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2008 | Book

Introduction Read chapter Read first chapter

Inflation and Unemployment in a Monetary Union

Author: Professor Dr. Michael Carlberg

Publisher: Springer Berlin Heidelberg

Part of: Springer Professional "Wirtschaft+Technik" , Springer Professional "Wirtschaft"

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About this book

This book studies the coexistence of inflation and unemployment in a monetary union. The focus is on how to reduce the associated loss. The primary target of the European central bank is low inflation in Europe. The primary target of the German government is low unemployment in Germany. And the primary target of the French government is low unemployment in France. The European central bank has a quadratic loss function. The same applies to the German government and the French government. The key questions are: To what extent can the sequential process of monetary and fiscal decisions reduce the loss caused by inflation and unemployment? Is monetary and fiscal cooperation superior to the sequential process of monetary and fiscal decisions? The present book is part of a larger research project on European Monetary Union, see the references given at the back of the book. Some parts of this project were presented at the World Congress of the International Economic Association, at the International Conference on Macroeconomic Analysis, at the International Institute of Public Finance, and at the International Atlantic Economic Conference. Other parts were presented at the Macro Study Group of the German Economic Association, at the Annual Meeting of the Austrian Economic Association, at the Göttingen Workshop on International Economics, at the Halle Workshop on Monetary Economics, at the Research Seminar on Macroeconomics in Freiburg, at the Research Seminar on Economics in Kassel, and at the Passau Workshop on International Economics.

Table of Contents

Frontmatter

The Rate of Inflation

Introduction
This book studies the coexistence of inflation and unemployment in a monetary union. The focus is on how to reduce the loss caused by inflation and unemployment. The targets of the European central bank are zero inflation and zero unemployment in Europe. A reduction in European money supply lowers inflation in Europe. On the other hand, it raises unemployment there. We assume that the European central bank has a quadratic loss function. The European central bank changes European money supply so as to reduce the loss caused by inflation and unemployment in Europe.
2. Monetary Policy in Europe
For ease of exposition we make the following assumptions. The monetary union consists of two countries, say Germany and France. The member countries are the same size and have the same behavioural functions. An increase in European money supply raises producer inflation in Germany and France, to the same extent respectively. Here producer inflation in Germany refers to the price of German goods. Similarly, producer inflation in France refers to the price of French goods.
3. Fiscal Policies in Germany and France
For ease of exposition we make the following assumptions. The monetary union consists of two countries, say Germany and France. The member countries are the same size and have the same behavioural functions. An increase in German government purchases raises producer inflation in Germany. Correspondingly, an increase in French government purchases raises producer inflation in France. For ease of exposition we assume that fiscal policy in one of the countries has no effect on producer inflation in the other country.
4. Central Bank and Governments Decide Sequentially
The static model. As a point of reference, consider the static model. It can be represented by a system of three equations:
