Summary with the 2nd edition of Macroeconomics, a European Perspective by Blanchard

Chapter 1: The world economy

There are 27 European countries that form together the European Union or EU-27. The European Union has a great power; its combined output exceeds USA output. Macroeconomists look at three variables when they study an economy; output, the unemployment rate and the inflation rate.

The economic performance of the European Union since 2000 has not been as good as it was before, in the 1990s. Output growth was lower than before and this led to very high unemployment. The only positive thing to say is that inflation was at a favorable height.

There are a lot of problems in the EU as a result of the worldwide recession in 2008. Short-run problems dominate but there are three other things that have been great issues in the debate:

1. The high unemployment. Although the unemployment has declined from its high peak, it is still very high.

2. Income per person (or per capita).

3. The introduction of the common currency, the euro. Economists argue whether the Euro is good for the countries using it.

When we look at the economy of the US we can say without doubt that the 1990s were the best years. The output growth rate was positive while the unemployment rate was substantially lower than it was before. Also inflation rates were lower than in previous decades. However, the inflation rate was still slightly higher than in Europe.

However, since 2000 the economy of the US has slowed down. US families were hit by four shocks between 2007 and 2008:

• Increase in oil prices

• A fall in house prices. This led to a decrease in the wealth of American households, since the homes of Americans account for three-quarters of their total wealth.

• A fall of the stock market which led to a decrease in the value of households' wealth invested in equities.

• A restriction of credit made it more difficult and expensive to borrow from banks.

Brazil, China, India and Russia are often called the BRICs. This group has grown rapidly over the past few years. It is now seen as one of the major combined economic powers in the world. Its share of global output is now 15%, compared to 24% of the USA.

Economists argue about different reasons for the economic growth in China. Some say it is due to slower and better managed transition while others point out the role of the Communist party in the economic transition.

The economy of China is twice as large as the economy of the other members of the BRIC combined.

Chapter 2: Macroeconomics in general

The most important concepts macroeconomists use are:

1. Aggregate output (GDP)

2. Unemployment

3. Inflation

These three concepts are all connected with each other.

Aggregate output

The measure for aggregate output in national accounts is called the gross domestic product (GDP). There are three definitions for GDP:

• 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

There are two types of GDP:

• Real GDP: the sum of quantities of final goods times constant. It is also called GDP in terms or goods or GDP adjusted for inflation.

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

• Nominal GDP: the sum of the quantities of final goods produced times their current price. Nominal GDP is also called GDP at current prices.

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

The real GDP per capita is the ratio of GDP to the population of a country. It shows the average standard of living and is therefore an important measure. See attachment 2.1 for the formula of the GDP growth rate.

GDP increase (positive growth rate) is called an expansion.

GDP decrease (negative growth rate) is called a recession.

Unemployment

Employment: the number of people who have a job.

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 after some time gave up looking for a job; these people are called discouraged workers.

A country's labour force is the unemployment plus the employment (attachment 2.2)

Unemployment rate is the unemployed divided by the labor force.

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 and finding a new one.

The participation rate is the ratio of labor force to the total population of working age. A higher unemployment rate is generally associated with a lower participation rate.

Inflation

Inflation: Rise in the price level

Deflation: Decline in the price level

Economists often use two measures for the price level:

1. GDP deflator

In real GDP you use constant prices and with nominal GDP you use 'real' prices. So to calculate the fluctuation in price you use the equation in attachment 2.3.

P_t is called the GDP deflator. P_t is called an index number. In the 'begin year' nominal GDP was equal to real GDP because the prices of this year where the constant prices. In the begin year P_t is 1.

2. 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; the cost of living.

The most often used price index in Europe is the harmonised index of consumer prices (HICP). It provides comparable measures of inflation in different European country groups.

You want to have the same level of purchasing power so when the prices increase, you want your wage to rise with the same amount. This is the reason why inflation is important.

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.

The relationship between output growth and unemployment was first examined by Okun. He formed a theory that is called Okun's law. It states that if output growth is high, unemployment will decrease. According to this law one can decrease the unemployment rate to very low levels.

However, when unemployment becomes very low, this leads to an increased pressure on inflation. This relation is described with the Phillips curve. It is defined as a relation between the change in the inflation rate and the unemployment rate. There is a negative relationship between these two variables.

In macroeconomics we speak of three different time frames:

• 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.

• 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 labour force.

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

Macroeconomist 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 numbers.

1. Endogenous numbers: 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 numbers: 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

Goods market (simple) model:

• Production = Demand (Z=Y)

• Closed economy

When we want to understand demand for goods we must include that there are different goods being produced and that there are different buyers for these goods.

Consumption (C) is all the goods and services that consumers buy. Disposable income (Y-T) is the amount of money that is left after consumers paid taxes and received transfers (attachment 3.1).

When we include taxes the relation between consumption and disposable income can be rewritten, see attachment 3.2.

This is a linear relation. C1 is callled the marginal propensity to consume. It shows the effect of an additional dollar disposable income on consumption. Co represents what people would consume if their disposable income would be zero.

Investment (I) is the 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 investments) buying things for their firm. I is, in this simple model, an exogenous and constant number.

I = Io

Government (G) is the sum of government spending on goods and services. T= taxes, this is what the government 'earns'. T and G together describe fiscal policy. In words, T and G are the instruments of the government; with T and G they have an influence in the economy. They are both also exogenous.

G = Go

International Trade (NZ) is Export minus Import.

In a closed economy, like this one, NZ equals zero.

Demand for goods (Z) equation can be found in attachment 3.3

If we take in mind that the equilibrium in the goods market implies that Y=Z and we fill in the equations for consumption, investment and government, we get another demand function(attachment 3.4)

When you want to calculate with this equation, for example to calculate the change in Y, you could simplify the equation, see attachment 3.5. Now, you can easily see what kind of effect the change in, for example Go, will have on Y.

The first term 1/(1-C1) is called the multiplier. Because C1 < 1 (you will never consume more than 100% of your disposable income), G and Y will always have a positive relation.

An increase in autonomous spending has a more than one-for-one effect on the equilibrium output.

Savings: Supply capital

Borrows: Demand capital

Total saving = Private savings (S) + Public savings

Private saving is the saving by consumers, see attachment 3.6.

Public saving is equal to taxes minus government spending; T-G. If taxes exceed government spending, the government is running a budget surplus. If government spending is more than taxes, the government is running a budget deficit.

See attachment 3.7 for the derivation of the IS relation.

Chapter 4: The financial market / money market

Money is used as a payment for transactions and pays no interest.

Functions of money are:

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. The sum of currency and deposits is called M1.

Bonds cannot be used for transactions and pay a positive interest rate, I. There are many different bonds associated with specific interest rates.

You have to decide how much money and how much bonds you should hold. This decision depends on two things:

• The interest rate on bonds. The opportunity costs of bods. In other words, what will you miss by not investing in bonds, because when you hold money, you won't receive interest (i).

• Level 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 (see attachment 4.1)

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. See attachment 4.2 for the corresponding graph.

The graph of the demand function has a downwards slope, 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 of Y means a automatically rise of money)

You see a shift from M_d to M_d'. The interest rate stays the same. When Interest is changing, there will be a shift along the curve. 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 makes 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. These actions from the central bank are called open market operations. The money supply function is given by the equation: M_s=M

Also in the financial market there exists an equilibrium, see attachment 4.3. This equilibrium relation is called the LM relation. An increase in the supply of money leads to a decrease in the interest rate.

Fiscal policy in financial market is called monetary policy: The central bank is able to change the interest rate by changing the supply money. An increase in the supply of money leads to a decrease in the interest rate.

The central bank can in this way 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, supplying more money is of no need. This problem is called the liquidity trap.

If the central bank wants to decrease the amount of money in the economy, it can sell bonds and remove the money they receive for the bonds from circulation. These actions are called open market operations.

• When the central bank increases money supply we speak of an expansionary open market operation.

• When the central bank decreases money supply we speak of a contractionary open market operation.

There also exist 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 financial intermediaries.

The money they 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 reserves from the total deposits accounts. The reserves 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 are the sum of the reserves, the loans and the bonds.

