Deveco GPT Development Economics Lecture Notes PDF

Development economics 1 Lecture 1 - The Facts of Economic Growth VUONG Hung Cuong AEI International School Université Paris-Est Créteil September 11, 2024 1 / 33 Introduction Why do the richest...

Development economics 1 Lecture 1 - The Facts of Economic Growth VUONG Hung Cuong AEI International School Université Paris-Est Créteil September 11, 2024 1 / 33 Introduction Why do the richest countries grow at 2 percent per year Why are some countries 50x richer than others? X Economic Growth vs Economic Development: 2 / 33 Introduction Name that Country: X Life expectancy is less than 50 years 1 out every 10 infants dies before the age of one More than 90 percent of households have no electricity, refrigerator, telephone, or car Fewer than 10 What country is it? 3 / 33 The Power of Economic Growth In just a century, the U.S. is completely transformed Almost all households have electricity, refrigerators, cell phones, and cars Overwhelming majority graduates from high school, many college New goods: air-conditioning, dishwashers, jet planes, skyscrapers, contraception, smartphones Health: Life expectancy in 1900 = 50 years, today 79 years The rich person in the world in the mid 1800s - the great European financier Nathan Rothschild - died from an infection that 10 dollars of antibiotics would cure today Financial Times: ”The second richest man of all time was poorer than us. I would rather have antibiotics than gold plate, and I suspect Rothschild would have felt the same” 4 / 33 Plan First, what are the growth patterns exhibited by the richest countries in the world Second, how about development or economic growth throughout the world. To what extent are countries behind the frontier catching up, falling behind, or staying in place? And what characteristics do countries in these various groups share? Main reference: The Facts of Economic Growth by Charles I. Jones, available on Eprel 5 / 33 I. Growth pattern US example 6 / 33 I. Growth pattern (Cont.) For nearly 150 years, GDP per person in the U.S. economy has grown at a remarkably steady average rate of around 2 percent per year Starting at around 3,000 USD in 1870, per capita GDP rose to more than 50,000 USD by 2014, a nearly 17-fold increase One is the significant decline in income associated with the Great Depression. Despite the singular severity of the Great Depression, GDP per person fell by nearly 20 percent in just four years, it is equally remarkable that the Great Depression was temporary By 1939, the economy is already passing its previous peak and the macroeconomic story a decade later is once again one of sustained, almost relentless, economic growth One can see that growth was slightly slower pre-1929 than post as clearly shown in the following table 7 / 33 I. Growth pattern (Cont.) 8 / 33 I. Growth pattern (Cont.) Between 1870 and 1929, growth averaged 1.76 percent, versus 2.23 percent between 1929 and 2007 (using ”peak to peak” dates to avoid business cycle problems) Between 1900 and 1950, growth averaged 2.06 percent versus 2.16 percent since 1950. Before one is too quick to conclude that growth rates are increasing However, notice that the period since 1950 shows a more mixed pattern, with rapid growth between 1950 and 1973, slower growth between 1973 and 1995, and then rapid growth during the late 1990s that gives way to slower growth more recently 9 / 33 I. Growth pattern (Cont.) Living standards Sustained exponential growth in living standards is an incredibly recent phenomenon: only in the last two centuries has this changed, but in this relatively brief time, the change has been dramatic 10 / 33 I. Growth pattern (Cont.) Between the year 1 and the year 1820, living standards in the ”West” doubled, from 600 dollars per person to 1200 dollars per person Over the next 200 years, however, GDP per person rose by more than a factor of twenty, reaching 26,000 dollars 11 / 33 I. Growth pattern (Cont.) Living standards were comparatively stagnant for thousands and thousands of years before. For example, for much of pre-history, humans lived as simple hunters and gatherers, on the edge of subsistence. From this perspective, say for the last 200,000 years or more, the era of modern growth is spectacularly brief Over the very long run, economic growth at the frontier has accelerated, that is, the rates of economic growth are themselves increasing over time Various growth models have been developed to explain the transition from stagnant living standards for thousands of years to the modern era of economic growth For instance, Malthusian diminishing returns. there is assumed to be a fixed supply of land which is a necessary input in production. Adding more people to the land reduces the marginal product of labor (holding technology constant) and therefore reduces living standards 12 / 33 II. Economic development Why are some countries so much richer than others? Through the lens of a production function Inputs versus productivity? Why do some countries have more inputs? Why more efficient? Rules, institutions How do we understand ”catch-up” growth? 