I Economic Growth 5. Second Edition. Robert J. Barro Xavier Sala-i-Martin. The MIT Press Cambridge, Massachusetts London, England

Transcription

1 I Economic Growth 5 Second Edition 1 Robert J. Barro Xavier Sala-i-Martin The MIT Press Cambridge, Massachusetts London, England

2 Preface About the Authors xv xvii Introduction The Importance of Growth The World Income Distribution Empirical Regularities about Economic Growth A Brief History of Modern Growth Theory Some Highlights of the Second Edition 21 1 Growth Models with Exogenous Saving Rates (the Solow-Swan Model) The Basic Structure The Neoclassical Model of Solow and Swan The Neoclassical Production Function The Fundamental Equation of the Solow-Swan Model Markets The Steady State The Golden Rule of Capital Accumulation and Dynamic Inefficiency Transitional Dynamics Behavior of Input Prices During the Transition Policy Experiments An Example: Cobb-Douglas Technology Absolute and Conditional Convergence Convergence and the Dispersion of Per Capita Income Technological Progress A Quantitative Measure of the Speed of Convergence Models of Endogenous Growth Theoretical Dissatisfaction with Neoclassical Theory The AK Model Endogenous Growth with Transitional Dynamics Constant-Elasticity-of-Substitution Production Functions Other Production Functions... Other Growth Theories The Leontief Production Function and the Harrod-Domar Controversy Growth Models with Poverty Traps 74

3 VI Contents 1-5 App end i x: Proofs of Various Propositions Proof Thnf E,«i T_ i T»-,, x T, ^ for Production i a Neoclassical Production Function Properties of the Convergence Coefficient in the Solow-Swan Model 1.53 Proof That Technological Progress Must Be Labor Augmenting 15.4 Properties of the CES Production Function 1.6 Problems 2 Growth Models with Consumer Optimization (the Ramsey Model) 2.1 Households Setup of the Model First-Order Conditions 2.2 Firms 2.3 Equilibrium 2.4 Alternative Environments 2.5 The Steady State 2.6 Transitional Dynamics The Phase Diagram The Importance of the Transversality Condition The Shape of the Stable Arm Behavior of the Saving Rate The Paths of the Capital Stock and Output Speeds of Convergence Household Heterogeneity 2.7 Nonconstant Time-Preference Rates Results under Commitment Results without Commitment under Log Utility Population Growth and Technological Progress Results under Isoelastic Utility The Degree of Commitment 2.8 Appendix 2A: Log-Linearization of the Ramsey Model 2.9 Appendix 2B: Irreversible Investment

4 2.10 Appendix 2C: Behavior of the Saving Rate 2.11 Appendix 2D: Proof That yg Declines Monotonically If the Economy Starts from (0) < k* 2.12 Problems 3 Extensions of the Ramsey Growth Model 3.1 Government Modifications of the Ramsey Framework Effects of Tax Rates Effects of Government Purchases 3.2 Adjustment Costs for Investment The Behavior of Firms Equilibrium with a Given Interest Rate Equilibrium for a Closed Economy with a Fixed Saving Rate 3.3 An Open-Economy Ramsey Model Setup of the Model Behavior of a Small Economy's Capital Stock and Output Behavior of a Small Economy's Consumption and Assets The World Equilibrium 3.4 The World Economy with a Constraint on International Credit Setup of a Model with Physical and Human Capital The Closed Economy The Open Economy 3.5 Variations in Preference Parameters 3.6 Economic Growth in a Model with Finite Horizons Choices in a Model with Finite Horizons The Finite-Horizon Model of a Closed Economy The Finite-Horizon Model of an Open Economy 3.7 Some Conclusions 3.8 Appendix: Overlapping-Generations Models Households Firms Equilibrium 3.9 Problems

5 viii Contents 4 One-Sector Models of Endogenous Growth The AK Model Behavior of Households Behavior of Firms Equilibrium Transitional Dynamics The Phase Diagram Determinants of the Growth Rate A One-Sector Model with Physical and Human Capital Models with Learning by Doing and Knowledge Spillovers Technology Equilibrium Pareto Nonoptimality and Policy Implications A Cobb-Douglas Example Scale Effects Public Services and Endogenous Growth A Public-Goods Model A Congestion Model Transitional Dynamics, Endogenous Growth A Cobb-Douglas Example A CES Example Concluding Observations Appendix: Endogenous Growth in the One-Sector Model Problems Two-Sector Models of Endogenous Growth (with Special Attention to the Role of Human Capital) A One-Sector Model with Physical and Human Capital The Basic Setup The Constraint of Nonnegative Gross Investment Different Technologies for Production and Education The Model with Two Sectors of Production The Uzawa-Lucas Model The Generalized Uzawa-Lucas Model The Model with Reversed Factor Intensities Conditions for Endogenous Growth 268

