Preface xiii

Chapter 1: Introduction 1
1.1 Dynamic General Equilibrium versus Traditional Macroeconomics 1
1.2 Traditional Macroeconomics 3
1.3 Dynamic General Equilibrium Macroeconomics 4
1.4 The Structure of This Book 7

Chapter 2: The Centralized Economy 12
2.1 Introduction 12
2.2 The Basic Dynamic General Equilibrium Closed Economy 12
2.3 Golden Rule Solution 14
2.3.1 The Steady State 14
2.3.2 The Dynamics of the Golden Rule 17
2.4 Optimal Solution 17
2.4.1 Derivation of the Fundamental Euler Equation 17
2.4.2 Interpretation of the Euler Equation 19
2.4.3 Intertemporal Production Possibility Frontier 20
2.4.4 Graphical Representation of the Solution 21
2.4.5 Static Equilibrium Solution 21
2.4.6 Dynamics of the Optimal Solution 23
2.4.7 Algebraic Analysis of the Saddlepath Dynamics 25
2.5 Real-Business-Cycle Dynamics 27
2.5.1 The Business Cycle 27
2.5.2 Permanent Technology Shocks 28
2.5.3 Temporary Technology Shocks 29
2.5.4 The Stability and Dynamics of the Golden Rule Revisited 29
2.6 Labor in the Basic Model 30
2.7 Investment 32
2.7.1 q-Theory 33
2.7.2 Time to Build 36
2.8 Conclusions 37

Chapter 3: Economic Growth 39
3.1 Introduction 39
3.2 Modeling Economic Growth 40
3.3 The Solow-Swan Model of Growth 42
3.3.1 Theory 42
3.3.2 Growth and Economic Development 44
3.3.3 Balanced Growth 44
3.4 The Theory of Optimal Growth 45
3.4.1 Theory 45
3.4.2 Additional Remarks on Optimal Growth 49
3.5 Endogenous Growth 50
3.5.1 The AK Model of Endogenous Growth 51
3.5.2 The Human Capital Model of Endogenous Growth 51
3.6 Conclusions 53

Chapter 4: The Decentralized Economy 54
4.1 Introduction 54
4.2 Consumption 55
4.2.1 The Consumption Decision 55
4.2.2 The Intertemporal Budget Constraint 56
4.2.3 Interpreting the Euler Equation 57
4.2.4 The Consumption Function 59
4.2.5 Permanent and Temporary Shocks 61
4.3 Savings 64
4.4 Life-Cycle Theory 65
4.4.1 Implications of Life-Cycle Theory 65
4.4.2 Model of Perpetual Youth 67
4.5 Nondurable and Durable Consumption 68
4.6 Labor Supply 70
4.7 Firms 73
4.7.1 Labor Demand without Adjustment Costs 73
4.7.2 Labor Demand with Adjustment Costs 75
4.8 General Equilibrium in a Decentralized Economy 77
4.8.1 Consolidating the Household and Firm Budget Constraints 77
4.8.2 The Labor Market 79
4.8.3 The Goods Market 80
4.9 Comparison with the Centralized Model 81
4.10 Conclusions 83

Chapter 5: Government: Expenditures and Public Finances 84
5.1 Introduction 84
5.2 The Government Budget Constraint 86
5.2.1 The Nominal Government Budget Constraint 86
5.2.2 The Real Government Budget Constraint 88
5.2.3 An Alternative Representation of the GBC 88
5.3 Financing Government Expenditures 89
5.3.1 Tax Finance 89
5.3.2 Bond Finance 91
5.3.3 Intertemporal Fiscal Policy 93
5.3.4 The Ricardian Equivalence Theorem 93
5.4 The Sustainability of the Fiscal Stance 96
5.4.1 Case 1 (Stable Case) 98
5.4.2 Implications 99
5.4.3 Case 2: (Unstable Case) 100
5.4.4 Implications 101
5.4.5 The Optimal Level of Debt 102
5.5 The Stability and Growth Pact 103
5.6 The Fiscal Theory of the Price Level 104
5.7 Optimizing Public Finances 105
5.7.1 Optimal Government Expenditures 106
5.7.2 Optimal Tax Rates 109
5.8 Conclusions 119

Chapter 6: Fiscal Policy: Further Issues 121
6.1 Introduction 121
6.2 Time-Consistent and Time-Inconsistent Fiscal Policy 121
6.2.1 Lump-Sum Taxation 123
6.2.2 Taxes on Labor and Capital 126
6.2.3 Conclusions 131
6.3 The Overlapping-Generations Model 131
6.3.1 Introduction 131
6.3.2 The Basic Overlapping-Generations Model 132
6.3.3 Short-Run Dynamics and Long-Run Equilibrium 135
6.3.4 Comparison with the Representative-Agent Model 137
6.3.5 Fiscal Policy in the OLG Model: Pensions 138
6.3.6 Conclusions 143

