Modern Economic Development: A Beginner’s Guide

Modern Economic Development

Modern Economic Development

Samir Ganaka

Modern Economic Development

Samir Ganaka

ISBN - 9789361523182

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Preface

This book is intended to serve two purposes. Firstly, this is a book about economic growth and long-run economic development. Therefore, the growth of the economy and the sources of differences in economic performance across nations are several very interesting, important, and challenging areas in modern science. This book's main purpose is to introduce graduate students to these major questions and the theoretical tools necessary for studying them. Hence, this book 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 provides a clear discussion of the broad empirical patterns and historical processes underlying the current state of the world economy. It helps us understand why some countries grow and others fail to do so; economists have to move beyond the mechanics of models and pose questions on the elemental causes of the economic process.

Secondly, in a somewhat different capacity, this book is also a graduate-level introduction to modern macroeconomics and dynamic economic analysis. Sometimes it is commented that, unlike basic microeconomic theory, there is no core of current macroeconomic theory that all economists share. This is not entirely true. Although these are all models of economic growth, a thorough treatment of modern economic growth can also introduce this core material of modern macroeconomics. However, since 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 also the dynamics of economics on the one hand and general equilibrium theory on the other.

In contrast, this book doesn't cover any of the short-run topics in macroeconomics but provides a radical and rigorous introduction to what I view to be the core of macroeconomics. The topics selected are designed to strike a balance between the two purposes of the book. 1st, 3rd and 4th Chapters introduce most of the salient features of economic growth and the sources of cross-country differences in economic performance.

Although these chapters cannot do justice to the large literature on economic growth empirics, they provide sufficient background for students to appreciate the central to studying the economic process and a platform for further study of this large literature. Chapters 5–7 cover the conceptual and mathematical foundations of recent macroeconomic analysis. Chapter 5 provides the micro-foundations for much of the rest of the book, while Chapters 6 and 7 supply a quick but relatively rigorous introduction to dynamic optimization. Most books on macroeconomics or economic process use either continuous time or discrete time exclusively. A serious study of both economic growth and modern macroeconomics requires the student to move between formulations using discrete and continuous time, choosing the most convenient or appropriate approach for the set of questions at hand. Therefore I even have deviated from standard practice and included both continuous-time and discrete-time material throughout the book. 2nd, 8th, 9th, and 10th Chapter introduces the basic workhorse models of modern macroeconomics and traditional economic growth, while Chapter 11 presents the first-generation models of sustained economic growth. The 12th–15th Chapter covers models of technological progress, which are an essential part of any modern economic growth course.

