Economic Growth, second edition

, by Barro, Robert J.; Sala-I-Martin, Xavier I.

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ISBN: 9780262025539 | 0262025531
Cover: Hardcover
Copyright: 10/10/2003

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This graduate level text on economic growth surveys neoclassical and more recent growth theories, stressing their empirical implications and the relation of theory to data and evidence. The authors have undertaken a major revision for the long-awaited second edition of this widely used text, the first modern textbook devoted to growth theory. The book has been expanded in many areas and incorporates the latest research. After an introductory discussion of economic growth, the book examines neoclassical growth theories, from Solow-Swan in the 1950s and Cass-Koopmans in the 1960s to more recent refinements; this is followed by a discussion of extensions to the model, with expanded treatment in this edition of heterogenity of households. The book then turns to endogenous growth theory, discussing, among other topics, models of endogenous technological progress (with an expanded discussion in this edition of the role of outside competition in the growth process), technological diffusion, and an endogenous determination of labor supply and population. The authors then explain the essentials of growth accounting and apply this framework to endogenous growth models. The final chapters cover empirical analysis of regions and empirical evidence on economic growth for a broad panel of countries from 1960 to 2000. The updated treatment of cross-country growth regressions for this edition uses the new Summers-Heston data set on world income distribution compiled through 2000.

Preface

About the Authors

xvii

Introduction

(22)

I.1 The Importance of Growth

(5)

I.2 The World Income Distribution

(6)

I.3 Empirical Regularities about Economic Growth

(4)

I.4 A Brief History of Modern Growth Theory

(5)

I.5 Some Highlights of the Second Edition

(2)

1 Growth Models with Exogenous Saving Rates (the Solow-Swan Model)

(62)

1.1 The Basic Structure

(3)

1.2 The Neoclassical Model of Solow and Swan

(35)

1.2.1 The Neoclassical Production Function

(4)

1.2.2 The Fundamental Equation of the Solow-Swan Model

(1)

1.2.3 Markets

(2)

1.2.4 The Steady State

(1)

1.2.5 The Golden Rule of Capital Accumulation and Dynamic Inefficiency

(3)

1.2.6 Transitional Dynamics

(3)

1.2.7 Behavior of Input Prices During the Transition

(1)

1.2.8 Policy Experiments

(2)

1.2.9 An Example: Cobb-Douglas Technology

(1)

1.2.10 Absolute and Conditional Convergence

(6)

1.2.11 Convergence and the Dispersion of Per Capita Income

(1)

1.2.12 Technological Progress

(5)

1.2.13 A Quantitative Measure of the Speed of Convergence

(5)

1.3 Models of Endogenous Growth

(10)

1.3.1 Theoretical Dissatisfaction with Neoclassical Theory

(2)

1.3.2 The AK Model

(3)

1.3.3 Endogenous Growth with Transitional Dynamics

(2)

1.3.4 Constant-Elasticity-of-Substitution Production Functions

(3)

1.4 Other Production Functions ... Other Growth Theories

(6)

1.4.1 The Leontief Production Function and the Harrod-Domar Controversy

(3)

1.4.2 Growth Models with Poverty Traps

(3)

1.5 Appendix: Proofs of Various Propositions

(4)

1.5.1 Proof That Each Input Is Essential for Production with a Neoclassical Production Function

(1)

1.5.2 Properties of the Convergence Coefficient in the Solove-Swan Model

(1)

1.5.3 Proof That Technological Progress Must Be Labor Augmenting

(2)

1.5.4 Properties of the CES Production Function

(1)

1.6 Problems

(4)

2 Growth Models with Consumer Optimization (the Ramsey Model)

(58)

2.1 Households

(8)

2.1.1 Setup of the Model

(3)

2.1.2 First-Order Conditions

(5)

2.2 Firms

(3)

2.3 Equilibrium

(1)

2.4 Alternative Environments

(1)

2.5 The Steady State

(3)

2.6 Transitional Dynamics

102

(19)

2.6.1 The Phase Diagram

102

(2)

2.6.2 The Importance of the Transversality Condition

104

(1)

2.6.3 The Shape of the Stable Arm

105

(1)

2.6.4 Behavior of the Saving Rate

106

(4)

2.6.5 The Paths of the Capital Stock and Output

110

(1)

2.6.6 Speeds of Convergence

111

(7)

2.6.7 Household Heterogeneity

118

(3)

2.7 Nonconstant Time-Preference Rates

121

(11)

2.7.1 Results under Commitment

123

(1)

2.7.2 Results without Commitment under Log Utility

124

(5)

