Gärtner M. (2009) - Macroeconomics - Instructor's Manual - Third Edition

Instructor’s Manual Macroeconomics Third Edition

Susanne Burri Manfred Gärtner

For further instructor material please visit:

www.pearsoned.co.uk/gartner ISBN: 978-0-273-71791-1

© Manfred Gärtner 2009 Lecturers adopting the main text are permitted to download and photocopy the manual as required.

Pearson Education Limited Edinburgh Gate Harlow Essex CM20 2JE England and Associated Companies around the world Visit us on the World Wide Web at: www.pearsoned.co.uk ---------------------------------This edition published 2009 © Manfred Gärtner 2009 The right of Susanne Burri to be identified as author of this work has been asserted by him in accordance with the Copyright, Designs and Patents Act 1988. ISBN: 978-0-273-71791-1 All rights reserved. Permission is hereby given for the material in this publication to be reproduced for OHP transparencies and student handouts, without express permission of the Publishers, for educational purposes only. In all other cases, no part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise without either the prior written permission of the Publishers or a licence permitting restricted copying in the United Kingdom issued by the Copyright Licensing Agency Ltd. Saffron House, 6-10 Kirby Street, London EC1N 8TS. This book may not be lent, resold, hired out or otherwise disposed of by way of trade in any form of binding or cover other than that in which it is published, without the prior consent of the Publishers.

2 © Manfred Gärtner 2009

Contents Chapters

Pages

1.

Macroeconomic essentials

2.

Booms and recessions (I): the Keynesian cross

13

3.

Money, interest rates and the global economy

22

4.

Exchange rates and the balance of payments

32

5.

Booms and recessions (II): the national economy

38

6.

Enter aggregate supply

48

7.

Booms and recessions (III): aggregate supply and demand

56

8.

Booms and recessions (IV): Dynamic aggregate supply and demand

66

9.

Economic growth (I): basics

74

10.

Economic growth (II): advanced issues

83

11.

Endogenous economic policy

91

12.

The European Monetary System and Euroland at work

96

13.

Inflation and central bank independence

103

14.

Budget deficits and public debt

110

15.

Unemployment and growth

116

16.

Sticky prices and sticky information: new perspectives on booms and recessions I

123

Real business cycles: new perspectives on booms and recessions (II)

130

A primer in econometrics

136

17. Appendix


5

Manfred Gärtner, Macroeconomics, 3rd Edition, Instructor’s Manual

Supporting resources Visit www.pearsoned.co.uk/gartner to find valuable online resources Companion Website for students • Macroeconomic tutorials with interactive models, guided exercises, and animations, plus an interactive road map connecting key concepts and models • A data bank with macroeconomic time series for many countries, along with a graphing module • Extensive links to valuable resources on the web, organised by chapter • Self assessment questions to check your understanding, with instant grading • Index cards to aid navigation of resources, plus chapter summaries, macroeconomic dictionaries in several languages, and more For instructors • Downloadable Instructor’s Manual including the solutions to chapter exercises and questions • Downloadable PowerPoint slides of all figures and tables from the book For more information please contact your local Pearson Education sales representative or visit www.pearsoned.co.uk/gartner


1 Macroeconomic essentials Chapter focus This chapter attempts three things: 1. Provide an international perspective of macroeconomic issues and data. Since it tries to cover the European countries rather comprehensively plus the major players in the global economy, it can only feature a limited set of the most important macroeconomic data. It is desirable to augment this streamlined international information with a more detailed discussion of your own country’s national macroeconomic data and sources. 2. Repeat some basic macroeconomic concepts. These are being used extensively in the remainder of the book. These include the circular flow of income as a first ‘model’ of the macroeconomy and the circular flow identity that is related to it, the government budget and the balance of payments. The role of money is also already introduced at this stage by tying it to the circular flow via the quantity equation. The book assumes that students have previously taken an economic principles course. Then the first (and probably the next two) chapter(s) can be dealt with rather quickly. In case this is the first encounter of students with macroeconomics, then the concise treatment of Chapter 1 should be augmented with additional reading assignments from some principles text. 3. Motivate students that macroeconomics is an exciting field with an applied focus. To this end, the chapter features a case study on the subprime crisis that started in 2007–2008 that demonstrates that even the basic concepts introduced in this chapter provide some useful insights into the issues and policy choices surrounding this crisis. The chapter ends with an appendix on logarithms, logarithmic scales and growth rates. It provides an understanding of the growth rates of products (say PY) and fractions (say M/P) and motivates the graphical display of trended time series using logarithmic scales. In an attempt not to leave students with a less mathematical mind behind, numerical illustrations that students may follow with their pocket calculator are being used instead of formal proofs.

Additional case studies Case study C1.1 Germany's current account before and after unification Germany’s traditional current account surpluses, which had culminated at 4.8% of GDP in 1989, disappeared after unification. In the first full calendar year after the two Germanies had merged the current account dropped from a regular surplus into a deficit the size of about 1% of GDP (see Figure C1.1(a)). The circular flow model and the identity of leaks and injections, S – I T– G IM – EX 0, provides a first clue as to what had happened. First note, however, that while we are treating the current account CA and net exports as synonyms in Chapter 1, and throughout most of the text, this is only an approximation. The main difference between the two aggregates in reality is that the current account also includes transfers across borders that are not related to the export and import of goods and services. Examples are aid to developing countries, a

Turkish family living in Germany sending money to their parents in Ankara, or the contributions of the German government to international organizations such as NATO, the United Nations, or the European Union. Since such things also constitute leakages out of the circular flow of income, the current account is actually a more precise measure of a country’s net leakages to the rest of the world than net exports. It is often argued that the dramatic shift in Germany’s current account was the result of rising government budget deficits triggered by public investment in East Germany’s infrastructure and transfer payments to the East. This interpretation is often motivated by comparing West Germany’s last full budget in the year before unification, 1989, with the years that followed. This implies that unification drove a more or less balanced government budget


rd

Manfred Gärtner, Macroeconomics, 3 Edition, Instructor’s Manual

into deficit by some 3% of GDP. Panel (b) in Figure C1.1, shows that this is a misleading story. The year 1989 is clearly atypical, given that the budget had been in deficit for years before and exceeded 2% of GDP in 1988 already. Ignoring 1989 as exceptional, unification increased the budget deficit only by about 1% point from 2% to 3% of GDP. In terms of the circular flow identity: while the increase of the budget deficit may have caused the current account to deteriorate, its magnitude of 1% point only partly explains the change in the current account by some 5 points. What seems to have mattered much more is the change in private net savings documented in panel (c) of Figure C1.1.

While private savings exceeded investment by some 6% of GDP before unification, this difference dropped to about 2% after unification. This accounts for the remaining change in the current account that was not explained by the change in the government budget deficit. Of course, the change in private net savings also reflects government policies towards the eastern part of Germany. Net savings did not fall because savings fell, but because investment increased due to investment bonus packages put into action by the Kohl government. Figure C1.2 shows that savings were still about the same in 1995 as they had been 10 years earlier, while investment had risen by about 4% points. Using stylized, rounded numbers for the time before and after unification Table C1.1 summarizes the observed changes: the current account deficit rose to – 4% to 1%. One percentage point of this reflects the change in government spending behaviour, i.e. the increase of the budget deficit from 2% to 3% of GDP. The remaining 4 percentage points (that is, the remaining 80%) of the change in the current account reflect the change in net private savings, which dropped from 6% to 2% of GDP.

Figure C1.2 Table C1.1 1986-1990 1991-1995

Figure C1.1 6 © Manfred Gärtner 2009

6% 2%

2% 3%

4% 1%

0 0 0

rd


Exercises Exercise 1.1 The following are nominal incomes for some European countries in 2007, expressed in US dollars: A 42,700; B 40,710; CH 59,880; D 38,860; DK 54,910; E 29,450; F 38,500; GB 42,740; GR 29,630; I 33,540; IRL 48,140; LUX 75,880; N 76,450; NL 45,820; P 18,950; S 46,060. Real incomes are as follows: A 38,140; B 34,790; CH 43,870; D 33,530; DK 36,300; E 30,820; F 33,600; GB 33,800; GR 32,330; I 29,850; IRL 37,090; LUX 63,590; N 53,320; NL 39,310; P 20,890; S 36,590. (a) What is your country’s price level relative to the United States price level of 1 (If your country is not included, choose any country)? (b) Rank your country and any two other countries according to their price levels. (a) To compute relative price levels, we use the data on nominal and real incomes given in the exercise. From the definition of real income (cf. pg. 3) it follows that for any country i, real income can be expressed as nominal income divided by the price level: / If we rearrange this equation and solve for the price level, we get / The price levels relative to the United States are: ⁄ ⁄ ⁄ ⁄ ⁄ ⁄ ⁄ ⁄ ⁄ ⁄ ⁄ ⁄ ⁄ ⁄ ⁄ ⁄

⁄ ⁄

⁄1 42,700⁄38,140 1.12 ⁄1 40,710⁄34,790 1.17 ⁄ ⁄1 59,880/43,870 1.36 ⁄ ⁄1 38,860/33,530 1.16 ⁄ ⁄1 54,910/36,300 1.51 ⁄ ⁄1 29,450/30,820 0.96 ⁄ ⁄1 38,500/33,600 1.15 ⁄ ⁄1 42,740/33,800 1.26 ⁄ ⁄1 29,630/32,330 0.92 ⁄ ⁄1 33,540/29,850 1.12 ⁄ ⁄1 48,140/37,090 1.30 ⁄ ⁄1 75,880/63,590 1.19 ⁄ ⁄1 76,450/53,320 1.43 ⁄ ⁄1 45,820/39,310 1.17 ⁄ ⁄1 18,950/20,890 0.91 ⁄ ⁄1 46,060/36,590 1.26

(b) Denmark (DK) has the highest price level, followed by N, CH, IRL, GB, S, LUX, B, NL, D, F, I, A, E, GR and P.

Exercise 1.2 Which of the following transactions constitute leakages, and which ones injections? (a) The home country receives aid from the International Monetary Fund. (b) Immigrant workers transfer their salaries to their home countries. (c) Domestic firms invest in foreign countries. (d) The government raises taxes and uses the proceeds to buy computers abroad. Any part of domestic income that does not generate demand for domestically produced goods and services is a leakage. Any exogenous demand for domestically produced goods, coming from some source other than domestic income, is an injection into the circular flow of income. (a) Injection (b) Leakage (c) Leakage (d) Leakage 7 © Manfred Gärtner 2009

rd


Exercise 1.3 Table 1.5 contains data for the Netherlands, Germany and Spain in 2006. All numbers are in billions of US dollars. Fill in the missing numbers, following the logic of the circular flow model. The numbers missing in Table 1.5 have been added in bold type in Table I1.1 below. Generally, the missing numbers can be calculated using the circular flow identity and simplified definitions of the budget deficit and the current account, respectively: :

0

Table I1.1 Saving S

Investment I

Taxes T

174

Netherlands Germany Spain

527 380

520 260

Government expenditure G 179 563

Budget deficit

Imports IM

Exports EX

Current account

421 1149

469 1304 327

155 77

4 25

Source: World Bank, Eurostat

Exercise 1.4 You head your country's central bank and must determine the amount of money to circulate next year. You know that every euro circulates four times a year. The statistical office forecasts that production will remain unchanged at 1,000 barrels of whisky (the only good produced in your country) next year. (a) What is the slope of the aggregate supply curve if the production of whisky remains constant as forecasted? (b) Compute the price of one barrel of whisky if you fix the money supply at €4,000. (c) What would be the price of one barrel of whisky if the velocity of money circulation rose to five while the money supply remained at €4,000? (d) Given the rising velocity of money circulation from (c) and constant production of whisky, how would you fix the money supply if your targeted price level was €5 per barrel of whisky? (e) What is the price of whisky if output rises to 1,600 barrels in the following year while the money supply remains at €4,000 and money circulates four times a year? (a) Since the quantity of whisky produced remains constant no matter what the price level is, the aggregate supply curve is vertical in quantity-price space. (b) Plugging the numbers given in the exercise into the quantity equation ( €4,000

4

) we get

1,000

This can be solved for

€16/

to obtain

.

(c) Plugging the new numbers into the quantity equation we get €4,000

5

1,000


to get

€20/

.

(d) Again we can plug in the numbers into the quantity equation, this time to compute €

5

€5/

This yields

:

1,000 €1,000.

(e) Plugging the new numbers into the quantity equation we get €4,000 Solving the equation yields

€10/

.


4

€ /

1,600

rd


Exercise 1.5 Some time after an increase in the money supply from 50 billion to 100 billion units, the government of country A learns that the price level has increased from 100 to 150 although the velocity of money circulation has remained constant. What does that tell you about the slope of the aggregate supply curve? The quantity equation suggests that the money supply and the price level of country A should rise by the same proportions if output and the velocity of money remain constant. In our example, the money supply has doubled (i.e. it has risen by 100%) while the price level has risen by 50% only. With the velocity of money remaining constant, output – or aggregate supply – must therefore have increased as well. This means that the aggregate supply curve has a positive (finite) slope in quantity-price space: An increase in prices raises output.

Exercise 1.6 The government of country B plans to spend €10,000 next year. Due to political constraints, taxes cannot exceed €5,000. Eighty percent of the budget deficit will be financed by issuing government bonds to the private sector, the rest by issuing bonds to the central bank in exchange for money. (a) Compute the anticipated change in the money supply if neither international trade nor international capital movements take place. (b) What will be the effect on the price level if real output stays constant at Y = 10,000 and V at 4? (c) Compute the anticipated change in the money supply if international trade in goods takes place, but international capital movements are still forbidden. The statistical office forecasts a current account deficit of €3,000. (d) Can you think of arguments that render the assumption of a constant level of real production (employed above) implausible? (a) The increase in the money supply equals the amount of bonds issued to the central bank, which is €1,000. 20% of €5,000, i.e. €1,000: ∆ ∆ (b) We can use the quantity equation and our knowledge of the increase in the money supply to compute the change in the price level. Let and denote the current period money supply and price level. The quantity equation after the increase of the money supply can then read ∆

∆

or, in expanded form

∆

Since the quantity equation holds in the current period, i.e. since out these terms from the above expanded equation to get ∆

∆

∆

. , we can cancel

.

Solving this for the change in the price level yields ∆P

∆M

V⁄Y

€1,000

4⁄10,000

0.4.

(c) If we consider an economy that engages in international trade, the money supply is determined not only by the amount of government bonds issued to the central bank, but also by the amount of ). If there is a current account foreign currency reserves the central bank holds ( deficit, the country imports more than it exports. The private demand for foreign currency thus exceeds its supply by €3,000, which means that the central bank has to reduce its foreign currency reserves by €3,000 in order to add to the foreign currency supply. This follows from 0, 0 and ∆ . To determine how this changes the money supply we can write: ∆

∆

∆

€1,000

€3,000

€2,000.

(d) Changes in government spending and the money supply may influence the interest rate (crowding out; cf. chapter 3) and/or the exchange rate (depending on the level of capital mobility and the exchange rate regime; chapters 4 and 5) and thus affect real output.


rd


Exercise 1.7 A country’s net foreign assets stand at 500. Next year’s exports are expected to be 30, expected imports are 20. The central bank will not intervene in the foreign exchange market. What are the country's net foreign assets by the end of next year? In the absence of central bank intervention in the foreign exchange market, the change in foreign assets is determined by the current account balance, i.e. by the difference between exports and imports: ∆

30

20

10.

The new level of net foreign assets is therefore

∆

500

10

510.

Exercise 1.8 Consider Figure 1.15. The graph shows a stylized demand curve for DVD recorders.

Figure 1.15 (a) (b) (c) (d)

(e) (f) (g) (h)

What are the endogenous variables in this model? The price of a DVD recorder is 1,500 Swiss francs. What is the quantity demanded? If the price fell to only one-third of its previous level, what would market demand be? The supply curve can be described by the following equation: 500 0.000025 Draw the curve into the diagram in Figure 1.10. Determine the equilibrium price level and the quantity sold graphically. It becomes unfashionable to waste time in front of the TV. Show how this change of preferences affects market demand. What will be the effect on the equilibrium price level and quantity? Due to a new technology it becomes cheaper to produce DVD recorders. How will that affect the diagram above? The government introduces a tax on DVDs. How will that affect the diagram? What happens if the government introduces a tax on visits to the cinema but does not levy a tax on DVDs?

(a) Endogenous variables are determined within the model. To describe their behaviour is the very purpose of the model. In the above model, the price and the quantity are endogenous variables. (b) The quantity demanded at a price of 1,500 Swiss francs can be read off the graph; it is approximately 24 million units (The more exact number is 23,333,333 units). (c) One third of 1,500 Swiss francs is 500 Swiss francs. The quantity demanded at a price level of 500 Swiss francs is 50 million units; this can be read off the graph. (d) The supply curve is drawn into Figure I1.1. According to the equation given, the intercept of the supply curve ( 0) is at 500. For every price increase of 250 Swiss francs, 10 million additional units are supplied. 10 © Manfred Gärtner 2009

rd


Figure I1.1 (e) The equilibrium price and the quantity sold in equilibrium can be read off the intersection of the demand and supply curve. The equilibrium price is 1,250 Swiss francs, the equilibrium quantity is 30 million units. (f)

The change in preferences induces consumers to demand fewer DVD recorders at any given price level. Graphically, this is equivalent to the demand curve shifting left (or down). After the shift has occurred, the new equilibrium price and amount will necessarily be lower than the initial equilibrium values (see Figure I1.2).

Figure I1.2 (g) The new technology makes it possible to produce more DVD recorders at any given price level. Graphically, this is equivalent to the supply curve shifting right (or down). After the shift has occurred, the new equilibrium price will be lower and the new equilibrium quantity will be higher than the old equilibrium values (see Figure I1.3).

Figure I1.3 11 © Manfred Gärtner 2009

rd


(h) The tax on DVDs has an adverse effect on the demand for DVD recorders since DVDs and DVD recorders are complements. Hence, the demand for DVD recorders falls at any given price level, and the demand curve will shift to the left (or down). By contrast, a tax on visits to the cinema will stimulate the demand for DVD recorders, since DVD recorders (together with DVDs) are a substitute for visits to the cinema. Hence the demand of DVD recorders rises at any given price level and the demand curve shifts to the right (see Figure I1.4).

Figure I1.4


2 Booms and recessions (I): the Keynesian cross Chapter Focus This chapter brings students all the way from the use of the circular flow of income ‘model’ in Chapter 1 as a descriptive device to setting the circular flow of income up as a genuine model with a unique equilibrium in Chapter 2. Introducing the concept of a macroeconomic equilibrium constitutes a big step. When the circular flow of income is being used merely as a descriptive device, the circular flow identity holds at all times. Income may be at any level as long as we permit investment demand to comprise both planned (voluntary) and unplanned (involuntary) investment. While such a descriptive model helps streamline our thinking about what seems an incomprehensible macroeconomic reality, it does not explain why income is at a unique level, and at no other. To build a model with a unique equilibrium requires the following: 1.

The introduction of behavioural equations: the consumption function, the investment function, the export function and the import function. These functions are being kept deliberately simple in order to arrive at a first macroeconomic model, the Keynesian cross, quickly, without distracting detours. If so desired, and if time permits, refined discussions of one or more of the behavioural equations may be discussed in more detail: – the permanent income or life cycle hypothesis of consumption; – the q theory of investment; – or the role of the J curve in international trade. As said, these detours are being avoided in Chapter 2. The only refinement offered is a brief discussion of how consumption and investment decisions depend on expected future movements of income, which leads to the result that marginal consumption out of a transitory increase in income is much smaller than out of a permanent increase in income. 2.

The distinction between planned and unplanned investment and, hence, spending. It is important to stress that equilibrium income defined as a situation in which income equals all planned spending defines a point of gravity only. Actual income in any given year may well deviate from this. But market forces will eventually move income towards this gravity point.

Additional case studies Case study C2.1 The 2008 US stimulus package As the US subprime mortgage crisis unfolded at the beginning of 2008, President Bush and Congress responded to rising fears of a severe economic slowdown with calls for a swift economic stimulus package. On 13 February the president signed a $152 billion fiscal stimulus package into law which granted tax rebates of up to $1,200 to most people who had paid income taxes in 2007. Figure C2.1 shows how these rebates affected US disposable income and consumption and puts developments into perspective. Figure C2.1 13 © Manfred Gärtner 2009

rd


The lower line reveals that short-lived increases in income may be expected to generate only small, if any, responses in consumption, in particular at times when households worry about their savings, their future income and the security of their jobs.

The drop in consumption during the second half of 2008, when income was still rising, gives proof of increased saving efforts in order to make up for lost wealth and prepare for an uncertain future.

Exercises Exercise 2.1 Consider French real output between 1900 and 1994 as given in Figure 2.16. Add your guess of the paths of steady-state income and potential income to the graph. See Figure I2.1. It is important to note that French potential income and French steady-state income coincided in the years between 1900 and 1914, and again in the years between 1970 and 1994. The deviations of potential income from its secular trend (i.e. steady-state income) were caused by the two world wars. Subsequent reversions indicate transition dynamics.

Figure I2.1 Exercise 2.2 Figure 2.20 displays the evolution of real GDP between 1978 and 2002 for the United States and France. (a) Try to identify business cycles, marking peaks and troughs on the graphs. (b) Identify the US position in 1991 in a diagram with prices on the vertical axis and income on the horizontal axis. Mark potential income, steady-state income and actual income. Two US economists, Arthur F. Burns and Wesley C. Mitchell, claimed half a century ago that the typical business cycle lasts between 6 and 32 quarters. (c) Does this agree with your findings? (a) See Figures I2.2 and I2.3. (b) Figure 2.20 shows no deviation of potential income from steady-state income for the United States. There was, in other words, no massive reduction of the capital stock in the years between 1978 and 2002. Potential income can thus be assumed to match steady-state income. Moreover, the US business cycle reached a trough in 1991 (cf. Figure I2.2). This means that by definition, actual income was below potential income in 1991, which is reflected by the actual income line in Figure I2.4. (c) According to Figures I2.2 and I2.3, entire business cycles last approximately 9 years or 36 quarters in the United States and approximately 8 years or 32 quarters in France. They are thus at (or above) the upper bound of what Burns and Mitchell consider to be a typical business cycle period.


rd


Figure I2.2

Figure I2.3

Figure I2.4

Exercise 2.3 Consider an economy with the following data (note that actual investment): 750

500

0

250

is planned investment, which may not coincide with 250

1,000

(a) Is this economy’s circular flow in equilibrium in the sense that firms do not have to change inventories involuntarily? (b) Translate the above data into a diagram with demand on the vertical axis and income on the horizontal axis. Add the assumption 0.75 . 15 © Manfred Gärtner 2009

rd


(c) Draw the aggregate-expenditure and the actual-expenditure lines. Identify demand-determined income in equilibrium in your graph and analytically. (d) What happens to equilibrium income if government expenditure increases by 500 units? Show your result in a graph and verify that it is supported by the multiplier formula of Equation 2.9. (e) Using a graph, show what happens if net exports fall from 250 to 100. (f) Using a graph, show what happens if the marginal propensity to consume rises from 0.75 to 0.8. (a) The circular flow is not in equilibrium since planned (aggregate) demand 750 500 250 250 1,750 exceeds output (1,000). Firms have to undertake unplanned negative investment of 250 instead. (b) See Figure I2.5.

Figure I2.5 (c) See Figure I2.6. Since consumption now depends on income, the aggregate-expenditure line slopes upward in income-expenditure space. The intersection of the aggregate-expenditure line with the actualexpenditure line determines equilibrium income. Equilibrium income can be derived analytically by solving the circular flow equation: 0.75 500 250 250 for , which yields 4,000. Note that we implicitly used the multiplier 1⁄ 1 0.75 4.

Figure I2.6 (d) At the old level of government expenditure, the aggregate-expenditure line intersects the vertical axis at 1,000. If government expenditure increases by 500 units, the new intercept is at 1,500 and equilibrium income (which can be found at the point where the aggregate-expenditure and the actual-expenditure line intersect) amounts to 6,000. This can be verified by using the formula ∆ 1⁄1 ]∆ . Plugging in 0.75 and ∆ 500 yields ∆ 2,000, which confirms the graphical result in Figure I2.7.


rd


Figure I2.7 (e) The decline in exports makes the aggregate-expenditure line shift downward by 150 units and the new intercept with the vertical axis is at 850. The new point of intersection with the actual-expenditure line is at 3,400 (see Figure I2.8). This can be verified by computing ∆ 1⁄1 ]∆ with ∆ 150 and 0.75, which yields ∆ 600.

Figure I2.8 (f)

If the marginal propensity to consume changes, the slope of the aggregate-expenditure line changes. In our case increases from 0.75 to 0.8, which makes the aggregate-expenditure line steeper ( actually is the slope of the aggregate-expenditure line). If we compute income for the initial values of investment, government consumption, and net exports, we have to solve the equation 0.8 500 250 250 for , which yields 5,000 (see Figure I2.9).

Figure I2.9


rd


Exercise 2.4 One effect of German unification was a rise in demand for most Western countries’ exports. However, the impact differed considerably among European countries, depending on the multipliers that transform an exogenous change in demand into a change in income. Consider the Netherlands and the United Kingdom. The share of imports in Dutch GDP is 52%, the share of imports in British GDP is 27%. Assume that these average import propensities are also the marginal propensities to import. Assume, further, that for both countries the marginal propensity to consume is 80% and the average tax rate is 30%. What is the slope of the aggregate supply curve if the production of whisky remains constant as forecasted? (a) Calculate the equilibrium effect of an exogenous increase of export demand by 100 units on Dutch and British GDP. (b) Employ the successive-rounds interpretation of the multiplier. By how much has income increased after round #3 in total?

(a) The multiplier for an open economy with taxes is . For the Netherlands this yields a multiplier of .

.

.

1.042.

For the United Kingdom the multiplier is .

.

.

1.408.

The increases in income induced by the hike in export demand are thus 104.2 for the Netherlands and 140.8 for the United Kingdom.

(b) The results derived above hold in equilibrium after the full multiplier effect has played out. This means that the increases in income calculated above will be reached only after an infinite number of virtual rounds. However, most of the increase in income is reached after the first few rounds. We will thus trace the evolution of income over the first three rounds only. In round #1, only the direct effect of the increased export demand on income occurs, hence ∆ ∆ 100. This holds both for the Netherlands and the United Kingdom. In round #2, the additional output feeds into consumption and import demand. The incremental increase in output in this second round is ∆

1

]∆ .

Plugging in ∆ 100 and the given values for the marginal propensity to import, the tax rate and the marginal propensity to consume we get ∆

0.8 1

0.3

0.52]

100

4.

100

29.

for the Netherlands and ∆

0.8 1

0.3

0.27]

for the United Kingdom. In round #3, the incremental output of round #2, ∆ , feeds into consumption and import demand. Hence ∆

1

∆

0.8 1

]∆ , which yields 0.3

0.52]

4

0.16

for the Netherlands, and ∆

0.8 1

0.3

0.27]

29

8.41

for the United Kingdom. The additional output resulting after the first three rounds can be determined by computing ∆ ∆ ∆ , which yields 100 4 0.16 104.16 for the Netherlands and 100 29 8.41 137.41 for the 18 © Manfred Gärtner 2009

rd


United Kingdom. Hence, both countries are very close to reaching the new equilibrium values after as little as three rounds. Exercise 2.5 In the summer of 1991 the German parliament imposed a surcharge of 7.5% on the personal and corporate income tax (the so-called Solidaritätszuschlag), promising that this tax surcharge would be removed after one year. However, following a decision in March 1993 the solidarity surcharge was reintroduced in January 1995 and was still in effect in 1996. What would you expect aggregate consumption to look like, starting at the first announcement of the solidarity surcharge? Does it make any difference whether individuals believed the government’s pledge that the surcharge would be removed after one year? Following the permanent income hypothesis, we would predict that temporary changes in income do not strongly affect consumption. Hence, the first announcement should have only slightly lowered consumption given the government’s pledge to remove the tax surcharge after one year. However, if consumers did not believe the government’s announcement and instead anticipated that the tax surcharge was to persist for the years to come, they should have consumed considerably less due to the anticipated sizeable fall in permanent (disposable) income.

Exercise 2.6 Figure 2.21 shows quarterly data for nominal GDP and nominal consumption in France. (Both time series are deviations from a non-linear trend.) What is your interpretation of these time series in the light of the hypothesis that consumption only responds to permanent changes of income?

Figure 2.21 It is apparent from Figure 2.18 that deviations from trend are more pronounced for nominal GDP than for nominal consumption (GDP is ‘more volatile’ than consumption). This supports the permanent income hypothesis, which postulates that consumption does not react strongly to changes in income if these are considered to be only temporary.

Exercise 2.7 Consider an economy characterized by , with 0.75, 0, 250, 250, and , with 500 and 5,000. Note that investment depends on the interest rate. (a) Assume that, because of increasingly pessimistic expectations of investors, autonomous investment decreases from 500 to 300. The interest rate and all other exogenous variables stay constant. Calculate the resulting change in income. (b) At the same time the interest rate decreases from 0.06 to 0.05. Calculate the effect on equilibrium income. (a) From

we get (by using the parameter values given above)

0.75 i.e.

4

250 500

250 5,000

5,000

,

, and 19 © Manfred Gärtner 2009

rd


∆

4

∆ .

By plugging in the given autonomous investment decrease of 200 we get ∆

4

200

800, i.e. the resulting change in income is

800.

(b) A decline of the interest rate from 0.06 to 0.05 increases equilibrium income by 200 units: ∆

4

5,000

∆

20,000

0.01

200.

Combining the effects of the autonomous investment decrease and the decline of the interest rate on equilibrium income yields ∆ 800 200 600.

