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Introduction to ModernEconomic Growth: Parts 1-5Daron AcemogluDepartment of Economics,Massachusetts Institute of Technology

ContentsPrefacePart 1.xi1IntroductionChapter 1. Economic Growth and Economic Development:The Questions1.1. Cross-Country Income Diﬀerences1.2. Income and Welfare1.3. Economic Growth and Income Diﬀerences1.4. Origins of Today’s Income Diﬀerences and World Economic Growth1.5. Conditional Convergence1.6. Correlates of Economic Growth1.7. From Correlates to Fundamental Causes1.8. The Agenda1.9. References and Literature33610121620222527Chapter 2. The Solow Growth Model2.1. The Economic Environment of the Basic Solow Model2.2. The Solow Model in Discrete Time2.3. Transitional Dynamics in the Discrete Time Solow Model2.4. The Solow Model in Continuous Time2.5. Transitional Dynamics in the Continuous Time Solow Model2.6. Solow Model with Technological Progress2.7. Comparative Dynamics2.8. Taking Stock2.9. References and Literature2.10. Exercises3132405055596676787980Chapter 3. The Solow Model and the Data3.1. Growth Accounting3.2. Solow Model and Regression Analyses3.3. The Solow Model with Human Capital3.4. Solow Model and Cross-Country Income Diﬀerences: Regression Analyses3.5. Calibrating Productivity Diﬀerences3.6. Estimating Productivity Diﬀerences3.7. Taking Stock3.8. References and Literature3.9. Exercises87879098104113118123125126Chapter 4. Fundamental Determinants of Diﬀerences in Economic Performance4.1. Proximate Versus Fundamental Causes129129iii

Introduction to Modern Economic Growth4.2.4.3.4.4.4.5.4.6.4.7.4.8.4.9.4.10.Part 2.Economies of Scale, Population, Technology and World GrowthThe Four Fundamental CausesThe Eﬀect of Institutions on Economic GrowthWhat Types of Institutions?Disease and DevelopmentPolitical Economy of Institutions: First ThoughtsTaking StockReferences and owards Neoclassical GrowthChapter 5. Foundations of Neoclassical Growth5.1. Preliminaries5.2. The Representative Household5.3. Infinite Planning Horizon5.4. The Representative Firm5.5. Problem Formulation5.6. Welfare Theorems5.7. Sketch of the Proof of the Second Welfare Theorem, Theorem 5.7*5.8. Sequential Trading5.9. Optimal Growth in Discrete Time5.10. Optimal Growth in Continuous Time5.11. Taking Stock5.12. References and Literature5.13. 1Chapter 6. Dynamic Programming and Optimal Growth6.1. Brief Review of Dynamic Programming6.2. Dynamic Programming Theorems6.3. The Contraction Mapping Theorem and Applications*6.4. Proofs of the Main Dynamic Programming Theorems*6.5. Fundamentals of Dynamic Programming6.6. Optimal Growth in Discrete Time6.7. Competitive Equilibrium Growth6.8. Taking Stock6.9. References and Literature6.10. Exercises215216220224229236245250252253254Chapter 7. Review of the Theory of Optimal Control7.1. Variational Arguments7.2. The Maximum Principle: A First Look7.3. Infinite-Horizon Optimal Control7.4. More on Transversality Conditions7.5. Discounted Infinite-Horizon Optimal Control7.6. Existence of Solutions 7.7. A First Look at Optimal Growth in Continuous Time7.8. The q-Theory of Investment7.9. Taking Stock259260268273283285290291292297iv

