Chapter 1: Tour of the World & Chapter 2: Tour of the Book

The most important concepts macroeconomists use are:

1. Aggregate output

2. Unemployment

3. Inflation

These three concepts are all connected with each other.

1. Aggregate output (total output)

Gross domestic product (GDP) can have three definitions:

• Market value of all the final goods and services in the economy

• The sum of all the added value in the economy

• Sum of incomes in the economy
   

Two types of GDP:

Real GDP 
Measured in constant prices. Goods x constant price. Adjusted for inflation (Yt)

Nominal GDP
Measured in current prices. Goods x current prices (€Yt)

GDP Deflator: the ratio of nominal to real GDP
Appendix (figure 1.1)

GDP Deflator inflation: Measure of the increase in price level of goods produced in the economy during a given year, Yt.
π = growth rate of nominal GDP – growth rate of real GDP
Appendix (figure 1.2)

GDP increases (positive growth rate) is called an expansion
GDP decreases (negative growth rate) is called a recession

Hedonic pricing: Treat goods as providing a collection of characteristics, each with an implicit price. For example, you do not price a computer, but you price each characteristic/part of the computer individually.

2. Unemployment

Unemployment: All the people who are jobless but are looking for one. Is the unemployment a good indicator? Well, it is hard to say whether a person is looking for a job or not. There are persons who are looking for a job, for example students who like to work after graduating but are not legally registered as jobless. There are also people who are registered as unemployed but gave up looking for a job, these people are called discouraged workers.

Appendix (figure 1.3)

Appendix (figure 1.4)

The unemployment rate tells you a lot about the economy. For example how rich an economy is or how easy it is to lose a job or to find a new one.

3. Inflation

Inflation: Sustained rise in the price level

Deflation: Decrease of the price level

The rate of inflation is the rate at which the price level increases

Appendix (figure 1.5)

Consumer price index

The consumers want to know how much they can consume. Another way to calculate what the fluctuation in price is, is to look at the average price of consumption.

Why is inflation important for an economy?

- You want have the same level of purchasing power so when the prices increase, you want you're wage to rise the same amount.

- If you know what the inflation will be, you can choose whether you'll invest now or wait till a moment that prices are lower.

In macroeconomics yu’re speaking of three different time frames:

1. Short run (few years). In the short run markets are not fully able to adjust. Changes in output are often the result of movements in demand.

2. Medium run (a decade). Changes in output are often the result of changes in factors such as capital stock, the level of technology and the size of labor force.

3. Long run (>few decades). Changes in output are the result of changes in factors as education systems, saving rate and education system.

Macro economists use a lot of models.

Models are defined as tools to simplify the complex reality. Models are always true, but they don't give an explanation.

Within models there are two types of variables

1. Endogenous: an endogenous number is something you have to calculate yourself. Y is for example endogenous, it's not constant and you have to calculate it.

2. Exogenous: an exogenous number is a given number and you have to take it for granted. For example G, the governmental expenses are often given and constant.

Chapter 3: The goods market

We start with introducing the goods market by a simple model.
We assume that the economy is closed and demand equals production (Z=Y)

Consumption (C)

All goods and services that consumers buy. Disposable income is the amount of money that is left after consumers paid taxes and received transfers.

Appendix (figure 3.1)

Appendix (figure 3.2)

When disposable income increases, so does consumption.
Parameter c1 is the marginal propensity to consume.
Parameter c0 is what people would consume if Yd were 0.

Investment (I)

Purchase of capital goods. There are two different types of investments, one by households (residential investments) who buy houses or apartments and one by firms (non-residential) buying things for their firm. I is in this simple model an exogenous, constant number.

Appendix (figure 3.3)

Government spending (G)
The sum of government spending on goods and services. T= taxes, this is what the government 'earns'. T+G = fiscal policy. In words, T&G are the instruments of the government, with T&G they have an influence in the economy. T&G are also exogenous, the variables are chosen by the government

International Trade
Export (X) – Import (IM).
Exports > Imports: Trade Surplus
Exports < Imports: Trade deficit

Demand for goods (Z)

Appendix (figure 3.4)

In a closed economy, where X-IM=0 and Y=Z (this means inventory investment equals 0)

Appendix (figure 3.5)

When you want to calculate with this equation, for example to calculate the change in Y you could simplify the equation.

Appendix (figure 3.6)

Where is the multiplier and is the amount of autonomous spending.

An alternative way to calculate the goods market equilibrium is to assume that Investment is equal to savings. By savings we mean public (government) and private (consumer) saving.

Appendix (figure 3.7)

Appendix (figure 3.8)

We can now derive the IS Relation, where investment equals savings
Appendix (figure 3.9)

We can now fill in our previous equations and re-arrange them to get:
Appendix (figure 3.10)

Chapter 4: Financial Markets

Money: payment for transactions, pays no interest

Functions of money:

1. Unit of account (provides the terms in which prices are quoted)

2. Money is a medium of exchange

3. Money is a store of value

There are two types of money. You can hold money in currency and hold money in deposit accounts. When do you invest the money in bonds and when will you keep it in your wallet? This depends on two things:

1. The opportunity cost of holding money (in other words, what will you miss by not invest in bonds, because when you hold money, you won't receive interest (i))

2. Number of transactions you make (When you make a lot of transactions, you must be sure that you have enough money on hand, otherwise you'll have to sell bonds to often)

If you have a money market account you indirectly invest in bonds. The money market funds hold all the money of many people and invest it in bonds to make profit.

The demand for money (money that people want to hold in their pockets) is described in the following equation:
Appendix (figure 4.1)

In words: When you multiply the nominal income with the interest rate you will find the money that people want to hold. This is a negative relationship because when the interest rate goes up, more people will invest in bonds and the demand for money will decrease. In the other direction: when the interest rate goes down, more people choose to not invest in bonds and the money demand will increase.

Appendix (graph 4.1)
The graph of the demand function is has a downwards sloping curve. When the interest is decreasing, more people want to hold their money. Note that: When €Y changes, there will be a shift of the curve. When €Y rises, the curve will shift to the right (a decrease in Y means an automatic rise of money). You will see a shift from 1 to 2. The interest rate stays the same. When Interest is changing, there will be a shift along the curve, from point 1 to point 3. This is caused by the increasing demand for money.

The money supplied is all the money that the central bank supplies. The central bank does not make the money in a machine every day and just make more money when the economy needs it. The way they supply money is buy selling and buying government bonds. The money supply rises when the central bank buys government bonds. They buy the bonds with money, so they offer money to the government. When the central bank sells the bonds the money supply decreases. This actions from the central bank are called open market operations. The money supply function is given by the equation:

Appendix (figure 4.2)

The financial market equilibrium is therefore:
Appendix (figure 4.3)

The central bank can change money supply by buying or selling bonds. This is called an open market operation. When the supply is expanded (the bank buys bonds), it is called an expansionary open market operation. When supply is contracted (the bank sells bonds), it is called a contractionary open market operation.

Fiscal policy in financial market is called monetary policy. The central bank is able to change the interest rate by changing the supply money. The central bank can control the interest rate, but there is one problem. The interest rate can't be lower than zero. The central bank could decrease the interest rate by supplying more money (buy bonds) but when the interest rate is equal to zero, monetary policy becomes powerless. This problem is called the liquidity trap.

There are also financial intermediaries. Financial intermediaries are funds that on one side receive funds from people and firms and on the other side make loans to other people and firms. A bank is an example of a financial intermediaries.

The money banks get from people and firms are called deposit accounts and are their liabilities. The bank keeps some money they receive as a reserve. When a bank keeps all their money received as a reserve it is called full reserve banking.

It is called fractional reserve banking when a bank keeps a fraction of the deposits as a reserve. The reserve ratio (θ) tells you which percentage the bank keeps as a reserve from the total deposits accounts. The reserve are held in cash and in deposits accounts from the central bank. The rest is invested in bonds or to make loans. The assets of a bank is the sum of the reserve, the loans and the bonds. Banks keep reserves because daily inflow and outflow are not equal to each other. The law also requires banks to keep a certain amount reserved, the reserve ratio. This is mainly to avoid bank runs.

The total sum of demand of money is the demand for currency by people plus the demand for reserves by banks.

Demand for money (currency and deposit accounts)

Appendix (figure 4.4)
Where is the demand for currency and is the demand for deposit accounts. The c stands for the proportion of each.

Demand for reserves

The larger the amount of deposit accounts, the larger the amount of reserves a bank must hold.

Appendix (figure 4.5)

Given these two equations, the demand for central bank money is given by:
Appendix (figure 4.6)

Which can be rewritten as:
Appendix (figure 4.7)

To determine the interest rate, set the supply of central bank money (H) equal to the demand for central bank money.

The money multiplier equals
Appendix (figure 4.8)

Chapter 5: Goods & Financial markets: the IS-LM Relation

Goods market:

In chapter 3 [3.3] we saw that investment was a given, constant number. In reality, investments depend on two things: The level of sales and the interest rate. The new relation becomes:

Appendix (figure 5.1)
And therefor the new equilibrium function (in the closed economy) becomes:

Appendix (figure 5.2)

Because the goods market now depends also on i, we can draw the following figure:
Appendix (graph 5.1)
 

When I increases --> I increases --> Y increases

This curve is called the IS curve. This curve is a line of all the equilibriums in the goods market.

The IS curve will shift when there is a change in the exogenous factors, G and T.

Appendix (graph 5.2)

From IS 1 to IS 2: G increases or T decreases

From IS 1 to IS 3: G decreases or T increases

An increase in T shifts the IS curve to the right. And increase of equilibrium level of output also shifts the IS curve to the right.

Financial market:

In the financial market we saw that the demand for money already depends on i.

To compare the IS curve with the financial market we have to rewrite . Appendix (figure 4.1)

This is because the IS curve is related to the real income (Y) and not the nominal income (€Y)

The new equation will become:
Appendix (figure 5.3)

Now we can draw this relation in the same graph as the IS curve
Appendix (graph 5.3)

When Y increases, the demand for money increases but money supply will stay the same. Because of this, i has to go up to let the Md and Ms intersect, so i will increase when Y increases.

This curve is called the LM curve and is a line of all the equilibriums in the financial market.