Content

Part I

Chapter 1. Economic Growth and Economic Development: The Questions 3

1.1 Cross-Country Income Differences 3

1.2 Income and Welfare 5

1.3 Economic Growth and Income Differences 7

1.4 Origins of Today’s Income Differences and World Economic Growth 9

1.5 Conditional Convergence 11

1.6 Correlates of Economic Growth 13

1.7 From Correlates to Fundamental Causes 13

1.8 Summary 15

1.9 Exercise 16

Chapter 2. The Solow Growth Model 19

2.1 The Economic Environment of the Basic Solow Model 20

2.2 The Solow Model in Discrete Time 27

2.3 Transitional Dynamics in the Discrete-Time Solow Model 33

2.4 The Solow Model in Continuous Time 35

2.5 Summary 35

2.6 Exercise 36

Chapter 3. The Solow Model and the Data 40

3.1 Growth Accounting 41

3.2 The Solow Model and Regression Analyses 42

3.3 The Solow Model with Human Capital 43

3.4 Solow Model and Cross-Country Income Differences: Regression Analyses 45

3.5 Calibrating Productivity Differences 49

3.6 Summary 50

3.7 Exercise 51

Chapter 4. Fundamental Determinants of Differences in Economic Performance 55

4.1 Proximate versus Fundamental Causes 55

4.2 Economies of Scale, Population, Technology, and World Growth 59

4.3 The Four Fundamental Causes 61

4.4 The Effect of Institutions on Economic Growth 68

4.5 What Types of Institutions? 71

4.6 Summary 71

4.7 Exercise 72

Part II

Chapter 5. Foundations of Neoclassical Growth 78

5.1 Preliminaries 78

5.2 The Representative Household 79

5.3 Infinite Planning Horizon 80

5.4 The Representative Firm 81

5.5 Problem Formulation 81

5.6 Welfare Theorems 82

5.7 Proof of the Second Welfare Theorem 84

5.8 Sequential Trading 84

5.9 Optimal Growth 85

5.10 Summary 86

5.11 Exercise 86

Chapter 6. Infinite-Horizon Optimization and Dynamic Programming 89

6.1 Discrete-Time Infinite-Horizon Optimization 90

6.2 Stationary Dynamic Programming 90

6.3 Stationary Dynamic Programming Theorems 92

6.4 The Contraction Mapping Theorem and Applications 94

6.5 Proofs of the Main Dynamic Programming Theorems 94

6.6 Applications of Stationary Dynamic Programming 95

6.7 No stationary Infinite-Horizon Optimization 96

6.8 Optimal Growth in Discrete Time 97

6.9 Competitive Equilibrium Growth 98

6.10 Computation 99

6.11 Summary 99

6.12 Exercise 100

Chapter 7. An Introduction to the Theory of Optimal Control 104

7.1 Variation Arguments 105

7.2 The Maximum Principle: A First Look 106

7.3 Infinite-Horizon Optimal Control 107

7.4 More on Transversality Conditions 109

7.5 Discounted Infinite-Horizon Optimal Control 109

7.6 Existence of Solutions, Concavity, and Differentiability 110

7.7 A First Look at Optimal Growth in Continuous Time 111

7.8 The q-Theory of Investment and Saddle-Path Stability 112

7.9 Summary 112

7.10 Exercise 113

Part III

Chapter 8. The Neoclassical Growth Model 118

8.1 Preferences, Technology, and Demographics 118

8.2 Characterization of Equilibrium 121

8.3 Optimal Growth 124

8.4 Steady-State Equilibrium 124

8.5 Transitional Dynamics and Uniqueness of Equilibrium 125

8.6 Neoclassical Growth in Discrete Time 126

8.7 Technological Change and the Neoclassical Canonical Model 127

8.8 The Role of Policy 127

8.9 Comparative Dynamics 128

8.10 A Quantitative Evaluation 129

8.11 Extensions 129

8.12 Summary 130

8.13 Exercise 131

Chapter 9. Growth with Overlapping Generations 134

9.1 Problems of Infinity 135

9.2 The Baseline Overlapping Generations Model 136

9.3 The Canonical Overlapping Generations Model 138

9.4 Over accumulation and Pareto Optimality of Competitive

Equilibrium in the Overlapping Generations Model 139

9.5 Role of Social Security in Capital Accumulation 140

9.6 Overlapping Generations with Impure Altruism 140

9.7 Overlapping Generations with Perpetual Youth 141

9.8 Overlapping Generations in Continuous Time 142

9.9 Summary 143

9.10 Exercise 144

Chapter 10. Human Capital and Economic Growth 148

10.1 A Simple Separation Theorem 148

10.2 Schooling Investments and Returns to Education 150

10.3 The Ben-Porath Model 151

10.4 Neoclassical Growth with Physical and Human Capital 152

10.5 Capital-Skill Complementarily in an Overlapping Generations Model 154

10.6 Physical and Human Capital with Imperfect Labor Markets 155

10.7 Human Capital Externalities 156

10.8 The Nelson-Phelps Model of Human Capital 157

10.9 Summary 158

10.10 Exercise 160

Chapter 11. First-Generation Models of Endogenous Growth 165

11.1 The AK Model Revisited 166

11.2 The AK Model with Physical and Human Capital 167

11.3 The Two-Sector AK Model 168

11.4 Growth with Externalities 169

11.5 Summary 171

11.6 Exercise 172

Part IV

Chapter 12. Modeling Technological Change 177

12.1 Different Conceptions of Technology 177

12.2 Science and Profits 181

12.3 The Value of Innovation in Partial Equilibrium 182

12.4 The Dixit-Stiglitz Model and Aggregate Demand Externalities 184

12.5 Individual R&D Uncertainty and the Stock Market 185