Chapter 7: The Open Economy 144
7.1 Introduction 144
7.2 The Optimal Solution for the Open Economy 145
7.2.1 The Open Economy's Resource Constraint 145
7.2.2 The Optimal Solution 148
7.2.3 Interpretation of the Solution 149
7.2.4 Long-Run Equilibrium 150
7.2.5 Shocks to the Current Account 152
7.3 Traded and Nontraded Goods 154
7.3.1 The Long-Run Solution 158
7.4 The Terms of Trade and the Real Exchange Rate 159
7.4.1 The Law of One Price 160
7.4.2 Purchasing Power Parity 160
7.4.3 Some Stylized Facts about the Terms of Trade and the Real Exchange Rate 161
7.5 Imperfect Substitutability of Tradeables 163
7.5.1 Pricing-to-Market, Local-Currency Pricing, and Producer-Currency Pricing 163
7.5.2 Imperfect Substitutability of Tradeables and Nontradeables 163
7.6 Current-Account Sustainability 167
7.6.1 Balance of Payments Sustainability 167
7.6.2 The Intertemporal Approach to the Current Account 173
7.7 Conclusions 174

Chapter 8: The Monetary Economy 176
8.1 Introduction 176
8.2 A Brief History of Money and Its Role 176
8.3 Nominal Household Budget Constraint 179
8.4 The Cash-in-Advance Model of Money Demand 181
8.5 Money in the Utility Function 183
8.6 Money as an Intermediate Good or the Shopping-Time Model 185
8.7 Transactions Costs 188
8.8 Some Empirical Evidence 190
8.9 Hyperinflation and Cagan's Money-Demand Model 192
8.10 The Optimal Rate of Inflation 194
8.10.1 The Friedman Rule 194
8.10.2 General Equilibrium Solution 195
8.11 The Super-Neutrality of Money 199
8.12 Conclusions 201

Chapter 9: Imperfectly Flexible Prices 203
9.1 Introduction 203
9.2 Some Stylized "Facts" about Prices and Wages 204
9.3 Price Setting under Imperfect Competition 206
9.3.1 Theory of Pricing in Imperfect Competition 207
9.3.2 Price Determination in the Macroeconomy with Imperfect Competition 209
9.3.3 Pricing with Intermediate Goods 213
9.3.4 Pricing in the Open Economy: Local and Producer-Currency Pricing 216
9.4 Price Stickiness 217
9.4.1 Taylor Model of Overlapping Contracts 218
9.4.2 The Calvo Model of Staggered Price Adjustment 219
9.4.3 Optimal Dynamic Adjustment 221
9.4.4 Price Level Dynamics 222
9.5 The New Keynesian Phillips Curve 224
9.5.1 The New Keynesian Phillips Curve in an Open Economy 227
9.6 Conclusions 228

Chapter 10: Asset Pricing and Macroeconomics 230
10.1 Introduction 230
10.2 Expected Utility and Risk 231
10.2.1 Risk Aversion 231
10.2.2 Risk Premium 232
10.3 No-Arbitrage and Market Efficiency 233
10.3.1 Arbitrage and No-Arbitrage 233
10.3.2 Market Efficiency 233
10.4 Asset Pricing and Contingent Claims 234
10.4.1 A Contingent Claim 234
10.4.2 The Price of an Asset 235
10.4.3 The Stochastic Discount-Factor Approach to Asset Pricing 235
10.4.4 Asset Returns 235
10.4.5 Risk-Free Return 236
10.4.6 The No-Arbitrage Relation 236
10.4.7 Risk-Neutral Valuation 237
10.5 General Equilibrium Asset Pricing 238
10.5.1 Using Contingent-Claims Analysis 238
10.5.2 Asset Pricing Using the Consumption-Based Capital Asset-Pricing Model (C-CAPM) 240
10.6 Asset Allocation 247
10.6.1 The Capital Asset-Pricing Model (CAPM) 250
10.7 Consumption under Uncertainty 251
10.8 Complete Markets 252
10.8.1 Risk Sharing and Complete Markets 253
10.8.2 Market Incompleteness 256
10.9 Conclusions 256

Chapter 11: Financial Markets 258
11.1 Introduction 258
11.2 The Stock Market 259
11.2.1 The Present-Value Model 259
11.2.2 The General Equilibrium Model of Stock Prices 262
11.2.3 Comment 265
11.3 The Bond Market 265
11.3.1 The Term Structure of Interest Rates 266
11.3.2 The Term Premium 272
11.3.3 Estimating Future Inflation from the Yield Curve 277
11.3.4 Comment 279
11.4 The FOREX Market 279
11.4.1 Uncovered and Covered Interest Parity 280
11.4.2 The General Equilibrium Model of FOREX 289
11.4.3 Comment 292
11.5 Conclusions 293

