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**Unformatted text preview: **Introduction to Modern
Economic Growth: Parts 1-5
Daron Acemoglu
Department of Economics,
Massachusetts Institute of Technology Contents
Preface
Part 1. xi
1 Introduction Chapter 1. Economic Growth and Economic Development:
The Questions
1.1. Cross-Country Income Diﬀerences
1.2. Income and Welfare
1.3. Economic Growth and Income Diﬀerences
1.4. Origins of Today’s Income Diﬀerences and World Economic Growth
1.5. Conditional Convergence
1.6. Correlates of Economic Growth
1.7. From Correlates to Fundamental Causes
1.8. The Agenda
1.9. References and Literature 3
3
6
10
12
16
20
22
25
27 Chapter 2. The Solow Growth Model
2.1. The Economic Environment of the Basic Solow Model
2.2. The Solow Model in Discrete Time
2.3. Transitional Dynamics in the Discrete Time Solow Model
2.4. The Solow Model in Continuous Time
2.5. Transitional Dynamics in the Continuous Time Solow Model
2.6. Solow Model with Technological Progress
2.7. Comparative Dynamics
2.8. Taking Stock
2.9. References and Literature
2.10. Exercises 31
32
40
50
55
59
66
76
78
79
80 Chapter 3. The Solow Model and the Data
3.1. Growth Accounting
3.2. Solow Model and Regression Analyses
3.3. The Solow Model with Human Capital
3.4. Solow Model and Cross-Country Income Diﬀerences: Regression Analyses
3.5. Calibrating Productivity Diﬀerences
3.6. Estimating Productivity Diﬀerences
3.7. Taking Stock
3.8. References and Literature
3.9. Exercises 87
87
90
98
104
113
118
123
125
126 Chapter 4. Fundamental Determinants of Diﬀerences in Economic Performance
4.1. Proximate Versus Fundamental Causes 129
129 iii Introduction to Modern Economic Growth
4.2.
4.3.
4.4.
4.5.
4.6.
4.7.
4.8.
4.9.
4.10.
Part 2. Economies of Scale, Population, Technology and World Growth
The Four Fundamental Causes
The Eﬀect of Institutions on Economic Growth
What Types of Institutions?
Disease and Development
Political Economy of Institutions: First Thoughts
Taking Stock
References and Literature
Exercises 133
136
147
164
167
170
171
171
174
177 Towards Neoclassical Growth Chapter 5. Foundations of Neoclassical Growth
5.1. Preliminaries
5.2. The Representative Household
5.3. Infinite Planning Horizon
5.4. The Representative Firm
5.5. Problem Formulation
5.6. Welfare Theorems
5.7. Sketch of the Proof of the Second Welfare Theorem, Theorem 5.7*
5.8. Sequential Trading
5.9. Optimal Growth in Discrete Time
5.10. Optimal Growth in Continuous Time
5.11. Taking Stock
5.12. References and Literature
5.13. Exercises 179
179
182
188
190
192
193
201
203
207
208
209
210
211 Chapter 6. Dynamic Programming and Optimal Growth
6.1. Brief Review of Dynamic Programming
6.2. Dynamic Programming Theorems
6.3. The Contraction Mapping Theorem and Applications*
6.4. Proofs of the Main Dynamic Programming Theorems*
6.5. Fundamentals of Dynamic Programming
6.6. Optimal Growth in Discrete Time
6.7. Competitive Equilibrium Growth
6.8. Taking Stock
6.9. References and Literature
6.10. Exercises 215
216
220
224
229
236
245
250
252
253
254 Chapter 7. Review of the Theory of Optimal Control
7.1. Variational Arguments
7.2. The Maximum Principle: A First Look
7.3. Infinite-Horizon Optimal Control
7.4. More on Transversality Conditions
7.5. Discounted Infinite-Horizon Optimal Control
7.6. Existence of Solutions∗
7.7. A First Look at Optimal Growth in Continuous Time
7.8. The q-Theory of Investment
7.9. Taking Stock 259
260
268
273
283
285
290
291
292
297 iv Introduction to Modern Economic Growth
7.10. References and Literature
7.11. Exercises
Part 3. 299
301
307 Neoclassical Growth Chapter 8. The Neoclassical Growth Model