2.7.3 Population Growth and Technological Progress

129

(1)

2.7.4 Results under Isoelastic Utility

130

(2)

2.7.5 The Degree of Commitment

132

(1)

2.8 Appendix 2A: Log-Linearization of the Ramsey Model

132

(2)

2.9 Appendix 2B: Irreversible Investment

134

(1)

2.10 Appendix 2C: Behavior of the Saving Rate

135

(4)

2.11 Appendix 2D: Proof That γk Declines Monotonically If the Economy Starts from k(0) less than k* 137

2.12 Problems

139

(4)

3 Extensions of the Ramsey Growth Model

143

(62)

3.1 Government

143

(9)

3.1.1 Modifications of the Ramsey Framework

143

(3)

3.1.2 Effects of Tax Rates

146

(1)

3.1.3 Effects of Government Purchases

147

(5)

3.2 Adjustment Costs for Investment

152

(9)

3.2.1 The Behavior of Firms

152

(3)

3.2.2 Equilibrium with a Given Interest Rate

155

(4)

3.2.3 Equilibrium for a Closed Economy with a Fixed Saving Rate

159

(2)

3.3 An Open-Economy Ramsey Model

161

(4)

3.3.1 Setup of the Model

161

(1)

3.3.2 Behavior of a Small Economy's Capital Stock and Output

162

(1)

3.3.3 Behavior of a Small Economy's Consumption and Assets

163

(1)

3.3.4 The World Equilibrium

164

(1)

3.4 The World Economy with a Constraint on International Credit

165

(12)

3.4.1 Setup of a Model with Physical and Human Capital

166

(1)

3.4.2 The Closed Economy

167

(1)

3.4.3 The Open Economy

168

(9)

3.5 Variations in Preference Parameters

177

(2)

3.6 Economic Growth in a Model with Finite Horizons

179

(10)

3.6.1 Choices in a Model with Finite Horizons

179

(4)

3.6.2 The Finite-Horizon Model of a Closed Economy

183

(3)

3.6.3 The Finite-Horizon Model of an Open Economy

186

(3)

3.7 Some Conclusions

189

(1)

3.8 Appendix: Overlapping-Generations Models

190

(10)

3.8.1 Households

190

(2)

3.8.2 Firms

192

(1)

3.8.3 Equilibrium

193

(7)

3.9 Problems

200

(5)

4 One-Sector Models of Endogenous Growth

205

(34)

4.1 The AK Model

205

(6)

4.1.1 Behavior of Households

205

(1)

4.1.2 Behavior of Firms

206

(1)

4.1.3 Equilibrium

207

(1)

4.1.4 Transitional Dynamics

208

(1)

4.1.5 The Phase Diagram

209

(1)

4.1.6 Determinants of the Growth Rate

210

(1)

4.2 A One-Sector Model with Physical and Human Capital

211

(1)

4.3 Models with Learning by Doing and Knowledge Spillovers

212

(8)

4.3.1 Technology

212

(4)

4.3.2 Equilibrium

216

(1)

4.3.3 Pareto Nonoptimality and Policy Implications

216

(1)

4.3.4 A Cobb-Douglas Example

217

(1)

4.3.5 Scale Effects

218

(2)

4.4 Public Services and Endogenous Growth

220

(6)

4.4.1 A Public-Goods Model

220

(3)

4.4.2 A Congestion Model

223

(3)

4.5 Transitional Dynamics, Endogenous Growth

226

(6)

4.5.1 A Cobb-Douglas Example

226

(4)

4.5.2 A CES Example

230

(2)

4.6 Concluding Observations

232

(1)

4.7 Appendix: Endogenous Growth in the One-Sector Model

232

(3)

4.8 Problems

235

(4)

5 Two-Sector Models of Endogenous Growth (with Special Attention to the Role of Human Capital)

239

(46)

5.1 A One-Sector Model with Physical and Human Capital

240

(7)

5.1.1 The Basic Setup

240

(2)

5.1.2 The Constraint of Nonnegative Gross Investment

242

(5)

5.2 Different Technologies for Production and Education

247

(21)

5.2.1 The Model with Two Sectors of Production

247

(4)

5.2.2 The Uzawa-Lucas Model

251

(15)

5.2.3 The Generalized Uzawa-Lucas Model

266

(1)

5.2.4 The Model with Reversed Factor Intensities

267

(1)

5.3 Conditions for Endogenous Growth

268

(3)

5.4 Summary Observations

271

(1)