$$ \begin{array}{*{20}l} {{\rm{\pi }}_1 = }& {\rm{A}}_1 {{\rm{ + \alpha M + \beta G}}_1 } & {\left( {\rm{1}} \right)} \\ {{\rm{\pi }}_2 = } & {\rm{A}}_2 {{\rm{ + \alpha M + \beta G}}_2 } & {\left( 2 \right)} \\ {{\rm{\pi }} = } & 0.5{\rm{\pi }}_1 { + 0.5{\rm{\pi }}_2 } & {\left( 3 \right)} \\ \end{array} $$
Of course this is a reduced form. π1 denotes producer inflation in Germany, π2 is producer inflation in France, π is producer inflation in Europe, M is European money supply, G1 is German government purchases, G2 is French government purchases, α is the monetary policy multiplier, β is the fiscal policy multiplier, A1 is some other factors bearing on producer inflation in Germany, and A2 is some other factors bearing on producer inflation in France.
The endogenous variables are producer inflation in Germany, producer inflation in France, and producer inflation in Europe. According to equation (1), producer inflation in Germany is a positive function of European money supply and a positive function of German government purchases. According to equation (2), producer inflation in France is a positive function of European money supply and a positive function of French government purchases. According to equation (3), producer inflation in Europe is the average of producer inflation in Germany and France.
5. Central Bank and Governments Cooperate
As a starting point, take the model of inflation. It can be represented by a system of three equations:
$$ \begin{array}{*{20}l} {{\rm{\pi }}_1 = }& {\rm{A}}_1 {{\rm{ + \alpha M + \beta G}}_1 } & {\left( {\rm{1}} \right)} \\ {{\rm{\pi }}_2 = } & {\rm{A}}_2 {{\rm{ + \alpha M + \beta G}}_2 } & {\left( 2 \right)} \\ {{\rm{\pi }} = } & 0.5{\rm{\pi }}_1 { + 0.5{\rm{\pi }}_2 } & {\left( 3 \right)} \\ \end{array} $$
Here π1 denotes producer inflation in Germany, π2 is producer inflation in France, π is producer inflation in Europe, M is European money supply, G1 is German government purchases, and G2 is French government purchases. The endogenous variables are producer inflation in Germany, producer inflation in France, and producer inflation in Europe.
2) The policy model. At the beginning there is inflation in Germany and France. More precisely, inflation in Germany is high, and inflation in France is low. The policy makers are the European central bank, the German government, and the French government. The targets of policy cooperation are zero inflation in Germany and zero inflation in France. The instruments of policy cooperation are European money supply, German government purchases, and French government purchases. There are two targets and three instruments, so there is one degree of freedom. As a result, there is an infinite number of solutions. In other words, monetary and fiscal cooperation can achieve zero inflation in Germany and France.
6. The Countries Differ in Size
In this chapter we assume that the countries only differ in size. To be more specific, we assume that the German economy is large and the French economy is small. More precisely, we assume that full-employment output in Germany is large and full-employment output in France is small. An increase in European money supply raises producer inflation in Germany and France, to the same extent respectively.
7. The Countries Differ in Behaviour
In this chapter we assume that the countries only differ in behaviour. To be more specific, we assume that the countries only differ in monetary policy multipliers. An increase in European money supply raises producer inflation in Germany to a large extent. By contrast, it raises producer inflation in France to a small extent.
8. The Monetary Union of Three Countries
The monetary union consists of three countries, say Germany, France and Italy. The member countries are the same size and have the same behavioural functions. An increase in European money supply raises producer inflation in Germany, France and Italy, to the same extent respectively.