The curve will shift when there is a change in the money supply or a change in price level:
Appendix (graph 5.4)

When money supply increases there will be a shift from LM 1 to LM 3.

When money supply decreases there will be a shift from LM 1 to LM 2.

Putting the IS&LM Relation together

We have seen that the IS and the LM curve fit in the same graph. When you draw these curves in the same graph they will intersect. Where these lines intersect there is an equilibrium.

Effects of fiscal policy in IS-LM equilibrium

1Fiscal contraction (consolidation) T ? or G ?.

T increases/G decreases, thus C (Y-T?) + I + G? leads to Y? leads to C? leads to Y? and so forth.

The IS curve shifts to the left and a new equilibrium is founded
 

1Fiscal expansion T? or G?

T?/G?, thus C(Y-T?) + I + G? leads to Y? leads to C? leads to Y? and so forth.

The IS curve shifts to the right and a new equilibrium is founded
 

Effects of monetary policy in the IS-LM equilibrium

1Monetary contraction (tightening)

Money supply decreases

The LM curve shifts to the left and a new equilibrium is founded

1Monetary expansion

Money supply increases

The LM curve shifts to the right and a new equilibrium is founded (see page 92 figure 5.9)
 

Policy mix: combination of fiscal and monetary policy
 

Why do you use a policy mix?

• When you want to increase / decrease I but Y has to stay constant

• When you want to reduce budget deficit but Y has to stay constant

Etc.

Appendix (graph 5.5)

Example:

1. LM and IS intersect in ?.

2. The government increases their taxes (T)

3. This leads to a shift of the IS curve to the left

4. A new equilibrium is found in ??

5. Y is not allowed to decrease, so LM has to shift to the right by increasing money supply

6. A new equilibrium is founded ??? with a lower level off interest and the same level of output, Y.

NB: The liquidity trap does still exist! Shifting the LM curve is of no use when i equals zero.

It is also possible to make an analytical version of the IS-LM model.

Chapter 6: The IS-LM Model in an open economy

Openness in the goods market:

Consumers get the choice: will they buy domestic or foreign products? Important in this decision is the exchange rate. How expensive / cheap are foreign product expressed in your own currency? There are to different methods to look at this exchange rate:

1. When you use the nominal exchange rate you look at the price of domestic goods relative to foreign goods. The rate in which one countries currency trades to another counties currency

2. You can also use the real exchange rate. Then you use the rate at which one countries goods are trade for foreign goods. This is descripted in the following equation: You divide the prices of your own goods by the prices of the foreign goods

Appendix (figure 6.1)

Increase in exchange rate: Appreciation

Decrease in exchange rate: Depreciation

In a system with fixed exchange rate, an increase in exchange rate is called a revaluation and a decrease in exchange rate is called a devaluation.

An exchange rate can be seen as bilateral or multilateral. Bilateral means it’s the real exchange rate between two countries. A multilateral exchange rate means the exchange rate between one country and all other countries it trades with. Each country gets a weight, based on how important they are.

In an open economy exports minus imports are not equal to zero. The difference between exports and imports is called NX.

Appendix (figure 6.2)

Note: Because the imports are given in foreign goods, you must divide it by the exchange rate

NX depends on Y, Y* and on .

Y: When Y increases, imports will increase (negative relation with NX)

Y*: When the aggregate output of a foreign country increases, they will import more and your export will increase (positive relation with NX)

: When the exchange rate increases, import will increase because foreign product will be cheaper in proportion to the domestic prices. The export will decrease because your price are now more expensive for foreign countries.

The IS curve will remain downwards sloping. The only change in the IS curve caused by adding import and export is that the slope will be different. When Y will increase, some of the output will leak to imports. Because of this the slope of the IS curve is flatter.

Openness in financial markets:

Balance of payments: a country’s transactions with the rest of the world, including trade flows and financial flows. It is divided by one line:

• Transactions above the line are the current account transactions: payments to and from the rest of the world

• Current account balance: the sum of net payments to and from the rest of the world

• Current account surplus: positive current account balance

• Current account deficit: negative current account balance

• Transactions under the line are the capital account transactions

• Capital account balance: the sum of the net capital flows

• Capital account surplus: positive capital account balance

• Capital account deficit: negative capital account balance

• Statistical Discrepancy is the difference between the current account balance and the capital account balance. In theory, they should be equal. In practice, they are not. And thus the difference is also given on the balance of payments.

Investors get also a choice: Will they buy domestic or foreign bonds? Important in this decision are two things:

1. Differences in interest rate. In which countries is the interest rate the highest?

2. Differences in exchange rate between these countries. A higher level of interest does not explicitly mean a higher income on bonds. You have to keep in mind that you have to ‘translate’ the income you got from holding foreign bonds in your own currency. Sometimes this means that a higher level of i in foreign countries does not refer to a higher income from your foreign bonds. There is an equation that describes this problem

Interest Parity Condition: Appendix (figure 6.3)

This condition is not always true. There are a lot of risks and transactions costs when you invest in foreign bonds. So also if it is more attractive to invest in foreign bonds according to the interest parity condition, a lot of investors will stick to domestic bonds. In the interest parity condition, the bonds have the same expected rate of return.

The interest parity condition changes when the interest rate and expected rate of return are not too large. The new equation will become:

Appendix (figure 6.4)

The LM curve will stay exactly the same, because money supply is exogenous

This means when the ‘new’ IS and LM curve intersect there is an equilibrium founded which gives use a number for I, we can see which number belongs to the exchange rate. The slope of the interest parity condition is upwards sloping. From the equation above we can see that i and E have a positive relation.

When for example, the government increase their spending G? and the IS curve shifts to the right, interest will increase. When interest increases, your domestic bonds are more attractive to foreign investors. This will lead to an appreciation of the currency.

Let’s go back to the demand for domestic goods.

Imports depend on domestic income and the real exchange rate. This gives
Appendix (figure 6.5)

This relation implies that an increase in Y or will lead to an increase in IM.
Exports depend on foreign income and the real exchange rate. This gives

The new equilibrium condition in an open economy, where Y=Z, becomes
Appendix (figure 6.7)

Where Appendix (figure 6.8)
Since we are still in the short run, so the real exchange rate and the nominal exchange rate move together. This implies that = E.

Chapter 7: Output, interest rate & exchange rate

Real depreciation: decrease in the real exchange rate – decrease in the relative price of domestic goods in terms of foreign goods.

There are two important differences between and open and a closed economy:
- In an open economy, there is an effect on the trade balance, for example if government spending increases.
- The effect on output in an open economy is smaller. This is because the multiplier effect is smaller.

We assume that price levels are fixed and inflation equals zero. The interest parity condition hold and demand is determined by output.
When domestic demand increases, the ZZ curve shifts up, which leads to an increase in output and a fall in the trade balance.

Higher foreign output leads to higher exports of domestic goods, which leads to an increase in domestic output and increase in demand for domestic goods through multiplier effect. This improves the trade balance.

If during a worldwide recession, one country wants to follow a policy of expansion, this country will generate a trade deficit. This is because the increase in income will increase imports as well.
? Coordinated expansion work better, but are difficult to arrange.
This is because some countries might have to do more than others, but are not willing to do so. Countries also have a strong incentive to promise to coordinate, while not planning on doing so.

Recall the trade balance: Appendix (figure 6.8)

Real depreciation has two effects:
1. Increase in exports and decrease in imports (quantity effect), leads to an increase in the trade balance.
2. Increase in the relative price of imports (price effect), leads to a reduction in the trade balance.

Whether the trade balance will actually increase or decrease depends on the Marshall-Lenner condition. This condition implies that real depreciation leads to an increase in net exports.

Depreciation leads to a shift in demand (foreign & domestic), toward domestic goods. This leads to an increase in domestic output, which improves the trade balance.

The best way to reduce a trade deficit is to use a mix of policies.

The J-Curve
The dynamic effect of real depreciation: The price effect happens immediately, but the quantity effect takes some time. Therefore, there will be a temporary fall followed by a step by step improvement. This process is called the J-curve.

We will now look at savings, investment and the trade balance. Appendix (figure 7.1)

Where Appendix (figure 3.9)

An increase in the budget deficit leads to an increase in saving, leads to a decrease in investment.

Effects of policy in an open economy
Increase in G, means an increase in output, increase in interest rate & an appreciation.
Monetary contraction, means a decrease in output, increase in interest rate & an appreciation.

Fixed exchange rates
Pegging: Method of stabilizing a country’s currency by fixing its exchange rate to that of another country. (Often the dollar)
Crawling peg: Countries have inflation rate that exceeds the US inflation rate.

If the exchange rate is fixed, expected depreciation is zero, and i=i*

When the exchange rate is fixed
- the central bank loses monetary policy as a policy instrument. However, fiscal policy becomes more powerful than with flexible exchange rates.
- The domestic interest rate must be equal to the foreign interest rate.
- To maintain the interest rate, money supply must be adjusted.

Why fixed exchange rates are not optimal:
- The government loses their monetary policy, which can be a powerful tool.
- It also loses control of the interest rate.
- It is better to have two policy instruments.

Chapter 8: The Labour Market

Whole population: The whole population exist of all the people in the working age and the population out of working age (<15 or >65). The working population consists of the labor force and the people out of the labor force. The labor force consists of the sum of employment and unemployment.

There are different formulas to calculate the division of the labour market.
Appendix (figure 8.1)

Appendix (figure 8.2)

Some economists say that the unemployment rate is not a good indication of the employment/unemployment ratio, because of the discouraged workers. These people are unemployed but are not actively looking for a job, but when they find one they will take it. In this case, the economists say, it’s better to look at the non-employment rate: employed population in working age/ unemployed population in working age.

We will now look at the determination of wages.
One way to determine wages is through collective bargaining: bargaining between firms and unions.

There are two facts in wage bargaining:
* Workers are typically paid a wage that exceeds their reservation wage
* Wages depend on labour market conditions.

Why do firms pay more than the reservation wage? Because of the efficiency wage theories. Firms believe that an employer works more productively, more efficient and the turnover rate would be lower (less workers will quit their job)

But how much the wage exceeds the reservation wage depends on two things:
- The nature of the job: high-tech firms pay higher wages than firms where workers’ activities are more a routine.
- Labour market conditions: low unemployment means higher turnover, since it’s easier to find a new job.