Introduction to Modern Economic Growth7.10. References and Literature7.11. ExercisesPart 3.299301307Neoclassical GrowthChapter 8. The Neoclassical Growth Model8.1. Preferences, Technology and Demographics8.2. Characterization of Equilibrium8.3. Optimal Growth8.4. Steady-State Equilibrium8.5. Transitional Dynamics8.6. Technological Change and the Canonical Neoclassical Model8.7. Comparative Dynamics8.8. The Role of Policy8.9. A Quantitative Evaluation8.10. Extensions8.11. Taking Stock8.12. References and Literature8.13. 7Chapter 9. Growth with Overlapping Generations9.1. Problems of Infinity9.2. The Baseline Overlapping Generations Model9.3. The Canonical Overlapping Generations Model9.4. Overaccumulation and Pareto Optimality of Competitive Equilibrium in theOverlapping Generations Model9.5. Role of Social Security in Capital Accumulation9.6. Overlapping Generations with Impure Altruism9.7. Overlapping Generations with Perpetual Youth9.8. Overlapping Generations in Continuous Time9.9. Taking Stock9.10. References and Literature9.11. er 10. Human Capital and Economic Growth10.1. A Simple Separation Theorem10.2. Schooling Investments and Returns to Education10.3. The Ben-Porath Model10.4. Neoclassical Growth with Physical and Human Capital10.5. Capital-Skill Complementarity in an Overlapping Generations Model10.6. Physical and Human Capital with Imperfect Labor Markets10.7. Human Capital Externalities10.8. Nelson-Phelps Model of Human Capital10.9. Taking Stock10.10. References and Literature10.11. er 11. First-Generation Models of Endogenous Growth11.1. The AK Model Revisited11.2. The AK Model with Physical and Human Capital417418424v

Introduction to Modern Economic Growth11.3.11.4.11.5.11.6.11.7.Part 4.The Two-Sector AK ModelGrowth with ExternalitiesTaking StockReferences and LiteratureExercises426430434435436Endogenous Technological .12.8.12. Modeling Technological ChangeDiﬀerent Conceptions of TechnologyScience and ProfitsThe Value of Innovation in Partial EquilibriumThe Dixit-Stiglitz Model and “Aggregate Demand Externalities”Individual R&D Uncertainty and the Stock MarketTaking StockReferences and ter13.1.13.2.13.3.13.4.13.5.13.6.13.7.13. Expanding Variety ModelsThe Lab Equipment Model of Growth with Input VarietiesGrowth with Knowledge SpilloversGrowth without Scale EﬀectsGrowth with Expanding Product VarietiesTaking StockReferences and 14.1.14.2.14.3.14.4.14.5.14.6.14.7.14. Models of Schumpeterian Growth505A Baseline Model of Schumpeterian Growth506A One-Sector Schumpeterian Growth Model517Innovation by Incumbents and Entrants and Sources of Productivity Growth 522Step-by-Step Innovations*539Taking Stock552References and Literature553Exercises555Chapter 15. Directed Technological Change15.1. Importance of Biased Technological Change15.2. Basics and Definitions15.3. Baseline Model of Directed Technological Change15.4. Directed Technological Change with Knowledge Spillovers15.5. Directed Technological Change without Scale Eﬀects15.6. Endogenous Labor-Augmenting Technological Change15.7. Generalizations and Other Applications15.8. An Alternative Approach to Labor-Augmenting Technological Change15.9. Taking Stock15.10. References and Literature15.11. Exercises563564567570585589591594595600602604Part 5.611Stochastic Growthvi

Introduction to Modern Economic .8.16. Stochastic Dynamic ProgrammingDynamic Programming with ExpectationsProofs of the Stochastic Dynamic Programming Theorems*Stochastic Euler EquationsGeneralization to Markov Processes*Applications of Stochastic Dynamic ProgrammingTaking StockReferences and . Stochastic Growth ModelsThe Brock-Mirman ModelEquilibrium Growth under UncertaintyApplication: Real Business Cycle ModelsGrowth with Incomplete Markets: The Bewley ModelThe Overlapping Generations Model with UncertaintyRisk, Diversification and GrowthTaking StockReferences and art echnology Diﬀusion, Trade and Interdependences18. Diﬀusion of TechnologyProductivity Diﬀerences and TechnologyA Benchmark Model of Technology DiﬀusionTechnology Diﬀusion and Endogenous GrowthAppropriate and Inappropriate Technologies and Productivity DiﬀerencesContracting Institutions and Technology AdoptionTaking StockReferences and hapter 19. Trade and Growth19.1. Growth and Financial Capital Flows19.2. Why Doesn’t Capital Flow from Rich to Poor Countries?19.3. Economic Growth in a Heckscher-Ohlin World19.4. Trade, Specialization and the World Income Distribution19.5. Trade, Technology Diﬀusion and the Product Cycle19.6. Trade and Endogenous Technological Change19.7. Learning-by-Doing, Trade and Growth19.8. Taking Stock19.9. References and Literature19.10. Exercises751751757760770784789792796799801Part 7.807Economic Development and Economic GrowthChapter 20. Structural Change and Economic Growth20.1. Non-Balanced Growth: The Demand Side20.2. Non-Balanced Growth: The Supply Sidevii813813821