The total sum for demand of money is the demand for currency by people plus the demand for reserves by banks. See attachment 4.4 for demand for deposits, demand for reserves and for central bank money.

The money multiplier can be found in attachment 4.5. The overall supply of money is equal to central bank money times the money multiplier.

Chapter 5: The IS-LM relation

In the IS-LM model the goods market meets the financial market.

The goods market:

In part B we saw that investment was an exogenous number, it was a given, constant number. In reality, investment depends on two things:

1. Level of sales

The more a firm sells, the more a firm needs to invest I= I(Y)

(a positive relation)

2. The interest rate

The higher the interest rate, the riskier it is to borrow money for new investment.

I = I(i) (negative relation)

Therefore we rewrite the investment equation, see attachment 5.1 for formula and graph.

When the interest rate increases, output decreases. This curve is called the IS curve. This curve is a line of all the equilibria in the goods market. The IS curve will shift when there is a change in the exogenous factors, G and T.

When taxes increase or when government decreases, the IS curve will shift down to the left. When taxes decrease or when government increases, the IS curve will shift up to the right.

The 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 write M= €YL(i) as M=YL(i) because the IS curve is related to the real income (Y) and not the nominal income (€Y)

See attachment 5.2 for the LM-relation.

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 it will increase when Y increases.

This curve is called the LM curve and is a line of all the equilibria in the financial market. The curve will shift when there is a change in the money supply or a change in price level

• 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

See attachment 5.3.

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. We can find the equilibrium where the two lines intersect.

Effects of fiscal policy in IS-LM equilibrium

1. Fiscal contraction (consolidation) : T ↑ or G ↓.

T increases/G decreases -> C (Y-T↑) + I + G↓ -> Y↓ -> C↓ -> Y↓ -> etc.

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

2. Fiscal expansion: T↓ or G↑

T↓/G↑ -> C(Y-T↓) + I + G↑ -> Y↑ -> C↑ -> Y↑ -> etc.

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

Effects of monetary policy in the IS-LM equilibrium

1. Monetary contraction (tightening)

Money supply decreases

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

2. Monetary expansion

Money supply increases

The LM curve shifts to the right and a new equilibrium is found at a lower interest rate.

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

Example (see attachment 5.4):

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 founded 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.

In the presence of a liquidity trap, the LM curve is a flat segment with an interest rate equal to zero, for low levels of output. For high levels of output, it is upward sloping.

Chapter 6: The IS-LM model

Openness in the goods market

Tradable goods are goods that compete with foreign goods in either domestic markets or foreign markets.

Non-tradable goods: goods like medical services, haircuts, meals at restaurants etc.

Consumers get the choice: will they buy domestic or foreign products? Important in this decision is the exchange rate. How expensive / cheap are foreign products expressed in your own currency? There are two 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 the price of foreign goods. The rate in which one country’s currency trades to another county’s currency.

2. You can also use the real exchange rate. Then you use the rate at which one country’s goods are traded for foreign goods. This is described in the following equation: You divide the prices of your own goods by the prices of the foreign goods. See attachment 6.1 for the formula of the exchange rate.

Appreciation: An increase in the exchange rate.

Depreciation: A decrease in the exchange rate.

An increase in the real exchange rate is called a real appreciation. A decrease in the real exchange rate is called a real deprecation.

In a system with fixed exchange rates, an increase in the exchange rate is called a revaluation and a decrease in the 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 currencies. A multilateral real exchange rate reflects the exchange rate between one country and all other countries it trades with. Each country gets a weight, based on how much it trades with that one country.

Openness in financial markets

Balance of payments: a country’s transactions with the rest of the world, including trade flows and financial flows. Transactions are either above or below the line.

Transactions above the line are the current account transactions: payments to and from the rest of the world. The first two lines contain imports and exports. Another source of payments is the investment income that the country receives. Finally, countries receive and give foreign aid, recorded as net transfers received.

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

2. Current account surplus: positive current account balance

3. Current account deficit: negative current account balance

Transactions under the line are the capital account transactions

1. Capital account balance: the sum of the net capital flows

2. Capital account surplus: positive capital account balance

3. 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.

Openness in financial markets implies that people, like investors, face a new financial decision: whether to hold domestic or foreign assets. There are two important things to consider when making this decision:

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

2. Differences in exchange rates 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 income in foreign countries does not refer to a higher income from your foreign bonds. There is an equation that describes this problem. This equation is shown in the Uncovered Interest Parity Condition (UIP). See attachment 6.2 for the formula.

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.

As long as interest rates and the expected rate of return are not too large, we can create a new equation (see attachment 6.3).

This equation shows that arbitrage by investors implies that the domestic interest rate must equal the foreign interest rate minus the expected appreciation rate of the domestic currency.

The IS relation in an open economy

The demand for domestic goods in an open economy can be found in attachment 6.4.

The first three components of the domestic demand formula, C, I and G, reflect the domestic demand for goods. Then we must subtract the imports, IM/ε. Last we have to add the exports, X.

The domestic demand factors depend on other factors. We can rewrite these three factors. The plus and minus signs below the equation show the relation between the factors (see attachment 6.5).

So an increase in Y-T leads to an increase in C. An increase in Y leads to and increase in I and an increase in the interest rate, i, leads to a decrease in I.

Imports depend on domestic income and the real exchange rate. An increase in Y or the exchange rate leads to an increase in imports.

Exports depend on foreign income and the real exchange rate. In this relationship an increase in Y* leads to an increase in X and an increase in the exchange rate leads to a decrease in X.

When putting all these components together we get a new equilibrium condition in an open economy, where Y=Z, see attachment 6.6.

Since we are still in the short run, the real exchange rate and the nominal exchange rate move together. This implies that ε = E.

The LM relation in an open economy

In the determination of the IS-LM model we have the condition that the supply of money is equal to the demand for money:

M/P = YL(i)

As we look at the decision between foreign and domestic bonds we must rely on the interest parity condition. If we take the expected return as given and drop the time indices than we get another formula (see attachment 6.7).

From this formula we can conclude that:

• An increase in the domestic interest rate, i, leads to an increase in E.

• An increase in the foreign interest rate, i*, leads to a decrease in E.

• An increase in the expected future exchange rate, Ē^e, leads to an increase in E.

Putting goods and financial markets together

If we combine the interest parity condition, the equality of money supply and demand, and the equation for demand for domestic goods, we can obtain the IS and LM relations. See attachment 6.8 for the formulas and a graph.

The IS curve is downward sloping and the LM curve is upward sloping.

An increase in the interest rate has two effects:

1. A direct effect on investment. An increase in the interest rate leads to a decrease in investment. A reduction in investment leads to a lower output level.

2. An effect through the exchange rate, only present in an open economy. An increase in the domestic interest rate leads to a appreciation of the exchange rate. This appreciation leads to a reduction in net exports and thus to a reduction in output.

These two effects work in the same direction; both lead to a reduction in domestic output.

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 an open and a closed economy:

1. In an open economy, there is an effect on the trade balance, for example if government spending increases.

2. 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 holds and demand is determined by output. In the initial situation the demand is given by the ZZ curve. When the government increases spending, the ZZ curve shifts up, which leads to an increase in output and a fall in the trade balance (see attachment 7.1).

When domestic demand increases, the ZZ curve also shifts up, which thus also leads to an increase in output and a fall in the trade balance. Higher foreign demand leads to higher exports of domestic goods, which leads to an increase in domestic output and increase in demand for domestic goods through the 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 works better, but it is 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.

Depreciation and the trade balance

Real depreciation affects the trade balance through two channels:

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 foreign goods in terms of domestic goods (price effect), leads to a reduction in the trade balance because the import component increases.

Whether the trade balance will actually increase or decrease depends on the Marshall-Lerner condition. This condition implies that a 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 (from A to B) followed by a step by step improvement. This process is shown with the J-curve (see attachment 7.2).

We will now look at savings, investment and the trade balance.

If we combine the equations for the national income identity, net exports and savings, (S=Y – C – T), we get a slightly different formula (see attachment 7.3).

From this it follows that a trade deficit must correspondent to an excess of investment over saving. An increase in investment must be reflected in either an increase in private saving or public saving or in a deterioration of the trade balance.