The level of bargaining power depends on:

1. Costs of replacing worker (nature of the job)

2. How hard is it to find a new job

How high the unemployment is, is a very important factor for the level of bargaining power.

When the unemployment is high, it is easy to find new employers for the firm + hard to find a new job for the employers. Therefore, there is less bargaining power.

When the unemployment is low, It is hard to find new employers for the firm + easy to find a new job for the employers. Therefore, there is more bargaining power.

Wages
We can determine wages through the following formula:
Appendix (figure 8.3)
Where W is the aggregate nominal wage, is the expected price level, u is the unemployment rate and z is a catchall variable (all other variables that may affect outcome)
Workers and firms do not care about real wage, but about nominal wage. They want to know how much they can buy with the wage they receive.

Appendix (figure 8.4)

When P?, You can buy less with the same nominal income, so real wage decreases. Thus, Employees want a higher nominal income (They want the real wages to stay constant.)

The expected price level is used because, to determine the nominal wages for the next few years. (These wages are always determined for a few years in the future) they look at the price fluctuation they expect in the following years. This is a positive relation, how higher they expect P to be, how higher they’ll set W.

The relation between unemployment and wages is as you can see, negative.
 

All other variables
Of course the unemployment rate and the expected price level are not the only factors that determine the wage. These are some examples of other factors:

-Unemployment insurance
-Employment protection
-Minimum wage

Prices
How high/low the firm the price will set depends on the costs of production. We therefore look at the production function:
Appendix (figure 8.5)
We assume, however, that labor productivity is a constant, A=1. The equation therefore becomes Y=N

The cost of producing one more unit of output is the cost of hiring one more worker, at wage W. The marginal cost of production are therefore equal to W.

The equation of the price looks like this:
Appendix (figure 8.6)

Where μ is the mark-up of price over cost.

In a perfectly competitive market the mark-up is equal to zero because MC=MP. (W=P) When there is less competition, the mark-up is > 0.

The product market regulation (PMR) determines how competitive a product is. When there are for example a lot of trade barriers there is less competition. So
Appendix (figure 8.7)

This is a positive relation: When PMR is high, there is low competition, and thus a higher mark-up.

To determine the unemployment we have to plot the wage setting relation and the price setting relation in the same graph.

As we noted before, the wage-setting relation:

Appendix (figure 8.8)

But since we are more interested in the real wage than in nominal wage we rewrite the equation like this: (this is a negative relation, thus a downward sloping line)
Appendix (figure 8.8)

The price-setting relation:

Appendix (figure 8.6)

To plot the price-setting relation in the same graph as the wage setting relation we have to adjust this equation.

Appendix (figure 8.9)

μ is exogenous in this graph, so a constant number. This causes that the price-setting relation is a vertical line.

When the W/P determined by price-setting and the W/P determined by wage-setting are equal you’ll find the natural rate of unemployment.

Shifting of the Wage-setting (WS):

Employment protection increases --> z increases --> W/P increases for same u --> W/P shifts to the right --> natural rate of unemployment goes up

Shifting of the Price-setting (PS):

When PMR decreases, there is more competition, so the Mark-up goes up. W/P decreases, and therefore, PS shifts down, so the natural rate of unemployment becomes higher.

We can rewrite the relation between (un)employment and the labour force to get:
Appendix (figure 8.10)

We can rewrite this in terms of employment to get:
Appendix (figure 8.11)

The small n stands for the natural rate.
From the natural level of employment we can derive the equation for the natural level of output.

Appendix (figure 8.12)

So the natural level of output satisfies:
Appendix (figure 8.13)

Chapter 9: All markets together: AS-AD Model

The aggregate supply (AS) function captures the effects of output on the price level.
We can find this function through the wage & price determination relations.
Appendix (figure 9.1)
The AS relation has two properties: an increase in output leads to an increase in price level, and an increase in expected price level leads, one-for-one, to an increase in P.

The AS curve is upward sloping, goes through point A (where output is equal to its natural level and the price level is equal to the expected price level.) An increase in the expected price level shifts the AS curve up.

The aggregate demand (AD) function captures the effects of price level on output. We can find this function through the IS & LM relations.
Appendix (figure 9.2)
The AD curve is downward sloping: an increase in price level leads to a decrease in output. If government spending goes up, the curve shifts to the right. The same happens when nominal money decreases.

Short run equilibrium.
In the short run, is a given. This implies that the natural rate of output is below the actual output in the short run.

Medium run equilibrium
In the medium run output will be equal to the natural level of output. Since the expected price level is below the actual price level, wage setters will expect a higher price level. If the expected price level increase, the economy will move along the AD curve. The equilibrium shifts and output will decrease. This continues until output is back to its natural level.

Effects of a monetary expansion 
We will look at the AD curve: if M increases, output increases. The AD curve shifts to the right in the short run. In the medium run, it has no effect on output, because of the neutrality of money.

Effects of a decrease in budget deficit
We will now look at the AD curve. If government spending (G) decreases, the AD curve shifts to the left. In the short run, output and price level will decrease. There is a possibility that investment will decreases as well.
In the medium run, Y remains unchanged and investment increases. This is because over time, output always goes back to its natural level.

Changes in the price of oil
When the price of oil goes up, the cost of production will go up. This will cause an increase in P since P is determined by the costs of production. When P increases, W/P decreases.

Appendix (figure 8.9)

So when the left side of the equation decreases, the right side has to decrease too. Because the mark-up is the only variable, the mark-up has to increase to let this right side decrease too. When 1/ (1+ μ) decreases, the price setting curve will shift down. In the new equilibrium, the unemployment is higher.
In the short run, the AS curve will shift up. The natural level of output decreases.

Chapter 10: The Phillips curve, natural rate of unemployment & inflation

Recall the AS Relation:

Appendix (figure 10.1)
We know that F come from the wage setting relation:

Appendix (figure 9.2)

We shall assume that this function F is exponential, given in the form:

Appendix (figure 10.2)
To get rid of e, we will replace F in our AS relation with the new form. After, we will use logarithms to get to the following function:
* Appendix (figure 10.3)
Note that we added indexes, t, which stands for year.
This function shows us that an increase in expected inflation, , leads to an increase in actual inflation, .
Given expected inflation, an increase in the mark-up or an increase in factors that affects wage determination, leads to increase in inflation. An increase in unemployment rate leads to a decrease in inflation.

Phillips curve
In the past, the average inflation rate was equal to zero. This resulted in an expected inflation which was also equal to zero.
Appendix (figure 10.4)
This leads to the wage-price spiral:
- In response to a higher nominal wage, firms raise prices and the price level goes up.
- A higher price level leads to a higher nominal wage the next time the wage is set.
- A higher nominal wage leads to higher prices and again a higher price level
- This continues over time.
- Low unemployment leads to a higher nominal wage.

In the beginning of 1970, the Phillips curve vanished in the USA. This was because of two reasons:

1. The USA was hit twice by large increases in oil prices.

2. In 1960, inflation became consistently positive and more persistent. Therefore, wage setters changed the way they formed expectations. (If you expected inflation, it will be true)

Suppose expectations of inflation are formed according to:

Appendix (figure 10.5)
The higher the value of , the more last year’s inflation leads workers & firms to revise their expectations. If is (close to) zero, expected inflation equals zero. If equals one, the expected inflation equals last year’s inflation. We can now add the expectations of inflation in our original formula:
Appendix (figure 10.6)
If is zero, we get our original Phillips curve. When is positive, the inflation rate depends on unemployment and last year’s inflation.
For equal to one, our formula becomes:

Appendix (figure 10.7)
This implies that unemployment does not affect the inflation rate, but change in inflation rate. If the change in inflation is positive, unemployment is low.
The natural rate of unemployment is such that expected inflation = actual inflation. In such case, the left side of the equation becomes zero. If we solve that for the natural rate of unemployment, we get: Appendix (figure 10.8)
We can now rewrite our equation to get (when expected inflation equals actual inflation)
Appendix (figure 10.9)
The natural rate of unemployment is the rate of unemployment required to keep the inflation rate constant: non-accelerating inflation rate of unemployment (NAIRU)

The EU since 1970
The main problem in Europe is the labor market rigidities. There is a generous system of unemployment insurance (and thus a high replacement rate: the ratio of unemployment benefits to after-tax wage), a high degree of employment protection, there are minimum wages and bargaining rules are set.
However, there are two facts we should remember. The first is that unemployment in Europe was not always high, and the second is that many European countries actually have low unemployment.
Let’s imagine that the economy has two types of labour contracts
- proportion, , of labor contracts is indexed
- proportion, 1-, of labor contracts is not indexed

Therefore, we get: Appendix (figure 10.10)

When =0, all wages are set based on expected inflation. This gives us our previous equation:

Appendix (figure 10.9)
When is positive, a proportion of wages is set on basis of actual inflation rather than expected inflation. We reorganize our equation to get
Appendix (figure 10.11)
Wage indexation increases the effect of unemployment on inflation.

Chapter 11: Inflation, money growth & real rate on interest

The economy is characterized by three relations
1) Okun’s Law: the relation between output growth and change in unemployment.
2) Phillips curve: the relation between unemployment, inflation & expected inflation.
3) AD relation: relation between output growth, money growth and inflation.

Okun’s Law
In Chapter 7, we assumed that Y=N and that the labour force is constant.

We now make new assumptions:
- If employment increases by 1%, output increases by 1% (they move together)
- If employment increases by 1%, unemployment decreases by 1% (opposite movement)
The following relation would hold:
Appendix (figure 11.1)
 

Where is the growth rate of output from year t-1 to year t.
If we look at 30 years of data, the line that fits best is

Appendix (figure 11.2)
This implies that to maintain a constant unemployment rate, output growth must be 3% per year. This growth rate of output is the normal growth rate (Rate of output needed to maintain a constant unemployment rate).

Labour hoarding: In bad times firms hoard labour – labor they will need when times are better.

We can rewrite our last equation [11.2] with letters rather than number’s:
Appendix (figure 11.3)
where is the normal growth rate and is the effect of output growth above normal change in unemployment rate.

