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Dynamic Macroeconomics

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Dynamic Macroeconomics

George Alogoskoufis

The MIT PressCambridge, MassachusettsLondon, England

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c⃝ 2019 The Massachusetts Institute of Technology

All rights reserved. No part of this book may be reproduced in any form by any electronic or mechanical means(including photocopying, recording, or information storage and retrieval) without permission in writing from thepublisher.

This book was set in Times New Roman by Westchester Publishing Services. Printed and bound in the UnitedStates of America.

Library of Congress Cataloging-in-Publication Data

Names: Alogoskoufis, George, author.Title: Dynamic macroeconomics / George Alogoskoufis.Description: Cambridge, MA :MIT Press, [2019] | Includes bibliographicalreferences and index.

Identifiers: LCCN 2018060935 | ISBN 9780262043014 (hardcover : alk. paper)Subjects: LCSH: Macroeconomics—Mathematical models. | Equilibrium(Economics)—Mathematical models.

Classification: LCC HB172.5 .A396 2019 | DDC 339—dc23 LC record available athttps://lccn.loc.gov/2018060935

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To Spyros, Athinais, and Danae

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Contents

List of Figures and Table xxiPreface xxvii

1 Introduction 11.1 The Nature and Evolution of Macroeconomics 2

1.1.1 Pre-Keynesian Macroeconomics 21.1.2 Classical and Keynesian Macroeconomics 41.1.3 Microeconomic Foundations of Macroeconomics 61.1.4 Deterministic and Stochastic Dynamic General Equilibrium Models 7

1.2 Key Facts about Long-Run Economic Growth 111.2.1 Cross-Country Differences in Per Capita Output and Income 111.2.2 Evolution of Per Capita Output and Income over Time 131.2.3 Economic Growth and Convergence since 1820 14

1.3 Key Facts about Aggregate Fluctuations 181.3.1 Frequency, Severity, and Duration of Recessions 181.3.2 Unemployment in Booms and Recessions 201.3.3 Trends and Fluctuations in the Price Level and Inflation 221.3.4 Monetary Policy and Government Debt 261.3.5 Monetary Policy and Inflation in the Postwar Period 31

1.4 Conclusion 32

2 The Intertemporal Approach 332.1 Models, Variables, and Functions 342.2 General Equilibrium in a One-Period Competitive Model 36

2.2.1 Endowments, Preferences, and the Optimal Behavior of Households 362.2.2 The Production Function and the Profit-Maximizing Behavior

of Firms 382.2.3 The Cobb-Douglas Production Function 402.2.4 General Equilibrium in the One-Period Model 40

2.3 Savings and Investment in a Two-Period Competitive Model 422.3.1 The Representative Household in a Two-Period Model 422.3.2 Implications of the Euler Equation for Consumption 452.3.3 The Case of a Constant Elasticity of Intertemporal Substitution 462.3.4 Firms, Technology, and the Optimal Output Path 48

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2.3.5 General Equilibrium in the Two-Period Model 492.3.6 Diagrammatic Exposition of the Intertemporal Equilibrium 532.3.7 Implications for Growth and Business Cycle Theory 55

2.4 Consumption and Labor Supply in a One-Period Competitive Model 562.4.1 The Optimal Choice of Consumption and Labor Supply 562.4.2 Income and Substitution Effects on Labor Supply 582.4.3 The Frisch Elasticity of Labor Supply 602.4.4 The Production Function and the Optimal Decisions of Firms 612.4.5 General Equilibrium and the Determination of Output

and Employment 612.5 Consumption and Labor Supply in a Two-Period Competitive Model 62

2.5.1 Optimal Consumption and Labor Supply in a Two-Period Model 632.5.2 Intertemporal Substitution in Consumption and Labor Supply 642.5.3 Optimal Production Decisions of Firms 652.5.4 General Equilibrium and the Determination of Output

and Employment 662.5.5 Implications for Business Cycle Theory 68

2.6 Money, Prices, and Inflation in a Two-Period Competitive Model 692.6.1 The Representative Household and the Demand for Money 692.6.2 The Classical Dichotomy and the Neutrality of Money 712.6.3 The Two-Period Competitive Model and Classical Monetary

Theory 742.7 Fiscal Policy in a Two-Period Competitive Model 74

2.7.1 Government Expenditure and Taxes in a One-Period Economy 742.7.2 Income Taxes and Labor Supply 762.7.3 Government Expenditure, Taxes, and Debt in a Two-Period Economy 772.7.4 Ricardian Equivalence between Tax and Debt Finance 782.7.5 Income Taxation and Aggregate Savings and Investment 812.7.6 Implications for Fiscal Policy and Government Debt 81

2.8 The Treatment of Time and the Intertemporal Approach 822.9 Conclusion 84

3 Savings, Investment, and Economic Growth 853.1 The Solow Growth Model 87

3.1.1 The Neoclassical Production Function 873.1.2 The Cobb-Douglas Production Function 893.1.3 Population Growth and Technical Progress 903.1.4 Savings, Capital Accumulation, and Economic Growth 903.1.5 The Balanced Growth Path and the Convergence Process 923.1.6 The Rate of Growth of Capital and Output 933.1.7 Significance of the Inada Conditions 95

3.2 Competitive Markets, the Real Interest Rate, and Real Wages 963.3 The Savings Rate and the Golden Rule 97

3.3.1 The Savings Rate and the Balanced Growth Path 983.3.2 The Savings Rate, the Golden Rule, and Dynamic Inefficiency 993.3.3 The Elasticity of Steady State Output with Respect to

the Savings Rate 101

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Contents ix

3.4 Total Factor Productivity and Population Growth 1023.4.1 Dynamic Effects of Total Factor Productivity in the Solow Model 1033.4.2 Dynamic Effects of Population Growth in the Solow Model 104

3.5 Speed of Convergence toward the Balanced Growth Path 1043.6 The Process of Economic Growth and the Solow Model 106

3.6.1 The Kaldor Stylized Facts of Economic Growth 1073.6.2 Differences in Per Capita Output and Income between Developed

and Less Developed Economies 1083.6.3 Conditional Convergence 110

3.7 Convergence with a Cobb-Douglas Production Function 1103.8 Dynamic Simulations of a Calibrated Solow Model 111

3.8.1 The Solow Model in Discrete Time 1123.8.2 The Calibrated Solow Model 1133.8.3 Dynamic Simulations of the Model 114

3.9 Conclusion 117

4 The Representative Household Model of Optimal Growth 1194.1 The Optimal Intertemporal Path of Consumption 1214.2 The Ramsey Model of Economic Growth 124

4.2.1 The Production Function 1244.2.2 The Utility Function of the Representative Household 1254.2.3 The Accumulation of Capital and the Optimality of the Decentralized

Competitive Equilibrium 1264.2.4 Conditions for Utility Maximization by the Representative Household 1284.2.5 The Euler Equation for Consumption 1294.2.6 The Intertemporal Budget Constraint of the Representative

Household 1304.2.7 The Transversality Condition with an Infinite Time Horizon 1324.2.8 The Consumption Function of the Representative Household with

an Infinite Horizon 1334.3 Dynamic Adjustment and the Balanced Growth Path 135

4.3.1 Dynamic Adjustment toward the Balanced Growth Path 1354.3.2 The Balanced Growth Path and the Modified Golden Rule 1384.3.3 Effects of a Permanent Increase in the Pure Rate of Time Preference 1394.3.4 Effects of a Permanent Increase in Total Factor Productivity 1414.3.5 Effects of a Permanent Increase in the Rate of Growth of Population 142