8.1. Preferences, Technology and Demographics
8.2. Characterization of Equilibrium
8.3. Optimal Growth
8.4. Steady-State Equilibrium
8.5. Transitional Dynamics
8.6. Technological Change and the Canonical Neoclassical Model
8.7. Comparative Dynamics
8.8. The Role of Policy
8.9. A Quantitative Evaluation
8.10. Extensions
8.11. Taking Stock
8.12. References and Literature
8.13. Exercises 309
309
313
317
318
320
323
329
330
332
335
336
337
337 Chapter 9. Growth with Overlapping Generations
9.1. Problems of Infinity
9.2. The Baseline Overlapping Generations Model
9.3. The Canonical Overlapping Generations Model
9.4. Overaccumulation and Pareto Optimality of Competitive Equilibrium in the
Overlapping Generations Model
9.5. Role of Social Security in Capital Accumulation
9.6. Overlapping Generations with Impure Altruism
9.7. Overlapping Generations with Perpetual Youth
9.8. Overlapping Generations in Continuous Time
9.9. Taking Stock
9.10. References and Literature
9.11. Exercises 345
346
348
353
355
358
360
364
368
374
376
377 Chapter 10. Human Capital and Economic Growth
10.1. A Simple Separation Theorem
10.2. Schooling Investments and Returns to Education
10.3. The Ben-Porath Model
10.4. Neoclassical Growth with Physical and Human Capital
10.5. Capital-Skill Complementarity in an Overlapping Generations Model
10.6. Physical and Human Capital with Imperfect Labor Markets
10.7. Human Capital Externalities
10.8. Nelson-Phelps Model of Human Capital
10.9. Taking Stock
10.10. References and Literature
10.11. Exercises 383
383
386
387
392
397
401
406
408
411
413
414 Chapter 11. First-Generation Models of Endogenous Growth
11.1. The AK Model Revisited
11.2. The AK Model with Physical and Human Capital 417
418
424 v Introduction to Modern Economic Growth
11.3.
11.4.
11.5.
11.6.
11.7.
Part 4. The Two-Sector AK Model
Growth with Externalities
Taking Stock
References and Literature
Exercises 426
430
434
435
436 Endogenous Technological Change 443 Chapter
12.1.
12.2.
12.3.
12.4.
12.5.
12.6.
12.7.
12.8. 12. Modeling Technological Change
Diﬀerent Conceptions of Technology
Science and Profits
The Value of Innovation in Partial Equilibrium
The Dixit-Stiglitz Model and “Aggregate Demand Externalities”
Individual R&D Uncertainty and the Stock Market
Taking Stock
References and Literature
Exercises 445
445
449
452
459
466
468
468
470 Chapter
13.1.
13.2.
13.3.
13.4.
13.5.
13.6.
13.7. 13. Expanding Variety Models
The Lab Equipment Model of Growth with Input Varieties
Growth with Knowledge Spillovers
Growth without Scale Eﬀects
Growth with Expanding Product Varieties
Taking Stock
References and Literature
Exercises 473
473
485
488
491
495
496
497 Chapter
14.1.
14.2.
14.3.
14.4.
14.5.
14.6.
14.7. 14. Models of Schumpeterian Growth
505
A Baseline Model of Schumpeterian Growth
506
A One-Sector Schumpeterian Growth Model
517
Innovation by Incumbents and Entrants and Sources of Productivity Growth 522
Step-by-Step Innovations*
539
Taking Stock
552
References and Literature
553
Exercises
555 Chapter 15. Directed Technological Change
15.1. Importance of Biased Technological Change
15.2. Basics and Definitions
15.3. Baseline Model of Directed Technological Change
15.4. Directed Technological Change with Knowledge Spillovers
15.5. Directed Technological Change without Scale Eﬀects
15.6. Endogenous Labor-Augmenting Technological Change
15.7. Generalizations and Other Applications
15.8. An Alternative Approach to Labor-Augmenting Technological Change
15.9. Taking Stock
15.10. References and Literature
15.11. Exercises 563
564
567
570
585
589
591
594
595
600
602
604 Part 5. 611 Stochastic Growth
vi Introduction to Modern Economic Growth
Chapter
16.1.
