Table of contents for Introduction to modern economic growth / Daron Acemoglu.

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Preface xv
Part I: Introduction
Chapter 1 Economic Growth and Economic Development: The
Questions 3
1.1 Cross-Country Income Differences 3
1.2 Income and Welfare 7
1.3 Economic Growth and Income Differences 9
1.4 Origins of Today's Income Differences and World Economic Growth 11
1.5 Conditional Convergence 15
1.6 Correlates of Economic Growth 18
1.7 From Correlates to Fundamental Causes 19
1.8 The Agenda 21
1.9 References and Literature 23
Chapter 2 The Solow Growth Model 26
2.1 The Economic Environment of the Basic Solow Model 27
2.2 The Solow Model in Discrete Time 34
2.3 Transitional Dynamics in the Discrete-Time Solow Model 43
2.4 The Solow Model in Continuous Time 47
2.5 Transitional Dynamics in the Continuous-Time Solow Model 51
2.6 A First Look at Sustained Growth 55
2.7 Solow Model with Technological Progress 56
2.8 Comparative Dynamics 67
2.9 Taking Stock 68
2.10 References and Literature 69
2.11 Exercises 71
Chapter 3 The SolowModel and the Data 77
3.1 Growth Accounting 77
3.2 The Solow Model and Regression Analyses 80
3.3 The Solow Model with Human Capital 85
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3.4 Solow Model and Cross-Country Income Differences: Regression Analyses 90
3.5 Calibrating Productivity Differences 96
3.6 Estimating Productivity Differences 100
3.7 Taking Stock 105
3.8 References and Literature 106
3.9 Exercises 107
Chapter 4 Fundamental Determinants of Differences in Economic
Performance 109
4.1 Proximate versus Fundamental Causes 109
4.2 Economies of Scale, Population, Technology, and World Growth 112
4.3 The Four Fundamental Causes 114
4.4 The Effect of Institutions on Economic Growth 123
4.5 What Types of Institutions? 136
4.6 Disease and Development 137
4.7 Political Economy of Institutions: First Thoughts 140
4.8 Taking Stock 140
4.9 References and Literature 141
4.10 Exercises 143
Part II: Toward Neoclassical Growth
Chapter 5 Foundations of Neoclassical Growth 147
5.1 Preliminaries 147
5.2 The Representative Household 149
5.3 Infinite Planning Horizon 156
5.4 The Representative Firm 158
5.5 Problem Formulation 160
5.6 Welfare Theorems 161
5.7 Proof of the Second Welfare Theorem (Theorem 5.7)* 168
5.8 Sequential Trading 171
5.9 Optimal Growth 174
5.10 Taking Stock 176
5.11 References and Literature 176
5.12 Exercises 178
Chapter 6 Infinite-Horizon Optimization and Dynamic Programming
6.1 Discrete-Time Infinite-Horizon Optimization 182
6.2 Stationary Dynamic Programming 185
6.3 Stationary Dynamic Programming Theorems 187
6.4 The Contraction Mapping Theorem and Applications* 190
6.5 Proofs of the Main Dynamic Programming Theorems* 194
6.6 Applications of Stationary Dynamic Programming 201
6.7 Nonstationary Infinite-Horizon Optimization 211
6.8 Optimal Growth in Discrete Time 215
6.9 Competitive Equilibrium Growth 219
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Contents . ix
6.10 Computation 221
6.11 Taking Stock 221
6.12 References and Literature 222
6.13 Exercises 223
Chapter 7 An Introduction to the Theory of Optimal Control 227
7.1 Variational Arguments 228
7.2 The Maximum Principle: A First Look 235
7.3 Infinite-Horizon Optimal Control 240
7.4 More on Transversality Conditions 250
7.5 Discounted Infinite-Horizon Optimal Control 253
7.6 Existence of Solutions, Concavity, and Differentiability* 259
7.7 A First Look at Optimal Growth in Continuous Time 268
7.8 The q-Theory of Investment and Saddle-Path Stability 269
7.9 Taking Stock 274
7.10 References and Literature 275
7.11 Exercises 278
Part III: Neoclassical Growth
Chapter 8 The Neoclassical Growth Model 287
8.1 Preferences, Technology, and Demographics 287
8.2 Characterization of Equilibrium 293
8.3 Optimal Growth 298
8.4 Steady-State Equilibrium 300
8.5 Transitional Dynamics and Uniqueness of Equilibrium 302
8.6 Neoclassical Growth in Discrete Time 305
8.7 Technological Change and the Canonical Neoclassical Model 306
8.8 The Role of Policy 312
8.9 Comparative Dynamics 313
8.10 A Quantitative Evaluation 315
