Fernando de Holanda Barbosa Macroeconomic Theory Fluctuations, Inflation and Growth in Closed and Open Economies Macroeconomic Theory Fernando de Holanda Barbosa Macroeconomic Theory Fluctuations, Inflation and Growth in Closed and Open Economies Fernando de Holanda Barbosa FGV EPGE Escola Brasileira de Economia e Finanỗas Rio de Janeiro, Brazil ISBN 978-3-319-92131-0 ISBN 978-3-319-92132-7 https://doi.org/10.1007/978-3-319-92132-7 (eBook) Library of Congress Control Number: 2018942891 © Springer Nature Switzerland AG 2018 This work is subject to copyright All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed The use of general descriptive names, registered names, trademarks, service marks, etc in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations This Springer imprint is published by Springer Nature, under the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland “IT DOES REQUIRE MATURITY TO REALIZE THAT MODELS ARE TO BE USED BUT NOT TO BE BELIEVED” [Theil (1971), p.VI] “THE PROOF OF THE PUDDING IS IN THE EATING.” “ANY POLICY-MAKER OR ADVISER WHO THINKS HE IS NOT USING A MODEL IS KIDDING BOTH HIMSELF AND US” [Tobin, James, quoted by Lombra and Moran (1980), p 41] “ IN THE DYNAMIC FIELD OF SCIENCE THE MOST IMPORTANT GOAL IS TO BE SEMINAL AND PATHBREAKING, TO LOOK FORWARD BOLDLY EVEN IF IMPERFECTLY” [Samuelson (1971), p X-XI] “IT IS MUCH EASIER TO DEMONSTRATE TECHNICAL VIRTUOSITY THAN TO MAKE A CONTRIBUTION TO KNOWLEDGE UNFORTUNATELY IT IS ALSO MUCH LESS USEFUL” [Summers (1991) p 18] “GENTLEMEN, IT IS A DISAGREEABLE CUSTOM TO WHICH ONE IS TO EASILY LED BY THE HARSHNESS OF THE DISCUSSIONS, TO ASSUME EVIL INTENTIONS IT IS NECESSARY TO BE GRACIOUS AS TO INTENTIONS; ONE SHOULD BELIEVE THEM GOOD, AND APPARENTLY THEY ARE; BUT WE DO NOT HAVE TO BE GRACIOUS AT ALL TO INCONSISTENT LOGIC OR TO ABSURD REASONING BAD LOGICIANS HAVE COMMITTED MORE INVOLUNTARY CRIMES THAN BAD MEN HAVE DONE INTENTIONALLY” [Pierre S du Pont, quoted in Friedman (1994), p 265] Preface This book grew out of the macroeconomics graduate courses I have taught at the Production Engineering Department, Fluminense Federal University and at FGV EPGE Brazilian School of Economics and Finance over more than three decades During this period, macroeconomics has evolved greatly, as I describe succinctly in the Introduction, giving up the Keynesian Agenda with its behavioral equations and entering the Lucas Agenda, with its equations based on microeconomic foundations I have tried very hard not to be idiosyncratic, presenting models that are considered to be the core of mainstream macroeconomics, using both microeconomicbased and ad hoc models There are at least two reasons that justify the inclusion of ad hoc models in a macroeconomics textbook: (i) pedagogical and (ii) empirical evidence From a pedagogical point of view, nobody disputes that the simple and elegant Solow model is the best way to introduce economic growth models From an empirical point of view, the traditional Keynesian models of fluctuations, either for closed or for small open economies (the Mundell-Fleming-Dornbusch model) have not been rejected by the empirical evidence I like to say that a teacher is a storyteller and the classroom a stage I try to make each story as simple as possible without loss of generality What lessons these stories teach? The moral of each one is explicitly conveyed Models are falsifiable representations of certain phenomena Thus, I strive to present, for each model, empirically testable falsifiable predictions The structure of almost every section is the same, consisting of: (i) model specification; (ii) algebra to transform the model into a dynamical system; (iii) system equilibrium and stability analysis; and (iv) comparative dynamics experiments The book is self-contained There is a mathematical appendix that simply and succinctly provides the required tools to understand the material In a market of monopolistic competition, producers need to differentiate their products This book differs from other macroeconomics textbooks for its emphasis on open economies My experience in teaching macroeconomics in Brazil has convinced me that a great number of Brazilian economists analyze the Brazilian economy as if it were a closed economy For example, it is not unusual for someone vii viii Preface to adopt the same technique as the FED, the US Central Bank, to estimate the natural rate of interest You can find this type of ‘vice’ all over the world One just has to search for international works that estimate the natural rate of interest in small open economies My hypothesis is that this behavior stems from studying macroeconomics textbooks that follow the English and American tradition of analyzing their economies as if they were closed economies Those books not provide enough scope for the analysis of open economies The representative agent model became the workhorse of modern macroeconomics Chapter might seem to be an idiosyncratic chapter, but this is not the case It presents several hypotheses that allow for the use of the representative agent model for open economies However, these hypotheses are either ad hoc, contrary to common sense, or they are rejected by empirical evidence A model with heterogeneous agents, such as the overlapping generations model, presented in Chap 3, is well suited to model open economies Latin America, as well as many other countries all over the world, has vast experience with economic crises These crises can be understood by studying four pathologies: (i) public debt default; (ii) chronic inflation; (iii) hyperinflation; and (iv) foreign debt default Chapter 10 of this book deals with the government budget constraint, the framework that allows for analysis of the sustainability of public debt and hyperinflation Foreign debt default can be analyzed as a simple extension of public debt default, as Chap 4, Section shows The sixth section of Chap presents a model of chronic inflation that requires a minor change to the Keynesian models, namely, that of changing the monetary policy rule Instead of an interest-rate rule, the monetarypolicy rule states that the Central Bank issues money to finance the public deficit This book can be used as basic material for four different graduate courses: (i) Macroeconomics; (ii) Open Economy Macroeconomics; (iii) Monetary Theory; and (iv) Economic Growth The Macroeconomics course should include Chaps 1, 3, 6, 7, and 10 The Open Economy Macroeconomics course would cover Chaps 1, 2, 3, 8, and The Monetary Theory course should include Chaps 1, 6, 7, 10, and 11 The Economic Growth course would cover Chaps 1, 3, 4, and Each course should be supplemented by a reading list of papers at the frontier of each field This book can also be used in an advanced undergraduate Macroeconomics course The book was written in Portuguese Allan Vidigal translated it into in English and I revised it to make sure that we are using accurate economic terms I thank Allan for his excellent job I am responsible for any errors and imperfections I thank my students, from different cohorts, whose feedback has helped me to improve my ability as a Macroeconomics ‘storyteller.’ I hope that they will approve of the outcome of this long endeavor I thank Mariana Biojone Brandão at Springer for her support, which has made publication of this book possible My thanks also go to Regina Helena Luz for the wonderful job and hard work in drawing up most of the phase diagrams for this book Vera Lúcia de Abreu went on to complete this task and I thank her for helping me to finalize this book Rio de Janeiro, Brazil Fernando de Holanda Barbosa Introduction Macroeconomics Macroeconomics is a branch of economics that applies economic theory to study growth, business cycles, and price-level determination Macroeconomics takes account of stylized facts observed in the real world and builds theoretical frameworks to explain these facts Generally speaking, these frameworks include two types of mechanism: impulse and propagation The impulse mechanisms, or shocks, are the cause of changes in the model’s variables Propagation mechanisms, as the name indicates, transmit impulses over time and are responsible for the model’s dynamics Economic growth has been a stylized fact of market economies since England’s 19th-century industrial revolution Until then, poverty was a common good for humanity Economic growth consists of the persistent, smooth, and sustained increase of income per-capita Why does one country have a higher level of income per-capita than another? What forces cause one country to grow faster than another? What are the roles of the market and the state in the growth process? This question is part of any economic discussion In most cases, the answer is based on value judgments This book is about positive economics only, and does not address any issue from the perspective of normative economics Any market economy shows fluctuations in output and other variables, with periods of expanding and contracting economic activity This phenomenon is called the business cycle The cycle’s main characteristics are as follows: (i) brief economic contraction phase and lengthy economic expansion phase, and (ii) variable duration What causes the business cycle? What kinds of nominal and (or) real shocks cause the economic activity to fluctuate? What are the roles of the market and the state in the cycle? Determination of the price level, or the value of money, is a fascinating macroeconomic issue The value of money is its purchasing power measured in terms of a basket of goods and services Therefore, purchasing power equals the inverse of the ix x Introduction price level Why does a financial asset such as paper currency, with no intrinsic value whatsoever, and dominated by another interest-bearing asset, have value? Does the value of money affect the business cycle? Does the value of money affect growth? Under what circumstances does the value of money go to zero, as is the case with hyperinflation? A stylized fact observed in market economies is the short run non-neutrality of money A nominal interest rate reduction by the Central Bank causes output to expand An interest rate increase causes a contraction of the economy’s output Successful stabilization programs end hyperinflation without bringing about recession How can one reconcile the non-neutrality of money over the cycle with its neutrality at the end of hyperinflation episodes? In addition to issuing money by the Central Bank, the government, through the Treasury, issues interest-bearing securities with varying characteristics Does issuing securities affect the economy’s real and (or) nominal variables? Under what circumstances does public debt become unsustainable? Economies are not autarchic, closed to the rest of world, but rather live in permanent contact with other economies in an increasingly globalized world Each country (or group of countries) has its own currency, goods and services, capital, and flow across countries The mobility of labor is generally restricted by immigration policies Does the foreign exchange rate regime affect the functioning of the economy? A stylized fact of the flexible exchange rate regime, since its adoption in the first half of the 1970s by the world’s leading economies, is a positive correlation between nominal and real exchange rates How does one explain this non-neutrality of money? Are growth and the business cycle affected by the economy’s degree of openness? Keynes Agenda Macroeconomics began with the General Theory This innovative book by Keynes (1936) was motivated by the great depression that began in 1929 and extended through the 1930s The adjustment of the market economy, under conditions of unemployment, should be done through the price system Real wages and real interest rates would bring the economy to full employment The mechanism, according to Keynes, was not working The purpose of the General Theory was not just to explain what was going on, but also to propose economic policies to address the problem The General Theory set the research agenda for almost half a century The Keynes agenda led Hicks (1937), Modigliani (1944), Phillips (1958), Mundell (1963), Fleming (1962), and Friedman (1968) to design the architecture of the macroeconomic model of the late 1960s and to write undergraduate textbooks in the latter half of the 1970s The agenda’s basic short-term model for a closed economy consists of the combination of Hicks’s IS/LL model (1937), which Hansen (1949) calls IS/LM, Bibliography 441 Phelps, Edmund S (1967) Phillips Curves, Expectations of Inflation and Optimal Unemployment Over Time Economica 34, 254–281 Poole, William (1970) Optimal Choice of Monetary Policy