Excerpt

## List of Contents

1. Introduction

2. The Public Debt Model

2.1. The Government Budget Constraint

2.2. Sustainability of the Public Debt

2.2.1. General Dynamics

2.2.2. Monetization of Debt

2.2.3. The Fiscal Theory of the Price Level (FTPL)

2.3. Special Case of a Monetary Union

2.3.1. Common Monetary Policy

2.3.2. Budget Rules in the EMU

2.3.3. No Bailout Clause in the EMU

2.3.4. Result

3. Case Study of Greece

3.1. Development of the Government Budget Constraint

3.1.1. Government Debt Development

3.1.2. Government Deficit Development

3.1.3. Net Government Lending/Borrowing

3.1.4. Interest-Growth Differential

3.1.5. Monetary Policy in the EMU

3.1.6. Result

3.2. Welfare Implications of Public Debt

3.2.1. Crowding-out Effect

3.2.2. Economic Growth

3.2.3. Limitations of Policy Discretion

3.2.4. Redistribution Effect

3.2.5. Result

3.3. Rationale of Public Debt

3.3.1. Business-cycle Smoothing

3.3.2. Intertemporal Burden Sharing

3.3.3. Political Process

3.3.4. Result

4. Policy Options for Greece and the EMU

4.1. Credible Budget Rules

4.2. Debt Default

4.3. Money Finance

4.4. Structural Reform, Austerity Measures and Affirmative Actions

4.5. Expansive Monetary Policy despite of a Liquidity Trap

4.6. Expansive Fiscal Policy despite of high Debt

5. Conclusion

A Appendix

A.1 Derivation of the Government Budget Constraint:

A.2 Derivation of the Circular Flow Identity:

A.3 Tables:

## Abstract

This bachelor thesis discusses the sustainability of government debt on a theoretical level with the model of the government budget constraint and its application in a case study. Therefore, the situation of Greece is used as a prime example for the current sovereign debt crisis in the European Monetary Union. It points out with quantitative data, what has led to the high public debt in Greece and what are the consequences of this debt accumulation. For this the sustainability and the development of government debt and its determinants will be analysed. In conclusion, it discusses the options to escape of this sovereign debt crisis for Greece and the European Monetary Union as a whole