The Rate of Unemployment

9. Monetary Policy in Europe
For ease of exposition we make the following assumptions. The monetary union consists of two countries, say Germany and France. The member countries are the same size and have the same behavioural functions. An increase in European money supply lowers unemployment in Germany and France, to the same extent respectively. Here, strictly speaking, unemployment in Germany refers to the rate of unemployment in Germany. Similarly, unemployment in France refers to the rate of unemployment in France.
10. Fiscal Policies in Germany and France
For ease of exposition we make the following assumptions. The monetary union consists of two countries, say Germany and France. The member countries are the same size and have the same behavioural functions. An increase in German government purchases lowers unemployment in Germany. Correspondingly, an increase in French government purchases lowers unemployment in France. For ease of exposition we assume that fiscal policy in one of the countries has no effect on unemployment in the other country.
11. Central Bank and Governments Decide Sequentially
The static model. As a point of reference, consider the static model. It can be represented by a system of three equations:
$$ \begin{array}{*{20}l} {{\rm{u}}_1 {\rm{ = }}} & {{\rm{B}}_1 {\rm{ - \gamma M - \delta G}}_1 } & {\left( {\rm{1}} \right)} \\ {{\rm{u}}_2 {\rm{ = }}} & {{\rm{B}}_2 {\rm{ - \gamma M - \delta G}}_2 } & {\left( 2 \right)} \\ {{\rm{u = }}} & {0.5{\rm{u}}_1 + 0.5{\rm{u}}_2 } & {\left( 3 \right)} \\ \end{array} $$
Of course this is a reduced form. u1 denotes the rate of unemployment inGermany, u2 is the rate of unemployment in France, u is the rate of unemployment in Europe, M is European money supply, G1 is German government purchases, G2 is French government purchases, γ is the monetary policy multiplier, δ is the fiscal policy multiplier, B1 is some other factors bearing on the rate of unemployment in Germany, and B2 is some other factors bearing on the rate of unemployment in France.
The endogenous variables are the rates of unemployment in Germany, France and Europe. According to equation (1), the rate of unemployment in Germany is a negative function of European money supply and a negative function of German government purchases. According to equation (2), the rate of unemployment in France is a negative function of European money supply and a negative function of French government purchases. According to equation (3), the rate of unemployment in Europe is the average of the rates of unemployment in Germany and France.
12. Central Bank and Governments Cooperate
As a starting point, take the model of unemployment. It can be represented by a system of three equations:
$$ \begin{array}{*{20}l} {{\rm{u}}_1 {\rm{ = }}} & {{\rm{B}}_1 {\rm{ - \gamma M - \delta G}}_1 } & {\left( {\rm{1}} \right)} \\ {{\rm{u}}_2 {\rm{ = }}} & {{\rm{B}}_2 {\rm{ - \gamma M - \delta G}}_2 } & {\left( 2 \right)} \\ {{\rm{u = }}} & {0.5{\rm{u}}_1 + 0.5{\rm{u}}_2 } & {\left( 3 \right)} \\ \end{array} $$
Here u1 denotes the rate of unemployment in Germany, u2 is the rate of unemployment in France, u is the rate of unemployment in Europe, M is European money supply, G1 is German government purchases, and G2 is French government purchases. The endogenous variables are the rates of unemployment in Germany, France and Europe.
2) The policy model. At the beginning there is unemployment in Germany and France. More precisely, unemployment in Germany is high, and unemployment in France is low. The policy makers are the European central bank, the German government, and the French government. The targets of policy cooperation are zero unemployment in Germany and zero unemployment in France. The instruments of policy cooperation are European money supply, German government purchases, and French government purchases. There are two targets and three instruments, so there is one degree of freedom. As a result, there is an infinite number of solutions. In other words, monetary and fiscal cooperation can achieve zero unemployment in Germany and France.
13. The Countries Differ in Size
In this chapter we assume that the countries only differ in size. To be more specific, we assume that the German economy is large and the French economy is small. More precisely, we assume that full-employment output in Germany is large and full-employment output in France is small. An increase in European money supply lowers the rates of unemployment in Germany and France, to the same extent respectively.
14. The Countries Differ in Behaviour
In this chapter we assume that the countries only differ in behaviour. To be more specific, we assume that the countries only differ in monetary policy multipliers. An increase in European money supply lowers the rate of unemployment in Germany to a large extent. By contrast, it lowers the rate of unemployment in France to a small extent.
15. The Monetary Union of Three Countries
The monetary union consists of three countries, say Germany, France and Italy. The member countries are the same size and have the same behavioural functions. An increase in European money supply lowers unemployment in Germany, France and Italy, to the same extent respectively.

Inflation and Unemployment

16. The Model
In Part One the focus was on inflation. In Part Two the focus was on unemployment. In Parts Three and Four the focus will be on the coexistence of inflation and unemployment. To be more specific, Part Three will deal with the monetary union as a whole. And Part Four will deal with the monetary union of two countries. Part Three will only deal with monetary policy in Europe. Part Four will deal with
  • monetary policy in Europe
  • fiscal policies in Germany and France
  • central bank and governments decide sequentially
  • central bank and governments cooperate
  • central bank and governments differ in loss function.
17. Some Numerical Examples
For ease of exposition we make the following assumptions. The targets of the European central bank are zero inflation and zero unemployment in Europe. The weights of inflation and unemployment in the loss function are equal. The monetary policy multipliers are unity. A unit increase in European money supply lowers the rate of unemployment in Europe by 1 percentage point. On the other hand, it raises the rate of inflation in Europe by 1 percentage point. For easy reference, the solution is reproduced here:
$$\Delta {\rm{M = 0}}{\rm{.5}}\left( {{\rm{u}} - {\rm{\pi }}} \right)$$
(1)
ΔM denotes the required change in European money supply, π is the initial rate of inflation in Europe, and u is the initial rate of unemployment in Europe.
18. Monetary Policy in the Phillips Curve Diagram
In Figure 1 we assume that unemployment causes deflation whereas overemployment causes inflation. It proves useful to study two distinct cases:
  • the case of unemployment and deflation
  • the case of overemployment and inflation.