Instrument in a Simple Stochastic Macro Model Quarterly Journal of Economics 84, 197– 216 Prachowny, Martin F J (1993) Okun’s Law: Theoretical Foundations and Revised Estimates Review of Economics and Statistics 75, 331–336 Rebelo, Sergio (2005) Real Business Cycle Models: Present and Future Scandinavian Journal of Economics 107, 217–238 Reis, Ricardo (2007) The Analytics of Non-Neutrality in the Sidrauski Model Economics Letters 94, 129–135 Roberts, John M (1995) New Keynesian Economics and the Phillips Curve Journal of Money, Credit and Banking 27, 975–984 Rogoff, Kenneth (1985) The Optimal Degree of Commitment to an Intermediate Monetary Target Quarterly Journal of Economics 100, 1169–1189 Romer, David (2000) Keynesian Macroeconomics Without the LM Curve Journal of Economics Perspectives 14, 149–169 Romer, Paul M (1994) The Origins of Endogenous Growth Journal of Economic Perspectives 8, 3–22 Rotemberg, J J and M Woodford (1997) An Optimizing-Based Econometric Framework for the Evaluation of Monetary Policy NBER Macroeconomics Annual 12, 297–346 Ryder, Jr., Harl E and Geoffrey M Heal (1973) Optimal Growth with Intertemporally Dependent Preferences Review of Economic Sudies 40, 1– 31 Salter, W (1959) Internal and External Balance The Role of Price and Expenditure Effects Economic Record 35, 226–238 Samuelson, Paul A (1939) Interaction Between the Multiplier and the Principle of Acceleration Review of Economics and Statistics 21, 75–78 Samuelson, Paul A (1947) Foundations of Economic Analysis New York: Atheneum Samuelson, Paul A and Robert M Solow (1960) Analytical Aspects of Anti-Inflationary Policy, American Economic Review 50, 177–194 Sargent, Thomas (1982) The End of Four Big Inflations In Robert H Hall (Editor), Inflation: Causes and Effects Chicago: Chicago University Press Sargent, Thomas and Neil Wallace (1973) The Stability of Models of Money and Growth with Perfect Foresight Econometrica 41, 1043–1048 Sargent, Thomas and Neil Wallace (1981) Some Unpleasant Monetarist Arithmetic Federal Reserve Bank of Minneapolis Quarterly Review 5, 1– 17 Sargent, Thomas and Neil Wallace (1987) Inflation and the Government Budget Constraint In Razin, A and E Sadke (Editors) Economic Policy in Theory and Practice McMillan: New York Sidrauski, Miguel (1967) Rational Choice and Patterns of Growth in a Monetary Economy American Economic Review 57, 534–544 Slutsky, Eugen (1937) The Summation of Random Causes as the Source of Cyclic Processes Econometrica 5, 312–330 Smets, Frank R and Rafael Wouters (2003) An Estimated Dynamic Stochastic General Equilibrium Model of the Euro Area Journal of the European Economic Association 1, 1123–1175 Solow, Robert M (1994) Perspectives on Growth Theory Journal of Economic Perspectives 8, 45–54 Strotoz, Robert H (1956) Myopia and Inconsistency in Dynamic Utility Maximization Review of Economic Studies 23, 165–180 Summers, Lawrence H (1991) The Scientific Illusion in Empirical Macroeconomics In Hylleberg, Svend and Martin Paldam (Editors) New Approaches to Empirical Macroeconomics Oxford: Blackwell Publishers Swan, Trevor (1956) Economic Growth and Capital Accumulation Economic Record 32, 334–361 Swan, Trevor (1960) Economic Control in a Dependent Economy Economic Record 36, 51–66 442 Bibliography Taylor, John B (1979) Staggered Wage Setting in a Macro Model American Economic Review 69, 108–113 Temin, Peter (1989) Lessons from the Great Depression Cambridge, Massachusetts: MIT Press Theil, Henri (1971) Principles of Econometrics New York: John Wiley Tinbergen, Jan (1952) On the Theory of Economic Policy Amsterdam: North-Holland Tobin, James (1955) A Dynamic Aggregative Model Journal of Political Economy 63, 103–15 Tobin, James (1958) Liquidity Preference as Behavior Towards Risk Review of Economic Studies 25, 65–86 Tobin, James (1965) Money and Economic Growth Econometrica, 33, 671–684 Tobin, James (1967) The Neutrality of Money in Growth Models: A Comment Economica 34, 69–72 Tobin, James (1968) Notes on Optimal Monetary Growth Journal of Political Economy 76, 833–859 Tobin, James (1969) A General Equilibrium Approach to Monetary Theory Journal of Money, Credit and Banking 1, 15–29 Tobin, James (1975) Keynesian Models of Recession and Depression American Economic Review 65, 195–202 Tobin, James (1980) Asset Accumulation and Economic Activity Chicago: Chicago University Press Tobin, James and William C Brainard (1977) Asset Markets and the Cost of Capital In Bela Belassa and Richard Nelson (Editors), Economic Progress, Private Values and Public Policy: Essays in Honour of William Fellner Amsterdam: North-Holland Uzawa, Hirofumi (1968) Time Preference, the Consumption Function, and Optimum Asset Holdings In J N Wolfe (Editor) Value, Capital and Growth: Papers in Honor of Sir John Hicks Chicago: Aldine Publishing Company Weil, Philippe (1989) Overlapping Families of Infinitely-Lived Agents Journal of Public Economics 38, 183–198 Weil, Philippe (1991) Is Money Net Wealth? International Economic Review 37, 37–53 Wilson, Charles (1979) Anticipated Shocks and Exchange Rate Dynamics Journal of Political Economy 87, 639–647 Woodford, Michael (1995) Price Level Determinacy without Control of a Monetary Aggregate Carnegie-Rochester Conference Series on Public Policy 43, 1–46 Yaari, Menahen E (1965) Uncertain Lifetime, Life Insurance, and the Theory of the Consumer Review of Economic Studies 32, 137–150 II Classic References Barro, Robert J (1974) Are Governments Bonds Net Wealth? Journal of Political Economy 82, 1095–1117 Calvo, Guillermo A (1983) Staggered Prices in a Utility Maximization Framework Journal of Monetary Economics 12, 983–998 Cass, David (1965) Optimum Growth in an Aggregative Model of Capital Accumulation Review of Economic Studies 32, 233–40 Diamond, Peter (1965) National Debt in a Neoclassical Growth Model American Economic Review 55, 1126–50 Domar, Evsey V (1946) Capital Expansion, Rate of Growth and Employment Econometrica 14, 137–47 Dornbusch, Rudiger (1976) Expectations and Exchange Rate Dynamics Journal of Political Economy 84, 1161–76 Fisher, Irving (1930) The Theory of Interest New York: Macmillan Fleming, J Marcus (1962) Domestic Financial Policies under Fixed and under Floating Exchange Rates International Monetary Fund Staff Papers 9, 369–79 Bibliography 443 Friedman, Milton (1968) The Role of Monetary Policy American Economic Review 