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PrefaceThis book is intended to serve two purposes:(1) First and foremost, this is a book about economic growth and long-runeconomic development. The process of economic growth and the sourcesof differences in economic performance across nations are some of the mostinteresting, important and challenging areas in modern social science. Theprimary purpose of this book is to introduce graduate students to thesemajor questions and to the theoretical tools necessary for studying them.The book therefore strives to provide students with a strong backgroundin dynamic economic analysis, since only such a background will enable aserious study of economic growth and economic development. It also triesto provide a clear discussion of the broad empirical patterns and historicalprocesses underlying the current state of the world economy. This is motivated by my belief that to understand why some countries grow and somefail to do so, economists have to move beyond the mechanics of models andpose 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 issometimes commented that, unlike basic microeconomic theory, there is nocore of current macroeconomic theory that is shared by all economists. Thisis not entirely true. While there is disagreement among macroeconomistsabout how to approach short-run macroeconomic phenomena and what theboundaries of macroeconomics should be, there is broad agreement aboutthe workhorse models of dynamic macroeconomic analysis. These includethe Solow growth model, the neoclassical growth model, the overlappinggenerations model and models of technological change and technology adoption. Since these are all models of economic growth, a thorough treatmentof modern economic growth can also provide (and perhaps should provide)an introduction to this core material of modern macroeconomics. Althoughthere are several good graduate-level macroeconomic textbooks, they typically spend relatively little time on the basic core material and do notdevelop the links between modern macroeconomic analysis and economicdynamics on the one hand and general equilibrium theory on the other.xi

Introduction to Modern Economic GrowthIn contrast, the current book does not cover any of the short-run topics in macroeconomics, but provides a thorough and rigorous introductionto what I view to be the core of macroeconomics. Therefore, the secondpurpose of the book is to provide a first graduate-level course in modernmacroeconomics.The topic selection is designed to strike a balance between the two purposesof the book. Chapters 1, 3 and 4 introduce many of the salient features of theprocess of economic growth and the sources of cross-country differences in economicperformance. Even though these chapters cannot do justice to the large literatureon economic growth empirics, they provide a sufficient background for students toappreciate the set of issues that are central to the study of economic growth andalso a platform for a further study of this large literature.Chapters 5-7 provide the conceptual and mathematical foundations of modernmacroeconomic analysis. Chapter 5 provides the microfoundations for much of therest of the book (and for much of modern macroeconomics), while Chapters 6 and7 provide a quick but relatively rigorous introduction to dynamic optimization.Most books on macroeconomics or economic growth use either continuous time ordiscrete time exclusively. I believe that a serious study of both economic growth andmodern macroeconomics requires the student (and the researcher) to be able to gobetween discrete and continuous time and choose whichever one is more convenientor appropriate for the set of questions at hand. Therefore, I have deviated from thisstandard practice and included both continuous time and discrete time materialthroughout 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 covermodels of technological progress, which are an essential part of any modern economicgrowth course.Chapter 16 generalizes the tools introduced in Chapter 6 to stochastic environments. Using these tools, Chapter 17 presents the canonical stochastic growthmodel, which is the foundation of much of modern macroeconomics (though it isoften left out of economic growth courses). This chapter also includes a discussion of the canonical Real Business Cycle model. Chapter 18 covers another majorworkhorse model of modern macroeconomics, the neoclassical growth model withincomplete markets. As well as the famous Bewley-Aiyagari model, this chapter discusses a number of other approaches to modeling the interaction between incompletemarkets and economic growth.Chapters 19-23 cover a range of topics that are sometimes left out of economicgrowth textbooks. These include models of technology adoption, technology diffusion, appropriate technology, interaction between international trade and technology, structural change, poverty traps, inequality, and population growth. Thesexii

Introduction to Modern Economic Growthtopics are important for creating a bridge between the empirical patterns we observe in practice and the theory. Most traditional growth models consider a singleeconomy in isolation and often after it has already embarked upon a process ofsteady economic growth. A study of models that incorporate cross-country interdependences, structural change and the possibility of takeoffs will enable us to linkcore topics of development economics, such as structural change, poverty traps orthe demographic transition, to the theory of economic growth.Finally, Chapters 24-26 consider another topic often omitted from macroeconomics and economic growth textbooks; political economy. This is motivated bythe belief that the study of economic growth would be seriously hampered if wefailed to ask questions about the fundamental causes of why countries differ intheir economic performances. These questions invariably bring us to differences ineconomic policies and institutions across nations. Political economy enables us todevelop models to understand why economic policies and institutions differ acrosscountries 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 beuseful for students and teachers. The underlying philosophy of the book is that allthe results that are stated should be proved or at least explained in detail. Thisimplies a somewhat different organization than existing books. Most textbooks ineconomics do not provide proofs for many of the results that are stated or invoked,and mathematical tools that are essential for the analysis are often taken for grantedor developed in appendices. In contrast, I have strived to provide simple proofs ofalmost all results stated in this book. It turns out that once unnecessary generalityis removed, most results can be stated and proved in a way that is easily accessibleto graduate students. In fact, I believe that even somewhat long proofs are mucheasier to understand than general statements made without proof, which leave thereader wondering about why these statements are true.I hope that the style I have chosen not only makes the book self-contained, butalso gives the students an opportunity to develop a thorough understanding of thematerial. In addition, I present the basic mathematical tools necessary for analysis within the main 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 stability of dynamical systems, dynamic programming in discrete timeand optimal control in continuous time are all introduced within the main body ofthe text. This should both help the students appreciate the foundations of thetheory of economic growth and also provide them with an introduction to the maintools of dynamic economic analysis, which are increasingly used in every subdiscipline of economics. Throughout, when some material is technically more difficultand can be skipped without loss of continuity, it is clearly marked with a “*”. Thexiii