6 5.4 Summary Observations 5.5 Appendix 5A: Transitional Dynamics with Inequality Restrictions on Gross Investment in the One-Sector Model 5.6 Appendix 5B: Solution of the Uzawa-Lucas Model 5.7 Appendix 5C: The Model with Reversed Factor Intensities 5.8 Problems 6 Technological Change: Models with an Expanding Variety of Products 6.1 A Baseline Model with a Variety of Products The Producers of Final Output Research Firms Households General Equilibrium Determinants of the Growth Rate Pareto Optimality Scale Effects and the Cost of R&D A Rising Cost of R&D 6.2 Erosion of Monopoly Power, Competition 6.3 Romer's Model of Technological Change 6.4 Concluding Observations 6.5 Problems 7 Technological Change: Schumpeterian Models of Quality Ladders 7.1 Sketch of the Model 7.2 The Model The Producers of Final Output: Levels of Quality in the Production Technology The Research Sector Consumers Behavior of the Aggregate Quality Index and Endogenous Growth Scale Effects Again 7.3 Innovation by the Leader Interactions Between the Leader and the Outsiders The Leader as a Monopoly Researcher

7 7.4 Pareto Optimality Summary Observations about Growth Appendix Intermediates of Various Quality Grades The Duration of a Monopoly Position The Market Value of Firms Research by the Industry Leader Problems The Diffusion of Technology Behavior of Innovators in the Leading Country Behavior of Imitators in the Follower Country Producers of Final Output Imitating Firms Consumers Steady-State Growth The Dynamic Path and Convergence Constant (or Slowly Rising) Costs of Imitation The Steady State Transitional Dynamics Foreign Investment and Intellectual Property Rights General Implications for Growth Rates in Follower Countries Switchovers of Technological Leadership, Leapfrogging Welfare Considerations Summary Observations about Diffusion and Growth Problems Labor Supply and Population Migration in Models of Economic Growth Migration in the Solow-Swan Model Migration in the Ramsey Model The Braun Model of Migration and Growth Fertility Choice " An Overlapping-Generations Setup The Model in Continuous Time Labor/Leisure Choice 422

8 9.4 Appendix: The Form of the Utility Function with Consumption and Work Effort 9.5 Problems 10 Growth Accounting 10.1 Standard Primal Growth Accounting Basic Setup Measuring Inputs Results from Growth Accounting A Note on Regression-Based Estimates of TFP Growth 10.2 Dual Approach to Growth Accounting 10.3 Problems with Growth Accounting An Increasing-Returns Model with Spillovers Taxes Multiple Types of Factors 10.4 TFP Growth and R&D Varieties Models Quality-Ladders Models 10.5 Growth Accounting Versus Sources of Growth 11 Empirical Analysis of Regional Data Sets 11.1 Two Concepts of Convergence 11.2 Convergence Across the U.S. States fi Convergence Measurement Error a Convergence 11.3 Convergence Across Japanese Prefectures ft Convergence a Convergence Across Prefectures 11.4 Convergence Across European Regions p Convergence a Convergence 11.5 Convergence Across Other Regions Around the World 11.6 Migration Across the U.S. States 11.7 Migration Across Japanese Prefectures 11.8 Migration Across European Regions

9 11.9 Migration and Convergence j8 Convergence in Panel Data with Fixed Effects Conclusions Appendix on Regional Data Sets Data for U.S. States Data for European Regions Data for Japanese Prefectures Empirical Analysis of a Cross Section of Countries Losers and Winners from 1960 to An Empirical Analysis of Growth Rates Effects from State Variables Control and Environmental Variables Regression Results for Growth Rates A Basic Regression Tests of Stability of Coefficients Additional Explanatory Variables Summary and Conclusions about Growth Robustness Levine and Renelt (1992) Bayesian Averaging of Classical Estimates (BACE) Main Results in Sala-i-Martin, Doppelhofer, and Miller (2003) Robustness Analysis Appendix: Long-Term Data on GDP 559 Appendix on Mathematical Methods 567 A.I Differential Equations 568 A. 1.1 Introduction 568 A. 1.2 First-Order Ordinary Differential Equations 569 A. 1.3 Systems of Linear Ordinary Differential Equations 576 A.2 Static Optimization 597 A.2.1 Unconstrained Maxima 597 A.2.2 Classical Nonlinear Programming: Equality Constraints 598 A.2.3 Inequality Constraints: The Kuhn-Tucker Conditions 600 A.3 Dynamic Optimization in Continuous Time 604 A.3.1 Introduction 604

10 xm A.3.2 The Typical Problem A.3.3 Heuristic Derivation of the First-Order Conditions A.3.4 Transversality Conditions A.3.5 The Behavior of the Hamiltonian over Time A.3.6 Sufficient Conditions A.3.7 Infinite Horizons A.3.8 Example: The Neoclassical Growth Model A.3.9 Transversality Conditions in Infinite-Horizon Problems A.3.10 Summary of the Procedure to Find the First-Order Conditions A.3.11 Present-Value and Current-Value Hamiltonians A.3.12 Multiple Variables A.4 Useful Results in Matrix Algebra: Eigenvalues, Eigenvectors, and Diagonalization of Matrices A.5 Useful Results in Calculus A.5.1 Implicit-Function Theorem A.5.2 Taylor's Theorem A.5.3 L'Hopital's Rule A.5.4 Integration by Parts A.5.5 Fundamental Theorem of Calculus A.5.6 Rules of Differentiation of Integrals References Index