8.11 Extensions 317
8.12 Taking Stock 317
8.13 References and Literature 318
8.14 Exercises 319
Chapter 9 Growth with Overlapping Generations 327
9.1 Problems of Infinity 328
9.2 The Baseline Overlapping Generations Model 329
9.3 The Canonical Overlapping Generations Model 335
9.4 Overaccumulation and Pareto Optimality of Competitive Equilibrium in the
Overlapping Generations Model 336
9.5 Role of Social Security in Capital Accumulation 339
9.6 Overlapping Generations with Impure Altruism 342
9.7 Overlapping Generations with Perpetual Youth 345
9.8 Overlapping Generations in Continuous Time 348
9.9 Taking Stock 353
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9.10 References and Literature 354
9.11 Exercises 355
Chapter 10 Human Capital and Economic Growth 359
10.1 A Simple Separation Theorem 359
10.2 Schooling Investments and Returns to Education 361
10.3 The Ben-Porath Model 363
10.4 Neoclassical Growth with Physical and Human Capital 367
10.5 Capital-Skill Complementarity in an Overlapping Generations Model 371
10.6 Physical and Human Capital with Imperfect Labor Markets 374
10.7 Human Capital Externalities 379
10.8 The Nelson-Phelps Model of Human Capital 380
10.9 Taking Stock 382
10.10 References and Literature 384
10.11 Exercises 384
Chapter 11 First-Generation Models of Endogenous Growth 387
11.1 The AK Model Revisited 388
11.2 The AK Model with Physical and Human Capital 393
11.3 The Two-Sector AK Model 395
11.4 Growth with Externalities 398
11.5 Taking Stock 402
11.6 References and Literature 404
11.7 Exercises 404
Part IV: Endogenous Technological Change
Chapter 12 Modeling Technological Change 411
12.1 Different Conceptions of Technology 411
12.2 Science and Profits 414
12.3 The Value of Innovation in Partial Equilibrium 416
12.4 The Dixit-Stiglitz Model and Aggregate Demand Externalities 422
12.5 Individual R&D Uncertainty and the Stock Market 428
12.6 Taking Stock 429
12.7 References and Literature 430
12.8 Exercises 431
Chapter 13 Expanding VarietyModels 433
13.1 The Lab-Equipment Model of Growth with Input Varieties 433
13.2 Growth with Knowledge Spillovers 444
13.3 Growth without Scale Effects 446
13.4 Growth with Expanding Product Varieties 448
13.5 Taking Stock 452
13.6 References and Literature 453
13.7 Exercises 453
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Chapter 14 Models of Schumpeterian Growth 458
14.1 A Baseline Model of Schumpeterian Growth 459
14.2 A One-Sector Schumpeterian Growth Model 468
14.3 Innovation by Incumbents and Entrants 472
14.4 Step-by-Step Innovations* 479
14.5 Taking Stock 489
14.6 References and Literature 490
14.7 Exercises 491
Chapter 15 Directed Technological Change 497
15.1 Importance of Biased Technological Change 498
15.2 Basics and Definitions 500
15.3 Baseline Model of Directed Technological Change 503
15.4 Directed Technological Change with Knowledge Spillovers 514
15.5 Directed Technological Change without Scale Effects 518
15.6 Endogenous Labor-Augmenting Technological Change 519
15.7 Generalizations and Other Applications 522
15.8 An Alternative Approach to Labor-Augmenting Technological Change* 523
15.9 Taking Stock 526
15.10 References and Literature 527
15.11 Exercises 529
Part V: Stochastic Growth
Chapter 16 Stochastic Dynamic Programming 537
16.1 Dynamic Programming with Expectations 537
16.2 Proofs of the Stochastic Dynamic Programming Theorems* 544
16.3 Stochastic Euler Equations 549
16.4 Generalization to Markov Processes* 552
16.5 Applications of Stochastic Dynamic Programming 554
16.6 Taking Stock 561
16.7 References and Literature 561
16.8 Exercises 562
Chapter 17 Stochastic Growth Models 566
17.1 The Brock-Mirman Model 567
17.2 Equilibrium Growth under Uncertainty 571
17.3 Application: Real Business Cycle Models 579
17.4 Growth with Incomplete Markets: The Bewley Model 583
17.5 The Overlapping Generations Model with Uncertainty 586
17.6 Risk, Diversification, and Growth 588
17.7 Taking Stock 603
17.8 References and Literature 604
17.9 Exercises 605
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Part VI: Technology Diffusion, Trade, and Interdependences
