Introduction to Modern Economic Growth

Preface xv

Part I: Introduction

Chapter 1: Economic Growth and Economic Development...

Preface xv

Part I: Introduction

Chapter 1: Economic Growth and Economic Development: The Questions 3

1.1 Cross-Country Income Differences 3

1.2 Income and Welfare 7

1.3 Economic Growth and Income Differences 9

1.4 Origins of Today’s Income Differences and World Economic Growth 11

1.5 Conditional Convergence 15

1.6 Correlates of Economic Growth 18

1.7 From Correlates to Fundamental Causes 19

1.8 The Agenda 21

1.9 References and Literature 23

Chapter 2: The Solow Growth Model 26

2.1 The Economic Environment of the Basic Solow Model 27

2.2 The Solow Model in Discrete Time 34

2.3 Transitional Dynamics in the Discrete-Time Solow Model 43

2.4 The Solow Model in Continuous Time 47

2.5 Transitional Dynamics in the Continuous-Time Solow Model 51

2.6 A First Look at Sustained Growth 55

2.7 Solow Model with Technological Progress 56

2.8 Comparative Dynamics 67

2.9 Taking Stock 68

2.10 References and Literature 69

2.11 Exercises 71

Chapter 3: The SolowModel and the Data 77

3.1 Growth Accounting 77

3.2 The Solow Model and Regression Analyses 80

3.3 The Solow Model with Human Capital 85

3.4 Solow Model and Cross-Country Income Differences: Regression Analyses 90

3.5 Calibrating Productivity Differences 96

3.6 Estimating Productivity Differences 100

3.7 Taking Stock 105

3.8 References and Literature 106

3.9 Exercises 107

Chapter 4: Fundamental Determinants of Differences in Economic Performance 109

4.1 Proximate versus Fundamental Causes 109

4.2 Economies of Scale, Population, Technology, and World Growth 112

4.3 The Four Fundamental Causes 114

4.4 The Effect of Institutions on Economic Growth 123

4.5 What Types of Institutions? 136

4.6 Disease and Development 137

4.7 Political Economy of Institutions: First Thoughts 140

4.8 Taking Stock 140

4.9 References and Literature 141

4.10 Exercises 143

Part II: Toward Neoclassical Growth

Chapter 5: Foundations of Neoclassical Growth 147

5.1 Preliminaries 147

5.2 The Representative Household 149

5.3 Infinite Planning Horizon 156

5.4 The Representative Firm 158

5.5 Problem Formulation 160

5.6 Welfare Theorems 161

5.7 Proof of the Second Welfare Theorem (Theorem 5.7) * 168

5.8 Sequential Trading 171

5.9 Optimal Growth 174

5.10 Taking Stock 176

5.11 References and Literature 176

5.12 Exercises 178

Chapter 6: Infinite-Horizon Optimization and Dynamic Programming 182

6.1 Discrete-Time Infinite-Horizon Optimization 182

6.2 Stationary Dynamic Programming 185

6.3 Stationary Dynamic Programming Theorems 187

6.4 The Contraction Mapping Theorem and Applications * 190

6.5 Proofs of the Main Dynamic Programming Theorems * 194

6.6 Applications of Stationary Dynamic Programming 201

6.7 Nonstationary Infinite-Horizon Optimization 211

6.8 Optimal Growth in Discrete Time 215

6.9 Competitive Equilibrium Growth 219

6.10 Computation 221

6.11 Taking Stock 221

6.12 References and Literature 222

6.13 Exercises 223

Chapter 7: An Introduction to the Theory of Optimal Control 227

7.1 Variational Arguments 228

7.2 The Maximum Principle: A First Look 235

7.3 Infinite-Horizon Optimal Control 240

7.4 More on Transversality Conditions 250

7.5 Discounted Infinite-Horizon Optimal Control 253

7.6 Existence of Solutions, Concavity, and Differentiability * 259

7.7 A First Look at Optimal Growth in Continuous Time 268

7.8 The q-Theory of Investment and Saddle-Path Stability 269

7.9 Taking Stock 274

7.10 References and Literature 275

7.11 Exercises 278

Part III: Neoclassical Growth

Chapter 8: The Neoclassical Growth Model 287

8.1 Preferences, Technology, and Demographics 287

8.2 Characterization of Equilibrium 293

8.3 Optimal Growth 298

8.4 Steady-State Equilibrium 300

8.5 Transitional Dynamics and Uniqueness of Equilibrium 302

8.6 Neoclassical Growth in Discrete Time 305

8.7 Technological Change and the Canonical Neoclassical Model 306

8.8 The Role of Policy 312

8.9 Comparative Dynamics 313

8.10 A Quantitative Evaluation 315

8.11 Extensions 317

8.12 Taking Stock 317

8.13 References and Literature 318

8.14 Exercises 319

Chapter 9: Growth with Overlapping Generations 327

9.1 Problems of Infinity 328

9.2 The Baseline Overlapping Generations Model 329