13 / 33 II. Economic development (Cont.) One of the best sources of evidence on this question was provided by Olson who observed that history itself provides us with ”natural experiments” that allow us to see the large impact of institutions on economic success For example, prior to World War II, North and South Korea were not separate countries. As a rough approximation, the north and south of Korea contained people that shared a cultural heritage, a government, institutions, and even a geography In fact, if anything, North Korea was economically advantaged relative to the South, containing a disproportionate share of electricity production and heavy industry After the Korean War ended in 1953, North and South Korea were divided and governed according to very different rules The resulting economic growth of the next half century was dramatically different 14 / 33 II. Economic development (Cont.) 15 / 33 II. Economic development (Cont.) The picture in this figure was taken by an astronaut on the International Space Station in early 2014 and shows North and South Korea at night South Korea is brightly lit, while North Korea is almost completely dark, barely indistinguishable from the ocean. Whatever was different between North and South Korea after 1953 apparently had an enormous influence on their long-term economic success Similar ”natural” experiments can be observed in East and West Germany after World War II, Hong Kong and southeastern China, and across the Rio Grande between Mexico and Texas 16 / 33 II. Economic development (Cont.) 17 / 33 II. Economic development (Cont.) 18 / 33 How growth is spreading across countries: how are different countries moving relative to the rich ones? The spread of growth over the very long run occurred at different points in time, resulting in what is commonly referred to as ”The Great Divergence.” 19 / 33 How growth is spreading across countries: how are different countries moving relative to the rich ones? Figure above illustrates this point. GDP per person differs modestly prior to the year 1600 according to The Maddison Project data For example, GDP per person in the year 1300 ranges from a high of 1620 dollars in the Netherlands (in 1990 dollars) to a low of 610 dollars in Egypt. But Egypt was surely not the poorest country in the world at the time Following an insight by Pritchett (1997), notice that the poorest countries in the world in 1950 had an income around 300 dollars, and this level, less than one dollar per day, seems very close to the minimum average income likely to prevail in any economy at any point in time Therefore in 1300, the ratio of the richest country to the poorest was on the order of 1620/300 which is about 5 times. Even smaller ratios are observed in Maddison’s data prior to the year 1300 20 / 33 How growth is spreading across countries: how are different countries moving relative to the rich ones? The spread of growth since 1870 in an alternative way, by plotting incomes relative to the U.S. level 21 / 33 How growth is spreading across countries: how are different countries moving relative to the rich ones? A key fact that stands out when the data are viewed this way is the heterogeneity of experiences Some countries like the U.K., Argentina, and South Africa experience significant declines in their incomes relative to the United States, revealing the fact that their growth rates over long periods of time fell short of the 2 percent growth rate of the frontier Other countries like Japan and China see large increases in relative incomes Figure below illustrates the ”lost decades” that Japan has experienced. After rapid growth in the 1980s (and before) 22 / 33 How growth is spreading across countries: how are different countries moving relative to the rich ones? 23 / 33 How growth is spreading across countries: how are different countries moving relative to the rich ones? Japan peaked at an income relative to the U.S. of 85 percent in 1995 Since 1995, though, Japan has fallen back to around 75 percent of the U.S. level The rapid growth of China since 1980 and India since around 1990 are also evident in this figure The contrast with Sub-Saharan Africa is particularly striking, as that region as a whole falls from 7.5 percent of U.S. income in 1980 to just 3.3 percent by 2000 Since 2000, many of the countries and regions catchup to the United States 24 / 33 How growth is spreading across countries: how are different countries moving relative to the rich ones? Figure below shows GDP per person relative to the United States in 1960 and 2011 for 107 countries 25 / 33 How growth is spreading across countries: how are different countries moving relative to the rich ones? Countries scatter widely around the 45-degree line, and the first impression is that there is no systematic pattern to this scattering Some countries are moving up relative to the U.S. and some countries are falling further behind, and the movements can be large, as represented by the deviations from the 45-degree line Looking more closely at the graph, there is some suggestion that there are more middle-income countries above the 45-degree line than below At least between 1960 and 2011, countries in the middle of the distribution seemed more likely to move closer to the U.S. than to fall further behind In contrast, for low income countries, the opposite pattern appears in the data: poor countries are on average more systematically below the 45-degree line rather than above 26 / 33 How growth is spreading across countries: how are different countries moving relative to the rich ones? Figure below shows one of the more famous graphs from the empirical growth literature, illustrating the ”catch-up” behavior of OECD countries since 1960 27 / 33 How growth is spreading across countries: how are different countries moving relative to the rich ones? Among OECD countries, those that were relatively poor in 1960, like Japan, Portugal, and Greece, grew rapidly While those that were relatively rich in 1960, like Switzerland, Norway, and the United States, grew more slowly. The pattern is quite strong in the