58, 1–17 Harrod, Roy F (1939) An Essay in Dynamic Theory Economic Journal 49, 14–33 Hicks, John R (1937) Mr Keynes and the ‘Classics’: A Suggested Interpretation Econometrica 5, 147–59 Keynes, John Maynard (1936) The General Theory of Employment, Interest and Money London: Macmillan Koopmans, Tjalling C (1965) On the Concept of Optimal Economic Growth In The Econometric Approach to Development Planning Amsterdam: North-Holland Kydland, Finn E and Edward C Prescott (1982) Time to Build and Aggregate Fluctuations Econometrica 50, 1345–70 Lucas, Robert E., Jr (1972) Expectations and the Neutrality of Money Journal of Economic Theory 4, 103-24 Lucas, Robert E., Jr (1976) Econometric Policy Evaluation: A Critique In The Phillips Curve and the Labor Market (Editors: Karl Brunner & Allan H Meltzer), 19–46 Amsterdam: NorthHolland Lucas, Robert E., Jr (1988) On the Mechanics of Economic Development Journal of Monetary Economics 22, 3–42 Modigliani, Franco (1944) Liquidity Preference and the Theory of Interest and Money Econometrica 12, 45–88 Mundell, Robert A (1963) Capital Mobility and Stabilization Policy under Fixed and Flexible Exchange Rates Canadian Journal of Economics and Political Science 29, 475–85 Phillips, A W (1958) The Relationship between Unemployment and the Rate of Change of Money Wages in the United Kingdom, 1861-1957 Economica 25, 283–99 Ramsey, Frank R (1928) A Mathematical Theory of Saving Economic Journal 38, 543–59 Romer, Paul M (1986) Increasing Returns and Long-Run Growth Journal of Political Economy 94, 1002–37 Romer, Paul M (1990) Endogenous Technological Change Journal of Political Economy 98, 71–102 Samuelson, Paul A (1958) An Exact Consumption-Loan Model of Interest with or without the Social Contrivance of Money Journal of Political Economy 66, 467–82 Solow, Robert M (1956) A Contribution to the Theory of Economic Growth Quarterly Journal of Economics 70, 65–94 Solow, Robert M (1957) Technical Change and the Aggregate Production Function Review of Economics and Statistics 39, 312–20 Taylor, John B (1993) Discretion versus Policy Rules in Practice Carnegie-Rochester Conferences Series on Public Policy 39, 195–214 Wicksell, Knuck (1907) The Influence of the Rate of Interest on Prices Economic Journal 17, 213–19 III Textbooks, Handbooks and Collected Works Acemoglu, Daron (2009) Introduction to Modern Economic Growth Princeton: Princeton University Press Agénor, Pierre Richard and Peter J Montiel (1996) Development Macroeconomics Princeton: Princeton University Press Aghion, Phillippe and Peter Howitt (2009) The Economics of Growth Cambridge, Massachusetts: MIT Press Aghion, Philippe and Peter Howitt (1998) Endogenous Growth Theory Cambridge, Massachusetts: MIT Press Azariadis, Costas (1993) Intertemporal Macroeconomics Cambridge, Massachusetts: Blackwell 444 Bibliography Barro, Robert J (Editor) (1989) Modern Business Cycle Theory Cambridge, Massachusetts: Harvard University Press Barro, Robert J and Xavier Sala-I-Martin (1995) Economic Growth New York: McGraw-Hill Bernanke, Ben S , Thomas Laubach, Frederic S Mishkin and Adam S Posen (1999) Inflation Target Lessons from the International Experience Princeton: Princeton University Press Bernanke, Ben S and Michael Woodford (2005) The Inflation-Targeting Debate Chicago: The University of Chicago Press Blanchard, Olivier J and Stanley Fischer (1989) Lectures on Macroeconomics Cambridge, Massachusetts: MIT Press Braun, Martin (1993) Differential Equations and their Applications, 4th Edition New York: Springer-Werlag Brock, W A and A G Malliaris (1989) Differential Equations, Stability and Chaos in Dynamic Economics Amsterdam: North-Holland Chiang, Alpha C (1992) Elements of Dynamic Optimization New York: McGraw-Hill Cooley, Thomas F (Editor) (1995) Frontiers of Business Cycle Research Princeton: Princeton University Press Claassen, Emil-Maria (1996) Global Monetary Economics Oxford: Oxford University Press Galí, Jordi (2008) Monetary Policy, Inflation and the Business Cycle, an Introduction to the New Keynesian Framework Princeton: Princeton University Press Gartner, Manfred (1993) Macroeconomics under Flexible Exchange Rates New York: Harvester Wheatsheaf Hartley, James E , Kevin D Hoover and Kevin D Salyer (Editors) (1998) Real Business Cycle a Reader London: Routledge Havrilesky, Thomas M (Editor) (1985) Modern Concepts in Macroeconomics Arlington Heights, Ill.: Harlan Davidson Heijdra, Ben J and Frederick van der Ploeg (2002) Foundations of Modern Macroeconomics Oxford: Oxford University Press Intriligator, M D (1971) Mathematical Optimization and Economic Theory Englewood Cliffs, New Jersey: Prentice Hall Kamien, Morton I and Nancy L Schwartz (1991) Dynamic Optimization: The Calculus of Variations and Optimal Control in Economics and Management Amsterdam: North-Holland Leonard, Daniel and Ngo Van Long (1992) Optimal Control Theory and Static Optimization in Economics Cambridge: Cambridge University Press Ljungqvist, Lars and Thomas J Sargent (2004) Recursive Macroeconomic Theory Cambridge, Massachusetts: MIT Press Lucas, Robert E., Jr., and Thomas J Sargent (Editors) (1981) Rational Expectations and Econometric Practice, Vols and Minneapolis: The University of Minnesota Press Lucas, Robert E, Jr (2002) Lectures on Economic Growth Cambridge, Massachusetts: Harvard University Press Mankiw, N Gregory and David Romer (Editors) (1991) New Keynesian Economics, Vols and Cambridge, Massachusetts: MIT Press Miller, Preston J (Editor) (1994) The Rational Expectations Revolution-Readings from the Frontline Cambridge, Massachusetts: MIT Press Nagatani, Keizo (1981) Macroeconomic Dynamics Cambridge: Cambridge University Press Obstfeld, Maurice and Kenneth Rogoff (1996) Foundations of International Macroeconomics Cambridge, Massachusetts: MIT Press Ploeg, Frederick van der (1994) The Handbook of International Economics Oxford: Blackwell Romer, David (2006) Advanced Macroeconomics 3th Edition New York: McGraw-Hill Sargent, Thomas J (1979) Macroeconomic Theory New York: Academic Press Sehti, Suresh P and Gerald L Thompson (2000) Optimal Control Theory Applications to Management Science and Economics, 2th Edition Norwell, Ma.: Kluwer Academic Publishers Seierstad, A and K Sydsaeter (1987) Optimal Control Theory with Economic Applications New York: Elsevier Bibliography 445 Snowdon, Bian and Howard R Vane (Editors) (1997) A