Exercise 2.8 Consider the economy of Exercise 2.7, except that consumption now depends on disposable income: . The government increases expenditure from 250 to 750 (i.e. ∆ 500). This additional expenditure is financed partly by taxes, which account for 50% of government revenue, and partly by issuing bonds. This sudden appearance of huge quantities of government bonds on the capital market drives up interest rates from 0.05 to 0.06. What is the effect of all these changes on equilibrium income? Would it have been better to finance the expenditure entirely by taxes (then ∆ ∆ 500 and ∆ 0 ? The aggregate-expenditure function reads , which can be solved for Y to get ]. By plugging in the given parameter values we can compute the overall change in equilibrium income: ∆

4

∆

∆

∆ ]

4

0.75

250

500

5,000

0.01]

1,050.

Without bond financing (and assuming that the interest rate stays constant) ∆ ∆

4

∆ ]

∆

4

0.75

500

500]

∆

500 and, therefore,

500.

Thus the multiplier under the restriction ∆ ∆ , the balanced budget multiplier, is ∆ ⁄∆ 1. Without bond financing, the effect of the increase in government spending on income would have been much smaller. Given the above parameter values, refraining from bond financing is not the most favourable option.

Exercise 2.9 Investment decisions not only depend on the interest rate but also on expectations of the future overall economic situation, represented by future GDP. (a) Through what channels might Y enter the investment decision? (b) Assume that, to form their expectations about future GDP, investors simply extrapolate today’s GDP, i.e. . Moreover, assume that these expectations enter the investment function in the following form (note that we neglect the influence of the interest rate): . (i) (ii)

How will this modification affect the multiplier? Derive the multiplier for this case, in which Y influences investment.

(a) Expectations about future booms or recessions co-determine expectations about future revenues and profits and therefore the firms' propensity to invest. (b) From Y = c × Y + G + NX + α × Y, we can derive the (investment-augmented) multiplier 1/(1 – c – α). If α + c < 1, this multiplier is higher than the multiplier that does not consider the influence of output on investment. Exercise 2.10 An open economy exhibits the following aggregate-expenditure function: AE = C+ I + G + NX where C = c(Y–T) and T = tY. I, G and NX are exogenous variables. 20 © Manfred Gärtner 2009

rd


(a) The country enters a war, which boosts government expenditure G. Show the effect on income

in the Keynesian cross. (b) You recognize that the actual increase in Y is smaller than the one you found in question (a). What factors may be responsible for this ‘too small’ multiplier? Specify the variants that go with the given aggregate-expenditure function and illustrate them in the Keynesian cross. (a) See Figure I2.10. An increase in government expenditure shifts the aggregate-expenditure curve upwards. Because of the multiplier, the effect on Y is larger than the original increase in G.

Figure I2.10 (b) We implicitly assumed that all parameters and exogenous variables remain constant. But in reality this need not be the case. It is rather likely that people increase their savings rate (thereby reducing their propensity to consume ) because of the uncertainty during wartime. Also, the government might increase the tax rate to finance its war expenditure. A higher and a lower make the aggregateexpenditure curve flatter (In Figure I2.11, the vertical axis intercept remains the same). It is furthermore possible that the autonomous expenditure components and fall during wartime, which would result in a downward-shift of the aggregate-expenditure curve. Figure I2.11 shows that with all the mentioned changes, the resulting increase in is smaller than in (a).

Figure I2.11


3 Money, interest rates and the global economy Chapter focus This chapter develops the IS-LM model (also called the global economy model) and discusses its two constituent markets, the goods market and the money market. The goods market, which was already introduced in Chapter 2, is refined by making investment depending on the interest rate. Considerable space is devoted to the money market, reflecting latest developments. The chapter also shows how the goods and the money market interact, and brings a first encounter with monetary and fiscal policy. Recent years brought an engaged discussion among academic teachers on whether we should continue to teach IS-LM with a fully spelled out money market in which the central bank exercises discretionary control over the money supply; or instead focus on the currently predominant practice of conducting monetary policy via a monetary policy rule that may feature the interest rate or the money supply as an instrument. There are good arguments in favour of both. In our judgement, the conventional approach is more difficult to teach, but also more complete and, therefore, more robust. Treating the interest rate as the monetary policy instrument simplifies the analysis enormously. The price to be paid is that extraordinary events such as bank runs, liquidity traps or even the implications of risk premiums appear more difficult to teach without a fully worked-out money market. The unfolding of the global economic crisis that follows the US subprime mortgage crisis of 2007–2008 seems to suggest that this price may indeed be high. The third edition has expanded the treatment of the money market considerably by giving interest rate targeting and monetary policy rules their proper place while still using the conventional treatment of the money market (meaning a focus on the interaction between supply and demand) as a foundation. After working through Chapter 3, students should be familiar with both approaches and know how they are related. The key insight that this chapter attempts to convey is that the qualitative properties of the IS-LM model are not dependent on whether we represented the money market by an LM curve or use a policy rule (called an LM curve in this chapter).

Additional case studies Case study C3.1 Liquidity traps and Japan’s prolonged recession Japan’s long economic slump experienced during the second half of the 1990s baffled many observers. While the real money supply increased by almost 40% between 1996 and 2000, income rose by a barely observable 3.2%. So contrary to what we have learned from this chapter’s analysis, monetary policy in this case does not really seem to have an effect on income worth talking about. Does this mean the model is of no help in trying to understand Japan’s recent slump? One might be tempted to think so. And, in fact, the simple version of the model developed above fails to account for Japan’s experience. A generalized version,

however, will provide new insights and an interesting application. In this textbook most relationships are drawn as straight lines, as in the curve. This is easy to draw, can be based on simple linear equations, and under most circumstances is a useful approximation of a (possibly) more complicated reality. That is the case in most circumstances, but in extreme situations this is sometimes not so. Recall that the curve slopes upwards because, when interest rates go down and bonds lose part of their advantage as a store of value, individuals hold larger shares of their wealth in the form of money.


rd


Since bonds lose their dominance as a store of value completely once the interest rate is at (or near) zero, the curve cannot extend into the region of negative interest rates. To avoid this, the curve must become flatter as i falls, becoming horizontal at or just above a zero interest rate. The existence of a horizontal segment of the curve does not really matter as long as the curve intersects on the upward sloping section. This is the configuration that we have in mind in this textbook. In the unlikely case that the intersects where it is flat, we have a problem. Then the economy is in a liquidity trap.

that the public was prepared to hold this additional nominal wealth in the form of money, the interest rate could not go down any further. As a consequence, the money supply increase could not stimulate investment demand and income. The economy stayed very much where it was in 1996. Table C3.1 gives key data for the Japanese economy. Table C3.1 1996

2000

Real GDP ( )

514,852

531,133

Real money supply ( / )

163,201

227,210

Price Index ( )

100.0

101.4

Interest rate ( )

0.59%

0.25%

Food for thought Japan raised government spending several times in order to get out of the recession, with little effect. What might be the cause(s) of this? In the spirit of the quantity equation, we concluded in Chapter 1 that a money supply increase raises nominal income . In Japan neither nor rose to a relevant extent. How does this fit in with the quantity equation? Figure 1 The possibility of a liquidity trap is a well-known concept and had been taught to generations of students. However, recent generations of economists considered the liquidity trap to be dead – an academic nicety that did not have any basis in the real world. That is, until US economist Paul Krugman came forward with the suggestion that Japan had fallen into a liquidity trap in the 1990s. Figure 1 sketches Japan’s experience according to this argument. Suppose Japan was in the situation indicated in 1996. Putting this point on the horizontal part of Japan’s curve appears justified by a 1996 interest rate of 0.59%, barely above zero. In the course of the next four years, the nominal money supply rose by some 40%, as did the real money supply, since prices did not change much. This shifted the curve massively to the right, into the dark blue position. Since the interest rate was already so low

Food for thought – possible answers Regarding the ineffective increase in government spending, some other demand category must have been reduced, leading to a very small multiplier. As for the increase in the money supply, we can see by looking at the quantity equation that if increased without affecting either or , then the velocity of money circulation must have fallen. This may be the case because at near zero interest rates, speculative and precautionary money holdings increased.

Exercises Exercise 3.1 Which of the following variables are flow variables, and which are stock variables? (a) A nation’s GDP. (b) A firm’s cars and machines. (c) The gold reserves in the vaults of your country’s central bank. (d) Ferrari Testarossa sales between 1987 and 2008. (e) Aggregate investment. (f) British lager consumption per capita in 2007. (g) The number of Rioja bottles in your cellar. 23 © Manfred Gärtner 2009

rd


(h) The profits of your country’s central bank in 2009. (i) The number of all Škoda models registered in Warsaw. Remember: A flow variable is measured over a period of time, while a stock variable is measured at a point in time. (a) A nation’s GDP – flow.

(b) A firm’s cars and machines – stock. (c) The gold reserves in the vaults of your country’s central bank – stock. (d) Ferrari Testarossa sales between 1987 and 2008 – flow. (e) Aggregate investment – flow. (f) British lager consumption per capita in 2007 – flow. (g) The number of Rioja bottles in your cellar – stock. (h) The profits of your country’s central bank in 2009 – flow. (i) The number of all Škoda models registered in Warsaw – stock. Exercise 3.2 Recall the quantity equation from Chapter 1: . In this chapter, the velocity of money circulation was assumed to be constant. Is this assumption reasonable in the light of the model of money demand? How would you expect to change with an increase in the interest rate? Assume that the interest rate remains at its new higher level, with and unchanged. How does this affect the price level? A higher interest rate raises the opportunity costs of holding money and thereby reduces the demand for money. It should thus be expected that an increase in the interest rate leads to an increase in the velocity of money. Given that people still spend the same amount, i.e. given that consumption remains the same, the average monetary unit will have to circulate more often once people hold less money. In the case of Germany, this conjecture is supported by empirical evidence. In the short run, increases of the short-term interest rate tended to coincide with an increase of the velocity of M1. Hence, given that and remain constant, an increase in the interest rate will increase the price level.

Exercise 3.3 (a) In recent years, a number of institutional and technical innovations, such as cash machines, have made it less and less expensive to obtain cash. Explain the consequences of this development by using the model of money demand in the text. If this trend continues, will average cash holdings decrease or increase? (b) How do decreasing transaction costs affect the LM curve? (Hint: start with the money demand equation and show how transaction costs determine the slope of the money demand function. Look at two different interest rates, including 0. Then work your way through to Figure 3.6 and decide whether – with lower transaction costs – a given increase in money supply leads to a larger or to a smaller shift of the curve.)

(a) The innovations reduce the transaction costs for obtaining money, i.e. for converting other types of wealth such as interest bearing assets into cash. Given the same opportunity costs of holding money (the level of the interest rate), this will make it worthwhile to hold less money and make more trips to the bank. Therefore, average cash holdings will decrease.

(b) Decreasing transaction costs make the money demand curve rotate counter-clockwise around its horizontal-axis intercept, i.e. the demand curve becomes flatter (see the left-hand side of Figure I3.1 for a graphical illustration of this). Lower transaction costs imply that less money is demanded at any positive interest rate level (c.f. solution to Exercise 3.3.a). They furthermore imply that money demand becomes more sensitive to changes in the interest rate, since for a given increase in the interest rate the resulting decrease in money demand will be more pronounced. (This could be proven by noting that for any positive interest rate, money demand is now lower thanks to decreased transaction costs. At an interest rate of zero, however, the money demand should remain constant since holding money here involves no 24 © Manfred Gärtner 2009

rd


opportunity costs. Analytically it follows that sinking transaction costs correspond to a higher in the money demand function. At an interest rate of zero, money demand, i.e. , is independent of transaction costs. Furthermore, an increase of corresponds to a rotation of the money demand curve ⁄ ( 1/ ) around its horizontal-axis intercept.) It follows that the curve is flatter at lower transaction costs as well. To see why, consider that a given increase in income, ∆ , moves the money demand curve by ∆ to the right (i.e. ∆ ⁄∆ ); this change is the same under both transaction cost regimes since is unaffected by transaction costs. While ∆ ⁄∆ remains unaffected by changing transaction costs, ∆ ⁄∆ / decreases when h increases (i.e. when transaction costs decrease). This means that the change of the interest rate needed to bring the money market back to equilibrium after an increase in income becomes smaller once transaction costs fall. The curve must thus become flatter. A quick look at the formula of the curve ( / / ) helps understand this. An increase in makes the curve flatter.

Figure I3.1 It is relatively easy to see that with lower transaction costs, a given increase in the money supply leads to a smaller shift of the curve. In the left-hand panel, we see that an increase in the money supply leads to a smaller decrease in the interest rate when transaction costs are low (analytically ∆ ⁄∆ ∆ ⁄∆ 1/ becomes smaller in absolute terms when h increases). Since the change in the interest rate ∆ ⁄∆ 1/ corresponds to the ‘vertical shift’ of the curve in the right hand panel, this shift will also be smaller. (Also note that the ‘horizontal shift’ of the curve, ∆ ⁄∆ 1/ , remains unaffected by transaction costs.)

Exercise 3.4 Consider Table 3.1, which shows end-of-month exchange rates for the British pound (GBP), the US dollar (USD) and the Chinese yuan (CNY) versus the euro (EUR) during the first half of 2008. Which month recorded the largest appreciation of the euro versus the dollar? How many yuan did one dollar cost in Mai? In which months did the yuan appreciate against the pound? Table 3.1 GBP/EUR USD/EUR CNY/EUR

January 0.7477 1.4870 10.679

February 0.7652 1.5121 10.786

March 0.7958 1.5812 11.078

April 0.7901 1.5540 10.858

May 0.7860 1.5508 10.765

June 0.7922 1.5764 10.805

The second row shows the price of euro expressed in US dollars. If the euro appreciates, the price of euro increases. The month with the (absolutely and relatively) largest appreciation was thus March. To calculate the price of one yuan in US dollars in May 2008, we first note that for one euro, one had to pay 10.765 yuan. For this one euro, one then received 1.5508 dollar. So one dollar cost 10.765/1.5508 6.9416 yuan. Formally: . .

6.9416.

To determine in which months the yuan appreciated against the pound, we first calculate the exchange rate (direct notation) CNY/GBP: 25 © Manfred Gärtner 2009

rd


January:

10.679⁄0.7477

February: 10.786⁄0.7652

14.096

March: 11.078⁄0.7958 April: 10.858⁄0.7901

14.282

13.921 13.743

May: 10.765⁄0.7860

13.696

June: 10.805⁄0.7922

13.639

Since the exchange rate in direct notation expresses how many yuan one has to pay for £1, an appreciation of the yuan is associated with a falling exchange rate. The yuan thus appreciated against the British pound in February, March, April, May, and June (because we are missing data for the previous month, for January we cannot say whether the exchange rate fell or rose).

Exercise 3.5 In Table 3.2, prices for an Italian mid-range car and a man’s haircut for both St Gallen (Switzerland) and Stuttgart (Germany) are listed, as well as the Swiss franc/euro exchange rate. Focus on one of the two goods to decide whether the Swiss franc is over- or undervalued. What might explain the apparent difference? Table 3.2 Average exchange rate in 2008: €1 1.6 Italian Car Haircut

Price in Stuttgart (Germany) €12,500 €20

Price in St. Gallen (Switzerland) 23,500 48

Calculated from the car prices, the purchasing power parity (the nominal exchange rate which sets the real / ) equal to 1) is 1.84. Hence, judging from the car prices, the Swiss franc is exchange rate ( slightly overvalued with respect to the euro at an exchange rate of 1.6. Calculated from the prices for a haircut, the purchasing power parity would be 2.4. Hence, judging from the haircut prices, the Swiss franc is heavily overvalued. The much larger price gap between the two haircuts (as compared to the car price difference) can be explained by the fact that cars are easily traded across national boundaries, while it is much harder to sell a haircut from Germany to Switzerland.

Exercise 3.6 You are a Swiss girl visiting Barcelona. On a shopping tour you buy a black winter coat at Zara for €140. You saw exactly the same coat at a Zara store located in Zurich, where it cost 250 Swiss francs. When you exchanged your Swiss francs for euros, you had to pay 1.5 Swiss francs for €1. Assuming the winter coat is a representative basket of goods, calculate the real exchange rate and interpret your result. Plugging the given values into the formula for the real exchange rate we get: .

0.84.

The real exchange rate of 0.84 means that the Swiss girl pays only 84% of what the coat costs in Switzerland when she buys the coat in Spain. Since the Zara coat in Barcelona is cheaper than the one in Zurich, the Swiss franc is overvalued ( 1 .

Exercise 3.7 The Economist regularly publishes its Big Mac Index. Data on the cost of a Big Mac is gathered in several countries and these prices are then translated into the US dollar price equivalent to produce the index. What are the advantages and disadvantages of using such an index for the purpose of making comparisons? Big Macs are the same across countries, hence homogeneity of the good is guaranteed and a comparison of prices makes sense. However, it is quite implausible to imagine a person from Bern (Switzerland), whose currency is overvalued (by Big Mac standards) travelling to the United States in order to enjoy a meal at McDonald’s, i.e. the 26 © Manfred Gärtner 2009

rd


mechanisms that usually establish purchasing power parity are not really appealing in this example. Hence, the statement that the Swiss franc is burger-economically overvalued does not imply that such an overvaluation will be removed over time by the forces establishing purchasing power parity. Another aspect is that a Big Mac does not constitute a representative basket of goods, i.e. it may be possible that a Big Mac is relatively expensive in a country, which leads to a burger-economically overvalued currency, while when looking at a representative basket of goods and services, the currency may not be overvalued. Exercise 3.8 (a) What would happen to the slope of the curve if trade was completely abolished? (b) What happens to the slope of the curve if investment does not depend on the interest rate? (a) The

curve would become flatter. This can easily be seen from Equation (3.9) describing the

The slope of the

curve:

curve therefore is

. With regard to the slope of the curve, abolishing trade corresponds to setting 0. With being a positive parameter, this reduces the slope of the curve. This result is intuitively plausible: The curve shows, by definition, all those combinations of income and the interest rate for which aggregate expenditure equals income (or output). It has a negative slope in income-interest space because c.p., higher income must be accompanied by a lower interest rate which stimulates investment demand. Now when there is international trade, part of any increase in domestic income leaks away from the circular flow system in the form of import demand. With trade taking place, the increase in investment must thus be larger, i.e. the interest rate has to fall farther as long as there is trade, because the leakage constituted by imports has to be compensated with investment demand. (b) If investment does not depend on the interest rate, the curve is vertical in income-interest space and the level of income for which aggregate expenditure equals income (or output) is independent of the interest rate level. In other words, for a given set of parameter values, there is only one income level which equilibrates the goods market. Analytically, if investment is independent of the interest rate, 0 then the slope of the curve approaches infinity.

Exercise 3.9 How do the following changes of exogenous variables shift the and the curves? (Note: apply the thought experiment suggested in Box 3.3. Make sure you understand the economic reasoning.) (a) An increase in money supply. (b) A decrease in government expenditure. (c) A decrease in foreign income. (d) An increase in the foreign price level. (a) An increase in the money supply shifts the curve to the right. Remember that the curve identifies combinations of income and the interest rate for which the demand for money equals the money supply. A higher money supply must be met by a higher money demand. This means with regard to the curve that at any given interest rate, income must be higher, or, alternatively, at any given income level, the interest rate must be lower. (b) A decrease in government expenditure shifts the curve downward, meaning that at any level of income, the interest rate is now lower. In this way the reduction in aggregate demand brought about by lower government expenditure is compensated by increased investment demand. That a decrease in government expenditure shifts downwards can analytically be seen from equation (3.9), which shows that is a shift parameter with a positive effect on . (c) A decrease in foreign income lowers export demand and therefore shifts the curve downward. As in 3.9.b, increased investment has to compensate for the reduction in aggregate demand. 27 © Manfred Gärtner 2009

rd


(d) An increase in the foreign price level c.p. increases the real exchange rate / , i.e. leads to a depreciation of the domestic currency. The associated increase in export demand shifts the curve upward, since decreased investment has to compensate for the increase in aggregate demand.

Exercise 3.10 Suppose that the demand-for-money function for three different levels of income looks as shown in Figure 3.20.

Figure 3.20 (a) What does the curve look like? It may help to identify points A-D in your new diagram. (b) What happens to and i if income initially is 80, the interest rate is and the real money supply expands? (a) See Figure I3.2

Figure I3.2 (b) This will shift the curve to the right. Despite of this shift, the point of intersection between the and the curve will not change, however, for we are in a so-called liquidity trap, i.e. the and curves intersect where the curve is horizontal. In a liquidity trap, an expansion of the money supply has no effect on and .

Exercise 3.11 Suppose the central bank and the government cannot agree on the direction of economic policy, so that the government raises spending while the central bank contracts the money supply. Trace in a diagram what happens to income and the interest rate. As Figure I3.3 shows, the interest rate definitely increases. The change in output is ambiguous, i.e. it cannot be determined from the information given. 28 © Manfred Gärtner 2009

rd


Figure I3.3 Exercise 3.12 Assume the central bank sets an interest rate target range between 2 and 3%, meaning it allows the interest rate to be determined by market forces within this range, but does not permit it to move above 3 or below 2%. (a) How does income fluctuate when the goods market is subject to occasional shocks? (b) How does income fluctuate when there are stochastic shocks to the demand for money? Draw diagrams similar to those used in Box 3.4. Compare your results with those obtained when the central bank targets the money supply and when it targets the interest rate. The answers to both (a) and (b) depend on the position of the initial equilibrium in income-interest space (see Figure I3.4). We subsequently presume that the economy is initially in an equilibrium such as A in Figure I3.4. If the economy initially was in A' or A'', its response to a shock would be similar to the response of an economy with a fixed interest rate.

(a) See Figure I3.4. If shocks are typically small (within dashed lines in Figure I3.4), the economy behaves as if the money supply were fixed. Larger shocks (up to dotted lines) must be accommodated by raising or lowering , in order to keep from moving out of bounds. This increases the income response to large shocks (compared to the income response when the money supply is fixed).

Figure I3.4


rd


(b) See Figure I3.5. For small shocks to money demand (within dashed lines in Figure I3.5), the interest rate remains within bounds and does not respond. Within the dashed lines, income is thus affected, that is, it will fluctuate after a shock to the demand for money. If shocks move the curve outside the dashed lines, responds and moves back towards the dashed position. So an interest rate target range limits the fluctuation of to the range in Figure I3.5.

Figure I3.5

Exercise 3.13 Suppose country A's central bank follows the monetary policy rule while country B's monetary policy is determined by . (a) Please compute the equations for both countries' curves. (b) Compare each of these two curves with a conventional curve. Discuss any observed differences. (c) Which monetary policy rule would you recommend for a country that is subject to occasional demand shocks in the money market and wants to stabilize income? (d) Consider another country that is subject to occasional demand shocks in the goods market and wants to adopt country B's policy rule. Please identify parameter values for b that would make this policy rule superior to what happens under a conventional curve. (a) A: B: Country B's policy rule is already an

curve:

.

(b) Country A's curve converges to the conventional curve if 0. For 0 it is steeper. This makes fiscal policy and monetary policy (changes of ) less effective. B's curve is steeper or flatter than depending on specific parameter values. Fiscal policy may thus be more or less effective. (c) B's rule is better, since parameters of money demand do not enter its A's curve. (d) Demand shocks in the goods market shift when

. Given shifts in

is steep. B's rule is preferable to A's when its

curve, while they do enter

translate into small income shocks

curve is steeper, i.e. if

.

Exercise 3.14 The text does not distinguish between the interest rate that banks pay on savings accounts and the interest rate they charge firms for loans (which would make it difficult for banks to earn any profits). More realistically, suppose that while banks pay an interest rate on savings accounts, they charge firms an interest rate that is 2% points higher for extended loans. (a) How does that affect the curve? Please compute the equation for the global-economy curve. (b) Draw a diagram with and Y on the axes, featuring your modified model. Does monetary and fiscal policy work in ways similar to or different from the discussion in the text? (c) Suppose reduced competition in the banking sector permits banks to increase the mark-up on interest rates for loans to 3% points over . How does this affect income? 30 © Manfred Gärtner 2009

rd


(a) If firms have to pay a mark-up of two percentage points on the interest rate , the investment function reads 2 2 . For the global-economy IS curve, this means: 2 The mark-up shifts the IS curve down (the vertical axis intercept shifts down by 2). The slope of the curve remains unaffected. (b) Since the mark-up only shifts down (see (a)) and the general mechanisms discussed in the text do not change and fiscal and monetary policy works the same. However, a different equilibrium (with a lower interest rate and lower income ) obtains. (c) Income would fall, i.e. would shift down even further, by 3 instead of 2. This yields the insight that competition among banks, which lowers the mark-up on the interest rate charged for loans, can raise an economy’s equilibrium level of income.


4 Exchange rates and the balance of payments Chapter focus After dealing with the global or closed economy in Chapter 3, the text wastes no time, before proceeding to the more realistic and relevant setting of an open economy. This is done in two steps. Chapter 4 introduces a new building block: the balance of payments, as a record of all cross-border transactions, and its mirror image, the foreign exchange market. It then combines the foreign exchange market with the familiar building blocks of the IS-LM model to assemble the Mundell–Fleming model, also called the IS-LM-FE model in this text in order to emphasize its roots. The detailed analysis of the Mundell–Fleming model is postponed until Chapter 5. Sticking with traditional balance of payments terminology, three groups of participants in the foreign exchange market are identified as follows: (a) people who trade in goods and services (recorded in the current account); (b) financial investors who move wealth across borders (recorded in the capital account); (c) central banks (recorded in the official reserves account). A central argument that simplifies the analysis and affects much of the rest of the text is that the first and the third group's activities only account for a very small share of world-wide transactions in the foreign exchange markets. Thus the second group dominates this market, which makes open interest parity the equilibrium condition for the foreign exchange market and renders the FE curve, the foreign exchange market equilibrium line, horizontal in i/Y space. Adding a third market to the model adds another endogenous variable to the model. Under flexible exchange rates this is the nominal exchange rate. Fixed exchange rates make the money supply endogenous.

Exercises Exercise 4.1 How open is your country’s economy at present (a) as measured by the export ratio? (b) as measured by the import ratio? Use data from Eurostat, the IMF, the OECD or national sources to address this question. Table I4.1 contains export and import ratios for selected countries. Table I4.1

Export and import ratios in 2006 in %

EX IM

Austria 57.7 52.0

Belgium 87.7 85.1

Denmark 51.9 49.0

France 26.9 28.3

Germany 45.1 39.6

EX IM

Norway 46.4 28.6

Portugal 31.1 38.9

Spain 26.1 32.3

Sweden 51.3 43.2

Switzerland 47.9 41.1

Italy 27.8 28.7 UK 28.7 32.9

Netherlands 74.2 66.5 USA 10.5 16.3

source: World Bank, WDI online 32 © Manfred Gärtner 2009

rd


Exercise 4.2 Suppose an artificial country called Spain recorded the cross-border transactions listed below: 500 Seat Toledos sold to Ireland 10,000 Duffy CDs sold in Spain Sergio Garcia flies Air France to New York 10 times, using the A380 from Paris Franz Beckenbauer spends several golf holidays in Marbella Ruud van Nistelrooy sends cheques home to mum in Holland Julio Iglesias earns dividend on Microsoft stocks Spain’s government contributes to EU budget Ford acquires office building in Barcelona Real Madrid invests in Eurosport TV stocks Government pays interest on Spanish government bonds held abroad

€7,500,000 €150,000 €70,000 €40,000 €200,000 €1,900,000 €1,000,000 €10,000,000 €5,000,000 €2,800,000

Assemble Spain’s balance of payments. Assume there are no statistical discrepancies. What is the current account balance? What are net exports? What is the capital account balance? Is the balance of payments in surplus or deficit? Table I4.2 provides an overview of Spain's balance of payments. Table I4.2 Account Account balance CA 5,220,000

CP

5,000,000

OR

–10,220,000

Accounting record

Credit

Export of goods (Seat Toledo) Import of goods (CDs) Import of services (A380) Export of services (Marbella) Transfer payments to abroad (van Nistelrooy, EU) (Transfer payments from abroad) Income received on investment (Microsoft) Income paid on investment (Spanish gov't bonds) Investment from abroad (Ford) Investment abroad (Real Madrid) 0, i.e. the balance of payments must always balance

7,500,000

Debit

150,000 70,000 40,000 1,200,000 (0) 1,900,000 2,800,000 10,000,000 5,000,000 10,220,000

Net exports are: 7,500,000 150,000 70,000 40,000 7,320,000. Remember that the current account balance only matches net exports if there are no transfer payments or income on investment. The balance of payments is neither in deficit nor in surplus; it must always balance if there are no statistical discrepancies. Exercise 4.3 Consider a small open economy that faces the macroeconomic situation as shown in Figure 4.13.

Figure 4.13 33 © Manfred Gärtner 2009

rd


Describe the mechanisms that bring about a macroeconomic equilibrium in which all three market equilibrium lines intersect (a) under flexible exchange rates. (b) under fixed exchange rates. The situation in Figure 4.8 shows a balance of payments surplus: Since the domestic interest rate is higher than the interest rate abroad, domestic capital is in high demand, i.e. there is a capital account surplus. (a) With flexible exchange rates, the demand surplus for the domestic currency will cause the domestic currency to appreciate. The appreciation leads to a decline in net exports and, thereby, to a reduction in aggregate demand. The curve shifts left (or down) until the , , and curves all intersect in one point, i.e. until an equilibrium in all three markets is reached (see Figure I4.1). In the process, falls.

Figure I4.1

(b) With fixed exchange rates, the domestic central bank has to increase the money supply to maintain parity when domestic capital is in high demand. The expansion of the money supply shifts the curve to the right (or down) until the , , and curves all intersect in one point, i.e. until an equilibrium in all three markets is reached (see Figure I4.2). In the process, increases.