Chapter 18 Diffusion of Technology 611
18.1 Productivity Differences and Technology 611
18.2 A Benchmark Model of Technology Diffusion 613
18.3 Technology Diffusion and Endogenous Growth 619
18.4 Appropriate and Inappropriate Technologies and Productivity Differences 623
18.5 Contracting Institutions and Technology Adoption 630
18.6 Taking Stock 642
18.7 References and Literature 643
18.8 Exercises 644
Chapter 19 Trade and Growth 648
19.1 Growth and Financial Capital Flows 648
19.2 Why Does Capital Not Flow from Rich to Poor Countries? 653
19.3 Economic Growth in a Heckscher-Ohlin World 655
19.4 Trade, Specialization, and the World Income Distribution 663
19.5 Trade, Technology Diffusion, and the Product Cycle 674
19.6 Trade and Endogenous Technological Change 678
19.7 Learning-by-Doing, Trade, and Growth 680
19.8 Taking Stock 684
19.9 References and Literature 685
19.10 Exercises 687
Part VII: Economic Development and Economic Growth
Chapter 20 Structural Change and Economic Growth 697
20.1 Nonbalanced Growth: The Demand Side 697
20.2 Nonbalanced Growth: The Supply Side 703
20.3 Agricultural Productivity and Industrialization 715
20.4 Taking Stock 719
20.5 References and Literature 720
20.6 Exercises 721
Chapter 21 Structural Transformations and Market Failures in
Development 725
21.1 Financial Development 726
21.2 Fertility, Mortality, and the Demographic Transition 729
21.3 Migration, Urbanization, and the Dual Economy 736
21.4 Distance to the Frontier and Changes in the Organization of Production 744
21.5 Multiple Equilibria from Aggregate Demand Externalities and the Big Push 752
21.6 Inequality, Credit Market Imperfections, and Human Capital 758
21.7 Toward a Unified Theory of Development and Growth? 764
21.8 Taking Stock 768
21.9 References and Literature 769
21.10 Exercises 771
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Contents . xiii
Part VIII: The Political Economy of Growth
Chapter 22 Institutions, Political Economy, and Growth 781
22.1 The Impact of Institutions on Long-Run Development 781
22.2 Distributional Conflict and Economic Growth in a Simple Society 784
22.3 The Canonical Cobb-Douglas Model of Distributional Conflict 792
22.4 Distributional Conflict and Competition 793
22.5 Subgame Perfect versus Markov Perfect Equilibria 799
22.6 Inefficient Economic Institutions: A First Pass 802
22.7 Heterogeneous Preferences, Social Choice, and the Median Voter* 805
22.8 Distributional Conflict and Economic Growth: Heterogeneity and the Median
Voter 814
22.9 The Provision of Public Goods: Weak versus Strong States 817
22.10 Taking Stock 822
22.11 References and Literature 823
22.12 Exercises 825
Chapter 23 Political Institutions and Economic Growth 831
23.1 Political Regimes and Economic Growth 832
23.2 Political Institutions and Growth-Enhancing Policies 834
23.3 Dynamic Trade-offs 837
23.4 Understanding Endogenous Political Change 850
23.5 Taking Stock 856
23.6 References and Literature 857
23.7 Exercises 858
Epilogue Mechanics and Causes of Economic Growth 861
861What Have We Learned?864A Possible Perspective on Growth and Stagnation over
the Past 200 Years872Many Remaining Questions
Part IX: Mathematical Appendixes
Appendix A Odds and Ends in Real Analysis and Applications to
Optimization 877
A.1 Distances and Metric Spaces 878
A.2 Mappings, Functions, Sequences, Nets, and Continuity 880
A.3 A Minimal Amount of Topology: Continuity and Compactness* 885
A.4 The Product Topology* 889
A.5 Absolute Continuity and Equicontinuity* 891
A.6 Correspondences and Berge's Maximum Theorem 894
A.7 Convexity, Concavity, Quasi-Concavity, and Fixed Points 898
A.8 Differentiation, Taylor Series, and the Mean Value Theorem 900
A.9 Functions of Several Variables and the Inverse and Implicit Function Theorems904
A.10 Separation Theorems* 907
A.11 Constrained Optimization 910
A.12 Exercises 915
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Appendix B Review of Ordinary Differential Equations 917
B.1 Eigenvalues and Eigenvectors 917
B.2 Some Basic Results on Integrals 918
B.3 Linear Differential Equations 920
B.4 Solutions to Linear First-Order Differential Equations 921