Introduction to Modern Economic Growth20.3.20.4.20.5.20.6.Agricultural Productivity and IndustrializationTaking StockReferences and LiteratureExercises835841843844Chapter 21. Structural Transformations and Market Failures in Development21.1. Financial Development21.2. Fertility, Mortality and the Demographic Transition21.3. Migration, Urbanization and The Dual Economy21.4. Distance to the Frontier and Changes in the Organization of Production21.5. Multiple Equilibria From Aggregate Demand Externalities and the Big Push21.6. Inequality, Credit Market Imperfections and Human Capital21.7. Towards a Unified Theory of Development and Growth?21.8. Taking Stock21.9. References and Literature21.10. Exercises849851857865876886894907912913916Part 8.925Political Economy of . Institutions, Political Economy and Growth931The Impact of Institutions on Long-Run Development932Distributional Conflict and Economic Growth in a Simple Society938Distributional Conflict and Competition951Ineﬃcient Economic Institutions: A First Pass964Distributional Conflict and Economic Growth: Concave Preferences*969Heterogeneous Preferences, Social Choice and the Median Voter*975Distributional Conflict and Economic Growth: Heterogeneity and the MedianVoter99522.8. The Provision of Public Goods: Weak Versus Strong States100122.9. Taking Stock100722.10. References and Literature101122.11. 23.7.23.8.23. Political Institutions and Economic GrowthPolitical Regimes and Economic GrowthPolitical Institutions and Growth-Enhancing PoliciesDynamic TradeoﬀsUnderstanding Endogenous Political ChangeDynamics of Political and Economic Institutions: A First LookTaking StockReferences and 91090Chapter24.1.24.2.24.3.24. Epilogue: Mechanics and Causes of Economic GrowthWhat Have We Learned?A Possible Perspective on Growth and Stagnation over the Past 200 YearsMany Remaining Questions1095109511001111Part 9.1115Mathematical Appendicesviii

Introduction to Modern Economic .10.A.11.A. Odds and Ends in Real Analysis and Applications to Optimization1117Distances and Metric Spaces1118Mappings, Functions, Sequences, and Continuity1121A Minimal Amount of Topology: Continuity and Compactness1126The Product Topology1131Correspondences and Berge’s Maximum Theorem1134Convexity, Concavity, Quasi-Concavity and Fixed Points1138Diﬀerentiation, Taylor Series and the Mean Value Theorem1142Functions of Several Variables and the Inverse and Implicit Function Theorems1145Separation Theorems1149Constrained Optimization1153Exercises1156Chapter B. Review of Ordinary Diﬀerential EquationsB.1. Review of Eigenvalues and EigenvectorsB.2. Some Basic Results on IntegralsB.3. Linear Diﬀerential EquationsB.4. Stability for Nonlinear Diﬀerential EquationsB.5. Separable and Exact Diﬀerential EquationsB.6. Existence and Uniqueness of SolutionsB.7. Continuity of SolutionsB.8. Diﬀerence EquationsB.9. hapterC.1.C.2.C.3.C.4.11791179118311871189C. Brief Review of Dynamic GamesBasic DefinitionsSome Basic ResultsApplication: Repeated Games With Perfect ObservabilityExercisesChapter D. List of TheoremsChapter 2Chapter 5Chapter 6Chapter 7Chapter 10Chapter 16Chapter 22Appendix Chapter AAppendix Chapter BAppendix Chapter ences (incomplete)1197ix