5.5 Appendix 5A: Transitional Dynamics with Inequality Restrictions on Gross Investment in the One-Sector Model

271

(3)

5.6 Appendix 5B: Solution of the Uzawa-Lucas Model

274

(6)

5.7 Appendix 5C: The Model with Reversed Factor Intensities

280

(2)

5.8 Problems

282

(3)

6 Technological Change: Models with an Expanding Variety of Products

285

(32)

6.1 A Baseline Model with a Variety of Products

285

(20)

6.1.1 The Producers of Final Output

285

(4)

6.1.2 Research Firms

289

(6)

6.1.3 Households

295

(1)

6.1.4 General Equilibrium

295

(2)

6.1.5 Determinants of the Growth Rate

297

(1)

6.1.6 Pareto Optimality

297

(3)

6.1.7 Scale Effects and the Cost of R&D

300

(3)

6.1.8 A Rising Cost of R&D

303

(2)

6.2 Erosion of Monopoly Power, Competition

305

(5)

6.3 Romer's Model of Technological Change

310

(3)

6.4 Concluding Observations

313

(1)

6.5 Problems

313

(4)

7 Technological Change: Schumpeterian Models of Quality Ladders

317

(32)

7.1 Sketch of the Model

317

(2)

7.2 The Model

319

(14)

7.2.1 The Producers of Final Output: Levels of Quality in the Production Technology

319

(2)

7.2.2 The Research Sector

321

(7)

7.2.3 Consumers

328

(1)

7.2.4 Behavior of the Aggregate Quality Index and Endogenous Growth

329

(2)

7.2.5 Scale Effects Again

331

(2)

7.3 Innovation by the Leader

333

(6)

7.3.1 Interactions Between the Leader and the Outsiders

333

(3)

7.3.2 The Leader as a Monopoly Researcher

336

(3)

7.4 Pareto Optimality

339

(3)

7.5 Summary Observations about Growth

342

(1)

7.6 Appendix

343

(4)

7.6.1 Intermediates of Various Quality Grades

343

(2)

7.6.2 The Duration of a Monopoly Position

345

(1)

7.6.3 The Market Value of Firms

346

(1)

7.6.4 Research by the Industry Leader

346

(1)

7.7 Problems

347

(2)

8 The Diffusion of Technology

349

(34)

8.1 Behavior of Innovators in the Leading Country

351

(1)

8.2 Behavior of Imitators in the Follower Country

352

(11)

8.2.1 Producers of Final Output

352

(1)

8.2.2 Imitating Firms

353

(4)

8.2.3 Consumers

357

(1)

8.2.4 Steady-State Growth

357

(2)

8.2.5 The Dynamic Path and Convergence

359

(4)

8.3 Constant (or Slowly Rising) Costs of Imitation

363

(5)

8.3.1 The Steady State

364

(1)

8.3.2 Transitional Dynamics

365

(3)

8.4 Foreign Investment and Intellectual Property Rights

368

(2)

8.5 General Implications for Growth Rates in Follower Countries

370

(3)

8.6 Switchovers of Technological Leadership, Leapfrogging

373

(3)

8.7 Welfare Considerations

376

(3)

8.8 Summary Observations about Diffusion and Growth

379

(1)

8.9 Problems

380

(3)

9 Labor Supply and Population

383

(50)

9.1 Migration in Models of Economic Growth

383

(24)

9.1.1 Migration in the Solow-Swan Model

384

(9)

9.1.2 Migration in the Ramsey Model

393

(5)

9.1.3 The Braun Model of Migration and Growth

398

(9)

9.2 Fertility Choice

407

(15)

9.2.1 An Overlapping-Generations Setup

408

(3)

9.2.2 The Model in Continuous Time

411

(11)

9.3 Labor/Leisure Choice

422

(5)

9.4 Appendix: The Form of the Utility Function with Consumption and Work Effort

427

(1)

9.5 Problems

428

(5)

10 Growth Accounting

433

(28)

10.1 Standard Primal Growth Accounting

433

(9)

10.1.1 Basic Setup

433

(3)

10.1.2 Measuring Inputs

436

(2)

10.1.3 Results from Growth Accounting

438

(3)

10.1.4 A Note on Regression-Based Estimates of TFP Growth

441

(1)

10.2 Dual Approach to Growth Accounting

442

(2)

10.3 Problems with Growth Accounting

444

(6)

10.3.1 An Increasing-Returns Model with Spillovers

445

(2)

10.3.2 Taxes

447

(2)

10.3.3 Multiple Types of Factors

449

(1)

10.4 TFP Growth and R&D

450

(7)