Chapter 12: Nominal Exchange Rates 295
12.1 Introduction 295
12.2 International Monetary Arrangements 1873-2007 297
12.2.1 The Gold Standard System: 1873-1937 298
12.2.2 The Bretton Woods System: 1945-71 299
12.2.3 Floating Exchange Rates: 1973-2007 300
12.3 The Keynesian IS-LM-BP Model of the Exchange Rate 304
12.3.1 The IS-LM Model 305
12.3.2 The BP Equation 309
12.3.3 Fixed Exchange Rates: The Monetary Approach to the Balance of Payments 312
12.3.4 Exchange-Rate Determination with Imperfect Capital Substitutability 313
12.4 UIP and Exchange-Rate Determination 315
12.5 The Mundell-Fleming Model of the Exchange Rate 317
12.5.1 Theory 317
12.5.2 Monetary Policy 318
12.5.3 Fiscal Policy 319
12.6 The Monetary Model of the Exchange Rate 320
12.6.1 Theory 320
12.6.2 Monetary Policy 321
12.6.3 Fiscal Policy 325
12.7 The Dornbusch Model of the Exchange Rate 325
12.7.1 Theory 325
12.7.2 Monetary Policy 328
12.7.3 Fiscal Policy 330
12.7.4 Comparison of the Dornbusch and Monetary Models 330
12.8 The Monetary Model with Sticky Prices 332
12.9 The Obstfeld-Rogoff Redux Model 334
12.9.1 The Basic Redux Model with Flexible Prices 335
12.9.2 Log-Linear Approximation 341
12.9.3 The Small-Economy Version of the Redux Model with Sticky Prices 343
12.10 Conclusions 346

Chapter 13: Monetary Policy 348
13.1 Introduction 348
13.2 Inflation and the Fisher Equation 353
13.3 The Keynesian Model of Inflation 355
13.3.1 Theory 355
13.3.2 Empirical Evidence 358
13.4 The New Keynesian Model of Inflation 358
13.4.1 Theory 358
13.4.2 The Effectiveness of Inflation Targeting in the New Keynesian Model 365
13.4.3 Inflation Targeting with a Flexible Exchange Rate 369
13.5 Optimal Inflation Targeting 371
13.5.1 Social Welfare and the Inflation Objective Function 372
13.5.2 Optimal Inflation Policy under Discretion 374
13.5.3 Optimal Inflation Policy under Commitment to a Rule 378
13.5.4 Intertemporal Optimization and Time-Consistent Inflation Targeting 380
13.5.5 Central Bank versus Public Preferences 382
13.6 Optimal Monetary Policy using the New Keynesian Model 384
13.6.1 Using Discretion 384
13.6.2 Rules-Based Policy 386
13.7 Monetary Policy in the Euro Area 387
13.7.1 New Keynesian Model of the Euro Area 389
13.7.2 Model 389
13.7.3 Optimal Monetary Policy 390
13.7.4 Competitiveness and Absorbtion 392
13.7.5 Is There Another Solution? 393
13.8 Conclusions 393

Chapter 14: Real Business Cycles, DGE Models, and Economic Fluctuations 396
14.1 Introduction 396
14.2 The Methodology of RBC Analysis 397
14.2.1 Steady-State Solution 400
14.2.2 Short-Run Dynamics 401
14.3 Empirical Evidence on the RBC Model 405
14.3.1 The Basic RBC Model 406
14.3.2 Extensions to the Basic RBC Model 408
14.3.3 The Open-Economy RBC Model 410
14.4 DGE Models of the Monetary Economy 415
14.4.1 The Smets-Wouters Model 416
14.4.2 Empirical Results 420
14.5 Conclusions 422

Chapter 15: Mathematical Appendix 424
15.1 Introduction 424
15.2 Dynamic Optimization 424
15.3 The Method of Lagrange Multipliers 426
15.3.1 Equality Constraints 426
15.3.2 Inequality Constraints 431
15.4 Continuous-Time Optimization 432
15.4.1 Calculus of Variations 433
15.4.2 The Maximum Principle 434
15.5 Dynamic Programming 434
15.6 Stochastic Dynamic Optimization 438
15.7 Time Consistency and Time Inconsistency 440
15.8 The Linear Rational-Expectations Models 442
15.8.1 Rational Expectations 443
15.8.2 The First-Order Nonstochastic Equation 444
15.8.3 Whiteman's Solution Method for Linear Rational-Expectations Models 446
15.8.4 Systems of Rational-Expectations Equations 453

References 459
Index 471