PrefaceThis book is intended to serve two purposes:(1) First and foremost, this is a book about economic growth and long-run economicdevelopment. The process of economic growth and the sources of diﬀerences ineconomic performance across nations are some of the most interesting, importantand challenging areas in modern social science. The primary purpose of this book isto introduce graduate students to these major questions and to the theoretical toolsnecessary for studying them. The book therefore strives to provide students with astrong background in dynamic economic analysis, since only such a background willenable a serious study of economic growth and economic development. It also triesto provide a clear discussion of the broad empirical patterns and historical processesunderlying the current state of the world economy. This is motivated by my beliefthat to understand why some countries grow and some fail to do so, economists haveto move beyond the mechanics of models and pose questions about the fundamentalcauses of economic growth.(2) In a somewhat diﬀerent capacity, this book is also a graduate-level introductionto 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. Whilethere is disagreement among macroeconomists about how to approach short-runmacroeconomic phenomena and what the boundaries of macroeconomics should be,there is broad agreement about the workhorse models of dynamic macroeconomicanalysis. These include the Solow growth model, the neoclassical growth model, theoverlapping-generations model and models of technological change and technologyadoption. Since these are all models of economic growth, a thorough treatment ofmodern economic growth can also provide (and perhaps should provide) an introduction to this core material of modern macroeconomics. Although there are severalgood graduate-level macroeconomic textbooks, they typically spend relatively littletime on the basic core material and do not develop the links between modern macroeconomic analysis and economic dynamics on the one hand and general equilibriumtheory on the other. In contrast, the current book does not cover any of the shortrun topics in macroeconomics, but provides a thorough and rigorous introductionto what I view to be the core of macroeconomics. Therefore, the second purpose ofthe 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 thebook. Chapters 1, 3 and 4 introduce many of the salient features of the process of economicgrowth and the sources of cross-country diﬀerences in economic performance. Even thoughthese chapters cannot do justice to the large literature on economic growth empirics, theyprovide a suﬃcient background for students to appreciate the set of issues that are central tothe study of economic growth and also a platform for a further study of this large literature.xi

Introduction to Modern Economic GrowthChapters 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 oreconomic 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 (andthe researcher) to be able to go between discrete and continuous time and choose whicheverone is more convenient or appropriate for the set of questions at hand. Therefore, I havedeviated from this standard practice and included both continuous time and discrete timematerial throughout the book.Chapters 2, 8, 9 and 10 introduce the basic workhorse models of modern macroeconomicsand 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 modernmacroeconomics (though it is often left out of economic growth courses). The canonicalReal Business Cycle model is presented as an application. This chapter also covers anothermajor workhorse model of modern macroeconomics, the incomplete markets model of Bewley.Finally, this chapter also presents a number of other approaches to modeling the interactionbetween incomplete markets and economic growth and shows how models of stochastic growthcan be useful in understanding how economies transition from stagnation or slow growth toan equilibrium with sustained growth.Chapters 18-21 cover a range of topics that are sometimes left out of economic growthtextbooks. These include models of technology adoption, technology diﬀusion, the interactionbetween international trade and technology, the process of structural change, the demographictransition, the possibility of poverty traps, the eﬀects of inequality on economic growth andthe interaction between financial and economic development. These topics are important forcreating a bridge between the empirical patterns we observe in practice and the theory. Mosttraditional growth models consider a single economy in isolation and often after it has alreadyembarked upon a process of steady economic growth. A study of models that incorporatecross-country interdependences, structural change and the possibility of takeoﬀs will enableus to link core topics of development economics, such as structural change, poverty traps orthe demographic transition, to the theory of economic growth.Finally, Chapters 22 and 23 consider another topic often omitted from macroeconomicsand economic growth textbooks; political economy. This is motivated by the belief that thestudy of economic growth would be seriously hampered if we failed to ask questions about thefundamental causes of why countries diﬀer in their economic performances. These questionsinvariably bring us to diﬀerences in economic policies and institutions across nations. Politicaleconomy enables us to develop models to understand why economic policies and institutionsdiﬀer 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 forstudents and teachers. The underlying philosophy of the book is that all the results that arestated should be proved or at least explained in detail. This implies a somewhat diﬀerentorganization than existing books. Most textbooks in economics do not provide proofs formany of the results that are stated or invoked, and mathematical tools that are essentialxii

Introduction to Modern Economic Growthfor the analysis are often taken for granted or developed in appendices. In contrast, I havestrived to provide simple proofs of almost all results stated in this book. It turns out thatonce unnecessary generality is removed, most results can be stated and proved in a way thatis easily accessible to graduate students. In fact, I believe that even somewhat long proofsare much easier to understand than general statements made without proof, which leave thereader wondering about why these statements are true.I hope that the style

13.4. Growth with Expanding Product Varieties 491 13.5. Taking Stock 495 13.6. References and Literature 496 13.7. Exercises 497 Chapter 14. Models of Schumpeterian Growth 505 14.1. A Baseline Model of Schumpeterian Growth 506 14.2. A One-Sector Schumpeterian Growth Model 517 14.3. Innovation by Incumbents and Entrants and Sources of .

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