Figure I4.2 Exercise 4.4 Suppose investment is independent of the interest rate and the curve is horizontal. Sketch the macroeconomic equilibrium under fixed and flexible exchange rates and describe the mechanisms that help achieve it. If investment is independent of the interest rate, the shows a possible macroeconomic equilibrium in the -

curve is vertical in income-interest space. Figure I4.3 model with a vertical and a horizontal curve.


rd


Figure I4.3 The general adjustment mechanisms for fixed and flexible exchange rates as discussed in Question 4.3 remain unchanged: Adjustments to new equilibrium values still take place through changes in the exchange rate and in the money supply, respectively. Exercise 4.5 Consider an economy that is characterized by constant prices, flexible exchange rates and perfect capital mobility, and where the and curves can be written as follows: 0.25 0.1

10 0.1

0.4

40

Initially, the exogenous variables take the following values: 500 5 5,000 160 200 (a) Draw the equilibrium curves for the money market, the foreign exchange market and the goods market into an - diagram. (b) Compute the equilibrium levels of the interest rate, income and the foreign exchange rate.

(a)

curve: 0.025 50, curve: 86 0.04 4 , 5. curve: The graphical solution is shown in Figure I4.4.

Figure I4.4

(b) With perfect capital mobility, the equilibrium interest rate is pinned down by the world interest rate, i.e. 5. By substituting 500

0.25

50

550⁄0.25

5 into the

curve, we get

2,200. 35 © Manfred Gärtner 2009

rd


5 and

Substitution of 50

860

2,200 into the

2,200⁄40

0.4

curve (solved for ) yields

1.75.

The equilibrium values for , , and

5,

are thus

2,200,

1.75.

Exercise 4.6 Consider an economy with fixed exchange rates and perfect capital mobility. It is characterized as follows: 0.25 0.1

( ) ( ) ( )

5 0.2

0.2

50 )

Use the following initial values of the exogenous variables: 100 100 500 5 (a)

Suppose the exchange rate is fixed at 1, what is the resulting equilibrium level of income and the resulting money supply? (b) To what level does the world interest rate have to move to obtain an income level of 1,600? What is the corresponding money supply? (a) With the exchange rate fixed, money supply is endogenous. Equilibrium income is obtained by plugging the values for the world interest rate and (as well as and ) into the curve: 5

0.1 100

100

0.2

500

0.2

50

1

1,500.

The money supply which allows for a fixed exchange rate of 1 is derived through the 0.25

1,500

5

5

350.

(b) The interest rate can be calculated by plugging the appropriate values into the 0.1 100

100

100

curve:

0.2

1600

50

curve:

3.

The equation shows that to raise income to a level of 1,600 while keeping the exchange rate fixed, the world interest rate would have to decrease from 5 to 3%. The corresponding money supply is once again obtained by plugging the numeric values obtained from into the curve: 0.25

1,600

5

3

385.

Exercise 4.7 Usually, we assume the simplified curve represented by equation . We now introduce taxes on interest earnings. Analyze Switzerland (a small country with bank secrecy law) and the rest of the world using the graphical apparatus of the Mundell-Fleming model. Suppose that foreigners pay taxes on their interest earnings at home at the rate , and the Swiss pay taxes at the rate . Distinguish between scenarios (a) and (b): (a) The governments of both countries are perfectly informed about interest earnings of their inhabitants. Investors have to pay taxes in their country of residence independent of where their returns are generated. What is the equilibrium condition on the international capital market ( curve)? (b) Suppose that foreigners do not report their returns realized in Switzerland to their revenue authorities. This is possible because of the bank secrecy law in Switzerland. They prefer to pay the withholding tax, which is set to for simplicity. What is the equilibrium condition on the capital market? Suppose the curve is characterized by the situation described in (b). (c) What happens to the Swiss economy if the bank secrecy law is abolished? Does your answer depend on whether the exchange rate is flexible or fixed?


rd


(a) Since foreigners pay the same tax rate

on their home and Swiss earnings, the equilibrium

condition on the capital market reads: 1

1

(b) Foreigners now pay the withholding tax rate

on their returns generated in Switzerland and the tax on returns generated in the rest of the world. The curve then reads:

rate 1 Since

1 ,

1 and, thus,

. The Swiss interest rate is lower in equilibrium

because foreigners can take advantage of the lower tax rate in Switzerland.

(c) Initially, that is in the situation described in (b),

. If the bank secrecy law is abolished, must rise to , which makes the curve shift up (see Figure I4.5). The reason for this is that with is no longer a competitive return on capital, meaning that at any the bank secrecy law abolished, Swiss interest rate of , there is an excess supply of Swiss francs and an excess demand for foreign currency. Under flexible exchange rates, the surplus in supply will cause a depreciation of the Swiss franc. This will shift the curve to the right (or up) until it passes through point A, as shown in Figure I4.5. Under flexible exchange rates, income will increase after the abolition of the bank secrecy law. Under fixed exchange rates, the Swiss National Bank has to decrease the money supply (i.e. buy Swiss francs) once the bank secrecy law is abolished. Since there is excess supply of Swiss francs, it has to do so in order to maintain parity. The decrease in the money supply shifts the curve to the left (or up) until it passes through point B (see Figure I4.5). When the exchange rate is fixed, income thus decreases once the bank secrecy law is abolished.

Figure I4.5


5 Booms and recessions (II): the national economy Chapter focus This chapter starts with discussions of fiscal and monetary policy in the Mundell-Fleming model. The discussions reveal that the world of an open economy is more complex. Mainly because whether fiscal or monetary policy works or how outside shocks affect the domestic economy, depends on the exchange rate system. Further complications arise when that standard assumption of perfect capital mobility is replaced by that of inhibited or completely absent capital mobility. Other, less standard themes being emphasized are: 1. Comparative statics versus adjustment dynamics. It is important to reiterate that and - are equilibrium models and that the experiments conducted are exercises in comparative statics that say little about adjustment dynamics. Section 5.4 is a brief intuitive excursion into adjustment dynamics. 2. Endogenous adjustment dynamics. Section 5.5 provides a more refined discussion of adjustment dynamics in which endogenous depreciation expectations play a pivotal role. The result is an adjustment process with exchange rate overshooting in the spirit of the Dornbusch model. 3. Flexible prices. This is the first time aggregate demand is confronted with a limited output supply. A simple, intuitive discussion attempts to show that any discrepancy between aggregate demand and supply that occurs this way can only be resolved when prices may respond. 4. The dependence of today's exchange rate on the future. Section 5.7 uses a version of the Mundell-Fleming model with flexible prices to show that the exchange rate today is affected by what we expect to happen in the future. This is an important insight students should be reminded of time and again during the remainder of the text.

Exercises Exercise 5.1 Suppose the government raises the income tax rate. What are the effects on income, the interest rate and the exchange rate (a) with a flexible exchange rate? (b) with a fixed exchange rate? (Derive your results graphically, assuming perfect international capital mobility). An increase of the income tax rate reduces disposable income and, thereby, consumption demand. This moves the curve left. Within the Mundell-Fleming model, this means that the domestic interest rate is temporarily pushed below , which decreases the return on investment for domestic assets and thus leads investors to sell their assets in domestic currency. (a) With a flexible exchange rate, the lowered domestic interest rate leads to a depreciation of the domestic currency. The depreciation stimulates export demand and moves the curve back to its initial position. This is shown in Figure I5.1. While income and the interest rates remain unchanged in the new equilibrium, the currency has depreciated.


rd


Figure I5.1 (b) Under fixed exchange rates the exchange rate cannot depreciate to balance supply and demand in the foreign exchange market. Therefore, the central bank has to purchase domestic currency, thereby reducing the money supply . This shifts the curve to the left. In the new equilibrium, income has fallen, while the interest rate and the real exchange rate remain unchanged (see Figure I5.2).

Figure I5.2

Exercise 5.2 The central bank reduces the money supply. What are the consequences for income, the interest rate and the exchange rate (a) with a flexible exchange rate? (b) with a fixed exchange rate? (Derive your results graphically, assuming perfect international capital mobility). A reduction of the money supply shifts the curve to the left. This temporarily pushes the domestic interest rate above , which increases the return on investment for domestic assets and thus stimulates the demand for domestic currently. (a) With a flexible exchange rate, the temporarily higher interest rate leads to an appreciation. The appreciation reduces export demand and thus shifts the curve to the left. In the new equilibrium, the exchange rate and income have fallen, while the interest rate remains unchanged (see Figure I5.3).


rd


Figure I5.3 (b) With a fixed exchange rate, the temporarily higher domestic interest rate increases the demand for domestic currency. Since under fixed exchange rates the exchange rate cannot appreciate to balance supply and demand in the foreign exchange market, the central bank has to sell domestic currency, thereby expanding the money supply. This expansion goes on until the original reduction of the money supply is completely undone (see Figure I5.4). In the new equilibrium, all variables are exactly the same as in the old equilibrium.

Figure I5.4

Exercise 5.3 Analyse the consequences of an increase of the world interest rate. Assume fixed exchange rates and perfect international capital mobility. What might be the reason for the increasing foreign interest rate? What does the result tell you about problems of international policy coordination? Under perfect international capital mobility, an increase in the foreign interest rate shifts the curve up. This makes the domestic interest rate fall temporarily below the world interest rate and domestic assets lose their international competitiveness. Investors wish to sell their domestic assets and thereby increase the supply of domestic currency. Under fixed exchange rates, the central bank has to purchase domestic currency in order to absorb the increased supply in the foreign exchange market, thereby reducing the money supply. This shifts the curve left. In the new equilibrium, the domestic interest rate equals the new world interest rate and output is below its former level (see Figure I5.5).


rd


Figure I5.5 The increase in the foreign interest rate might be caused by expansionary fiscal (as depicted in Figure I5.5) or contractionary monetary policy in a large foreign country. Since there are externalities to fiscal and monetary policy actions (especially if the country where such policies are conducted is large), policy-making may give rise to political disputes between countries. Expansionary fiscal policy in a large country may, e.g. cause serious recessions in other (smaller) countries.

Exercise 5.4 How does a devaluation of the domestic currency in a system with fixed exchange rates and perfect capital mobility affect the domestic interest rate and output? In the Mundell–Fleming model, a devaluation of the domestic currency directly affects the position of the curve. On the one hand, it increases foreign demand for domestic products which have become cheaper to foreigners thanks to the devaluation. On the other hand, it decreases domestic demand for foreign products which have become more expensive to domestic consumers. The increase in exports and the decrease in imports make net expsorts increase. This shifts the curve to the right. This, in turn, leads to a temporary increase of the domestic interest rate. It rises above the level of the world interest rate. Under fixed exchange rates, the central bank must in answer to this expand the money supply, which shifts the curve to the right. In the new equilibrium, income has increased, as has the exchange rate, while the interest rate is back at its old equilibrium level (see Figure I5.6).

Figure I5.6 Exercise 5.5 Your country is exposed to a positive demand shock (say, foreign demand for domestic goods increases) and you are in charge of monetary and fiscal policy. Formally, your country maintains a regime of flexible exchange rates with all trading partners, but for some reason you wish to keep the exchange rate where it was before the shock. What can you do? Use the graphical apparatus of the Mundell–Fleming model to explain your answer.


rd


On impact, the positive demand shock shifts the curve to the right. This temporarily increases the domestic interest rate. Without policy intervention, the domestic currency would have to appreciate in order to balance demand and supply in the foreign exchange market, and the curve would shift back to its old position. If the exchange rate has to be kept at its initial level, expansionary monetary policy could be used to balance demand and supply in the foreign exchange market instead. Expansionary monetary policy would shift the curve to the right, leading to a higher level of output at an unchanged exchange rate. See Figure I5.7.

Figure I5.7

Exercise 5.6 Suppose that investors suddenly lose confidence in the domestic currency and expect it to depreciate by 5% every period from now on. Trace the consequences in the Mundell–Fleming model. What does the result tell you about ‘self-fulfilling prophecies’? Will the induced changes in output and the (flexible) exchange rate last (Hint: work with the general equilibrium condition .)? Remember that the original equation characterizing the

curve (with perfect capital mobility) is:

. If, as described, the domestic currency is expected to depreciate, the second term on the right-hand side (which is usually assumed to be zero) is positive. For the foreign exchange market to be in equilibrium, the domestic interest rate has to rise above the world level in order to compensate investors for the expected depreciation. In the Mundell–Fleming diagram, this means that the curve shifts upward (see Figure I5.8). At the new (and higher) domestic interest rate, the goods and the money market are no longer simultaneously in equilibrium. To reestablish an equilibrium in all three markets, the domestic currency has to actually depreciate, which shifts the curve to the right. A new (temporary) equilibrium is reached in point B.

Figure I5.8 In point B, the curves do not shift anymore and the exchange rate remains constant. This new equilibrium cannot persist, however, unless agents expect a further depreciation of the domestic currency. Given that the exchange rate remains constant in the new equilibrium, it seems that this is not a very realistic assumption: Instead, agents 42 © Manfred Gärtner 2009

rd


will probably adjust their expectations after some time and expect no further depreciation. If this is the case, the curve will shift back to its initial level and the exchange rate will appreciate back to its initial level as well (see Figure I5.8). If expectations are thus not completely exogenous, it seems that the Mundell–Fleming model does allow for self-fulfilling prophecies, but they will produce only temporary results. Exercise 5.7 Consider Figure 5.19, which depicts returns to US and German government bonds since 1960. What do these time series tell us about investors' expectations concerning the Deutschmark/dollar exchange rate?

Figure 5.19 Interest rates in Germany and the US From 1960 until the mid-1970s, the German interest rate was higher than the American interest rate. However, since under the Bretton Woods system the exchange rates were fixed until 1973, it may be incorrect to ascribe this difference in interest rates to expectations about exchange rate depreciations or appreciations. It is in this context worthwhile to note that (even under perfect capital mobility) interest rate differentials may persist due to factors other than exchange rate expectations, e.g. risk premia. With the abolition of the Bretton Woods system, the US interest rate started to rise to historical heights and from about 1976 to 1990 was markedly above the German level. Since the original curve reads , the higher US interest rate indicates that agents expected a depreciation of the dollar vis-à-vis the Deutschmark throughout this period. Exercise 5.8 Consider the macroeconomic situation shown in Figure 5.20 where the

curve is vertical:

Figure 5.20 (a) Discuss the conditions under which the curve might be vertical. (b) Describe the mechanisms that bring about a macroeconomic equilibrium where all three lines intersect under flexible exchange rates, and under fixed exchange rates. 43 © Manfred Gärtner 2009

rd


(c) Analyse the effect of expansionary monetary and fiscal policy in a system of flexible exchange rates with perfect capital immobility. (a) The curve by definition depicts all combinations of and for which the balance of payments (BOP) is in equilibrium. The curve is vertical if and only if the nominal interest rate has no influence whatsoever on the BOP. Since current account and official reserve account transactions never react to changes in the interest rate anyway, this is equivalent to saying that has no influence whatsoever on the capital account. This holds when there is perfect international capital immobility, i.e. when capital flows across borders are either prohibited or when agents voluntarily (and completely) refrain from investing in a country due to risk considerations. (b) Figure 5.15 shows a BOP deficit (i.e. a current account deficit, as with completely immobile capital, the capital account is always zero). In other words, at the point of intersection of and , imports are too high for the BOP to be in equilibrium and we experience an excess demand for foreign currency. With flexible exchange rates, the domestic currency will depreciate. This increases net exports and shifts the curve to the right. As exports increase in response to the depreciation of the domestic currency, the curve also shifts to the right. Looking at the two equations, we can show that the shift of the curve will be bigger than the shift of the curve. The curve reads: : Solving for Y gives

and thus the effect of a change of the exchange rate on income for the goods market equilibrium is:

If the curve is vertical, the BOP is only in equilibrium if the current account balances (see also Section 4.3 in the book): :

0

Hence, the effect of an exchange rate change on income for the BOP equilibrium is:

Since

,

the curve shifts by more than the curve in response to an exchange rate change. This guarantees that with flexible exchange rates, the economy will reach a new equilibrium, which is stable. The new equilibrium is shown in Figure I5.9.

Figure I5.9 With fixed exchange rates, the central bank has to reduce the domestic money supply to keep the exchange rate unchanged. This shifts the curve upward until it reaches the intersection of the and curves. The graphical solution is shown in Figure I5.10. 44 © Manfred Gärtner 2009

rd


Figure I5.10 (c) Expansionary monetary policy shifts the curve to the right in the Mundell–Fleming model (see Figure I5.11). In point B, the BOP is not in equilibrium, since domestic import demand is too high. The current account deficit in B leads to an excess demand for foreign currency. To establish BOP equilibrium, the domestic currency has to depreciate, which means that the and curves have to shift to the right (with the curve shifting further to the right than , cf. solution to Exercise 5.8 (b) above). A new equilibrium is reached in point C of Figure I5.11.

Figure I5.11 Expansionary fiscal policy shifts the curve to the right (see Figure I5.12). By the same logic as in Figure I5.11, the BOP is not in equilibrium (domestic import demand too high) in point B. As under expansionary monetary policy, the exchange rate then depreciates and both and shift to the right. A new equilibrium is reached in point C of Figure I5.12.

Figure I5.12


rd


Exercise 5.9 Suppose investment is independent of the interest rate and the curve is vertical. Sketch the macroeconomic equilibrium under fixed and flexible exchange rates and describe the mechanisms that help achieve it. If investment is independent of the interest rate, the curve is vertical. A vertical curve furthermore means that because of perfect international capital immobility, the capital account and, thus, the BOP is independent of the interest rate. An equilibrium in the Mundell–Fleming model then only exists if the and the curve are identical, as shown in Figure I5.13. Such an equilibrium only holds for a specific value of the exchange rate (for a given level of , and ), which we denote .

Figure I5.13 How do the adjustment mechanisms work under such circumstances? Suppose government expenditures are relatively high such that we encounter a scenario similar to the one shown in Figure I5.14. In this situation, the country runs a current account (and a BOP) deficit.

Figure I5.14 With flexible exchange rates, the country will experience a depreciation of its currency, which will increase net exports. This shifts both the and the curve to the right. As was shown in the answer to Exercise 5.8 (b), the curve shifts further to the right than the curve in response to an exchange rate increase. This makes it possible that under flexible exchange rates, the economy always reaches a new equilibrium (see Figure I5.15 for a graphical illustration of this).


rd


With fixed exchange rates, the situation is quite different. In this case, there are no adjustment mechanisms ensuring that the economy reaches a new equilibrium within the Mundell–Fleming model. Assume again a situation similar to the one shown in Figure I5.14 where government expenditures are high. Again the country runs a current account deficit (and also a BOP deficit). In reaction to this, the central bank will sell foreign currency, thereby tightening the money supply, in an attempt to keep the exchange rate fixed. This measure will shift the curve upward, while the and curves remain unaffected. Thus, there is no mechanism that drives the economy back into an equilibrium. Hence under fixed exchange rates, only one possible equilibrium exists, where as, under flexible exchange rates there are (infinitely) many possible equilibria.


6 Enter aggregate supply Chapter focus This chapter switches the focus from the demand side to the supply side. It introduces the concept of a production function and discusses its properties. With production technology given and the capital stock considered predetermined in the short run, the remaining crucial determinant for output in the short run is employment. Therefore, the labour market and related issues of voluntary and involuntary unemployment take centre stage. Point of departure is the classical labour market in which a flexible wage rate does not permit involuntary unemployment (Voluntary unemployment is, of course, possible, and may be hidden in official unemployment data). The rest of the chapter covers departures from this ideal classical setting that may be responsible for involuntary unemployment. A straightforward explanation is the presence of minimum wages. More refined ones are trade unions that exercise monopoly power, trade unions with insider power, efficiency-wage theories or the existence of various forms of mismatch. In a next step it is shown how such features of the labour market (called real wage rigidities) that affect employment shift the vertical long-run aggregate supply curve to the left. A final section explains why employment may temporarily deviate from long-run (or ‘equilibrium’) employment. The explanation used here rests on sticky nominal wage rates due to one-period contracts, which brings price expectations into the picture (Alternative explanations focussing on sticky prices or sticky information are avoided here to keep the line of argument transparent, but they are being discussed in Chapter 16).

Additional boxes Box B6.1 A flow model of the labour market We start by noting that the labour force (which we suppose to equal the active population) comprises employment and unemployment :

Changes in unemployment must equal the net changes of the labour force and of employment: ∆

∆

∆

Unemployment can change during a given period of time because: some fraction of employed people lose their job; a fraction of unemployed workers find a job; a fraction quits the labour force, say because of retirement, out of which the was previously unemployed; fraction a fraction enters the labour force, say upon graduating from school, out of which becomes unemployed the fraction immediately:

∆ The equilibrium level of unemployment , which obtains if does not change any more, is obtained by letting ∆ 0 and solving for : ]/ The equilibrium rate of unemployment after dividing both sides by : ⁄

⁄

results /

After noting ⁄ 1 and collecting terms, we obtain an equation that shows how the rate of unemployment depends on a few structural coefficients which characterize flows in the labour market. ⁄

/

The numerator in the second term of the equation focuses on demographic characteristics. The effect of those characteristics on the equilibrium unemployment rate is straightforward and can be read off the equation without recourse to caculus:


rd


the more people enter the labour force each period, the more of those become unemployed, the higher is the unemployment rate. This would predict that unemployment rises when baby boomers enter the labour market, or also that increasing participation ratio of women temporarily, until quit ratios are also affected, raises equilibrium unemployment. Similarly, unemployment is affected in the opposite direction by rising quit rates and quits out of unemployment. This explains why early retirement programmes for workers are so popular a policy tool among politicians. The effects of finding and separation rates are a bit more complicated: 0 1

0

The formal results do conform with intuition that a higher finding rate reduces equilibrium

unemployment and a higher separation rate raises it. The magnitudes of each of these effects do depend on the current size of the other variable, however. For example, the quantitative effect that a given increase of the finding rate has on the unemployment rate depends on the separation rate: the higher the separation rate, the smaller will be the accomplished reduction of the unemployment rate. The obvious reason is that if jobs are lost easily, an increase in job findings does not do all that much to unemployment. Similarly, the quantitative effect of a given reduction in the separation rate on the unemployment rate depends on the current finding rate. So the two rates do not affect unemployment additively, but interactively. Policies geared towards reducing are thus, well advised to go for improvements in both the separation and the findings rate rather than emphasizing only one of them.

Exercises Exercise 6.1 Suppose that, due to a technological innovation, labour productivity increases significantly. How does this affect the partial production function? How does it affect the labour demand curve? The partial production function tilts upward, indicating that any given labour input produces a higher level of output. The labour demand curve tilts upward, indicating that for every level of labour supply, firms are ready to pay a higher real wage. See Figure I6.1. To address the question mathematically, one may want to introduce the Cobb–Douglas function (which the text introduces in Chapter 9) at this point already and derive the labour demand curve from profit maximization: Π Π⁄

1

0

1 Most of the text uses linear approximations of the labour demand curve.


rd


Figure I6.1 Exercise 6.2 Suppose that the nominal wage rate rises from £11 to £13.22, while the index of the price level increases from 241 to 296. Does this increase or decrease the real wage rate? The old real wage was 11⁄241 decreased.

0.046. The new real wage is 13.22⁄296

0.045. The real wage has thus

Exercise 6.3 Explain why both labour demand and labour supply depend on the real wage rate instead of the nominal wage rate. The basic intuition behind this is that economic agents (firms, individuals) do not suffer from money illusion and instead care about the implied exchange rate of real variables. Labour demand: If wages increase in lockstep with inflation – i.e. if the real wage does not change – firms should not alter the amount of labour they demand since the increased price of labour is matched by a proportional increase in the price of the output produced with labour. This is what makes it intuitively wrong for a firm to adjust its labour demand to changes in the nominal wage rate that leave the real wage rate unchanged. However, if the real wage rate does change, firms should adjust their labour demand since the changed price for labour is not matched by a change in the price of the output produced. Labour supply: According to microeconomic theory, individuals decide how much they want to work by equating the marginal utility of leisure time (which is lost through work) with the marginal utility of consumption goods (made affordable through work). If only the nominal wage rate changes, the marginal rate of substitution between leisure time and other goods remains unchanged, so the labour supply should remain unchanged as well. If by contrast the real wage rate changes, then the marginal rate of substitution and, thereby, the optimal amount of individual labour supply changes as well.

Exercise 6.4 What happens to potential output if workers attribute a higher value to leisure than before, which makes them supply less labour at any given real wage rate? Trace the consequences step by step, using Figure 6.8. 50 © Manfred Gärtner 2009

rd


The change in preferences shifts the labour supply curve to the left (or upward), indicating that workers demand a higher real wage for a given level of labour supply (see Figure I6.2, lower left panel). As a consequence, equilibrium labour input decreases in the lower left panel. Via the production function (the upper left panel), this leads to a decrease in potential output, i.e. the vertical aggregate supply curve in the lower right panel shifts left.

Figure I6.2 Exercise 6.5 Suppose that the government levies a proportional tax on labour income. (a) The government uses the tax revenue for government consumption. What are the effects on potential output? (b) Suppose that the government uses the tax revenue for public investment, improving the infrastructure and thus labour’s productivity. What happens to the result you derived in (a)? Derive your results using Figure 6.8. (a) A tax on labour income shift the labour supply curve to the left (or upward), indicating that individuals demand a higher (gross) real wage at any level of labour supply since the government now taxes away part of their income. The new equilibrium employment lies below the former and (via the partial production function) potential output falls below its pre-taxation level (see Figure I6.3).


rd


(b) If the government invests the tax revenue in infrastructure which raises labour productivity, the marginal product of labour increases. This tilts the partial production function upward and shifts a simplified (i.e. linearized) labour demand curve up: Due to higher labour productivity, firms want to hire more labour at any wage rate. The labour supply still drops, however, because with part of their income taxed away, individuals demand a higher (gross) real wage at any level of labour they supply. Since the effect on labour demand is positive but the effect on labour supply is negative, the ultimate effect of taxation on the new equilibrium level of labour is ambiguous and depends on the relative strengths of the two effects. Figure I6.4 shows an illustration for a situation in which the effect on labour supply outweighs the effect on labour demand. In that case, the equilibrium level of labour drops.

Figure I6.4 It should be noted that since labour productivity increases, a new equilibrium in the labour market is possible where both labour and the real wage rate have increased. It is also possible that employment falls but income increases.

Exercise 6.6 Measuring unemployment is trickier than it may seem at first glance. Find out how it is measured in (a) the United States (b) Germany (c) the United Kingdom. Which procedure comes closes to measuring the concept of ‘involuntary unemployment’ suggested by theory? If you are not living in one of these countries, how does the definition employed in your country fit in? There are two basic methods for measuring unemployment – the use of registration data and the use of data from household surveys. The first method, which considers all those as unemployed who draw unemployment benefits of some sort has the advantage of being relatively cheap. However, the data it delivers often does not correspond to the theoretical concept of unemployment (i.e. it does not specifically measure the number of people who are currently not working, but who are ready and willing to work and who are actively looking for a job). For example, people who are ineligible for unemployment benefits may not register at the employment service despite actually fulfilling all of the above criteria. The second method tries to avoid these shortcomings by directly asking a representative sample of individuals about their employment status. (a) In the United States, unemployment is measured using household surveys. (b) In Germany, unemployment figures cover persons who have registered at the government employment service. (c) In the United Kingdom, unemployment figures refer to claimants at Unemployment Benefit Offices.


rd


Exercise 6.7 The argument in this chapter (illustrated in Figure 6.10) seems to make a compelling case against minimum wages. Can you think of arguments in favour of minimum wages? Most arguments in favour of minimum wages are driven by distributional objectives. If one is not willing to accept an extremely wide dispersion of incomes with "working poor" at the bottom of the income distribution, a minimum wage may be an appropriate measure to reach an income distribution perceived as fairer. However, since an effective minimum wage creates unemployment, its introduction may in some cases actually exacerbate distributional conflicts instead of mitigating them.

Exercise 6.8 Figure 6.23 depicts average rates of unionization and unemployment from 1985 to 1995 for 13 European countries. (a) Do these data support the link between monopoly power of trade unions and the rate of unemployment suggested by theory? (b) Is the rate of unionization a good measure to reflect the degree of monopoly power on the supply side of the labour market?

Figure 6.23 (a) If at all, the graph suggests a negative relationship between unionization and unemployment, this is in conflict with a theory predicting that a higher degree of monopoly power leads to higher unemployment. (b) According to the graph, it is not. Percentage figures of unionization should be considered as no more than a first approximation in determining the degree of monopoly power on the supply side of the labour market. For a more accurate estimate, it is important to also consider the legal scope for action open to trade unions and the actual significance they possess in the wage bargaining process.

Exercise 6.9 In past decades one of the dominant ideas was that there was a fairly constant ‘natural rate’ of unemployment in equilibrium, not affected by transitory business cycle fluctuations. Use the insider–outsider model to explain why reality seems to contradict this idea. Figure 6.13 demonstrates how temporary shocks (i.e. shifts of the labour demand curve) can have permanent consequences. In the example of Figure 6.13, equilibrium unemployment is higher after a temporary decline of labour demand than before Thus the insider–outsider theory is one possible explanation for the observation that there is no stable ‘natural rate’ of unemployment.

Exercise 6.10 Use the logic of the efficiency-wage model to determine the effects of rising unemployment benefits on the optimal real wage rate (Hint: how do unemployment benefits influence the effort curve in Figure 6.15?). 53 © Manfred Gärtner 2009

rd


Higher unemployment benefits lower the costs of losing your job and thus increase the incentive to shirCeteris paribus, this turns the effort curve upward, since workers will choose a lower level of effort at any given wage rate. As a consequence, the level of effort that is optimal for the firm decreases and the real wage that minimizes unit labour costs increases.

Exercise 6.11 What happens to the curve (a) if the government improves the flow of information between enterprises with vacant positions and potential employees? (b) if administrative prescriptions prevent workers from moving across regions? (c) if programmes to change professional qualifications are increasingly supported by the government? (a) If the government improves the flow of information between enterprises and potential employees, this reduces unemployment due to mismatch phenomena and thereby increases potential output, i.e. shifts the curve to the right. (b) If administrative prescriptions prevent workers from moving across regions, geographical mobility is reduced and mismatch phenomena are exacerbated. The curve shift to the left. (c) If programmes to change professional qualifications are supported, this increases professional mobility and reduces mismatch unemployment. The curve shifts to the right.