4.4 Properties of the Adjustment Path and the Speed of Convergence 1434.5 Dynamic Simulations of a Calibrated Ramsey Model 146

4.5.1 The Ramsey Model in Discrete Time 1464.5.2 The Calibrated Ramsey Model 1484.5.3 Dynamic Simulations of the Model 149

4.6 Conclusion 152

5 Overlapping Generations Models of Growth 1535.1 The Diamond Model 154

5.1.1 Definitions 1555.1.2 The Production Function 155

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5.1.3 The Intertemporal Utility Function of Households 1555.1.4 Markets and the Behavior of Households 1565.1.5 Capital Accumulation and the Dynamic Adjustment of the Economy 1575.1.6 A Simplified Diamond Model with Logarithmic Preferences

and Cobb-Douglas Technology 1595.1.7 The Speed of Adjustment in the Simplified Diamond Model 1635.1.8 Welfare Implications of the Diamond Model and the Possibility

of Dynamic Inefficiency 1645.1.9 Dynamic Simulations of a Calibrated Diamond Model 165

5.2 The Blanchard-Weil Model 1695.2.1 Definitions 1695.2.2 The Production Function 1705.2.3 The Intertemporal Utility Function of Households

and Household Consumption 1705.2.4 Aggregation across Generations 1725.2.5 The Model in Terms of Efficiency Units of Labor 1735.2.6 The Balanced Growth Path and the Adjustment Path 173

5.3 Dynamic Simulations of a Calibrated Blanchard-Weil Model 1775.3.1 The Blanchard-Weil Model in Discrete Time 1785.3.2 Dynamic Simulations of the Model 178

5.4 Conclusion 182

6 Fiscal Policy and Economic Growth 1836.1 The Government Budget Constraint 185

6.1.1 Government Deficits, Debt, and Solvency 1856.2 Ricardian Equivalence and the Ramsey Model 187

6.2.1 Ricardian Equivalence between Government Debt and Taxes 1876.2.2 Government Expenditure, Taxes, and Debt in the Ramsey Model 188

6.3 Dynamic Effects of Fiscal Policy in the Blanchard-Weil Model 1916.3.1 The Blanchard-Weil Model with Government Expenditure and Debt 1916.3.2 Government Debt, Taxes, and Redistribution across Generations 1926.3.3 Dynamic Simulations of Fiscal Policy in a Calibrated

Blanchard-Weil Model 1946.4 Dynamic Effects of Distortionary Taxation 201

6.4.1 Distortionary and Nondistortionary Taxes 2016.4.2 Dynamic Effects of Capital Income and Business Gross

Profits Taxation 2036.4.3 Dynamic Simulations of Increases in Capital Income and Business

Gross Profits Taxation 2056.5 Conclusion 206

7 Money, Inflation, and Economic Growth 2097.1 Private Consumption and Money Demand in a Representative

Household Model 2117.1.1 Money in the Utility Function of Households 2117.1.2 Nominal and Real Interest Rates and the Opportunity Cost

of Real Money Balances 212

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Contents xi

7.1.3 First-Order Conditions for an Optimum 2127.1.4 The Money Demand Function 2137.1.5 Growth Rate of the Money Supply and Inflation 2147.1.6 The Euler Equation for Consumption 215

7.2 Aggregate Capital Accumulation in a Ramsey Model with Money 2167.2.1 The Production Function, the Real Interest Rate, and the Real Wage 2167.2.2 The Inflation Tax and the Accumulation of Capital 216

7.3 Effects of the Growth Rate of the Money Supply in the RamseyMonetary Model 2187.3.1 The Balanced Growth Path in the Ramsey Model with Money 2197.3.2 The Superneutrality of Money and Inflation 2207.3.3 The Welfare Costs of Inflation in a Ramsey Model 221

7.4 Effects of Monetary Growth in an OLG Model 2227.4.1 The Blanchard-Weil Model with Money 2237.4.2 Real Effects of the Growth Rate of the Money Supply 2247.4.3 A Dynamic Simulation of the Effects of a Rise in the Growth

Rate of the Money Supply in a Calibrated Blanchard-Weil Model 2277.5 Conclusion 229

8 Externalities, Human Capital, and Technical Progress 2318.1 Externalities from Capital Accumulation and Economic Growth 232

8.1.1 Definitions 2338.1.2 The Production Function 2338.1.3 Externalities from the Accumulation of Capital 2248.1.4 Determination of the Real Interest Rate and the Real Wage 2378.1.5 The Savings Rate and the Endogenous Growth Rate 2388.1.6 Externalities and Endogenous Growth in the Ramsey Model 2398.1.7 The Suboptimality of the Competitive Equilibrium with Externalities

Due to Capital Accumulation 2418.1.8 Externalities and Endogenous Growth in the Blanchard-Weil Model 2428.1.9 Fiscal Policy and Endogenous Growth 2458.1.10 Convergence in Exogenous and Endogenous AK Growth Models 247

8.2 Investment in Human Capital and Economic Growth 2488.2.1 The Extended Solow Model and the Share of Spending on Education

and Training 2498.2.2 The Balanced Growth Path in the Extended Solow Model 2508.2.3 Endogenous Growth in the Extended Solow Model 2518.2.4 The Jones Model of Human Capital Accumulation 2528.2.5 The Lucas Model of Human Capital Accumulation

and Endogenous Growth 2538.2.6 A Detailed Analysis of the Lucas Model 254

8.3 Ideas, Innovations, and Technical Progress 2588.3.1 Key Features of Ideas and Innovations 2588.3.2 Key Elements of an Ideas-and-Innovations Growth Model 2598.3.3 Endogenous Determination of the Rate of Technical Progress 2618.3.4 The Balanced Growth Path with Endogenous Technical Progress 261

8.4 Unified Growth Theory and the Transition from Stagnation to Growth 262

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8.5 Institutions and Long-Run Growth 2638.6 The New Stylized Facts of Economic Growth 2658.7 Conclusion 266

9 Dynamic Stochastic Models under Rational Expectations 2699.1 A Stochastic Expectational Model of a Competitive Market 271

9.1.1 Absence of Uncertainty and Perfect Foresight 2729.1.2 Uncertainty and Adaptive Expectations 2739.1.3 The Rational Expectations Hypothesis 275

9.2 Rational Expectations for Linear Autoregressive Processes 2779.3 First-Order Linear Expectational Models 279

9.3.1 The Method of Repeated Substitutions 2799.3.2 The Method of Factorization 2819.3.3 The Method of Undetermined Coefficients 2829.3.4 Two Additional Economic Examples 2829.3.5 Alternative Assumptions about the Evolution

of Exogenous Variables 2849.3.6 The Expectational Competitive Market Model Revisited 286

9.4 Second-Order Linear Expectational Models 2869.4.1 The Method of Factorization 2879.4.2 The Method of Undetermined Coefficients 2889.4.3 An Economic Example of a Second-Order System 290

9.5 Multivariate Linear Models with Rational Expectations 2919.5.1 The Blanchard-Kahn Method 2919.5.2 Other Solution Methods 2939.5.3 A Second-Order Example of the Blanchard-Kahn Method 293

9.6 Rational Expectations and Learning 2959.7 Conclusion 295

10 Consumption and Portfolio Choice under Uncertainty 29710.1 Consumption and Portfolio Choice 298

10.1.1 The Random Walk Model of Consumption 30110.1.2 The Consumption Capital Asset Pricing Model 302

10.2 Full Analysis of Consumption and Portfolio Choice 30310.2.1 The Case of Logarithmic Preferences 30310.2.2 Quadratic Preferences and Certainty Equivalence 30510.2.3 The Permanent-Income Hypothesis with Quadratic