## List of Figures

Figure 1: Debt Dynamics Scenarios

Figure 2: Debt Dynamics - Case A

Figure 3: Debt Dynamics - Case B

Figure 4: Debt Dynamics - Case C

Figure 5: Debt Dynamic - Case D

Figure 6: Debt Dynamics with Money Financing from Case A to Case B

Figure 7: Debt Dynamics with Money Financing from Case C to Case D

Figure 8: Greece - Government Debt Development

Figure 9: Greece - Government Deficit Development

Figure 10: Greece - Net Government Lending/Borrowing

Figure 11: Greece - Interest-Growth Differential

Figure 12: Greece - Composition of the Real Interest Rate

Figure 13: Greece - Monetary Aggregates

Figure 14: Greece - Money Supply and Inflation

Figure 15: Greece - Circular Flow Identity

Figure 16: Greece - Output Gap, Public Net Savings and Real Interest Rate

Figure 17: Greece - Net Fixed Capital Formation to GDP

Figure 18: Greece - Real GDP and GDP-growth Rate at constant Prices

Figure 19: Bond Market Dynamics Model

Figure 20: Shifts in the Bond Market Dynamics Model

Figure 21: Greece - Bond Rating and Long-run Interest Rates

Figure 22: Greece - Bond Rating and Long-run Interst Rates since the Crisis

Figure 23: Greece - Structural and Cyclical Component of Net Lending

Figure 24: Greece - GFCF compared to Net Debt

## List of Tables

Table 1: Greece in EMU - Money Growth and the Seigiorage to GDP-ratio

Table 2: Greece - Interest Burden since the Financial Crisis

Table 3: Bond Rating Index

Table 4: Greece - Financial Account

## List of Abbreviations

Abbildung in dieser Leseprobe nicht enthalten

## 1. Introduction

In consequence of the Great Recession, which started in 2007 as a subprime mortgage crisis and developed to a financial crisis, the public debt have reached new dimensions in many countries ,especially in the European Union (EU). Actually the most discussed issue in the European political debate is the Greek government-debt crisis, which has already reached such a symbolic meaning for the European debt crisis and the future of the EU, that there is no way back anymore. The debt of Greece has reached as a peak 312.7 billion euro in July 2015, what is a debt-to-GDP level of 177.1% (Trading economics 2015). The Greek economy has already suffered from structural weaknesses for decades. Finally in 2009 the fears of a sovereign debt crisis in Greece has led to a crisis in trust that Greece will not be able to bring its debts under control. In May 2010 the Eurogroup arranged from the European Commission or so called Greek Loan Facility (GLF) and the International Monetary Fund (IMF) a 107.3 billion euro bailout loan to rescue Greece from sovereign default and to cover its financial needs until June 2013 (European Commission 2015). As a consequence Greece had to implement austerity measures, structural reforms and privatize government assets. In March 2012 Greece received another bailout loan of 144.7 billion euro from the European Financial Stability Facility (EFSF) and 19.8 billion euro from the IMF in several tranches until 2014 after a worsening recession and the missing implementation of the conditions (European Commission 2015). In July 2015 the European Commission arranged to mobilise more than 35 billion euro until 2020, while they already paid out up to this point 4.4 billion euro (European Commission 2015). Still the problem has not been solved yet and Greece is still not able to get control of its debt by itself. The government debt is a relevant topic in economics and has become even more relevant since the outbreak of the European sovereign debt crisis. Further research in the issue of government debt could help us to understand how government-debt crisis develop, how the current sovereign debt crisis may be solved as well as how we could prevent from future crises. To understand the problem of high debt, we also need to understand the necessity of public debt, the arithmetic behind it and its implications on the economy of a country and the whole economic system.

This Bachelor Thesis will explain public debt in an intuitive and mathematical way to discuss further in detail the situation for the Greek government debt crisis and the implication for the European Monetary Union. For this purpose the government budget constraint will be derived as well as its sustainability for Greece will be verified. As a next step it will be shown with reference to the government budget constraint and its variables and in what way the implications of growing debt influences the economy and may lead to an unstoppable doom loop. Then the rationale of debt rise will be discussed. In conclusion, the taken measures as well as other possible options to reach sustainable government debt in Greece will be listed and discussed to issue finally a statement about the European sovereign debt crisis.

## 2. The Public Debt Model

### 2.1. The Government Budget Constraint

Just like the private individuals, the government has to finance its expenditures with revenues. The government spending is composed of the regular government spending (G), which contains all the public spending on consumption, investment, and the nominal interest payment on its debt stock (iB), which has been accumulated in the past. In this context we are always talking about the interest rates on government bonds, because these are the concerned interests, which have to be paid to the debtors of the government. The main revenues are taxes and fees minus transfer payments (T). If we take the public spending minus the taxes (G-T), we receive the primary balance, which shows the balance of direct fiscal intervention on the economy in the actual period. If the revenues of taxes are bigger than the expenditures of public spending, it is called primary surplus, otherwise it is called primary deficit. After accounting the total revenues with spendings we figure out the deficit (Δ5) which can be positive or negative and describes the development of the public debt (B). It is the difference of the public debt between the actual and the last period. If it is positive the public debt raises, otherwise it falls. The Government budget constraint looks now like this^{[1]} (Blanchard und Illing 2004, p. 760):

Abbildung in dieser Leseprobe nicht enthalten

This equation shows, that the government can finance its expenditures of spendings and/or interest payments by taxes and/or higher public debt. By rewriting the equation 1, we receive the equation for the nominal government debt (Blanchard und Illing 2004, p. 760):

Abbildung in dieser Leseprobe nicht enthalten

The nominal government debt is composed of the amount of debt of the last period including the interest payment for the debt from last to this period plus the primary balance. To obtain the real government debt, we divide the equation 2 by the price level of the actual time period (Blanchard und Illing 2004, p. 760):

Abbildung in dieser Leseprobe nicht enthalten

The real interest rate (r) gives us approximately the nominal interest rate minus the inflation rate. Since the government debt is price adjusted we are able to compare the amount of debt between different time periods. But it is not possible to compare the amount of debt between different countries with this ratio, because bigger countries have a bigger amount of debt than smaller ones. To make them comparable, we will calculate the real government debt in terms of the gross domestic product (GDP) of a country. For this we divide the equation 3 by the GDP (Y) (Anselmann 2012,p. 26,27):

Abbildung in dieser Leseprobe nicht enthalten

Equation 4 shows, that the debt to GDP-ratio in terms of the nominal GDP of the current period is defined by the debt to GDP-ratio of the last period plus the interest rate payment minus the real GDP-growth rate of the last period plus the primary balance. To receive the deficit again, but this time in terms of the nominal GDP, we rearrange equation 4 to receive the following equation:

