A Theory of Economic Growth: Dynamics and Policy in Overlapping Generations

, by David de la Croix , Philippe Michel

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ISBN: 9780521806428 | 0521806429
Cover: Hardcover
Copyright: 11/11/2002

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Inter-generational transfers are at the center of economic policy debates today. Reducing public debt; financing social security; taxing capital and bequests; and designing the education system imply substantial inter-generational transfers. The tool that economists employ to analyze these issues is the overlapping generations model, which reflects the different periods of life. When the model includes capital accumulation, it also allows researchers to formalize the development of an economy, relating its growth path to the savings behavior of young agents. The aim of this book is an in-depth analysis of this model that includes its major policy implications.

Introduction

xiii

Overlapping Generations and Macro-economics

xiii

Overlapping Generations in Other Fields

Outline of the Book

xvi

Acknowledgments

xvii

Competitive Equilibria

(71)

The Model

(3)

Two-period-lived Individuals

(1)

Neo-classical Technology

(1)

Firms

(1)

Main Assumptions

(6)

The Assumptions on the Utility Function

(2)

The Assumptions on the Production Function

(4)

The Behavior of the Agents at Period t

(6)

The Young Individuals

(1)

The Inter-temporal Elasticity of Substitution

(1)

The Properties of the Savings Function

(3)

The Old Individuals

(1)

The Firms

(1)

The Temporary Equilibrium

(3)

The Inter-temporal Equilibrium with Perfect Foresight

(8)

Existence of Equilibria

(2)

Uniqueness of the Inter-temporal Equilibrium

(5)

Capital Dynamics at a Rational Inter-temporal Equilibrium

(12)

Steady States and Stability

(2)

Dynamics

(5)

The Behavior Near 0

(3)

A Quick Look at the Empirics of Growth

(2)

Comparison of Myopic and Perfect Foresight

(6)

The Steady States

(1)

Local Stability

(1)

Uniqueness of the Steady State

(2)

Applications and Extensions

(25)

Myopic and Perfect Foresight in an Example

(5)

A Demographic Shock

(1)

Non-separable Utility Function

(2)

Homothetic Preferences

(1)

Heterogeneous Agents

(2)

Technical Progress

(1)

Imperfect Credit Market

(7)

Three-period-lived Households

(2)

Borrowing Constraints in the Three-period Model

(4)

Conclusion

(2)

Optimality

(57)

Optimality of Stationary Paths

(9)

Feasible Long-run Capital Stock

(3)

The Optimal Stationary Path: The Golden Age

(3)

Under- and Over-accumulation of Capital

(2)

Optimality of the Dynamics

(8)

Dynamic Efficiency

(4)

Pareto Optimality of Dynamics

(4)

The Planning Problem

(11)

The Objective Function

(1)

Properties of the Value Function

(3)

Existence and Monotonicity of Optimal Paths

(4)

Limit of the Optimal Path and Optimal Steady State

(2)

Marginal Analysis of Optimal Solutions

101

(11)

The Optimality Conditions

102

(4)

The Planner's Stationary Solution

106

(1)

Local Dynamics

106

(2)

A Graphical Exposition

108

(4)

Unbounded Optimal Growth

112

(5)

Existence of Optimal Paths When σ > 1

112

(2)

Existence of Optimal Paths When σ > 1 (and γ ≥ 1) < 1 (and γ ≥ 1)

114

(1)

Existence of Optimal Paths When σ > = 1

115

(1)

General Result

116

(1)

The Long-run Growth Rate

116

(1)

Applications and Extensions

117

(10)

Properties of the Policy Functions When f(0) > 0

118

(2)

Application: The Optimal Speed of Convergence

120

(1)

Application: Rise in β

121

(1)

A Mixed CES-Linear Production Function

122

(2)

Optimal Growth in the Ak Model

124

(3)

Conclusion

127

(2)

Policy

129

(50)

Lump-sum Transfers and the Second Welfare Theorem

129

(11)

Equilibrium with Lump-sum Transfers

129

(7)

The Second Welfare Theorem

136

(2)

The Direction of Optimal Transfers in the Long Run

138

(1)

Reversal of Optimal Transfers Over Time: An Example

139

(1)

Pensions

140

(15)

Fully Funded System

141

(2)

Pay-as-you-go System: Existence of Equilibrium

143

(1)

Pay-as-you-go Systems with Constant Pensions

144

(6)

Capital Accumulation and Pay-as-you-go Pensions

150

(2)

Further Comments

152

(3)

Public Spending

155

(6)

Public Spending in the Competitive Economy

155

(3)