Preferences 30610.2.4 The Consumption CAPM with Quadratic Preferences 30710.2.5 The Efficient Markets Hypothesis 308

10.3 Precautionary Savings and Borrowing Constraints 31010.4 Conclusion 311

11 Investment and the Cost of Capital 31311.1 Optimal Investment with Convex Adjustment Costs 315

11.1.1 The Choice of Optimal Investment 31511.1.2 The Case of Zero Adjustment Costs 317

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11.1.3 The Investment Function with Convex Adjustment Costs 31711.1.4 The Determinants of q 31711.1.5 Dynamic Adjustment of q and the Capital Stock K 318

11.2 Optimal Investment under Uncertainty 32011.2.1 The Value of a Firm under Uncertainty 32111.2.2 The Lucas-Prescott Model of Investment under Uncertainty 32311.2.3 Rational Expectations Equilibrium and Aggregate Investment

in the Lucas-Prescott Model 32511.3 Conclusion 327

12 Money, Interest, and Prices 32912.1 The Functions of Money 33112.2 The Supply of Money and Central Banks 332

12.2.1 Central Banks and Their Functions 33212.2.2 Central Banks and the Money Supply 333

12.3 The Demand for Money 33612.4 Nominal Interest Rates and Short-Run Equilibrium in the Money Market 33912.5 The Long-Run Neutrality of Money 343

12.5.1 Monetary Growth, Inflation, and Nominal Interest Ratesin the Long Run 345

12.5.2 The Welfare Cost of Inflation 34612.5.3 The Long-Run Neutrality of Money and Monetary Reforms 346

12.6 Money and the Price Level in Dynamic General Equilibrium Models 34712.6.1 The Samuelson OLG Model 34712.6.2 Money in the Utility Function of a Representative

Household 35112.6.3 Cash in Advance in a Representative Household Model 35312.6.4 Cash in Advance in an OLG Model 355

12.7 Nominal and Real Interest Rates and the Money Supply 35712.7.1 Money in the Utility Function of a Representatitve Household 35712.7.2 Cash in Advance in a Representative Household Model 35912.7.3 Cash in Advance in an OLG Model 35912.7.4 The Liquidity Effect in Representative Household Models 360

12.8 Interest Rate Pegging and Price Level Indeterminacy 36112.8.1 Interest Rate Pegging and Price Level Indeterminacy in Representative

Household Models 36112.8.2 The Wicksell Solution to the Problem of Price Level

Indeterminacy 36212.8.3 The Fiscal Theory of the Price Level 36312.8.4 The Pigou Effect and Price Level Determinacy in OLG Models 364

12.9 Money Growth, Seigniorage, and Inflation 36412.9.1 Relations between Monetary Growth, Seigniorage, and Inflation 36512.9.2 The Seigniorage Laffer Curve 36712.9.3 The Demand for Seigniorage and Equilibrium with High Inflation 36812.9.4 The Transition to Hyperinflation 36812.9.5 How Can High Inflation and Hyperinflation be Tackled? 371

12.10 Conclusion 372

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13 The Stochastic Growth Model of Aggregate Fluctuations 37513.1 The Stochastic Growth Model 376

13.1.1 Extending the Ramsey Model to Account for AggregateFluctuations 377

13.1.2 The Representative Firm 37713.1.3 The Representative Household 37813.1.4 Exogenous Population Growth, Efficiency of Labor,

and Government Expenditure 37813.1.5 Labor Supply of the Representative Household 38013.1.6 Intertemporal Substitution in Labor Supply 38113.1.7 Uncertainty and the Behavior of the Representative

Household 38213.2 A Simplified Version of the Stochastic Growth Model 383

13.2.1 Fluctuations of Output in the Simplified Stochastic GrowthModel 384

13.2.2 The Simplified Stochastic Growth Model and the Evidenceon Aggregate Fluctuations 385

13.3 A Log-Linear Approximation to the General Stochastic Growth Model 38613.3.1 The Steady State 38713.3.2 Log-Linearizing the Model around the Steady State 388

13.4 Solving the Log-Linear Stochastic Growth Model 39013.4.1 Aggregate Fluctuations around the Steady State 39113.4.2 A Dynamic Simulation of the Log-Linear Stochastic Growth

Model 39113.5 Conclusion 393

14 Perfectly Competitive Models with Flexible Prices 39514.1 A Perfectly Competitive Model without Capital 396

14.1.1 The Representative Household 39614.1.2 The Representative Firm 39714.1.3 General Equilibrium 398

14.2 Monetary Factors in a Perfectly Competitive Model 40014.2.1 An Exogenous Path for the Money Supply 40014.2.2 An Exogenous Path for the Nominal Interest Rate 40114.2.3 An Inflation-Based Nominal Interest Rate Rule 40114.2.4 Optimal Monetary Policy 402

14.3 Imperfect Information and the Nonneutrality of Money 40314.3.1 Competitive Equilibrium under Imperfect Information

about the Price Level 40314.3.2 The Determination of Output and Employment 40614.3.3 The Real Effects of Monetary Shocks in a Rational

Expectations Equilibrium 40714.3.4 Optimal Monetary Policy in the Lucas Model 41014.3.5 The New Classical Model and the Great Depression 41014.3.6 Models of Informational Frictions and Rational Inattention 411

14.4 Conclusion 411–10+1

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Contents xv

15 Keynesian Models and the Phillips Curve 41315.1 The Original Keynesian Models 415

15.1.1 The Keynesian Cross 41615.1.2 The IS-LM Model 41915.1.3 The AD-AS Model 42215.1.4 The Impact of Aggregate Demand Policies 424

15.2 The Samuelson Multiplier Accelerator Model 42715.3 The Theory of Discretionary Monetary and Fiscal Policy 429

15.3.1 The Tinbergen-Theil Theory of Discretionary AggregateDemand Policies 431

15.3.2 Monetary and Fiscal Policy with a Full Employment Target 43115.3.3 Monetary and Fiscal Policy with a Full Employment Target

and a Price Level Target 43215.4 The Phillips Curve and Inflationary Expectations 435

15.4.1 The Phillips Curve and the Trade-off between Inflationand Unemployment 435

15.4.2 Instability of the Phillips Curve and Inflationary Expectations 43715.5 The Natural Rate of Unemployment and Aggregate Demand Policies 439

15.5.1 The Path of Inflation and Unemployment under AdaptiveExpectations 440

15.5.2 Rules versus Discretion in Aggregate Demand Policy 44415.5.3 Inflation and Unemployment under Rational Expectations 446

15.6 Conclusion 447

16 A Model of Imperfect Competition and Staggered Pricing 44916.1 An Imperfectly Competitive Model of Aggregate Fluctuations 451

16.1.1 The Representative Household 45416.1.2 The Representative Firm and Optimal Pricing 45416.1.3 Full Price Flexibility and the Natural Rate 45516.1.4 Inefficiency of the Natural Rate 456

16.2 Staggered Price Adjustment and Aggregate Fluctuations 45716.2.1 Optimal Pricing with Staggered Price Adjustment 45916.2.2 Equilibrium in the Market for Goods

and Services and the New Keynesian IS curve 46116.2.3 Labor Market Equilibrium and the New Keynesian Phillips Curve 46216.2.4 The Imperfectly Competitive Model with Staggered Pricing

and the Taylor Rule 46316.2.5 Real and Monetary Shocks and Aggregate Fluctuations 46416.2.6 The Divine Coincidence and Optimal Monetary Policy in the

