Contents

Preface xi

Part 1. Introduction 1

Chapter 1. Economic Growth and Economic Development:

The Questions 3

1.1. Cross-Country Income Differences 3

1.2. Income and Welfare 6

1.3.

1.4. Origins of Today’s Income Differences and World Economic Growth 12

1.5. Conditional Convergence 16

1.6. Correlates of Economic Growth 20

1.7. From Correlates to Fundamental Causes 22

1.8. The Agenda 25

1.9. References and Literature 27

Chapter 2. The Solow Growth Model 31

2.1. The Economic Environment of the Basic Solow Model 32

2.2. The Solow Model in Discrete Time 40

2.3. Transitional Dynamics in the Discrete Time Solow Model 50

2.4. The Solow Model in Continuous Time 55

2.5. Transitional Dynamics in the Continuous Time Solow Model 59

2.6. Solow Model with Technological Progress 66

2.7. Comparative Dynamics 76

2.8. Taking Stock 78

2.9. References and Literature 79

2.10. Exercises 80

Chapter 3. The Solow Model and the Data 87

3.1. Growth Accounting 87

3.2. Solow Model and Regression Analyses 90

3.3. The Solow Model with Human Capital 98

3.4. Solow Model and Cross-Country Income Differences: Regression Analyses 104

3.5. Calibrating Productivity Differences 113

3.6. Estimating Productivity Differences 118

3.7. Taking Stock 123

3.8. References and Literature 125

3.9. Exercises 126

Chapter 4. Fundamental Determinants of Differences in Economic Performance 129

4.1. Proximate Versus Fundamental Causes 129

4.2. Economies of Scale, Population, Technology and World Growth 133

4.3. The Four Fundamental Causes 136

4.4. The Effect of Institutions on Economic Growth 147

4.5. WhatTypesofInstitutions? 164

4.6. Disease and Development 167

4.7. Political Economy of Institutions: First Thoughts 170

4.8. Taking Stock 171

4.9.

4.10. Exercises 174

Part 2. Towards Neoclassical Growth 177

Chapter 5. Foundations of Neoclassical Growth 179

5.1. Preliminaries 179

5.2. The Representative Household 182

5.3. Infinite Planning Horizon 188

5.4. The Representative Firm 190

5.5. Problem Formulation 192

5.6. Welfare Theorems 193

5.7. Sketch of the Proof of the Second Welfare Theorem, Theorem 5.7* 201

5.8. Sequential Trading 203

5.9. Optimal Growth in Discrete Time 207

5.10. Optimal Growth in Continuous Time 208

5.11. Taking Stock 209

5.12. References and Literature 210

5.13. Exercises 211

Chapter 6. Dynamic Programming and Optimal Growth 215

6.1. Brief Review of Dynamic Programming 216

6.2. Dynamic Programming Theorems 220

6.3. The Contraction Mapping Theorem and Applications* 224

6.4. Proofs of the Main Dynamic Programming Theorems* 229

6.5. Fundamentals of Dynamic Programming 236

6.6. Optimal Growth in Discrete Time 245

6.7. Competitive Equilibrium Growth 250

6.8. Taking Stock 252

6.9. References and Literature 253

6.10. Exercises 254

Chapter 7. Review of the Theory of Optimal Control 259

7.1. Variational Arguments 260

7.2. The Maximum Principle: A First Look 268

7.3. Infinite-Horizon Optimal Control 273

7.4. More on Transversality Conditions 283

7.5. Discounted Infinite-Horizon Optimal Control 285

7.6. Existence of Solutions* 290

7.7. A First Look at Optimal Growth in Continuous Time 291

7.8. The q-Theory of Investment 292

7.9. Taking Stock 297

7.10. References and Literature 299

7.11. Exercises 301

Part 3. Neoclassical Growth 307

Chapter 8. The Neoclassical Growth Model 309

8.1. Preferences, Technology and Demographics 309

8.2. Characterization of Equilibrium 313

8.3. Optimal Growth 317

8.4. Steady-State Equilibrium 318

8.5. Transitional Dynamics 320

8.6. Technological Change and the Canonical Neoclassical Model 323

8.7. Comparative Dynamics 329

8.8.

