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 © Manfred Gärtner 2009 Contents Chapters Pages Macroeconomic essentials Booms and recessions (I): the Keynesian cross 13 Money, interest rates and the global economy 22 Exchange rates and the balance of payments 32 Booms and recessions (II): the national economy 38 Enter aggregate supply 48 Booms and recessions (III): aggregate supply and demand 56 Booms and recessions (IV): Dynamic aggregate supply and demand 66 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 © Manfred Gärtner 2009 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 © Manfred Gärtner 2009 Macroeconomic essentials Chapter focus This chapter attempts three things: 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 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 should be augmented with additional reading assignments from some principles text 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 © Manfred Gärtner 2009 rd Manfred Gärtner, Macroeconomics, 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 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 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 © Manfred Gärtner 2009 6% 2% 2% 3% 4% 1% 0 rd Manfred Gärtner, Macroeconomics, Edition, Instructor’s Manual 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 (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 © Manfred Gärtner 2009 rd Manfred Gärtner, Macroeconomics, Edition, Instructor’s Manual 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: : 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 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 ) 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 1,000 This can be solved for to get €20/ (d) Again we can plug in the numbers into the quantity equation, this time to compute € €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/ © Manfred Gärtner 2009 € / 1,600 rd Manfred Gärtner, Macroeconomics, Edition, Instructor’s Manual 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, 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 and 5) and thus affect real output © Manfred Gärtner 2009 rd Manfred Gärtner, Macroeconomics, Edition, Instructor’s Manual 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 Manfred Gärtner, Macroeconomics, Edition, Instructor’s Manual 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 124 © Manfred Gärtner 2009 rd Manfred Gärtner, Macroeconomics, Edition, Instructor’s Manual 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 Manfred Gärtner, Macroeconomics, Edition, Instructor’s Manual (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 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) 0.9 0.1 The equilibrium inflation rate is 5% 1 0.9 0.1 Period 2: 0.9 0.1 8.6 Period 3: 0.9 8.6 Period 4: 0.9 6.84 Period 5: 0.9 6.296 (b) Period (shock): 0.1 0.1 0.1 0.9 0.1 0.2 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 only 126 © Manfred Gärtner 2009 rd Manfred Gärtner, Macroeconomics, Edition, Instructor’s Manual 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 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): 127 © Manfred Gärtner 2009 rd Manfred Gärtner, Macroeconomics, Edition, Instructor’s Manual 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 moves into (see Figure I16.2) The position of is determined by inflation expected for period The rational expectation for period , which shifts the curve into and makes the economy jump from point into point is 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 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 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 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 equilibrium In period 3, moves down to and income returns to potential income information sets of all groups , the curve moves into Period sees the economy settle into its new long-run equilibrium point 128 © Manfred Gärtner 2009 rd Manfred Gärtner, Macroeconomics, Edition, Instructor’s Manual 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 of reduced money growth from period onwards leaves all curves and, hence, the equilibrium in point When moves into in period 2, this is still a surprise for group 1, but not so for group Again, group knows of group 1’s information deficit Hence, their expectations must be compatible with the first group’s curve, which rests unmoved Group expects and , which makes its curve compatible with the first ] ] group's, leaves the aggregate curve in position , and renders the equilibrium point In , , periods and 4, the economy first moves onto the curve and then into its new long-run equilibrium Figure I16.4 129 © Manfred Gärtner 2009 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: 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 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) 130 © Manfred Gärtner 2009 rd Manfred Gärtner, Macroeconomics, Edition, Instructor’s Manual 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? 131 © Manfred Gärtner 2009 rd Manfred Gärtner, Macroeconomics, Edition, Instructor’s Manual (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 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 and 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 17.10-17.12 132 © Manfred Gärtner 2009 rd Manfred Gärtner, Macroeconomics, Edition, Instructor’s Manual 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? 133 © Manfred Gärtner 2009 rd Manfred Gärtner, Macroeconomics, Edition, Instructor’s Manual Figure I17.5 sketches the short-run response and shows the new long-run equilibrium 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 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 and intersect in point 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 I17.6 134 © Manfred Gärtner 2009 rd Manfred Gärtner, Macroeconomics, Edition, Instructor’s Manual The destruction of the capital stock shifts left in period 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 Income falls, however, and the economy ends up in a point such as B in period 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 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 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 Real interest rate: The empirical observations here 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 135 © Manfred Gärtner 2009 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 8 5 and : 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.1 136 © Manfred Gärtner 2009 rd Manfred Gärtner, Macroeconomics, Edition, Instructor’s Manual 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 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 137 © Manfred Gärtner 2009 rd Manfred Gärtner, Macroeconomics, Edition, Instructor’s Manual (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, 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 (c) When past rates of return in the stock market not explain future returns, the parameter : is zero: 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: : It cannot be concluded, however, that the US business cycle indeed does affect your country’s business cycle once , i.e correlation should not be confused with causation 138 © Manfred Gärtner 2009