Abbildung in dieser Leseprobe nicht enthalten

From equation 5 we see, that the change of the real debt to GDP-ratio is determined by the primary balance-ratio (Gt Tt), the nominal interest rate (i), the inflation rate (π) and the growth rate of the GDP (y). In further analysis we will call the difference of the real interest rate (nominal interest rate minus the inflation rate) and the real GDP growth rate the interest-growth differential (Anselmann 2012, p. 28,139). To visualize the deficit-ratio, which is mentioned in the Maastricht Treaty or the Stability and Growth Pact of the EU, we rearrange the equation 5 (Anselmann (2012, p. 29):

Abbildung in dieser Leseprobe nicht enthalten

The deficit-ratio is defined as[illustration not visible in this excerpt], which we can divide in the revenue-[illustration not visible in this excerpt]ratio [illustration not visible in this excerpt]. The deficit-ratio shows the new indebtedness of a period in terms of the nominal GDP (Anselmann (2012, p. 29).

### 2.2. Sustainability of the Public Debt 2.2.1. General Dynamics

To make predictions about the future, we need to know under which conditions the public debt stays constant. For this we analyse the deficit from equation 5 and set the change of debt to zero.

Abbildung in dieser Leseprobe nicht enthalten

The dynamics of this equation will lead to an equilibrium. This means, the debt as well as the price level and the GDP will stay the same over time in this point given a constant primary balance and assuming the interest rate, the GDP-growth rate and the inflation rate stay constant too ceteris paribus. To implement this in the equation, we can delete all the time variables (t). So, the equation for the equilibrium situation looks like following (Burda und Wyplosz 2009, p. 430):

Abbildung in dieser Leseprobe nicht enthalten

By rearranging and substitute (^)with the letter (b) and ("^r)with (g-t) we receive the equilibrium debt to GDP-ratio:

Abbildung in dieser Leseprobe nicht enthalten

Now we can analyse the characteristics of this equilibrium. In the short-run government is able financing its expenditures by debt. But in the long-run bond holders must belief in the credibility of the government to redeem its obligations. As soon as government expenditures exceed revenues, the fiscal stance would rise indefinitely and is not sustainable anymore. Therefore, investors are unwilling to hold government bonds. Crucial for debt sustainability is the interest- growth differential from equation 8 (Wickens 2011, p. 96-97).

Figure 1 illustrates the four different possible equilibria. The equilibrium debt to GDP-ratio can be a positive amount, where the country is a debtor, or it can be a negative amount, where it is a creditor. In Case A and D the sign of the primary deficit and of the difference of the GDP- growth rate and the real interest rate are the same, so the equilibrium debt to GDP-ratio is positive and the country is a debtor. In Case B and C, where the signs of the numerator and denominator of the fraction are different, the debt to GDP-ratio is negative and the country is a creditor. In Case A and B the GDP-growth rate is higher than the interest rate. Consequently, the interest-growth differential is negative and so public debt is sustainable. This means, there is existing a stable equilibrium of debt to GDP-ratio, which is not plus or minus infinite. In Case C and D, where the interest rate exceeds the income growth rate, debt to GDP-ratio is not sustainable and will explode to plus or minus infinite as soon as it leaves the unstable equilibrium (Gärtner 2013, p. 407-409).

Abbildung in dieser Leseprobe nicht enthalten

Reference: Gärtner (2013, p. 409), own figure.

We can take a more detailed view of the four cases in the phase diagrams in figures 2-5. They visualise the development of dynamic models over time. In the upper graph of the figures 2-5 the deficit in nominal GDP from equation 5 is plotted on the y-axis in relation to the debt to GDP-ratio from equation 4 on the x-axis. In the lower graph the debt to GDP-ratio of the next period is plotted on the y-axis in relation to the debt to GDP-ratio of the next period as in equation 4 on the x-axis. To transform the debt to GDP-ratio of the next period to the current period, we transfer it on the 45 degree-axis. So, if we are on the 45 degree-axis, debt to GDP- ratio stays constant. The intercept is the primary balance to GDP-ratio and the slope is defined by (1+r- y). As long as the slope is lower than one in the lower graph like in case A and B, the slope of the upper graph is negative and leads to a stable equilibrium. In case C and D the slope of the lower graph is higher than one and the slope of the upper graph is positive, what shows, that the dynamics lead to an instable equilibrium (Gärtner 2013, p. 408-412).

In Case A we have a primary deficit and the GDP-growth is higher than the interest payment on the debts. This overhang can be used to pay a part of the primary deficit. In the long-run, equilibrium will end at a point where the overhang of GDP-growth over the interest rate will be equal the primary deficit. No matter how high the debt to GDP-ratio was, the economy will end with a stable positive debt to GDP-ratio (Gärtner 2013, p. 409-410).