Okun’s law implies that
- If > , then <
- If < , then >

Phillips curve
Appendix (figure 10.7)

Aggregate Demand Relation
Recall Appendix (figure 9.2)
We will make two simplifications:
- Ignore changes in factors other than real money
- Assume a linear demand between real money balances & output.
Then, we get the following equation:
Appendix (figure 11.4)
Where is a positive parameter. If is a constant, it follows that
Appendix (figure 11.5)
The growth rate of output depends on the growth rate of nominal money minus the growth rate of the price level
- If the growth rate of money > inflation, the growth rate of output > 0
- If the growth rate of money < inflation, the growth rate of output < 0

Effects of money growth
Medium run: Assume that the bank maintains a constant growth rate of nominal money, .
- The unemployment rate is constant. In the medium run, output must grow at its normal rate of growth (Okun’s law)
- The AD relation is constant. The expression for inflation becomes: *
- If inflation is constant, the Phillips curve implies that unemployment is at its natural rate.
> Thus, the only determinant of inflation in the medium run is .

Nominal & real interest rate in the medium run
We rewrite the IS equation, assuming that output is at its natural rate.
Appendix (figure 11.6)
If output growth equals zero, the rate of inflation is equal to nominal money growth.

The relation between nominal and real interest rate is:

Appendix (figure 11.7)

In the medium run, the real interest rate is equal to the natural real interest rate and expected inflation is equal to actual inflation. Since inflation is also equal to money growth, we get: Appendix (figure 11.8)
In the medium run, money growth does not affect the real interest rate, but it affects both inflation and nominal interest rate one-for-one.

Short run
Suppose that the market is in its medium run equilibrium and the bank decides to decrease nominal money growth. A tighter monetary policy leads initially to lower output growth and lower inflation. There will be a temporary increase in unemployment. In the medium run, output growth returns to normal and unemployment to its natural rate. Money growth and inflation are both permanently lower.

From short run to medium run
Lower interest rate leads to higher demand, which leads to Higher output. Eventually, there will be higher inflation, which leads to a Decrease in real money stock, and finally an Increase in interest rate.

Fisher Hypothesis 
(Medium run) Increases in inflation lead to one-for-one increases in nominal interest rate.
There are two types of evidence for this hypothesis:
- Relation between nominal interest rates and inflation across countries
- Relation between nominal interest rate & inflation over time in a given country

Disinflation A decrease in the inflation rate
Situation: medium run equilibrium.

According to the Phillips curve, for inflation to decrease, unemployment must be higher than the natural rate of unemployment.
> This can be achieved quickly or slowly, but the amount of unemployment summed over the years will be the same.

Point-year of excess unemployment – difference between natural and actual unemployment rates of 1 percentage point for one year.

Appendix (figure 11.10)

Lucas Critique
It is naïve to try to predict the effects of a change in economic policy entirely on basis of relationships observed in historical data.
Instead of a policy, one should change their expectations to achieve a wanted outcome.
There is one essential ingredient for successful disinflation: the credibility of monetary policy.

Nominal Rigidities (by Fisher & Taylor)
Many wages and prices are set in nominal terms for some time and are not typically re-adjusted when there is a change in policy.
Fisher: even with credibility, too rapid a decrease in nominal money growth would lead to higher unemployment.

Taylor: Wage contracts are not all signed at the same time, but they stagger over time. This staggering of wage decisions imposed strong limits on how fast disinflation could proceed without triggering higher unemployment.

Laurence Ball came to three main conclusions:
- Disinflations typically lead to a period of higher unemployment
- Faster disinflations are associated with smaller sacrifice ratios
- Sacrifice ratios are smaller in countries that have shorter wage contracts.

Chapter 12: Medium Run in Open Economy

Fixed nominal exchange rate regime, two methods of adjustment:
- Slow, in medium run, through movement of prices and real exchange rate.
- Fast, through devaluation.

Optimum currency area: group of countries that satisfy at least one of the following two conditions:
- similar economic shocks
- high factor mobility within group

Recall: Appendix (figure 6.1)

We can adjust the real exchange rate through the nominal exchange rate, E, or through a change in the domestic price level, P, relative to foreign price level, P*.

Appendix (figure 12.1)

Remember what happens with fixed exchange rates [Chapter 7].
Open economy with fixed exchange rates: price level affects output through its effect on its real exchange rate.

Increase in the price level, leads to a real appreciation and a decrease in output: the aggregate demand curve is downward sloping. An increase in output leads to an increase in the price level: the aggregate supply curve is upward sloping.

Equilibrium in short and medium run

Appendix (figure 9.1)

Whenever output is below its natural level, the decreasing price level leads to a steady real depreciation.
- Short run: Fixed nominal exchange rate means fixed real exchange rate.
- Medium run: Fixed nominal exchange rate means real exchange rate adjusts through price level movements.

For given price level, a devaluation leads to a depreciation, and finally an increase in output.

Devaluation in the right amount can bring the economy back to its natural level after a recession. However, this is often too good to be true. One main reason is the dynamics of adjustment.

Gold standard
system in which each country fixed the price of its currency in terms of gold and stood ready to exchange gold for currency at the stated parity.

Under fixed exchange rate: interest parity condition holds!

Appendix (figure 6.4)

When there are expectations of devaluation, banks/government have a few options:
- Convince markets there is no interest in devaluating.
- Increase interest rate.
- Choice is between the two options mentioned above.
Of course, the government can also react by making expectations come true.

Exchange rate movements under flexible exchange rates
Rewrite interest parity condition for year (y+1) rather than year t. This gives
Appendix (figure 12.2)

We can modify this equation until we get an equation that continues to solve the same way in time.

Appendix (figure 12.3)

This tells us the current exchange rate depends on two factors: (if n=10)
1. Current and expected domestic and foreign interest rates for each year over the next 10 years.
2. The expected exchange rate 10 years from now.

If domestic and foreign interest rates are expected to be the same for n years, the equation reduced to:
Appendix (figure 12.4)

News about the current account is likely to affect the current exchange rate. The same goes for news about current and future interest rates.

Exchange rate volatility makes it difficult to predict what will actually happen.

Flexible exchange rates are preferred, expected when:
- Group of countries is tightly integrated.
- When central bank cannot be trusted to follow responsible monetary policy.

Hard peg is a symbolic or technical mechanism by which a country plans to maintain exchange rate parity. Extreme form of hard peg is dollarization.

Currency board: Central bank stands ready to exchange foreign currency for domestic currency at official exchange rate set by the government. The bank cannot engage in open market operations.

Common currency areas (like European union): optimal currency area is satisfied two conditions:
1. Countries have similar shocks, thus similar monetary policy.
2. Countries have high factor mobility.

Chapter 13: The facts of growth

We care about growth because we care about the standard of living. The standard of living is an important indicator.

How can we measure the size of the standard of living per country?

Just translating one’s currency in the currency of the other country via exchange rates is not the best thing to do because the exchange rate fluctuates a lot and the price of living varies from country to country.

The solution is to use the Purchasing Parity Power (PPP). Here you use the adjusted real GDP, so you look at how much somebody can buy, instead of how much money someone has. We have three remarks:
1. We are more interested in how much we can consume rather than how much the output (GDP) would be. But since consumption and output move in the same direction this problem is not disturbing.
2. Productivity is more important than the total output. When you calculate output per worker you get a clearer and more precise view of an economy. (Soon we will adjust this remark and start calculating with the output per worker)
3. We probably care about the standard of living because we care about happiness. But is there a relation between happiness and standard of living? Research proved that there is a positive relation between this factors but only until a certain level.

Since 1950 there are two main conclusions with regard to growth:
1. There has been an increase in output per person
2. The difference between output per worker between countries decreased.

Long ago there wasn’t any growth in the economy. This was caused by the Malthusian trap. Any rise of the productivity would lead to an increase in the population that leads to a decrease in the productivity per person.

We can also look at growth across different countries (since 1950)
- Rich OECD countries start at high levels of output per person and there is a clear evidence of convergence.
- Asian countries also convergence. Japan is the highest, but the four tigers (Hong Kong, Singapore, Taiwan & South Korea) are catching up.
- In African countries, there is no convergence. Many countries have had a negative output per person.

Growth theory: Takes many of a country’s institutions as a given.
Development economies: Asks what institutions are needed to sustain steady growth and how to put these institutions in place.

We will now update our production function with two inputs: Capital & Labour.

Appendix (figure 13.1)

Two sorts of input determine production. The first one is K, capital. This is the sum of all the machines, plants and office buildings. The second one is N, labour. This is the amount of people that are working

The state of technology determines how much input leads to how much output.

Returns to scale: What happens with output if you double the input?

Appendix (figure 13.2)
If a scale of operation is doubled, output will also double.
There are also decreasing and increasing returns to scale. With decreasing returns to capital, increase in capital will lead to smaller and smaller increases in output (given the labor). The output/capital per worker with constant returns to scale is x = 1/N
With a decreasing return to production factors, the output per worker equals:
Appendix (figure 13.3)
Where is the capital per worker.
The relation between output per worker (Y/N) and capital per worker (K/N) is positive. But because of decrease returns to capital, the growth of Y/N, when K/N increases will become smaller and smaller.

Now we can say that the growth of production is coming from two things:
1. Capital accumulation (K/N increases)
2. Technological progress.

Capital and output affect each other in different ways.
- The amount of capital affect the amount of output directly.
- The amount of output determines the amount of capital indirectly.

Chapter 14: Saving, capital accumulation & output

Recall the function Appendix (figure 14.1)
To simplify, we say: Appendix (figure 14.2)

We make two assumptions:
- Population size, participation rate & unemployment rate all are constant (thus, N is a constant).
-To focus on the role of capital we assume that there’s no technological progress.

Effects of output on capital accumulations

Output & Investment
We assume to have a closed economy, where T-G=0, so we can focus on the behavior of private saving. Investment is equal to private saving, which is proportional to income. We get: Appendix (figure 14.3)
This is a positive relation, higher output implies higher investment and so higher savings.

Investment & capital accumulation
How much does capital increase/decrease per year?
There is one proportion of capital stock that becomes useless (depreciation), which we denote by . We add investments to calculate the new amount of capital stock.