16.2.
16.3.
16.4.
16.5.
16.6.
16.7.
16.8. 16. Stochastic Dynamic Programming
Dynamic Programming with Expectations
Proofs of the Stochastic Dynamic Programming Theorems*
Stochastic Euler Equations
Generalization to Markov Processes*
Applications of Stochastic Dynamic Programming
Taking Stock
References and Literature
Exercises 613
613
621
626
629
631
639
640
641 Chapter
17.1.
17.2.
17.3.
17.4.
17.5.
17.6.
17.7.
17.8.
17.9. 17. Stochastic Growth Models
The Brock-Mirman Model
Equilibrium Growth under Uncertainty
Application: Real Business Cycle Models
Growth with Incomplete Markets: The Bewley Model
The Overlapping Generations Model with Uncertainty
Risk, Diversification and Growth
Taking Stock
References and Literature
Exercises 645
646
651
659
663
667
670
689
690
691 Part 6.
Chapter
18.1.
18.2.
18.3.
18.4.
18.5.
18.6.
18.7.
18.8. Technology Diﬀusion, Trade and Interdependences
18. Diﬀusion of Technology
Productivity Diﬀerences and Technology
A Benchmark Model of Technology Diﬀusion
Technology Diﬀusion and Endogenous Growth
Appropriate and Inappropriate Technologies and Productivity Diﬀerences
Contracting Institutions and Technology Adoption
Taking Stock
References and Literature
Exercises 697
701
701
704
713
718
727
741
744
745 Chapter 19. Trade and Growth
19.1. Growth and Financial Capital Flows
19.2. Why Doesn’t Capital Flow from Rich to Poor Countries?
19.3. Economic Growth in a Heckscher-Ohlin World
19.4. Trade, Specialization and the World Income Distribution
19.5. Trade, Technology Diﬀusion and the Product Cycle
19.6. Trade and Endogenous Technological Change
19.7. Learning-by-Doing, Trade and Growth
19.8. Taking Stock
19.9. References and Literature
19.10. Exercises 751
751
757
760
770
784
789
792
796
799
801 Part 7. 807 Economic Development and Economic Growth Chapter 20. Structural Change and Economic Growth
20.1. Non-Balanced Growth: The Demand Side
20.2. Non-Balanced Growth: The Supply Side
vii 813
813
821 Introduction to Modern Economic Growth
20.3.
20.4.
20.5.
20.6. Agricultural Productivity and Industrialization
Taking Stock
References and Literature
Exercises 835
841
843
844 Chapter 21. Structural Transformations and Market Failures in Development
21.1. Financial Development
21.2. Fertility, Mortality and the Demographic Transition
21.3. Migration, Urbanization and The Dual Economy
21.4. Distance to the Frontier and Changes in the Organization of Production
21.5. Multiple Equilibria From Aggregate Demand Externalities and the Big Push
21.6. Inequality, Credit Market Imperfections and Human Capital
21.7. Towards a Unified Theory of Development and Growth?
21.8. Taking Stock
21.9. References and Literature
21.10. Exercises 849
851
857
865
876
886
894
907
912
913
916 Part 8. 925 Political Economy of Growth Chapter
22.1.
22.2.
22.3.
22.4.
22.5.
22.6.
22.7. 22. Institutions, Political Economy and Growth
931
The Impact of Institutions on Long-Run Development
932
Distributional Conflict and Economic Growth in a Simple Society
938
Distributional Conflict and Competition
951
Ineﬃcient Economic Institutions: A First Pass
964
Distributional Conflict and Economic Growth: Concave Preferences*
969
Heterogeneous Preferences, Social Choice and the Median Voter*
975
Distributional Conflict and Economic Growth: Heterogeneity and the Median
Voter
995
22.8. The Provision of Public Goods: Weak Versus Strong States
1001
22.9. Taking Stock
1007
22.10. References and Literature
1011
22.11. Exercises
1014 Chapter
23.1.