Exercise 6.12 Let the production function be , and suppose the government installs a value-added tax of % on all sales in the economy. (a) Please derive the labour demand curve that results under profit maximization. (b) Show graphically how the introduction of this tax affects equilibrium in the labour market. What happens to unemployment? Do nominal wages respond fully to this new tax? (a) After the instalment of a value-added tax and with the production function given in the exercise, the firms' general (nominal) profit function Π , can be rewritten as Π

1

.

To derive the labour demand curve that maximizes profits, we set Π⁄ 1

1

1

1

Since the new term 1 of the nominal wage.

equal to zero:

0 /

.

lies between 0 and 1, firms will now employ less labour for any given level

(b) See Figure I6.5. In a - -diagram, the labour demand curve moves down by % of the nominal wage. A new labour market equilibrium with lower employment and a lower nominal wage obtains. The nominal wage does not respond fully to the introduction of the tax in the sense that it will have fallen by less than % once the new equilibrium is reached. (This holds true as long as the labour supply curve is not vertical.) As far as unemployment is concerned, in a classical labour market model, involuntary unemployment will remain zero. Voluntary unemployment will increase.


rd


Figure I6.5 Exercise 6.13 Suppose that the labour market is dominated by binding long-term contracts, giving rise to an positively sloped in the short run. How does an increase in the productivity of labour affect this

curve that is curve?

If productivity increases, firms are willing to employ more workers at any given real wage rate. Hence for a given price level (i.e. a constant real wage), firms produce a higher level of output. This is equivalent to saying that the curve shifts to the right (or down) in income-price space.


7 Booms and recessions (III): aggregate supply and demand Chapter focus This is the first full-fledged macroeconomic model for the short-run, explaining a comprehensive set of macroeconomic variables that comprises income and the various components of aggregate demand, prices, the interest rate, wages, employment and the current account. On the surface the - model contains two building blocks: – The aggregate supply ( ) curve, which was derived in Chapter 6. – The aggregate demand ( ) curve, which is derived in the first section of Chapter 7 for economies with flexible and fixed exchange rates. For a thorough understanding of students need to understand the background, what goes on behind (the labour market) and (Mundell–Fleming). So slowing down to show how movements in the diagram can be traced in the labour market and Mundell–Fleming diagrams is time well spent. Figure 7.11 provides one example of how this might be done. The chapter offers two major innovations that resonate through the rest of the book: – - is the first dynamic model. It moves beyond the comparative static approach of earlier models, tracing the transition from one equilibrium to another. An important new insight is that we need to specify the time horizon when we talk about macroeconomic effects. Responses in the short-run may differ from those in the medium and the long-run. – For the first time, expectations (here, of the price level) play an explicit role. Expectations had made a brief appearance in Chapter 2 (when we discussed the multiplier effects of permanent versus transitory income shocks) and in Chapter 5, where we made an excursion on open interest parity with depreciation expectations. Now price expectations enter the picture to adopt and maintain a leading role. Price expectations are formed adaptively. The introduction of rational expectations is held back until Chapter 8. If so desired and time permits, rational expectations may also be introduced in the context of the model in this chapter.

Exercises Exercise 7.1 When deriving the curve in Chapter 6, we assumed that real rigidities (say, in the form of monopolistic trade unions) cause involuntary unemployment at normal employment levels. Now consider an economy in which no such real rigidities exist. Normal employment is determined by the point of intersection between the individual labour supply and the labour demand curves. What does the curve look like in such an environment? Does it make a difference whether individuals enter longer-term wage contracts or whether wages can be renegotiated any time? If no real rigidities exist, potential income is higher and the vertical curve is positioned further to the right than if there are real rigidities. This holds no matter how often wages can be renegotiated.


rd


As for the shape of the curve, if wages can be renegotiated any time, firms can adjust the nominal wage instantaneously to changes in the price level and will always produce exactly the amount they planned to produce. This makes the curve vertical even in the short-run, i.e. . However, when nominal wages are fixed by contract, things change and the curve is derived as shown in Figure I7.1.

Figure I7.1 , i.e. if prices are as expected, the labour market clears at and potential income is If prices are at in Figure I7.1, real wages are higher than expected and, as produced. If prices are lower than expected, say at we move up the labour demand curve, employment falls to and income to . If the price level turns out to be unexpectedly high, say at , labour is cheaper than expected, and firms would like to hire more workers. But since without real rigidities there is no involuntary unemployment, firms cannot find more workers who are willing to work once the real wage falls. Instead an unexpected increase in the price level reduces the supply of labour as we move down the labour supply curve. Employment falls to and income to . The result is a kinked curve. Exercise 7.2 This chapter derives the curve for the national economy from the Mundell–Fleming model. Derive the global-economy curve graphically from the model. In the global economy, a rise in prices reduces the real money supply / , moving to the left. As we move up the curve in order to reach a new equilibrium in both the goods and the money market simultaneously, the interest rate increases and investment demand falls. In the new equilibrium after the price hike, the interest rate will thus have risen and income will have fallen. Since income depends negatively on the price (or the price depends negatively on income, for that matter), the global-economy curve must have a negative slope in income-price space (see Figure I7.2).


rd


Figure I7.2

Exercise 7.3 Figures 7.2 and 7.4 derive the curve for the national economy under flexible and fixed exchange rates. Find out by means of graphical analysis, under which exchange rate system the curve is steeper. In the Mundell-Fleming model, both the curve (because the real money supply is reduced) and the curve (because of a real appreciation of the domestic currency) shift left when the price level goes up. How far each curve shifts depends on two independent sets of coefficients (see Equations 3.2 and 3.9). These make it impossible to say whether or shifts further. It is possibly more plausible to assume that shifts further because it may be assumed that the reduction of the real money supply at home exerts upward pressure on the home interest rate (in monetary policy vocabulary, tightening the money supply is often used interchangeably with raising the interest rate). If we assume such a relationship, has to shift further than (see Figure I7.3). If were to shift further, there would instead be downward pressure on the home interest rate. In Figure I7.3 (top panel), the initial effect of the rise in is to drive the economy from its initial equilibrium in A towards point B, where there is upward pressure on the home interest rate. Since B is not an equilibrium: under flexible exchange rates (top panel of Figure I7.3), the nominal exchange rate will appreciate, . shifting further left, until a new equilibrium obtains at income under fixed exchange rates (bottom panel of Figure I7.3), the central bank is forced to increase the . nominal money supply, shifting back until a new equilibrium obtains at income Since , we arrive at the conclusion that the curve is steeper under fixed exchange rates, meaning that income under fixed exchange rates is less sensitive to changes in the price level (see centre panel of Figure I7.3). Note, however, that this result depends on the assumption that a price change moves further than . If it was which moved further, we would obtain the opposite result.


rd


Figure I7.3

Exercise 7.4 Suppose world interest rates go up, driving the world into a recession (i.e. world income falls). Use the model to analyse how this affects prices and income in our national economy. Do your results depend on whether exchange rates are fixed or flexible? From the Mundell-Fleming model we know that under fixed exchange rates, a rise in world interest rates and a fall in world income both drive domestic income down (at any price level). The curve thus moves left. under flexible exchange rates, a rise in world interest rates raises domestic income, while a fall in world income has no effect on income (the fall in home income induced by the fall in world income is neutralized by a depreciation of the home currency). Since income is thus higher at any price level, the curve shifts right. Figure I7.4 illustrates how the domestic economy is affected. Under fixed (flexible) exchange rate, there is a temporary fall (rise) in income and a permanent reduction (increase) of the price level.


rd


Figure I7.4 Exercise 7.5 What happens to the curve with flexible exchange rates and perfect international capital mobility if (a) the money supply increases? (b) the world interest rate decreases? (c) the government reduces spending? (a) An increase in the money supply under flexible exchange rates shifts the and the curve to the right. The curve shifts because of the exogenous money supply increase. The curve shifts because the domestic currency depreciates endogenously once there is downward pressure on the domestic interest rate. For any given price level, output is higher in the new equilibrium. The curve thus shifts right as well. (b) If the world interest rate decreases, the curve shifts downward. The resulting balance of payments disequilibrium (the domestic currency is in excess demand) necessitates an appreciation of the domestic currency. The appreciation shifts the curve to the left. In the new equilibrium, output has fallen. Since this holds at any given price level, the curve shifts left. (c) A reduction in government spending corresponds to a reduction in demand. The curve shifts left. Under flexible exchange rates, however, the domestic currency endogenously depreciates and the curve moves back to its initial position. Thus government spending does not affect the position of the curve under flexible exchange rates. Exercise 7.6 Why does an increase in the world interest rate shift the under fixed exchange rates?

curve up under flexible exchange rates, but down

Under flexible exchange rates, a higher world interest rate endogenously brings about a depreciation of the domestic currency (since there is excess supply of domestic currency). The depreciation stimulates net exports, which shifts the curve to the right. In the new equilibrium, output will have increased. Since this holds at any given price level, the curve shifts up (or right). Under fixed exchange rates, a higher world interest rate endogenously brings about a contraction of the domestic money supply, i.e. in order to keep the exchange rate fixed, the central bank has no choice but to buy domestic currency. This shifts the curve to the left. In the new equilibrium, output has fallen. Since this holds at any given price level, the curve shifts down (or left). Exercise 7.7 Why does a change in world income shifts the curve under fixed exchange rates but not when exchange rates are flexible? Start with the Mundell–Fleming model to determine which curves shift (and which do not) as foreign income increases. Does that mean that changes in foreign income do not change anything if exchange rates are flexible?


rd


Under flexible exchange rates, an increase in world income stimulates net exports (i.e. it stimulates exports and lowers imports), thereby shifting right. However, the initial shift of the curve is undone by the endogenously induced appreciation of the domestic currency, which shifts the curve back to its initial position. In the new equilibrium, output is back at its initial level, but the real exchange rate is lower than before, i.e. there was a real appreciation of the domestic currency (see Figure I7.5).

Figure I7.5 One could remind students of the usefulness of the circular flow identity when the - diagram remains rose and R fell. From vague by asking what happened to exports. This does not appear to be clear since

?

we see that exports must have increased. Under fixed exchange rates, an increase in world income stimulates net exports and shifts the curve to the right as well. Since exchange rates are fixed and the domestic currency cannot appreciate, the central bank has to supply domestic currency in order to meet excess demand in the foreign exchange market. As a result, shifts right. This brings about a higher level of output in the new equilibrium (see Figure I7.6).

Figure I7.6 Exercise 7.8 We examine a small open economy with fixed exchange rates. In period 0, the country is in its long-run equilibrium. The government carries out a one-time revaluation of the currency in period 1. Trace the effects of such a revaluation in the model for period 1 and 2. Where is the new long-run equilibrium? Assume that price expectations are formed adaptively ( ). The revaluation in period 1 shifts the curve to the left. Since firms expect prices in period 1 to remain where they were in period 0, the curve stays put. The short-term equilibrium in period 1 is reached in point in Figure I7.7. In period 2, price expectations adapt to the level prices reached in period 1 (i.e. to the price level . Since the revaluation is permanent, the curve does not shift implied in point ). The curve shifts into any more. The price expectations adjustment process (and with it shifts of the curve) continues, however, until the economy reaches its new long-run equilibrium in point C (see Figure I7.7). In C, prices are permanently lower than before the revaluation, and income is back at its potential level.


rd


Figure I7.7

Exercise 7.9 Suppose a country’s potential income Y* increases because lawmakers reduce trade union monopoly power. What will be the short-, medium- and long-run effects on prices and income in the – model? Let price expectation be formed according to . Consider Figure I7.8. We assume that the economy is initially in the equilibrium ‘old’. When union monopoly power falls, the curve shifts right.

Figure I7.8 In period 1, wages are renegotiated. Since price expectations for this period match the former period’s price level, (so that it intersects at the period 0 price level). The economy moves the curve shifts down into to its first period short-term equilibrium (1). In short-term equilibrium 1, prices have fallen. Price along expectations (which are formed adaptively) thus fall in period 2, moving further to the right. This goes on for a number of periods, until the economy eventually ends up in its new long-run equilibrium with higher income and lower prices.

Exercise 7.10 Suppose the economy’s demand-side can be described by the Keynesian cross with the equilibrium condition 0.4 1000 (a) What is the level of income? (b) Suppose government spending rises by 100. What is the new demand-side equilibrium income? (c) If the income level computed under (a) was equal to potential income and the short-run curve was positively sloped, what is the excess demand generated by the increase of government spending by 100 at the initial price level? 62 © Manfred Gärtner 2009

rd


(a) (b)

0.4 , .

1,000

, .

1,666.67

1,833.33, i.e. equilibrium income rises by

.

166.67.

(c) The excess demand generated by this increase is only 100. Since the short-term curve is positively sloped, firms will only supply more output at higher prices. At the initial price level, firms supply an output of 1,666.67, while 0.4 1,666.67 1,100 1,766.67 is demanded. Notice that the excess demand is only 100; it does not equal the horizontal distance between the and the curve, which would be 166.67 as calculated in (b).

Figure I7.9 Figure I7.9 provides a graphical illustration in a / diagram. Initially, the economy is in point 0. After government spending rose by 100, demand increases to point 1. Demand could only increase to 1’ on if supply could increase as well.

Exercise 7.11 Box 5.1 demonstrated that the curve is vertical when a country controls cross-border capital flows. Derive the curve graphically for this case of controlled capital flows. (a) Consider flexible exchange rates first. Which policy variables and exogenous variables shift the curve? (b) Now derive the curve for fixed exchange rates. Which variables determine the position of the curve? (a) Figures I7.10 (a) and (b) show what happens under flexible exchange rates when prices increase. A price increase reduces the real money supply. The real exchange rate

also falls. If capital flows are

controlled, the two effects shift the , the and the curve to the left. In panel (a), moves only modestly and the economy moves toward B’. The incipient excess demand for foreign currency leads to a depreciation of the home currency, which moves and back just until a new equilibrium is obtained in C (at an income level of ). Panel (b) shows what happens if the shift of is large instead of modest. In B″, there is an incipient excess demand for home currency, which leads to an appreciation. This moves both and further to the left until a new equilibrium obtains in C. No matter how far shifts, the relationship between and is always negative. The curve for flexible exchange rates and controlled capital flows will thus have a negative slope in income–price space.


rd


Figure I7.10 (a)

Figure I7.10 (b) It is quite easy to analyse the effects of monetary policy – an increase in the money supply shifts the curve to the right. and initially remain unaffected. To restore equilibrium in all markets, the domestic currency must depreciate just enough to shift the and curves to the right until all curves intersect in one point on the new curve. Since the new equilibrium obtains at a higher level of income (with the price level unchanged), an increase in the money supply shifts the curve right. Changes to autonomous demand components also shift the curve. Consider an increase in government expenditure. The increase shifts to the right. To restore equilibrium in all three markets, the exchange rate has to change. Since a change of the exchange rate shifts both and in the same direction, but with a larger horizontal shift for , equilibrium can only be restored if the domestic currency depreciates. It must depreciate enough to shift both and into a position where all three curves intersect in one point. Again, since the new demand-side equilibrium obtains at a higher level of income (with the price level unchanged), an increase in government expenditure shifts the curve right. Quite surprisingly, neither changes to foreign income nor to the foreign price level have an effect on the curve, since the endogenously induced exchange rate movement exactly offsets the initial change. (b) Figures I7.11 shows what happens under fixed exchange rates when prices increase. First, the real money supply

/ is reduced. Second, the real exchange rate

falls. If capital flows are

controlled, the two effects shift the , the and the curve to the left. From Equation 3.9 and Equation (2) in Box 5.1, we can see that moves further left than . We don’t need to differentiate between whether moves far or not because the nominal money supply adjusts endogenously under fixed exchange rates.


rd


Figure I7.11

Suppose moves into ′ . We now ask to what point the economy would move if we ignore the foreign exchange market. The answer is B′. Lying to the right of , domestic income is too high for a foreign exchange market equilibrium to obtain. In such a situation, there is excess demand for foreign currency. Under fixed exchange rates, the central bank is forced to supply foreign currency, thereby reducing the domestic money supply. This moves and the economy ends up in point C. Income fell from to after to the left into prices increased. If moves further into ′′ , the economy moves towards point B″. But there income is too low for an equilibrium in the foreign exchange market to obtain, and there is excess demand for domestic currency. Under fixed exchange rates, the central bank is forced to supply domestic currency, thereby expanding the domestic money supply. This moves to the right until the economy ends up in point C. Again income fell from to after the price increase.

Under fixed exchange rates, the position of the curve is solely determined by the position of the curve. Hence only shifts only when those variables change which shift . From Equation (2) of Box and E (which both enter ) and . Of course, changes in also shift 5.1, we see that these are the curve, but these will only cause a movement along a given curve (since the curve is drawn in income–price space). Fiscal policy has no effect on the curve under fixed exchange rates. Obviously no sovereign monetary policy is possible under this regime, either. In all four cases discussed here, demand-side equilibrium income falls when prices rise, which can be generalized by drawing a negatively sloped curve.


8 Booms and recessions (IV): Dynamic aggregate supply and demand Chapter focus This chapter progresses mainly on a technical level by developing the - model, which features the price level as an endogenous variable to be displayed on the vertical axis of the price–income diagram, into the model which features the rate of inflation instead. Making these transformations to the and curves is fairly straightforward if students are familiar with logarithms. A course that does not shy away from on math may note that while the adaptive expectations version of yields reduced-form equations for one of the endogenous variables as first-order difference equations, reducedform equations for inflation and income are second-order difference equations in the – model. This leads to slightly more complex dynamic patterns that are also more difficult to trace in graphs. An important new concept introduced in this chapter is rational expectations. While this is done in an intuitive fashion and mainly dealt with in terms of diagrams, there is also a box that provides a simple recipe for solving rational expectations models algebraically. An important point to stress is that – and – are simply two different dresses for the same model. Attentive students may come up with the question of why, then, a one-time shock in the – model triggers cyclical income responses while in the – model the response is simpler, noncyclical. The answer is that we are not really using the same kind of adaptive expectations in the two models. While our treatment of – assumes that expected inflation adapts according to , the discussion of – assumes that expected prices adapt according to , which obviously implies 0. Instructors may not want to spend the time it takes a number of students to grasp the dynamic aspect of positioning properly. In this case an option is to use the monetary policy rule instead of the curve. While a thorough foundation for such a rule is not developed until Chapter 12, it should be fairly straightforward to introduce the rule, which also features in the context of Chapter 16, on an intuitive basis.

Exercises Exercise 8.1 In this chapter the curve was written as when inflation expectations equal actual inflation.

. Derive aggregate supply in the long-run, i.e.

In the long-run equilibrium, expected inflation equals actual inflation. We can thus set and then subtract from both sides to get 0 , which implies . In the long run, firms produce potential income and the curve is vertical in inflation–income space.

Exercise 8.2 Under flexible exchange rates, domestic inflation is determined by the growth rate of domestic money supply, whereas inflation is determined by the foreign inflation rate if the exchange rate is fixed. (a) Explain why. 66 © Manfred Gärtner 2009

rd


(b) Suppose you govern a country whose economy is linked to other economies by fixed exchange rates. A reduction of inflation is overdue. Are you inclined to switch to a regime of flexible exchange rates? (a) You will find an in-depth explanation for this in the book in Sections 7.2 through 8.3, where the curve is derived for flexible and fixed exchange rate regimes. In short, under flexible exchange rates, changes in the domestic money supply affect aggregate demand (i.e. income in the Mundell–Fleming model), whereas changes in the foreign price level do not. With fixed exchange rates, the opposite holds true. To derive dynamic aggregate demand under flexible and fixed exchange rates, we have to transform the different levels of the domestic money supply and the foreign price level, respectively, into growth rates. This yields Equations (8.5) and (8.6). (b) In a small open economy with fixed exchange rates, inflation is ‘imported’, i.e. domestic inflation is determined by the larger trading partners’ inflation rate. Hence letting the exchange rate float may be an attractive option if the imported inflation is too high. The condition is that we expect .

Exercise 8.3 Consider an economy with flexible exchange rates, which can be described by the following curves: 0.025 0.075

and

curve curve

Assume that output in the preceding period was 150 units, which is 50 units below full employment output *. The growth rate of money supply is 10% and agents expect an inflation rate of 5%. (a) Draw the and the curves and compute current output and inflation. (b) The central bank considers reducing the money growth rate from 10% to 5%. Assume that the inflation expectations of the agents remain unchanged and draw the new and curves to analyse the immediate effect on inflation and output of such a policy change. (a) Plugging the given values into the and curves yields 13.75 0.025 for the curve and 10 0.075 for the curve in period 0. The easiest way to draw these curves is to pick out two particular values for , to compute the corresponding ’s, and then to draw a line through these points. 150

10

200

8.75

For the SAS curve: 150

1.25

200

5

The intersection of and in period 0 gives the short-term equilibrium values of output and equal to , i.e. inflation (point A in Figure I8.1). To compute these values, we set 13.75

0.025

10


0.075 . to get

237.5. Substituting

into

or

yields

7.8.

(b) Since the reduction of the money growth rate comes as a surprise, the curve does not move immediately. The curve shifts downward. To determine how far exactly it shifts down, we look at last period’s short-term equilibrium (point A in Figure I8.1) and from there move vertically down to the new target money growth rate of 5%. In Figure I8.1, this ends up in point B. The new curve ( ) will thus go through point B and will be parallel to . Equilibrium output and and the curve (point C in Figure I8.1). inflation in period 1 are given by the intersection of


rd


Figure I8.1

Exercise 8.4 It is often claimed that the government can permanently keep output above potential output, but at an ever ‘accelerating’ inflation rate. Explain this statement using the model. The dynamics of the model imply that a government can temporarily increase domestic output, e.g. by raising the growth rate of the money supply if the exchange rate is flexible. However, in the long run, output returns to its long-run equilibrium, and the inflation rate levels off at the money growth rate. To get back to an output level above long-run equilibrium, the monetary authority has to further increase the money growth rate – again with only temporary effects on output. Thus, output can only be held permanently above its long-run equilibrium if the central bank continuously increases the money growth rate, which brings about an ever accelerating inflation. Even this effect disappears under rational expectations or appropriate learning.

Exercise 8.5 Trace the short-run and long-run effects of a surprising once-and-for-all increase in the foreign inflation rate for an economy with adaptive inflation expectations and (a) a flexible exchange rate. (b) a fixed exchange rate. (a) Under flexible exchange rates, the increase in the foreign inflation rate has no influence on domestic income and inflation. Instead, the increase is offset by exchange rate fluctuations (Here: a lower depreciation or a higher appreciation rate of the domestic currency). (b) Under fixed exchange rates, the increase in the foreign inflation rate shifts the curve to the right (the induced change in the real exchange rate stimulates net exports). Since the shift of in period 1 comes as a surprise, the curve stays where it was in period 0. Output and inflation and in period 1 are thus determined by the intersection of , in Figure I8.2. The further evolution of the economy in income–inflation space is shown in Figure I8.2. Since will always intersect at , i.e. at the inflation expectations are formed adaptively, inflation rate realized in the previous period. will always pass through the point where last period’s income and the new world inflation rate (or intersect, i.e. through the point , .


rd


Figure I8.2

Exercise 8.6 Trace the short-run and long-run effects of an unexpected reduction of foreign inflation for an economy with a fixed exchange rate for the case of (a) adaptive inflation expectations. (b) rational inflation expectations. No matter whether inflation expectations are adaptive or rational, the reduction of foreign inflation makes the real exchange rate either fall faster or increase slower. Through a decrease in net exports, this shifts the curve left in period 1. Since foreign inflation falls unexpectedly, the curve does not move in period 1. (a) Adaptive expectations: In period 2, inflation expectations adjust to , i.e. the inflation level is lower than , so shifts down. Since is still higher than , the reached in period 1. process of adjustment to the new long-run equilibrium is extended over several periods (see Figure I8.3). As in Exercise 8.5.(b), will always intersect at , i.e. at the inflation rate realized in the previous period. will always pass through the point where last period’s income and the new world inflation rate (or ) intersect, i.e. through the point , .

Figure I8.3 (b) Rational expectations: In period 2, rational inflation expectations anticipate the position of and thus turn out correctly. Output returns to its long-run (potential) level in period 2 already. In in Figure I8.4). This is again anticipated by , period 3, reaches its long-run position (


rd


which makes the economy reach its long-run equilibrium with income at as early as in period 3 (see Figure I8.4).

and inflation at

Figure I8.4 Exercise 8.7 Consider an economy with a flexible exchange rate. Inflation expectations are formed rationally, but contracts extend over two periods. Every period, 50% of the contracts expire and are rewritten for the following two periods. Analyse the effect of a once-and-for-all increase in the money growth rate if (a) the policy change comes as a surprise. (b) the policy change is announced one period ahead. (a) If the policy comes as a surprise, all workers are stuck in their contracts in the current period. In the second period, only 50% of the workers can adapt their wage contracts to their changed expectations, whereas the other 50% are still tied to their old contracts. As a consequence, output does not immediately return to its long-run level after the surprise period is over (as it would under rational expectations if wages were fully flexible). (b)

If the policy change is announced one period ahead, 50% of the workers can take this information into account in their current wage negotiations. As a consequence, the positive effect of the monetary expansion on income is lower than without such prior information. However, unlike in a model in which contracts are written every period (and wages thus considered to be flexible), there is at least some effect of announced monetary policy when expectations are rational.

Exercise 8.8 Suppose a country’s economy is initially at point A (Figure 8.21). One year later it sits in point B. Please indicate what has happened to the variables listed under scenarios (a) to (e) by completing the table. Assume to be constant. See Table I8.1 for an overview. Table I8.1 Exchange rate system Real money supply Real wage Real exchange rate World interest rate World prices Government spending

(a) Flexible Up Down Up Unchanged Unknown Unchanged

(b) Flexible Up Down Unknown Down Up Unchanged

(c) Flexible Up Down Unknown Unchanged Unknown Up


(d) Fix Up Down Down Unchanged Down Up

(e) Fix Down Down Up Up Up Down

rd


Figure 8.21 Compared with point A, point B in Figure 8.21 features both higher supply and higher demand. Aggregate supply is determined in the labour market. As we argued in Chapter 6, the relevant labour market scenario for the – model features involuntary unemployment in equilibrium. Under this assumption, we are always on the firms’ labour demand curve, and when the real wage changes, we move up and down the demand curve. Employment only rises (and output only increases) when the real wage falls. The real wage must thus have fallen in all cases (a)–(e). Aggregate demand is determined in the Mundell–Fleming model. Relevant variables within this model must have changed so as to yield a point of intersection between , and at some higher level of income. In the following, we discuss demand-side details for all cases (a)–(e). (a) With the world interest rate unchanged, point B must lie on an unchanged curve to the right of A. Both and must have shifted right. For , this means that the real money supply must have increased. For , with government spending unchanged, this means that the real exchange rate must have gone up. See Figure I8.5 for a graphical illustration.

Figure I8.5 (b) At a lower world interest rate (with the curve having shifted downward), two qualitatively different equilibria (both with a higher real money supply and a higher income level) may have and require to shift to the right. However, calls for to obtained: In Figure I8.6, both shift left (and the real exchange rate to fall) and calls for to shift right (and the real exchange rate to increase). Hence the movement of the real exchange rate is unknown.

Figure I8.6


rd


(c) This case is similar to (a), except that this time government spending is up, which shifts to the right. Depending on the magnitude of this shift, the real exchange rate may have risen or fallen in order to make pass through B. See Figure I8.7 for illustration.

Figure I8.7 (d) This case is again similar to (a), except that this time the (nominal) exchange rate is fixed. Since domestic prices have risen (we can read this off Figure 8.17 where we can see that 0) and foreign prices have fallen, the real exchange rate must have fallen. This would shift to the left. Since needs to shift right in order to pass through B, government spending must be up (see Figure I8.8).

Figure I8.8 (e) Since LM has shifted left (the real money supply has been reduced), the new equilibrium must obtain in a point such as B in Figure I8.9. This requires an upward shift of both and . Hence the world interest rate must have risen and, with decreasing government spending, the real exchange rate must have gone up. With the nominal exchange rate fixed and domestic prices moving up (as we can read it off Figure 8.17), this means that world prices must have gone up even more.

Figure I8.9


rd


Exercise 8.9 An open economy with fixed exchange rates is characterized by the following equations: SAS curve: DAD curve:

∆

Find the rational expectation solution for income does income exceed potential income ?

using the recipe explained in Box 8.1. Under what conditions

In step 1, we have to find the reduced form for income . We set the for :

curve equal to the

∆

∆

.

Income depends on expected inflation, which we can calculate in step 2 by using the expressed in expected variables: ( ∆

∆

We have found a rational expectations solution for expression for the endogenous variable (step 3): ∆ ∆

∆

]

(

curve and solve

and the

curve

) )

, which we substitute into the reduced form to get an ∆

.

The last equation shows that if the actual increase in government spending ∆ exceeds the expected increase ∆ exceeds expected world inflation , then actual income is higher than and/or if actual world inflation potential income . This result is consistent with the results obtained earlier through graphical analysis of the – model.