Appendix (figure 14.4)

We combine both expressions for the relation from output to capital accumulation.
Since economist want to calculate in capital per worker we divide both sides by N.
Appendix (figure 14.5)
Which we reorganize to get: Appendix (figure 14.6)
The change in capital is equal to the saving/investment per working minus the depreciation.

Since Appendix (figure 14.2) we will write this equation as:

Appendix (figure 14.7)

When depreciation exceeds investment per worker there is a negative growth in capital. When investment exceeds depreciation per worker there’s a positive growth in capital.

How do you come to a steady state?
A steady state is a state where there is no growth in capital per worker. In other words, the saving/investments per worker equal the depreciation per worker. In the long run, an economy will reach this point. This can be explained with an example.

Assume that in a country the investment per worker exceeds the depreciation per worker. This will cause an increase in capital per worker, which will lead to an increase in output per worker. When the output per worker increases, the point on the line of output per worker shifts to the right. When investment still exceeds depreciation and capital, so output per worker increases, the point on this line will shift further to the right, until the moment that investment equals output. At this point you’re in the steady state.

Appendix (figure 14.8)

The saving rate & output
1. The saving rate has no effect on long-run growth of output per worker, which is zero.
Stalinist growth: Growth resulting from a higher & higher saving rate over time.
2. The saving rates determines the level of output per worker in the long run. Countries with a higher saving rate achieve higher steady-state level of output per worker.
3. An increase in the saving rate will lead to a higher growth of output per worker for some time, but not forever.

A country that is closer to its steady state level of capital per worker will grow less quickly than a country that is more distant to its state level of capital per worker.

The saving rate & consumption
Governments can affect the savings rate
- They can vary public saving. A public saving leads to a budget surplus, a public dissaving leads to a budget deficit.
- They can use taxes to influence savings.

An increase in saving leads to a decrease in consumption.
- A country in which the saving rate is zero, capital will be zero. In this case, output and consumption will also be zero.

- if the saving rate is one, people save all their income. The level of output and capital will be high, but consumption will also be zero.

Golden-rule level of capital
The level of capital associated with the value of the savings rate that yields the highest level of consumption in a steady state. This value is the saving rate golden rule.

Getting a sense of magnitudes
Assume a production function in the following form:
Appendix (figure 14.9)
To get output per worker, divide both sides by N:
Appendix (figure 14.10)
So Appendix (figure 14.11)
The evolution of capital over time: Appendix (figure 14.12)
The effects of the saving rate on steady state output
In the steady state, the amount of capital per worker is constant, so the left side equals zero. Thus we get:
Appendix (figure 14.13)
We square both sides, and after we divide them by K*/N and change the order to get:
Appendix (figure 14.14)

Appendix (figure 14.15)
A doubling of the savings rate leads in the long run to the doubling of output per worker.

The savings rate and the Golden Rule
The steady state consumption is the largest when s equals 0.5

Physical versus Human capital
Human capital: A set of skills of workers in the economy (education is key).

We can extend to production function to include human capital
Appendix (figure 14.16)
The same conclusions go for human capital accumulation as for physical capital accumulations.

There are some complications:
- (Higher) education is partly consumption and partly investment. We include only investment for our purpose.
- For post-secondary education, opportunity costs are the foregone wages one could have earned while acquiring education. This should be included in spending on education.
- Formal education is only part of education. We do not include costs for on-job training.
- Compare investment rates net of depreciation.

Countries that save/spend more on education can achieve substantially higher steady-state levels of output per worker.

Endogenous growth: A higher level of output is not always equal to a higher growth of output.
Challenge this conclusion: Joint accumulations of physical & human capital might be enough to sustain growth.
Models of endogenous growth: Models that generate steady growth even without technological progress.

Chapter 15: Technological Progress and Growth

First, we assumed that the production function could only be affected by capital (K) and labor (N). The production function looked like this: Appendix (figure 13.1)

We will now add the technological progress to our function. We name it A. The new equation will become:
Appendix (figure 15.1)
We multiply A by N so that it’s easy to calculate the relation between K, A and N. When you multiply N by A, you are no longer speaking of labor. Because you multiply the labor by the productivity you are speaking of effective labor.

All our equations will change a bit. Instead of dividing Y and K by N, you’ll now divide it by AN. We will no longer speak of output per worker or capital per worker, but we we’ll speak of output per effective worker and capital per effective worker.

There will also be a change in the steady state. As you remember, in steady state, capital per effective worker is constant. This implies that investment per effective worker and depreciation per effective worker need to be equal. How high does the amount of investment/savings need to be to equal the change in capital? First we assumed that the change in capital was just the depreciation times the amount of capital. But the amount of labor (N) and technology (A) are also likely to change of time.

Appendix (figure 15.2)

When the population increases: labor increases, Nt x At increases so the level of capital per effective worker decreases.
When technology increases: At x Nt increases so the level of capital per effective worker decreases.

We assume constant returns to scale. We also assume decreasing returns to scale for each of the two factors.
Capital per effective worker and output per effective worker converge to constant values in the long run.

Appendix (figure 15.3)

Where is the rate of the technological progress and is the rate of the population growth. So put it in other words: in steady state, the growth rate is equal to the Gn+Ga. This is a balanced growth.

The change in capital per worker is not only the depreciation times the capital per worker, but now also the growth rates of N and A times capital per worker. So, saving per effective worker needs to be equal to the change in capital per effective worker:

Appendix (figure 15.4)

How does the saving rate affect the growth in steady state? Because the growth rate is equal to , there’s a constant growth and the saving rate is not able to affect this growth. But as we have seen in the previous part, the equilibrium of change in capital () and the investments is at a higher level of output per effective worker, there’ll be for some time a bigger growth until it reached again the slope of .

We talk all the time about technological progress, but what is this and how could there be a progress in it? The most technological progress in modern economies would be the result of the research and development (R&D) activities. The amount of R&D depends on the fertility of research, how much do firms really benefit from their results of R&D. The fertility of research depends also on different factors:
- Nature of the research product.
- Legal protection. When there won’t exist any patents, firms won’t be eager to discover new things. The will just wait till some other firm discovered it, see if it works on the market and copy it.

IT revolution: new economy
- In IT, technological progress has proceeded at extraordinary pace.
- Steady decreases in the prices of IT equipment has led to increase in stock of IT capital
- IT revolution does not appear to have had a major direct effect on pace of technological progress in non-IT sector.

Because the discovery of a new product can lead to a better discovery by another firm, no firm will find investment worthwhile. Therefore, there should be legal protections for new products, like patent.

The facts of growth revised
Capital accumulations versus technological progress in rich countries since 1950:
Fast growth may come from two sources:
- It may reflect a high rate of technological progress under balances growth.
- May reflect instead the adjustment of capital per effective worker, K/AN, to a higher level.

Appendix (figure 15.5)
Conclusions:
- Growth since 1950 has been a result of rapid technological progress
- Convergence of output per worker across countries has come from higher technological progress

Two sources of convergence between countries:
1 – Poorer countries are poorer because they have less capital to start with. Over time, they accumulate capital faster than others.
2 – They are less technologically advances, over time they become more sophisticated.

Capital accumulation versus technological progress in China since 1980
- Growth in China has been nearly balanced.
- High growth of output per worker reflects a high rate of technological progress.

This requires a high investment rate. How has China been able to achieve such technological progress?
- China has transferred labor from the countryside to service and industry in the city
- China has imported technology of more technologically advanced countries.

Technological frontier More advanced economies
Technological catch-up Imitation in easier than innovation

Expectations: an introduction

Nominal interest rate – Interest rate in terms of units of a national currency. This is denoted by

Real interest rate – Interest rate in terms of a basket of goods. This is denoted by

The relation between real and nominal > adjust nominal interest rate to take into account expected inflation.
We will now look at this relation, given that there is one good in the economy.
The price of a good this year equals . To buy one more item of the good, one must borrow the price of a good.
Appendix (figure E.1)
Appendix (figure E.2)
Appendix (figure E.3)
We can now rewrite our formula from chapter 6 to get our exact relation:
Appendix (figure E.4)
When the interest rate and the inflation are not too large, we have an approximation of our equation, which is:
Appendix (figure E.5)
- If the expected inflation equals zero, the nominal and real interest rate are equal.
- If the expected inflation is positive, real interest rate is bigger than the nominal interest rate.
- For a given nominal interest rate, the higher the expected inflation, the lower the real interest rate.

Instead of one good, we use the price level (price of a basket of goods).

Nominal and real interest rates in UK since 1980
- Real interest rate is based on expected inflation.
ex-ante: before fact, the real interest rate
ex-post: after fact, inflation known. Realized interest rate.

How can expected inflation be measured?
- From surveys of customers and firms
- Comparing yield on nominal government bonds with that on real government bonds of same maturity.

Nominal and real interest rates and IS-LM model
In the IS relation, firms care about the real interest rate
Appendix (figure 11.7)
In the LM relation, money demand depends on the nominal interest rate of the bonds.
Appendix (figure 5.3)
We also saw in the relationship between real and nominal interest rate in chapter 11:
Appendix (figure 11.8)

Effects of a monetary policy on output depend on how movements in the nominal interest rate can translate into movements in the real interest rate.

Money growth, inflation, nominal & real interest rates
- Higher money growth leads to lower nominal interest rates in the short run but to higher nominal interest rates in the medium run.
- Higher money growth leads to lower real interest rates in the short run but has no effect on real interest rates in the medium run.

Revisiting the IS-LM model
> The IS curve is still downward sloping. For a given , i & r move together.
> The LM curve is upward sloping. Given the money stock, an increase in output leads to an increase in money demand. This requires an increase in i.
> The equilibrium is in point A.

Nominal and real interest rates in the short run.
The economy is at its natural rate, where output equals the natural rate of output.
When the rate of money growth increases, M/P increases. Both i & r decrease, and Y increases. An increase in the real money stock causes the LM curve to shift down.

Expected Present Discount Values
of a sequence of future payments is the value today of this expected sequence of payments. If the value of these payments exceed the costs, one should make the investment.

Computing the expected present discount values
- 1€ next year is worth this year.
- (discount factor) is the present discounted value of 1€ next year.
- If the discount rate, , goes up, the discount factor goes down.

The general formula
Appendix (figure E.6)
Where represents today’s payment, and stands for the present discounted value of a sequence of payments. The more distant the payment, the smaller the discount factor. If we write with z to the power of e, we calculate the value with expected values.