Macroeconomic Reader London: Routledge Snowdon, Bian and Howard R Vane (2005) Modern Macroeconomics, its Origins, Development and Current State Cheltenhan, UK: Edward Elgar Solow, Robert M (2000) Growth Theory an Exposition, 2th Edition New York: Oxford University Press Stiglitz, Joseph E and Hirofumi Uzawa (Editors) (1969) Readings in the Modern Theory of Economic Growth Cambridge, Massachusetts: MIT Press Takayama, Akira (1993) Analytical Methods in Economics Ann Harbor: University of Michigan Press Taylor, John B and Michael Woodford (Editor) (1999) Handbook of Macroeconomics NorthHolland: Amsterdam Turnovsky, Stephen J (1995) Methods of Macroeconomic Dynamics Cambridge, Massachusetts: MIT Press Turnovsky, Stephen J (1997) International Macroeconomic Dynamics Cambridge, Massachusetts: MIT Press Walsh, Carl E (1998) Monetary Theory and Policy Cambridge, Massachusetts: MIT Press Wickens, Michael (2008) Macroeconomic Theory, a Dynamic General Equilibrium Approach Princeton: Princeton University Press Woodford, Michael (2003) Interest and Prices Foundations of a Theory of Monetary Policy Princeton: Princeton University Press Index A Absolute convergence, 98–99 Acemoglu and Ventura AK model, 133 budget stock constraint and transversality condition, 140 consumer and investment goods, 140 growth rate of real output, 137 labor productivity, 137–139 price index of intermediate inputs, 141 production functions, 140–141 Arbitrage differential equation, 342, 344, 345 Asset-pricing model, 387–388 Assets-to-GDP ratio, 310, 311 B Balance of payments algebra, 281 current account, 279 surplus, 272–273 Bang-bang control, 402 Bank reserves market, 368 C Calvo Phillips curve, 280 Cash in advance constraint (CIA), 173, 340 Central Bank balance sheets, 307–310 discount rate, 359 loss function, 349, 359, 367, 368 monetary policy rule, 346 nominal interest rate control, 17 real interest rate, 422–423 Taylor rule, 423–424, 432 © Springer Nature Switzerland AG 2018 F H Barbosa, Macroeconomic Theory, https://doi.org/10.1007/978-3-319-92132-7 Chronic inflation model algebra, 229 dynamical system, 229 equilibrium points, 229–231 periodical orbits and hopf bifurcation, 231–233 Cobb-Douglas function, 104 Constant primary deficit (surplus), 310–312 Constant stock of money, 310 Consumer’s utility function, 190–191 D Debt-to-GDP ratio, 309–312 Difference equations backward-looking model, 420–421 first-order difference equation backward solution, 418 endogenous variable, 417 forward solution, 418 linear system, 418–419 forward-looking model, 419–420 hybrid models characteristic equation, 426–427 matrix, 426 one equation case, 427–430 partitioned matrix, 427 Phillips curve example, 430 hybrid new Keynesian model, 431–434 Keynesian model, 421–422 encompassing specification, 424–426 stability, 425 new Keynesian model, 435 IS curve, 422, 435 Phillips curve, 422, 435 447 448 Difference equations (cont.) real interest rate, 422–423 Taylor rule, 423–424 Differential equations asset-pricing model, 387–388 economy’s model, 388 explicit/implicit rent of a house, 391–392 first-order linear differential equation equation’s solution, 371 homogeneous, 371 n first-order differential equations, 381–382 non-homogeneous, 372 stability analysis, 372 stable solution, 372 system, 376–381 unstable solution, 372, 373 goods market model, 387 government’s fiscal policy, 391 growth rate of money stock, 391 Harrod-Domar economic growth model, 387 hysteresis stable system, 384, 385 unstable solution, 385, 386 initial and terminal conditions, 382–383 model’s equilibrium and stability, 389–391 second-order linear differential equation, 372–373 complex conjugate roots, 374–375 distinct real roots, 374 equal real roots, 374 non-homogeneous, 375 Discounted infinite horizon optimal control, 399–402 Dynamic inconsistency, 347–349 E Endogenous growth models AK model, 132, 152 Cobb-Douglas function, 133 vs exogenous model, 135–136 human capital model, 132, 150, 151 inputs model, 132, 134 R&D investment, 132 Schumpeterian creative destruction model, 132, 134–135 Equilibrium inflation rate, 347 Euler equation, 280 European Union’s Maastricht Treaty, 38 Extended Mundell-Fleming-Dornbusch model fixed exchange rate algebra, 274 Index balance of payments surplus, 272–273 dynamical system, 274–275 experiment, 278, 279 fixed exchange rate, 273 growth rate of potential output, 273 interest rate parity equation, 273 IS curve, 273 monetary policy rule, 273 net exports, 272–273 Phillips curve, 273 predictions, 276–277 flexible exchange rate algebra, 293 dynamical system, 293–294 monetary policy rule, 293 predictions, 294–296 F Fiat-money economy, 345 First-order linear differential equation equation’s solution, 371 homogeneous, 371 n first-order differential equations, 381–382 non-homogeneous, 372 stability analysis, 372 stable solution, 372 system, 376–377 equilibrium solution, 377 stable system, 377–379 unstable system, 380–381 unstable solution, 372, 373 Fiscal deficit, 310 Fixed exchange rate extended Mundell-Fleming-Dornbusch model algebra, 274 balance of payments surplus, 272–273 dynamical system, 274–275 experiment, 278, 279 fixed exchange rate, 273 growth rate of potential output, 273 interest rate parity equation, 273 IS curve, 273 monetary policy rule, 273 net exports, 272–273 Phillips curve, 273 predictions, 276–277 Mundell-Fleming-Dornbusch model algebra, 268–269 dynamical system, 269–271 experiment, 270–272 IS curve, 267, 268 Index monetary policy rule, 267 Phillips curve, 267 uncovered interest rate parity equation, 267 new Keynesian model algebra, 281 BP curve, 279–280 dynamical system, 281–283 IS curve, 278–280 monetary policy rule, 280 predictions, 283–284 uncovered interest rate parity, 280 Flexible exchange rate extended Mundell-Fleming-Dornbusch model algebra, 293 dynamical system, 293–294 monetary policy rule, 293 predictions, 294–296 Mundell-Fleming-Dornbusch model algebra, 284–285, 288–289 dynamical system, 285–287, 289–291 experiment, 287–288, 291–292 IS curves, 284 Phillips curves, 284 new Keynesian model algebra, 296–297 dynamical system, 297–298 IS and Phillips curves, 296 predictions, 299 Foreign-currency denominated securities, 307 Friedman rule, 345 Friedman’s model algebra, 223–224 dynamical system, 224–226 monetary policy experiment, 227–228 G Goods aggregation aggregator equation, 34 Cobb-Douglas function, 