data; a simple regression line leads to an R-squared of 75 percent Figure below shows that a simplistic view of convergence does not hold for the world as a whole. There is no tendency for poor countries around the world to grow either faster or slower than rich countries. For every Botswana and South Korea, there is an El Salvador and Niger 28 / 33 How growth is spreading across countries: how are different countries moving relative to the rich ones? 29 / 33 How growth is spreading across countries: how are different countries moving relative to the rich ones? Figure below shows the standard deviation of log GDP per person over time for this stable 107-country sample 30 / 33 How growth is spreading across countries: how are different countries moving relative to the rich ones? As an alternative measure of dispersion, it also shows the ratio of GDP per person between the 5th richest and 5th poorest countries in the sample Both measures reveal the same thing: between 1960 and the late-1990s, there was a widening of the world income distribution, at least when each country is a unit of observation In the last decade or so, this pattern seems to have stabilized. In fact, some of this pattern was already evident back in Figure 24 The poorest countries in 1960 such as Mozambique were only about 50 times poorer than the United States By 2011, there are many countries with relative incomes below this level, and both El Salvador and the Democratic Republic of the Congo are more than 128 times poorer than the United States 31 / 33 How growth is spreading across countries: how are different countries moving relative to the rich ones? Table below examines the dynamics of the distribution of incomes across countries in a more systematic fashion 32 / 33 How growth is spreading across countries: how are different countries moving relative to the rich ones? First, we sort 107 countries with data in both 1960 and 2010 based on their income relative to the US. Then, using decadal growth rates Second, for the 5 decades between 1960 and 2010, we calculate the sample probabilities that countries move from one bin to another Finally, we compute the stationary distribution of countries across the bins that is implied by assuming these sample probabilities are constant forever 33 / 33 Development economics Lecture 2 VUONG Hung Cuong AEI International School Université Paris-Est Créteil September 26, 2024 1 / 22 Introduction How to measure the economy? How hard it is to measure ”an economy” What should we include? What should we leave out? How can we add up things that are wildly dissimilar - automobile production and grocery store employment and resales of homes and on and on - into one number that tells us what is happening? This lecture explains the composition of GDP and compares it over time and across countries Main reference: Chapter 2, Macroeconomics, Charles Jones 2 / 22 What is Gross Domestic Product (or GDP)? Simon Kuznets was awarded the 1971 Nobel Prize in economics largely for creating the definition of GDP that we use today Gross Domestic Product (GDP) is the market value of the final goods and services produced in an economy during the year Example: In 2021, U.S. GDP = 23.0 trillion dollars, or 69,000 dollars per person GDP is one of the vital signs of the nation’s economic health ”market value” means that GDP is valued in some currency, such as dollars ”final” is needed to accurately measure GDP to avoid double counting ”produced” implies that GDP doesn’t include sales of used items (such as homes and cars), and doesn’t include purely financial transactions (such as buying stocks or moving money between bank accounts) ”services” means that a large part of economic activity isn’t about making things - it’s about providing valuable services: transportation, medical care, tourism, and ”other” 3 / 22 Measurement of GDP There are three equivalent ways to measure GDP Suppose the entire economy consists of a single firm ABC which hires workers to make wine (I) Production approach: GDP is the total amount of wine produced in a year Count the bottles as they are made (II) Expenditure approach: GDP is the total amount of wine sold in a year Note that: As long as all the produced wine bottles end up being sold, these two measures will be equal Count the bottles as they are sold to consumers (III) Income approach: GDP is the total income earned by the workers plus the ”profits” made by ABC In short, According to national income accounting, GDP in an economy equals production, expenditure, and income 4 / 22 The Expenditure Approach to GDP The national income accounts divide the goods and services that are purchased into several categories This breakdown appears in one of the fundamental accounting equations called the national income identity Y = C + I + G + NX where Y : GDP (in dollars), C : consumption, I : investment, G : government purchases, and NX : net exports = exports - imports 5 / 22 The Expenditure Approach to GDP 6 / 22 The Expenditure Approach to GDP In the U.S. in 2012, consumption expenditures accounted for 70 percent of GDP, including expenditures on motor vehicles, food, housing services, and medical care Investment expenditures made up about 13 percent of GDP Government purchases (about 20 percent of GDP) are the purchases that directly involve new production including expenditures on public schools, highways, government-funded research, and national defense Government spending includes Government purchases plus transfers (like Social Security and Medicare) and interest payments on any outstanding government debt Finally, 13.9 percent of the goods