Constant interest rates
When the interest rate is a constant:
- The present value is the weighted sum of current and expected future payments, with weights that decline geometrically through time.
- The weight on payment n years from now is

Constant interest rates and payments
Appendix (figure E.7)
Where the equation between brackets is the geometric series. The whole formula can be rewritten as:

Appendix (figure E.8)
If there are infinite constant payments, €z, we can simplify our equation to the form:
Appendix (figure E.9)
If there are zero interest rates, 1/(1+i) equals 1 for any power of n.

Nominal versus real interest rates and the present value
Appendix (figure E.10)

Chapter 16: Financial Markets & Expectations

Bonds differ in two dimensions:
- Default risk: Risk that issuers of the bond will not pay back the full amount promised by the bond.
- Maturity: Length of time over the bonds promises to make payments to the bondholder.

Before we continue, we will first look at some vocabulary related to bonds.
Government bonds Bonds issued by the government.
Corporate bonds Bonds issued by firms.
Bond ratings Bonds are rated for their default risk.
Risk premium Difference between interest paid on a given bonds and the interest paid on a bond with the highest rate.
Junk bonds Bonds with the highest default risk.
Discount bonds Bonds that promise a single payment at maturity.
Face Value The name of this single payment.
Coupon bonds Bond that promises multiple payments before maturity and one payment at its maturity.
Coupon payments Payments before maturity.
Coupon rate Ratio of coupon payments to face value.
Current yield Ratio of coupon payment to price of the bond.
Life of a bond Amount of time left until a bond matures.
Nominal bonds Bonds that promise a sequence of fixed nominal payments.
Indexed bonds Bonds that promise payments adjusted for inflation.

Yield on short-term bonds is called short-term interest rates. Yield on bonds with a longer maturity is called long-term interest rates. The Yield curve shows the relation between maturity and yield of a bond. (It shows how yield depends on maturity.) This can also be called the term structure of the interest rate.

The determination of the yield curve and the relation between short- and long-term interest rates can be done in two steps:
1. Derive bonds prices for bonds of different maturities.
2. Go from bond prices to bond yields and examine the determinants of the yield curve and the relation between short- & long-term interest rates.

Bond prices as present values
Assume a bond promises to pay €100,- at the end of its maturity.

Appendix (figure 16.1)

Appendix (figure 16.2)

A two year bond does not only depend on the current-one-year rate (like the one year bond), but also on the on-year rate expected for next year.

Arbitrage and bond prices
Should you go for a one or a two year bond, assuming you only care about expected return

Appendix (figure 16.3)

Appendix (figure 16.4)

If bonds have the same expected return (arbitrage relations):

Appendix (figure 16.5)

Arbitrage implies that the price of a two year bond today is the present value of the expected price of the bond next year.

If we replace we get our old equation, [16.2]

From bond prices to bond yields
Bond yields contain the same information about future expected interest rates as bond prices. However, bond yields do this in a much easier way

Yield-to-Maturity (On an n-year interest rate) is defined as the constant annual interest rate that makes the bond prices today equal to the present value of future payments on the bond.

This satisfies the following relation:
Appendix (figure 16.6)

Replace with equation [16.2] to get:
Appendix (figure 16.7)

Re-arrange to get:
Appendix (figure 16.8)

We have a general principle: Long-term interest rates reflect current and future expected short-term interest rates.

We can approximate our relation [16.8] by
Appendix (figure 16.9)

Interpreting the yield curve
Before we continue, we multiply equation [16.9] by two and we re-arrange it.
Appendix (figure 16.10)

• When he yield curve is upward sloping: we expect short term interest rates to be higher in the future.

• When the yield curve is downward sloping: we expect short term interest rates to be lower in the future

We can also look at the yield curve and economic activity, by using the IS/LM model. Expected inflation is assumed to be zero.

In 2008, the economic situation was worse than expected. Looking at the UK, there were two major developments:
1. There was stronger reduction in spending than expected.
2. The bank of England shifted to a monetary expansion policy. This caused a shift in the LM curve (down), with as a result higher output and lower interest rates.

A decline in short-term interest rates was the result of a shift in spending, combined with a strong response of the central bank aimed at limiting the size of the decrease in output.
Long term interest rates remained high because of expectations by financial markets. They expected output to recover and short-term interest rates to increase.

The stock market and movement in stock prices
Firms can raise funds in two ways
- Debt finance: Bonds and loans
- Equity finance: Issuing stocks (shares). Stocks pay dividends.

There are several indexes of stock prices, like the FT30 in the UK and the Dow Jones Industrial in the US.

Stock prices as a present value
Appendix (figure 16.11)

Where D stands for dividend.
Ex-dividend price Price of stock after dividend has been paid this year.

We can rewrite equation [16.11] to get the real instead of nominal stock price
Appendix (figure 16.12)

The real stock price is the present value of future real dividends, discounted by the sequence of one-year real interest rates.

Two important implications:
- Higher expected future real dividends lead to a higher stock price.
- Higher current & expected future one year real interest rates lead to a lower real stock price.

In the stock market, we can also look at economic activity. Movement in stock prices should be, and are, unpredictable. People can choose between stocks and bonds. If it is expected that stock prices will be high this year, this will lead to a high stock price today.

However, stock prices follow a random walk: a sign of a well-functioning stock market are unpredictable movements.

We can still do two things
- We can use hindsight to see how the market reacted to certain news.
- We can ask what-if questions, like what if expected inflation is zero.

A monetary expansion and the stock market
An increase in M shifts the LM curve down.

If this move was (partly) unexpected, stock prices will increase.
- A monetary policy focused on more expansions implies a lower interest rate for some time.
- It also implies higher output for some time. Therefore, dividends will be higher.

If the move was expected, nothing will happen to the stock market.

An increase in consumer spending and the stock market
The IS curve shifts to the right, unexpected.
- A flat LM curve has a small increase in i, a large increase in output and therefore an increase in stock prices.
- A steep LM curve leads to a large increase in i, a small increase in output and therefore a decrease in stock prices.

How do banks react?
- Banks increase money supply with demand to avoid an increase in interest rate.
- Banks keep the same monetary policy, the economy moves along LM curve.
- If actual output is close to natural output, and actual output increases, inflation will go up. However, output does not change if the bank choses a policy of monetary contraction. In that case, the LM curve shifts up and stock prices go down.

How stock prices react to a change in output depends on market expectations, the source behind the change in output and how banks react.

Stock prices are not always equal to their fundamental value, defined as the present value of expected dividends. Sometimes stock are over or under priced.

Rational speculative bubbles: Movements in stock prices are based on speculations/expectations. People are willing to pay more if they expected stock prices to go up. An increase in stock prices often creates extreme optimism, which can lead to an unreasonably overvalued stock.

Fads: Investors simply extrapolate from past returns to predict future returns. In this case, stocks can become ‘hot’ for no other reason than a past increase.

Chapter 17: Expectations, consumption & Investment

Consumption also depends on expectations, not only on income.
- Milton Friedman, 1950’s, Permanent Income Theory of Consumption.
- Franco Modigliani, Life cycle theory of consumption.

We begin with the assumption that we have a very foresighted consumer. He would first calculate his financial and housing wealth (non-human wealth), and after he would calculate his human wealth.
By calculating both, he can estimate his total wealth (non-human + human wealth). Formally, this can be written as:
Appendix (figure 17.1)

Next, he computes the present value of his labour income as a value of real expected after tax labour income.
is his real labour income in year t, are the real taxes in year t. This gives us
Appendix (figure 17.2)

If you want to be able to consume the same every year, you have to make calculations.

The inter-temporal budget constraint
Assume that there is one representative customers, that is, all individuals are identical. There are only two goods.

The value of consumption must be equal to the value of resources.
Appendix (figure 17.3)

The y stands for endowments, the amount of goods 1 and 2 owned by the consumer.

Expressed in terms of 1 good:
Appendix (figure 17.4)

Where is consumption at time 1 (today), and is consumption at time 2(tomorrow). The relative price is the price of current consumption in terms of future consumption.

We can now look at how much future consumption can increase by lending one more unit of a good today
Appendix (figure 17.5)

We can now write the budget constraint
Appendix (figure 17.6)

Where is expected endowments of tomorrow.

The budget constraint allows us to analyze consumption choices across two subsequent periods. Therefore, it is called the inter-temporal budget constraint.

Our representative consumer chooses a basket of goods that maximizes his utility.
Indifference curve: Each curve represents combinations of current and future consumption that provide the same utility level.
Consumption smoothing: Preference for a balance consumption path over time.

Appendix (figure 17.7)

The function is the instatenous utility function. The flow of utility provided by consumption at a certain time. ≥ 0 is the discount rate, the weight consumer attaches to future compared to the present.

If = 0, the consumer attached the same importance to increase in consumption []
If > 0: the factor <1 – an increase of consumption increase the total utility to a great extent if it occurs in the current period.

Slope of the indifference curve: the Marginal Substitution Rate [MSR] between two goods
Appendix (figure 17.8)

The slope of the budget constraint is . Therefore, we get
Appendix (figure 17.9)

If r = ,
If r > , consumer will choose

We will now look at a more realistic description. There is no perfect consumer.

Why does consumption react so much to income?
- You may not plan constant consumption over a lifetime.
- The computations used exceeds amounts used in own decisions.
- Expectations, for example in wealth, may not come true.
- If you lend, you need to find someone who will lend you money.

Appendix (figure 17.10)

Appendix (figure 17.11)
The last sum is the expected discount value of net income (Y-T)
- Consumption is an increasing function of total wealth and of current after tax labour income.
- Total wealth is the sum of non-human and human wealth.

Consumption is very sensitive to temporary changes in current income  consumers face liquidity constraint. An additional constraint if there if there is no means of getting credit:

Expectations affect consumption in two ways:
1. Directly through human wealth: people make their own expectations.
2. Indirectly through non-human wealth.

There are two main implications for the relationship between consumption and income
1. Consumption is likely to respond less than one-for-one to fluctuations in current income.
2. Consumption may move even if current income does not change.