23.2.
23.3.
23.4.
23.5.
23.6.
23.7.
23.8. 23. Political Institutions and Economic Growth
Political Regimes and Economic Growth
Political Institutions and Growth-Enhancing Policies
Dynamic Tradeoﬀs
Understanding Endogenous Political Change
Dynamics of Political and Economic Institutions: A First Look
Taking Stock
References and Literature
Exercises 1023
1024
1029
1034
1057
1069
1086
1089
1090 Chapter
24.1.
24.2.
24.3. 24. Epilogue: Mechanics and Causes of Economic Growth
What Have We Learned?
A Possible Perspective on Growth and Stagnation over the Past 200 Years
Many Remaining Questions 1095
1095
1100
1111 Part 9. 1115 Mathematical Appendices
viii Introduction to Modern Economic Growth
Chapter
A.1.
A.2.
A.3.
A.4.
A.5.
A.6.
A.7.
A.8.
A.9.
A.10.
A.11. A. Odds and Ends in Real Analysis and Applications to Optimization
1117
Distances and Metric Spaces
1118
Mappings, Functions, Sequences, and Continuity
1121
A Minimal Amount of Topology: Continuity and Compactness
1126
The Product Topology
1131
Correspondences and Berge’s Maximum Theorem
1134
Convexity, Concavity, Quasi-Concavity and Fixed Points
1138
Diﬀerentiation, Taylor Series and the Mean Value Theorem
1142
Functions of Several Variables and the Inverse and Implicit Function Theorems1145
Separation Theorems
1149
Constrained Optimization
1153
Exercises
1156 Chapter B. Review of Ordinary Diﬀerential Equations
B.1. Review of Eigenvalues and Eigenvectors
B.2. Some Basic Results on Integrals
B.3. Linear Diﬀerential Equations
B.4. Stability for Nonlinear Diﬀerential Equations
B.5. Separable and Exact Diﬀerential Equations
B.6. Existence and Uniqueness of Solutions
B.7. Continuity of Solutions
B.8. Diﬀerence Equations
B.9. Exercises 1161
1161
1162
1164
1170
1171
1173
1174
1175
1177 Chapter
C.1.
C.2.
C.3.
C.4. 1179
1179
1183
1187
1189 C. Brief Review of Dynamic Games
Basic Definitions
Some Basic Results
Application: Repeated Games With Perfect Observability
Exercises Chapter D. List of Theorems
Chapter 2
Chapter 5
Chapter 6
Chapter 7
Chapter 10
Chapter 16
Chapter 22
Appendix Chapter A
Appendix Chapter B
Appendix Chapter C 1191
1191
1191
1191
1192
1192
1193
1193
1193
1194
1195 References (incomplete) 1197 ix Preface
This book is intended to serve two purposes:
(1) First and foremost, this is a book about economic growth and long-run economic
development. The process of economic growth and the sources of diﬀerences in
economic performance across nations are some of the most interesting, important
and challenging areas in modern social science. The primary purpose of this book is
to introduce graduate students to these major questions and to the theoretical tools
necessary for studying them. The book therefore strives to provide students with a
strong background in dynamic economic analysis, since only such a background will
enable a serious study of economic growth and economic development. It also tries
to provide a clear discussion of the broad empirical patterns and historical processes
underlying the current state of the world economy. This is motivated by my belief
that to understand why some countries grow and some fail to do so, economists have
to move beyond the mechanics of models and pose questions about the fundamental
causes of economic growth.