12.6 Summary 186

12.7 Exercise 186

Chapter 13. Expanding Variety Models 189

13.1 The Lab-Equipment Model of Growth with Input Varieties 189

13.2 Growth with Knowledge Spillovers 192

13.3 Growth without Scale Effects 194

13.4 Growth with Expanding Product Varieties 196

13.5 Summary 196

13.6 Exercise 197

Chapter 14. Models of Schumpeterian Growth 201

14.1 A Baseline Model of Schumpeterian Growth 202

14.2 A One-Sector Schumpeterian Growth Model 204

14.3 Innovation by Incumbents and Entrants 206

14.4 Summary 208

14.5 Exercise 209

Chapter 15. Directed Technological Change 213

15.1 Importance of Biased Technological Change 214

15.2 Basics and Definitions 216

15.3 Baseline Model of Directed Technological Change 217

15.4 Directed Technological Change with Knowledge Spillovers 220

15.5 Directed Technological Change without Scale Effects 221

15.6 Endogenous Labor-Augmenting Technological Change 221

15.7 Generalizations and Other Applications 223

15.8 An Alternative Approach to Labor-Augmenting Technological Change 224

15.9 Summary 226

15.10 Exercise 227

Glossary 233

Appendix A: List of Theorems 245

Index 248

Part I

Introduction

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 30 times as rich as those at the bottom. For example, in 2000, gross domestic product (GDP; or income) per capita in the United States was more than $34,000. In contrast, income per capita is much lower in many other countries: about $8,000 in Mexico, about $4,000 in China, just over $2,500 in India, only about $1,000 in Nigeria, and much, much lower in some other sub-Saharan African countries, such as Chad, Ethiopia, and Mali. These numbers are all in 2000 U.S. dollars and are adjusted for purchasing power parity (PPP) to allow for differences in relative prices of different goods across countries.1 The cross-country income gap is considerably larger when there is no PPP adjustment. For example, without the PPP adjustment, GDP per capita in India and China relative to the United States in 2000 would be lower by a factor of four or so. It plots estimates of the distribution of PPP-adjusted GDP per capita across the available countries in 1960, 1980, and 2000. A number of features are worth noting. First, the 1960 density shows that 15 years after World War II, most countries had an income per capita of less than $1,500; the distribution mode is around $1,250. The rightward shift of the distributions for 1980 and 2000 shows the growth of average income per capita for the next 40 years. In 2000, the model was slightly above $3,000, 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.

The spreading out of the distribution in Figure 1.1 is partly because of the increase in average incomes. It may therefore be more informative to look at the logarithm (log) of income per capita. It is more natural to look at the log of variables, such as income per capita, that grow over time, especially when growth is approximately proportional. This is for the simple reason that when x (t) grows at a proportional rate, log x (t) grows linearly, and if x1 (t) and x2 (t) both grow by the same proportional amount, log x1 (t) − log x2 (t) remains constant, while x1 (t) − x2 (t) increases, but now the spreading is more limited because the absolute gap between rich and poor countries has increased considerably between 1960 and 2000, while the proportional gap has increased much less. Nevertheless, it can be seen that the 2000 density for log GDP per capita is still more spread out than the 1960 density.

In particular, both figures show that there has been a considerable increase in the density of relatively rich countries, while many countries remain quite poor. This last pattern is sometimes referred to as the stratification phenomenon, corresponding to the fact that some middle-income countries of the 1960s have joined the ranks of relatively high-income countries, while others have maintained their middle-income status or even experienced relative impoverishment.

Fig 1.1 Estimates of the distribution of countries according to log GDP per capita (PPP adjusted) in 1960, 1980, and 2000.

An equally relevant concept might be inequality among individuals in the world economy. An alternative shows the population-weighted distribution. In this case, countries such as China, India, the United States, and Russia receive greater weight because they have larger populations. However, the picture that emerges, in this case, is quite different. The 2000 distribution looks less spread out, with a thinner left tail than the 1960 distribution. This reflects that in 1960 China and India were among the poorest nations in the world, whereas their relatively rapid growth in the 1990s puts them into the middle-poor category by 2000. Therefore, Chinese and Indian growth has created a powerful force for relative equalization of income per capita among the inhabitants of the globe.