B.5 Systems of Linear Differential Equations 924
B.6 Local Analysis and Stability of Nonlinear Differential Equations 926
B.7 Separable and Exact Differential Equations 927
B.8 Existence and Uniqueness of Solutions 929
B.9 Continuity and Differentiability of Solutions 930
B.10 Difference Equations 930
B.11 Exercises 932
Appendix C Brief Review of Dynamic Games 934
C.1 Basic Definitions 934
C.2 Some Basic Results 937
C.3 Application: Repeated Games with Perfect Observability 941
C.4 Exercises 942
Appendix D List of Theorems 944
944Chapter 2944Chapter 5944Chapter 6945Chapter 7945Chapter 10945Chapter
16946Chapter 22946Appendix A947Appendix B947Appendix C
References 949
As long as a branch of science offers an abundance of problems, so long is it alive.
-David Hilbert, Paris, 1900
This book is intended to serve two purposes. 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. I also try to provide a
clear discussion of the broad empirical patterns and historical processes underlying the current
state of the world economy. This narrative is motivated by my belief that to understand why
some countries grow and others fail to do so, economists have to move beyond the mechanics
of models and pose questions about the fundamental causes of economic growth.
Second, 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 short-run topics in macroeconomics, but provides
a thorough and rigorous introduction to what I view to be the core of 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
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xvi . Preface
chapters cannot do justice to the large literature on economic growth empirics, they provide
a sufficient background for students to appreciate the issues that are central to the study of
economic growth and a platform for further study of this large literature.
Chapters 5-7 cover 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 supply 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 move between formulations using discrete and continuous time, choosing the
more convenient or appropriate approach for the set of questions at hand. Therefore I have
deviated from 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 courses on economic growth). The canonical
Real Business Cycle model is presented as an application. This chapter also covers another
majorworkhorse model of modern macroeconomics, the incomplete markets model of Bewley.
Finally, Chapter 17 also presents a number of other approaches to modeling the interaction
between incomplete markets and economic growth and shows howmodels 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 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, often after it has already
embarked on a process of steady economic growth. A study of models that incorporate crosscountry
interdependences, structural change and the possibility of takeoffs make it possible
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. Inclusion of this material is motivated
by my belief that the study of economic growth would be seriously hampered if we failed to
ask questions about the fundamental causes of differences among countries in their economic
performances. These questions inexorably 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.
Afewwords 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 organization than
found in other books. Most textbooks in economics do not provide proofs for many of the
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Preface . xvii
results that are stated or invoked, and mathematical tools that are essential for the analysis are
often taken for granted or developed in appendixes. In contrast, I have strived to provide simple
proofs of almost all results stated in this book. It turns out that once unnecessary generality is
removed, most results can be stated and proved in a way that is easily accessible to graduate
students. In fact, I believe that even somewhat long proofs are much easier to understand than
general statements made without proof, which leave the readerwondering why these statements
are true.