New Keynesian Model with Staggered Pricing 46816.2.7 A Dynamic Simulation of the Model 469

16.3 The Rotemberg Model of Convex Costs of Price Adjustment 47016.4 Conclusion 473

17 A Model of Unemployment and Nominal Wage Contracts 47517.1 Alternative Views of the Labor Market and Equilibrium Unemployment 47717.2 Households and Optimal Consumption and Money Demand 478

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17.3 Firms and Optimal Pricing and Production 48117.4 Wage Setting and Employment in a Model with Insiders and Outsiders 483

17.4.1 Wage Determination, Unemployment Persistence,and the Phillips Curve 485

17.4.2 The Relation between Output and Unemployment Persistence 48717.4.3 The Phillips Curve in Terms of Deviations of Output

from Its Natural Rate 48817.5 The Implications of Staggered Pricing 489

17.5.1 Optimal Pricing with Staggered Price Adjustment 49017.5.2 Inflation and Unit Labor Costs under Staggered Pricing 491

17.6 An Extended New Keynesian Phillips Curve: Combining Staggered Pricingwith Periodic Nominal Wage Contracts 492

17.7 Inflation and Aggregate Fluctuations under a Taylor Rule 49417.7.1 New Neoclassical Synthesis IS-LM Functions 49417.7.2 The Natural and Equilibrium Real Interest Rate 49417.7.3 Equilibrium Fluctuations with Exogenous Preference

and Productivity Shocks 49517.7.4 Does Staggered Pricing Matter for Inflation Persistence? 50017.7.5 Inflation Stabilization and the Divine Coincidence 501

17.8 The Optimal Taylor Rule 50217.8.1 Optimal Inflation Policy 502

17.9 A Dynamic Simulation of the Effects of Monetary and Real Shocks 50417.10 Conclusion 506

18 Matching Frictions and Equilibrium Unemployment 50918.1 The Matching Function 510

18.1.1 The Probability of Filling a Vacancy and Labor MarketTightness 511

18.1.2 The Probability of the Unemployed Finding a Job 51118.2 Flows into and out of Employment, Equilibrium Unemployment,

and the Beveridge Curve 51218.3 Firms and the Creation of Vacancies 513

18.3.1 The Present Value of Net Expected Profits from an Existing Job 51418.3.2 The Present Value of Net Expected Profits from a Vacancy

and the Creation of Vacancies 51518.3.3 Free Entry and the Job Creation Condition 516

18.4 The Behavior of Unemployed Job Seekers 51718.4.1 The Permanent Income of an Unemployed Job Seeker 51818.4.2 The Permanent Income of an Employed Worker 51818.4.3 Comparing the Permanent Income of the Employed

and the Unemployed 51818.5 Wage Bargaining and the Wage Equation 51918.6 Wage Determination and Equilibrium Unemployment 52118.7 Determinants of Equilibrium Unemployment, Real Wages,

and Labor Market Tightness 52318.7.1 An Increase in Labor Productivity 52318.7.2 An Increase in Unemployment Benefits 525

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18.7.3 An Increase in the Real Interest Rate 52718.7.4 An Increase in the Probability of Job Destruction 527

18.8 Dynamic Adjustment to the Steady State 52718.8.1 The Dynamic Adjustment of Unemployment and Vacancies 53018.8.2 Numerical Simulations of the Model 532

18.9 Matching Models and Nominal Rigidities 53418.10 Conclusion 535

19 The Macroeconomic Implications of Financial Frictions 53919.1 The Role of Finance and Financial Markets 539

19.1.1 Financial Frictions and Financial Intermediation 54119.1.2 The Risks of Financial Intermediation, Leverage,

and the External Finance Premium 54219.1.3 The Links between the Financial Sector and Real Activity

in the Presence of Frictions 54319.2 Financial Frictions in a New Keynesian Model with Staggered Pricing 54419.3 Financial Frictions in a Model with Unemployment Persistence

and Nominal Wage Contracts 54619.4 Conclusion 548

20 The Role of Monetary Policy 55120.1 Rules versus Discretion in Monetary Policy 55220.2 Rules, Discretion, and Credibility in a New Keynesian Model 554

20.2.1 The Social Welfare Loss from Inflation and Unemployment 55520.2.2 Monetary Policy under Discretion: The Problem of Credibility 55620.2.3 Monetary Policy under a Fixed Inflation Rule 55920.2.4 Central Bank Constitutions 55920.2.5 Reputation as a Solution to the Problem of Inflationary Bias 560

20.3 Optimal Monetary Policy in the Presence of Stochastic Shocks 56220.4 The Mechanics of Monetary Policy 564

20.4.1 Financial Markets and Open Market Operations 56520.4.2 The Term Structure of Interest Rates 566

20.5 Optimal Monetary Policy and the Taylor Rule 56720.6 Monetary Policy Shocks and the Optimal Policy Rule 56920.7 Monetary Policy, Financial Frictions, and the Zero Lower Bound

on Interest Rates 57120.7.1 The Liquidity Trap 57220.7.2 Monetary Policy at the Zero Lower Bound 57320.7.3 The Zero Lower Bound and Unconventional Monetary Policy 574

20.8 Conclusion 576

21 Fiscal Policy and Government Debt 57921.1 Tax Smoothing and Government Debt Accumulation 581

21.1.1 The Barro Tax-Smoothing Model 58121.1.2 Steady State Implications of Tax Smoothing 583

21.2 Keynesian Stabilization Policy, Automatic Stabilizers, and Fiscal Implicationsof the Zero Lower Bound 585

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xviii Contents

21.3 Optimal Dynamic Ramsey Taxation 58621.4 Fiscal Policy and Politics 589

21.4.1 Distributional Considerations and Politics 58921.4.2 Electoral Factors and Partisan Differences 590

21.5 The Burden of High Government Deficits and Debt 59221.6 A Model of Government Debt Crises 593

21.6.1 The Calvo Model 59321.6.2 Multiple Equilibria and Self-Fulfilling Prophecies 598

21.7 Conclusion 600

22 Bubbles, Multiple Equilibria, and Sunspots 60122.1 Bubbles in Linear Rational Expectations Models 602

22.1.1 Bubbles versus Fundamentals 60322.1.2 Deterministic versus Stochastic Bubbles 60422.1.3 Bubbles as Self-Fulfilling Prophecies in Inherently Unstable Models 60522.1.4 Higher-Order Linear Models 607

22.2 Bubbles in Models of Stock and Money Markets 60722.2.1 Stock Market Bubbles 60722.2.2 Money Market Bubbles, the Price Level, and Inflation 609

22.3 Ruling Out Unstable Bubbles 61122.4 Indeterminacy, Self-Fulfilling Prophecies, and Sunspots 612

22.4.1 The Samuelson OLG Model with Money, Revisited 61422.4.2 Other Models of Indeterminacy and Sunspots in Macroeconomics 619

22.5 Conclusion 620

23 The Interaction of Events and Ideas in Dynamic Macroeconomics 62323.1 The Financial Crisis and Recent Developments in Dynamic Macroeconomics 62423.2 The Interaction of Events and Ideas and the Role

of Empirical Macroeconomics 62623.3 Policy Evaluation and DSGE Models 62823.4 Conclusion 629