8.9. A Quantitative Evaluation 332

8.10. Extensions 335

8.11. Taking Stock 336

8.12. References and Literature 337

8.13. Exercises 337

Chapter 9. Growth with Overlapping Generations 345

9.1. ProblemsofInfinity 346

9.2. The Baseline Overlapping Generations Model 348

9.3. The Canonical Overlapping Generations Model 353

9.4. Overaccumulation and Pareto Optimality of Competitive Equilibrium in the

Overlapping Generations Model 355

9.5. Role of Social Security in Capital Accumulation 358

9.6. Overlapping Generations with Impure Altruism 360

9.7. Overlapping Generations with Perpetual Youth 364

9.8. Overlapping Generations in Continuous Time 368

9.9. Taking Stock 374

9.10. References and Literature 376

9.11. Exercises 377

Chapter 10. Human Capital and Economic Growth 383

10.1. A Simple Separation Theorem 383

10.2. Schooling Investments and Returns to Education 386

10.3. The Ben-Porath Model 387

10.4. Neoclassical Growth with Physical and Human Capital 392

10.5. Capital-Skill Complementarity in an Overlapping Generations Model 397

10.6. Physical and Human Capital with Imperfect Labor Markets 401

10.7. Human Capital Externalities 406

10.8. Nelson-Phelps Model of Human Capital 408

10.9. Taking Stock 411

10.10. References and Literature 413

10.11. Exercises 414

Chapter 11. First-Generation Models of Endogenous Growth 417

11.1. The AK Model Revisited 418

11.2. The AK Model with Physical and Human Capital 424

11.3. The Two-Sector AK Model 426

11.4. Growth with Externalities 430

11.5. Taking Stock 434

11.6. References and Literature 435

11.7. Exercises 436

Part 4. Endogenous Technological Change 443

Chapter 12. Modeling Technological Change 445

12.1. DifferentConceptionsofTechnology 445

12.2. Science and Profits 449

12.3. The Value of Innovation in Partial Equilibrium 452

12.4. The Dixit-Stiglitz Model and “Aggregate Demand Externalities” 459

12.5.

12.6. Taking Stock 468

12.7. References and Literature 468

12.8. Exercises 470

Chapter 13. Expanding Variety Models 473

13.1. The Lab Equipment Model of Growth with Input Varieties 473

13.2. Growth with Knowledge Spillovers 485

13.3. Growth without Scale Effects 488

13.4. Growth with Expanding Product Varieties 491

13.5. Taking Stock 495

13.6. References and Literature 496

13.7. Exercises 497

Chapter 14. Models of Schumpeterian Growth 505

14.1. A Baseline Model of Schumpeterian Growth 506

14.2. A One-Sector Schumpeterian Growth Model 517

14.3. Innovation by Incumbents and Entrants and Sources of Productivity Growth 522

14.4. Step-by-Step Innovations* 539

14.5. Taking Stock 552

14.6. References and Literature 553

14.7. Exercises 555

Chapter 15. Directed Technological Change 563

15.1. Importance of Biased Technological Change 564

15.2. Basics and Definitions 567

15.3. Baseline Model of Directed Technological Change 570

15.4. Directed Technological Change with Knowledge Spillovers 585

15.5. Directed Technological Change without Scale Effects 589

15.6. Endogenous Labor-Augmenting Technological Change 591

15.7. Generalizations and Other Applications 594

15.8. An Alternative Approach to Labor-Augmenting Technological Change 595

15.9. Taking Stock 600

15.10. References and Literature 602

15.11. Exercises 604

Part 5. Stochastic Growth 611

Chapter 16. Stochastic Dynamic Programming 613

16.1. Dynamic Programming with Expectations 613

16.2. Proofs of the Stochastic Dynamic Programming Theorems* 621

16.3. Stochastic Euler Equations 626

16.4. Generalization to Markov Processes* 629

16.5. Applications of Stochastic Dynamic Programming 631

16.6. Taking Stock 639

16.7. References and Literature 640

16.8. Exercises 641

Chapter 17. Stochastic Growth Models 645

17.1. The Brock-Mirman Model 646

17.2.