Abbildung in dieser Leseprobe nicht enthalten

Reference: Gärtner (2013, p. 410-411,417), own figure.

In Case B we have the same situation, only the government runs a primary surplus. So in the long-run the government will now be a creditor instead of a debtor as in Case A. The equilibrium debt to GDP-ratio is stable just like in Case A. Case A as well as Case B are both desirable states, because the government debt is sustainable (Gärtner (2013, p. 409,410).

Abbildung in dieser Leseprobe nicht enthalten

Reference: Gärtner (2013, p. 410-411,417), own figure.

In Case C we have a primary deficit like in Case A, but now the interest rate exceeds the GDP- growth rate. This means, that the interest payments are bigger than GDP grows. The only way to be in equilibrium is to start in the equilibrium point b*. This equilibrium is instable. This means, that every deviation leads to a movement away from the equilibrium point. If we start with a positive debt to GDP-ratio, there will be added more debt in every time period, what will end in infinite debt. Unfortunately this is mostly the situation countries are nowadays confronted with (Gärtner 2013, p. 409-410).

Abbildung in dieser Leseprobe nicht enthalten

Reference: Gärtner (2013, p. 410-411,417), own figure.

In Case D the dynamics lead like in Case C to an instable equilibrium, where a deviation ends in an infinite plus or minus debt to GDP-ratio. Because government runs a primary surplus, we would need a positive debt to GDP-ratio to be in equilibrium. In this case the equilibrium situation is not the preferred status, because a primary balance lower as the equilibrium one would lead to profitable dynamic with infinite assets (Gärtner (2013, p. 409,410).

Abbildung in dieser Leseprobe nicht enthalten

Reference: Gärtner (2013, p. 410-411,417), own figure.

These dynamics are a theoretical approach to explain what would happen if all the variables we look at in this equation stayed constant. In reality these variables differ over time. A country which runs a primary deficit does not has to run the same primary deficit in the next year. Also the interest rate, the inflation rate as well as the GDP-growth rate can change over time. But these dynamics are a good way to illustrate the situation a country is confronted with, to analyse why the situation is changing over time and how it can be revised.

#### 2.2.2. Monetization of Debt

One way to reduce the real public debt from equation 4 is to increase the inflation rate, such that the price level increases and the debt devalues in real terms. To illustrate this, we can take a look at the equation of the quantity theory of money.

Abbildung in dieser Leseprobe nicht enthalten

In this equation M is the stock of money applied by the central bank, also called high powered money, V is the velocity, what measures how often one unit of money in average is used in a time period. P is the price level and Y is the nominal GDP (Burda und Wyplosz (2009, p. 139). Because we want to analyse the growth rate of money, we have to rearrange the equation 9 and take the differential. When we solve for the price level P and assume the velocity or alias the liquidity of money being constant. Finally we receive the following equation (Burda und Wyplosz (2009, p. 144):

Abbildung in dieser Leseprobe nicht enthalten

From equation 10 we can see how money growth is determining inflation. In this equation for being in equilibrium the growth of the money supply must be equal the growth of the money demand. Thus, in the long-term inflation is adjusting in the corresponding amount (Burda und Wyplosz (2009, p. 142-144).

In the past there have been situations, in which we observed very high inflation rates. This phenomenon is called hyperinflation and is mostly the result of monetization of public debt. It describes the process, when bonds emitted by government are paid with money printed by the central bank itself. It is mostly seen in high dimension in a budget crisis. Because the government is unable to finance the deficit in regular ways as discussed in chapter 2.2.1, the money-growth will be increased. When the money growth rises and money growth is higher than GDP growth, inflation will ceteris paribus increase too. With higher inflation the public debt will lose its value in nominal terms and the deficit shrinks.This action of the central bank can happen when the central bank is not totally independent of the government and so the government can influence the decisions of the central bank. Even if the central bank is independent, it is possible, that the central bank feels forced to monetize debt. If the central bank does not monetize debt in the current period, government debt grows even more until the next period and the central bank faces an even higher debt (Blanchard und Illing (2004, p. 672674).