Appendixes 631

A Variables, Functions, and Optimization 633A.1 Models, Variables, and Functions 633

A.1.1 Functions 634A.1.2 Derivatives and Partial Derivatives of Functions 635A.1.3 Maxima and Minima of Functions 642

A.2 Mathematical Optimization under Constraints 644A.2.1 Constrained Optimization in the Case of a Function of One

Variable 644A.2.2 Optimal Consumption under an Income Constraint 645A.2.3 The Lagrange Method 647

A.3 Some Useful Functional Forms 651A.3.1 The Two-Factor CES Production Function and the Elasticity

of Substitution 652

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A.3.2 Special Cases of the CES Production Function 653A.3.3 The CES Production Function and the Solow Model

of Economic Growth 653A.3.4 The CES Utility Function 655A.3.5 Additively Separable Utility and the CEIS Utility Function 655

B Linear Models and Linear Algebra 659B.1 Linear Models 659B.2 Elements of Linear Algebra 660

B.2.1 Matrix Addition, Subtraction, and Multiplication 661B.2.2 The Inverse of a Square Matrix 661

B.3 An Example with Two Endogenous Variables 663B.3.1 Cramer’s Rule 664B.3.2 The Augmented Matrix and Gauss-Jordan Elimination 664B.3.3 Diagonalization, Eigenvalues, and Eigenvectors 665B.3.4 Solving a System with Two Endogenous and Two Exogenous

Variables 665

C Ordinary Differential Equations 667C.1 Definitions 667C.2 First-Order Linear Differential Equations 669

C.2.1 Constant Coefficients 669C.2.2 Variable Right-Hand Side 670C.2.3 Variable Coefficients 671C.2.4 Homogeneous and Nonhomogeneous Differential Equations 671C.2.5 Convergence and Stability of First-Order Differential Equations 672

C.3 Second-Order Linear Differential Equations 673C.3.1 Homogeneous Equations with Constant Coefficients 673C.3.2 Nonhomogeneous Equations with Constant Coefficients 674

C.4 A Pair of First-Order Linear Differential Equations 675C.4.1 The Method of Substitution 675C.4.2 The Method of Eigenvalues 676

C.5 A System of n First-Order Linear Differential Equations 678C.5.1 Eigenvalues and Eigenvectors 679C.5.2 Solving the nth-Order System of Linear Differential Equations 679

D Difference Equations 683D.1 Lag Operators and Difference Equations 683D.2 First-Order Linear Difference Equations 686D.3 Second-Order Linear Difference Equations 687D.4 A Pair of First-Order Linear Difference Equations 689D.5 A System of n First-Order Linear Difference Equations 690

E Methods of Intertemporal Optimization 693E.1 The Form of Dynamic Optimization Problems 693E.2 The Method of Optimal Control 694E.3 The Optimal Control Method in Continuous Time 696

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E.4 Dynamic Programming and the Bellman Equation 697E.5 An Example Based on Optimal Savings in Continuous Time 700

F Random Variables and Stochastic Processes 703F.1 Probability 703F.2 Random Variables and Probability Distributions 704

F.2.1 Discrete Probability Distributions 704F.2.2 Continuous Probability Distributions 705F.2.3 Mathematical Expectation, Variance, and Higher Moments 706F.2.4 Some Useful Probability Distributions 707F.2.5 Convergence of Random Variables 712F.2.6 The Law of Large Numbers 713F.2.7 The Central Limit Theorem 714F.2.8 Joint Probability Distributions 714

F.3 Stochastic Processes 715F.4 Univariate Linear Stochastic Processes in Discrete Time 716

F.4.1 The White Noise Process 717F.4.2 Moving Average Stochastic Processes 717F.4.3 Autoregressive Stochastic Processes 718F.4.4 Autoregressive Moving Average Stochastic Processes 720

F.5 Vector Stochastic Processes and Vector Autoregressions 720

References 723Index 000

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List of Figures and Table

Figures

1.1 Distribution of countries by per capita GNI, 2012 121.2 Long-run growth of (natural log) per capita GDP in the United Kingdom,

the United States, and Japan 161.3 Long-run growth of (log) per capita GDP in the major European economies 171.4 Recessions (shaded areas) and (log) per capita GDP in the United States 191.5 Recessions (shaded areas) and (log) per capita GDP in the United Kingdom 201.6 Recessions (shaded areas) and the unemployment rate in the United States 211.7 Recessions (shaded areas) and the unemployment rate in the United Kingdom 221.8 Evolution of the price level in the United States 231.9 Evolution of the price level in the United Kingdom 241.10 Evolution of consumer price index (CPI) inflation in the United States 251.11 Evolution of CPI inflation in the United Kingdom 261.12 Money growth and inflation in 110 countries, 1960–1990 271.13 Money growth and real GDP growth in 110 countries, 1960–1990 281.14 Evolution of US federal debt as a percentage of GDP 291.15 Evolution of UK public debt as a percentage of GDP 302.1 Equilibrium capital accumulation in a two-period economy 512.2 Intertemporal equilibrium in a two-period economy 532.3 Optimal consumption and leisure in a one-period economy 582.4 Income and substitution effects on labor supply 593.1 The production function in intensive form 893.2 Equilibrium in the Solow model 933.3 Determination of the growth rate 943.4 Implications of a rise in the savings rate 983.5 Impulse response function of a rise in the savings rate 993.6 Implications of a rise in total factor productivity 1033.7 Implications of a rise in population growth 1043.8 Convergence in the Solow model in discrete time 1133.9 Impulse response functions of the Solow model following a permanent increase in the

savings rate of 1% 115 –101

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xxii List of Figures and Table

3.10 Impulse response functions of the Solow model following a permanent increase in totalfactor productivity of 1% 116

3.11 Impulse response functions of the Solow model following a permanent increase in the rateof population growth of 1% 117

4.1 The balanced growth path and dynamic adjustment in the Ramsey model 1364.2 Short- and long-run effects of a permanent increase in the pure rate

of time preference 1404.3 Impulse response function of consumption and capital stock following a permanent

increase at t0 in the pure rate of time preference 1414.4 Short- and long-run effects of a permanent increase in total

factor productivity 1424.5 Effects of a permanent increase in the population growth 1434.6 Impulse response functions of the calibrated Ramsey model

for a 1% permanent drop in the pure rate of time preference 1504.7 Impulse response functions of the calibrated Ramsey model for a 1% permanent increase

in total factor productivity 1515.1 Multiple equilibria in the diamond model 1585.2 Unique balanced growth path in the simplified diamond model 1605.3 Effects of a permanent rise in the pure rate of time preference 1615.4 Effects of a permanent rise in total factor productivity 1625.5 Impulse response functions of the diamond model for a permanent rise

in the pure rate of time preference of 1% 1675.6 Impulse response functions of the Diamond model for a permanent rise in total factor

productivity of 1% 1685.7 The balanced growth path and the adjustment path for the Blanchard-Weil model 1745.8 Short- and long-run effects of an increase in the pure rate of time preference in the

Blanchard-Weil model 1765.9 Short- and long-run effects of an increase in the rate of population growth in the

Blanchard-Weil model 1775.10 Impulse response functions for a 1% increase in the pure rate of time preference in the

calibrated Blanchard-Weil model 1795.11 Impulse response functions for a 1% increase in the population growth rate

in the calibrated Blanchard-Weil model 1805.12 Impulse response functions for a 1% increase in total factor productivity

in the calibrated Blanchard-Weil model 1816.1 Primary government expenditure in the Ramsey model 1906.2 Primary government expenditure and debt in the Blanchard-Weil model 1926.3 An increase in government debt in the Blanchard-Weil model 1936.4 An increase in primary government expenditure in the