(2) In a somewhat diﬀerent capacity, this book is also a graduate-level introduction
to modern macroeconomics and dynamic economic analysis. It is sometimes commented that, unlike basic microeconomic theory, there is no core of current macroeconomic theory that is shared by all economists. This is not entirely true. While
there is disagreement among macroeconomists about how to approach short-run
macroeconomic phenomena and what the boundaries of macroeconomics should be,
there is broad agreement about the workhorse models of dynamic macroeconomic
analysis. These include the Solow growth model, the neoclassical growth model, the
overlapping-generations model and models of technological change and technology
adoption. Since these are all models of economic growth, a thorough treatment of
modern economic growth can also provide (and perhaps should provide) an introduction to this core material of modern macroeconomics. Although there are several
good graduate-level macroeconomic textbooks, they typically spend relatively little
time on the basic core material and do not develop the links between modern macroeconomic analysis and economic dynamics on the one hand and general equilibrium
theory on the other. In contrast, the current book does not cover any of the shortrun topics in macroeconomics, but provides a thorough and rigorous introduction
to what I view to be the core of macroeconomics. Therefore, the second purpose of
the book is to provide a first graduate-level course in modern macroeconomics.
The selection of topics is designed to strike a balance between the two purposes of the
book. Chapters 1, 3 and 4 introduce many of the salient features of the process of economic
growth and the sources of cross-country diﬀerences in economic performance. Even though
these chapters cannot do justice to the large literature on economic growth empirics, they
provide a suﬃcient background for students to appreciate the set of issues that are central to
the study of economic growth and also a platform for a further study of this large literature.
xi Introduction to Modern Economic Growth
Chapters 5-7 provide the conceptual and mathematical foundations of modern macroeconomic analysis. Chapter 5 provides the microfoundations for much of the rest of the book
(and for much of modern macroeconomics), while Chapters 6 and 7 provide a quick but relatively rigorous introduction to dynamic optimization. Most books on macroeconomics or
economic growth use either continuous time or discrete time exclusively. I believe that a serious study of both economic growth and modern macroeconomics requires the student (and
the researcher) to be able to go between discrete and continuous time and choose whichever
one is more convenient or appropriate for the set of questions at hand. Therefore, I have
deviated from this standard practice and included both continuous time and discrete time
material throughout the book.
Chapters 2, 8, 9 and 10 introduce the basic workhorse models of modern macroeconomics
and traditional economic growth, while Chapter 11 presents the first generation models of sustained (endogenous) economic growth. Chapters 12-15 cover models of technological progress,
which are an essential part of any modern economic growth course.
Chapter 16 generalizes the tools introduced in Chapter 6 to stochastic environments.
Using these tools, Chapter 17 presents a number of models of stochastic growth, most notably,
the neoclassical growth model under uncertainty, which is the foundation of much of modern
macroeconomics (though it is often left out of economic growth courses). The canonical
Real Business Cycle model is presented as an application. This chapter also covers another
major workhorse model of modern macroeconomics, the incomplete markets model of Bewley.
Finally, this chapter also presents a number of other approaches to modeling the interaction
between incomplete markets and economic growth and shows how models of stochastic growth
can be useful in understanding how economies transition from stagnation or slow growth to
an equilibrium with sustained growth.
Chapters 18-21 cover a range of topics that are sometimes left out of economic growth
textbooks. These include models of technology adoption, technology diﬀusion, the interaction
between international trade and technology, the process of structural change, the demographic
transition, the possibility of poverty traps, the eﬀects of inequality on economic growth and
the interaction between financial and economic development. These topics are important for
creating a bridge between the empirical patterns we observe in practice and the theory. Most
traditional growth models consider a single economy in isolation and often after it has already
embarked upon a process of steady economic growth. A study of models that incorporate
cross-country interdependences, structural change and the possibility of takeoﬀs will enable
us to link core topics of development economics, such as structural change, poverty traps or
the demographic transition, to the theory of economic growth.
Finally, Chapters 22 and 23 consider another topic often omitted from macroeconomics
and economic growth textbooks; political economy. This is motivated by the belief that the
study of economic growth would be seriously hampered if we failed to ask questions about the
fundamental causes of why countries diﬀer in their economic performances. These questions
invariably bring us to diﬀerences in economic policies and institutions across nations. Political
economy enables us to develop models to understand why economic policies and institutions
diﬀer across countries and must therefore be an integral part of the study of economic growth.
A few words on the philosophy and organization of the book might also be useful for
students and teachers. The underlying philosophy of the book is that all the results that are
stated should be proved or at least explained in detail. This implies a somewhat diﬀerent
organiz...

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