While this measure is relevant for the welfare of the population, much of the growth theory focuses on the productive capacity of countries. Therefore, the theory is easier to map to data when we look at output (GDP) per worker. Moreover, key sources of difference in economic performance across countries are national policies and institutions. So to understand the sources of differences in income and growth across countries (as opposed to assessing welfare questions), the unweighted distribution is more relevant than the population-weighted distribution. Consequently, look at the unweighted distribution of countries according to GDP per worker. Workers here refers to the total economically active population. Second, there is a slight but noticeable increase in inequality across nations.

1.2 Income and Welfare

Should we care about cross-country income differences? The answer is definitely yes. High-income levels reflect high standards of living. Economic growth sometimes increases pollution or may raise individual aspirations so that the same bundle of consumption may no longer satisfy an individual. But at the end of the day, when one compares an advanced, rich country with a less-developed one, there are striking differences in the quality of life, standards of living, and health. Have a glimpse of these differences and depict the relationship between income per capita in 2000 and consumption per capita and life expectancy at birth in the same year. Consumption data also come from the Penn World Tables, while data on life expectancy at birth is available from the World Bank Development Indicators.

Fig. 1.2 Cross-country income differences

These figures document that income per capita differences are strongly associated with differences in consumption and health as measured by life expectancy. Recall that these numbers refer to PPP-adjusted quantities; thus, consumption differences do not reflect the differences in costs for the same bundle of consumption goods in different countries. The PPP adjustment corrects for these differences and attempts to measure the variation in real consumption. Thus the richest countries are not only producing more than 30 times as much as the poorest countries but are also consuming 30 times as much. Similarly, cross-country differences in health are quite remarkable; while life expectancy at birth is as high as 80 in the richest countries, it is only between 40 and 50 in many sub-Saharan African nations. These gaps represent huge welfare differences.

Understanding why some countries are so rich while others are so poor is one of the most important, perhaps the most important, challenges facing social science. It is important both because these income differences have major welfare consequences and because a study of these striking differences will shed light on how the economies of different nations function and how they sometimes fail to function. The emphasis on income differences across countries implies neither that income per capita can be used as a sufficient statistic for the welfare of the average citizen nor that it is the only feature that we should care about. As discussed in detail later, the efficiency properties of the market economy do not imply that there is no conflict among individuals or groups in society. Economic growth is generally good for welfare, but it often creates winners and losers.

The famous notion of creative destruction emphasizes precisely this aspect of economic growth; productive relationships, firms, and sometimes individual livelihoods will be destroyed by economic growth because growth is brought about by introducing new technologies and creating new firms, replacing existing firms and technologies. This process creates a natural social tension, even in a growing society. Another source of social tension related to growth and development is that growth and development are often accompanied by sweeping structural transformations, destroying certain established relationships and creating yet other winners and losers in the process. One of the important questions of political economy, which is discussed in the last part of the book, concerns how institutions and policies can be arranged so that those who lose out from economic growth can be compensated or prevented from blocking economic progress via other means. A stark illustration of the fact that growth does not always mean an improvement in the living standards of all or even most citizens in a society comes from South Africa under apartheid.

Available data suggest that from the beginning of the twentieth century until the fall of the apartheid regime, GDP per capita grew considerably, but the real wages of black South Africans, who make up the majority of the population, likely fell during this period. This, of course, does not imply that economic growth in South Africa was not beneficial. On the contrary, South Africa is still one of the richest countries in sub-Saharan Africa. Nevertheless, this observation alerts us to other aspects of the economy and underlines the potential conflicts inherent in the growth process. Similarly, most existing evidence suggests that during the early phases of the British industrial revolution, which started the process of modern economic growth, the living standards of the majority of the workers may have fallen or, at best, remained stagnant. This pattern of potential divergence between GDP per capita and the economic fortunes of large numbers of individuals and society is not only interesting in and of itself, but it may also inform us about why certain segments of the society may be in favor of policies and institutions that do not encourage growth.

1.3 Economic Growth and Income Differences

How can one country be more than 30 times richer than another? The answer lies in differences in growth rates. Take two countries, A and B, with the same initial level of income at some date. Imagine that country A has 0% growth per capita, so its income per capita remains constant, while country B grows at 2%per capita. In 200 years, country B will be more than 52 times richer than country A. This calculation suggests that the United States might be considerably richer than Nigeria because it has grown steadily over an extended period, while Nigeria has not. We will see that there is a lot of truth to this simple calculation. In fact, even in the historically brief postwar era, there are tremendous differences in growth rates across countries.