Expectations of higher future output
Expected future output increase leads to an expected future labour income increases. In turn, human wealth increases and finally, consumption increases.
Expected future output increases leads to an expected future dividends increase. In turn, stock prices increase, non-human wealth increases and finally, consumption increases.

Investment
Theory of investment: Investment should be made if present value exceeds the costs of buying a machine.

Before making a decision, you have to take certain steps.
You have to take into account depreciation, denoted by depreciation rate

We assume that when we buy a machine, it becomes operational immediately and starts depreciating in year t.

Appendix (figure 17.12)

The year after, expected profits will be
Appendix (figure 17.13)

Present value of expected profits

Appendix (figure 17.14)

The investment decision
Assume that the real price of a machine equals 1.
Appendix (figure 17.15)

Investment depends positively on expected present value of the future profits (per unit of capital).
Higher current profits, means higher expected present value, thus a higher level of investment.
Higher current/expected real interest rates, means lower expected present value, thus a lower level of investment.

If we assume static expectations, we expected that the future will be like the present. Our equation becomes
Appendix (figure 17.16)

We can replace this in our investment function.
Appendix (figure 17.17)

User cost of capital: sum of real interest rate and deprecation. Also: rental costs. It captures the implicit costs (shadow costs)

One empirical fact about investment: it strongly moves with fluctuations in current profit.

Behaviors of firms:
- Low profits: a firms needs to borrow money to buy a new machine. A firms with high profits is more likely to invest.
- Firms may have difficulties borrowing.

To fit investment behavior with profits, equation [17.15] becomes:
Appendix (figure 17.18)

What determines profit per unit of capital? The level of sales and existing capital stock.
Appendix (figure 17.19)

Volatility of consumption & investment
- The more transitory consumer expected a current increase in income to be, the less they will increase consumption.
- The same goes for firms and investment

However, there are important differences between investment and consumption decisions
- A permanent nature of an increase in consumption implies that consumers can afford to increase income by the same amount as the increase in income.
- An increase in investment spending may exceed the increase in sales.

• Investment should be more volatile than consumption

• Consumption and investment usually move together, for example, in regression

Chapter 18: Expectations, output and policy

An increase in current or expected after tax real labour income and/or a decrease in future or expected real interest rate, which leads to an increase in human wealth and an increase in consumptions.

Before we look at expectations and the IS relation, we make two major simplifications. We reduce the future and the present to two periods. The present stands for the current period/year and the future stands for all future years together.

Recall the IS relation: Appendix (figure 11.7)

We will rewrite this. First, we add aggregate private spending
Appendix (figure 18.1)
So

So that the IS relation becomes:
Appendix (figure 18.2)

If Y increase, A increases. If T or r increase, A decreases

We will now extend the equation with the role of expectations.
Appendix (figure 18.3)

When we draw the IS curve, we take all variables except Y and r as a given.
- The IS curve is still downward sloping, but much steeper.
- A large decrease in r is likely to have only a small effect on equilibrium output.

• A decrease in the current real interest rate, without changing expectations of the future real interest rate, does not have much effect on spending

• The multiplier is likely to be small

Changes in the IS curve:
- If government spending increases at a given real interest rate: the IS curve shifts to the right.
- If taxes increases: the IS curve shifts to the left.
- Changes in expectations also shift the IS curve. If we expected output to increases: the IS curve shifts to the right.

We do not change the LM relation, since decisions about money are based on current variables.

Monetary Policy, Expectations and Output
Keep two distinctions in mind: the distinction between real and nominal interest rate, and the distinction between current and expected interest rate.

We saw that Appendix (figure 11.8)

similarly, Appendix (figure 18.4)

If the central bank increases money supply, the nominal interest rate decreases. The effects on the current real interest rate and the expected real interest rate depend on:
- Whether the expectations of the future nominal interest rate are revised.
- Whether the expected inflation (current and future) are revised.

We will now, for simplicity reasons, only focus on the first. We expected that current and future inflation are zero. If i=r, our IS relation does not change [18.3], but our LM relation does.
Appendix (figure 18.5)

Assume an economy in recession, where the central bank decides to increase money supply. Expectations remain unchanged.

Given expectations, an increase in money supply shifts in the LM curve, thus there will be a movement down the steep IS curve. This leads to a large decrease in r and a small increase Y.

The prospect of lower future interest rate and higher future output both increase spending and output.

Rational expectations: Expectations formed in a formal-looking manner.

Deficit reduction, expectations & output
Recall previous conclusions about the effects of a budget deficit reduction.
- Long run: budget deficit is beneficial for the economy. A higher investment means higher capital and output.
- Medium run: a lower budget deficit means higher savings and investment.
- Short run: a reduction of the budget deficit, unless offset by monetary expansion. Lower spending means output contraction.

Suppose expected output and expected future real interest rate do not change.
Decrease in government spending: the IS curve shifts to the left. This leads to a decrease in equilibrium output.

Medium run: a deficit has no effects on output but leads to lower interest rates and higher investment.
Long run: Investment increases, Capital increases, Output increases

Future period: includes both the medium and the short run
If you have rational expectations, developments take place in the future.

We revise expectations: future output increases and future real interest rate decreases.

In a response to the announcement of a deficit reduction, 3 factors shift the IS curve
- Government spending decreases: the IS curve to the left. Thus, Output decreases
- Expected output increases: the IS curve to the right. At a given real interest rate, an increase in expected output increases savings and current output.
- Expected real interest rate increases: the IS curve to the right

Which factor dominates?
A few hints that output may go up
- The small the decrease in government spending, the small the adverse effect on spending today. Back loading is more likely to increase output.
- Credibility will the government do what it promised?
- Government must play a balancing act.

The reforming of the social security system is likely to have two effects on spending and output in the short run
1. It has an adverse effect on consumption of the unemployed.
2. It has a positive effect on spending through expectations.

Output may increase in the short run during a program deficit reduction. This depends on credibility, timing, composition and the state of government finances in the first state.

Chapter 19: The euro at fourteen

The euro: seventeen countries decided to have one common currency. The euro had its birth in 1999, after which more and more countries joined the common currency area. For macro economist, the euro is extremely interesting to look at.

The idea for a common currency is the most extreme form of fixed exchange rates between countries. There are three reasons why people in Europe have been interested in exchange rate volatility between their countries:
- The economies are very open. A big part of national income is international trade.
- Wide exchange rates between 1920 and 1930 are said to be the biggest reason for the crisis that followed between wars.
- The common agricultural market

In the past, after the Second World War until about 1971, the Bretton Woods agreements were the main component in how the international monetary system worked. This system, however, collapsed, due to disagreements in economic policy between The United States and Germany. From March 1973, exchange rates started to freely fluctuate. Wide fluctuations in the relative competiveness in EU countries made an end to this. The ineffectiveness of exchange rates was a bump for economic policy: inflation is many countries increased. As a result, the European Monetary System (EMS) was introduced, but without success. The EMS collapsed in 1992. The exchange rates were stable under this system, but deflation also occurred.

The Maastricht Treaty marks the official decision for a common currency, in February 1992. This Treaty also included rules for countries who were joining, in regard to public debt and inflation. It should be noted that a single currency for many countries makes it impossible to devalue.

We will now look at how the monetary system worked.
When the maximum devaluation against the German mark (DM) was reached - that is, when the top margin of the fluctuation band was reached - the central bank of the country of interest had two options:
- Raise interest rates
- Ask for a change in the margins of the fluctuation band

We can look at this with the following expression, with the French Franc (FF) and the DM.

Appendix (figure 19.1)

Appendix (chapter 19)

This equation shows how the ratio between interest rates fluctuates with changing market expectations about a devaluation.

Controls on capital flows where several criteria by the Maastricht Treaty to be allowed to enter the EMU (European Monetary Union).
- In the year before entering the EMU, the inflation rate must not exceed 1.5 percentage points.
- The ratio of actual (or planned) government deficit to GDP must not exceed 3% of the GDP.
- Exchange rate movements must follow normal fluctuation margins provided for by the exchange rate mechanism of the EMS, for at least two years, without devaluing against the currency of any other member state.
- A new member of the EMU must have had an average nominal long-term interest rate not exceeding 2 percentage points of the three best performing member states (in terms of price stability).

What are the costs and benefits of a monetary union? 
There are microeconomic as well as macroeconomic benefits. The microeconomic benefits are: reduced uncertainty, reduced transaction costs and price transparency. The macroeconomic benefits are: trade effects, coordination of monetary policy, European seigniorage and an anti-inflationary reputation.
The biggest costs is the loss as an exchange rate as an automatic stabilizer against shocks.

Is it optimal to have one currency area in Europe?
To have an optimal currency area, as we saw, countries need to have similar shocks. In the European area, there are possibilities for different shocks. Regarding the fact that there is also low labour mobility among the area, it can discussed whether the Euro area is an optimal currency area.

The European Central Bank (ECB) controls the monetary policy in Europe, along with 27 other banks (a bank from each country, called the European Systems of Monetary Banks (ESMB)). Monetary policy is centralized, so the policy is unique. However, tasks are decentralized and should be implemented by the bank of each country.

Governing Council and the Executive Board: ECB's decision makers
Governing Council: responsible for formulating monetary policy and establishing implementation guidelines
Executive Board: implements monetary policy in accordance with the guidelines and decisions laid down by the Governing Council.
General Council: no decision-making capacity in the field of monetary policy but has some monitoring activities and may act in an advisory capacity.

Taylor’s Rule
Appendix (figure 19.2)

According to Taylor’s rule, monetary authorities will set interest rates based on formula [19.2].
After a period of following a similar policy as the German Bundesbank, the ECB looked further than ‘the German experience’. For the European Central Bank, it is of great importance to have structure and objectives. There are different surveys to measure euro area inflation for the coming twelve months. Another measure are the financial-based market measures. We will now look at the history of the Euro, by looking at the first fourteen years. From its birth, the Euro rapidly became more popular, becoming the world’s second most important currency. But success has a downside: economic tensions have occurred among the countries that use the Euro. This was due to the fact that Europe can be split in two country groups: countries with current account trade surpluses and countries with current account trade deficits. For example, Germany runs a current account surplus, whereas Greece runs a current account deficit. Germany has invested in Greece by having a share in its total foreign assets. In Ireland and Spain there was a housing bubble (we will learn more about this in chapter 20). The main problem was the way capital was used: instead of investing and producing more goods, consumption increased.

