate and the fiscal policies more accurately, we should set the fiscal factors more carefully.

The effects of fiscal policy were also discussed a lot in the previous literatures.

The expansionary fiscal policy can stimulate the country economy, boost the demand, but it also results in accumulating the government deficits, raises the government bond premium. This is always a dilemma to every country to weigh gains and losses between the costs of government debts and the effects of expansionary fiscal policy.

Furceri and Mourougane (2009) used DSGE model to prove that although it will increase the deficits, the fiscal policy has great effects to boost the demand in the short term. The increase in the public investment has the largest short-term effect. The rise in the public consumption can also significantly affect the GDP. Tax cut is the least effective in supporting the aggregate demand. In the paper of Devereux (2010) also talks about the effectiveness of fiscal policy. But it sets the time during the crisis that is usually accompanied by a liquidity trap. Under the liquidity trap, the government spending is more useful with deficit-financed than with tax-financed. The tax cut that usually have no effects in the normal time can also be highly expansionary in the liquidity trap.

Expansionary fiscal policy seems to have benefits to the economy but it also makes the country’s deficits increased. In the next section we will built a model of the relationship between the fiscal policy and the government default rate. Then, we will analyze what kind of fiscal policies will cause the default rate change.

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Consider an economy with a large number of identical households, and the preferences described by the utility function

0

max

_t ^t

( , )

_{t t}

t

E

^∞ β

U c l

∑

= ⁽¹⁾

Where

c

_t denotes consumption of perishable goods and

l

_t denotes leisure.

( , )

_{t t}

U c l

denotes the single-period utility function, β

∈ (0,1)

denotes the subjective discount factor, and

E

_tdenotes the mathematical expectation operator conditional on

the information available in period

t . The function U c l ( , )

_{t t} is assumed to be increasing, strictly concave, and continuously differentiable. In each period

t ,

households distribute their wealth to consumption and labor supply to maximize their utility.

In each period, households have incomes, firm’s profits and interest rate from government debts holding, as their wealth. But the government bonds are risky assets that they may default for a percentage of the amount, denoted by

δ

_t. Thus, the gross

interest rate return in period

t is denoted by R B

_{t−1 t−1}(1−

δ

_t). Households earn incomes by offering their labor, but they have to pay a percentage of income for tax.

B denotes nominal government debts that households want to purchase in period t .

t

In addition, this model is under the perfect competitive market which means that the firms’ profits is zero, thus we will not put the factor of firm’s profits in the budget constraint. Totally, we can derive the budget constraint of the household in period

t

as follows:

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