Fig. 1.3 Economic growth and income differences

These differences are shown for the postwar era, which plots the density of growth rates across countries in 1960, 1980, and 2000. The growth rate in 1960 refers to the average growth rate between 1950 and 1969, the growth rate in 1980 refers to the average growth rate between 1970 and 1989, and 2000 refers to the average between 1990 and 2000. There is considerable variability in growth rates; the cross-country distribution stretches from negative rates to average rates as high as 10% per year. It also shows that average growth in the world was more rapid in the 1950s and 1960s than in the subsequent decades.

Another look at these patterns by plotting log GDP per capita for several countries between 1960 and 2000. At the top of the figure, U.S. and U.K. GDP per capita increase at a steady pace, with slightly faster growth in the United States, so that the log gap between the two countries is larger in 2000 than it was in 1960. Spain starts much poorer than the United States and the United Kingdom in 1960 but grows very rapidly between 1960 and the mid-1970s, thus closing the gap between itself and the latter two countries. The three countries that show the most rapid growth in this figure are Singapore, South Korea, and Botswana. Singapore starts much poorer than the United Kingdom and Spain in 1960 but grows rapidly, and by the mid-1990s, it has become richer than both. South Korea has a similar trajectory, though it starts poorer than Singapore and grows slightly less rapidly so that by the end of the sample, it is still a little poorer than Spain. The other country that has grown very rapidly is the African success story Botswana, which was extremely poor at the beginning of the sample. Its rapid growth, especially after 1970, has taken Botswana to the ranks of the middle-income countries by 2000.

The two Latin American countries, Brazil and Guatemala, illustrate the often discussed Latin American economic malaise of the postwar era. Brazil starts richer than South Korea and Botswana and has a relatively rapid growth rate between 1960 and 1980. But it experiences stagnation from 1980 on so that by the end of the sample, South Korea and Botswana have become richer than Brazil. Guatemala’s experience is similar but even bleaker. Contrary to Brazil, there is little growth in Guatemala between 1960 and 1980 and no growth between 1980 and 2000.

Finally, Nigeria and India start at similar income levels per capita as Botswana but experience little growth until the 1980s. Starting in 1980, the Indian economy experiences relatively rapid growth, though this has not been sufficient for its income per capita to catch up with the other nations. Finally, Nigeria, in a pattern that is unfortunately all too familiar in sub-Saharan Africa, experiences a contraction of its GDP per capita, so that in 2000 it is, in fact, poorer than it was in 1960. The patterns shown in Figure 1.8 are what we would like to understand and explain. Why is the United States richer in 1960 than other nations and able to grow steadily thereafter? How did Singapore, South Korea, and Botswana manage to grow at a relatively rapid pace for 40 years? Why did Spain grow relatively rapidly for about 20 years but then slow down? Why did Brazil and Guatemala stagnate during the 1980s? What is responsible for the disastrous growth performance of Nigeria?

1.4 Origins of Today’s Income Differences and World Economic Growth

The growth rate differences are interesting in their own right and could also be, in principle, responsible for the large differences in income per capita we observe today. But are they? The answer is a large no. In 1960 there was already a very large gap between the United States on the one hand and India and Nigeria on the other.

This pattern can be seen more easily in Figure 1.9, which plots log GDP per worker in 2000 versus log GDP per capita in 1960 superimposed over the 45◦ lines. Most observations are around the 45◦ lines, indicating that the relative ranking of countries has changed little between 1960 and 2000. Thus the origins of the very large income differences across nations are not found in the postwar era. There are striking growth differences during the postwar era, but the evidence presented so far suggests that world income distribution has been more or less stable, with a slight tendency toward becoming more unequal. If not in the postwar era, when did this growth gap emerge? The answer is that much of the divergence took place during the nineteenth and early twentieth century. Taking a glimpse of these developments by using the data for GDP per capita differences across nations going back to 1820.

Fig 1.4 Estimates of the population-weighted distribution of countries according to log GDP per capita (PPP adjusted) in 1960, 1980, and 2000.