35 consumption of, 34 expenditure function, 34–35 instantaneous utility function, 35–36 structures, 33–34 Goods and services market equilibrium, 330 Government budget constraint, 333–338 fiscal theory of price level, 330–331 hyperinflation (see Hyperinflation) inflation tax consumer surplus, 315–316 money demand curve, 314, 315 449 money demand equation, 314 representative agent, 317–318 revenue source, 314 public debt sustainability constant primary deficit (surplus), 310–312 constant stock of money, 310 real interest rate, 310 variable primary deficit (surplus), 312–314 Ricardian equivalence assumptions, 327 private and public sectors, 330 private sector’s budget constraint, 328–329 public sector’s budget constraint, 329 sustainable monetary regime, 332 treasury and Central Bank balance sheets consolidation, 307–310 Government’s intertemporal constraint, 325, 332 Gross domestic product (GDP), 309 Growth accounting factors of production, 113–114 labor productivity, 114, 116 potential output, 114–116 variable’s index, 114 H Harberger-Laursen-Metzler (HLM) Effect, 263–264 Harrod-Domar economic growth model, 387 Hazard rate, 78 Human capital accumulation of, 106–107 dynamical system, 107–108 labor productivity, 108–109 production function, 106–107 Hybrid models characteristic equation, 426–427 matrix, 426 one equation case, 427–430 partitioned matrix, 427 Phillips curve example, 430 Hybrid new Keynesian model (HNKM), 431–434 Hyperinflation bubble, 320 fiscal crisis and rational expectations government’s intertemporal constraint, 325 money-financed public deficit, 325, 326 450 Hyperinflation (cont.) non-autonomous differential equation, 326 strong hyperinflation, 326–327 weak hyperinflation, 327 fiscal crisis and rigidity with adaptive expectations, 322 algebra, 322–323 hyperinflation dynamics, 323–325 hypotheses, 318 inflation dynamics demand for money, 319 real quantity of money, 319 value of services of money, 319, 320 multiple equilibria hypothesis, 321 public debt and rate of change, 318 stylized facts, 318 Hysteresis, differential equations stable system, 384, 385 unstable solution, 385, 386 I Inflation acceleration, 269 Inflation rate, 268, 274, 281, 283 domestic inflation rates, 269, 272 dynamics of, 270 expected and observed, 349 foreign inflation rate, 269–272, 278, 279 loss function, 349 and output gap coefficient, 348 phase diagram, 270, 271 predicted, 360 Inflation rate inertia, 346, 347 Inflation tax money demand curve, 314, 315 money demand equation, 314 revenue source, 314 social cost consumer surplus, 315–316 representative agent, 317–318 Interest rate corridor, 360, 361 smoothing, 349–350 Keynesian model, 350–354 new Keynesian model, 354–358 term structure of algebra, 364 dynamical system, 364–365 experiment, 365–366 model with, 364 securities maturing, 362, 363 short-and long-term rates, 361–364, 369 yield curves, 361, 362 Index Interest rate parity, 281 International Reserves (IR), 307 Intertemporal approach government’s intertemporal constraint, 325 money-financed public deficit, 325, 326 non-autonomous differential equation, 326 strong hyperinflation, 326–327 weak hyperinflation, 327 IS curve, 156, 189 algebraic manipulation, 158–160 consumer preferences, 160–163 fixed exchange rate extended Mundell-Fleming-Dornbusch model, 273 Mundell-Fleming-Dornbusch model, 267, 268 new Keynesian model, 278–280 flexible exchange rate, 284 goods and services market equilibrium, 156 interest rate smoothing Keynesian model, 350 New Keynesian model, 354 natural rate of interest, 157–158 open economy, 52–53 real exchange rate gap, 254 real interest rate, 156 real international interest rate and current account deficit, 254 real long-term interest rate, 157 saving and investment, 253 sum of investment and public deficit, 254 wealth in, 255–256 J Jacobian matrix, 269, 274, 281, 289, 294, 297 K Keynesian model difference equations, 421–422 encompassing specification, 424–426 stability, 425 encompassing of, 217–218 inflation inertia algebra, 198 coordination of monetary and fiscal policies, 203–204 demand shock, 201–202 dynamical system, 198–199 monetary policy experiment, 199–201, 204–206 supply shock, 202–203 without inflation inertia, 206–208 Index inflation target, 220, 221 interest rate smoothing in continuous-time model, 350 differential equation, real interest rate, 351 dynamical system, 351–353 experiment, 352–354 IS curve, 350 Phillips curve, 351 IS curve, 214 algebraic manipulation, 158–160 consumer preferences, 160–163 goods and services market equilibrium, 156 natural rate of interest, 157–158 real interest rate, 156 real long-term interest rate, 157 LM curve CIA, 173 MIU, 171–173 money market’s equilibrium, 170 money supply, 170 nominal stock of money, 170 opportunity cost, 169 real quantity of money, 169 transaction cost, 173–174 transactions volume, 169 natural interest rate, 168 new Keynesian IS curve consumer equilibrium, 163–164 continuous variables, 167–168 discrete variables, 164–167 new Keynesian Phillips curve, 186–189 open economy algebra, 250–251 equation, 251–252 phase diagram of, 218, 219 Phillips curve, 215 inflation and output gap, 181–182 inflation and unemployment, 179–180 inflation inertia, 182–184 Keynesian vs New Keynesian, 186 market power and price setting, 176–179 Okun’s law, 180–181 without inflation inertia, 184–185 stability of, 218 Taylor rule monetary policy rule, 176 reserve market, 175 See also Mundell-Fleming-Dornbusch model Keynesian Phillips Curve, 257–259 451 L Leibnitz rule, 337 Linear optimal control, 402 Liquidity services of money, 340 LM curve CIA, 173 MIU, 171–173 money market’s equilibrium, 170 money supply, 170 nominal stock of money, 170 opportunity cost, 169 real quantity of money, 169 transaction cost, 173–174 transactions volume, 169 Loss function, 348, 349 Lucas human capital model growth of the co-state variables, 143 growth rate of human capital, 142 growth rate of labor productivity, 144 physical capital accumulation, 142 production function, 141, 142 M Marshall-Lerner condition, 248–249 MIU, see Money in the utility function Monetary Base (M ), 307 Monetary policy rule (MPR) fixed exchange rate extended Mundell-Fleming-Dornbusch model, 273 Mundell-Fleming-Dornbusch model, 267 new Keynesian model, 280 flexible exchange rate extended Mundell-Fleming-Dornbusch model, 293 Mundell-Fleming-Dornbusch model, 289, 292 