I hope that the style I have chosen not only makes the book self-contained, but also gives the
students an opportunity to develop a thorough understanding of the material. In line with this
philosophy, I present the basic mathematical tools necessary for the development of the main
material in the body of the text. My own experience suggests that a linear progression, where
the necessary mathematical tools are introduced when needed, makes it easier for the students
to follow and appreciate the material. Consequently, analysis of the stability of dynamical
systems, dynamic programming in discrete time and optimal control in continuous time are
all introduced in the main body of the text. This should both help the students appreciate the
foundations of the theory of economic growth and provide them with an introduction to the
main tools of dynamic economic analysis, which are increasingly used in every subdiscipline
of economics. Throughout, when some material is technically more difficult and can be skipped
without loss of continuity, it is marked with an asterisk (*). Material that is only tangentially
related to the main results in the text or that should be familiar to most graduate students is left
for the appendixes.
I have also included a large number of exercises. Students can gain a thorough understanding
of the material only by working through the exercises. Exercises that are somewhat more
difficult are also marked with an asterisk.
This book can be used in a number of different ways. First, it can be used in a one-quarter
or one-semester course on economic growth. Such a course might start with Chapters 1-4,
then depending on the nature of the course, use Chapters 5-7 either for a thorough study
of the general equilibrium and dynamic optimization foundations of growth theory or only
for reference. Chapters 8-11 cover traditional growth theory, and Chapters 12-15 provide the
basics of endogenous growth theory. Depending on time and interest, any selection of Chapters
16-23 can be used for the last part of such a course.
Second, the book can be used for a one-quarter first-year graduate-level course in macroeconomics.
In this case, Chapter 1 would be optional. Chapters 2, 5-7, 8-11, 16-17 and a
selection from 12-15 would be the core of such a course. The same material could also be
covered in a one-semester course, but in this case, it could be supplemented either with some
of the later chapters or with material from one of the leading graduate-level macroeconomic
textbooks on short-run macroeconomics, fiscal policy, asset pricing, or other topics in dynamic
Third, the book can be used for an advanced (second-year) course in economic growth or
economic development. An advanced course on growth or development could use Chapters
1-11 as background and then focus on selected chapters from Chapters 12-23.
Finally, since the book is self-contained, I also hope that it can be used for self-study.
This book grew out of the first graduate-level introduction to macroeconomics course I have
taught at MIT. Parts of the book have also been taught as part of second-year graduate courses
on macroeconomics and economic growth. I thank the students who attended these lectures
and made comments that have improved the manuscript. I owe special thanks to Nathan
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xviii . Preface
Hendren, Derek Li, Monica Martinez-Bravo, Plamen Nemov, Samuel Pienknagura, Anna
Zabai, and especially to Georgy Egorov, Michael Peters, and Alp Simsek for outstanding
research assistance.
Alp deserves more than a special mention. He has been involved with almost every aspect
of the book for more than two years.Without Alp's help, the book would have taken me much
longer to complete and would have contained many more errors. I am deeply indebted to him.
I also thank Pol Antras, Gabriel Carroll, Francesco Caselli, Melissa Dell, Kiminori, Matsuyama,
James Robinson, Jesus Fernandez-Villaverde, and Pierre Yared for very valuable
suggestions on multiple chapters, and George-Marios Angeletos, Binyamin Berdugo, Truman
Bewley, Olivier Blanchard, Leopoldo Fergusson, Peter Funk, Oded Galor, Hugo Hopenhayn,
Simon Johnson, Chad Jones, Christos Koulovatianos, Omer Moav, Eduardo Morales, Ismail
Saglam, Ekkehart Schlicht, Patricia Waeger, Luis Zermeno, and Jesse Zinn for useful suggestions
and corrections on individual chapters.
Last but not least, I thank Lauren Fahey for editorial suggestions on multiple chapters and
help with the references, CydWestmoreland for truly exceptional copyediting and editorial suggestions,
and Seth Ditchik and the Princeton University Press for support and help throughout
the process.
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Library of Congress Subject Headings for this publication:

Economic development.