9 Economic growth (I): basics Chapter focus This chapter shifts the focus to the long run. For the most part, Chapters 1–8 deal with the question of what makes income deviate from potential income. An exception is Chapter 6 which discusses the determinants of equilibrium employment which, in turn, also affect potential income. There the capital stock is given. Now we ask: what determines the capital stock? For a start, we note that investment has two sides: (1) it is part of aggregate demand; and (2) it adds to the capital stock and, thus, increases aggregate supply, i.e. potential income. Chapter 9 ignores deviations from potential income. Instead, it attempts to explain how certain behavioural characteristics of a country affect its capital stock and, thus, potential income itself. In this context, is reserved for steady-state income. denotes potential income, and The chapter looks at growth, or income patterns, from two quite different angles (both of which are related to the name of Robert Solow, the 1987 Nobel laureate in economics). The first one is growth accounting, which uses the production function to attribute changes in income to changes in the factors of production and technology. This is most easily done via the introduction of the Cobb–Douglas production function. Here again, it helps if students have a good grasp of logarithms. A nice side effect of growth accounting is that it provides us with an estimate of technological change, called the Solow residual. The question growth accounting remains silent about what makes the factors of production change. This is what growth theory studies, the second and major subject of Chapter 9. While it still considers technology and employment exogenous, the Solow or neoclassical growth model (these terms are being used interchangeably) looks at what determines a country’s capital stock in the long run. The simple idea is that the capital stock is driven by what we add to it each year, through investment, and what is lost, due to depreciation, and that it comes to rest when these two effects balance. To introduce this in the simplest possible context, we start with a first version of the Solow model that has no population growth and no technological progress. This baseline version is also used to introduce the golden rule of capital accumulation, and the related concepts of dynamic efficiency and inefficiency. After that the introduction of population growth and labour-augmenting technological progress is fairly straightforward, though students typically need time to come to grips with the latter and its implication for per-capita income growth.

Additional case studies Case study C9.1 Growth accounting in Italy As Figure C9.1 shows, Italian GDP rose by almost 30% between 1981 and 1996. If we plug Italy’s average labour income share of 71% during that period into a logarithmic Cobb–Douglas function we obtain ln

ln

0.29 ln

0.71 ln

To display the percentages that each of the righthand side factors contributed to income growth since 1981, we may normalize , and to one for this year, so that their respective logarithms become zero. Figure C9.1 74 © Manfred Gärtner 2009

rd


The upper curve in Figure C9.1 shows the logarithm of income, which is the variable we set out to account for. The lowest curve depicts 0.71 ln , the contribution of employment growth. It shows that if income growth had relied on employment growth alone, it would even have been lower in 1996 than it had been in 1981. The second curve adds the

contribution of capital stock growth to employment growth. This combined effect is clearly positive. The remaining vertical distance to the ln line must be due to technological progress. It is obvious that improvements in production technology constitute the major factor behind Italy’s income growth.

Additional boxes Box B9.1 Does faster growth mean catching up? The convergence of incomes suggested by the Solow model (apparently supported by Figure 9.2 and, in relative terms, by Figure 9.20) led researchers to postulate an equation of the form ∆

2003 it grew by a whopping 22.73%, much faster than British income, which grew by 5.88% only. With these growth rates the two countries’ incomes rose to $540 and $25,560 respectively, in 2003. Table B9.1

(1)

The constant must be the same for all countries when we postulate absolute convergence of (per capita) incomes, but may differ to reflect differences in savings and population growth rates when we search for relative convergence. Such an equation puts a (regression) line into a cloud of data points as shown in Figure 9.20. Crucial to whether convergence exists or not is the sign of the coefficient . When is negative, low-income countries tend to grow faster and there is convergence. Because the result hinges upon the slope coefficient in a bivariate regression equation, which is routinely denoted by the Greek letter beta as done in Equation (1), we call this kind of convergence beta convergence. While the existence of relative or absolute beta convergence is an encouraging statistical finding, does it guarantee that incomes actually grow closer? Consider India and the United Kingdom, showcased in table B9.1. The UK is rich, boasting per capita income of $24,140 in 1999. India is still poor by comparison, with per capita income of only $440. Luckily, because there is beta convergence, India’s income grows quickly. Between 1999 and

UK Per capita income Growth rate of India Per capita income Growth rate of

1999

2003

$24,140

$25,560 5.88%

$440

$540 22.73% $25,020

$23,700

Source: IMF, IFS

Despite a strong case of beta convergence, the table conveys perhaps the surprising result that the income gap between the United Kingdom and India has widened, from $23,700 in 1999 to $25,020 in 2003. The reason is that the 5.88% increase in the United Kingdom put another $1,420 into British pockets, while the 22.73% hike in India generated no more than $100. The lesson to be learned from this is that beta convergence does not necessarily guarantee India to eventually reach the same per capita income as the United Kingdom. The British may well maintain an income advantage over India that grows larger and larger in terms of dollars, euros or pounds sterling, though their lead will obviously shrink in percentage terms.

Exercises Exercise 9.1 . . A country’s production function is given by . In the year 2001 we observed 10,000, 100 and 10,000. Suppose that during the following year income grew by 2.5%, the capital stock by 3% and employment by 1%. What was the rate of technological progress? (a) Address this question first by computing the Solow residual from the growth accounting equation. (b) The text stated that the growth accounting formula is only an approximation. To quantify the imprecision involved, answer the above question next by proceeding directly from the production function. This yields the precise number. Compare the results obtained under (a) and (b).


rd


(a) Plugging the relevant variables into the growth accounting equation (Equation 9.4) yields: ∆

∆

∆

1

0.025

0.5

.03

0.5

0.01

0.005,

or 0.5%. ,

(b)

√ , , √

,

10

,

10.0495.

√

∆

Hence the rate of technological progress can be calculated as

.

0.00495,

which is the same as 0.495%. This is slightly lower than the result derived in (a). The absolute error of the result derived through the growth accounting equation is 0.005%, to be exact.

Exercise 9.2 Consider the Cobb–Douglas production function: . (a) Under what conditions do marginal returns to capital diminish if labour stays constant? (b) Under what conditions does the function display constant returns to scale? (c) Suppose marginal returns to capital do not diminish. Is it still possible for the function to exhibit constant returns to scale? (a) Marginal returns to capital can be determined by taking the production function’s first derivative with respect to capital: . To determine the properties of the marginal product of capital, we take the second derivative with respect to : 1

.

For the partial production function to exhibit diminishing marginal returns to capital, this second derivative must be negative. This is equivalent to saying that the (positive) slope of the partial production function must decrease as increases. The second derivative is negative if and only if 0 1. (b) The mathematical condition for constant returns to scale is: , or, after collecting terms on the left-hand side, . This simplifies to

1 for constant returns to scale.

, which yields the condition

(c) If marginal returns to capital do not diminish, this means that 1 (cf. part (a) of this exercise. Also, and are usually assumed to be positive). For 1, this can be reconciled with the condition for constant returns to scale if 0.

Exercise 9.3 The per capita production function of a country is given by The parameters take the following values: 0.2 Calculate the per capita capital stock

0.05

and per capita output

.

0.2

. 5

in the steady state.


rd


In the steady state, savings must equal required investment: .

This condition can be solved for . By plugging in the given parameter values, we get .

. .

.

4

:

16.

Steady-state income then is: .

5

4

20.

Exercise 9.4 Suppose two countries have the same steady-state capital stock, but in country A this is because of a larger population, whereas in country B it is because of a more advanced technology and thus higher productivity. How does the steady-state income of country A differ from the steady-state income of country B? Does it make sense to say that country B is richer than country A? Since both countries have the same capital stock in the steady state, steady-state output is also equal for both countries. However, per capita values differ, since in country A the population is higher than in country B. This makes per capita income in country A lower than in country B. Since this means that the average citizen in country B has more income and can consume more than the average citizen in country A, it is reasonable to say that country B is richer than country A.

Exercise 9.5 Consider two countries C and D that are identical except for the savings rate, which is higher in country C than in country D. Which country is richer? Does this necessarily mean that welfare is higher in the richer country? From the Solow diagram in Figure I9.1, one can see that C, the country with the higher savings rate, has the higher (per capita) capital stock in the steady state and therefore a higher level of per capita steady-state output as well. Country C is thus richer than country D. This does not necessarily mean that people in country C are better off, however, since welfare depends on consumption rather than income (or so we assume) and the inhabitants of country C consume a smaller fraction of their income than do the inhabitants of country D. To determine which country is better off, we would need to know in which country per capita consumption is higher. In Figure I9.1, we have assumed that country D’s savings rate is the one implied by the golden rule, whereas country C saves too much and therefore enjoys a lower level of welfare in the steady state.

Figure I9.1

Exercise 9.6 Suppose two countries, Hedonia and Austeria, are characterized by the following production function: . . . In both countries the labour supply is constant at one, there is no technological progress, and the depreciation rate is 30% (an unrealistically high portion, compared with empirical estimates). (a) Compute the golden-rule level of the capital stock. 77 © Manfred Gärtner 2009

rd


(b) What is the savings rate that leads to the golden-rule capital stock? (c) Suppose you are in charge of the economy of Hedonia where the savings rate is 10%. Your goal is to lead Hedonia to eternal happiness by implementing the golden-rule steady state. To this end, you impose the golden-rule savings rate. Compute the levels of income and consumption for the first five periods after the change of the savings rate, starting at the initial steady state. Draw the development of output and consumption and explain why you might run into trouble as a politician. (d) Being kicked out of Hedonia, you are elected president of Austeria where people save 50% of their income. Do the same experiment as before and explain why, in the not too distant future, Austerians will build a monument in your honour. (a) In Section 9.5, it is shown that the golden-rule steady state is characterized by a partial production function with the slope (the depreciation rate). Note that in Section 9.5, labour supply was assumed to be constant, i.e. 0. To compute the golden-rule steady state for Hedonia and Austeria, we have to take the first derivative of the production function with respect to and set it equal to . As indicated in the exercise, we set 1. .

0.3

0.3.

Dividing both sides by 0.3 and solving for 1. one) yields

(which is easy, since on the right-hand side we now have

(b) Once we have determined the golden-rule capital stock , we can use the equation that characterizes the steady state (here: savings must be equal to depreciations) to determine the savings rate necessary to : maintain .

0.3 1, we get

Plugging in

0.3.

(c) To do our simulation, we first have to compute the initial steady state for Hedonia. We start with the equation that characterizes the steady state (here: savings must be equal to depreciations), using the parameter values for Hedonia: 0.1

.

Solving for

0.3 yields the steady-state capital stock ⁄

1⁄3

~0.208.

Plugging this into the production function yields ‘Hedonish’ output in the initial steady state: 1⁄3

⁄

~0.624.

Consumption is 0.9

1/3

⁄

~0.562.

To compute the levels of the capital stock, output and consumption for the first five periods after the change of the savings rate, we use a step-by-step method. First compute output for the current period. Consumption then equals the consumption rate 1 times output , and savings equals the savings rate times output . By subtracting the capital that depreciates in a given period (current capital stock times the depreciation rate) from savings , we get net investment. The current capital stock plus net investment yields the capital stock for the following period. The values for the first five periods are given by the bold numbers in Table I9.1. The first row (period 0) represents the old steady state, which was characterized by zero net investment. Once the savings rate increases in period 1, consumption falls, whereas output is still determined by the old steady state’s capital stock and thus remains the same. Because of the higher savings rate, net investment becomes positive and the capital stock starts to increase. This leads to a higher output in period 2 and all following periods. In the long run, consumption will increase, too. However, in the first three periods consumption is lower than in the initial steady state. This reduction of welfare in the first three periods may make the golden-rule savings rate difficult to impose. Stylized time paths of output and consumption are given in Figure I9.2.


rd


Table I9.1 Period 0 1 2 3 4 5

0.208 2.075 0.208 2.075 0.333 1.825 0.449 1.637 0.550 1.494 0.636 1.384

0.624 1.245 0.624 1.245 0.719 1.200 0.786 1.160 0.836 1.128 0.873 1.102

0.562 0.622 0.437 0.872 0.503 0.840 0.550 0.812 0.585 0.790 0.611 0.771

0.062 0.623 0.187 0.373 0.216 0.360 0.236 0.348 0.251 0.338 0.262 0.331

0.062 0.623 0.062 0.623 0.100 0.548 0.135 0.491 0.165 0.448 0.191 0.415

Net investment 0 0 0.125 -0.250 0.116 -0.188 0.101 -0.143 0.086 -0.110 0.071 -0.084

Note: For each period and variable, the upper (bold) numbers refer to Hedonia, the lower numbers to Austeria.

Figure I9.2 (d) The values for Austeria are calculated in exactly the same way as those for Hedonia (see above). You will find the numbers in Table I9.1 for your reference (lower non-bold rows). Because implementing the golden-rule steady state for the Austerians means lowering the savings rate, Austerians in period 1 enjoy a higher level of consumption (than in their initial steady state) while still benefitting from their initial steady state’s high capital stock and output. In the following periods, negative net investment reduces the capital stock and, thereby, output and consumption. However, consumption will always remain above the initial steady state’s level of consumption. Hence Austerians both in the short and in the long run improve their welfare by lowering their savings rate to the golden-rule savings rate. Stylized time paths of output and consumption are given in Figure I9.3.


rd


Exercise 9.7 Judge the prosperity of an economy in which the growth rate of income is 8% because of a constant rate of population growth of 8%. Is this economy better or worse off than an economy with 4% growth and a population growth rate of 3%? The growth rate of income is the sum of the growth rate of the labour force and the growth rate of exogenous technological progress. The growth rate of per capita income equals the growth rate of exogenous technological progress. In the first country, there is no technological progress. Per capita incomes thus remain constant. In the second country, however, per capita income increases by a constant growth rate of 1%, which makes citizens in the second country better off than those in the first country. In formal terms one may note that in a general steady state . After taking logs and time derivatives we obtain the following approximation for per capita income growth: ∆

∆

∆

Plugging in numbers we obtain 8%

8%

0% for the first country and 4%

3%

1% for the second.

Exercise 9.8 How does a change in the savings rate affect the steady-state growth rate of output and consumption? Does this result also hold for the transition period (i.e. until the new steady state is reached)? In the Solow growth model, the savings rate does not affect steady-state growth rates. These are determined exclusively by population growth and exogenous technological progress. This does not hold for transition periods, however. An increase in the savings rate yields higher growth rates during the transition to the new steady state.

Exercise 9.9 Consider an economy in which population growth amounts to 2% and the exogenous rate of technological progress to 4%. What are the steady-state growth rates of (a) , , ̂ (where the hats denote ‘per efficiency units of labour’)? (b) , , (i.e. per capita capital, income and consumption)? (c) , , ? (a) These variables remain constant in the steady state. (b) In the steady state, per capita variables grow at the rate of technological progress, i.e. at 4%. (c) In the steady state, aggregate variables grow at the sum of the population growth rate and the rate of technological progress, i.e. at 2% 4% 6%.

Exercise 9.10 The economy is in a steady state at 100. The efficiency of labour grows at a rate of 0.025 (or 2.5%), the population growth is 0.01, and the depreciation is 0.05 annually. (a) At what rate does grow? (b) At what rate does per capita income grow? If the production function is 10 . , what is the steadystate output per efficiency unit of labour? (c) What is the country’s savings rate? (d) What should the country save according to the golden rule?


rd


(a) In the steady state, the growth rate of the aggregate capital stock equals the sum of the growth rate of labour efficiency and the population growth rate. Here the capital stock grows at a rate of 2.5% 1% 3.5%. (b) The growth rate of per capita income equals the rate of exogenous technological progress, i.e. 0.025. To find the steady-state output (per efficiency unit of labour) for the given level of the steady-state capital stock, we substitute 100 into the given production function, which yields 10

100

.

100.

(c) Since we know the aggregate production function and the steady-state capital stock (per efficiency unit of labour), we can derive the savings rate from the equation that characterizes the steady state: 10

100

.

0.025

0.01

0.05

100.

This can be solved for s to get the savings rate 8.5⁄100

0.085

8.5%.

(d) In the golden-rule steady state, the following condition has to be satisfied (the slope of the partial production function must equal the slope of the requirement line): .

5

.

If we plug in the given parameter values and solve for the steady-state capital stock (per efficiency unit of labour), we get 5⁄0.085

3460.21.

The golden-rule savings rate can be determined by substituting the golden-rule capital stock into the equation which characterizes the steady state: .

10

.

Solving for the savings rate, this yields 0.5

50%.

Since the actual savings rate 8.5% is too low when compared with capital stock is also lower than the one required by the golden rule.

50%, the steady-state

Exercise 9.11 Per capita income in the Netherlands was $25,270 in 1999 and grew by 3.8% during the following 4 years. Per capita income in China was $780 in 1999, but it had risen to 24.43% by 2003. (a) Show that, despite this large difference in income growth rates, absolute per capita incomes did not grow closer. (b) Given the Dutch income growth rate between 1999 and 2003, how large would China’s growth rate have to be in order to make the absolute income gap between the two countries shrink? (c) Compute the ratio between Chinese and Dutch per capita incomes in 1999 and in 2003. Compare your results with the results obtained under (a). Discuss. (a) China’s per capita income in 2003 was $970.6 $780 1.2443 and Dutch per capita income amounted to was equal to $25,259.7 in $26,230.3 ($25,270 1.038 in 2003. The income gap ( 2003, whereas it was $24,490 in 1999. In absolute terms, the income gap has thus increased. (b) Since we know the Dutch income growth rate, we know the Dutch income level in 2003 as well. It is $26,230.3. In order to obtain the same income gap between the Netherlands and China in 1999 and 2003, China’s per capita income would have had to be at least $1,740.3 in 2003 ($26,230.3 $24,490 $1740.3). Since per capita income in 1999 was $780, China’s per capita income would have had to be more than double in the four years between 1999 and 2003 (to be precise, it would have had to increase by 123.12%). (c) The ratios between Chinese and Dutch per capita income in 1999 and 2003 are the following: 1999:

$ $

,

0.0309

3.09%

2003:


$ $

. ,

.

0.037

3.7%.

rd


We observe that this ratio has increased from 1999 to 2003. This means that the Dutch income advantage over China has increased in terms of dollars (absolute values) in this four-year period, but the income lead has shrunk in percentage terms during this same time. The fact that the relative distance between the two incomes has shrunk – i.e. the fact that the poorer country has a higher per capita income growth rate than the richer country – is often referred to as beta convergence.


10 Economic growth (II): advanced issues Chapter focus This chapter takes students a lot further than intermediate macroeconomics texts typically do. Building on the baseline model of neoclassical growth introduced in Chapter 9, and using questions left unanswered by this model for motivation, the new topics addressed in this chapter are: 1. Public finances and economic growth. Adding government spending and taxes to the Solow model graph is relatively straightforward. However, solving for steady-state income is not possible any longer. The important messages are, first, that public deficit spending deprives the firms of funds for their investment projects, and second, that it may be justified if the government invests rather than consumes. 2. Growth in open economies. Putting issues of growth into a global environment is an important step. It shows that a country’s capital stock may be financed (but also owned) by foreigners. This makes the distinction between GNP and GDP important. Box 10.1 illustrates by means of a simple numerical example that both rich and poor countries may benefit from a removal of barriers to capital flows in terms of GNP. The downside is that the income distribution in rich countries becomes more uneven. In fact wage incomes may be lower than prior to globalization. 3. Poverty traps. The empirical observation that a number of developing economies, typically from sub-Saharan Africa, appear stuck at very low levels of income without any noteworthy growth, is addressed by showing that certain anomalies, i.e. deviations from the standard properties of the production function, of the saving function or of the investment requirement line, may give rise to multiple equilibria and specific challenges for economic policy and development aid. 4. Human capital. In a first step, the production function is augmented by human capital, the accumulation of skills and knowledge attached to a person. Treated as an exogenous variable at this stage, human capital is one more factor explaining differences in income between countries. 5. Endogenous growth. In a second step, human capital is endogenized by making it dependent on the capital stock. The result is an AK model that lacks a stationary steady state but features endogenous growth through capital accumulation which, in turn, depends on certain characteristics of the economy.

Exercises Exercise 10.1 Suppose we are looking at the global economy with a standard constant return to scale production function. Let us now introduce the public sector, where – is public saving. (a) What happens to the steady-state income if the government raises (without increasing public spending)? What happens to per capita consumption in the long and in the short run? (Can you make a definite/unconditional statement?) (b) Suppose the government is not able to save the increase in tax revenue, but spends all of the surplus immediately for government consumption. What happens now to steady-state income? (c) Finally, suppose that not all the government spending is used for consumption goods, but a part of it is used for public investment. What share of the additional tax revenue must the government invest if steady-state income should increase in response to the policy action, and the private savings rate is 20%? (a) Steady-state income – absolute and per capita – rises, because the increase in taxes leads to higher national savings. Net investments thus turn positive, which means that the capital stock (and with it income) increases during a transition phase to a higher steady-state capital stock. 83 © Manfred Gärtner 2009

rd


In the short-run, per capita consumption will decrease, since production does not change immediately, whereas the taxes must be paid for. In the long-run, the change in per capita consumption is ambiguous, depending on the total size of national savings: If total savings are very high (i.e. if the savings rate is higher than the one implied by the golden rule of capital accumulation), it is possible that despite the increase in production, per capita consumption remains below the pre-tax-increase level. (b) Since national savings decrease in this case (provided that the private savings rate is greater than zero), the capital stock and production/income will decline. (c) If the government spends all of its additional tax revenue, it has to use at least 20% of it for public investment projects in order to increase the national savings rate and, thereby, income in the new steadystate.

Exercise 10.2 A country’s goods and capital markets are isolated from the rest of the world. Consumption out of disposable income is given by 0.8 . (a) How does the steady-state capital stock respond if only government spending is raised while taxes remain unchanged? What happens if taxes are raised while government spending is unchanged? Show this formally. (b) Let the government raise spending and taxes by the same amount. How does this affect the steady-state capital stock? Explain. (c) How is the result obtained under (b) affected if 50% of government spending is public investment? (a) To analyse this formally, we start by restating the equation from Section 10.1 and use the savings rate 0.2 implied in the above consumption function: ∆

0.2

,

0.8

.

The steady state is characterized by 0.8

0.2

,

.

Although we do not know the functional form of the production function, we can formally derive the effects of various fiscal policy measures. To this end, we take the total differential of the equation characterizing the steady state to get 0.8

0.2

]

,

.

Note that the term in squared brackets on the right-hand side is negative, since the savings function intersects the requirement line from above in the steady-state. We can thus derive the reaction of the steady-state capital stock to an increase in government expenditure (keeping taxes constant, i.e. 0): 1/ 0.2

]

,

0,

which confirms the result that was derived graphically in the chapter. If the government’s budget deficit increases, the steady-state capital stock (and, hence, steady-state income) decreases. In much the same way we can compute the reaction of the steady-state capital stock to an increase in taxes (keeping government expenditure constant, i.e. 0): 0.8/ 0.2

]

,

0,

which also confirms the graphical result in the chapter. (b) To compute the reaction of the economy to a ‘balanced budget’ increase in government expenditure, we set in the equation used in the answer to (a). This yields: 0.8

0.2

,

]

1

0.8 / 0.2

,

]

0.

Hence an increase in government expenditure depresses the steady-state capital stock and income even if it is accompanied by an increase in taxes in the same amount. This does intuitively make sense. If the government raises taxes and expenditure by the same amount, the savings rate for this respective amount is zero, which is much lower than the savings rate of 20% previously prevailing in the economy. The effect of the balanced budget increase is thus to reduce the economy’s savings rate. 84 © Manfred Gärtner 2009

rd


(c) If 50% of government expenditure is used for public investment, we have to start from the equation ∆ , 1 1 for a formal analysis of the effects. We from this equation derive the one that characterizes the steady state (∆ 0 and take the total differential (as in (a)). This yields (with ) 0.5

0.8 / 0.2

,

]

0.

In this case, a ‘balanced budget’ increase in government expenditure increases steady-state income since the government invests a larger fraction of its (tax) income than private agents do.

Exercise 10.3 . . Consider an economy with the following production function: . The labour force is 100, the savings rate is 0.3, and the rate of depreciation is 0.1. (a) Determine the steady-state levels of per capita income and consumption. (b) Now suppose that the government wants to increase national savings by levying an income tax of 20%. Compute the new level of steady-state per capita consumption. Does it increase or decrease when compared with the result obtained in (a)? What happens to per capita consumption in the short-run? (c) Consider the steady state where 0.5. Is it dynamically inefficient? Proceed as in (b). 300,

(a) ∆

0.3 30

3, .

.

.

30

440,

(b)

0.7

3

2.1. Derivation of

10

300.

4.4,

1

∆

2.464. Derivation of the new

:

0 1 0.3 44

1 0.2

] 0.7]

10

.

44

10

.

.

.

0.1 440.

Per capita consumption thus increases in the long run (∆ 0.7 1

0.2

650,

(c)

:

0 0.1

10 .

1

3

1.68

∆

6.5,

1

∆

0.42

0.364

0). In the short run, it decreases:

0.

2.275. Derivation of

:

0 1 0.3 65

1 0.5

] 0.7]

10

.

65

10

.

.

.

0.1 650.

We know from the solution to part (b) that by reducing the tax rate from 0.5 to 0.2 we can increase per capita consumption both in the long and in the short run. The situation in (c) is thus dynamically inefficient.

Exercise 10.4 Consider two separate economies that are identical in the size of their labour force 100 and the production function including technology, but differ in their savings rates. The production function for both . . economies is . Let the rate of depreciation be 10%. Suppose the savings rate in country A is 25%, whereas people in country B do not save at all. (a) Determine the autonomous steady-state incomes and capital stocks in both countries. What is the level of per capita consumption in each country? Now suppose that a global capital market is introduced, such that capital can be transferred from one country to another costlessly. 85 © Manfred Gärtner 2009

rd


(b) Determine the steady-state incomes and capital stocks in both countries in this new environment. What happens to income (GNP) and thus consumption, both in the long and in the period when the capital market is opened? (a) Autonomous steady-state incomes and capital stock in both countries are given in Table I10.1. Without savings, country B will have no capital stock and hence no income in its autonomous steady state. Table I10.1

⁄

Country A 250 625 187.5 1.875

Country B 0 0 0 0

(b) See Box 10.1 in the book on how to calculate steady states when capital markets are global. Table I10.2 shows that in the long-run, the level of production will be the same in both countries. This is due to the fact that the production functions and the labour forces are identical in both countries. However, income measured as GNP will differ. Since the whole capital stock used for production in country B is owned by investors from country A, country A’s GNP is augmented by interest payments from country B, while country B’s GNP is reduced by that same amount. For the specific production function used in this exercise, interest payments make up for exactly half of total income/production. This makes consumption levels in country A and B differ considerably (see Table I10.2). Table I10.2

Interest payments GNP

Country A 187.5 93.75 281.25 351.5625 210.9375

Country B 187.5 -93.75 93.75 351.5625 93.75

The short-run effects of introducing a global capital market are summed up in Table I10.3. Since just after the opening of capital markets capital yields a higher return in country B than in country A, country A will immediately transfer half of its capital stock to country B (remember, we assume that this can be done at zero cost). Production - as well as labour income and consumption - in country B increase. In country A, capital income increases, but labour income decreases. Since the former effect dominates, GNP (and thus consumption and saving) in country A increase in the short run. (Due to the increase in savings, the world capital stock grows to a higher long-run level.) Consumption rises both in the short and in the long run in both countries. Table I10.3

Interest payments GNP

Country A 625⁄2 312.5 10 312.5 . 176.7767 0.5 10 312.5 . 88.388 265.165 198.874

Country B 312.5 176.7767 -88.388 88.388 88.388

Exercise 10.5 Consider a world with two economies and a global capital market. The two countries are alike except for their savings rate (the savings rate in country B is smaller). Thus, in the initial steady state: , , but and, thus, . (a) What will happen to investment flows (and thus , , and ) if technology in country B improves? (b) Suppose next that the depreciation rate of capital in country A increases (because of ecological reasons, e.g. in country A there are more floods, thunderstorms or fires). Does this have any impact on the steady-state variables of , , or ? 86 © Manfred Gärtner 2009

rd


(c) Finally, imagine that the population in country B doubles (say, because of reunification). What implications does this have on the two economies? (Consider again , , and , but also per capita consumption.) (a) Improved technology in country B shifts the production function upward. This implies a higher marginal product of capital at the given capital stock, meaning that the interest rate in country B increases. Capital exports from country A to country B grow. (b) If the depreciation rate increases, maintaining a certain capital stock becomes more expensive. Capital will thus be transferred from country A to country B until the ‘net interest rate’ (the marginal product of capital less the depreciation rate) is again equal in both countries. With the reduction of the capital stock, production in country A will decrease. The higher ‘aggregate world depreciation rate’ means that the ‘world capital stock’ and world and ) will decrease, for more saving would now be needed to maintain the production (the sum of same capital stock. It cannot be said which of the two above-mentioned effects will dominate in country B. The effects on the capital stock and production in country B are thus ambiguous. (c) A doubling of the population in country B shifts the production function upwards (similar to (a)). The marginal product of capital at the given capital stock again rises, as do capital transfers from A to B. World production will be higher, although production in country A will decrease. GNP and aggregate consumption will rise in both countries. Per capita income will fall, however. In order for per capita consumption to remain constant, the capital stock in country B would have to double (recall that the production function exhibits constant returns to scale). But this will not happen. While transferring capital from A to B, the marginal product of capital in country A increases. This means that in the new equilibrium, the marginal product of capital in country B must also be higher. With constant technology, this will only be the case if capital increases by less than labour. That is why per capita income and consumption in country B must decrease.

Exercise 10.6 Start from the basic scenario supplied in Box 10.1. In a situation with a global capital market, how are GDP, GNP and factor income shares affected if (a) the savings rate in country A falls to 0.1? (b) country B’s population is four times as large as country A’s ( 4 )? (a) The steady-state per capita capital stock must be the same in A and B. Hence the new steady-state capital stock: 0.1 10

.

0.5

10

.

0.1

. First solve for

. 2

Solving for the world capital stock (

yields 2

112.5.

Hence: 10 0.5 0.5

75 1.5 75

√56.25

112.5

37.5.

GDP and GNP in both countries fall; the factor incomes fall by the same proportions as do GDP and GNP. Factor income shares (given by the exponents in the production function) remain the same. (b) Again, we first solve for the new steady-state capital stock (after defining 0.2 10

.

0.5

20

4

.