Blanchard-Weil model 1946.5 A tax-financed increase of primary government expenditure in the calibrated

Blanchard-Weil Model 1976.6 A debt-financed increase of primary government expenditure in the calibrated

Blanchard-Weil Model 1986.7 A debt financed tax cut in the calibrated Blanchard-Weil model 1996.8 Short- and long-run effects of capital income taxation in the Ramsey model 2036.9 Dynamic effects of a 10% tax on interest income in the calibrated Ramsey model 204

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6.10 Dynamic effects of a 10% tax on business profits, before interest and depreciation, in thecalibrated Ramsey model 205

7.1 The demand for real money balances and the welfare cost of inflation 2227.2 The balanced growth path and the adjustment path in the Blanchard-Weil

model with money 2257.3 Dynamic effects of an increase in the growth rate of money supply in the Blanchard-Weil

model with money 2267.4 Dynamic simulation of an increase in the growth rate of the money supply

in a calibrated Blanchard-Weil model with money 2288.1 The aggregate production function for different values of β 2358.2 Determination of the consumption-to-output ratio and the endogenous growth rate in the

Blanchard-Weil model 2448.3 Determination of private consumption and the growth rate with government expenditure

and debt 2468.4 The path of per capita output in exogenous and endogenous growth models 2489.1 The cobweb model under adaptive expectations 27411.1 Adjustment cost of investment 31611.2 Determination of q and the capital stock K 31911.3 Dynamic effects of a permanent rise in the real interest rate 32011.4 Dynamic effects of a permanent rise in total factor productivity 32112.1 The demand for money and the nominal interest rate 33712.2 An increase in real income and the demand for money 33812.3 Short-run equilibrium in the money market 33912.4 Short-run effects of a rise in the money supply: the liquidity effect 34012.5 Short-run effects of an exogenous rise in real income 34112.6 Equilibrium in the money market with interest rate pegging 34212.7 Money demand indeterminacy in the Samuelson OLG Model 35012.8 The seigniorage Laffer curve 36712.9 Equilibrium with high inflation 36912.10 Equilibria with high inflation and the transition to hyperinflation 37213.1 Dynamic simulation of the stochastic growth model following

a 1% persistent shock to productivity 39215.1 Exogenous investment and government expenditure:

the Keynesian cross 41815.2 Aggregate output and the nominal interest rate: The IS-LM model 42015.3 Aggregate output and the price level: the AD-AS model 42315.4 Aggregate demand disturbances and their effects on aggregate output

and the price level 42515.5 Aggregate supply disturbances and their effects on aggregate output

and the price level 42615.6 Convergence of real output for different values of the accelerator 43015.7 The Phillips curve 43615.8 The Phillips curve and the socially optimal combination of inflation

and unemployment 43715.9 Shifts of the Phillips curve due to inflationary expectations 43815.10 Continuous shifts of the Phillips curve due to rising inflationary

expectations 442–101

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xxiv List of Figures and Table

15.11 Determination of steady state inflation and unemployment under discretion andcommitment to an inflation rule 445

16.1 Impulse response functions of the staggered pricing model followinga contractionary monetary shock 470

16.2 Impulse response functions of the staggered pricing model followinga positive productivity shock 471

17.1 Impulse response functions following a 1% unanticipated temporary positive shockto the nominal interest rate 505

17.2 Impulse response functions following a 1% unanticipated persistent positive shockto productivity 506

18.1 The beveridge curve and equilibrium unemployment 51418.2 The job creation condition 51718.3 The determination of real wages and labor market tightness 52218.4 Labor productivity and equilibrium unemployment 52418.5 Unemployment benefits and equilibrium unemployment 52618.6 The real interest rate and equilibrium unemployment 52818.7 The probability of job destruction and equilibrium unemployment 52918.8 Dynamic adjustment of unemployment and vacancies 53118.9 Dynamic adjustment of unemployment and vacancies to an increase

in the job destruction rate 53318.10 Dynamic adjustment of unemployment and vacancies to an increase

in the replacement rate 53418.11 Dynamic adjustment of unemployment and vacancies to an increase

in the real interest rate 53420.1 Inflation and lack of credibility under a discretionary policy 55720.2 The liquidity trap 57221.1 Expected default and the debt holding condition 59521.2 The actual probability of default and the cumulative distribution

of the primary surplus 59621.3 Determination of the interest factor and the probability of default

for a low rate of return of the safe asset 59721.4 Determination of the interest factor and the probability of default for a high rate of return

of the safe asset 59922.1 Deterministic bubbles 60422.2 A stochastically bursting bubble versus a deterministic bubble 60622.3 Equilibrium consumption in the Samuelson OLG model 61622.4 Saddle point equilibrium money balances in the Samuelson OLG model 61822.5 Multiple convergence paths for money balances in the Samuelson OLG model 61922.6 Multiple equilibria, sunspots, and cycles in the Samuelson OLG model 620A.1 Utility as a function of consumption 636A.2 Output as a function of capital and labor 637A.3 Isoquants: capital labor combinations that produce given amounts of output 638A.4 Output as a function of the capital stock for a given level of employment of labor 639A.5 Utility and marginal utility: the derivative of the utility function 640A.6 Stationary points: maxima, minima, and points of inflection 643A.7 Maximization with a binding and a nonbinding constraint 646A.8 Maximization of consumer utility subject to an income constraint 647

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A.9 Optimal choice of a consumption bundle 651F.1 The uniform distribution 709F.2 The CDF of the continuous uniform distribution 710F.3 The normal distribution 711F.4 The CDF of the standard normal distribution 712

Table

1.1 Per capita GDP and average annual growth rates over time 15

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Preface

Macroeconomics deals with the structure, behavior and performance of economies in theirentirety. It concentrates on aggregate variables, such as output and income (gross domesticproduct), unemployment rates, price indices, and inflation. It studies the structure and inter-relations among economy-wide markets for output, labor, capital, and financial instrumentsand their implications for aggregate economic performance.Macroeconomics mainly focuses on the determinants of long-run economic growth in

living standards and the causes and implications of short-term fluctuations in economicaggregates.This book is an advanced treatment of modern macroeconomics using a sequence of

dynamic general equilibrium models which are based on intertemporal optimization on thepart of economic agents, such as households, firms, and the government. The book alsoanalyzes and discusses the role of monetary and fiscal policy in the context of such dynamicmodels.The intertemporal approach, based on the use of dynamic general equilibrium models, is

currently the dominant approach to macroeconomics. This approach is adopted in this text.The book is addressed to advanced undergraduate as well as first-year graduate students ofeconomics. It is also suitable for trained economists who wish to deepen and broaden theirgrasp of dynamic macroeconomics. It highlights the potential but also some limitations ofthe modern intertemporal approach.Chapter 1 serves as an introduction and overview, providing a brief survey of the evolution

of macroeconomics, as well as presenting the key facts about long-run economic growth andaggregate fluctuations. Accounting for these key facts is the main objective of the dynamicmacroeconomic models that are analyzed in the rest of the book.Chapter 2 introduces themain elements of the intertemporal approach tomacroeconomics

by means of two-period competitive general equilibrium models. Two-period models arethe simplest possible intertemporal models. They help highlight both the strengths andthe weaknesses of modern intertemporal macroeconomics without the need for advancedmathematical methods. –1

