# Macroeconomic models

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We have now reached the second part of this book. The first **interest rate** was a description of the **macroeconomic variables** and institutions. In the second part, we will analyze how these variables fit together and present models that explain the main **macroeconomic variables**.

Using these models we can, for example, analyze what happens when the government increases consumption, when the central bank increases the target **interest rate** and when domestically produced goods do well in foreign markets. We can also understand important observations of the economy, such as cyclical fluctuations in growth, correlation between **unemployment** and inflation and the relationship between **interest rates** and foreign exchange rates.

Macroeconomics is not an exact science such as physics. No one knows exactly how the **macroeconomic variables** are related. Instead, there exist a number of models that try to explain various observations and relationships between **macroeconomic variables**. Unfortunately, not all of these models consistent - one model may predict that unemployment will fall if the central bank lowers the target **interest rate** while another may claim that such a change will not affect unemployment.

This type of problem is something you have to get used to and accept. Economics is not a subject where you can perform an experiment to find out what is really “true”. Observed phenomena may have different explanations in different models and different models will lead to different predictions of **macroeconomic variables**. If you conclude that “An increase in x will lead to an increase in y” you really should not think of this as a property of the real world but rather as the property of a particular model.

One model that is very popular in virtually all basic courses in macroeconomics all over the world is the so-called **neo-classical synthesis**. As the name suggests, this is a combination or a synthesis of two models, namely the classical model and the Keynesian model. In short, the neo-classical synthesis claims that the Keynesian model is correct in the short term while the classical model is correct in the long run. The rest of this book builds up the neo-classical synthesis. Note that there are actually many minor variations of the neoclassical synthesis. I try to present the most common version.

## Common assumptions

All models require a number of assumptions to be able to say anything of interest. In this section we will describe the assumptions that will apply throughout the rest of the book. Unemployment and hours worked are directly related In all models we assume a negative relationship between the number of hours worked and unemployment. If the number of hours worked increases, the unemployment will fall and vice versa.

This assumption will be true if the workforce is constant and individuals in the labor force either work full time or not at all. In reality, this relationship need not hold. We may see an increase in the labor force (for example from immigration) that is larger than the increase in employment which would lead to an increase in both hours worked and unemployment but we disregard this possibility.

### The central bank has complete control over money supply

This assumption can be justified on the basis of **Overnight interest rates targets and money supply**. Remember that the money supply is equal to the money multiplier times the monetary base. We will assume that the money multiplier is constant and since the monetary base is completely under the control of the central bank, the central bank will control the money supply.

### Monetary policy = change in money supply

The **central bank** actually has other**monetary policy** instrument apart from being able to determine the money supply. The most important one is the target **interest rate** for the overnight market. In this book we will not consider the possibility of changing the target interest rate. However, we know that there is a negative relationship between the target rate and the money supply. Therefore, if you want to investigate the effect of an increase in the target interest rate, you may just as well investigate a decrease in the money supply.

### There is just one interest rate

Including different **interest rates** with different maturities would complicate the models but it would not buy you very much. Since interest rates with different maturities are highly correlated, they typically move in the same direction and the direction of a variable is typically what we are interested in. If you like, think of “the interest rate” as the one-year **interest rate** on government securities.

### Exchange rate

In all models except those in Chapter 16 we will assume that the **exchange rate** is flexible.

Furthermore, we assume that the exchange rate is determined by the ratio of the domestic price level to the foreign price level. If, for example, domestic prices increase by 10% while foreign prices are constant, the domestic currency will depreciate by 10% against the foreign currency. Motivation for this assumption and the consequences of this assumption can be found in section 16.2.

With this assumption, exports and imports may be assumed to be independent of the domestic price level. If domestic prices increase by 10% while the currency loose 10%, the price of domestically produced goods abroad will be unchanged. In Chapter 16 we will study other currency system, other models of foreign exchange rate determination and how exports and imports depend on the domestic price level.