Effects of policy in an open economy

An increase in G leads to an increase in output, an increase in the interest rate and an appreciation; an increase in the exchange rate.

A monetary contraction, a decrease in the money stock, leads to a decrease in output, an increase in the interest rate and an appreciation.

Fixed exchange rates

So far we have looked at countries with flexible exchange rates. At the other hand we have countries with fixed exchange rates. These countries keep a fixed exchange rate in terms of some foreign currency.

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

When the exchange rate is fixed:

1. The central bank loses monetary policy as a policy instrument. However, fiscal policy becomes more powerful than with flexible exchange rates.

2. The domestic interest rate must be equal to the foreign interest rate.

3. To maintain the interest rate, money supply must be adjusted.

Why fixed exchange rates are not optimal:

• The government loses its monetary policy, which can be a powerful tool.

• It also loses control of the interest rate.

• It is better to have two policy instruments.

Under fixed exchange rates, fiscal policy is more powerful than it is under flexible exchange rates. This is because fiscal policy triggers monetary accommodation.

There are also countries that use another method than a fixed exchange rate. They make an arrangement to keep their exchange rates within some bands around a central parity. A central parity is a given value for the exchange rate. The most know example of such as system was the Bretton Woods system.

Another example was the European Monetary System (EMS). This system determined the movements of exchange rates in the EU from 1978 to 1998.

A country can also decide to peg its exchange rate at a chosen value. Pegging: Method of stabilizing a country’s currency by fixing its exchange rate to that of another country. (Often the dollar)

Crawling peg: Countries that operate under a crawling peg have inflation rates that exceed the US inflation rate.

Chapter 8: The labour market

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 labour force and the people out of the labour force. The labour force consists of the sum of employment and unemployment

Participation rate: Labour force divided by population of working age

Unemployment rate: Unemployed people divided by labour force

Some economists say that the unemployment rate is no 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: the ratio of working age population, minus employment, to population.

An unemployment rate may reflect both separations, workers who are leaving for another job or losing their jobs, and hires, newly employed workers.

The duration of unemployment is very useful information. The longer it takes for people to find a job, the higher the average duration of unemployment. When the duration is low than being unemployed is just a short transition between jobs.

How are wages determined?

• Collective bargaining: bargaining between firms and unions.

Firms and unions negotiation

There are common forces at work in all countries, although they differ from country to country. Two facts stand out:

1. Wages exceed the reservation wage (wage that makes people indifferent between working or being unemployed)

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) when they are paid more.

But how much the wage exceeds the reservation wage depends on two things:

• Nature of the job. High-tech firms pay higher wages than firms where workers’ activities are more a routine.

• Labour market conditions. Low unemployment -> high turnover (easy to find a new job) .To prevent a high turnover wages will be higher.

2. Wages depend on labour market conditions. The lower the unemployment rate, the higher the wage.

Level of bargaining power depends on:

• Costs of replacing worker (nature of the job)

• 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 -> Easy to find new employers for the firm + hard to find a new job for the employers -> less bargaining power.

When the unemployment is low -> Hard to find new employers for the firm + easy to find a new job for the employers -> more bargaining power.

Wage equation (see attachment 8.1):

• P^e= expected price level

• u= actual unemployment rate

• z= All other variables that determine wages

Nominal wage is the real wage times the price.

Your nominal wages tells you how much money you’ll get. In fact, this is not the most important thing to know. Firms and employers are more interested in how much they can buy with their wage. This is the reason that you look at real wage instead of nominal wage.

Real wage is the nominal wage divided by the price (W / P)

What happens when P changes?

P↑  You can buy less with the same nominal income -> real wage decreases -> Employers want a higher nominal income. They want the real wages to stay constant.

When the unemployment rate is low it is easy to find new job (as we have seen before). This leads to higher bargaining power and thus to higher wages. The relation between unemployment and wages is as you can see, negative.

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

When there is some insurance to workers who loose their job it’s less stressful to become unemployed. As a cause of the insurance, the turnover rate will be higher which leads to higher wages. (Positive effect)

• Employment protection

When there’s a high State protection for workers, it becomes more expensive to fire workers. Because of the higher bargaining power, wages will be higher. (Positive effect)

• Minimum wage

By setting a minimum wage, wages can never be extremely low.

How high/low the firm the price will set depends on the costs of production.

The production function can be found in attachment 8.2.

Labour productivity is for now a constant number, when we say A=1, then Y=N.

When production increases with 1, the cost will increase with 1x the cost of employment, which is wages.

So the marginal cost is W. The equation of the price can be found in attachment 8.3.

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

The product market regulation determines how competitive a product is. When there are for example a lot of trade barriers there is less competition.

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

The wage-setting relation (see attachment 8.4) is a negative relation, so downwards sloping line.

To plot the price-setting relation in the same graph as the wage setting relation we have to adjust the price-setting equation (see attachment 8.5).

μ is exogenous and so a constant number. This causes that the price-setting relation is a vertical line. Where the price setting relation and the wage-setting relation are equal you will find the equilibrium unemployment rate called the natural rate of unemployment.

An increase in unemployment benefits can be seen as an increase in z. This increases the reservation wage and therefore the nominal wage. This shifts the wage-setting relation up and the natural rate of unemployment increases.

With attachment 8.6 you can calculate the natural level of employment (N) from the natural level of unemployment (u). From the natural level of employment we can derive the equation for the natural level of output since we know that Y=N, see attachment 8.7.

Chapter 9: The AS-AD model

Aggregate supply

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. See attachment 9.1 for the formula of the AS relation.

The AS relation has two properties:

1. An increase in output leads to an increase in price level.

2. An increase in expected price level leads, one-for-one, to an increase in P.

The AS curve is upward sloping and 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. See attachment 9.2 for an example of an AS curve.

When the expected price level increases this will lead to an increase in wages, which leads in turn to an increase in prices

Aggregate demand

The aggregate demand (AD) function captures the effects of price level on output. We can find this function through the IS & LM relations. See attachment 9.3 for the AD relation.

An increase in nominal money and an increase in government spending will both shift the aggregate demand curve to the right. An increase in taxes will shift the aggregate demand curve to the left.

The AD curve is downward sloping. An increase in price from P to P’ leads to a decrease in output from Y to Y’. If government spending goes up, the curve shifts to the right. The same happens when nominal money decreases. In attachment 9.4 one can see a graph with an example of an AD curve.

Any variable, other than the price, that shifts either the LM or the IS curve also shifts the aggregate demand curve.

The equilibrium

Short run equilibrium:
In the short run, the actual output level is higher or lower than the natural output level. This also implies that the actual price is higher or lower than the expected price level.

Medium run equilibrium:
In the medium run, output will be equal to the natural level of output. Assume that the expected price level is below the actual price level in the short run. In this case 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 first look at the AD curve: if M increases this leads to an increase in the real money stock M/P. This results in an output increase. 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. The neutrality of money implies that monetary policy can be used to affect output in the short run but that the monetary policy cannot sustain higher output forever.

As output is higher that the natural level of output, the price is higher than the wage setters expected. They revise their expectations and this causes the AS curve to shift up over time. This goes on until the output has returned to its natural level. The price level ends up at a higher level. If the initial increase in nominal money is equal to 10%, then the price level also ends up 10% higher.

When nominal money increases, the LM curve will initially shift down. This leads to a decrease in the interest rate and to an increase in output. Over time the price level increases and the LM curve will shift back until the natural output level is reached.

Effects of a decrease in budget deficit

If government spending (G) decreases, the AD curve shifts to the left.

• In the short run, output and price levels 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 and the interest rate declines further.

• In the long run output will increases and investment will also increase. This increase in the long run is due to capital accumulation; a lower deficit leads to a higher investment and thus to a higher level of capital stock. The higher amount of capital stock will lead to a higher output.

Changes in the price of oil

When the price of oil goes up, the cost of production will go up. In the short run this will cause an increase in P since P is determined by the costs of production and output will decrease. This results in an AS curve that shifts to the left. Over time, the AS curve will shift more and more to the left resulting in output decreasing further and the price level increasing further.

An increase in the oil price also has an effect on the natural level of unemployment. The increased oil prices lead to a lower real wage and this will lead to a higher natural rate of unemployment.