new Keynesian model, 296 money stock control agent’s budget constraint, 12–13 consumption and money services, 12 current-value Hamiltonian, 13–14 dynamical system, 14–16 goods and services market, 14 government budget constraint, 14 nominal interest rate control algebra, 17–20 central bank, 17 current-value Hamiltonian, 17 dynamical system, 20–21 government budget constraint, 17 452 Monetary policy rule (MPR) (cont.) Hessian matrix, 16 real stock of money, 16 utility function’s concavity, 16 with zero nominal interest rate, 346 Monetary theory and policy, 367–369 dynamic inconsistency, 347–349 inflation targeting, 358–360 interest rate smoothing, 349–350 Keynesian model, 350–354 new Keynesian model, 354–358 monetary policy operational procedures, 360–362 optimum quantity of money, 345–346 price of money arbitrage equation, 342 bubble solution, 342 demand for money, 340, 341 essentiality, 340–341 fundamentals solution, 342 indeterminacy, 344 inverse of price level, 339 liquidity services of money, 340 multiple equilibria, 343–344 phase diagram, 344 real quantity of money demanded, 340 unique equilibrium, 343 value of the services of money, 340, 341 term structure of interest rates (see Interest rate, term structure of) zero lower bound nominal interest rate, 346–348 Money in the utility function (MIU), 171–173, 340 MPR, see Monetary policy rule Multiple equilibria, 343 Mundell-Fleming-Dornbusch model fixed exchange rate algebra, 268–269 dynamical system, 269–271 experiment, 270–272 IS curve, 267, 268 monetary policy rule, 267 Phillips curve, 267 uncovered interest rate parity equation, 267 flexible exchange rate algebra, 284–285, 288–289 dynamical system, 285–287, 289–291 experiment, 287–288, 291–292 IS curves, 284 Phillips curves, 284 Index N Natural exchange rate, 253–256 Natural rate of interest, 168 Net exports, 272–273 Net wealth, 281 New Keynesian model, 252–253 aggregate consumption, 46–47, 74 algebra, 75–76, 209 consumer equilibrium, 163–164 continuous variables consumer decision-making, 167 interest rate gap, 167–168 difference equations, 435 IS curve, 422, 435 Phillips curve, 422, 435 real interest rate, 422–423 Taylor rule, 423–424 discrete variables equations, 165 vs Keynesian IS curves, 165–166 log approximation, 166–167 log-linear approximation, 164 log of potential output, 165 domestic and foreign goods, 47–49 domestic and imported goods, 47–48 dynamical system, 209–210 equilibrium real output, 50–51 Euler equation, 51–52 financial markets, 49–50, 74–75 fixed exchange rate algebra, 281 BP curve, 279–280 dynamical system, 281–283 IS curve, 278–280 monetary policy rule, 280 predictions, 283–284 uncovered interest rate parity, 280 flexible exchange rate algebra, 296–297 dynamical system, 297–298 IS and Phillips curves, 296 predictions, 299 inflation rate changes, 221 inflation target, 221 interest rate smoothing algebra, 354 Calvo Phillips curve, 354 dynamical system, 354–355 experiment, 357–358 IS curve, 354 model’s solution, 355–356 prediction, 356–357 international interest rate, 54–55 Index IS curve, 52–53, 76–77, 214–215 log-linear approximation, 76 long-term equality, 75 monetary policy experiment, 210–213 natural interest rate, 54–55 net creditor, 72, 74 net debtor, 73, 74 objective function, 46–47 perfect foresight stationary equilibrium, 55–57 phase diagram of, 220 Phillips curve, 215–217, 220, 222 time dedicated to labor, 46–47 uncovered interest rate parity, 53–54 New Keynesian Phillips curve, 186–189, 195, 259–261 Nominal exchange rate, 268 Nominal interest rate, 340, 359–360 No-Ponzi game hypothesis, 313 O Okun’s law, 180–181 Open economy, 57–61, 262–265, 299–304 budget constraint, 71 dynamical system, 72–73 Euler equation, 71 experiment, 73–74 finite-life, 84 fixed exchange rate extended Mundell-Fleming-Dornbusch model, 272–279 Mundell-Fleming-Dornbusch model, 267–272 new Keynesian model, 278–284 flexible exchange rate extended Mundell-Fleming-Dornbusch model, 293–296 Mundell-Fleming-Dornbusch model, 284–292 new Keynesian model, 296–299 goods aggregation aggregator equation, 34 Cobb-Douglas function, 35 consumption of, 34 expenditure function, 34–35 instantaneous utility function, 35–36 structures, 33–34 goods and services arbitrage purchasing power parity, 239–240 relative purchasing power parity, 240–241 453 terms of trade and real exchange rate, 242–243 tradable and non-tradable goods, 241–242 interest rate arbitrage covered interest rate parity, 246–247 exchange rate determination, 244–246 uncovered interest rate parity, 244 uncovered real interest rate parity, 247 Keynesian IS Curve algebra, 250–251 equation, 251–252 Keynesian Phillips Curve, 257–259 Marshall-Lerner condition, 248–249 natural exchange rate, 253–256 new Keynesian model, 252–253 aggregate consumption, 46–47, 74 algebra, 75–76 domestic and foreign goods, 47–49 domestic and imported goods, 47–48 equilibrium real output, 50–51 Euler equation, 51–52 financial markets, 49–50 financial wealth, 74–75 international interest rate, 54–55 IS curve, 52–53, 76–77 log-linear approximation, 76 long-term equality, 75 natural interest rate, 54–55 net creditor, 72, 74 net debtor, 73, 74 objective function, 46–47 perfect foresight stationary equilibrium, 55–57 time dedicated to labor, 46–47 uncovered interest rate parity, 53–54 new Keynesian Phillips Curve, 259–261 risk premium, 43–46 Solow growth model current account, 111–112 domestic savings, 109–110 foreign debt, sustainability, 113 foreign savings, 109–110 gross domestic product growth, 110 technological progress and population, 110 Taylor Rule, 256–257 time preference (see Time preference) Opportunity cost of resources, 340 Optimal control theory, 407–415 basic problem, 393–395 comparative dynamics first-order condition equations, 402–403 454 Index Optimal control theory (cont.) permanent change, 403–405 transitory change, 405–407 discounted infinite horizon, 399–402 dynamical system, 397–398 economic interpretation, 399 Hamiltonian’s partial derivative, 395–396 linear optimal control, 402 transversality condition, 396–397 Overlapping generation (OLG) model, 85–87, 149, 340 budget constraint, 128 capital-consumption ratio, 128 consumption per-capita, 127, 128 dynamical system, 129–131 Euler equation, 127 exogenous growth model, 129 finite-life actuarial notes, 78–79 aggregate consumption, 81–82 aggregate wealth, 82–83 consumer, 79–81 dynamical