Introduction to Modern Economic Growthonly material that is left for the Mathematical Appendix are those that should be familiar to most graduate students. Therefore the Mathematical Appendix is includedmostly for reference and completeness.I have also included a large number of exercises. Students can only gain athorough understanding of the material by working through the exercises. Theexercises that are somewhat more difficult are also marked with a “*”.This book can be used in a number of different ways. First, it can be used in aone-quarter or one-semester course on economic growth. Such a course might startwith Chapters 1-4, then use Chapters 5-7 either for a thorough study or only forreference. Chapters 8-11 cover the traditional growth theory. Then Chapters 12-15can be used for endogenous growth theory. Depending on time and interest, anyselection of Chapters 18 and 19-26 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 coursein macroeconomics. In this case, Chapter 1 is optional. Chapters 8, 3, 5-7, 8-11 and16-18 would be the core of such a course. The same material could also be coveredin a one-semester course, but in this case, it could be supplemented either withsome of the later chapters or with material from one of the leading graduate-levelmacroeconomic textbooks on short-run macroeconomics, fiscal policy, asset pricing,or other topics in dynamic macroeconomics.Third, the book can be used for an advanced (second-year) course in economicgrowth or economic development. An advanced course on growth or developmentcould use Chapters 1-11 as background and then focus on selected chapters fromChapters 19-26.Finally, since the book is self-contained, I also hope that it can be used forself-study.Acknowledgments. This book grew out of the first graduate-level introduction to macroeconomics course I have taught at MIT. Parts of the book have alsobeen taught as part of a second-year graduate macroeconomics course. I would liketo thank the students who have sat through these lectures and made commentsthat have improved the manuscript. I owe a special thanks to Monica MartinezBravo, Samuel Pienknagura, Lucia Tian Tian and especially Alp Simsek for outstanding research assistance, to Lauren Fahey for editorial suggestions, and to PolAntras, George-Marios Angeletos, Olivier Blanchard, Simon Johnson, Chad Jones,and James Robinson for suggestions on individual chapters.Please note that this is a very preliminary draft of the bookmanuscript. Comments are welcome.Version 1.1: April 2007xiv

Part 1Introduction

We start with a quick look at the stylized facts of economic growth and the mostbasic model of growth, the Solow growth model. The purpose is both to prepare usfor the analysis of more modern models of economic growth with forward-lookingbehavior, explicit capital accumulation and endogenous technological progress, andalso to give us a way of mapping the simplest model to data. We will also discuss differences between proximate and fundamental causes of economic growth andeconomic development.

CHAPTER 1Economic Growth and Economic Development:The Questions1.1. Cross-Country Income DifferencesThere are very large differences in income per capita and output per workeracross countries today. Countries at the top of the world income distribution aremore than thirty times as rich as those at the bottom. For example, in 2000, GDP(or income) per capita in the United States was over 33000. In contrast, income percapita is much lower in many other countries: less than 9000 in Mexico, less than 4000 in China, less than 2500 in India, and only about 700 in Nigeria, and muchmuch lower in some other sub-Saharan African countries such as Chad, Ethiopia,and Mali. These numbers are all at 1996 US dollars and are adjusted for purchasingpower party (PPP) to allow for differences in relative prices of different goods acrosscountries. The gap is larger when there is no PPP-adjustment (see below).We can catch a glimpse of these differences in Figure 1.1, which plots estimates ofthe distribution of PPP-adjusted GDP per capita across the available set of countriesin 1960, 1980 and 2000. The numbers refer to 1996 US dollars and are obtainedfrom the Penn World tables compiled by Summers and Heston, the standard sourceof data for post-war cross-country comparisons of income or worker per capita. Anumber of features are worth noting. First, the 1960 density shows that 15 yearsafter the end of World War II, most countries had income per capita less than 1500(in 1996 US dollars); the mode of the distribution is around 1250. The rightwardsshift of the distributions for 1980 and for 2000 shows the growth of average incomeper capita for the next 40 years. In 2000, the mode is still slightly above 3000, butnow there is another concentration of countries between 20,000 and 30,000. Thedensity estimate for the year 2000 shows the considerable inequality in income percapita today.3