The formation of the Organization of Petroleum Exporting Countries (OPEC) in the 1970s led to two sharp increases in the price of oil. The OPEC was a cartel of oil producers.

These two sharp price increases were associated with a sharp recession and a large increase in inflation. This combination is called stagflation.

The real price of oil in Europe increased less rapidly than in the USA since 2003.

Chapter 10: The natural rate of unemployment and the Philips curve

Inflation, expected inflation and unemployment

We recall the AS relation. Assume that the function ,F, captures the effects on the wage of the unemployment rate, u, and of the other factors that affect wage setting, represented by the variable z. We shall assume that this function F is exponential, see attachment 10.1.

If we substitute this formula of F into the AS relation we can obtain an equation for inflation (see attachment 10.2).

The effects of the various variables in this equation:

1. An increase in the expected inflation, πe, leads to an increase in actual inflation π.

2. Given the expected inflation, an increase in the mark-up, μ, or an increase in the factors that affect wage determination, z, leads to an increase in inflation π.

3. Given the expected inflation, an increase in the unemployment rate, u, leads to a decrease in inflation π.

The Phillips curve

Phillips, Samuelson and Solow were the first ones that discovered a relation between unemployment and inflation. In the past, the average inflation rate was equal to zero. This resulted in an expected inflation which was also equal to zero. This leads to the equation in attachment 10.3.

This leads to the wage-price spiral:

1. In response to a higher nominal wage, firms raise prices and the price level goes up.

2. A higher price level leads to a higher nominal wage the next time the wage is set.

3. A higher nominal wage leads to higher prices and again a higher price level.

4. This continues over time.

5. 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:π_t^e = θπ_t-1
The higher the value of _θ, the more last year’s inflation leads workers & firms to revise their expectations. If _θis (close to) zero, expected inflation equals zero. If _θ equals one, the expected inflation equals last year’s inflation. We can now add the expectations of inflation in our original formula (see attachment 10.4).

• If _θis zero, we get our original Phillips curve.

• When _θis positive, the inflation rate depends on unemployment and last year’s inflation.

• For _θequal to one the formula becomes the modified Phillips curve, or also called the expectations-augmented Phillips curve:

for the Modified Phillips curve see attachment 10.5.

This implies that unemployment does not affect the inflation rate, but affects the change in the inflation rate over time. If the change in inflation is positive, unemployment is low.

The natural rate of unemployment is such that expected inflation = actual inflation. In such a case, the left side of the equation becomes zero. We can now rewrite our equation (see attachment 10.6).

The natural rate of unemployment is the rate of unemployment required to keep the inflation rate constant, also called the non-accelerating inflation rate of unemployment (NAIRU).

In the medium run unemployment returns to the natural rate and thus also output must return to its natural level. This implies that the rate of inflation must be equal to the rate of money growth: π = g_m

Europe

The main problems in Europe were the labor market rigidities. Several of those labor market rigidities are:

• 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. These rules increase the cost of layoffs for firms.

• Minimum wages.

• Bargaining rules. Labour contracts are subject to all kinds of agreements.

There are two facts we should remember:

1. The first is that unemployment in Europe was not always high.

2. The second is that many European countries actually have low unemployment.

Let’s imagine that the economy has two types of labour contracts
- proportion, _λ, of labor contracts is indexed
- proportion, 1-λ, of labor contracts is not indexed

Therefore, we get another formula for the inflation (see attachment 10.7). When _λ=0, all wages are set based on expected inflation. This gives us our previous equation.

When _λ is positive, a proportion of wages is set on basis of actual inflation rather than on basis of expected inflation. Wage indexation increases the effect of unemployment on inflation.

When the inflation is very low or negative, the Phillips curve relation appears to become weaker. During the Great Depression very high unemployment led only to limited deflation.

Chapter 11: Inflation and money growth

Output, unemployment and inflation

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: the relation between output growth, money growth and inflation.

Okun’s Law
We assumed that Y=N and that the labour force is constant.

We will 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)

There is a relation between unemployment and the growth rate of output (see attachment 11.1). Where g_yt is the growth rate of output from year t-1 to year t. So the change in the unemployment rate would be equal to the negative of the growth rate of output.

If we look at 30 years of data for the USA since 1970, the line that fits best is:

u_t – u_t-1 = -0.4 (g_yt – 3%)

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 (ḡ_y): rate of output needed to maintain a constant unemployment rate.

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

We can rewrite the last equation, leading to Okun's law (see attachment 11.2).

where ḡ_y is the normal growth rate and β is the effect of output growth above the normal change in unemployment rate.

Okun’s law implies that

• If g_yt > ḡ_y, then u_t < u_t-1

• If g_yt < ḡ_y, then u_t > u_t-1

• If g_yt = ḡ_y, then u_t = u_t-1

Recall the aggregate demand relation:

We will make two simplifications to this relation:

1. Ignore changes in factors other than real money

2. Assume a linear demand between real money balances & output.

From the AD relation we can create a formula for the growth rate of output (see attachment 11.3). The growth rate of output depends on the growth rate of nominal money minus the growth rate of the price level (inflation).

• 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

Nominal versus real interest rates

How do we get from nominal interest rates to real interest rates? This is done by adjusting the nominal interest rate to take into account expected inflation. When the nominal interest rate and expected inflation are not too large we get an approximation (see attachment 11.4).

The nominal interest rate has declined considerably since the 1980s in the UK. However, the real interest rate was higher in 2008 than in 1980.

Interest rates in the IS-LM model

When we look at the IS relation we look at consumption, investment and government spending. Investment depends on the interest rate, the real interest rate. Therefore, the demand for goods also depends on the real interest rate.

When we look at the LM relation we assumed that money demand depends on the interest rate. In this case we refer to the nominal interest rate. Therefore, we use the nominal interest rate in the LM relation.

Effects of money growth

Medium run

Assume that the bank maintains a constant growth rate of nominal money, ḡ_m.

1. The unemployment rate is constant. In the medium run, output must grow at its normal rate of growth (Okun’s law).

2. If inflation is constant, the Phillips curve implies that unemployment is at its natural rate.

3. The AD relation is constant. Thus the expression for inflation becomes nominal money growth minus output growth.

It can be stated that in the medium run, inflation equals adjusted nominal money growth.

Nominal & real interest rate in the medium run
If output is equal to the natural level of output we have to rewrite the AS equation into a formula where output, Y, is replaced by the natural output level, Y_n.

In the medium run, the real interest rate returns to the natural interest rate, r_n. It is independent of the rate of money growth.

If output growth equals zero, the rate of inflation is equal to nominal money growth.

The nominal interest rate is the real interest rate plus expected inflation. Since inflation is also equal to money growth, we get can replace it (see attachment 11.5).

The nominal interest rate is equal to the natural interest rate plus the rate of money growth. So an increase in money growth leads to an equal increase in the nominal interest rate.

Money growth does not affect the real interest rate in the medium run, but it affects both inflation and the 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 an increase in unemployment. Unemployment above the natural rate leads to a decrease in inflation. It may even lead to a recession. In other words: in the short run, monetary tightening leads to a slowdown in growth and a temporary increase in unemployment.

In the medium run, output growth returns to normal (g_t = g_n) and the unemployment rate returns to the natural rate (u_t = u_n). Money growth and inflation are both permanently lower.

From short run to medium run
The 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 the interest rate.

Fisher Hypothesis
The Fisher hypothesis states that, in the medium run, increases in inflation lead to a one-for-one increase in nominal interest rates.

There are two types of evidence for this hypothesis:

• Relation between nominal interest rates and inflation across countries.

• Relation between nominal interest rates and inflation over time in a given country.

Disinflation

Disinflation is a decrease in the inflation rate. We will look at a situation of 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 extra unemployment summed over the years will be the same.

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

The sacrifice ratio is the number of point-years of excess unemployment needed to achieve a decrease in inflation of 1%. see attachment 5.6 for the formula.

Lucas pointed out that it is naive to try to predict the effects of a change in economic policy entirely on basis of relationships observed in historical data. This statement is known as the Lucas critique. Instead of a policy, one should change their expectations to achieve a wanted outcome.

According to Lucas, there is one essential ingredient for successful disinflation: the credibility of monetary policy; the belief by wage setters that the central bank was truly committed to reducing inflation.