Moreover, the sample is more limited and does not include observations for all countries going back to 1820. Finally, while these data include a correction for PPP, this is less complete than the price comparisons used to construct the price indices in the Penn World Tables. Nevertheless, these are the best available estimates for differences in prosperity across a large number of nations beginning in the nineteenth century. It depicts the evolution of average income among five groups of countries: Africa, Asia, Latin America, Western Europe, and Western offshoots of Europe. It shows the relatively rapid growth of the Western offshoots and West European countries during the nineteenth century, while Asia and Africa remained stagnant and Latin America showed little growth. As a result, the relatively small income gap in 1820 had become much larger by 1960.

Western offshoots and West European nations experience a noticeable dip in GDP per capita around 1929 because of the famous Great Depression. Western offshoots, in particular the United States, only recovered fully from this large recession in the wake of World War II. How an economy can experience a sharp decline in output and how it recovers from such a shock are among the major macroeconomics questions. A variety of evidence suggests that differences in income per capita were even smaller before 1820. Estimates for average income for the same groups of countries going back to 1000 A.D. or even earlier. Although these numbers are based on scattered evidence and informed guesses, the general pattern is consistent with qualitative historical evidence and the fact that income per capita in any country cannot have been much less than $500 in terms of 2000 U.S. dollars, since individuals could not survive with real incomes much less than this level.

As we go further back in time, the gap among countries becomes much smaller. This further emphasizes that the big divergence among countries has taken place over the past 200 years. Another noteworthy feature that becomes apparent from this figure is the remarkable nature of world economic growth. Much evidence suggests that there was only limited economic growth before the eighteenth century and certainly before the fifteenth century. While certain civilizations, including ancient Greece, Rome, China, and Venice, managed to grow, their growth was either not sustained or progressed only at a slow pace. No society before nineteenth-century Western Europe and the United States achieved steady growth at comparable rates.

Notice that the estimates show a slow but steady increase in West European GDP per capita even earlier, starting in 1000. This assessment is not shared by all economic historians, many of whom estimate that there was little increase in income per capita before 1500 or even before 1800. For our purposes, this disagreement is not central, however. Economic historians also debate whether a discontinuous change in economic activity deserves the terms takeoff or industrial revolution. This debate is again secondary to our purposes. Whether or not the change was discontinuous, it was present and transformed the functioning of many economies. As a result of this transformation, the stagnant or slowly growing economies of Europe embarked upon a path of sustained growth. The origins of today’s riches and also of today’s differences in prosperity are to be found in this pattern of takeoff during the nineteenth century. At the same time that Western Europe and its offshoots grew rapidly, much of the world did not experience a comparable takeoff. Therefore an understanding of modern economic growth and current cross-country income differences ultimately necessitates an inquiry into the causes of why the takeoff occurred, why it did so about 200 years ago, and why it took place only in some areas and not in others.

The evolution of income per capita for the United States, the United Kingdom, Spain, Brazil, China, India, and Ghana confirms the patterns for averages, with the United States, the United Kingdom, and Spain growing much faster than India and Ghana throughout, and also much faster than Brazil and China except during the growth spurts experienced by these two countries.

Overall, based on the available information, we can conclude that the origins of the current cross-country differences in income per capita are in the nineteenth and early twentieth century. Moreover, this cross-country divergence took place simultaneously as several countries in the world took off and achieved sustained economic growth. Therefore, understanding the origins of modern economic growth is interesting and important in its own right and holds the key to understanding the causes of cross-country differences in income per capita today.

1.5 Conditional Convergence

The analysis was done earlier focused on the unconditional distribution of income per capita. In particular, we looked at whether the income gap between two countries increases or decreases regardless of these countries’ characteristics. However, it is instead more informative to look at the conditional distribution. The question is whether the income gap between two countries that are similar in observable characteristics is becoming narrower or wider over time. In this case, the picture is one of conditional convergence: in the postwar period, the income gap between countries that share the same characteristics typically closes over time. This is important for understanding the statistical properties of the world income distribution and as an input into the types of theories that we would like to develop.

How do we capture conditional convergence? Consider a typical growth regression: gi,t,t−1= a log yi,t−1+ X.T. i,t−1b + ei,t, (1.1) where gi,t,t−1 is the annual growth rate between dates t − 1 and t in country I, yi,t−1 is output per worker at date t − 1, X is a vector of other variables included in the regression with coefficient vector