and services produced by U.S. businesses were shipped abroad and sold to foreigners; these sales are exports At the same time, U.S. consumers and businesses imported goods and services from abroad equal in magnitude to 17.5 percent of GDP Thus, ”net exports” - exports minus imports - were equal to about 3.6 percent of GDP 7 / 22 The Expenditure Approach to GDP 8 / 22 The Expenditure Approach to GDP Figure above shows: Relative stable share in the composition of GDP (65 percent for C + 20 percent for G + 15 percent for I) High G during WWII ( 1945) Low I near Great Depression ( 1930) Recent trade deficit. Implications: Higher consumption today in exchange for tomorrow’s GDP and investment Note that ”net exports” = ”the trade balance” 9 / 22 The Expenditure Approach to GDP Attention: Make sure we count everything exactly once when computing NX For example, C contains all purchases of consumer goods within the United States, not all production of consumer goods within the United States So some of the C in GDP is really produced in Germany or China or Canada - and if our final measure of GDP is really going to measure U.S. production, we have to subtract that to make sure it doesn’t show up in our final number Example: when an American buys a 400 dollars Chinese TV from the local appliance store, it shows up twice on the right-hand side of the national income identity: as +400 dollars in C, and again as -200 dollars in NX. That’s how we make sure that the portion of the TVs produced abroad doesn’t show up in U.S. GDP 10 / 22  The Expenditure Approach to GDP Figure below illustrates the composition of China’s GDP with an increasing rate of investment but decreasing levels of government purchases and consumption (recently 2020) Often, we see investment’s share of GDP falling when there is a downturn in the economy, as consumption and government purchases’ shares are increasing (50's, as ppl still need to C, and gov tries to stabilize the eco by buying) shorter space (= X ds les 90%, mais plutot 100% - là où arrondi bleu) ! piege de lire que le violet = + d'I 80% eco et du gov purchases, car c'est du 80% consuption. (Gov est dans les 15% environ) - C° 11 / 22 The Income Approach to GDP From a national income accounting perspective, for every dollar of product sold, there is a dollar of income earned In other words, GDP is equal to the value of all goods and services produced in the economy, but it is also equal to the sum of all income earned in the economy 12 / 22 The Income Approach to GDP Table above shows that a large part of income, just under 55 percent, came in the form of compensation to employees - wages and salaries as well as the (growing) category of benefits, including health and retirement benefits The bulk of the remainder was the net operating surplus of businesses called ”profits” A much smaller category, depreciation of capital, constituted just over 10 percent of GDP. Capital refers to the inputs into production other than labor that are not completely used up in the production process, like a factory or office building and equipment like computers or copying machines Steel in an automotive factory is not capital, but an intermediate input that is used up in production: after the car is built, the factory remains but the steel is incorporated into the car The capital stocks are depreciated. Some of their income is implicitly compensation for this depreciation of the farm’s capital If we subtract out the depreciation when computing GDP, then the remainder is referred to as ”net domestic product” 13 / 22 THE PRODUCTION APPROACH TO GDP Illustration: if a steel company produces 10 million dollars worth of steel that is then used by an automobile company to make 100 million dollars worth of trucks, the value of the steel is not counted twice. Rather, GDP goes up by 100 million dollars This shows the importance of counting everything exactly once. In the production method, we have only two choices: (1) Either only measure final goods and services (as in the illustration above) (2) Only measure the value added at each stage of production as a good moves from firm to firm to the final purchaser This value-added, as it is called, is computed by subtracting the value of intermediate products (like steel or electricity; 10 million dollars in the above illustration) from the revenue generated by each producer In terms of value-added, then, the steel producer generates 10 million dollars of GDP, while the automobile producer generates 90 million dollars (100 million dollars - 10 million dollars), for a total increment once again of 100 million dollars. 14 / 22 THE PRODUCTION APPROACH TO GDP Another important implication of the production approach to GDP is that it is only new production that counts For example, if a construction company builds a new house and sells it for 200,000 dollars, this amount counts toward GDP But suppose a used-car dealer buys a 2004 minivan for 17,000 dollars and then sells it the next day to a family for 20,000 dollars; by how much does GDP change? The full 20,000 dollars does not count toward this year’s GDP: the car already existed and does not represent new production However, the ”profit” of 3,000 dollars earned by the dealer does count toward GDP 15 / 22 What Is Included in GDP and What’s Not? GDP includes only goods and services that transact in markets. For example: a restaurant bill vs costs of buying some ingredients to prepare a meal Similarly, the day-care service gets counted as GDP, but if you stay home to care the kids, no market transaction occurs and no contribution to GDP is recorded Implications