This view implies that if policy is fully credible, it can achieve disinflation at no cost in unemployment.

A contrary view was taken by Stanley Fisher and John Taylor. They emphasized the presence of nominal rigidities; meaning that 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 argued that, even with credibility, a too rapid decrease in nominal money growth would lead to higher unemployment.
Taylor argued that 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:

• Disinflation typically leads to a period of higher unemployment.

• Faster disinflation is associated with smaller sacrifice ratios.

• Sacrifice ratios are smaller in countries that have shorter wage contracts.

Chapter 12: Exchange rate regimes

The medium run

Under flexible exchange rates, a real deprecation could be achieved by relying on an expansionary monetary policy.

Under fixed exchange rates, a country cannot adjust its interest rate because the domestic interest rate had to remain equal to the foreign interest rate.

Fixed nominal exchange rate regimes, two methods of adjustment:

• Slow, in medium run, through movement of prices and real exchange rates.

• Fast, through devaluation.

Optimum currency area: a group of countries that satisfies at least one of the following two conditions: similar economic shocks and high factor mobility within the group.

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 the foreign price level, P*. In an open economy with fixed exchange rates, we can rewrite the aggregate demand relation (see attachment 12.1).

The price level affects output through its effect on its real exchange rate. An 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.

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 that the real exchange rate adjusts through price level movements.

For a given price level, 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 for this is the dynamics of adjustment.

Gold standard: is a 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.

Fixed exchange rates

Under fixed exchange rates the interest parity condition holds. When there are expectations of a devaluation, banks/governments have a few options:

1. Convince markets that they have no interest in devaluing.

2. The Central bank can increase the interest rate.

3. The Central bank can also decide to validate the market's expectations and devalue.

Flexible exchange rates

Under flexible exchange rates we have to rewrite the interest parity condition for year (y+1) rather than year t (see attachment 12.2).

We can modify this equation until we get an equation that continues to solve the same way in time (see attachment 12.3).

This tells us that 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 is reduced to:E_t = E_t+n

News about the current account is likely to affect the current exchange rate. The same holds 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 the Central bank cannot be trusted to follow responsible monetary policy.

Choosing an regime

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

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) or optimal currency areas have to satisfy two conditions:

1. Countries need to have similar shocks, thus similar monetary policy.

2. Countries need high factor mobility.

Chapter 13: Growth in the economy

We care about growth because we care about the standard of living. The standard of living is an important indicator. We usually use output per person to measure the differences in growth between countries.

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:

1. The exchange rate fluctuates a lot

2. The price of living varies a lot from country to country

The solution for these problems is to use the Purchasing Parity Power (PPP). Here you use the real GDP, so you look at how much somebody can buy, instead of how much money someone has. Some remarks pop-up:

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.

3. We probably care about the standard of living because we care about happiness. But is there a relation between happiness and the standard of living? Research proved that there is a positive relation between these factors but until a certain level.

Since 1950 there are two main conclusions regarding to growth:

• A large increase in output per person

• The difference between output per worker between countries decreased. This process is called convergence.

Long ago, around 1500, there wasn’t any growth in the European economy. This was caused by the Malthusian trap. Europe was unable to increase its output per person. Any rise of the productivity would lead to an increase in the population that leads to a decrease in the productivity per person. Eventually Europe was able to escape from that trap from 1500 to 1700.

We see convergence of output per worker in OECD and in many Asian countries. In African countries, however, we do not see this pattern. Many of these African countries had negative growth of output per person in the last period.

See attachment 13.1 for the aggregate production function.

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., the amount of people that is working.

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

Returns to scale shows what happens with output if you double the input. There are three different kinds of returns to scale:

• Constant returns to scale

Output will double

• Decreasing returns to scale

Output will be less than double

• Increasing returns to scale

Output will be more than double

When one input stays the same but the other one, let’s say labour, increases you’ll get decreasing returns to labour. To explain this you can look at an example. When the amount of secretaries grows but the amount of computer stays the same, the growth of output will finally be smaller than the increase of labour (secretaries).

This also works vice versa with increasing capital and the same amount of labour, called decreasing retuns to capital. These returns to scale are called the decreasing returns to production factors.

See attachment 13.2 for the formula and graph for output per worker.

K/N is capital per worker. The relation between output per worker (Y/N) and capital per worker (K/N) is positive. But because of decreasing returns to capital, the growth of Y/N, when K/N increases, will become smaller and smaller. One can see this in the following graph.

We can say that the growth of production is coming from two things:

1. Capital accumulation: K/N increases

2. Technological progress: An improvement in the state of technology.

Chapter 14: Capital and output

Capital and output affect each other in different ways:

1. The amount of capital affects the amount of output directly

2. The amount of output determines the amount of capital indirectly

When K changes Y will automatically change too. This is a positive relation, when K increases, output will also increase.

We make two assumptions:

• Employment (N) is a constant (exogenous) number. As a result of this, the labour force and unemployment are also constant because L=N+U.

• To focus on the role of capital we assume that there is no technological progress.

Output indirectly affects capital through its effect on investments and savings. In a closed economy we saw that I=S. When we assume that private savings is a percentage of income we can form an equation, see attachment 14.1 In this equation s is the savings rate.

Since I=S we obtain the formula of attachment 14.2. This means that there is a positive relationship; higher output implies higher investment and so higher savings.

Investment affects capital accumulation. Let’s say that every year, capital depreciates with the amount δ. So every year, the capital decreases with δ. The capital increases with the amount of investment made in that year. The evaluation of capital stock can be found in attachment 14.3.

Now we know how that the change in capital in one year is equal to the right side of the equation above. In words: The change in capital is equal to the saving/investment per working during year t minus the depreciation during year t. see attachment 14.4 for the corresponding formula.

• 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.

To understand the dynamics of capital per worker with respect to output per worker we will plot a graph, see the graph below. As you can see there are 3 lines plotted.

1. The first one is output per worker (f(K.N)). This line grows, but the growth becomes smaller when capital per worker increases, this is caused by the decreasing returns to capital.

2. Then the second line, investment per worker (sf(K/N)), this line is just the same as output per worker but then times the saving rate. Because the saving rate can’t be bigger than one, this line lies below the first line.

3. The third and last line is the depreciation per worker (sf(K/N)), since the depreciation is constant per year, this is a straight line.

See attachment 14.5 for the corresponding graph.

A steady state is a state where there is no growth in capital per worker. In other words, the saving/investments per worker is then equal to the depreciation per worker. In the long run, an economy will reach this point. The steady-state values can be found in attachment 14.6.

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.

As we have seen, in the long run, the economy will be in the steady state where the growth rate is zero. This implies that the saving rate wouldn’t have any effect on the growth.

But another view implies, when a country has a higher savings rate, the second line will shift as s changes. The depreciation per worker and the investment/savings per worker will thus be equal at another amount of capital per worker. There will be for some time an increase in growth until they reached this level.

The saving rate will lead to higher growth of output per worker for some time, but not forever.

Do we really appreciate a higher savings rate? Since we really care about how much we can consume instead of how much we produce or save, the consumption per worker is also interesting. When the savings rate changes, two things will happen:

• Short/Medium run: Because the output is the sum of consumption and saving (and taxes) an increase in the savings will lead to a decrease in consumption.

• Long run: In the long run a higher savings rate will mean a higher amount of capital per worker in the steady state. When output per worker will increase, consumption will also increase.

So what savings rate is the best so that consumption is the highest? This is called the golden-rule level of capital. Increases in capital beyond the golden-rule level reduce the steady-state consumption. See attachment 14.7.

One can see that an increase in the saving rate leads to an increase and then to a decrease in the steady-state consumption per worker.

You can rewrite the production function in various ways. We have seen it before as Y=K, N. But mister Cobb-Douglas liked it in another way. See attachment 14.8 for the formulas.

With this numbers we can calculate what kind of impact a change in the savings rate has on the output per worker in steady state.

Now you can see what happen to K*/N when s changes. When you calculated these numbers, we can calculate the consumption per worker which is equal to output per worker- depreciation per worker. See attachment 14.9.

When we implement the equations for steady-state values of output per worker and capital per worker, consumption per worker is given by equation in attachment 14.10.