01

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These two-period models are used to address issues such as savings and capital accumu-lation, intertemporal substitution in consumption and labor supply, the distinction betweenreal and nominal variables, the classical dichotomy and the neutrality of money, monetarygrowth and inflation, Ricardian equivalence between debt and tax finance of public expen-diture, and the effects of distortionary taxation. These are themes that recur again and againin macroeconomics. The two-period models of chapter 2 thus set the stage for the moreadvanced infinite-horizon dynamic and dynamic stochastic models that are the workhorsesof modern theories of economic growth and aggregate fluctuations.The remainder of the book is divided into 21 chapters, presenting models of economic

growth, aggregate fluctuations, and monetary and fiscal policy.The process of long-run economic growth is analyzed in chapters 3–8.Chapter 3 introduces and discusses the basic neoclassical model of savings, investment,

and economic growth. This model was developed by Solow [1956] and Swan [1956]. Itis based on a neoclassical production function and an exogenous savings and investmentrate. The model highlights the role of physical capital accumulation, technical progress,and population growth for the process of economic growth.Chapter 4 presents and analyzes the model of the representative household. In this model,

which was first put forward by Ramsey [1928] and later developed by Cass [1965] andKoopmans [1965], savings and investment are chosen optimally by a representative house-hold with an infinite time horizon. The household is assumed to be able to borrow and lendfreely in competitive capital markets.Overlapping generations models of growth are presented in chapter 5. These are models

in which different generations of households coexist. Younger households enter the economywith human capital being their only asset, because no intergenerational transfers of capitalor financial assets take place. Overlapping generations models were first developed by Allais[1947], Samuelson [1958], and Diamond [1965], and later by Blanchard [1985] and Weil[1989].Chapter 6 discusses models that highlight the intertemporal effects of fiscal policy, focus-

ing on the effects of government consumption and the ways it is financed, such as taxationand government debt.Chapter 7 discusses models that focus on the intertemporal effects of the money sup-

ply and monetary growth. Monetary models help determine the evolution not only of realvariables but also of nominal variables, expressed in money terms, such as the price level,nominal wages, inflation, and nominal interest rates.More general growth models based on externalities, human capital accumulation, and

endogenous technical change are discussed in chapter 8.Chapters 9–12 introduce decision making under uncertainty in the context of dynamic

stochastic models. These chapters highlight the role of expectations in macroeconomics.Chapter 9 introduces dynamic stochastic models under rational expectations, while chap-ters 10 and 11 focus on models of the microeconomic foundations of consumption under

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Preface xxix

uncertainty and investment and the cost of capital. Chapter 12 is an extended treatmentof the role of money, alternative general equilibrium models with money, and the relationbetween the need for seigniorage and inflation.Chapters 13–19 present and analyze alternative dynamic stochastic general equilibrium

models of aggregate fluctuations. Such models are the basis of the new neoclassical syn-thesis, which is the dominant modern approach to the study of aggregate fluctuations.Chapter 13 presents the stochastic growth model of aggregate fluctuations, and chapter 14

analyzes perfectly competitive models without capital. These are benchmark new classicalmodels, based on competitive markets and perfectly flexible wages and prices.Chapter 15 introduces and discusses the basic Keynesian model and the Phillips curve.

Two newKeynesian dynamic stochastic models of aggregate fluctuations are then presented.Keynesian models assume distortions in the adjustment of wages and prices. Chapter 16presents an imperfectly competitive model with staggered pricing; chapter 17 introduces analternative newKeynesian model with periodic wage setting by labor market insiders. Chap-ter 18 focuses on labor market frictions and analyzes a matching model of the determinationof the so-called natural rate of unemployment. Chapter 19 focuses on financial frictions andtheir macroeconomic implications.Chapters 20 and 21 delve deeper into the roles of monetary and fiscal policy. The role and

the effectiveness of monetary policy is analyzed in chapter 20, whereas fiscal policy and thedetermination and implications of government debt are analyzed in chapter 21.Chapter 22 focuses on dynamic stochastic models with bubbles, multiple macroeconomic

equilibria, self-fulfilling prophecies, and sunspots. Such models allow for a different viewof aggregate fluctuations than the standard dynamic stochastic general equilibrium modelsof the new neoclassical synthesis examined in chapters 13–19, which are usually based ona unique equilibrium.Finally, chapter 23 discusses the current state of macroeconomics, highlighting the role

of theoretical models and their interactions with empirical macroeonomics. It also discussesthe impact of the financial crisis and the Great Recession of 2008–2009. The incorporationof labor market and financial frictions into dynamic stochastic general equilibrium modelsseems to be the main direction in which macroeconomics has been heading since then.Dynamic Macroeconomics is predominantly based on the intertemporal approach. The

book presents and analyzes dynamic and dynamic stochastic general equilibrium models,in which households and firms (but also the government and the central bank) make theirdecisions taking full account of their intertemporal effects. The dynamic element of time,the element of uncertainty about stochastic shocks, and the techniques of intertemporaloptimization permeatemodernmacroeconomics and are central to the analysis of themodelsin this book.There are two exceptions to this rule about relying on models of intertemporal opti-

mization. Chapter 3 contains an extensive discussion of the Solow model, which, from theperspective of the intertemporal approach, is an ad hoc general equilibrium model. In the

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Solow model, the savings rate is assumed exogenous and is not derived from intertemporaloptimization on the part of households. However, this model is pivotal for the theory ofeconomic growth and provides the foundation for examining the implications of optimizinggrowth models, such as the representative household and overlapping generations model.The Solow model also provides the link to models with externalities, human capital accu-mulation, and endogenous growth. It is thus important that the Solow model and the role ofsavings and investment are fully analyzed and understood early on.The second exception is chapter 15, which contains a full presentation and discussion of

traditional Keynesian models, such as the Keynesian cross, the IS-LM model, the AD-ASmodel, and models of the Phillips curve. First sketched in the General Theory of Keynes[1936] and later developed by Hicks [1937], Modigliani [1944], Samuelson [1948], Hansen[1949], Patinkin [1956], and others, these models are the basis on which macroeconomicswas originally developed as a separate subdiscipline of economics. They led to the origi-nal neoclassical synthesis and are the foundation of the new neoclassical synthesis and thedistinction between the new classical and the new Keynesian approaches to intertemporalmacroeconomics. It is thus crucial that the properties, the strengths, and the weaknesses ofthese traditional Keynesian models are fully understood.Even though they belong to previous generations of macroeconomic models, the Solow

model and the traditional Keynesian models serve as the basis through which the studentof modern macroeconomics can appreciate the strengths, weaknesses, and policy implica-tions of the intertemporal approach. Unlike the traditional approach to macroeconomics, theintertemporal approach is based on dynamic and dynamic stochastic models derived fromexplicit microeconomic foundations.In the dynamic general equilibrium growth models that are discussed in this book, the

optimal and mutually compatible decisions of households, firms, and the government (orcentral bank) help determine key macroeconomic aggregates. These aggregates includeoutput and income, employment, consumption, investment, government expenditure andtaxes, the stock of physical and human capital, the stock of government debt, the pricelevel, real and nominal wages, real and nominal interest rates, and inflation. The perfor-mance of the economy depends on which distortions are present and how they are addressedby government policy.In the models of aggregate fluctuations, such as the new classical, and the new Keynesian

dynamic stochastic general equilibrium models presented here, fluctuations in aggregatereal and nominal variables are the result of the individually optimal and mutually compatiblereactions of households, firms, and the government and central bank to stochastic real ormonetary disturbances.Several elements differentiate this book from other advanced texts on macroeconomics.