Inflation and Unemployment

19. Monetary Policy in Europe
For ease of exposition we assume that the monetary union consists of two countries, say Germany and France. The member countries are the same size and have the same behavioural functions. An increase in European money supply lowers unemployment in Germany and France. On the other hand, it raises producer inflation there. Here producer inflation in Germany refers to the price of German goods. Similarly, producer inflation in France refers to the price of French goods.
20. Fiscal Policies in Germany and France
The case of Germany. The monetary union consists of two countries, say Germany and France. The member countries are the same size and have the same behavioural functions. An increase in German government purchases lowers unemployment in Germany. On the other hand, it raises producer inflation there. For ease of exposition we assume that fiscal policy in one of the countries has no effect on unemployment or producer inflation in the other country.
In the numerical example, a unit increase in German government purchases lowers the rate of unemployment in Germany by 1 percentage point. On the other hand, it raises the rate of inflation in Germany by 1 percentage point. For instance, let initial unemployment in Germany be 2 percent, and let initial inflation in Germany be equally 2 percent. Now consider a unit increase in German government purchases. Then unemployment in Germany goes from 2 to 1 percent. On the other hand, inflation in Germany goes from 2 to 3 percent.
The model of inflation and unemployment can be represented by a system of two equations:
$${\rm{\pi }}_{\rm{1}} = {\rm{A}}_1 + {\rm{\beta G}}_{\rm{1}}$$
(1)
$${\rm{u}}_{\rm{1}} = {\rm{B}}_1 {\rm{ - \delta G}}_{\rm{1}}$$
(2)
Of course this is a reduced form. π1 denotes the rate of inflation in Germany, u1 is the rate of unemployment in Germany, G1 is German government purchases, β is the fiscal policy multiplier with respect to inflation, δ is the fiscal policy multiplier with respect to unemployment, A1 is some other factors bearing on the rate of inflation in Germany, and B1 is some other factors bearing on the rate of unemployment in Germany. The endogenous variables are the rate of inflation and the rate of unemployment in Germany.
According to equation (1), the rate of inflation in Germany is a positive function of German government purchases. According to equation (2), the rate of unemployment in Germany is a negative function of German government purchases. A unit increase in German government purchases lowers the rate of unemployment in Germany by δ percentage points. On the other hand, it raises the rate of inflation in Germany by β percentage points.
21. Central Bank and Governments Decide Sequentially
The static model. As a point of reference, consider the static model. It can be represented by a system of six equations:
$${\rm{\pi }}_{\rm{1}} = {\rm{A}}_{\rm{1}} + {\rm{\alpha M + \beta G}}_{\rm{1}}$$
(1)
$${\rm{\pi }}_2 = {\rm{A}}_2 + {\rm{\alpha M + \beta G}}_2$$
(2)
$${\rm{\pi }} = 0.5{\rm{\pi }}_1 + 0.5{\rm{\pi }}_{\rm{2}}$$
(3)
$${\rm{u}}_{\rm{1}} = {\rm{B}}_{\rm{1}} {\rm{ - \gamma M - \delta G}}_{\rm{1}}$$
(4)
$${\rm{u}}_2 = {\rm{B}}_2 {\rm{ - \gamma M - \delta G}}_2$$
(5)
$${\rm{u}} = 0.5{\rm{u}}_1 + 0.5{\rm{u}}_{\rm{2}}$$
(6)
Of course this is a reduced form. π1 denotes the rate of inflation in Germany, π2 is the rate of inflation in France, π is the rate of inflation in Europe, u1 is the rate of unemployment in Germany, u2 is the rate of unemployment in France, u is the rate of unemployment in Europe, M is European money supply, G1 is German government purchases, G2 is French government purchases, α is the monetary policy multiplier with respect to inflation, β is the fiscal policy multiplier with respect to inflation, γ is the monetary policy multiplier with respect to unemployment, δ is the fiscal policy multiplier with respect to unemployment, A1 is some other factors bearing on the rate of inflation in Germany, A2 is some other factors bearing on the rate of inflation in France, B1 is some other factors bearing on the rate of unemployment in Germany, and B2 is some other factors bearing on the rate of unemployment in France. The endogenous variables are the rates of inflation and the rates of unemployment in Germany, France and Europe.