There is another type of capital we have not introduced yet. This type of capital is called human capital. Economists take this kind of capital also in account because highly skilled workers are much more likely to be more productive.

Output depends on the levels of both physical and human capital. These two forms can both be accumulated, one through investment and the other through education and training. Increasing the savings rate and or the fraction of output spent on education and training can lead to large increases in output in the long run.

When we include human capital, we can rewrite the production function (see attachment 14.11). An increase in both human and physical capital will lead to an increase in output per worker.

Chapter 15: Technological progress

First, we assumed that the production function could only be affected by capital (K) and labour (N). But as you read before, technological progress could lead to an increase in the production.

So we will add technological progress to our production function. We name it A (productivity), because you could see the state of technology as how much can be produced by the given amount of labour and capital. Our new production can be found in attachment 15.1.

Technological progress reduces the number of workers needed to produce a certain amount of output.

We multiply A by N so that it is easy to calculate the relation between K, A and N. When you multiply N by A, you are not longer speaking of labour. Because you multiply the labour by the productivity you are speaking of effective labour (AN).

All our equations will change a bit. Instead of dividing Y and K by N, you’ll now divide it by AN. We will not longer speak of output per worker or capital per worker, but we we’ll speak of output per effective worker and capital by effective worker. We also need to assume that there are constant returns to scale.

There will also be a change in the steady state. As you remember, in the 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 labour (N) and technology (A) are also likely to change with time.

Capital per effective worker (see attachment 15.2)

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

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

The change in A per worker is called g_a, and the growth rate of N is called g_n. So put it in other words: in steady state, the growth rate is equal to the g_a plus g_n. This is called a state of 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, see attachment 15.3.

An increase in the savings rate leads to an increase in the steady-state levels of output per effective worker and capital per effective worker. The savings rate leads to increased growth until the economy reaches its new, higher, balanced growth path.

When we imply all previous assumptions we can obtain the investment level needed to maintain a given level of capital per effective worker, see attachment 15.4.

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 appropriability of research, how much do firms really benefit from their results of R&D.

Patents give a firm that has discovered a new product the right to exclude anyone else from the production or use of the new product for some time.

When there will not exist any patents, firms are not eager to discover new things. They will just wait until some other firm discovered it, see if it works on the market and copy it.

The nature of technological progress is likely to be different in more and less advanced economies. The developed economies are seen as the technological frontier. They need to develop new products and ideas.

The other less developed countries wait on the developments of the technological frontier and will imitate its ideas. This is called technological catch-up.

Chapter 16: Financial markets and expectations

Expected present discounted value

1€ next year is worth €1/ (1+i_t) this year.
1/ (1+i_t) is the present discounted value of 1€ next year.
If the discount rate, i_t, goes up, the discount factor, 1/ (1+i_t), goes down.

The general formula to calculate the expected present discounted value is found in attachment 16.1.

Where €z_t represents today’s payment, and €V_t stands for the present discounted value of a sequence of payments. The more distant the payment, the smaller the discount factor. If we write €z_t with z to the power of e, we calculate the value with expected values.

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 1/(1+i)ⁿ

With constant interest rates and payments the present value formula simplifies. The whole formula can be rewritten (see attachment 16.2).

If there are infinite constant payments, €z, we can simplify our equation to the form:

€V_t = €z / I. 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 (see attachment 16.3).

Bond prices and bond yields

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 which the bond 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 the short-term interest rate. Yield on bonds with a longer maturity is called the long-term interest rate. 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 bond 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.

Assume a bond promises to pay €100,- at the end of its maturity. See attachment 16.4 for the one year and two year bond price.

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

Should you go for a one or a two year bond, assuming you only care about expected return? See attachment 16.5 for the expected return for a one year and two year bond. If bonds have the same expected return, arbitrage relations, see attachment 16.6.

Arbitrage implies that the price of a two year bond today is the present value of the expected price of the bond next year. The expected returns on the two assets must be equal.

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.See attachment 16.7.

We have a general principle: Long-term interest rates reflect current and future expected short-term interest rates. We can approximate our relation, see attachment 16.8.

The one-year interest rate expected for next year is equal to twice the yield on a two-year bond minus the current one-year interest rate.

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

2. 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 a 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 the result of 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:

1. Debt finance: Bonds and loans

2. 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.

See attachment 16.9 for the nominal price of stock.

In this equation D stands for dividend. The equation gives the stock price as the value of nominal dividends, discounted by nominal interest rates. e

Ex-dividend price: Price of stock after dividend has been paid this year.

We can rewrite the equation to get the real instead of nominal stock price, see attachment 16.10.

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:

1. Higher expected future real dividends lead to a higher real stock price.

2. Higher current and 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. Movements 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: unpredictable movements. These movements are a sign of a well-functioning stock market.

We can still do two things:

1. We can use hindsight to see how the market reacted to certain news.

2. We can ask what-if questions, like what if expected inflation is zero.

An increase in money, 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 unexpected to the right resulting for instance from stronger-than-expected consumer spending. There is a movement along the LM curve leading to an increase in both output and interest rates.

• 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 banks react to this:

• Banks increase money supply with demand to avoid an increase in the interest rate. This is called Central bank accommodation.

• Banks keep the same monetary policy, leaving the LM curve unchanged. The economy moves along the 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 chooses 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.

Risk

So far we have assumed that people are risk neutral. However, people are risk averse. Many theories are concerned with how people make decisions when they are risk averse.

If people perceive stocks to be riskier than bonds, they often require a risk premium to hold stocks rather than bonds. This risk premium is called the equity premium.

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

Rational speculative bubbles: Movements in stock prices are based on speculations/expectations. Financial investors might behave rationally as the bubble inflates. 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 and investment

Consumption does not only depend on income, it also depends on expectations. This theory was developed independently by two:

• Milton Friedman, 1950’s with the Permanent Income Theory of Consumption.

• Franco Modigliani with the 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).

Next, he computes the present value of his labour income as a value of real expected after tax labour income. Y_Lt is his real labour income in year t, T_t are the real taxes in year t. See attachment 17.1 for the human wealth equation.

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

The value of consumption must be equal to the value of resources, see attachment 17.2.

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

We can express all in terms of good 1, see attachment 17.3.

Where c₁ is consumption at time 1 (today), and c₂ is consumption at time 2(tomorrow). The relative price (p₂/p₁) 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:1 + r = p₁/p₂

We can now write the budget constraint, see attachment 17.4.

Where y^e_t is the expected endowment for 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.

To keep things simple, we assume that the inter-temporal utility function U (c₁, c₂) is additive with respect to current and future consumption, see attachment 17.5.

The function u(*) is called the instantaneous utility function. It can be seen as the flow of utility provided by consumption at a certain time. ρ ≥ 0 is the discount rate, the weight the consumer attaches to the future compared to the present.

• If ρ = 0, the consumer attached the same importance to increase in consumption

[c₁ = c₂]

• If ρ > 0: the factor 1 / (1+ρ) < 1. An increase of consumption increases 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 can be found in attachment 17.6.

The slope of the budget constraint is 1 + r. Therefore we can rewrite, see attachment 17.7.

• If r =ρ → c₁ = c₂

• If r > ρ → the consumer will choose c₁ < c₂

Realistic description

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 want to plan constant consumption over a lifetime.

• The computations used exceed amounts used in own decisions.

• Expectations, for example in wealth, may not come true.

• If you want to lend, you need to find someone who will lend you money.

When we incorporate after -tax labour income we get the consumption function, see attachment 17.8.

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 (financial wealth plus housing wealth) and human wealth (the present value of expected after-tax labour income).

Consumption is very sensitive to temporary changes in current income. Consumers face a liquidity constraint. An additional constraint if there is no means of getting credit: c₁ y₁.

Expectations affect consumption in two ways:

• Directly through human wealth: people make their own expectations.

• 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.

Expected future output increases lead to an expected future labour income increase. In turn, human wealth increases and finally, consumption increases.

Expected future output increases also lead to an expected future dividends increase. In turn, stock prices increase, non-human wealth increases and finally, consumption increases.

Investment

Investment should be made if the 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 δ.

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

Present value of expected profits can be calculated, see attachment 17.9.

