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

by David de la Croix , Philippe Michel

• ISBN13: 9780521806428
• ISBN10: 0521806429
• Format: Hardcover
• Copyright: 2002-11-11
• Publisher: Cambridge University Press

Summary

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.

Table of Contents

Introduction	xiii
Overlapping Generations and Macro-economics	xiii
Overlapping Generations in Other Fields	xv
Outline of the Book	xvi
Acknowledgments	xvii
Competitive Equilibria	1	(71)
The Model	1	(3)
Two-period-lived Individuals	2	(1)
Neo-classical Technology	3	(1)
Firms	4	(1)
Main Assumptions	4	(6)
The Assumptions on the Utility Function	4	(2)
The Assumptions on the Production Function	6	(4)
The Behavior of the Agents at Period t	10	(6)
The Young Individuals	10	(1)
The Inter-temporal Elasticity of Substitution	11	(1)
The Properties of the Savings Function	12	(3)
The Old Individuals	15	(1)
The Firms	15	(1)
The Temporary Equilibrium	16	(3)
The Inter-temporal Equilibrium with Perfect Foresight	19	(8)
Existence of Equilibria	20	(2)
Uniqueness of the Inter-temporal Equilibrium	22	(5)
Capital Dynamics at a Rational Inter-temporal Equilibrium	27	(12)
Steady States and Stability	27	(2)
Dynamics	29	(5)
The Behavior Near 0	34	(3)
A Quick Look at the Empirics of Growth	37	(2)
Comparison of Myopic and Perfect Foresight	39	(6)
The Steady States	41	(1)
Local Stability	42	(1)
Uniqueness of the Steady State	43	(2)
Applications and Extensions	45	(25)
Myopic and Perfect Foresight in an Example	45	(5)
A Demographic Shock	50	(1)
Non-separable Utility Function	51	(2)
Homothetic Preferences	53	(1)
Heterogeneous Agents	54	(2)
Technical Progress	56	(1)
Imperfect Credit Market	57	(7)
Three-period-lived Households	64	(2)
Borrowing Constraints in the Three-period Model	66	(4)
Conclusion	70	(2)
Optimality	72	(57)
Optimality of Stationary Paths	73	(9)
Feasible Long-run Capital Stock	74	(3)
The Optimal Stationary Path: The Golden Age	77	(3)
Under- and Over-accumulation of Capital	80	(2)
Optimality of the Dynamics	82	(8)
Dynamic Efficiency	82	(4)
Pareto Optimality of Dynamics	86	(4)
The Planning Problem	90	(11)
The Objective Function	91	(1)
Properties of the Value Function	92	(3)
Existence and Monotonicity of Optimal Paths	95	(4)
Limit of the Optimal Path and Optimal Steady State	99	(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