Because printing money is almost costless for the central bank, it can make profits with buying bonds from the government. Since central banks have to give their profits mostly as prescribed by law to the government, the government receives in the end the revenues from printing money, what is called Seigniorage. (Burda und Wyplosz (2009, p. 431) We can express the Seigniorage in an equation as the real money creation (^). To see the growth rate of nominal money supply explicitly, we rewrite the formula by expanding the fraction with the nominal money supply (M). Because we receive the money growth rate, we can substitute this with the definition from equation 10:

Abbildung in dieser Leseprobe nicht enthalten

Now we can look at the Seigniorage as the product of the growth rate of the nominal money supply and the stock of real money supply. The higher the growth rate of the money supply and/or the real money supply in an economy, the higher the Seigniorage. To receive the Seigniorage in relation to the GDP, we divide it by the nominal GDP (Y) (Gärtner (2013, p. 421):

Abbildung in dieser Leseprobe nicht enthalten

In the short-term the price level will not adjust very much, what means, that the Seigniorage can be quite high. But in the middle-term the price level will adjust completely and the real money demand goes down and the effect of monetization will shrink. Constant nominal money growth will not be sufficient anymore and the money growth rate has to be increased to reveive the same effect. But higher inflation normally leads to higher interest rates, what reduces the money demand and the Seigniorage shrinks again after a certain inflation rate^{[2]} (Gärtner (2013, p. 420,421).

To include the Seigniorage in our government budget constraint, we take the definition of Seigniorage from equation 12 and include it in the equation 4, 7 and 9 to receive the following equations. μ is the growth rate of money supply (^)and (m) is the nominal money supply in relation to the GDP ( ) :

Abbildung in dieser Leseprobe nicht enthalten

The two equations 14 and 15 show, that money creation can reduce the debt to GDP-ratio and the deficit of a government. From equation 16 we learn, that it is possible to achieve a lower debt to GDP-ratio in equilibrium, when the government could influence money creation to monetize its debt (Gärtner (2013, p. 419-421). A positive money growth rate would therefore shift down the graphs from figure 2-5. This could lead to a lower equilibrium debt to GDP- ratio, when we have a higher GDP-growth rate than interest rate, as in figure 6 the first shift, or even to a change of the government debt situation in equilibrium from being a debtor to being a creditor in equilibrium like the second shift in figure 6, so that we changed from a situation as in Case A to a situation as in Case B.

Abbildung in dieser Leseprobe nicht enthalten

Reference: Gärtner (2013, p. 408), own figure.

When we have a situation as in Case C like in figure 7, where the interest rate exceeds the GDP- growth rate, money financing of government spending can change the primary deficit to a surplus, what we can see in the shift of the lines. Thus, this can lead to a situation as in Case D. Now dynamics would not end in infinite debt, but instead now in infinite assets. Because of the change in interest payments, a situation like in Case B is preferred to a situation as in Case A and especially in a situation as in Case C the temptation is big to reach a situation as in Case D.

Abbildung in dieser Leseprobe nicht enthalten

Reference: Gärtner (2013, p. 408), own figure.

#### 2.2.3. The Fiscal Theory of the Price Level (FTPL)

As we have seen before in chapter 2.2.2 for a constant debt over time, we need a deficit of zero. If we assume central bank being independent and not monetizing debt, to still fulfil the equation 14, the logic result is a reaction of the primary deficit by an active intervention of the government in form of a restrictive fiscal policy. This kind of policy is called “Ricardian”. A situation in which the equation 14 is not satisfied and neither monetary nor fiscal policy will be adjusted therefor is called “non-Ricardian” policy.

The FTPL says, that even with a “non-Ricardian” policy the intertemporal budget constraint can be satisfied ceteris paribus by an adjustment in the price level (Wickens (2011, p. 105-106). The logic behind this is, when the government can communicate credibly, that it will chose a non-Ricardian policy, the people will anticipate this and chose the price level accordingly. If the people do not chose the price level to fulfil the government budget constraint, it will lead to excessive government debt and the people will not be willing to keep buying government debt in the form of government bonds, because they expect the government will not be able to pay it back in the future (Christiano und Fitzgerald 2000, p. 11-13). Since prices are sticky, this theory is not very plausible in the short-run. (Wickens 2011, p. 106) But in the long-run prices can adjust, that the government budget constraint is in equilibrium again.

**[...]**

^{[1]} To see the detailed derivation of the following equations describing the government budget constraint consult the Appendix A. 1.

^{[2]} As an example we can assume, people have an income per month of 2 and there is a 10% budget deficit of the real income and the government tries to finance this deficit fully by monetization. This gives us the calculation: 0.1=Δ~ *2. So Δ^ has to be equal to 0.05. To monetize the 10% deficit, we need a 5% nominal money growth rate. But if we want to finance 20% deficit, 10% nominal money growth will not be sufficient anymore, because with positive inflation, the price level will raise, what means the real money demand sinks and the Seigniorage has to be even higher (Blanchard und Illing (2004, p. 675-676).

- Quote paper
- Anonymous, 2015, Sustainability of Public Debt in the European Monetary Union. A Case Study of Greece, Munich, GRIN Verlag, https://www.grin.com/document/353300

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