Assume that the real price of a machine equals 1. We have an investment function, see attachment 17.10.

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

If we assume static expectations, we expected that the future will be like the present. Our investment equation under this assumption changes, see attachment 17.11.

User cost of capital: sum of real interest rate and deprecation. Also called rental costs, see attachment 17.12 for the equation.

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 firm with high profits is more likely to invest.

• Firms may have difficulties borrowing.

To fit investment behavior with profits we rewrite the investment equation, see attachment 17.13. Investment depends on both the expected present value of future profits and the current level of profit.

What determines profit per unit of capital? The level of sales and existing capital stock. See attachment 17.14 for this relation.

Volatility of consumption & investment

• The more transitory consumers expect a current increase in income to be, the less they will increase their consumption.

• The same holds 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, leads to an increase in human wealth and an increase in consumption.

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. We will rewrite this. First, we add aggregate private spending:

Aggregate private spending formula is given in attachment 18.1.

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

We will now extend the equation with the role of expectations. The natural extension is to allow spending to depend not only on current variables but also on their expected values in future periods.

When we draw the IS curve we take all variables, except Y and r, as given.

1. The IS curve is still downward sloping, but much steeper.

2. A large decrease in r is likely to have only a small effect on equilibrium output.

3. A decrease in the current real interest rate, without changing expectations of the future real interest rate, does not have a large effect on spending

4. 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 increase: the IS curve shifts to the left.

• Changes in expectations also shift the IS curve. If we expected output to increase -> the IS curve shifts to the right. If we expect the interest rate to rise, the IS curve shifts to the left.

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

Monetary policy, expectations and output

Keep two distinctions in mind: the distinction between real and nominal interest rates, and the distinction between current and expected interest rates.

If the central bank increases the money supply, the nominal interest rate decreases. The effects on the current real interest rate and the expected real interest rate depend on:

1. Whether the expectations of the future nominal interest rate are revised.

2. Whether expect of future and current inflation 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, but our LM relation does (see attachment 18.2).

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 the LM curve down, 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 rates 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: a 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, leads to lower spending and to a contraction in output.

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

Some more effects of a deficit reduction in the medium and in the long run:

1. Medium run: a deficit has no effects on output but leads to lower interest rates and higher investment.

2. 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 rates decrease.

In a response to the announcement of a deficit reduction, 3 factors shift the IS curve:

• Government spending decreases: the IS curve shifts to the left. Thus, output decreases

• Expected output increases: the IS curve shifts to the right. At a given real interest rate, an increase in expected output increases savings and current output.

• Expected future interest rate decreases: the IS curve shifts to the right.

Which factor dominates? We cannot say which factor dominates, but there are a few hints that tell us when output may go up:

• The smaller the decrease in government spending, the smaller the adverse effect on spending today. Back loading is more likely to increase output. Back loading is a deficit reduction program towards the future, with small cuts today and larger cuts in the future.

• Credibility: will the government do what it has promised to do?

• 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

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 concerned about exchange rate volatility between their countries:

• Degree of openness.

  The economies are very open. A big part of national income is international trade.

• Exchange rate fluctuations.

  Wide exchange rates between 1920 and 1930 are said to be the biggest reason for the crisis that followed between the wars. Competitive devaluation led to higher inflation everywhere and to the collapse of trade.

• 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 competitiveness in EU countries made an end to this. The ineffectiveness of exchange rates was a bump for economic policy: inflation in 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.

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

Controls on capital flows, also known as foreign exchange controls, 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).

There are microeconomic as well as macroeconomic benefits of a monetary union. The microeconomic benefits are: reduced uncertainty, reduced transaction costs and price transparency.

The macroeconomic benefits are: trade effects, coordination of monetary policy, European seignior age and an anti-inflationary reputation.
The biggest cost is the loss of the 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 be discussed whether the Euro area is an optimal currency area.

Structure and objectives

The European Central Bank (ECB) controls the monetary policy in Europe, which, along with 27 national central banks of all EU member states, forms 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.

According to Taylor’s rule, monetary authorities will set interest rates based on a formula, see attachment 19.1.

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. Other measures are the financial-based market measures. We will now look at the history of the Euro.

The first fourteen years of the euro

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.

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

From housing problem to financial 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.

In 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.

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.

See attachment 20.1 for a bank's capital ratio and leverage ratio.

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

The effect of the lower housing prices was amplified by the effects on the banking system. Same banks became insolvent due to very low capital ratios. Investors became reluctant to lend to banks and many banks became illiquid.

For simplicity, we assume that banks that borrow money pay no interest rate. 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.

In the 2000s banks decided to take on more risk. They had three reasons for this:

1. They underestimated the risk they were taking.

2. The compensation system and bonus payments gave an incentive to strive for higher returns without taking the risk into account.

3. Even though there was a regulation that required banks to have a minimum capital ratio, banks found a way to avoid this regulation.

An important development in the 2000s was the growth of securitisation. It is defined as the creation of securities based on a bundle of assets. An example is the returns of a bundle of mortgages, called a mortgage-based security (MBS). These often contain more than ten thousand mortgages. Banks or investors can buy these securities. These securities were sold, but made it impossible to check the quality of each individual loan.

Instead of bundling identical claims to returns one can also issue different types of securities. For example, one can issue two types of securities:

• Senior securities: these securities have first claims on the returns from the bundle.

• Junior securities: these securities come after and pay only if something is left after the senior securities have been paid.

Such combined junior/senior securities are known as collateralised debt obligations (CDOs).

Securitisation is a way of diversifying risk and increasing the group of investors involved in lending to households. However, it also raises a large cost.

Rating agencies are firms that assess the risk of various securities. When underlying mortgages went bad it was very hard to assess the value of the underlying bundles. These assets are known as toxic assets.

Wholesale funding: the bank's process of borrowing from other banks or investors in the form of short-term debt to finance the purchase of its assets.

The financial crisis led to a large increase in interest rates at which firms and people could borrow. It also led to a dramatic decline in confidence.

Use and limits of policy

Each firm gets a risk rating based on how many risk the firm takes on. Firms with an AAA rating are the safest and firms with a BBB rating are less safe. Safer firms will borrow at a lower interest rate than less safer firms.

We should note 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.

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.

The financial crisis led to a large deficit in output. The contraction of the US economy spread very fast to the rest of the world, especially to Europe. This was due to the exposure of banks to the US housing market bubble, the contraction of international trade flows and the increase of US interest rates.

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.

To deal with the problems of the financial crisis fiscal, monetary and financial policies were used. They did not prevent the recession but the did prevent a further decline in output.

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.

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

The slow recovery

It turned out that policy intervention did work to avoid depression. Once the world economy emerges from the recession, two legacies will remain: expansionary monetary policies will translate into higher inflation, and the expansionary fiscal policies will cause an increase in government debt across advanced countries. The biggest legacy was the increase in public debt, which will take a long time to be reversed.

Thus even though there is now positive output growth in both Europe and the US, recovery is very slow. It may be that the crisis has done some damage to the baking sector that will never be recovered.

Chapter 21: High debt

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

The next formula shows the deficit, where all variables are in real terms, measured in units of real output (see attachment 21.1).

Where rB_t-1 stands for real interest paid on government bonds in circulations. The equation 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

The government's budget deficit is found in attachment 21.2.

If we combine both equations we get another formula, see attachment 21.3.

Primary deficit: Total deficit minus interest payments. It is the last part in the equation.

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

1. Situation 1: Repayment in year 1.

The budget constraint in year 1 is given by: B₁ = (1 + r) B₀ + (G₁ – T₁)

When all debt is repaid at the end of year 1, debt will be zero. If we fill in B₀= 1 and B₁= 0, then we get: Budget constraint end of year 1: T₁ – G₁ = (1 + r)1 = 1 + r

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

2. Situation 2: Repayment after t years.

   The government decides to wait t years before raising taxes to repay the debt.

From year 1 to year t, the primary deficit will be zero.