Currently, there is a question of whether non-members in neighbor countries should join, especially after the crisis.

Chapter 20: The crisis

What happened in 2006 that led to a worldwide recession?

In the 1940’s, the US house prices went up after the war. This was reasonable: people came back from war and were ready to start a family and buy a house.

The first decade of this century, house prices in the US shot up for no reason. When the boom stopped, the house prices fell (2006-2009). This swept away the entire economy. A year later, the unemployment rate in the USA doubled, which led to a worldwide recession.

The increase of the house prices was an effect of a long period with extremely low interest rates. Because inflation was low, the FED kept low rates.

The ‘housing bubble’ made prices go up. There was irrational exuberance.
Banks were less strict in improving mortgage. Even ‘sub-prime’ clients (people who could not afford a mortgage) got a loan.

Mortgage backed security: Security in which contains thousands of mortgages. Banks or investors can buy these securities.

These securities were sold, but made it impossible to check the quality of each individual loan.

House prices fell, so the loan exceeds the market value of the house. Therefore, households get incentive to ‘walk away’ and the mortgage goes into default. If this happens, the house is ‘foreclosed’ and the property now belongs to the bank. The bank makes a loss because of the difference between the loan and the value of the house.

Not all people, however, left their home. Household consumption went down, but there was something else that amplified the shock.

We will now look at leverage.
Appendix (figure 20.1)

A high leverage ratio is risky: in the event of a drop in bank assets, banks might become insolvent.

For simplicity, we assume that banks that borrow money pay no interest rates. Banks like to have a high leverage ratio, because returns are higher when risk is higher. When house prices were high, high leverage led to huge profits for the bank. However, when the house prices fell, many banks went bankrupt.

Over time, the bad example and bad regulations of banks spread to other financial markets.
When some banks went bankrupt, other banks worried:
- They tried to raise more capital, something that is not easy in a crisis.
- They reduced the amount of loans they were holding.
- They sold assets (mostly stock) at whatever price they could get

This resulted in a credit freeze and a fire sale in the stock market.

Before we continue, we should not that there is no unique interest rate.
- Savers receive the rate on bank deposits, i
- Lenders pay a lending rate, which is higher than i.

Appendix (figure 20.2

Where x stands for a spread. With equation [20.2], we can rewrite our investment demand:
Appendix (figure 20.3)

The spread x depends on two factors.
- The capital of the bank, .
A fall in in the capital increases leverage. Remember:

Appendix (figure 20.4)

To face a fall in capital, a bank must increase capital or decrease assets (by the volume of loans)
- The capital of the firm, .
Assume a new machine costs €1,- so the loan is €1,-. The costs of the bank loan will depend on the difference between (1-), since capital can be used as a guarantee for a loan.
Beyond , the bank will charge a spread x, called the external finance premium.
The spread can be rewritten as:
Appendix (figure 20.5)

If firm capital decreases, the spread increases, so the costs of credit go up. The bank lending will fall, and output and investment will decrease.
If, for any level of p, the banks’ capital will decrease, the spread will increase, and it will have the same effect as mentioned before.

When we look at our IS-LM Model, only the IS relation needs to rewritten.
Appendix (figure 20.6)

The main channel of transmission nowadays is trade. The openness in markets allowed the USA crisis to spread worldwide very fast. The United States is the single largest importer of goods in the world. During the crisis, imports collapsed by nearly 50%. You can only imagine what this meant for exporting countries with close relations to the US!

What was the policy response to the crisis?
As we know, monetary policy shifts the LM curve and fiscal policy shifts the IS curve. In response to the crisis, monetary policy slashed interest rates close to zero and fiscal policy replaced private spending with public spending (an increase in government spending).
If the interest rate is zero, monetary policy becomes powerless.

Quantative easing: Solution when an increase in money supply by cutting interest rates is not working (liquidity trap)

It turned out that policy intervention did work to avoid depression, but what is the legacy of the crisis? The biggest legacy was the increase in public debt, which will take a long time to be reversed. Governments also need to unwind the effects of quantative easing. In the next chapter, we will look at the effects of a high debt.

Chapter 21: High debt

We assume a situation where a government has a balanced budget and decides to increase taxes, which will lead to budget deficit.

The next formula shows the deficit, where all variables are in real terms, measured in units of real output.

Appendix (figure 21.1)

Where stands for real interest paid on government bonds in circulations. Equation [21.1] has two important characteristics
- It measures the interest in real terms, thus real interest payments
- G includes neither interest payments nor transfers

Deficit financing: Selling securities to private investors

Appendix (figure 21.2)

Filling in equation [21.1] in [21.2], we get:
Appendix (figure 21.3)

Reorganize to get: Appendix (figure 21.4)

Primary deficit: Total deficit minus interest payments

In year 0, the government cuts taxes by 1 for one year. This means the debt at the end of year 0 will be 1. What will happen next? We will look at two situations.

Situation 1: Repayment in year 1.
Appendix (figure 21.5)

Appendix (figure 21.6)

To repay the debt in one year, the primary surplus should be (1+r). This can be achieved by reducing spending or increases taxes. A tax cut of 1 in year 0 must be compensated by an increase in taxes by 1+r in year 1.

Situation 2: Repayment after t year.
From year 0 to year t, the primary deficit is zero.
Appendix (figure 21.7)

The debt grows at a rate equal to the interest rate.
The budget constraint in year t, when the debt is paid back, can be written as:
Appendix (figure 21.4)

If the debt is fully repaid in one year, the formula can be rewritten and rearranged to get:
Appendix (figure 21.8)

To repay the debt, taxes should increase by .

We can also look at debt and primary surpluses.
 

Stabilisation: The government wants to keep the amount of existing debt constant.
 

Debt stabilization: Keeping equal to a given level.

We take the level of year 0 in this case, which is
We obtain: Appendix (figure 21.9)

Rearrange to get: Appendix (figure 21.10)

To avoid further increase: primary surplus should be equal to the real interest rate on existing debt (every year.)
Legacy of past deficits is a higher current debt. The longer governments wait before stabilizing debt, the more painful it will be.

Government budget constraint in terms of GDP
- Debt to GDP / debt ratio

Divide both sides of formula [21.4] by real output.
Appendix (figure 21.11)

Rewrite to get: Appendix (figure 21.12)

An approximation of the growth rate of output and real interest rates gives 1+r-g
Appendix (figure 21.13)

So, finally, we get:
Appendix (figure 21.14)

Debt ratio is equal to the sum of two terms:
- Differences between real interest rate & rate of growth of GDP multiplied by debt ratio at end of previous period.
- Ratio of primary deficit to GDP.

If r-g is negative, debt ratio will grow more slowly: it will decline from year to year.

Now, what will happen to the debt ratio given other variables?

Appendix (figure 21.15)

Can be applied to [21.13], where is the debt ratio, is (1-r-g) and A is .
To main cases can arise:
- Normal case: growth rate GDP < real interest rate, thus the debt ratio increases. The government must finance the servicing of the debt with adequate primary surpluses.
- The more exotic case: g > r
Over time, the debt ratio will converge into a steady state value, . In the steady state equilibrium, all variables are constant
Appendix (figure 21.16)

Evolution of the debt ratios in some EU countries
- 1960’s: r < g
- 1970’s: r < g, lower growth, but also lower real interest rate
- 1980’s: Countries didn’t create large surpluses, thus a sharp increase in debt ratios.
- 2007-2010 crisis: Many primary balances worsened, increase in debt-to-GDP ratios.

What are the dangers of a very high public debt?
If the debt ratio is > 100%, there is a vicious circle risk.

Recall Appendix (figure 21.14)

To increase primary surpluses, taxes should increase. This leads to more uncertainty, and therefore, the interest rate goes up. This leads to an even bigger recession, so the growth rate decreases. It gets more difficult to stabilize the debt ratio.
A high debt can be reduced through many years/decades of primary surpluses. A last resort could be the repudiation of debt, which means you cancel the debt, completely or partly.

A debt crisis makes it impossible to issue new debt except at extraordinary interest rates.
Why are corrective measures often late?
- Debt crisis are unpredictable, and governments are short sighted.
- Fiscal stabilization is often a political struggle between different groups and political representatives.

When r > g, there are three ways to reduce a high debt:
- Generate sufficient primary surpluses.
- Resort to monetary financing by the central bank.
- Repudiate debt, party or as a whole. (This does not only mean erasing debt, but also issuing taxes on government securities).

You can also inflate debt away by issuing money (directly) or by decreasing the real value of debt, if it has a long maturity (indirectly).

If money supply goes up, inflation increases, which leads to a reduction in disposable income. In this way, inflation can act like a tax.

Political theory of government debt
Forms of reducing debt do not differ much: they only differ because they affect different groups. The choice of how to reduce debt has an effect on income distribution.

Political stable situation: Political party has solid majority and controls economic policy decisions.
 

Unstable: Each group has enough power to block a measure, but not enough to turn it around.

A society can be divided into three groups:
- Rentiers hold wealth in the form of government bonds (annuity)
- Entrepreneurs hold wealth in the form of physical capital (profit)
- Workers own human wealth (salary)
Every group prefers another option to reduce high debt.

We will now look at the four episodes of the reduction of high debt by looking at four countries.

Germany in post-world war 1 period
Germany financed the war through borrowings. The budget deficit was financed mainly through issuing short-term debt. After the war, there was an unstable political situation. It was hard to collect taxes: there was a total cancellation of debt as a result of hyperinflation. The reduction of wealth mainly in middle class worsened the income distribution.

France in the post-world war 1 period
France also had an unstable political situation. They had an easy solution: let the Germans pay our debt. However, the Germans were unable to do so and this resulted in an endless debate in France. When there was greater political stability, a bill was made to shift the tax burden of the bond holders. The demand for government bonds recovered and inflation stopped.

United Kingdom in post-world war 1 period
The United Kingdom has a stable political situation. The objective was to stabilize the sterling and return to its pre-war value. The government produced budget surpluses, but this wasn’t enough. This led to a regressive tax system.

United States in power-world war 2 period
After WW 2, the US had a relatively stable political situation. Their economy was growing, which made it easier to reduce the high debt.