for computing GDP of a developing country? Another important omission from GDP is the health of a nation’s people, William Nordhaus calculates that the rise in U.S. life expectancy had roughly the same impact on the country’s economic welfare as the entire gain in per capita consumption Another potentially significant limitation of GDP is that it doesn’t include changes in environmental resources For example, when nonrenewable natural resources like oil and natural gas are extracted, GDP goes up because of the productive effort spent turning the reserves into products, but there is no deduction from GDP associated with the reduction of oil and natural gas reserves Finally, leisure can be seen as a good that is excluded from GDP 16 / 22 Measuring Changes in GDP over Time Economists use the word ”nominal” to refer to a measure like GDP when prices and quantities have not been separated out and use ”real” to refer only to the actual quantity of goods and services Nominal and real GDP are related by a simple equation: Nominal GDP = Price level x Real GDP Nominal GDP = Value in current dollars Price Level = Price index Real GDP = Quantity of goods and services, for instance ”in 2012 dollars” or ”in constant prices” Nominal GDP conflates both changes in the price level and changes in the number of goods and services Real GDP strips out changes in prices 17 / 22 Measuring Changes in GDP over Time Example: If an economy produces 37 cell phones and nothing else, and if the price of each is 100 dollars, then nominal GDP would equal 3,700 dollars, while real GDP would equal 37 cell phones Nominal GDP can go up either because the price level has gone up or because real GDP has gone up For instance: If GDP in 2021 was 23.0 trillion dollars, in 1995 was 7.4 trillion dollars, how much is more goods and services, and how much is higher prices? In this case, prices have changed over the 17 years. It is possible, for example, that all the increase in GDP is accounted for by higher prices, and real GDP has not changed Alternatively, it is equally possible that prices haven’t changed at all, and all the increase is explained by an increase in the quantity of real GDP The truth lies somewhere in between, and the challenge is to figure out exactly where 18 / 22 Real vs. nominal GDP: An alternative equation Percentage change in Nominal GDP = Percentage change in Price level x Percentage change in Real GDP The percentage change in a mathematical product is approximately equal to the sum of the percentage changes of the components The percentage change in the price level is the inflation rate 19 / 22 Quantity Indexes: Laspeyres, Paasche, and Chain Weighting The method of computing the change in real GDP with the initial prices is called the Laspeyres index, while the method that uses the final prices is called the Paasche index A third, preferred, approach to computing real GDP is called the Fisher index, or chain weighting To compute the chain-weighted index of real GDP, first compute the Laspeyres and Paasche indexes, then calculate the average of the two growth rates See the next table for more details 20 / 22 Real vs. nominal GDP: an economy with two products 21 / 22 Comparing Economic Performance across Countries When we try to compare GDP across countries, we will need to separate quantities and prices as we did with comparisons of GDP over time For example, how large China’s economy is in comparison with the U.S. economy? The national accounts for the two countries show that U.S. GDP was 14.5 trillion dollars in 2010, while China’s GDP was 39.4 trillion yuan Thus, we need to rely on exchange rate to exchange dollars for yuan Assume that in 2010, 1 USD = 6.77 yuan For instance, we use the 2010 exchange rate to convert China’s GDP of 39.4 trillion yuan into dollars, we get 39.4 trillion yuan x ((1 dollar)/(6.77 yuan)) = 5.8 trillion dollars Or, China’s economy was about 40 percent of the size of the U.S. economy that year 22 / 22  Development economics 1 Lecture 3: GDP and applications (asynchronous session) VUONG Hung Cuong AEI International School Université Paris-Est Créteil September 26, 2024 1 / 10 Remind National income accounting provides systematic measures of aggregate economic activity. Gross domestic product (GDP) is the key overall measure of economic activity in an economy. It can be viewed as total expenditure, total income, or total production in an economy The expenditure approach to GDP makes use of a fundamental national income identity: Y = C + I + G + NX. That is total spending is the sum of spending on consumption, investment, government purchases, and net exports A key lesson of the income approach is that labor’s share of GDP is relatively stable over time at about two-thirds In the production approach, it is only the value of final production that counts. Equivalently, GDP is the sum of value added at each stage of production. Nominal GDP refers to the value of GDP measured in current prices in a given year Real GDP involves computing GDP in two different years using the same set of prices. Changes in real GDP therefore reflect changes in actual production rather than changes in prices. 