0.1

5 .

Solving for country A's capital stock gives

144.

Hence: 10

√144

120,

4

480 87 © Manfred Gärtner 2009

and, hence,

4 ):

rd


0.5

120

0.5

240

360

240.

GDP falls in country A. Capital income as a proportion of GNP rises in country A, since labour income in country A decreases and capital income rises.

Exercise 10.7 . . Consider an economy with the Cobb–Douglas production function . The savings rate is 0.3, the rate of depreciation 0.05 and the rate of population growth depends on per capita income. If per capita income is low, population grows at a rate of 0.1. If per capita income is high, the population growth rate reduces to 0.05. (a) Determine per capita output and consumption in both steady states. Next suppose that the economy is initially in the steady state with 0.1. The population growth rate declines as soon as per capita income has reached 2.5 units. Now the World Bank decides on a development programme for this country. (b) How big does the help package from the World Bank need to be in order to be effective in the long-run? (Determine the required per capita capital transfer.) (c) What happens if the per capita capital transfer is smaller than required? (Explain why the steady-state income cannot rise in this case.) (a) Low population growth steady state: ∆

.

0 with .

. .

.

.

3

0.7

3

2.1.

High population growth steady state: ∆

0 with .

. .

.

2

.

. 0.7

2

1.4.

(b) In the high population growth steady state, the per capita capital stock is 4. Since n decreases as soon as per capita income is 2.5 (which implies a capital stock of 2.5 6.25), the per capita capital transfer of the programme needs to be 6.25 4 2.25 units high in order to be effective. (c) If the capital transfer is smaller than 2.25, the economy’s net savings remain negative (since the population still grows at the higher rate) and the higher per capita capital stock cannot be maintained. The help package in that case will not have a lasting impact on per capita income or consumption. It will however raise income and consumption temporarily. See Figure I10.1 for illustration.

Figure I10.1


rd


Exercise 10.8 . Consider an economy with the following production function: which grows at the constant rate 5% and the population growth rate is

.

, where 1%.

is human capital,

(a) Determine the steady-state levels of and ̃ for 0.2 and 0.1. (Hint: start by determining the steady-state condition for capital per human-capital-augmented efficiency unit labour.) (b) What are the growth rates of income, consumption and capital in the steady state? (c) What happens to per capita consumption, and why? Suppose now that the government wants to raise welfare and, therefore, starts an education reform, which raises from 5% to 10% at zero costs. (d) What are the short- and the long-run effects on per capita production, ̃ and per capita consumption? What do you conclude about the success of the education reform (does it unambiguously increase welfare)? (a) The steady-state condition here is: ∆

∆

0.

We then have: .

[η is the Greek letter "Eta"] . .

.

̃

.

1

. .

.

.

1.25 0.8

1.25

1. 6% in the steady state.

(b) Income, consumption and capital all grow at the same rate of

(c) Per capita consumption grows at 5%. Per capita variables grow at a slower pace than aggregate variables in the steady state because the population grows at a rate 0. (d) The increase in makes the investment requirement line steeper. This means that both in the short and in the long run, , and ̃ decrease. Nevertheless, the education reform does unambiguously increase welfare: An increase in the growth rate of human capital will both in the short and in the long run raise the per capita consumption growth rate and, thereby, per capita consumption. For welfare matters, this is the variable we are interested in.

Exercise 10.9 Recall our numerical exercise with data for Denmark and Sierra Leone in section 10.3. This time suppose the production function reads , which, after dividing both sides by , rewrites / √ √ . Given √ √ the data for , and 0.1, how many times higher would human capital have to be in Denmark in order to account for a 50 times higher level of per capita income? Assume 0. Let

denote output per efficiency unit of labour. In the steady state,

.

Using the numbers in the text, we can conclude that . .

.

Since 50

, and . .

.

2.02,

.

50

.

0.63.

:

15.59.

Human capital in Denmark would have to be about 15.6 times higher in order to account for the higher level of per capita income.

Exercise 10.10 Consider an economy with the per capita production function (a) How does the per capita capital stock evolve over time? (b) What happens to this economy if ? (c) What happens if ? 89 © Manfred Gärtner 2009

.

rd


(a) As we already know from Chapter 9, the equation describing the evolution of the per capita capital stock is: ∆

.

Plugging in the per capita production function for ∆

yields:

.

(b) If ,∆ 0, i.e. the per capita capital stock and with it per capita production and income in this economy will keep growing. (c) If ,∆ shrink to zero.

0, i.e. the per capita capital stock and with it per capita production and income will

Exercise 10.11 Again, let the production function be . Suppose now that 0.5, 0.2, (a) Determine the per capita consumption growth rate in this economy. (b) Where does growth in this model come from? (c) What would happen if the depreciation rate changed from 0.05 to 0.1?

0.03 and

0.05.

(a) Since per capita capital, production and consumption all grow at the same rate, we can simply calculate the per capita capital growth rate from ∆ : ∆

0.2

0.5

0.03

0.05

0.02.

The rate of per capita consumption growth is 2%. (b) In this model, growth is endogenous and comes from the constant returns to capital implied in the production function. Since the marginal productivity of capital does not decrease, the economy never stops growing. (c) If the depreciation rate rose from 0.05 to 0.1, the per capita capital stock (and thus per capita production and consumption) would start to shrink at a rate of 3% and would continue to shrink until 0.


11 Endogenous economic policy Chapter focus Chapter 11 makes the government, and, thus, fiscal monetary policy, an endogenous part of the economy. This is done by postulating that individuals (including voters, central bankers and politicians) have preferences over macroeconomic outcomes. This leads to a number of insights: 1. Political business cycles. Under certain conditions politicians may want to deliberately create cyclical movements of income and inflation, in order to improve re-election prospects. Since such business cycles are created for political reasons, they are called political business cycles. Conditions that foster the occurrence of political business cycles are: –Backward-looking voters. Voters who reward governments for what they achieved in the past rather than what they expect them to do in the future. Of course, it could also be that voters form expectations of future economic policy performance adaptively, from past experience. –Adaptive inflation expectations. There must be some exploitable nominal stickiness in the economy. Adaptive inflation expectations are but one possibility. If no such exploitable nominal stickiness exists, political business cycles may nevertheless occur occasionally, but not as a regular, repeating pattern. 2. Inflation bias. Under rational expectations the political business cycle, understood as a regular pattern, disappears. But an inflation bias remains. This permits the introduction of a host of new concepts that characterized recent policy discussions and research, including central bank independence, monetary policy conservativeness, or the game-theoretic analysis of policy decisions. 3. Policy rules. Policy rules are not discussed yet in an explicit fashion. But since it appears natural to replace the curve by such a rule when policy is endogenous, instructors may already want to introduce them here, or elaborate on their foundations, in case such a rule has been introduced on an intuitive basis in Chapter 8.

Exercises Exercise 11.1 Suppose that due to a shift in voters’ preferences, fighting inflation yields less political support compared with increasing output. How is this reflected in the slopes of the government indifference curves? What do these indifference curves look like if the public is entirely indifferent towards inflation? The less inflation matters to voters, the steeper the government’s indifference curves in income–inflation space. Steeper indifference curves reflect the fact that voters are willing to trade a larger increase in inflation for a given increase in output. If voters are entirely indifferent towards inflation, the government indifference curves become vertical (see Figure I11.1).


rd


Exercise 11.2 Let country A’s curve be 0.5 , i.e. it has slope 1 and normal output is 0.5. The public support or vote function is 49 0.5 . (a) What is the vote-maximizing inflation rate? (Hint: votes are maximized when the slope of the indifference curve equals the slope of . The math is much simpler If the indifference curve is solved for (and not for ) and its slope / is derived as a function of ). (b) Suppose inflation expectations are 0.5. Can the government win this election? (c) What are the government vote shares in the cases 0 and 1? (a) The vote-maximizing inflation rate can be found by substituting the curve into the public support function. The government then generates that inflation which maximizes 49

0.5

0.5

.

Differentiating this vote function with respect to and setting the derivative equal to zero yields the first-order condition for a maximum 1 0. The government’s optimal inflation rate is thus 1. The alternative approach suggested in the exercise is to solve the vote function for , which yields 49

0.5

and set its first derivative with respect to ,

⁄

(b) If the government chooses its optimal inflation rate then public support is 49

0.5

1

0.5

1

0.5

equal to 1 (the slope of

).

1 and if the inflation expectations are

0.5,

49.5.

The government cannot win this election; even if it chooses the vote-maximizing inflation rate, it still only receives a minority of votes. (c) To find out the respective vote shares, we simply plug the inflation rates into the vote function: 0 :

49

0.5

1

0

50.

1 :

49

0.5

1

1

49.

Exercise 11.3 The Fair election equation discussed in Case study 11.1 proposes that votes depend on the current income growth rather than the level of income. We may approximate this by postulating the support function 0.5 . Let the votes still be cast according to . (a) What does the political business cycle look like algebraically under these conditions, when the economy’s supply side is still standard , i.e. ? (b) Compare your result with the result provided in Box 11.1. What are the reasons for any observed differences? (a) Following the procedure described in Box 11.1 we obtain: 2 1 2

and .

Since the result is very similar to the one obtained in Box 11.1, see there for an interpretation of the result. (b) The amplitude of the swings of this cycle is twice as large. This is because now it pays double to create a non-election-period recession. Not only does such a recession now bring down inflation expectations, but it will also bring about higher income growth in the following election period (no matter what the current level of income is).

Exercise 11.4 Let country B’s is 95 0.5

curve be 10 .

0.5

, the same as country A’s in Exercise 11.2, while its vote function 92 © Manfred Gärtner 2009

rd


(a) By how much can B reduce its inflation bias by fixing the exchange rate between its currency and A’s currency? (b) What may keep B from entering such an exchange rate arrangement? (a) In a first step, we determine country B's inflation bias by substituting the support function 95

0.5

10 0.5

curve into the public

]

And from this deriving the first-order condition for a maximum, which is 10

0.

B’s inflation bias is thus 10. Since A’s inflation bias is 1, B could reduce its inflation bias by 9% points were it to tie its currency to A’s currency. (b) Whether fixing the exchange rate is attractive for B’s government depends on the effect of the lower inflation rate on the government’s public support. In fact, increase or decrease of political support depends on agents’ expectations about inflation. To see why, we consider the two cases of rational and adaptive expectation formation. After fixing the exchange rate, B’s curve will intersect the curve at A's inflation rate of 1%. Under rational expectations, the curve will also intersect in this same spot. Under rational expectations, B can thus lower its inflation rate considerably without any reduction of its output. The effect on public support in this case is unambiguously positive. In fact, the support for B's government would increase substantially from 95

0.5

10

95

0.5

100

95

0.5

10

95

0.5

1

10

0.5

50

to 10

0.5

99.5.

Under adaptive expectations of the form , the government would lose votes. This is easy to see once we notice that the curve stays put in the period where first shifts due to the fixing of the exchange rate. With staying put and shifting down because of the new exchange rate regime, the government will unambiguously lose votes and, starting from a vote share of 50%, will lose the election.

Exercise 11.5 We understand why a political business cycle (PBC) may occur if elections are to be held every two years. (a) What happens to the PBC if a coin is tossed each year and an election is called only if we have ‘tails’? (b) What happens to the PBC if a dice is rolled and only a six results in an election? (a) Under the coin toss scenario, the probability of having an election in the next period is always 0.5. The most important difference to the standard non-probabilistic model is that the government cannot be sure not to face an election in the period following an election period (in fact, there is always a chance of 50% that any period will turn out to be a non-election period). The government can thus not count on the opportunity to reduce inflation at low cost (in terms of votes lost) after a given election period. It must take this into account during any given election period. In particular, the government knows that a high inflation rate today will shift the next period’s curve, which will reduce the share of votes if an election is held. If the probability of an election is and if the government has an infinite time horizon but discounts future electoral successes with a discount factor of 0,1 , it can be shown that the government will optimally choose an inflation rate of

1

in election periods, and the

lowest possible inflation rate in non-election periods. For 0, the optimal inflation rate chosen during election periods is lower in the coin toss scenario than whenever elections are held regularly. The higher the probability of an election in the next period, i.e. the higher , the lower is the incentive for the government to raise inflation in any given current election period. (b) Since the probability of an election is 1/6 in this case, the inflation rate in election periods is higher than in (a). It is, however, lower than in the non-probabilistic scenario, because 1/6 0. 93 © Manfred Gärtner 2009

rd


Exercise 11.6 Suppose the popularity of a government in an economy with flexible exchange rates not only depends on inflation and income but also on the ‘strength’ of the domestic currency. How does this affect the government’s inclination to trigger off politically motivated monetary expansions? Do you think that putting ‘currency strength’ into the government’s utility function is a reasonable approach? If the ‘strength’ of the domestic currency also influences the government’s re-election prospects, the government has to take into account that expansionary monetary policy makes the domestic currency depreciate. The cost of inflation increases and the government indifference curves become flatter. For a given increase in output, voters are no longer willing to accept the same increase in inflation, for such an increase now also decreases their utility by making the domestic currency lose value. At first glance, it seems easy enough to reason that the exchange rate should indeed be incorporated into the government’s objective function, since the exchange rate influences the competitive position of domestic exporters. Note, however, that domestic exporters prefer a ‘weak’ domestic currency. The respective transmission channel is furthermore already incorporated in the model in the sense that monetary expansion stimulates output in the short run. All in all, it is quite difficult to justify why a weak currency in itself should harm a government.

Exercise 11.7 It was shown in this chapter that with a specific objective function of the government, the inflation bias amounts to / . Thus, the inflation bias increases with and decreases with . Explain intuitively the effect of these two parameters (Hint: for the influence of you have to go back to the derivation of the aggregate supply curve.) Why the inflation bias increases with 0.5

can easily be explained by looking at the public support function:

.

The higher , the stronger the influence of the level of output on public support and, consequentially, the stronger the government’s inclination to increase income through the generation of unexpected inflation. The negative effect of λ results from the specification of the curve: λ Y

Y .

λ is the slope of the curve in income-inflation space. If λ is high, is steep, and an increase in the inflation rate will have only a very moderate effect on income, or, to put it differently: with a high λ, the economy exhibits a short-term inflation-output trade-off that is not very favourable. The government in such an economy is less inclined to increase output by producing surprise inflation.

Exercise 11.8 In this chapter it was assumed that unions move first, choosing their expectations on inflation, and that the monetary authority decides on monetary policy afterwards. Assume a particular institutional framework that makes the government choose monetary policy first and lets the unions move second. Would such a reversal eliminate the inflationary bias? Pay-offs are as given in Table 11.1. If the government could credibly commit itself not to move after the trade unions had decided on the nominal wage rate, i.e. if the government had in fact no choice but to move first, such an institutional framework could indeed eliminate the inflationary bias. Moving first, the government would always choose not to use expansionary monetary policy, for if the trade unions knew what to expect, such a course of action would result in the highest possible pay-off for the government according to Table 11.1. (The government would receive a vote share of 45% and the real wage sum would remain unchanged. If the government as a first mover chose to expand the money supply, its vote share would fall to 42%. The unions moving second would in this case react by increasing the nominal wage rate, thereby keeping the real wage sum unchanged).


rd


Exercise 11.9 Consider the development of inflation in the United States and Germany from 1960 to 1990. Until 1973, the Deutschmark was tied to the US dollar by fixed exchange rates. Remember that in a system of fixed exchange rates a small country’s inflation bias is dictated by the larger country, to which its currency is tied. Does the graph you assembled support the hypothesis that Germany and the United States maintained such a relationship? Try to explain why the system of fixed exchange rates eventually broke down in 1973. Up until the mid-70s of the last century, inflation rates in the United States and in Germany were roughly equal (see Figure I11.2).

Figure I11.2 After 1973, US inflation started to rise, and throughout the 70s and early 80s, the inflation rate in the United States was much higher than in Germany. What led to the decoupling of the two inflation rates was the breakdown of the Bretton Woods system of fixed exchange rates in 1973. This breakdown was caused by an accelerating growth of the money supply in the United States, which eventually undermined the official parities defined within the Bretton Woods system.


12 The European Monetary System and Euroland at work Chapter focus This is the book’s first policy chapter. Using the European Union as a backdrop, its main thrust is to put the Mundell–Fleming model into the context of a real-world environment; by showing in a more realistic fashion how an individual country is affected by developments in other countries or the rest of the world, and by looking into how two countries of similar size interact under different international monetary arrangements, including the mainstays of flexible and fixed exchange rates, but the recent addition of a currency union as well. New concepts being introduced are: 1. The nth currency in a system of fixed exchange rates. This is used to study the effects on and risks for other EU members that originated from German unification, with the Deutschmark considered the nth currency within the EMS. 2. Exchange rate target zones. These are being used for two purposes. First, to reiterate and reemphasize the important role of expectations in the foreign exchange markets. The main insight from this is that target zones may stabilize the exchange rate compared to a system of flexible exchange rates, meaning they render the exchange rate less volatile even if the underlying fundamentals (variables such as money supplies) display the same volatility. 3. Credibility and self-fulfilling prophecy. The chapter also shows how the credibility of the bounds of target zones affects their power to stabilize, and it looks at the factors that determine credibility in this context. The theoretical insights are then used to interpret the speculative attack on the EMS that occurred in 1992 and resulted in Italy and the UK leaving the system. This discussion also adds to the discussion of self-fulfilling prophecy already touched on in Exercise 5.6. 4. Currency unions. In a final part, currency unions are being introduced. Key insights are there that monetary policy cannot be tailored to national needs any longer, and that expansionary fiscal policy has beggar-thyneighbour effects, which motivates pertinent restrictions such as the no-bailout clause and the EU’s Stability and Growth Pact.

Exercises Exercise 12.1 How would you check whether a country is in charge of the nth currency in a system of fixed exchange rates? 1. 2.

This country’s central bank does not have to intervene in the foreign exchange market. Hence official reserves (OR) in the balance of payments should be zero. In a system of fixed exchange rates, the country in charge of the nth currency dictates monetary policy. Hence one should try to establish whether there is a causal relationship between changes in the money supply in the country under consideration and other countries’ money supplies. There is some evidence that German monetary policy ‘Granger-caused’ changes in the money supplies in other European countries in the EMS (see e.g. Ronald MacDonald and Mark P. Taylor (1991), Exchange Rates, Policy Convergence and the European Monetary System, Review of Economics and Statistics, 73, 553–558).


rd


Exercise 12.2 Suppose that a small open economy within the EMS went through a transformation similar to that following German unification. How would the course of events differ from that induced by German unification (Hint: it is crucial to note at the outset what distinguishes a small open from a large economy.)? From a macroeconomic perspective, the crucial element in the chain of events surrounding German unification was that changes in the German interest rate affected interest rates in other European countries and thus drove them into recession. By definition, a small open economy is unable to influence the interest rates of other countries. Instead, it takes the ‘world interest rate’ as exogenously given. In the Mundell–Fleming model, a ‘unification-like’ fiscal expansion in a small open economy would shift the curve to the right. The resulting upward pressure on the interest rate would within a system of fixed exchange rates lead to a rightward shift of the curve (expansion of the money supply). In the – model (and assuming we started from a long-term equilibrium point), output would as a result of the fiscal expansion exceed potential output. Prices would increase, the real money supply would decrease, and the real exchange rate would appreciate until government spending would have perfectly crowded out net exports. Back in the Mundell–Fleming model, and would in this way return to their original positions (with output back at potential output and the interest rate back at the level of the world interest rate). All other economies would remain unaffected by these events.

Exercise 12.3 Recast the policy issues surrounding German unification and the 1992 EMS crisis in the – model. Recall that Germany controls the nth currency and thus determines the system’s interest and inflation rates. The – model can be used to illustrate the (actual and potential) course of events surrounding German unification. However, the basic model presented in Chapter 8 has to be extended in order to incorporate some additional insights gained in this chapter:

First, the model in Chapter 8 was based on the assumption that the economies under consideration were small, i.e. the interest rate was assumed to be exogenously given by the world interest rate. For this reason, the money supply did not appear in the curve when the exchange rate was fixed. However, as discussed in this chapter, such an assumption is not valid for Germany, because its monetary policy affects other countries' interest rates. Hence both fiscal and monetary policy variables appear in the German curve, which can be written as ∆

.

Second, the situation before and during German unification was characterized by the fact that not only the fiscal and the monetary policy variables were considered uncertain, but agents’ information about was also incomplete. potential output

Given these additional insights, we can graph Germany’s initial situation and its long-run equilibrium after unification (see Figure I12.1). The initial situation is represented by point A, which marks the intersection of the and the equilibrium aggregate demand curve ( . pre-unification equilibrium aggregate supply curve ( In the long-run equilibrium after unification, and have to intersect on the post-unification curve ( . The position of the latter is determined by unified Germany’s potential output. Note that both the conversion of East German currency into Deutschmarks and the transfer flows to Eastern Germany were one-time changes in the money supply and the level of government expenditure, respectively. This means that in the long run, the money growth rate moved back to its initial value and government expenditures were no longer subject to change (i.e. ∆ 0), which in turn implies that the long-run aggregate demand curve ( has to lie to the (assuming that period 1 was the period of unification). In the long run (which in Figure I12.1 is left of and ), inflation is back at its initial level, and income is higher than premarked by the intersection of unification income, but lower than it temporarily was under the influence of fiscal and monetary expansion.


rd


Figure I12.1 To determine the path of output and inflation during the transition, we have to follow the shifts of and . ) is determined by the increases in the money supply and government The initial shift of the curve (to expenditure. The initial shift of the curve depends on agents’ expectations. To establish the magnitude and the direction of this shift, we thus have to first make assumptions about the way expectations are formed (e.g. whether they are formed adaptively or rationally) and we have to establish what information was available to agents before implementation of the policies. We here assume that expectations were formed rationally and that agents were well informed about the increase of the money supply, but that both the government and the private sector underestimated the size of the hike in government expenditure and overestimated the level of unified Germany’s potential output (as the text in Case study 12.1 suggests). If individuals had perfectly anticipated both the magnitude of the additional government expenditure and the (where ‘FI’ stands for full information). level of potential output, the curve would have shifted to Output would have jumped to its new long-run level immediately. Given that the expectations concerning potential output were exaggerated and the change in government expenditure was underestimated, agents underestimated inflation and the curve did not adjust completely. The result was a temporary increase of output above its potential level (cf. point B in Figure I12.1). In period 2, without active policy intervention from the Bundesbank, the money growth rate and government term would have prevented the expenditure would have returned to their initial levels, and only the curve from shifting to its initial position. Without policy intervention, would thus have shifted into , (where ‘NR’ stands for ‘no reaction’). However, the Bundesbank’s reaction in the second period implied a . The shift of negative growth rate for the money supply, and the aggregate demand curve shifted into depends again on agents’ expectations of the inflation rate. Since the Bundesbank’s restrictive monetary policy , and output fell below potential output in period 2 was not anticipated, we may assume that shifted into (cf. point C in Figure I12.1). In period 3, output finally reached its long-run equilibrium, but due to the term in -level (period 3 short-term equilibrium is not shown in Figure I12.1). In , inflation was still below the and , with period 4, the economy finally settled into its long-run equilibrium at the intersection of output standing at the new unified potential output and inflation back at the long-run money growth rate.

Exercise 12.4 Consider the following EU members’ exports to Germany as a share of GDP. In the context of the Mundell– Fleming model, why does this suggest that option #1, to stay in the EMS, was less painful for the Netherlands than it was for Italy, France or the United Kingdom? NL I F GB

Exports to Germany as share of GDP 0.16 0.04 0.04 0.03

As a consequence of unification, Germany’s output expanded, resulting in an (exogenous) increase of export demand for all of Germany’s trading partners. The relative strength this effect had on the different trading partners depends on the intensity of trade relations. The table suggests that the Netherlands benefitted much more from increased German export demand than did Italy, France or the United Kingdom. Hence the negative 98 © Manfred Gärtner 2009

rd


impact of the rising interest rate on income was at least in the Netherlands perceptibly mitigated by the exogenous demand increase, making it less painful for the Netherlands to stay in the EMS.

Exercise 12.5 In this chapter you were introduced to the concept of a ‘random walk’ (Equation 12.3). To make this concept less abstract, generate your own random walk over 20 periods. This may be done as follows: toss a coin and write a ‘1’ if heads occur and ‘−1’ if tails occur. Repeat this and add the result of the second round to the previous outcome (remember that the equation characterizing a random walk was , where is a random disturbance – the outcome of the coin, in our case). Toss a third time and add the result, etc. What specific properties do you observe (Repeating this exercise may give you an even better idea about the properties of a ‘typical’ random walk.)? The central property of a random walk is its high degree of persistence: downward or upward swings of a time series tend to last over several periods. If we consider zero to be the long-run equilibrium of the variable , a onetime deviation from this equilibrium will usually take some time to be reversed (see the example of Figure I12.2).

Figure I12.2

Exercise 12.6 Recall that in Equation 12.1 the exchange rate was described as a weighted average of the money supply and expectations: 1 . We learned that when the central bank is known to intervene in the foreign exchange market after a shock, so as to return the exchange rate all the way to target values of zero next period, the exchange rate response line reads . Now suppose the central bank considers 0 a long-run target only and gives itself more time to reach it. (a) What does the exchange rate response line look like graphically when the central bank intervenes less vigorously in the described sense? (b) To make it more precise, suppose the central bank always aims at the middle between the exchange rate observed last period and the long-run target the market always expects the exchange rate 0.5 . Derive the exchange rate response line formally for this case. (a) To derive the exchange rate response line for the case of a weakly intervening monetary authority, we first look at the two extreme cases of a central bank which does not intervene at all and one that intervenes vigorously. The response line of a weakly intervening central bank then lies somewhere in between these two cases. Non-intervening monetary authority: If the market does not expect the money supply to change, its . If these expectations are substituted into the equation above, we exchange rate expectation is get the exchange rate response line . Its slope and intercept are independent of and the monetary authority’s target exchange rate. This is reflected by the grey line in Figure I12.3. 99 © Manfred Gärtner 2009

rd


Intervening monetary authority: Since the market expects the monetary authority to drive the exchange rate back to its target level irrespective of what happens to the money supply, we can substitute ̂ 0 into the exchange rate response line equation given above to get 1 0 . The exchange rate response line for a vigorously intervening central bank is given by the black line in Figure I12.3 Weakly intervening monetary authority: The exchange rate response line for a less vigorously intervening central bank lies between the two extreme cases described above. It is represented by the dashed black line in Figure I12.3.

Figure I12.3 (b) With

0.5 , Equation 12.1 becomes

2 Since 0

1

0.5 . Solving for the exchange rate

yields

. 1, we have 0

0.5 and

2 / 1

. The slope A of the exchange rate response

line thus satisfies 1. By this we have already shown formally that the exchange rate response line of a weakly intervening central bank lies between the lines of a non-intervening and a fully intervening monetary authority.

Exercise 12.7 Consider the stylized European Economic and Monetary Union comprising only two countries A and B. Suppose and are subject to occasional stochastic shocks (see our discussion in Box 3.5). Would you recommend the ECB to fix the money supply or to fix the interest rate if it wants to stabilize income? Discuss the issue under different assumptions about the nature of the shocks, which can either be synchronized (the same in both countries) or country-specific. This yields four constellations you need to discuss as listed in the following matrix: curve stochastic Synchronized shocks Country-specific shocks

(a) (c)

curve stochastic (b) (d)

If the curve is stochastic, say due to shocks to parameters that determine money demand, (cases (a) and (c)), it is always better to opt for fixing the interest rate. By fixing the interest rate, any shock to the curve will always be endogenously compensated by adjustments of the money supply, so that the curve will always remain in its original position. If the IS curve is stochastic and shocks are synchronized (case (b)), it is better to fix the money supply. As was shown in Box 3.5, this will make the deviations from potential output smaller. In case (d), the decision whether the interest rate or the money supply should be fixed is harder to make. As illustrated in Figure I12.4, a fixed interest rate will lead to more pronounced deviations from potential output in the country where the shock occurs, but will leave the other country unaffected, whereas fixing the money supply will reduce the deviation in the country where the shock occurs, but will cause the interest rate and output in the 100 © Manfred Gärtner 2009

rd


other country to change as well (the interest rate will move in the same direction and to the same degree in both countries, output will move in opposite directions).

Figure I12.4

Exercise 12.8 Suppose the two-country currency union discussed in the text is small when compared with the rest of the world, how, then, does an increase in Belgium’s government spending affect incomes in Belgium and Austria (assume A and B do not trade with each other, but do trade with the rest of the world) (a) when the exchange rate versus the rest of the world is flexible? (b) when the exchange rate versus the rest of the world is fixed? If the two-country currency union is small compared with the rest of the world and capital markets are perfectly integrated, the (equilibrium) interest rate of the currency union is fixed at the level of the world interest rate. (a) As in Section 12.5, an increase in Belgium’s government spending shift the curve in Belgium to the right and puts upward pressure on the Belgian interest rate (see Figure I12.5; 1.). Because of the currency union (CU) between Belgium and Austria, money will in reaction to this move endogenously from Austria to Belgium until the interest rate is the same in both countries (2.). The interest rate in the ) is now higher than the world interest rate . With flexible exchange rates between currency union the CU and the rest of the world, the temporarily high interest rate in the CU increases demand for CU currency, and the CU currency appreciates. Net exports of both Belgium and Austria decrease and the curves in both countries shift left (3.). This means that the negative income effect on Austria will be even more pronounced than it originally was, and the positive income effect in Belgium will be somewhat diminished.


rd


(b) With fixed exchange rates, the CU central bank has to increase the money supply in response to an . In equilibrium, Austria’s income in this case remains unaffected by Belgium’s excessive increase in government spending. Belgium benefits from a maximally large increase in income, for the rightward shift of induced by the increase in government expenditure is fully matched by a rightward shift of (see Figure I12.6).

