INTRODUCTION TO MODERN ECONOMIC GROWTH topics are important for creating a bridge between the empirical patterns we ob- serve 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 inter- dependences, 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 25-27 consider another topic often omitted from macroeco- nomics 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 organization than existing books. Most textbooks in economies 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 granted or developed in appendices. 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 reader wondering about why these statements are true I hope that the style I have chosen not only makes the book self-contained also gives the students an opportunity to develop a thorough understanding of t material. In addition, I present the basic mathematical tools necessary for analy- sis 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 time and optimal control in continuous time are all introduced within the main body of the text. This should both help the students appreciate the foundations of the theory of economic growth and also provide them with an introduction to the main tools of dynamic economic analysis, which are increasingly used in every subdisci pline of economics. Throughout, when some material is technically more difficult and can be skipped without loss of continuity, it is clearly marked with a"*. The XIll
Introduction to Modern Economic Growth 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 25-27 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 organization than existing books. Most textbooks in economics 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 granted or developed in appendices. 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 reader wondering about 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 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 time and optimal control in continuous time are all introduced within the main body of the text. This should both help the students appreciate the foundations of the theory of economic growth and also 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 clearly marked with a “*”. The xiii
INTRODUCTION TO MODERN ECONOMIC GROWTH only material that is left for the Mathematical Appendix are those that should be fa miliar to most graduate students. Therefore the Mathematical Appendix is included mostly for reference and completeness I have also included a large number of exercises. Students can only gain a thorough understanding of the material by working through the exercises. The exercises that are somewhat more difficult are also marked with a "*7 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 use Chapters 5-7 either for a thorough study or only for reference. Chapters 8-11 cover the traditional growth theory. Then Chapters 12-15 can be used for endogenous growth theory. Depending on time and interest, any selection of Chapters 18 and 19-27 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 l is optional. Chapters 8, 3, 5-7, 8-11 and 16-18 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 s or with material from one of the leading g graduate-level macroeconomic 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 economic growth or economic development. An advanced course on growth or development could use Chapters 1-1l as background and then focus on selected chapters from Chapters 19-27 Finally, since the book is self-contained, I also hope that used fo self-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 also been taught as part of a second-year graduate macroeconomics course. I would like to thank the students who have sat through these lectures and made comments that ipt. I owe a special thanks to Monica Martinez- Bravo Samuel Pienknagura and Alp Simsek for outstanding research assistance, to Lauren Fahey for editorial suggestions. and to Pol antras and ames robinson for many stions Please note that this is a very preliminary draft of the book Manuscript. Connents are welcone Version 1.0: January 2007
Introduction to Modern Economic Growth only material that is left for the Mathematical Appendix are those that should be familiar to most graduate students. Therefore the Mathematical Appendix is included mostly for reference and completeness. I have also included a large number of exercises. Students can only gain a thorough understanding of the material by working through the exercises. The exercises 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 a one-quarter or one-semester course on economic growth. Such a course might start with Chapters 1-4, then use Chapters 5-7 either for a thorough study or only for reference. Chapters 8-11 cover the traditional growth theory. Then Chapters 12-15 can be used for endogenous growth theory. Depending on time and interest, any selection of Chapters 18 and 19-27 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 is optional. Chapters 8, 3, 5-7, 8-11 and 16-18 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 macroeconomics. 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 19-27. Finally, since the book is self-contained, I also hope that it can be used for self-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 also been taught as part of a second-year graduate macroeconomics course. I would like to thank the students who have sat through these lectures and made comments that have improved the manuscript. I owe a special thanks to Monica Martinez-Bravo, Samuel Pienknagura and Alp Simsek for outstanding research assistance, to Lauren Fahey for editorial suggestions, and to Pol Antras and James Robinson for many suggestions. Please note that this is a very preliminary draft of the book manuscript. Comments are welcome. Version 1.0: January 2007 xiv
Part 1 Introduction
Part 1 Introduction
We start with a quick look at the stylized facts of economic growth and the most basic model of growth, the Solow growth model. The purpose is both to prepare us for the analysis of more modern models of economic growth with forward-looking behavior, explicit capital accumulation and endogenous technological progress, and also to give us a way of mapping the simplest model to data. We will also dis- cuss differences between proximate and fundamental causes of economic growth and economic development
We start with a quick look at the stylized facts of economic growth and the most basic model of growth, the Solow growth model. The purpose is both to prepare us for the analysis of more modern models of economic growth with forward-looking behavior, explicit capital accumulation and endogenous technological progress, and also 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 and economic development
CHAPTER 1 Economic Growth and Economic Development The Questions l.1. Cross-Country Income Differences There are very large differences in income per capita and output per worker across countries today. Countries at the top of the world income distribution are more than thirty times as rich as those at the bottom in purchasing power party (PPP) adjusted dollars. For example, in 2000, GDP(or income) per capita in the United States was over $33000(valued at 1996 US dollar prices). In contrast, income per capita is much lower in many other countries: less than $9000 in Mexico, less than $4000 in China. less than S2500 in India, and only about S700 in Nigeria and much much lower in some other sub-Saharan African countries such as Chad thiopia, and Mali (all figures are PPP-adjusted). The gap is larger when there is no PPP-adjustment(see below) a glimpse of these differences can be seen in Figure 1. 1, which plots(kernel) estimates of the distribution of PPP-adjusted gdP per capita across the available set of countries in 1960. 1980 and 2000. The numbers refer to 1996 uS dollars and are obtained from the standard source of data for cross-country comparisons of income or worker per capita, the Penn World tables compiled by Summers and Heston. A number of features are worth noting First, the 1960 density shows that 15 years after the end of World War Il, most countries had income per capita less than $1500 (in 1996 US dollars); the mode of the distribution is around $1250. The rightwards shift of the distributions for 1980 and for 2000 shows the growth of average income per capita for the next 40 years. In 2000, the mode is still slightly above $3000, but now there is another concentration of countries between S20.000 and S30.000. The density estimate for the year 2000 shows the considerable inequality in income per capita today
CHAPTER 1 Economic Growth and Economic Development: The Questions 1.1. Cross-Country Income Differences There are very large differences in income per capita and output per worker across countries today. Countries at the top of the world income distribution are more than thirty times as rich as those at the bottom in purchasing power party (PPP) adjusted dollars. For example, in 2000, GDP (or income) per capita in the United States was over $33000 (valued at 1996 US dollar prices). In contrast, income per capita 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 much much lower in some other sub-Saharan African countries such as Chad, Ethiopia, and Mali (all figures are PPP-adjusted). The gap is larger when there is no PPP-adjustment (see below). A glimpse of these differences can be seen in Figure 1.1, which plots (kernel) estimates of the distribution of PPP-adjusted GDP per capita across the available set of countries in 1960, 1980 and 2000. The numbers refer to 1996 US dollars and are obtained from the standard source of data for cross-country comparisons of income or worker per capita, the Penn World tables compiled by Summers and Heston. A number of features are worth noting. First, the 1960 density shows that 15 years after 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 rightwards shift of the distributions for 1980 and for 2000 shows the growth of average income per capita for the next 40 years. In 2000, the mode is still slightly above $3000, but now there is another concentration of countries between $20,000 and $30,000. The density estimate for the year 2000 shows the considerable inequality in income per capita today. 3