2 / 10 Remind Real GDP can be computed based on various types of price indexes - Laspeyres, Paasche, and chainweighted A simple intepretation: ”Real GDP in Year X Prices” Then use the basic equation: Nominal GDP = Real GDP × price level Thus, price level = Nominal GDP / Real GDP Problem: if we used 2010 prices to value production in 1950, we’d get a distorted ! picture: telephone service that was extremely valuable and expensive in 1950 as compared to the cheap modern prices Thus, chain weighting allows us to compare real GDP in 1950, for example, with real GDP in 2010 by gradually updating the prices: 1950 and 1951 prices are used to compare 1950 and 1951 real GDPs 1951 and 1952 prices are then used to compare 1951 and 1952 real GDPs, and so on By linking the chain of comparisons in this way, we construct a more accurate measure of real GDP 3 / 10 Remind Finally, the Consumer Price Index’s ”basket” method is different from the other price indexes covered here The CPI is used to index tax brackets and Social Security payments, so it has policy relevance International comparisons of GDP involve two conversions : First, we need exchange rates to convert the measures into a common currency Second, just as we need to use common prices to measure real GDP over time We also need to use common prices to compare real GDP across countries. 4 / 10 Exercise 1 - Basics By how much does GDP rise in each of the following scenarios? Explain. (a) You spend 5,000 usd on college tuition this semester (b) You buy a used car from a friend for 2,500 usd (c) The government spends 100 million usd to build a dam. (d) Foreign graduate students work as teaching assistants at the local university and earn 5,000 usd each 5 / 10 Exercise 2 - What counts as GDP By how much does GDP rise in each of the following scenarios? Explain. (a) A computer company buys parts from a local distributor for 1 million dollars,assembles the parts, and sells the resulting computers for 2 million dollars (b) A real estate agent sells a house for 200,000 dollars that the previous owners had bought 10 years earlier for 100,000 dollars. The agent earns a commission of 6,000 dollars (c) During a recession, the government raises unemployment benefits by 100 million dollars (d) A new U.S. airline purchases and imports 50 million dollars worth of airplanes from the European company Airbus (e) A new European airline purchases 50 million dollars worth of airplanes from the American company Boeing (f) A store buys 100,000 dollars of chocolate from Belgium and sells it to consumers in the United States for 125,000 dollars. 6 / 10 Exercise 3 - Capital gains: Why aren’t they part of GDP? If you buy a share of Microsoft stock for 100 usd and then sell it a year later for 150 usd, common sense tells you that you’ve earned 50 usd The 50 usd increase is called a ”capital gain.” Similarly, if you bought a house for 100,000 usd and sell it two years That 25,000 usd sure feels like income to you: it’s money you can spend just as if you had received a 25,000 usd bonus at work Why we do not consider this ”capital gain” as part of GDP? 7 / 10 Exercise 4 Let’s consider the economy of Pickupia. The only two companies in Pickupia produce steel (SteelCo) and trucks (TruckCo) There are four different customers for TruckCo’s trucks: Pickupia’s consumers buy 200 usd worth of trucks for personal use; Pickupia’s businesses buy 100 usd worth of trucks to haul products and workers; Pickupia’s government buys 150 usd worth of trucks to haul products and workers; Foreign countries buy 50 usd worth of trucks for unknown reasons Pickupia’s consumers also import 100 usd worth of other goods and services from foreign countries. Compute the GDP. 8 / 10 Exercise 5 - How large is the economy of India? Indian GDP in 2010 was 78.9 trillion rupees, while U.S. GDP was 14.5 trillion usd. The exchange rate in 2010 was 45.7 rupees per dollar. India turns out to have lower prices than the United States (this is true more generally for poor countries): the price level in India (converted to dollars) divided by the price level in the United States was 0.368 in 2010. (a) What is the ratio of Indian GDP to U.S. GDP if we don’t take into account the differences in relative prices and simply use the exchange rate to make the conversion? (b) What is the ratio of real GDP in India to real GDP in the United States in common prices? (c) Why are these two numbers different? 9 / 10 Exercise 6 - Earthquakes and GDP Suppose the rural part of a country is hit by a major earthquake that destroys 10 percent of the country’s housing stock. The government and private sector respond with a major construction effort to help rebuild houses. Discuss how this episode is likely to affect (a) the economic well-being of the people in the country (b) the economy’s measured GDP 10 / 10 Development economics 1 Lecture 4: Growth basics VUONG Hung Cuong AEI International School Université Paris-Est Créteil October 10, 2024 1 / 28 The Definition of Economic Growth The phrase “economic growth” has been used generically to refer to increases in living standards However, “growth” also has a more precise meaning, related to the exact rate of change of per capita GDP Let y stand for per capita income. Then, at least as an approximation: y2021 − y2020 = gby2020 where yi denotes per capita income of year i = 2020, 2021. gb is percentage change that we call a growth rate. That is, the change in per capita income between 2015 and 2016 is roughly proportional to the level of per capita income in 2015 2 / 28 The Definition of Economic Growth Thus, we obtain: y2021 − y2020 gb = y2020 The left-hand side of this equation is the percentage change in per capita income. This expression says that the percentage change in per capita income is the constant gb. 3 / 28 The Definition of Economic Growth Now, suppose yt is income in some period. Then we could study the growth rate between 2014 and 2015, or more generally between year t and year (t + 1). A growth rate in some variable y is the percentage change in that variable. The growth rate