Public Spending: Optimal Financing

158

(1)

Second-best Policies

159

(2)

Study of the Second-best Problem

161

(10)

Restating the Problem

161

(1)

Three Issues

162

(3)

A Standard Approach to the Problem

165

(2)

An Auxiliary Problem

167

(4)

Applications and Extensions

171

(7)

Optimal Growth Rate of Population

172

(1)

Application: The Tax on the First Old Generation

173

(1)

Application: Financing Future Spending

174

(1)

Proportional Government Spending

175

(3)

Conclusion

178

(1)

Debt

179

(59)

Diamond's Model with Debt

181

(3)

The Model

181

(1)

The Temporary Equilibrium

182

(1)

The Inter-temporal Equilibrium with Perfect Foresight

183

(1)

The Inter-temporal Budget Constraint of the Government

184

(9)

Debt with the Two Types of Lump-sum Taxes

186

(4)

Debt with a Restriction of Only One Type of Lump-sum Tax

190

(2)

Ponzi Games

192

(1)

Constant Deficit Policies

193

(23)

Balanced Budget Policies: Local Analysis

195

(3)

Balanced Budget Policies: Graphical Illustration

198

(5)

Non-zero Deficit: Local Analysis

203

(5)

Non-zero Deficit: Graphical Illustration

208

(3)

Ponzi Debt, Money, and Bubbles

211

(5)

Constant Debt Policies

216

(14)

Sustainability in the Short Run

216

(3)

Sustainability in the Long Run

219

(4)

Characteristics of Inter-temporal Equilibria

223

(3)

Policy Implications

226

(4)

Applications and Extensions

230

(6)

Constant Debt-Output Ratio

230

(3)

Deficits and Cycles

233

(3)

Conclusion

236

(2)

Further Issues

238

(67)

Dynastic Altruism: A Bequest Motive

239

(17)

Modeling Voluntary Bequests

239

(7)

Marginal Analysis of Bequests

246

(2)

Altruism and the Neutrality of Economic Policy

248

(4)

When are Bequests Positive?

252

(4)

Human Capital and Education

256

(24)

Modeling Education

257

(2)

Parental Funding: Private vs Public Education

259

(10)

Market Funding

269

(5)

The Tradeoff between Studying and Working

274

(6)

Inter-generational Externalities

280

(11)

Inter-generational Taste Externalities in the Competitive Economy

281

(5)

The Optimal Allocation

286

(3)

Extensions

289

(1)

Conclusion

290

(1)

Macro-economics and General Equilibrium

291

(14)

Modeling Arrow-Debreu Market Equilibria

292

(2)

Arrow-Debreu Market Equilibria from --∞ to +∞

294

(1)

Sequence Equilibrium from --∞ to +∞

295

(2)

Arrow-Debreu Equilibria from 0 to +∞

297

(3)

Example

300

(4)

Conclusion

304

(1)

Technical Appendices

305

(42)

Production Functions

305

(6)

Homogeneity

305

(2)

Limits of f(k) and f'(k)

307

(1)

The Marginal Productivity of Labor

308

(1)

The Limit of w(k)/k

309

(1)

The Cobb-Douglas Function as a Limit Case

310

(1)

Calculus

311

(3)

The Mean Value Theorem for Derivatives

311

(1)

The Implicit Function Theorem

311

(1)

Limits, lim sup, and lim inf

312

(2)

Limit Points of Multi-dimensional Sequences

314

(1)

Dynamical Analysis

314

(12)

Monotonic Dynamics

314

(1)

Local Stability (Dimension One)

315

(1)

Linear Dynamics in the Plane

316

(4)

Local Stability of Non-linear Dynamics (Dimension 2)

320

(2)

Bifurcations of Monotonic Dynamics

322

(4)

Dynamic Optimization

326

(12)

The Value Function

326

(9)

Necessary and Sufficient Conditions for Optimality

335

(3)

Calibration and Simulation

338

(6)

The Cobb--Douglas Model

338

(2)

The Model with a CES Production Function

340

(1)

Introduction of Policies in the Model with CES Production

341

(2)

Numerical Solution to Non-linear Forward-looking Models

343

(1)

Statistics

344

(3)

Dynamics of Distributions

344

(1)

Normal and Log-normal Distributions

345

(2)

List of Definitions

347

(2)

List of Propositions

349

(4)

List of Assumptions

353

(2)

Bibliography

355

(14)

Author Index

369

(4)

Subject Index

373

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A Theory of Economic Growth: Dynamics and Policy in Overlapping Generations

Summary

Table of Contents

Supplemental Materials