10.4.1 Varieties Models

451

(3)

10.4.2 Quality-Ladders Models

454

(3)

10.5 Growth Accounting Versus Sources of Growth

457

(4)

11 Empirical Analysis of Regional Data Sets

461

(50)

11.1 Two Concepts of Convergence

462

(4)

11.2 Convergence Across the U.S. States

466

(8)

11.2.1 β Convergence

466

(6)

11.2.2 Measurement Error

472

(1)

11.2.3 α Convergence

473

(1)

11.3 Convergence Across Japanese Prefectures

474

(5)

11.3.1 β Convergence

474

(4)

11.3.2 α Convergence Across Prefectures

478

(1)

11.4 Convergence Across European Regions

479

(3)

11.4.1 β Convergence

479

(3)

11.4.2 α Convergence

482

(1)

11.5 Convergence Across Other Regions Around the World

482

(1)

11.6 Migration Across the U.S. States

483

(3)

11.7 Migration Across Japanese Prefectures

486

(4)

11.8 Migration Across European Regions

490

(2)

11.9 Migration and Convergence

492

(3)

11.10 β Convergence in Panel Data with Fixed Effects

495

(1)

11.11 Conclusions

496

(1)

11.12 Appendix on Regional Data Sets

497

(14)

11.12.1 Data for U.S. States

497

(3)

11.12.2 Data for European Regions

500

(6)

11.12.3 Data for Japanese Prefectures

506

(5)

12 Empirical Analysis of a Cross Section of Countries

511

(56)

12.1 Losers and Winners from 1960 to 2000

511

(4)

12.2 An Empirical Analysis of Growth Rates

515

(6)

12.2.1 Effects from State Variables

517

(1)

12.2.2 Control and Environmental Variables

518

(3)

12.3 Regression Results for Growth Rates

521

(20)

12.3.1 A Basic Regression

521

(13)

12.3.2 Tests of Stability of Coefficients

534

(1)

12.3.3 Additional Explanatory Variables

535

(6)

12.4 Summary and Conclusions about Growth

541

(1)

12.5 Robustness

541

(18)

12.5.1 Levine and Renelt (1992)

542

(1)

12.5.2 Bayesian Averaging of Classical Estimates (BACE)

543

(4)

12.5.3 Main Results in Sala-i-Martin, Doppelhofer, and Miller (2003)

547

(9)

12.5.4 Robustness Analysis

556

(3)

12.6 Appendix: Long-Term Data on GDP

559

(8)

Appendix on Mathematical Methods

567

(60)

A.1 Differential Equations

568

(29)

A.1.1 Introduction

568

(1)

A.1.2 First-Order Ordinary Differential Equations

569

(7)

A.1.3 Systems of Linear Ordinary Differential Equations

576

(21)

A.2 Static Optimization

597

(7)

A.2.1 Unconstrained Maxima

597

(1)

A.2.2 Classical Nonlinear Programming: Equality Constraints

598

(2)

A.2.3 Inequality Constraints: The Kuhn-Tucker Conditions

600

(4)

A.3 Dynamic Optimization in Continuous Time

604

(14)

A.3.1 Introduction

604

(1)

A.3.2 The Typical Problem

605

(1)

A.3.3 Heuristic Derivation of the First-Order Conditions

606

(3)

A.3.4 Transversality Conditions

609

(1)

A.3.5 The Behavior of the Hamiltonian over Time

609

(1)

A.3.6 Sufficient Conditions

610

(1)

A.3.7 Infinite Horizons

610

(2)

A.3.8 Example: The Neoclassical Growth Model

612

(1)

A.3.9 Transversality Conditions in Infinite-Horizon Problems

613

(2)

A.3.10 Summary of the Procedure to Find the First-Order Conditions

615

(1)

A.3.11 Present-Value and Current-Value Hamiltonians

616

(1)

A.3.12 Multiple Variables

617

(1)

A.4 Useful Results in Matrix Algebra: Eigenvalues, Eigenvectors, and Diagonalization of Matrices

618

(2)

A.5 Useful Results in Calculus

620

(7)

A.5.1 Implicit-Function Theorem

620

(1)

A.5.2 Taylor's Theorem

621

(1)

A.5.3 L' Hôpital's Rule

622

(1)

A.5.4 Integration by Parts

623

(1)

A.5.5 Fundamental Theorem of Calculus

624

(1)

A.5.6 Rules of Differentiation of Integrals

624

(3)

References

627

(14)

Index

641

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Economic Growth, second edition

Summary

Author Biography

Table of Contents

Supplemental Materials