between period t and year (t + 1) is yt+1 − yt yb = yt If the growth rate of per capita income happens to equal some number g , then we can express the level of per capita income as ^y=^g yt+1 = yt (1 + g ) This equation determines the value of per capita income tomorrow if we know the value today and the growth rate 4 / 28 A Population Growth Example Suppose the population of the world is given by L0 ; we might suppose L0 is equal to 6 billion, to reflect the number of people in the world in the year 2000. Now consider the possibility that population growth will be constant over the next century at a rate given by n̂. For example, n̂ might equal 0.02, implying that the world’s population will grow at 2 percent per year. Under these assumptions, what will the level of the population be 100 years from now? 5 / 28 A Population Growth Example Applying the formula above, we have Lt+1 = Lt (1 + n̂) Thus, each additional period we must add Lt n̂ people to the original population Lt. Assume we have L0 in year 0. In the first year we get L1 = L0 (1 + n̂) In the second year we get L2 = L1 (1 + n̂) L2 = L0 (1 + n̂)(1 + n̂) L2 = L0 (1 + n̂)2 6 / 28 A Population Growth Example This process suggests that the population in year 100 is L100 = L0 (1 + n̂)100 With L0 = 6 billion and n̂ = 0.02, we thus find that the population 100 years from now would equal 43.5 billion Genrally, the constant growth rule indicates that if a variable starts at some initial value y0 at time 0 and grows at a constant rate g , then the value of the variable at some future time t is given by growth starts in period 0, then: yt = y0 (1 + g )t The “t” means the same thing on both sides of the equal sign: It is the number of years of growth, when growth starts in period 0. 7 / 28 The Rule of 70 and the Ratio Scale is it possible to tell from the figure that the rate of growth of the world population is constant over the 100 years? 8 / 28 The Rule of 70 and the Ratio Scale While the graph shows a curve that is consistent with constant exponential growth, it does not directly reveal whether the growth rate is constant without additional analysis. Not really. However, the picture draws based on a function with a constant growth factor. Thus, there is an alternative way of plotting these figures, called a “ratio scale” that makes it much easier to see what is happening to the growth rate. 9 / 28 The Rule of 70 and the Ratio Scale Suppose a country called Utopia has a per capita income that exhibits a constant growth rate g. How many years does it take before income doubles? yt = 2y0 yt = y0 (1 + g )t = 2y0 double (1 + g )t = 2 "ln" refers to the natural logarithm, The equation shows that the which is a logarithm with base e, natural logarithm of (1+g)t is equal where e=2.71828. ln [(1 + g )t ] = ln(2) to the natural logarithm of 2. The natural logarithm is commonly Taking the natural logarithm helps used in mathematics to deal with to linearize exponential exponential growth and decay t.ln(1 + g ) = ln(2) relationships, making it easier to processes. solve for variables like t or g. 10 / 28 The Rule of 70 and the Ratio Scale when g is small, ln(1 + g ) ≈ g. Furthermore, ln(2) ≈ 0.7 Thus, we have tg = 0.7 0.7 t= g Rule of 70: if yt grows at a rate of g percent per year, then the number of years it takes yt to double is approximately equal to 70/g. This is one of the most useful concepts this semester 11 / 28 The Rule of 70 and the Ratio Scale For example, if yt grows at 2 percent per year, then it doubles about every 70/2 = 35 years If something grows at a rate of X percent per year, it takes 70/X years to double. So something that grows at 10 percent per year doesn’t take 10 years to double; it only takes 7. Shortcut Whether they’re thinking about retirement planning, economic growth, or inflation, the rule of 70 (or 72) comes in handy. (est pratique) Note that applying the rule of 70 is about getting the units right: If something grows ! at 5 percent, it takes about 70/5 years to double, not 70/.05 years. 12 / 28 The Rule of 70 and the Ratio Scale Aslo, the rule of 70 is figuring out what happens when something doubles again and again. If your standard of living grows 5 percent per year on average (a reasonable estimate of China’s growth in recent decades), then living standards double every 14 years. But how long does it take for living standards to be 8 times higher? 14 years for 2 times. 28 years for 4 times. 42 years for 8 times more than the starting value 13 / 28 The Rule of 70 and the Ratio Scale Implications: (en soi) First, it is very informative in its own right. If a country’s income grows at 1 percent per year, then it takes about 70 years for income to double. However, if growth is slightly faster at 5 percent per year, then income doubles every 14 (70/5) years. Seemingly small differences in growth rates lead to quite different outcomes when compounded over time. The second implication of the Rule of 70 is that the time it takes for income to double depends only on the growth rate, not on the current level of income. If a country’s income grows at 2 percent per year, then it doubles every 35 years, regardless of whether the initial income is 500 dollars or 25, 000 dollars. 