17.3. Application: Real Business Cycle Models 659

17.4. Growth with Incomplete Markets: The Bewley Model 663

17.5. The Overlapping Generations Model with Uncertainty 667

17.6. Risk, Diversification and Growth 670

17.7. Taking Stock 689

17.8. References and Literature 690

17.9. Exercises 691

Part 6. Technology Diffusion, Trade and Interdependences 697

Chapter 18. Diffusion of Technology 701

18.1. Productivity Differences and Technology 701

18.2. A Benchmark Model of Technology Diffusion 704

18.3. Technology Diffusion and Endogenous Growth 713

18.4. Appropriate and Inappropriate Technologies and Productivity Differences 718

18.5. Contracting Institutions and Technology Adoption 727

18.6. Taking Stock 741

18.7. References and Literature 744

18.8. Exercises 745

Chapter 19. Trade and Growth 751

19.1. Growth and Financial Capital Flows 751

19.2. Why Doesn’t Capital Flow from Rich to Poor Countries? 757

19.3. Economic Growth in a Heckscher-Ohlin World 760

19.4. Trade, Specialization and the World Income Distribution 770

19.5. Trade, Technology Diffusion and the Product Cycle 784

19.6. Trade and Endogenous Technological Change 789

19.7. Learning-by-Doing, Trade and Growth 792

19.8. Taking Stock 796

19.9. References and Literature 799

19.10. Exercises 801

Part 7. Economic Development and Economic Growth 807

Chapter 20. Structural Change and Economic Growth 813

20.1. Non-Balanced Growth: The Demand Side 813

20.2. Non-Balanced Growth: The Supply Side 821

20.3. Agricultural Productivity and Industrialization 835

20.4. Taking Stock 841

20.5. References and Literature 843

20.6. Exercises 844

Chapter 21. Structural Transformations and Market Failures in Development 849

21.1. Financial Development 851

21.2. Fertility, Mortality and the Demographic Transition 857

21.3. Migration, Urbanization and The Dual Economy 865

21.4.

21.5. Multiple Equilibria From Aggregate Demand Externalities and the Big Push 886

21.6. Inequality, Credit Market Imperfections and Human Capital 894

21.7. Towards a Unified Theory of Development and Growth? 907

21.8. Taking Stock 912

21.9. References and Literature 913

21.10. Exercises 916

Part 8. Political Economy of Growth 925

Chapter 22. Institutions, Political Economy and Growth 931

22.1. The Impact of Institutions on Long-Run Development 932

22.2. Distributional Conflict and Economic Growth in a Simple Society 938

22.3. Distributional Conflict and Competition 951

22.4. Inefficient Economic Institutions: A First Pass 964

22.5. Distributional Conflict and Economic Growth: Concave Preferences* 969

22.6. Heterogeneous Preferences, Social Choice and the Median Voter* 975

22.7. Distributional Conflict and Economic Growth: Heterogeneity and the Median

Voter 995

22.8. The Provision of Public Goods: Weak Versus Strong States 1001

22.9. Taking Stock 1007

22.10. References and Literature 1011

22.11. Exercises 1014

Chapter 23. Political Institutions and Economic Growth 1023

23.1. Political Regimes and Economic Growth 1024

23.2. Political Institutions and Growth-Enhancing Policies 1029

23.3. Dynamic Tradeoffs 1034

23.4. Understanding Endogenous Political Change 1057

23.5. Dynamics of Political and Economic Institutions: A First Look 1069

23.6. Taking Stock 1086

23.7. References and Literature 1089

23.8. Exercises 1090

Chapter 24. Epilogue: Mechanics and Causes of Economic Growth 1095

24.1. What Have We Learned? 1095

24.2. A Possible Perspective on Growth and Stagnation over the Past 200 Years 1100

24.3. Many Remaining Questions 1111

Part 9. Mathematical Appendices 1115

Chapter A. Odds and Ends in Real Analysis and Applications to Optimization 1117

A. 1. Distances and Metric Spaces 1118

A. 2. Mappings, Functions, Sequences, and Continuity 1121

A. 3. A Minimal Amount of Topology: Continuity and Compactness 1126

A. 4. The Product Topology 1131

A.5. Correspondences and Berge’s Maximum Theorem 1134

A.6. Convexity, Concavity, Quasi-Concavity and Fixed Points 1138

A.7. Differentiation, Taylor Series and the Mean Value Theorem 1142

A.8. Functions of Several Variables and the Inverse and Implicit Function Theorem1145

A.9. Separation Theorems 1149

A.10. Constrained Optimization 1153

A. 11. Exercises 1156

Chapter B. Review of Ordinary Differential Equations 1161

B. 1. Review of Eigenvalues and Eigenvectors 1161

B. 2. Some Basic Results on Integrals 1162

B. 3. Linear Differential Equations 1164

B. 4. Stability for Nonlinear Differential Equations 1170

B.5. Separable and Exact Differential Equations 1171

B.6. Existence and Uniqueness of Solutions 1173

B.7. Continuity of Solutions 1174

B.8. Difference Equations 1175

B. 9. Exercises 1177

Chapter C. Brief Review of Dynamic Games 1179

C. 1. Basic Definitions 1179

C. 2. Some Basic Results 1183

C. 3. Application: Repeated Games With Perfect Observability 1187

C. 4. Exercises 1189

Chapter D. List of Theorems 1191

Chapter 2 1191

Chapter 5 1191

Chapter 6 1191

Chapter 7 1192

Chapter 10 1192

Chapter 16 1193

Chapter 22 1193

Appendix Chapter A 1193

Appendix Chapter B 1194

Appendix Chapter C 1195

References (incomplete) 1197