Debt at the end of year 1 will be: B₁ = (1 + r) B₀ + 0 = 1+r (since B₀=1)

Debt at the end of year 2 will be: B₂ = (1 + r) B₁ + 0 = (1+r) (1+r) = (1+r)²

The debt grows at a rate equal to the interest rate. Therefore, debt at the end of year is given by: B_t-1 = (1 + r)^t-1

The budget constraint in year t, when the debt is paid back, can be written as:

B_t = (1 + r) B_t-1 + (G_t – T_t)

If the debt is fully repaid in one year, the formula can be rewritten and rearranged to get: T_t – G_t = (1 + r)^t
To repay the debt, taxes should increase by (1 + r)^t.

We can also look at debt and primary surpluses.

Debt stabilization: The government wants to keep the amount of existing debt at a constant level.

To avoid further increases: 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.

Debt-to-GDP ratio

The debt to GDP or debt ratio is found by dividing both sides of the budget constraint by real output, see attachment 21.4.

An approximation of the growth rate of output and real interest rates leads to the equation in attachment 21.5.

This equation tells us that the debt ratio is equal to the sum of two terms:

1. Difference between real interest rate & rate of growth of GDP multiplied by debt ratio at end of previous period.

2. Ratio of primary deficit to GDP.

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

Now, what will happen to the debt ratio given other variables? See attachment 21.6 for the Simple difference equation.

Two main cases can arise:

• Normal case: growth rate of 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 ḃ. In the steady state equilibrium, all variables are constant, see attachment 21.7.

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.

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 level 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 too late?

• Debt crises 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, partly 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 the income distribution.

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

Political unstable situation: 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 had 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.

Chapter 22: Policy and policy makers

Uncertainty and policy

The effects of macroeconomic policies are always uncertain. This uncertainty should lead policy makers to be more cautious and to use less active policies. Policies must be broadly aimed at avoiding prolonged recessions, slowing down booms and avoiding inflationary pressure.

The higher the level of unemployment or inflation, the more active the policies should be. But they should stop well short of fine-tuning, of trying to maintain constant unemployment or constant output growth.

Years ago, methods of optimal control, developed initially to control and guide rockets, were being increasingly used to design macroeconomic policy. Nowadays economists do not think like this anymore.

Macroeconomic policy must be seen as a game between the policy makers and ‘the economy’; the people and the firms in an economy. It is a game of strategic interactions between the players. What people and firms do depends on what they expect policy makers to do. In turn, what policy makers do depends on what is happening in the economy.

When a central bank announces to follow a monetary policy consistent with zero inflation, then the relation between unemployment and inflation will change, see attachment 22.1.

If the central bank continues to follow this policy, it will choose an unemployment rate equal to the natural rate. This is not a bad outcome but a bank may actually do better.

Time inconsistency: The incentive to deviate from the announced policy once the player has made its move. The bank can use this in a way that it can deviate from its zero inflation announcement by accepting some inflation. In this way it can achieve a substantial reduction in unemployment. However, it will not stop with this small inflation.

As a reaction, wage setters expect a higher future inflation which will result in inflation going up. The economy ends up with the same unemployment rate that would have prevailed if the central bank had followed its announcement policy, but with much higher inflation.

How central banks can deal with the problem of time inconsistency:

• Make the central bank independent.

• Create incentive for banks to adapt the long term view.

• Appoint a conservative central banker; somebody that dislikes inflation.

Better methods typically involve designing better institutions (such as an independent central bank) that can reduce the problem of time inconsistency without eliminating monetary policy as a macroeconomic policy tool.

Politics

Another argument for putting restraints on policy makers is that policy makers may play games with the public or among themselves. These games may lead to undesirable outcomes.

Politicians may try to fool a short-sighted electorate by choosing policies with short-run benefits but large long-term costs. For example large budget deficits.

We often see a political business cycle with higher growth on average before the elections than afterwards.

Political parties may delay painful decisions, hoping that the other party will make adjustments and take the blame. In cases like this, tight restraints on policy, such as constitutional amendment to balance budget, again provide a rough solution.

Better ways typically involve better institutions and better ways of designing the process through which policy and decisions are made.

Chapter 23: Monetary and fiscal policy rules and constraints

Optimal inflation

At the moment, there is a large debate in the OECD countries between those who think some inflation is fine and those who want an inflation of 0%, i.e. price stability. The debate has not stopped yet but most banks aim for a low but positive inflation.

Economists identify four main costs of inflation:

1. Shoe-leather costs

In the medium run, higher inflation leads to a higher nominal interest rate and thus to a higher opportunity cost of holding money. People will go more often to the bank to decrease their money balances. The costs resulting from this are called shoe-leather costs. These costs would have been avoided if inflation were lower.

2. Tax distortions

This cost comes from the interaction between taxes and inflation. The higher the rate of inflation, the higher the tax.

3. Money illusion

Money illusion is the notion that people appear to make systematic mistakes in assessing nominal versus real changes. Price and income computations become more complicated when inflation is involved. Economist and psychologists have evidence that inflation often leads people and firms to make incorrect decisions.

4. Inflation variability

High inflation is often associated with more variable inflation. This means that financial assets such as bonds, which promise fixed nominal payments in the future, become riskier.

However, one can also identify three benefits of inflation:

1. Seignorage

One way for a government to finance its spending is through money creation, the ultimate source of inflation. Other things being equal, the revenues from money creation – that is seignorage – allow the government to borrow less from the public or to lower taxes.

2. The option of negative real interest rates for macroeconomic policy

An economy with a higher average inflation rate has more scope to use monetary policy to fight a recession. In an economy with a low inflation rate it may be impossible to use monetary policy to return to the natural level of output.

3. The use of the interaction between money illusion and inflation in facilitating real wage adjustments

The presence of inflation allows for downward real-wage adjustments more easily than when there is no inflation.

Monetary policy

Until the 1990s, monetary policy in OECD countries was as follows:

• The central bank chose a target rate for nominal growth corresponding to the wanted inflation rate.

• In the short run, the central bank allowed for deviations of the nominal money growth from the target.

• The central bank announced a range for the rate of nominal money growth it intended to achieve.

There is positive relation between inflation and nominal money growth. However, this relation is not very strong in practice. Starting in the beginning of the 1990s, a dramatic change in the thinking of monetary policy took place. Monetary policy was now based on inflation targeting instead of money growth targeting and the use of interest rate rules. Inflation targeting is achieving a low inflation rate, both in the short run and in the medium run.

In many countries, central banks define their main goal as the achievement of a low inflation rate. Suppose the bank could achieve its inflation target exactly in every period. Then the relation between inflation and the unemployment rate will change. The expected inflation can now be replaced by the target inflation, see attachment 23.1.

Inflation targeting makes good sense in the medium run and allows monetary policy to stabilize output around its natural level in the short run.

Taylor argued that the central bank should adopt the following rule, called the Taylor rule (see attachment 23.2)

where * stands for the target value of that variable.

• When π_t = π*, then the central bank should set the nominal interest rate, i_t,equal to its target value i*.

• When π_t > π*, then the central bank should increase the nominal interest rate above the target value. This will increase unemployment and thus lead to a decrease in inflation.

• When u_t > u_n, and thus π_t < π*, then the central bank should decrease the nominal interest rate. This will increase output and thus decrease unemployment.

Fiscal policy

How does taking into account the government budget constraint affect the way we think about the effects on output?

An extreme view is the Ricardian equivalence proposition: it states that when the government budget constraint is taken into account, neither deficits nor debts have an effect on economic activity.

His argument was further developed by Robert Barro. Therefore, this proposition is also known as the Ricardo-Barro proposition.

Under this proposition, a larger deficit is offset by an equal increase in private saving. Deficits have no effect on demand and on output. The accumulation of debt does not affect capital accumulation.

When the Ricardian equivalence fails, larger deficits lead to higher demand and higher output in the short run. The accumulation of debt leads to lower capital accumulation and thus to lower output in the long run.

Wars generally come with large budget deficits. There are two reasons why a country should run a deficit during war:

1. A deficit makes it possible to pass some of the burden of war to those people who are alive after the war. It seems fair that the future generations share the burden of the war.

2. Deficit spending helps to reduce tax distortions.

Member countries of a monetary union should impose constraints on their fiscal policy for two reasons:

• To correct the incentive of small countries to pass on the cost of a fiscal expansion to other members.

• To prevent that a financial crisis in a country spreads to all other members.