9.3 The Canonical Overlapping Generations Model 335

9.4 Overaccumulation and Pareto Optimality of Competitive Equilibrium in the Overlapping Generations Model 336

9.5 Role of Social Security in Capital Accumulation 339

9.6 Overlapping Generations with Impure Altruism 342

9.7 Overlapping Generations with Perpetual Youth 345

9.8 Overlapping Generations in Continuous Time 348

9.9 Taking Stock 353

9.10 References and Literature 354

9.11 Exercises 355

Chapter 10: Human Capital and Economic Growth 359

10.1 A Simple Separation Theorem 359

10.2 Schooling Investments and Returns to Education 361

10.3 The Ben-Porath Model 363

10.4 Neoclassical Growth with Physical and Human Capital 367

10.5 Capital-Skill Complementarity in an Overlapping Generations Model 371

10.6 Physical and Human Capital with Imperfect Labor Markets 374

10.7 Human Capital Externalities 379

10.8 The Nelson-Phelps Model of Human Capital 380

10.9 Taking Stock 382

10.10 References and Literature 384

10.11 Exercises 384

Chapter 11: First-Generation Models of Endogenous Growth 387

11.1 The AK Model Revisited 388

11.2 The AK Model with Physical and Human Capital 393

11.3 The Two-Sector AK Model 395

11.4 Growth with Externalities 398

11.5 Taking Stock 402

11.6 References and Literature 404

11.7 Exercises 404

Part IV: Endogenous Technological Change

Chapter 12: Modeling Technological Change 411

12.1 Different Conceptions of Technology 411

12.2 Science and Profits 414

12.3 The Value of Innovation in Partial Equilibrium 416

12.4 The Dixit-Stiglitz Model and Aggregate Demand Externalities 422

12.5 Individual R&D Uncertainty and the Stock Market 428

12.6 Taking Stock 429

12.7 References and Literature 430

12.8 Exercises 431

Chapter 13: Expanding VarietyModels 433

13.1 The Lab-Equipment Model of Growth with Input Varieties 433

13.2 Growth with Knowledge Spillovers 444

13.3 Growth without Scale Effects 446

13.4 Growth with Expanding Product Varieties 448

13.5 Taking Stock 452

13.6 References and Literature 453

13.7 Exercises 453

Chapter 14: Models of Schumpeterian Growth 458

14.1 A Baseline Model of Schumpeterian Growth 459

14.2 A One-Sector Schumpeterian Growth Model 468

14.3 Innovation by Incumbents and Entrants 472

14.4 Step-by-Step Innovations * 479

14.5 Taking Stock 489

14.6 References and Literature 490

14.7 Exercises 491

Chapter 15: Directed Technological Change 497

15.1 Importance of Biased Technological Change 498

15.2 Basics and Definitions 500

15.3 Baseline Model of Directed Technological Change 503

15.4 Directed Technological Change with Knowledge Spillovers 514

15.5 Directed Technological Change without Scale Effects 518

15.6 Endogenous Labor-Augmenting Technological Change 519

15.7 Generalizations and Other Applications 522

15.8 An Alternative Approach to Labor-Augmenting Technological Change* 523

15.9 Taking Stock 526

15.10 References and Literature 527

15.11 Exercises 529

Part V: Stochastic Growth

Chapter 16: Stochastic Dynamic Programming 537

16.1 Dynamic Programming with Expectations 537

16.2 Proofs of the Stochastic Dynamic Programming Theorems * 544

16.3 Stochastic Euler Equations 549

16.4 Generalization to Markov Processes * 552

16.5 Applications of Stochastic Dynamic Programming 554

16.6 Taking Stock 561

16.7 References and Literature 561

16.8 Exercises 562

Chapter 17: Stochastic Growth Models 566

17.1 The Brock-Mirman Model 567

17.2 Equilibrium Growth under Uncertainty 571

17.3 Application: Real Business Cycle Models 579

17.4 Growth with Incomplete Markets: The Bewley Model 583

17.5 The Overlapping Generations Model with Uncertainty 586

17.6 Risk, Diversification, and Growth 588

17.7 Taking Stock 603

17.8 References and Literature 604

17.9 Exercises 605

Part VI: Technology Diffusion, Trade, and Interdependences

Chapter 18: Diffusion of Technology 611

18.1 Productivity Differences and Technology 611

18.2 A Benchmark Model of Technology Diffusion 613

18.3 Technology Diffusion and Endogenous Growth 619

18.4 Appropriate and Inappropriate Technologies and Productivity Differences 623

18.5 Contracting Institutions and Technology Adoption 630

18.6 Taking Stock 642

18.7 References and Literature 643

18.8 Exercises 644

Chapter 19: Trade and Growth 648

19.1 Growth and Financial Capital Flows 648

19.2 Why Does Capital Not Flow from Rich to Poor Countries? 653