Figure I12.6


13 Inflation and central bank independence Chapter focus This is another policy chapter that both applies previously introduced concepts and adds extensions of these concepts as needed. The macroeconomic concept on which the chapter is built is the model. The political perspective is that of policymakers, governments or central banks, who are utility maximizers. The point of departure is the lesson learned in Chapter 11 that under rational inflation expectations democracies tend to end up with an inflation bias, and that the magnitude of this bias depends on the preferences that govern monetary policy, on instrument potency, and on the macroeconomics constraint (or trade-off). The chapter’s first section looks at these determinants from the perspective of international experience, with a focus on the European Union. The second section makes the model stochastic and, thus, more realistic, by adding random supply shocks to the curve. The important insight derived from this is that the popular remedy to the inflation bias, namely, to appoint arch-conservative central bankers and make them independent of governments, generates a stabilization bias. Such a central bank would tolerate too much volatility in income and unemployment in favour of little volatility in inflation. A third topic is the sacrifice ratio. After introducing the concept in the abstract, its empirical relevance is illustrated by means of real-world experiences. The point to emphasize is that while a reduction in inflation engineered by the central bank does not depress income permanently, income is lost in transition. These losses materialize as a lasting loss of wealth, or a reduction of permanent income. The chapter’s main insights are then used to draw some lessons for European monetary integration in general and the European Economic and Monetary Union (EMU) in particular.

Additional boxes Box B13.1 The SAS curve under fixed and flexible exchange rates Let the world consist of Germany and Italy only when both still had their national currencies. German consumers purchase a basket of goods containing a share of goods produced in Germany and a share 1 of goods produced in Italy. If the and respectively, the prices of these goods are . The lira German price index is prices of goods produced in Italy need to be multiplied by the DM/lira exchange rate to obtain their equivalent in marks. Taking logarithms of the price index equation and taking first differences then we obtain the following equation (in percentage rates of change): ∆

∆

1

∆

1

∆

Fixed exchange rate Fixing the exchange rate eliminates the middle term on the right-hand side (∆ 0 . Any change in German consumer price inflation is now a weighted

average of the domestic inflations of German and Italian goods: ∆

∆

1

∆

(1)

The control of the Bundesbank over both countries’ money supplies makes both economies function (on the aggregate level) like one economy. But then ∆ . Substituting this into Equation (1) gives ∆ ∆

∆

An increase in consumer price inflation by 10% points goes hand in hand with a 10% points increase in producer price inflation. This raises output by 10% as well if has slope 1. Flexible exchange rate Under flexible exchange rates the Banca d’Italia operates independently, isolating Italian producer prices from Bundesbank policy (for ease of 0). Any change in exposition, suppose ∆


rd


German consumer price inflation is now a weighted average of changes in German producer price inflation and exchange rate depreciation: ∆

∆

1

∆

(2)

Recall from Chapter 8 that when prices are sticky – which is what a positively sloped curve indicates – the real exchange rate depreciates as we move up . In other words, the initial exchange rate response is larger than the initial response in producer prices: ∆

∆

Substituting this inequality into Equation (2) gives ∆

∆

So when the Bundesbank generates surprise inflation, the initial effect on consumer prices is larger than the initial effect on producer prices. by less than 10%. Hence Raising by 10% raises output is raised by less than 10% as well. As a result, a steeper curve obtains under flexible exchange rates. Equation (2) suggests that flexible exchange rates make steeper, the more open the economy (as measured by ) is.

Exercises Exercise 13.1 Cukierman has provided another index of central bank independence. His values for the countries shown in Figure 13.2 are, where available, given in Table 13.1. Average inflation since 1973 is also given. Transfer the data onto a graph and judge visually whether the result obtained in the text also holds with this new index. Table 13.1 Country CBI Average inflation in % Country CBI Average inflation in %

A 0.31 8.91

AUS 0.58 4.72

B 0.19 5.89

DK 0.47 7.52

FIN 0.27 8.61

F 0.28 8.5

D 0.66 3.7

IRL 0.39 10.15

I 0.22 12.13

JP 0.16 5.23

NL 0.42 4.49

E 0.21 11.96

S 0.27 8.3

CH 0.68 4.04

GB 0.31 9.86

USA 0.51 6.24

The scatterplot shown in Figure I13.1 confirms the hypothesis that central bank independence is negatively correlated with average inflation. The correlation is not very strong, however. Japan and Belgium for example had relatively low inflation rates even though according to the Cukierman index, their central banks were not very independent.

Figure I13.1


rd


Exercise 13.2 Let a country’s stochastic curve be given by , where equals 5 in 50% of the cases and −5 in the other 50%. The government’s indifference curves are ellipse shaped, as postulated in the chapter. Whenever 5, inflation is set to 2%; when 5, inflation is 10%. (a) What is the rationally expected inflation rate? (b) Let 100. What are the income levels in periods of positive supply shocks and in periods of negative supply shocks, respectively? (c) What do the observed inflation rates tell you about where the government’s desired output is, relative to potential output? (a) Since inflation is 10% in 50% of the cases and 2% in the other half, the rationally expected inflation rate is 0.5 2% 10% 6%. (b) If we plug in 6% for For For

5: 5:

and 100 for 100 100

in the stochastic

curve we get:

2 6 5 101. 10 6 5 99.

(c) Since the government chooses to set 0 even in the event of a positive supply shock, it must be that the government’s desired output is above potential output (The intuition of this argument can easily be grasped from Figures 13.9 and 13.12).

Exercise 13.3 Let a country’s supply side be represented by the curve . Inflation expectations are being formed adaptively ( ). Suppose the country’s central bank decides to bring inflation down from 8% to 1%. The disinflation process starts in period 1 and follows this pattern: 4% in period 1; 2% in period 2; 1% in period 3 and after. (a) Compute the aggregate income losses and the sacrifice ratio. (b) Display your results in a – diagram. Compare your diagram with the Swiss disinflation engineered between 1974 and 1978, which is shown in the chapter. (a) Inflation , inflation expectations Table I13.1 Period

0 8% 8% 0

1 4% 8% 4

and output losses 2 2% 4% 2

3 1% 2% 1

are given in Table I13.1. 4 1% 1% 0

From this, one can easily compute the sacrifice ratio 1. (b) Figure I13.2 shows the disinflation process in our model economy (black arrows, circles) and the disinflation that took place in Switzerland between 1974 and 1978 (dashed grey arrows, squares). It is 100. Figure I13.2 shows that possible to draw both histories into the same graph if we assume that the disinflation costs in Switzerland were higher than the costs our model economy has to bear.


rd


Figure I13.2 Exercise 13.4 One disinflation engineered by the Bank of England began in the second quarter of 1980 and ended in the third quarter of 1983. At the start of this period, trend inflation was at 16.6%, at the end it was 4.4%. Real Gross Domestic Product (GDP) during this episode is given in Table 13.2. (a) Compute the aggregate income losses that may be attributed to this disinflation. (Assume that GDP was at its potential level in the second quarter of 1980 and again in the third quarter of 1984. Assume that potential income would have moved linearly from the first value to the second, had the disinflation not been implemented.) (b) Compute the sacrifice ratio for this disinflation episode. Table 13.2 Quarter UK real GDP* Quarter UK real GDP*

80.2 423.9 82.3 425.8

80.3 421.1 82.4 428.2

80.4 416.0 83.1 436.7

81.1 415.6 83.2 438.0

81.2 415.2 83.3 442.2

81.3 420.6 83.4 446.7

81.4 420.7 84.1 451.6

82.1 421.8 84.2 449.4

82.2 425.2 84.3 449.2

*In billions of pounds sterling (at 1990 prices).

(a) To compute potential output during the disinflation episode, we first determine the linear equation that characterizes the straight line connecting output in the second quarter of 1980 (80.2) and output in the third quarter of 1984 (84.3). To do this, we consider 80.2 as period 0 and 84.3 as period 17. We then have to compute the parameters and in the linear equation , with t running from 0 to 17. From Table 13.2 we know that 423.9 0 and 449.2 17. These are two equations in two unknowns, and it is easy to compute 423.9 and 449.2 423.9⁄17 1.488. Using the formula 423.9 1.488 , we can compute potential output and, subsequently, output losses for every period in the disinflation episode. The results are given in Table I13.2. Output losses for periods 83.4 through 84.3 were not calculated since according to the exercise, these losses do not enter the sacrifice ratio. Table I13.2 Quarter UK real GDP* Potential GDP Output loss Quarter UK real GDP* Potential GDP Output loss

80.2 423.9 423.9 0 82.3 425.8 437.3 11.5

80.3 421.1 425.4 4.3 82.4 428.2 438.8 10.1

80.4 416.0 426.9 10.9 83.1 436.7 440.3 3.6

81.1 415.6 428.4 12.8 83.2 438.0 441.8 3.8

81.2 415.2 429.9 14.7 83.3 442.2 443.2 1.0


81.3 420.6 431.3 10.7 83.4 446.7 444.7 –

81.4 420.7 432.8 12.1 84.1 451.6 446.2 –

82.1 421.8 434.3 12.5 84.2 449.4 447.7 –

82.2 425.2 435.8 10.6 84.3 449.2 449.2 –

rd


(b) The sacrifice ratio can be computed by adding all output losses from period 80.2 through 83.3 and dividing this sum by the reduction in the inflation rate. This yields the sacrifice ratio 118.6⁄12.2

9.72.

Exercise 13.5 Your country is stuck in an inflationary equilibrium with curve with adaptive expectations :

10% and

100. The economy is given by a

0.1 and the

curve 0.5

.

denotes oil price inflation. Although it would like to, your government does not dare to reduce inflation, since it does not want to bear the accompanying disinflation costs. Now in period 1, oil prices are cut in half permanently ( 50% . , (a) By how much can inflation be reduced in period 1 without affecting income? (b) What is the appropriate monetary policy that keeps income at 100 (Compute , , and .)? (c) What happens if the government uses the opportunity to reduce inflation, immediately and permanently, to 0 (Trace and .)? (d) Answer Questions (a)–(c) assuming that the fall in oil prices lasted only 1 year. (a) To find the inflation rate that keeps output at its potential level, we have to compute such that in the curve. Hence 10 0.1 50 5. Note that to achieve the goal of constant output, the growth rate of the money supply has to be reduced, too. This becomes evident if we substitute 5 into the curve and take into account that . We then get that

5.

(b) We first calculate the inflation rate for each period using the curve and imposing . This inflation rate can then be plugged into the curve to determine the necessary money growth rate (note that implies for all periods). Period 1: 10

5

5 5

Period 2: 5 5 Period 3: 5 5 5.

We thus have

(c) We can use the curve to curve to compute output in each period, given the central bank’s commitment to keep inflation at zero. can then be substituted into the curve to determine the money growth rate necessary to inflation at zero. Period 1: 0 0

10

100 5 0.5 95 100

95 2.5

0 0

0

100 0.5 100 95

100 2.5

0 0

0

100 0.5 100 100

100 0

Period 2:

Period 3:


rd


The answer to Question (a) remains the same irrespective of whether the oil price shock is permanent or transitory. The answer to Question (b) is different, however, once the shock is only transitory. It is essential to remember that oil price inflation in the last term of the oil-price augmented curve is an approximation of the change in the logarithm of the price of oil. This approximation is not precise enough and should not be used when a variable changes more than 10% or maybe 20%. The problem can be illustrated by letting the price of oil fall by half from 1 to 0.5 in period 1 and rise back to 1 in period 2. Then oil price inflation would be 50 % in period 1 and 100 % in period 2. Plugging these numbers into , the curve would shift up more in period 2 than it originally shifted down in period 1. To avoid this, we take the correct route and write the last term in its original form as 10 ln ln . We note that ln ln 1 0, ln ln 0.5 0.69, and ln ln 1 0. This gives , , , the following results for periods 1, 2 and 3. Period 1: 10

6.9

3.1

3.1

6.9

10

3.1

Period 2: 10

Period 3: 10

10

We thus have 3.1 and 10. If income is to be kept at its potential level, inflation and the money growth rate can only temporarily be reduced once the oil price shock does not last. The answer to Question (c) also changes. Period 1: 0 0

10

100 6.9 0.5 96.9 100

96.9 1.55

0 0

0

100 6.9 0.5 93.1 95

93.1 0.95

0 0

0

100 0.5 100 93.1

100 3.45

0 0

0

100 0.5 100 100

100 0

Period 2:

Period 3:

Period 4:

If the oil price shock is only temporary, the income losses that accompany a permanent reduction of inflation to zero are twice as large as the losses incurred under the permanent shock scenario. Only in period 4 will the economy reach its new equilibrium (with income back at potential income and a money growth rate of zero).

Exercise 13.6 Consider a economy that is regularly hit by supply shocks. The distribution of these shocks is bellshaped. Figure 13.23 shows the distribution of inflation and income that results when the preferences of the independent central bank and the public are identical. (a) Now a new and a more conservative central bank president is appointed. How does this affect the shapes and positions of the above distributions? (b) A more conservative central bank provides lower inflation. What may be the disadvantage of an ultraconservative central bank? (a) How the distribution of inflation and income changes once a more conservative central bank president takes office is shown in Figure I13.3: The continuous line shows the distribution before, the dashed line the distribution after the appointment of the new president. The inflation bias and the standard 108 © Manfred Gärtner 2009

rd


deviation of the inflation rate are lower than in the initial situation. By contrast, fluctuations in income have increased.

Figure I13.3 (b) Society not only prefers price stability over high inflation, but also high or predictable income levels over low income or unpredictable income deviations. Under an ultra-conservative central bank, supply shocks translate fully into income fluctuations. The central bank thus allows income (and employment) to be more volatile than considered optimal from the viewpoint of society. This suboptimal stabilization is called a stabilization bias: An increased focus on stabilization would raise society's utility.


14 Budget deficits and public debt Chapter focus This chapter looks at taxes and government spending from a new angle. Chapters on booms and recessions, mainly Chapters 2–5 and 7–8, had focussed on the demand-side effects of deficit spending. Chapter 10 on economic growth had focussed on the effects of deficit spending on capital formation and, hence, on the supply side. In both cases the longer-run repercussions of government budget deficits were ignored namely, that any deficit we run today adds to debt and needs to be serviced by interest payments tomorrow. By taking a closer look at the government budget, Chapter 14 reveals that there is a dynamic interaction between the government budget deficit in a given year and the accumulated public debt of a country. This interaction may be condensed into a dynamic equation for the debt ratio that takes the form of a linear first-order difference equation. If students are familiar with the required math, instructors may use the opportunity to draw on that knowledge and analyse debt dynamics in a more technical fashion. Instead, the chapter opts for a graphical approach and introduces phase diagrams as a tool for a qualitative analysis of dynamic economic models. The derived difference equation describes a purely technical relationship derived from the government balance sheet. And though the chapter discusses at some length how the dynamic properties of debt dynamics is affected by economic variables such as the real interest rate and economic growth, debt dynamics is not really integrated into a macroeconomic model. This needs to be stressed and, if time permits, may be used to motivate extended discussions, say, of how debt responds in the short run, when deficit spending spurs income growth, or of what kind of long-run relationship the Solow growth model implies between the real interest rate and income growth.

Exercises Exercise 14.1 Table 14.3 presents data on debt and GDP for a number of European countries in 1992. Compute the debt ratios and determine the level of debt that would just meet the Maastricht criterion of 60% of GDP. See Table I14.1. The debt ratio is computed by dividing nominal government debt by nominal GDP. The level of nominal debt that is still compatible with the Maastricht criterion is computed by multiplying nominal GDP with 0.6. Table I14.1 Country Nominal GDP Government debt Debt ratio ( / Debt for 60%

)

Germany 3076.6 1402.5 0.46 1846.0

France 6776.2 3076.1 0.45 4065.7

Italy 1504.0 1755.22 1.17 902.4

UK 597.2 284.9 0.48 358.3

Belgium 7098.4 9306.0 1.31 4259.0

Denmark 851.3 627.4 0.74 510.8

Finland 476.8 220.3 0.46 286.1

Greece 18,238.1 16,140.7 0.88 10,942.9

Exercise 14.2 Consider a country with a primary deficit ratio of 2%, an income growth rate of 5% and a real interest rate of 3%. (a) What is the equilibrium debt ratio ? Is the equilibrium stable? (b) What is the deficit ratio in the long-run equilibrium? 110 © Manfred Gärtner 2009

rd


(c) The government wants to increase the primary deficit to 3.5% of national income. What is the debt ratio in the new equilibrium? What is the deficit ratio? (d) Suppose the country wants to meet the Maastricht criterion of a maximum debt ratio of 60%. What would be the primary deficit that would just meet this criterion? (e) Unexpectedly, the interest rate rises to 4%, whereas the growth rate decreases to 2%. What is the new equilibrium debt ratio ? Starting from a primary deficit of 20%, does the country have a chance of reaching that equilibrium? (a) Given the parameter values from the exercise and the debt ratio dynamics equation ∆ , we can compute the equilibrium debt rate . .

.

1.

The equilibrium is stable since the slope of the phase line

is negative.

(b) The long-run deficit ratio can be computed by plugging the equilibrium debt ratio calculated in (a) into the equation for the deficit ratio: ∆ /

.

Assuming ∆ /

and plugging in the respective numerical values we get 0.02

0.03

1

0.05.

(c) Substituting the new primary deficit ratio into the equilibrium debt ratio equation, we get ⁄

0.035⁄ 0.05

0.03

1.75.

The deficit ratio is then computed as in (b): ∆ ⁄

0.035

0.03

1.75

0.0875.

(d) Plugging the target equilibrium debt ratio solving for the target primary deficit

into the equation defining the equilibrium debt ratio and yields

⁄ 0.6

0.02

0.012.

(e) Substituting the new real interest rate and the new growth rate into the equation for the equilibrium debt ratio we get ⁄

0.2⁄ 0.02

0.04

10.

This long-run equilibrium is not stable, since the slope coefficient is positive. This means that if the economy starts from a debt ratio other than (-10), it will move away from this long-run equilibrium.

Exercise 14.3 In this chapter, both the interest rate and the growth rate were taken as exogenously given. However, the Solow growth model presented in Chapter 9 provides us with the tools to determine whether, for a given country, the growth rate of income will be higher or lower than the interest rate in the steady state (Recall that the interest rate equals the marginal product of capital and the net interest rate is the interest rate minus the rate of depreciation.). Determine the relation between the growth rate of output and the interest rate for the following: . (a) Country A, where the production function is (where is output per efficiency unit), the savings rate is 20%, the exogenous rate of technological progress is 0.04, the population growth rate is 0.02 and the annual depreciation rate is 10%. . (b) Country B, where the production function is (where is output per efficiency unit), the savings rate is 30%, the exogenous rate of technological progress is 0.05, the population growth rate is 0.01 and the annual depreciation rate is 10%. (c) Are both countries dynamically efficient?

In the following, we first derive general formulas and only in a second step fill in the parameter values for countries A and B. 111 © Manfred Gärtner 2009

rd


The steady-state capital stock per efficiency unit can be computed from

The implied level of the interest rate (which is determined by the marginal product of capital net of the depreciation rate) is . In the steady state, the growth rate of national income is ∆ ⁄ . The difference between the growth rate of income in the steady state and the real interest rate can be computed as follows: . By plugging the parameter values into the general formulas we obtain: (a) Country A: .

.

0.02

0.04

0.1

0.08

.

.

0.01

0.05

0.1

0.107

.

.

1.375

.

2.01

.

(b) Country B: . . .

(c)

.

.

.

.

.

. .

: Plugging the respective parameter values into the formula for golden rule capital stocks in both countries: Country A:

.

.

2.455

1.375

.

.

0.593

2.01

.

Country B:

.

gives numerical values for the

.

A is dynamically efficient B is dynamically inefficient. Note: The Golden Rule requires . But then . Stable debt dynamics, requiring , only obtains if the savings rate is too high. But such a situation should be ruled out for being dynamically inefficient. So stable debt dynamics should not occur frequently in the real world. This result may not hold under imperfect competition, the presence of externalities, or when the government pays lower interest rates than firms.

Exercise 14.4 In 1994, British nominal interest rates were 7.83%, inflation was 2.67% and real GDP growth stood at 4%. The primary deficit ratio was 4.3%. What is the equilibrium debt ratio, assuming that , , and ( ) remain unchanged? Is the equilibrium stable? To compute the equilibrium debt ratio, we first need to find the real interest rate, which is the difference between the nominal interest rate and the inflation rate. Hence: 0.0783

0.0267

0.0516.

We can then plug the real interest rate into the equation defining the equilibrium debt ratio: . .

.

3.71.

The equilibrium is unstable (the real interest rate is higher than the real GDP growth rate).


rd


Exercise 14.5 Let debt dynamics follow the familiar equation . The interest rate includes a risk premium

,

. and the

increases linearly with the debt ratio: .

(a) Derive the phase line and discuss this country’s debt dynamics. Do your results and insights differ from those obtained for the simpler model discussed in the text? Suppose income growth exceeds the risk-free real interest rate which leads to the phase line shown in Figure 14.20. Our country is currently in point A.

Figure 14.20 (b) Where will your country's debt ratio move in the near future and eventually come to rest? Are there other equilibria? (c) While we are still in A, will it lower or raise the debt ratio if the government increases spending? Distinguish between the short run and the long run. (a) Substituting phase line ∆

for the interest rate

into the debt dynamics equation, we arrive at the modified .

Around a debt level of zero, the quadratic term is negligible, and the modified phase line and, thus, debt dynamics are close to the standard setup. However, as the debt level increases, the quadratic term grows exponentially, which makes it even harder to turn around unsustainable debt dynamics than previously assumed. (b) In point A, ∆ 0. This means that the debt ratio decreases. The country moves towards point C, which is a stable equilibrium. Point B is another equilibrium, but since the phase line exhibits a positive slope in point B, it is an unstable equilibrium. (c) A higher primary deficit shifts the phase line up. If the shift is large enough, no point of intersection between the ∆ -curve and the horizontal axis will remain. If this is the case, there will be no equilibrium point left in the model that could possibly be reached. Instead the debt ratio keeps increasing without end (since ∆ 0 at all times).

Exercise 14.6 In chapter 9 the dynamics of the Solow model was described by the nonlinear difference equation ∆ , . Please discuss the dynamic behaviour of the Solow model in a phase diagram by drawing the phase line and discussing its properties. Since the Solow diagram visualizes the difference between the savings-and-investment line , and the requirement line , it is easy to graphically derive the phase line Δ , from it (see Figure I14.1). 113 © Manfred Gärtner 2009

rd


Figure I14.1 The phase diagram for the Solow model capital stock dynamics then shows that there are two possible equilibria: Point A (which is the equivalent to the steady-state capital stock in the Solow model) represents a stable equilibrium. No matter what point the economy starts from (with the exception of point B), it will always end up in A. Point B (with zero capital stock and income) represents a degenerate equilibrium. As long as the economy is stuck in it, it will not grow. However, the slightest deviation from B is enough to trigger capital stock growth which will only come to a halt once the economy ends up in A.

Exercise 14.7 Consider a country with a primary deficit ratio of 25%, an income growth rate of 4%, a real interest rate of 6% and a debt ratio of 75%. Suppose that in preparation for entry into European Monetary Union, the government wants to stabilize the debt ratio by means of money creation, assuming an initial level of the real money supply of 41% of GDP. (a) By how many percentage points does the government have to reduce the primary deficit ratio in order to stabilize its debt ratio? Notice that to qualify for EMU this country also has to fulfill the criterion of not exceeding the EMU target inflation rate of 2% by more than 1.5 % points. (b) Is the reduction of a country's deficit ratio always a reasonable course of action? What arguments speak against a reduction in government spending? (a) The generalized formal description of debt ratio dynamics is ∆

.

To stabilize the debt ratio at 75%, the primary deficit ratio has to satisfy 2%

75%

3.5%

41%

0.00065

0.065%.

The government has to reduce its primary deficit ratio by slightly more than 25% points (thus turning it into a negative primary deficit ratio, or, so to speak, into a primary surplus ratio). (b) The answer depends on what kind of government spending we are dealing with. If the government spends only on public consumption, income will be reduced in the long run, since high deficit spending leads to an accumulation of debt. The burden is borne by future generations, who on the one side do not benefit from consumption which for them took place in the past and who on the other side have to service and repay the accumulated debt (strictly speaking, such a view of the matter is only valid if the debt is initially financed with savings from abroad).


rd


However, if current deficits are caused by investment spending which contributes to higher investment in the future or generates rates of return exceeding those of private investment projects, a cut in government spending can be detrimental in that it can lead to a decline in income growth both in the long- and in the short-run.


15 Unemployment and growth Chapter focus The purpose of Chapter 15 is to tie up loose ends, fill gaps and introduce useful concepts that would have interrupted the line of argument in the relevant preceding chapters. This makes the chapter less coherent than any other chapter in the text. But it also gives instructors the option to pick individual themes while skipping others they consider less important. The first concept introduced is Okun’s law. While brought into the picture as an empirical relationship between movements of income and unemployment, it serves the important purpose of transforming the SAS curve into its twin sister, the Phillips curve. The subsequent discussion of the empirical determinants of European unemployment features another new concept, the Beveridge curve – a tool purported to permit a theoretical distinction between and provide an empirical estimate of equilibrium unemployment and cyclical unemployment. Beyond that, this section looks at how well available data point towards an influential role of the theoretical determinants of unemployment discussed in Chapter 6. The bottom line of this discussion is that major surges in oil prices, combined with institutional features of many European labour markets that encourage insider-outsider behaviour, must be considered serious contenders in the explanation of Europe’s unemployment experience. The insight that persistent labour markets, labour markets that digest shocks slowly, are probably a key feature of many real-world economies leads to a pertinent modification of the DAD-SAS model. Augmenting DAD-SAS with supply-side persistence (or hysteresis, in the extreme case) is shown to leave the qualitative behaviour of the model unaffected, while making variables move slower, in a more realistic fashion.

Exercises Exercise 15.1 From statistical data, a country’s Phillips curve is found to be 9 0.5 , where inflation and unemployment rates are in percentages. (a) What is the equilibrium rate of unemployment? (b) By how much does a surprising rise of inflation from 2% to 4% reduce unemployment? (c) If Okun’s law for this country reads / 0.03 0.02 , by how much does income grow (given your result obtained in (b))? (a) Solving the Phillips curve given in the exercise for 18

2

yields

).

In the long run, expected and actual inflation are identical. In equilibrium, the last term on the righthand side thus disappears and we get 18. 2 into the Phillips curve (solved for ) yields

(b) Plugging 18

2

2

14.

Unemployment is reduced by 18%

14%

4%.

(c) If we plug our result obtained in (b) into the Okun’s Law equation, we get ∆ ⁄

0.03

0.02

4

0.11.

Output thus rises by 11%. 116 © Manfred Gärtner 2009

rd


Exercise 15.2 Suppose your country’s Beveridge curve is 4/ where v is the vacancy rate. (a) The current rate of unemployment is 6%. Your task is to reduce unemployment to 2%. Propose appropriate measures. Assume that and have the same ‘visibility’. (b) How is your proposal affected if you know that only has one-fourth of the visibility of ? (a) See Figure I15.1. If and line in - -space (where 4⁄

have the same visibility, the equilibrium line is equivalent to the 45-degree ). By setting equal to the Beveridge curve, we get 4

and, thus, equilibrium unemployment of 2% (point A in Figure I15.1). This means that 4% or two thirds of the observed unemployment rate of 6% (point B in Figure I15.1) reflect cyclical unemployment. An appropriate measure to reduce unemployment to 2% would thus be to stimulate demand, e.g. by increasing government expenditure or the growth rate of the money supply, thereby reducing cyclical unemployment. It is also possible (but not necessary) to fight both cyclical and structural (i.e. equilibrium) unemployment with measures that stimulate demand on the one side, and with measures aimed at removing frictions from the labour market on the other side. The latter will shift the Beveridge curve closer to the origin, while measures aimed at reducing cyclical unemployment imply moving up the Beveridge curve.

Figure I15.1 (b) If vacancies are less visible than unemployment , one has to take into account that the true number of vacancies exceeds the number reported by statistical institutions. In our example, if 100% of all unemployment is reported, only 25% of all vacancies are; one vacancy reported is thus tantamount to four cases of reported unemployment. The equilibrium line must reflect this fact. It turns flatter to 0.25 . As in (a), the equilibrium unemployment rate is determined by the intersection of the Beveridge curve and the equilibrium line: 0.25

4⁄

16

4.

Equilibrium unemployment now lies at 4% (point C in Figure I15.1). This means that only one-third of the observed unemployment rate is now due to cyclical factors. By stimulating demand, the government can reduce the unemployment rate to 2%, but only at the price of a constantly increasing inflation rate. The only way to sustainably (i.e. without ever-accelerating inflation) reach an unemployment rate of 2% is to combine demand-stimulating measures with measures that tackle structural and frictional unemployment.

Exercise 15.3 Let the labour market be characterized by the following demand and supply curves: 10,000 40,000

5,000 5,000

For five points in time you have data on the real wage and employment. 117 © Manfred Gärtner 2009

rd


Observation Real wage Employment

1 5 10,000

2 7 2,500

3 4 7,500

4 3 2,500

5 6 7,500

Draw the economy’s Beveridge curve. The Beveridge curve is drawn in Figure I15.3. It is derived from the five labour market observations given in the exercise. See Figure I15.2 for a graphical illustration of the five observations in a labour market diagram and Table I15.1 for the vacancy rates and the unemployment rates pertaining to the different observations. In Table I15.1, is calculated as , and is calculated as . Table I15.1 Observation

1 15 15 5 5

2 25 5 2.5 22.5

3 10 20 12.5 2.5

4 5 25 22.5 2.5

5 20 10 2.5 12.5

Note that in period 1 (first observation), labour demand equals labour supply; the demand and supply line intersect at 15,000. However, employment in period 1 lies at 10,000 only. Equilibrium unemployment thus amounts to 15,000 10,000 5,000. The wage rate in equilibrium is 5. When the wage rate lies above its equilibrium (as in observations 2 and 5, see Figure I15.2), and labour supply exceeds labour demand, then the economy is in a recession. The vacancy rate is lower and the unemployment rate is higher than in equilibrium. The position of the economy on the Beveridge curve is thus to the right of the equilibrium line (which here is the 45-degree line due to the implied same visibility of and ). If the wage rate lies below its equilibrium level (such as in observations 3 and 4, see Figure I15.2), labour demand exceeds labour supply, and the economy experiences a boom. Its position on the Beveridge curve is to the left of the equilibrium line.