According to equation (1), the rate of inflation in Germany is a positive function of European money supply and a positive function of German government purchases. According to equation (2), the rate of inflation in France is a positive function of European money supply and a positive function of French government purchases. According to equation (3), the rate of inflation in Europe is the average of the rates of inflation in Germany and France. According to equation (4), the rate of unemployment in Germany is a negative function of European money supply and a negative function of German government purchases. According to equation (5), the rate of unemployment in France is a negative function of European money supply and a negative function of French government purchases. According to equation (6), the rate of unemployment in Europe is the average of the rates of unemployment in Germany and France.
22. Central Bank and Governments Cooperate
As a starting point, consider the model of inflation and unemployment. It can be represented by a system of four equations:
$${\rm{\pi }}_{\rm{1}} = {\rm{A}}_{\rm{1}} + {\rm{\alpha M + \beta G}}_{\rm{1}}$$
(1)
$${\rm{\pi }}_2 = {\rm{A}}_2 + {\rm{\alpha M + \beta G}}_2$$
(2)
$${\rm{u}}_{\rm{1}} = {\rm{B}}_{\rm{1}} {\rm{ - \gamma M - \delta G}}_{\rm{1}}$$
(3)
$${\rm{u}}_2 = {\rm{B}}_2 {\rm{ - \gamma M - \delta G}}_2$$
(4)
Of course this is a reduced form. π1 denotes the rate of inflation in Germany, π2 is the rate of inflation in France, u1 is the rate of unemployment in Germany, u2 is the rate of unemployment in France, M is European money supply, G1 is German government purchases, G2 is French government purchases, α is the monetary policy multiplier with respect to inflation, β is the fiscal policy multiplier with respect to inflation, γ is the monetary policy multiplier with respect to unemployment, and δ is the fiscal policy multiplier with respect to unemployment. The endogenous variables are the rates of inflation and the rates of unemployment, in Germany as well as in France.
According to equation (1), the rate of inflation in Germany is a positive function of European money supply and a positive function of German government purchases. According to equation (2), the rate of inflation in France is a positive function of European money supply and a positive function of French government purchases. According to equation (3), the rate of unemployment in Germany is a negative function of European money supply and a negative function of German government purchases. According to equation (4), the rate of unemployment in France is a negative function of European money supply and a negative function of French government purchases.
An increase in European money supply lowers unemployment in Germany and France. On the other hand, it raises inflation there. An increase in German government purchases lowers unemployment in Germany. On the other hand, it raises inflation there. Correspondingly, an increase in French government purchases lowers unemployment in France. On the other hand, it raises inflation there.
23. Central Bank and Governments Differ in Loss Function
1) The static model. An increase in European money supply lowers unemployment in Germany and France. On the other hand, it raises inflation there. An increase in German government purchases lowers unemployment in Germany. On the other hand, it raises inflation there. Correspondingly, an increase in French government purchases lowers unemployment in France. On the other hand, it raises inflation there.
Backmatter
Metadata
Title
Inflation and Unemployment in a Monetary Union
Author
Professor Dr. Michael Carlberg
Copyright Year
2008
Publisher
Springer Berlin Heidelberg
Electronic ISBN
978-3-540-79301-4
Print ISBN
978-3-540-79300-7
DOI
https://doi.org/10.1007/978-3-540-79301-4