### Capital Flows

In all models except those in Chapter 16, the domestic **interest rate** is not affected by foreign interest rates. With free capital flows, this is a very unreasonable assumption. If we the domestic interest rate increase against the foreign interest rates, capital would flow into our country which would drive down the domestic interest rate again.

Most reasonable models in which the domestic **interest rate** is affected by foreign **interest rates** are more complicated. To understand such models, you must first understand the models where this complication does not arise. Also, the predictions from models where the domestic **interest rate** is not affected by foreign **interest rates** are fairly similar to the more realistic models wchich allows for capital flows. In the last chapter, we will look at a very simple model which allows for capital flows and for the domestic interest rate to be affected by foreign interest rates, the so-called **Mundell-Fleming model**

## The macroeconomic variables

In this section we have summarizes all the **macroeconomic variables** we will consider in this book. The first column indicates the symbol we use for the variable while column 2 shows the name of the variable. The third column shows you in which section the variable is defined.

**Variabel Variabelnamn Definition**

**Y****Real GDP****P**Price level**P * Y**Nominal GDP**U Unemployment****L**Hours worked**K**Amount of capital**W**Nominal wage**W**/**P**Real wage**M**Money supply (nominal)**R**Nominal interest rate**r**Real interest rate**C**Private consumption (real)**I**Investments (real)**G**Government expenditure (real)**NT**Net tax (real)**X**Exports (real)**Im**Imports (real)**NX**Net exports (real)**SH**Household savings (real)**SG**Government savings (real)**SR**Rest of the world savings (real)**π**Inflation**πe**expected inflation**πw**Wage inflation**πM**Growth in money supply**E**Exchange rate**π****E**Depreciation in exchange rate

Two of the variables are stock variables: K and M. Prices cannot be characterized as a stock or flow variable. P, W, R, r and E apply at a given point in time while π, πe, πw and πE apply over a period of time. π, πw and πE are changes in P, W and E during the previous time period while πe is the expected change in P during the next time period. All the other variables are flow variables measured in some unit per unit of time (for example, L is the number of hours worked per year or per any other unit of time).

## Supply and demand

In microeconomics, we are careful to distinguish between the demand, the supply and the observed quantity. The first two are hypothetical concepts which indicate the desired quantities from households and firms under various conditions. The observed quantity is the quantity that consumers actually end up buying from the firms.

The main difference is that demand and supply are functions - they depend on other variables – while observed quantities are variables. These functions are usually illustrated in a chart where we illustrate how demand and supply depend on other variables.

In macroeconomics, we also consider the demand and the supply of many of the variables. So far, each variable has represented an observed quantity. For example, **L **has been the symbol for the actual number of hours worked, a variable that we can measure. However, we have not made any distinction between the demand and the supply of labor which we need to do from now on. The variables for which we will consider the supply and the demand are: **Y**, **L**, **K M**, **C**, **I**, **G**, **X **and **Im**.

In order to separate the supply and the demand from the observed quantity, we use subscript S for supply and subscript D for demand. For example, L is still the observed amount of work (a variable) while LS and LD represent the supply of labour and the demand for labour. Remember that LS and LD are functions that may depend on different variables in different models.

## About the various models

We will in the rest of the book discuss a number of macroeconomic models. To make it easier to keep them apart we give the different names. We will talk about "the classical model", "the IS-LM model", etc.

Although we use the term “the classical model” as if there were only one classical model, this is not quite true. For all the models we discuss, there are many variations. However, the similarities between, for example, all the classical models are great enough to warrant the expression “the classical model”.

But you need to keep this in mind. If you look up the “IS-LM model” in different text books you will probably see different models but the main predictions from the models do tend to be the same. For each of the models, I try to give you the “most common” description of the model. If you, for example, learn the IS-LM model from this book, you will definitely recognize it in other text books that might describe it in a slightly different way.