19.3 Economic Growth in a Heckscher-Ohlin World 655

19.4 Trade, Specialization, and the World Income Distribution 663

19.5 Trade, Technology Diffusion, and the Product Cycle 674

19.6 Trade and Endogenous Technological Change 678

19.7 Learning-by-Doing, Trade, and Growth 680

19.8 Taking Stock 684

19.9 References and Literature 685

19.10 Exercises 687

Part VII: Economic Development and Economic Growth

Chapter 20: Structural Change and Economic Growth 697

20.1 Nonbalanced Growth: The Demand Side 697

20.2 Nonbalanced Growth: The Supply Side 703

20.3 Agricultural Productivity and Industrialization 715

20.4 Taking Stock 719

20.5 References and Literature 720

20.6 Exercises 721

Chapter 21: Structural Transformations and Market Failures in Development 725

21.1 Financial Development 726

21.2 Fertility, Mortality, and the Demographic Transition 729

21.3 Migration, Urbanization, and the Dual Economy 736

21.4 Distance to the Frontier and Changes in the Organization of Production 744

21.5 Multiple Equilibria from Aggregate Demand Externalities and the Big Push 752

21.6 Inequality, Credit Market Imperfections, and Human Capital 758

21.7 Toward a Unified Theory of Development and Growth? 764

21.8 Taking Stock 768

21.9 References and Literature 769

21.10 Exercises 771

Part VIII: The Political Economy of Growth

Chapter 22: Institutions, Political Economy, and Growth 781

22.1 The Impact of Institutions on Long-Run Development 781

22.2 Distributional Conflict and Economic Growth in a Simple Society 784

22.3 The Canonical Cobb-Douglas Model of Distributional Conflict 792

22.4 Distributional Conflict and Competition 793

22.5 Subgame Perfect versus Markov Perfect Equilibria 799

22.6 Inefficient Economic Institutions: A First Pass 802

22.7 Heterogeneous Preferences, Social Choice, and the Median Voter * 805

22.8 Distributional Conflict and Economic Growth: Heterogeneity and the Median Voter 814

22.9 The Provision of Public Goods: Weak versus Strong States 817

22.10 Taking Stock 822

22.11 References and Literature 823

22.12 Exercises 825

Chapter 23: Political Institutions and Economic Growth 831

23.1 Political Regimes and Economic Growth 832

23.2 Political Institutions and Growth-Enhancing Policies 834

23.3 Dynamic Trade-offs 837

23.4 Understanding Endogenous Political Change 850

23.5 Taking Stock 856

23.6 References and Literature 857

23.7 Exercises 858

Epilogue: Mechanics and Causes of Economic Growth 861

What Have We Learned? 861

A Possible Perspective on Growth and Stagnation over the Past 200 Years 864

Many Remaining Questions 872

Part IX: Mathematical Appendixes

Appendix A: Odds and Ends in Real Analysis and Applications to Optimization 877

A.1 Distances and Metric Spaces 878

A.2 Mappings, Functions, Sequences, Nets, and Continuity 880

A.3 A Minimal Amount of Topology: Continuity and Compactness * 885

A.4 The Product Topology * 889

A.5 Absolute Continuity and Equicontinuity * 891

A.6 Correspondences and Berge’s Maximum Theorem 894

A.7 Convexity, Concavity, Quasi-Concavity, and Fixed Points 898

A.8 Differentiation, Taylor Series, and the Mean Value Theorem 900

A.9 Functions of Several Variables and the Inverse and Implicit Function Theorems 904

A.10 Separation Theorems * 907

A.11 Constrained Optimization 910

A.12 Exercises 915

Appendix B: Review of Ordinary Differential Equations 917

B.1 Eigenvalues and Eigenvectors 917

B.2 Some Basic Results on Integrals 918

B.3 Linear Differential Equations 920

B.4 Solutions to Linear First-Order Differential Equations 921

B.5 Systems of Linear Differential Equations 924

B.6 Local Analysis and Stability of Nonlinear Differential Equations 926

B.7 Separable and Exact Differential Equations 927

B.8 Existence and Uniqueness of Solutions 929

B.9 Continuity and Differentiability of Solutions 930

B.10 Difference Equations 930

B.11 Exercises 932

Appendix C: Brief Review of Dynamic Games 934

C.1 Basic Definitions 934

C.2 Some Basic Results 937

C.3 Application: Repeated Games with Perfect Observability 941

C.4 Exercises 942

Appendix D: List of Theorems 944

Chapter 2 944

Chapter 5 944

Chapter 6 944

Chapter 7 945

Chapter 10 945

Chapter 16 945

Chapter 22 946

Appendix A 946

Appendix B 947

Appendix C 947

References 949

Name Index 971

Subject Index 977