Figure I15.2

Figure I15.3


rd


Exercise 15.4 In empirical work, the movement of macroeconomic variables over time is often found to follow what statisticians call an autoregressive process. Taking unemployment as an example, such a process may read

where is a random disturbance and the equation is an AR(1) – a first-order autoregressive process. To get a better feel of the economic implications of the parameter , do the following exercise. Suppose that initially is at its long-run equilibrium level, which is zero. In period 1, the series is hit by a shock of size 5 (i.e. 5). There are no further shocks, subsequently. Compute the values of for periods 1 – 6, letting 0.2, 0.9 and 1, respectively. How does affect the evolution of the time series? Considering Figure 15.16, what estimates of would you expect for unemployment series in the United States and in European countries? The values of the unemployment rate for the different levels of are given in Table I15.2. Time path graphs are depicted in Figure I15.4. The lower is, the quicker does the unemployment rate return to its long-run equilibrium level of 0. If 1, i.e. if unemployment follows a random walk, the unemployment rate will remain at the higher level of 5 until the economy is hit by a new shock. The stylized paths in Figure 15.16 indicate that in the United States, unemployment returned to its previous level after the oil price shocks, whereas it remained high in Europe. From Figure 15.16, the estimate for a European should thus be higher than the estimate for an American . Table I15.2 Period 0.2 0.9 1

0 0 0 0

1 5 5 5

2 1 4.5 5

3 0.2 4.05 5

4 0.04 3.645 5

5 0.008 3.2805 5

6 0.0016 2.95245 5

Figure I15.4

Exercise 15.5 Suppose that the trade union’s insider power is not perfect. By and by, some temporary outsiders regain employment and bid wages down. For concreteness, assume that in the medium run unions only manage to keep real wages in the middle, between where they would want to keep them if they had complete insider power and where wages would go if unions had no insider power at all. (a) Trace the effects of the two oil price explosions under these new assumptions. Start by modifying Figure 15.15. Then modify the time path given in Figure 15.16. (b) Does the result provide a better explanation of Dutch unemployment than the assumption of complete insider power? Consult Figure 15.17. (a) In a hybrid model that combines elements of the stylized US and European labour markets, unemployment does not completely disappear after a negative supply shock, but it also does not remain as high as it was immediately after the shock. Figures I15.5 and I15.6 correspond to Figures 15.15 and l5.16 in the book and show the evolution of the economy in a model with ‘limited insider power’. 119 © Manfred Gärtner 2009

rd


Figure I15.5

Figure I15.6 (b) The graphical results obtained in (a) bear indeed closer resemblance to the actual time series observed in the Netherlands, where unemployment exhibited a high degree of persistence but nevertheless slowly decreased over time.

Exercise 15.6 Suppose a country with fixed exchange rates reduces government spending convergence criteria. Use the graphical model with persistence ( income (a) under adaptive expectations ( ); (b) under rational expectations; (c) under perfect foresight. (a) See Figure I15.7.


in order to meet the Maastricht 0.5) to find out how this affects

rd


(b) See Figure I15.8.

Figure I15.8 (c) See Figure I15.9. What happens is the following: In period 1, government spending falls. But domestic inflation is lower than world inflation. So the real exchange rate falls and raises net exports to leave income unchanged. In period 2, we are back at former inflation, with permanently lower G and higher NX.

Figure I15.9

Exercise 15.7 An economy can be represented by 0.5 2 Initial income is 500. Inflation is 10%. In period 1, the money supply growth rate is reduced from 10% to 5%. What is the new level of income in the long run? (a) under adaptive expectations ( ) (b) under rational expectations (c) under perfect foresight. (a) It is intuitively clear that does never move in this case, because in any given period, aspired income is equal to the income level realized in the last period. This means that in any period, must pass through last period's income level at the inflation rate expected for the current period. And since inflation is assumed to remain where it was last period, will never be induced to move. This can easily be derived graphically as well. The curve shifts successively down the curve up to the point where . 121 © Manfred Gärtner 2009

rd


To calculate income in the long run, it is important to keep two things in mind: First, does not move. Second, is clearly defined (i.e. its slope and its vertical axis intercept are known) because we know that , 500,10 is a point on . Once we know slope and intercept of the curve, we can easily calculate the new level of income in the long run, because we know that in the long run, 5%. Slope and intercept: 2

10

Income in the long run: 2 990

5

2

990

2

500

2 995

2

990. 497.5.

(b) Under rational expectations, output only moves away from (initial) potential output if shocks are unexpected. In the exercise, the only unexpected shock is the change in monetary policy in period 1. Since potential output is always equal to last period’s output, the long-run level of income will then be equal to income obtained in period 1. and in order to find , we get: Equating 5

0.5

500

10

2

500

498.

(c) Under perfect foresight, no shock is unexpected, and output never deviates from (initial) potential output. Long-term income thus stays at 500.


16 Sticky prices and sticky information: new perspectives on booms and recessions (I) Chapter focus Chapters 16 and 17 attempt to narrow the gap between what is standard in intermediate macroeconomics and the more advanced topics discussed in recent business cycle research and held in store by graduate programmes, while avoiding the thrust of mathematical tools required there. To provide motivation, Chapter 16 starts by looking at stylized facts of empirical macroeconomics. Emphasizing intuition, it demonstrates how the empirical study of comovements and the volatility of macroeconomic variables can help evaluate the empirical merits of macroeconomic models. Key results that emerge are: – Most stylized facts fit the DAD–SAS model quite well. – An exception is the comovement between real wages and income. These two variables are found to move procyclically in most industrial countries. In DAD–SAS they move countercyclically, however, if the ups and downs of business cycles are caused by demand-side disturbances. Two responses to this partial failure are: – To conclude that supply-side disturbances dominate business cycles. This makes the DAD-SAS model generate procyclical wages. But then we might want to assemble a more sophisticated supply-side in the first place, rather than use a model that focuses on demand. Such an alternative are real business cycle models, which will be discussed in Chapter 17. – To look beyond one- or multi-period wage contracts as causes of nominal stickiness. Candidates that emerged from this line of research are sticky prices and sticky information. The rest of the chapter explores these New Keynesian responses. First by motivating how sticky prices generate procyclical real wages in an intuitive fashion. Then by studying two modifications of the DAD-SAS model – one that replaces the SAS curve by the New Keynesian Phillips Curve (based on sticky prices); and one that replaces SAS by the Sticky Information Phillips Curve. To facilitate the analysis of these models, and to move closer to how current research deals with aggregate demand, the DAD curve is replaced by a simple monetary policy rule.

Exercises Exercise 16.1 For the USA and various other industrial countries, nominal interest rates are procyclical. They fall during recessions and rise when the economy booms. Is this observation in line with the model? We may trace the behaviour of the model's interest rate within the underlying Mundell-Fleming model if the economy is small and open, and within the model if the economy is large and less open, such as is the case for the United States. In the model, the interest rate rises during a recession if the recession is caused by a reduction of the real money supply and the economy slides up the curve. In this case the interest rate is a countercyclical variable according to the and model, respectively.


rd


If the recession was triggered by, say, a reduction in government spending, i.e. if the curve shifts and the economy slides down the curve, the interest rate will fall during a recession. It then is a procyclical variable in the and model. A procyclical interest rate is thus in line with the model if business cycle fluctuations are driven mainly by shocks to the demand for goods and services.

Exercise 16.2 When simulating the model, / and / scatter plots result that line up the data on a straight line. By contrast, empirical scatter plots are more dispersed, like a cloud. Does this mean that the model is at odds with real world observations? Are there straightforward modifications under which the might also generate more ‘cloudy’ scatter plots rather than ‘pearls on a string’? In the textbook, we work with a deterministic version of the model. In a more realistic stochastic version, all postulated relationships would be prone to stochastic influences. The consumption function would for example have to be reformulated to or to (with being a random variable). All other equations would have to be made stochastic as well. This would soften the relationship between any pair of variables within the model and when simulating the model, one could subsequently create scatter plots that resemble those based on real-world data more closely.

Exercise 16.3 Redraw Diagram 16.3, this time assuming that not all prices are fixed, but only half of all firms’ prices. See Figure I16.1. As in Figure 16.3, the idea is to trace the economy’s response to a drop in aggregate demand, but now with only half of all firms having their output’s prices fixed at . The other firms will lower their flexible prices to where the goods market clears. Given that money wages are flexible, this happens at (not at ; this would require and (here the fixed money wages). The resulting aggregate price level is , which is a weighted average of weights are 0.5 each according to the exercise). Since fixed prices ration firms’ sales to , the labour demand curve turns vertical at that level of income. Flexible money wages fall to and the labour market clears in point . The fall in income is accompanied by a falling real wage. As when all firms' prices are fixed, the real wage is procyclical.


rd


Figure I16.1

Exercise 16.4 Suppose the economy’s supply side is characterized by the New Keynesian Phillips Curve, while aggregated demand is driven by the monetary policy rule . (a) Following the procedure described in Box 8.1, derive an equation describing the behaviour of inflation under rational inflation expectations. (b) Derive an equation describing the level of income generated by this model under rational expectations. (a) The model to analyse reads (1) 125 © Manfred Gärtner 2009

rd


(2) Step 1: Solving (2) for

and substituting into (1) and then solving (1) for

gives the reduced form

(3) with

.

Step 2: Rational individuals know the model and expect (3) to hold: ,

This is a linear difference equation that may be written as ,

or ,

Rational individuals should rule out explosive paths. The only expectation that does this is ,

(4)

Rational inflation expectations equal the central bank's expected inflation target. Step 3: Substituting (4) into (3) gives ,

,

or

,

(5)

So inflation is a weighted average of today's inflation target and the inflation target expected for tomorrow. (b) An equation for income obtains after substituting (5) into (2) and solving for : ,

.

The results are perfectly in line with what we saw in Figures 16.5 and 16.6 in the text.

Exercise 16.5 Take the equation 1 0.9 0.1 (with inflation rates measured in percent) that represents an empirical estimate we obtained for the UK. (a) What is the equilibrium inflation rate in the UK (the rate at which inflation would cease to move if no more shocks occurred)? (b) Suppose inflation is at its equilibrium rate. Now an inflation shock pushes inflation up by 4% points. How many periods does it take until inflation has receded to 6%? (a)

1 0.9 0.1 The equilibrium inflation rate is 5%.

1

1

0.9

5

0.1

5

4

Period 2:

1

0.9

9

0.1

5

8.6

Period 3:

1

0.9

8.6

Period 4:

1

0.9

6.84

Period 5:

1

0.9

6.296

(b) Period 1 (shock):

0.1 0.1 0.1

9

0.9

0.1

0

0.2

9

6.84 8.6 6.84

6.296 5.9824

If the shock occurs in period 1, the inflation rate will have receded to under 6% in period 5 only.


1

rd


Exercise 16.6 Suppose 50% of all firms update information each period. The other half updates information one period later. Let the economy's demand-side be described by the curve . (a) What does the truncated look like under these conditions? (b) Use the recipe provided in Box 8.1 to derive the behaviour of income under rational expectations. Compare your result with those obtained on the basis of the sticky-wage curve in Box 8.1. (c) Derive an equation for inflation under rational inflation expectations. (a) In this scenario the current price level is a weighted average of the prices set by firms with current information, , and with last period's information, ]: 0.5

0.5

(1)

]

Substituting the desired prices ̂ and ]

̂

]

]

into (1), solving for truncated )

]

and deducting

]

from both sides yields a sticky-information

curve (or

.

]

(b) The model to analyse reads ]

(1)

]

(2) We may omit the subscripts given in brackets, since all expectations are based on information available at time -1. Step 1: Equating the two equations eliminates solve for at this point):

and yields a reduced form for

(it is not necessary to

(3) Step 2: Compute rational expectations (for

and ). In expectations form, the model reads: (1 (2

From 1

we obtain

Plugging this into (2

gives

Step 3: Plugging expectations into the reduced form (3) and solving for

gives

(4) This result is identical to the one shown in Box 8.1, even though the employed supply curve is slightly different. (c) An equation for

obtains after inserting the result obtained in (b) (i.e. equation (4)) into (2): .


rd


Exercise 16.7 Figures 16.7–16.10 show how an economy characterized by a New Keynesian or a truncated Sticky Information Phillips Curve responds to unexpected and expected reductions in the central bank’s inflation target when the central bank follows a monetary policy rule. Now let the demand-side be characterized by a conventional curve. (a) Let aggregate supply be characterized by the . How does the economy respond to a surprise reduction in the money growth rate? (b) Let aggregate supply be characterized by the . How does the economy respond to a surprise reduction in the money growth rate, and how to an announced reduction? (a) A surprise reduction of the money growth rate to in period 1 moves into (see Figure I16.2). The position of is determined by inflation expected for period 2. The rational expectation for period , which shifts the curve into and makes the economy jump from point 0 into point 2 is 1 in Figure I16.2. This is the same result as described in the text for the case when the central bank follows a policy rule. [Convince yourself that only is rational by experimenting with inflation for period 2]. expectations above or below

Figure I16.2 (b) A surprise reduction of the money growth rate to in period 1 moves into (see Figure I16.3). The curve stays put since its position is determined by inflation expectations that were formed before the shock. Thus the economy moves into a recession in point 1. in figure I16.3. The position of the curve is influenced In period 2, the curve moves into by inflation expectations formed in period 0, before the shock, and in period 1, after the shock. The first group's curve, if they made up the entire economy, would read ]

]

That of the second group would read ]

]

The second group's information set includes the knowledge of the first group's curve. As experimentation will substantiate, the second group's inflation and income expectations are only rational curve. Point 2 shows this combination and marks if the pair ] and ] sits on the first group's . Since by now this is included in the the period 2 equilibrium. In period 3, moves down to and income returns to potential income. information sets of all groups , the curve moves into Period 4 sees the economy settle into its new long-run equilibrium point 4.


rd


Figure I16.3 See Figure I16.4 for a graphical representation of the economy’s response to an announced reduction in the money growth rate. The mere announcement in period 1 of reduced money growth from period 2 onwards leaves all curves and, hence, the equilibrium in point 1. When moves into in period 2, this is still a surprise for group 1, but not so for group 2. Again, group 2 knows of group 1’s information deficit. Hence, their expectations must be compatible with the first group’s curve, which rests unmoved. Group 2 expects and , which makes its curve compatible with the first ] ] group's, leaves the aggregate curve in position , and renders the equilibrium point 2. In , , periods 3 and 4, the economy first moves onto the curve and then into its new long-run equilibrium.

Figure I16.4


17 Real business cycles: new perspectives on booms and recessions (II) Chapter focus This chapter features the real business cycle model. Points to emphasize are: 1. The new methodology of building a macroeconomic model on microfoundations. This means that macroeconomic variables are determined through the optimizing behaviour of the economic agents portrayed by the model. 2. The more detailed modelling of supply-side decisions. In a way the model overcomes the distinction between supply and demand, since many decisions affect both sides at the same time. For didactical purposes, the graphical treatment of the real business cycle model draws on this distinction nevertheless. The model assumes all variables, nominal and real, to be perfectly flexible. There is no nominal stickiness. The model is always in equilibrium. The cyclical ups and downs of income are being caused by optimal responses to exogenous parameter changes (including technology and preferences). Initially, while acknowledging that all decisions are being taken simultaneously, current period decisions (how much to work) and intertemporal decisions (how much to consume today and how much tomorrow; how much to work today and how much tomorrow) are considered separately, emphasizing the role of intertemporal substitution. Representative households, whose utility is affected by consumption and leisure, decide on consumption spending and the supply of labour. Profit-maximizing firms decide on the demand for labour and on investment demand, which drives capital accumulation. The behaviour resulting from these partial analyses is then combined into a graphical version of the real business cycle model. While this is a compromise and lacks the precision of elaborate formal analyses, it features all the qualitative properties of real business cycle models and should provide a good intuitive understanding of the mechanisms at work.

Exercises Exercise 17.1 Consider the current-period optimum derived in Figure 17.2. (a) What is the effect on income and employment if household preferences change in the sense that more utility is being derived from leisure time than was previously the case? (b) A country decides to limit the work week to 35 hours by law. How does this affect the current-period choice? (a) If more utility is derived from leisure time, households' indifference curves turn steeper: For any amount they work, households now must receive more income in order to derive the same utility as before. With the indifference curves turning steeper and the production function unchanged, households will decide to work less and to generate less income (see Figure I17.1, where the economy moves from point A to point B on the production function).


rd


Figure I17.1 (b) See Figure I17.2. The current-period choice obviously remains unaffected at if 35. In such a case, 35, (point B in Figure I17.2), households work less than 35 hours a week by individual choice. If utility-maximizing households optimally work more than 35 hours a week. If work time in such a case is limited by law (and work is essentially rationed), a corner solution will obtain at 35 (point B in figure I17.2). In point B, household utility is lower than it was in point A.

Figure I17.2

Exercise 17.2 Figure 17.1 illustrates the labour-supply decision from a macroeconomic perspective. While it looks at one individual (or household), it assumes this to be a representative individual in the sense that its decisions are imitated by all other individuals. In what respect does the graphical treatment of the labour supply decision of a single individual who assumes to act independently of others differ from what is shown in Figure 17.1? From an individual perspective, the marginal product of labour MPL is considered constant, i.e. an individual knows that her decision on how much to work has no influence on where the economy as a whole ends up on the partial production function. An individual thus faces a linear constraint in consumption - work time space (i.e. the constraint has a constant, positive slope), whereas for the economy as a whole, the constraint (which is the partial production function) is characterized by a curve with positive but decreasing slope.

Exercise 17.3 Households are in a long-run equilibrium in the intertemporal consumption diagram. (a) Now this country obtains a sizable one-time grant from the World Bank, which it will not have to repay. How will this affect intertemporal consumption choices? (b) How will intertemporal consumption choices be affected if the World Bank only extended a loan this period that has to be repaid next period?


rd


(a) See Figure I17.3. The grant moves the initial endowment point more or less horizontally to the right from A into A′. In order to maximize utility , households will save about half of the grant for next period’s consumption and will end up in B ( ).

Figure I17.3 (b) If the grant has to be repaid, the endowment point shifts right on the one hand (it is possible to consume more in period 1) but it shifts down by a similar distance on the other hand (additional consumption in period 1 reduces consumption possibilities in period 2). If the grant must be repaid with interest, the endowment point moves down the intertemporal constraint into A″ in Figure I17.3. In this case, the grant has no effect on the intertemporal pattern of consumption (it remains in A). If the grant may be repaid without interest, the endowment point moves to a point slightly above A″ (not shown in Figure I17.3) for it slides down a line with slope –1, which is flatter than the intertemporal constraint. This moves intertemporal consumption into a point slightly higher than A on the 45-degree line. Households basically use the interest payments they were exempted from to add to consumption in periods 0 and 1. Their utility thus increases slightly.

Exercise 17.4 Suppose a country has implemented a 35-hour maximum working week, as postulated in Exercise 17.1(b). Suppose this restriction is binding in the sense that in equilibrium households actually would like to work more. (a) How does this country respond to a positive, permanent technology shock? (b) How does this country respond to a permanent deterioration of its production technology? (c) Are the effects derived under (a) and (b) symmetrical? (a) The difference between the case discussed here and the case sketched in Figure 17.9 is that with a binding 35-hour working week, the curve is kinked and vertical north of the equilibrium (see Figure I17.4). This means that no intertemporal substitution of labour is possible during the adjustment process. Despite this modification, the positive technology shock still triggers qualitatively the same response path as sketched in Figures 17.10-17.12.


rd


Figure I17.4 (b) The kinked curve is also vertical in some segment south of the initial equilibrium (see Figure I17.4; point A marks the initial equilibrium). It becomes positively sloped at the interest rate where households wish to work 35 hours a week. Despite this modification, the negative shock to technology triggers a qualitative response similar to the response sketched in Figures 17.10-17.12 (though with the opposite sign, of course). Whether intertemporal substitution kicks in during the adjustment process depends on whether period equilibria remain on the vertical section of the curve or not (in the latter case, intertemporal substitution will take place). (c) The responses to a positive or negative shock to technology derived in (a) and (b) are symmetrical as long as we remain on the vertical section of the curve in (b). Once we leave the vertical section of the curve in (b), intertemporal substitution kicks in and the responses are no longer symmetrical.

Exercise 17.5 Suppose there was no time to build. That means, investment would add to the productive capital immediately, without any lag. What kind of income response would a positive, permanent shock to technology trigger under these circumstances? Compare with the behaviour of the real business cycle model. If investment adds to productive capital without any lag, the long-run response as depicted in Figure 17.12 obtains immediately. All the effects discussed in connection with Figures 17.10–17.12 – the increase in savings and investment, the income gains, the growth of the capital stock – happen without any delay in the period of the technology shock.

Exercise 17.6 Suppose the time discount rate rises permanently. How does the economy respond to this according to the real business cycle model?


rd


Figure I17.5 sketches the short-run response and shows the new long-run equilibrium.

1

Figure I17.5 In the new long-run equilibrium (point C in Figure I17.5), the interest rate has risen to match the new time discount rate. Since the interest rate has risen, the marginal productivity of capital must have risen as well. The capital stock must thus have fallen, and with it income. The short-run response is somewhat complicated. Starting at , hypothetically assume that the interest rate had already risen to the new time discount rate. Then no intertemporal substitution of labour would take place, and the new curve would pass through point B, which is vertical above the initial equilibrium point 0 in Figure I17.5. Since there would be no intertemporal substitution of consumption either, the new consumption line would pass through B as well. Adding the unchanged investment line to the new consumption line gives the period 1 and intersect in point 1 where the interest rate has increased and there is negative net investment. line. The capital stock thus begins to shrink, and the economy moves towards point C. Exercise 17.7 A hurricane destroys about 20% of a country’s capital stock and infrastructure. According to the real business cycle model: (a) How does this affect employment in the short, medium and long run? (b) Is there intertemporal substitution in the supply of labour? (c) Is there intertemporal substitution in consumption? See Figure I17.6.

Figure I17.6


rd


The destruction of the capital stock shifts left in period 1. shifts left as well until it intersects at the equilibrium interest rate (which remains unchanged). A lower capital stock means an increased marginal productivity of capital; the investment line thus shifts right. As a result, the interest rate rises above the equilibrium interest rate in period 1. Income falls, however, and the economy ends up in a point such as B in period 1. In the following periods, the interest rate gradually falls and income increases until the economy has moved back to point A, which marks the economy’s long-run equilibrium. From the graph we can answer Questions (a)–(c): (a) Employment in the short-run falls (because of the destroyed capital stock, the marginal product of labour falls, which results in reduced employment). Employment then starts to rise together with the growing capital stock until capital and labour are back at where they originally were. (b) While the capital stock grows back to its initial level, there is intertemporal substitution of labour. Since as long as , households will choose to work more today in order to enjoy more leisure in the future. (c) While the capital stock grows, there is also intertemporal substitution of consumption. Since as long as , households will choose to consume less today and save in order to be able to consume more in the future.

Exercise 17.8 The following table shows correlations between income and other macroeconomic variables, as they are typically encountered in empirical studies of macroeconomic time series. Variable Coefficient of correlation (with income)

Consumption 0.7

Investment 1.3

Real interest rate –0.3

Employment 0.7

Which of these coefficients fit the basic real business cycle model developed in this chapter, and which do not? Explain why. Consumption: The model suggests a positive correlation between consumption and income. If income rises in the RBC model, consumption also rises. Furthermore, due to intertemporal substitution of consumption (households consume less ), the RBC model suggests a coefficient of correlation that is smaller than 1. This is also in line today if with empirical studies. Investment: Again the model suggests a positive correlation between consumption and income. A positive technology shock increases the marginal product of labour and of capital, both of which increase income, and the latter of which makes net investment positive. Since is made up of and , and since consumption has a coefficient of correlation smaller than 1, the RBC model implies a coefficient of correlation between income and investment greater than 1. Real interest rate: The empirical observations here do not fit with the RBC model. In the RBC model, the interest rate moves procyclically. After a positive technology shock, shifts more than (because already shifts as far as , and shifts as well). The interest rate must then rise in order for intertemporal substitution of labour and consumption to occur and, through this, for aggregate demand to match aggregate supply. Employment: Employment moves procyclically in the RBC model. The empirical coefficient thus fits the model. With rising interest rates during a boom, people choose to work more today, because it pays off to work more today in order to enjoy more leisure time later. All in all, according to the RBC model in which business cycles are caused by technology shocks, the long-run correlation should be close to zero, while the short-run correlation is positive but small. If changes in preferences drive real business cycles, the model implies a stronger positive correlation between employment and income, which is, however, still 1.


Appendix A primer in econometrics Chapter focus This optional appendix offers an intuitive introduction to ordinary least squares regression and hypothesis testing. Unless pertinent knowledge has already been acquired in a first applied statistics or econometrics course, the material covered here is needed if instructors wish to use the applied exercises provided at the end of most chapters of this text. It goes without saying that the bare-bones and strictly nontechnical description provided here cannot and does not aspire to be a substitute for an intermediate statistics or econometrics course. Still, students are oftentimes drowning in the formal material that tends to feature prominently in such courses, at the expense of intuition and the essential skill of actually doing econometrics, however small the project may be. The nontechnical descriptions provided here may either provide motivation as or before students embark on a proper statistics or econometrics course, or encourage students to apply their newly acquired but fragile skills to real world issues after the completion of such a course.

Exercises Exercise A.1 The following data have been observed for variables 1 2

8 4

8 6

3 2

5 3

5 4

2 1

and : 4 3

7 5

6 5

Show these points in a scatter diagram with y on the vertical and x on the horizontal axis. Draw a regression line through the data points using your hand and your head (do not use formulas). Read and off your graph. The combined series result in a set of 10 data points in - -space. Figure IApp.1 shows a strong positive relationship between the two series. The regression line calculated with ordinary least squares gives an of 0.67 and a of 0.58. It goes without saying that these numbers can only approximately be read off the graph.

Figure IApp.1


rd


Exercise A.2 Discuss the O. J. Simpson trial in statistical terms. What is the null hypothesis from which jurors are requested to start? Translate the requirement ‘beyond reasonable doubt’ into statistical concepts. Do you believe that the jurors committed an error? If yes, was it an error of Type I or of Type II? In the civil law suit subsequently filed against O. J. Simpson, the issue is not whether he is guilty ‘beyond reasonable doubt’ but with a probability of more than 50%. Does this increase the risk of committing an error of Type I or an error of Type II? ‘In dubio pro reo’ is the presumption from which jurors are requested to start. The null hypothesis is therefore: : . .

.

‘Beyond reasonable doubt’ in statistical terms means that the null hypothesis may only be discarded at a very high significance level of, say, 1%. This ensures that the jurors will only find O. J. Simpson guilty once the prosecution has presented enough compelling evidence and arguments to remove all reasonable doubt about O. J. Simpson’s guilt the jury could possibly entertain. The jurors ruled ‘not guilty’. If Simpson actually was guilty, the jury committed a Type II error by not rejecting the wrong null hypothesis. Statistically, type II errors will be more frequent the higher the significance level is. If thus in a civil lawsuit the null hypothesis is discarded at the much lower significance level of 50%, the risk of committing a Type II error will be reduced. Unfortunately the risk of committing a Type I error – rejecting the null hypothesis even though it is true – increases in this case.

Exercise A.3 You are engaged in a game of dice. Your opponent throws only fives and sixes. After how many rounds do you discard your initial presumption (your null hypothesis) that the dice is not loaded: (a) at the 10% level? (b) at the 5% level? (c) at the 1% level? Your null hypothesis is: :

.

The probabilities P of throwing only fives and sixes for different numbers of throws are as follows: 1⁄3 1⁄3

0.3333 1⁄3

1⁄9

1⁄3

1⁄3

0.3333 1⁄3

1⁄81

000123

1⁄243

0.0041.

1/27

0.0370

So the null hypothesis is rejected: (a) after three rounds at the 10% level, (b) after three rounds at the 5% level, (c) after five rounds at the 1% level.

Exercise A.4 You would like to check (a) whether the quantity theory of money holds. You therefore estimate the equation (in logarithms)

(b) whether the exchange rate forecasts published biannually in The Economist are rational in the sense that they are not systematically wrong. To look into this you estimate


rd


(c) whether the rate of return in your country’s stock market does not really possess any forecasting potential of the rate of return in the next quarter. You estimate –1 (d) that the business cycle in the United States does not affect the business cycle in your country. The estimation equation reads

Please formulate one or more appropriate null hypotheses for all the above questions. (a) From the quantity theory, we would expect a one-unit increase in the money supply when either the price level or GDP rises by one unit. From this, an appropriate null hypothesis is :

1,

1.

The constant is an estimate of the velocity of money circulation (to be exact, according to theory it corresponds to minus the logarithm of the velocity of money circulation). It may be positive or negative. Thus no hypothesis results for . (b) When there is no systematic bias, the constant value of one: :

0,

is zero. For

we would – if the forecasts are correct – expect a

1.

(c) When past rates of return in the stock market do not explain future returns, the parameter :

is zero:

0.

is of no interest when testing the forecasting potential of past returns. (d) The US business cycle has no effect on the business cycle fluctuations of your country if the correlation between the two unemployment rates is zero: :

0.

It cannot be concluded, however, that the US business cycle indeed does affect your country’s business cycle once 0. , i.e. correlation should not be confused with causation.


Gärtner M. (2009) - Macroeconomics - Instructor's Manual - Third Edition

Recommend Documents