First, many of the concepts and the characteristics of intertemporal macroeconomics areintroduced at an early stage (chapter 2) in the context of two-period intertemporal generalequilibriummodels, which can be analyzed with minimal mathematical superstructure. This

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allows the student to gain a fundamental understanding of the issues at stake early on andrelatively easily.Second, the book focuses on a full analysis of a limited number of key intertemporal

models. For example, in growth theory, the focus is on the representative household andoverlapping generations models, variants of which are combined with different assumptionsabout technology, externalities from capital accumulation, human capital accumulation, andendogenous technical progress. In the theory of aggregate fluctuations, the focus is on essen-tially four models. They are the stochastic growth model and three short-run models ofaggregate fluctuations: a new classical model without capital, an imperfectly competitivenew Keynesian model with staggered pricing and an alternative new Keynesian model withperiodic wage contracts. Such models form the basis of what has been termed the newneoclassical synthesis and are analyzed fully.A third distinguishing element of the approach adopted in this book is that the models

are stripped down to essentials, so that they can be fully solved and analyzed. Thus, most ofthe models used can be reduced to second-order dynamic systems whose solutions can befully characterized, either algebraically or with the help of simple two-dimensional phasediagrams. This approach allows students to focus on the dynamic properties of the modelsand gain a deep understanding of the economics of these dynamic processes. A varietyof exercises Scattered throughout the text encourages students to try their hand at solvingversions of the main dynamic models that define modern macroeconomics.But because dynamic simulation techniques are an important element of modern dynamic

macroeconomics and policy analysis (especially for higher-dimensional models), the dyna-mic models used in the book are also simulated numerically, and their impulse responsefunctions are plotted and discussed. This is something intended to help students of thistext gain a better grasp of the dynamic properties of models themselves. In addition, suchsimulations allow for an assessment of the quantitative significance of the various effectshighlighted in the theoretical models. They help determine which effects are quantitativelysignificant and which are not. Finally, the simulations demonstrate to students of this texthow to set up and simulate dynamic and dynamic stochastic general equilibrium macro-economic models, something that should familiarize them with the techniques and preparethem to analyze higher-dimensional, more complicated, and more realistic models.1

Modern macroeconomics is not based on a single generally accepted and all-encompassing model. For this reason, this book is eclectic. It treats macroeconomics asapplied and policy-oriented general equilibrium analysis, based on various alternative, rel-atively simple aggregate dynamic or dynamic stochastic models. We examine a plurality of

1. The dynamic simulations of the various models are carried out through the use of the software platformDynare (www.dynare.org), in conjunction with the programming language Matlab (www.mathworks.com). TheDynare programs used for carrying out the simulations are available through the dedicated website for the book(www.dynamicmacroeconomics.com).

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xxxii Preface

models, each of which is suitable for investigating specific issues and addressing specificquestions, but may be unsuitable for other issues or questions. The book highlights both thepotential strengths as well as the limitations of alternative models.2

However, some key unifying principles in the models are adopted. The most important ofthese principles is the assumption that economic agents base their decisions on intertemporaloptimization of some well-defined objective function under appropriate constraints. Thus,for the most part, we examine dynamic general equilibrium models with explicit intertem-poral microeconomic foundations. Where there are theoretical disagreements, alternativeapproaches are juxtaposed, their pros and cons are analyzed, and their compatibility withthe empirical evidence is also briefly discussed.Key facts about long-run economic growth and aggregate fluctuations are presented in

chapter 1. Additional facts are also presented as we move to the particular models in therelevant chapters and they relate to the specific issues these models seek to explain. Thediscussion of these facts facilitates the process of evaluating the relevance and usefulnessof the theoretical models in the rest of this book.However, note that the rigorous and full empirical evaluation and testing of alternative

theories and models is beyond the scope of this book. The present text, although concernedwith models that account for the key stylized facts about macroeconomic phenomena, isa text on macroeconomic theory, not empirical or applied macroeconomics. Texts thatfocus on empirical macroeconomics and macroeconometrics could complement the presenttext for empirically inclined students and economists, and should indeed be consulted, asmacroeconomics ultimately relies on the interactions between theory and evidence.3

The book assumes introductory knowledge of economic theory and mathematics foreconomists. The main mathematical techniques needed to analyze optimizing dynamicmacroeconomic models are fully reviewed in the appendixes. These appendixes assumesome basic prior knowledge of the material contained in mathematical textbooks foreconomists but are for the most part self-contained. They discuss some useful functionalforms for the production and utility functions used in macroeconomics, derivatives andpartial derivatives, optimization under constraints and the Lagrange method, linear alge-bra and the solution of linear models, solution methods for linear differential and differenceequations, dynamic optimization techniques, and randomvariables and stochastic processes.The book has emerged from my lectures more than 30 years at Birkbeck College, Uni-

versity of London, and the Athens University of Economics and Business, both at advanced

2. As noted by Keynes [1938], in a letter to Roy Harrod, “economics is a science of thinking in terms of models,joined to the art of choosing models which are relevant to the contemporary world.” See Rodrik [2015] for asimilarly eclectic approach to the role of models in economics in general, and the rules for setting up models andevaluating them.

3. Good examples of such texts are Favero [2001], Canova [2007], DeJong and Chetan [2011], and, Herbst andSchorfheide [2015].

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Preface xxxiii

undergraduate and postgraduate levels. The past 50 years have been a period of impressiveprogress for dynamic macroeconomics, which has transformed the discipline. The booktraces this evolution and the current trends in macroeconomics, and is thus suitable foradvanced undergraduates, professional economists, and graduate students in the first yearof degrees leading to an MSc or a PhD in economics or related subjects, such as finance

I thank a number of people who have contributed to this book, both directly and indirectly.First and foremost, I thank my PhD advisors during 1979–1981 at the London School of

Economics: George Akerlof, Steve Nickell, and Chris Pissarides. They had a great positiveinfluence on my training as a macroeconomist and on my attitude as an academic economist,which has stood me well over the years. I owe them a lot.More recently, my biggest debt is to successive generations of students, and especially the

students in the master’s and PhD programs in economics at the Athens University of Eco-nomics and Business over the past decade. They have suffered through successive versionsof my lecture notes between 2009 and 2016, provided useful feedback, and helped improvethe original notes.The Fletcher School at Tufts University was an ideal academic environment that allowed

me to complete and improve the manuscript between 2016 and 2018.Various colleagues have contributed through comments and discussions that have helped

bring about improvements in the book. I particularly thank Marios Angeletos, Yannis Ioan-nides, Michael Klein, Tryphon Kollintzas, Athanasios Orphanides, Apostolis Philippopou-los, and Plutarchos Sakellaris. Olivier Blanchard reviewed an early version of the fullmanuscript and provided helpful comments and much needed encouragement.I thank Emily Taber, the MIT Press economics acquisitions editor, for putting this

manuscript through a very efficient editorial process. I also acknowledge the very help-ful comments and suggestions of eight anonymous reviewers in the prepublication process.These reviews have been extremely useful and have led to a much improved manuscript.The copy editor, Cyd Westmoreland, has also helped improve the final manuscript, througha very efficient editing process.Through the long years of writing, revising, and rewriting, my wife Dika has provided

much needed support and encouragement, as she has done through the many years of ourcommon life. I cannot thank her enough.I remain solely responsible for all remaining errors.

George AlogoskoufisFletcher School, Tufts University, and Athens University of Economics and Business

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