Density of coutries.0001.00015.0002.00025Introduction to Modern Economic Growth.0000519601980020000100002000030000gdp per capita4000050000Figure 1.1. Estimates of the distribution of countries according toPPP-adjusted GDP per capita in 1960, 1980 and 2000.Part of the spreading out of the distribution in Figure 1.1 is because of theincrease in average incomes. It may therefore be more informative to look at thelogarithm of income per capita. It is more natural to look at the logarithm (log) ofvariables, such as income per capita, that grow over time, especially when growth isapproximately proportional (e.g., at about 2% per year for US GDP per capita; seeFigure 1.8). Figure 1.2 shows a similar pattern, but now the spreading-out is morelimited. This reflects the fact that while the absolute gap between rich and poorcountries has increased considerably between 1960 and 2000, the proportional gaphas increased much less. Nevertheless, it can be seen that the 2000 density for logGDP per capita is still more spread out than the 1960 density. In particular, bothfigures show that there has been a considerable increase in the density of relativelyrich countries, while many countries still remain quite poor. This last pattern issometimes referred to as the “stratification phenomenon”, corresponding to the fact4

.4Introduction to Modern Economic Growth1960.320000Density of coutries.1.21980678log gdp per capita91011Figure 1.2. Estimates of the distribution of countries according tolog GDP per capita (PPP-adjusted) in 1960, 1980 and 2000.that some of the middle-income countries of the 1960s have joined the ranks ofrelatively high-income countries, while others have maintained their middle-incomestatus or even experienced relative impoverishment.While Figures 1.1 and 1.2 show that there is somewhat greater inequality amongnations, an equally relevant concept might be inequality among individuals in theworld economy. Figures 1.1 and 1.2 are not directly informative on this, since theytreat each country identically irrespective of the size of their population. The alternative is presented in Figure 1.3, which shows the population-weighted distribution.In this case, countries such as China, India, the United States and Russia receivegreater weight because they have larger populations. The picture that emerges inthis case is quite different. In fact, the 2000 distribution looks less spread-out, withthinner left tail than the 1960 distribution. This reflects the fact that in 1960 Chinaand India were among the poorest nations, whereas their relatively rapid growth in5

Density of coutries weighted by population01.000e 092.000e 093.000e 09Introduction to Modern Economic Growth200019801960678log gdp per capita91011Figure 1.3. Estimates of the population-weighted distribution ofcountries according to log GDP per capita (PPP-adjusted) in 1960,1980 and 2000.the 1990s puts them into the middle-poor category by 2000. Chinese and Indiangrowth has therefore created a powerful force towards relative equalization of incomeper capita among the inhabitants of the globe.Figures 1.1, 1.2 and 1.3 look at the distribution of GDP per capita. While thismeasure is relevant for the welfare of the population, much of growth theory willfocus on the productive capacity of countries. Theory is therefore easier to map todata when we look at output per worker (GDP per worker). Moreover, as we willdiscuss in greater detail later, key sources of difference in economic performanceacross countries include national policies and institutions. This suggests that whenour interest is understanding the sources of differences in income and growth acrosscountries (as opposed to assessing welfare questions), the unweighted distributionmay be more relevant than the population-weighted distribution. Consequently,6

.4Introduction to Modern Economic Growth.31960Density of coutries.1.219800200068log gdp per worker1012Figure 1.4. Estimates of the distribution of countries according tolog GDP per worker (PPP-adjusted) in 1960, 1980 and 2000.Figure 1.4 looks at the unweighted distribution of countries according to (PPPadjusted) GDP per worker. Since internationally comparable data on employmentare not available for a large number of countries, “workers” here refer to the total economically active population (according to the definition of the InternationalLabour Organization). Figure 1.4 is very similar to Figure 1.2, and if anything,shows a bigger concentration of countries in the relatively rich tail by 2000, withthe poor tail remaining more or less the same as in Figure 1.2.Overall, Figures 1.1-1.4 document two important facts: first, there is a largeinequality in income per capita and income per worker across countries as shown bythe highly dispersed distributions. Second, there is a slight but noticeable increasein inequality across nations (though not necessarily across individuals in the worldeconomy).7

Introduction to Modern Economic Growth10USALUXlog consumption per capita FRAFINITANZL BELESPSWEGRCMUSISRPRTTTO CZEMACSVNKORARGURYSYCHUN OMCRI LJORSYRIDNBOLMDA AZE ECUKGZ JAMCHNNICCMRZWEPAKHNDCIVSENCOMBGDINDGMBGHA COGMOZBENKENNPLTJKSTP LSOUGAMDGRWATCDMLIMWIBFANERZMBTGOBDIGNBETH YEMTZA5NGA6789log gdp per capita 20001011Figure 1.5. The association between income per capita and consumption per capita in 2000.1.2. Income and WelfareShould we care about cross-country income differences? The answer is undoubtedly yes. High income levels reflect high standards of living. Economic growthmight, at least over some

Introduction to Modern Economic Growth 3.6. Estimating Productivity Differences 141 3.7. Taking Stock 148 3.8. References and Literature 150 3.9. Exercises 151 Chapter 4. Fundamental Determinants of Differences in Economic Performance 155 4.1. Proximate Versus Fundamental Causes 155 4.2.