system, 83 economy with production, 83 open economy, 84 private sector’s total wealth, 84–85 probability of death, 77–78 public debt, 84–85 infinite-life aggregate consumption, 66–67 budget constraint, 64 consumption function, 64–66 current-value Hamiltonian, 64 dynamical system, 69–70 financial wealth, 68 new generations growth rate, 63–64 output, 68 transversality condition, 64 labor productivity, 132 open economy budget constraint, 71 dynamical system, 72–73 Euler equation, 71 experiment, 73–74 new Keynesian curve, 72–77 Ricardian equivalence, 69–71 production function, 102 rate of saving, 102–103 rates of return on capital, 103–104 share of capital in output, 106 stationary equilibrium, 102 Phillips curve, 186, 194, 195 δ parameter, 347 fixed exchange rate extended Mundell-Fleming-Dornbusch model, 273 Mundell-Fleming-Dornbusch model, 267 flexible exchange rate Mundell-Fleming-Dornbusch model, 284 new Keynesian model, 296 inflation inertia, 182–184 and output gap, 181–182 and unemployment, 179–180 interest rate smoothing Keynesian model, 351 New Keynesian model, 354 market power and price setting, 176–179 Okun’s law, 180–181 output gap in loss function, 348 without inflation inertia, 184–185 Price of money arbitrage equation, 342 bubble solution, 342 demand for money, 340, 341 essentiality, 340–341 fundamentals solution, 342 indeterminacy, 344 inverse of price level, 339 liquidity services of money, 340 multiple equilibria, 343–344 phase diagram, 344 real quantity of money demanded, 340 unique equilibrium, 343 value of the services of money, 340, 341 Primary surplus, 309, 331 Public debt sustainability, 308 constant primary deficit (surplus), 310–312 constant stock of money, 310 real interest rate, 310 variable primary deficit (surplus), 312–314 P Per-capita income elasticity of substitution, 104–106 linear approximation, 102 population growth, 103 R Ramsey-Cass-Koopmans (RCK) model, 149 behavioral assumption, 119 dynamical system, 122–124 Euler Equation, 120–122 Index experiment, 125–126 growth rate of consumption, 122 labor productivity, 125 law of motion of capital, 119 Rational expectations equilibria, 433, 434 Real business cycle model agent’s income, 21–22 consumption and leisure, 21–23 dynamical system, 23–25 experiments, 24, 26–28 growth rate of consumption, 23 labor and leisure, 21 production function, 21 time constraint, 22 transversality condition, 22–23 Real interest rate, 268, 281, 289, 310 Relative convergence, 98–100 Representative agent model, 28–32 capital accumulation equation, 3–4 decision’s arbitrage condition, 4–5 dynamical system, 5–6 government spending budget constraints, 8–9 experiments, 9–12 phase diagram, private sector, public sector, initial capital-labor ratio, instantaneous utility flow, monetary economy (see Monetary policy rule (MPR)) open economy (see Open economy) optimal solution, production function, rate of time preference, 3, real business cycle agent’s income, 21–22 consumption and leisure, 21–23 dynamical system, 23–25 experiments, 24, 26–28 growth rate of consumption, 23 labor and leisure, 21 production function, 21 time constraint, 22 transversality condition, 22–23 Ricardian equivalence assumptions, 327 private sector’s budget constraint, 328–330 public sector’s budget constraint, 329, 330 Risk premium, 43–46, 54 Romer’s varieties of inputs model, 144–145 455 S Saddle point, 380–381 Second-order linear differential equation, 372–373 complex conjugate roots, 374–375 distinct real roots, 374 equal real roots, 374 non-homogeneous, 375 Social cost inflation tax consumer surplus, 315–316 representative agent, 317–318 of money production, 345 Solow growth model, 116–118 absolute convergence, 98–99 comparative dynamics labor productivity, 96–97 predictions, 93–96 dynamic inefficiency, 98 golden rule, 97–98 growth accounting factors of production, 113–114 labor productivity, 114, 116 potential output, 114–116 variable’s index, 114 human capital accumulation of, 106–107 dynamical system, 107–108 labor productivity, 108–109 production function, 106–107 income per-capita elasticity of substitution, 104–106 linear approximation, 102 population growth, 103 production function, 102 rate of saving, 102–103 rates of return on capital, 103–104 share of capital in output, 106 stationary equilibrium, 102 open economy current account, 111–112 domestic savings, 109–110 foreign debt, sustainability, 113 foreign savings, 109–110 gross domestic product growth, 110 technological progress and population, 110 rate of convergence, 100–102 real output algebra, 91–92 capital stock, 90 dynamical system, 92–94 labor force, 89–90 456 Solow growth model (cont.) labor productivity, 89–90 natural rate, 90–91 population growth, 90 technological progress, 91 warranted rate, 90–91 relative convergence, 98–100 Solow residual, 114 T Taylor rule, 284, 293, 296, 346, 350 Central Bank, 423–424, 432 monetary policy rule, 176 new Keynesian model, 423–424 open economy macroeconomics, 256–257 reserve market, 175 Terms of trade, 268, 274, 281 Term structure of interest rates, see Interest rate, term structure of Time preference constant rate adjustment dynamics, 38–39 agent’s wealth, 36 algebra, 37 comparative dynamics exercise, 38 dynamical system, 37–38 instantaneous utility flow, 36 international financial markets, 36–37 Index variable rate algebra, 41 dynamical system, 41–43 Hamiltonian’s expression, 40 new state variable, 39 utility flow, 39–40 Transaction costs (TC), 340 Treasury Bills and Bonds (BBC), 307 Treasury constraint, 308 Treasury Deposits (TD), 307 U Uncovered interest rate parity, 267, 280, 284 Unique equilibrium, 343 V Variable primary deficit (surplus) algebra, 312–313 debt sustainability, 313–314 in differential equation, 312 Z Zero lower bound nominal interest rate, 346–347 .. .Macroeconomic Theory Fernando de Holanda Barbosa Macroeconomic Theory Fluctuations, In ation and Growth in Closed and Open Economies Fernando de Holanda Barbosa FGV EPGE... courses: (i) Macroeconomics; (ii) Open Economy Macroeconomics; (iii) Monetary Theory; and (iv) Economic Growth The Macroeconomics course should include Chaps 1, 3, 6, 7, and 10 The Open Economy Macroeconomics... an increasing variety of intermediate goods used in the production process, an outcome of firms’ research -and- development investment; and (iv) technological innovations leading to machinery and