14 / 28 The Rule of 70 and the Ratio Scale Coming back to the picture above, because population is growing at a constant rate of 2 percent per year, it will double every 35 years; the points when the population hits 6 billion (today), 12 billion, 24 billion, and 48 billion are highlighted 15 / 28 The Rule of 70 and the Ratio Scale The key doubling points - the 6−, 12−, 24−, and 48−billion points - are equally far apart That is, rather than labeling the vertical axis in the usual “1, 2, 3, 4” fashion, we label it as “1, 2, 4, 8” so that each interval represents a doubling; this is shown in part (b) We observe: what was previously an ever-steepening curve has turned into a straight line. If the population is growing at a constant rate, we should hit our equally spaced markers every 35 years, and this is exactly what happens Practice with Excel ?! 16 / 28 Growth in practice 17 / 28 Growth in practice Tps pr doubler: 12ans. cherche half century= 50ans 50/12= 4 (Rev. vont doubler 4 fois en 50 ans In Taiwan, for example, which is growing at 6 percent per year, incomes will double every 12 years (remember the Rule of 70). Over the course of a half century — about two generations — incomes will increase by a factor of 24 = 16. In a country like Taiwan, young adults are 16 times richer than their grandparents. But in countries like Nicaragua and Madagascar, standards of living have been stagnant across these same two generations. 18 / 28 Growth in practice 19 / 28 Individual growth The picture above takes a different perspective on economic growth and treats the person rather than the country as the unit of observation. Rather than letting China count as 1 observation out of 150 countries, for example, we count the 1.3 billion people in China as about one-fifth of the world’s population. The figure, in other words, plots the distribution of the world’s population according to per capita GDP. It shows the fraction of people living in countries that have a per capita GDP below the number on the horizontal axis. Importantly, this per capita GDP is measured as a fraction of U.S. per capita GDP in the year 2010 The graph shows, for 1960 and 2010, the percentage of the world’s population living in countries with a per capita GDP less than or equal to the number on the horizontal axis. This per capita GDP is relative to the United States in the year 2010 for both lines. 20 / 28 Individual growth First, the general growth rate of per capita GDP throughout the world is evident in the way the distribution shifts out over time. The bulk of the world’s population is substantially richer today than it was in 1960. Second, the fraction of people living in poverty has fallen dramatically in the past half century. In 1960, 2 out of 3 people in the world lived in countries with a per capita GDP less than 5 percent of the 2010 U.S. level. In other words, in today’s prices, these people made about 5 dollars per day. By 2010, the fraction living in this kind of poverty had fallen to less than 1 out of 12. If the distribution had remained unchanged from its 1960 level, more than 4 billion people would fall below this poverty threshold today. Instead, because of economic growth, only about 600 million do. One of the major reasons for this has been the rapid economic growth in India and China, which together account for more than a third of the world’s population If we measure economic progress on a per person rather than a per country basis, a different picture emerges: living standards have dramatically risen for the median human over the past four decades 21 / 28 Properties Growth rates of ratios, products, and powers: Suppose two variables x and y have average annual growth rates of gx and gy , respectively. Then the following rules apply: 1. If z = x/y , then gz = gx − gy (ratio) 2. If z = xy , then gz = gx + gy (multiplication) 3. If z = x a , then gz = a.gx (exponentiation) In these expressions, gz is the average annual growth rate of z 22 / 28 Properties Rule 1: If both the numerator and denominator are growing at the same rate, then surely the ratio must be constant. If the numerator grows faster than the denominator, so we would expect the ratio to grow as well. In fact, rule 1 says the growth rate of the ratio should equal gx − gy Rule 2 says that the growth rate of the product of two variables is the sum of the two growth rates Rule 3 is related to exponentiation. Suppose y grows at rate gy. What is the growth rate of z = y 2 ? Since y 2 = y.y , we can apply our multiplication rule to see that gz = gy + gy = 2gy. etc... Similarly, the growth rate of y 3 will be 3.gy and the growth rate of y 10 will be 10.gy. 23 / 28 Example Suppose we have an equation that says a variable Yt is a function of some other variables At , Kt , and Lt. In particular, this function is 1/3 2/3 Yt = At Kt Lt What is growth rate of Yt in terms of At , Kt , and Lt ? 24 / 28 Example ? The second rule imples that 1/3 2/3 g (Yt ) = g (At ) + g (Kt ) + g (Lt ) The third rule implies that 1 2 g (Yt ) = g (At ) + g (Kt ) + g (Lt ) 3 3 Implications: the growth rate of output Y can be decomposed into the growth rate of a productivity term A and the contributions to growth from capital K and labor L 25 / 28 Exercises Exercise 1: In 2010, Ethiopia had a per capita income of 700 dollars, about 2 dollars per day. Compute per capita income in Ethiopia for the year 2050 assuming average annual growth is (a) 1 percent per year. (b) 2 percent per year. (c) 4 percent per year. (d) 6 percent per year. 26 / 28 Exercises Exercise 2: Population growth: Suppose the world population today is 7 billion, and suppose this population grows at a constant rate of 3 percent per year from now on. (This rate is almost certainly much faster than the future population growth rate; the high rate used here is useful for pedagogy. If you like, you can use a spreadsheet program to help you with this question.) (a) What would the population equal 100 years from now? (b) Compute the level of the population for t = 0, t = 1, t = 2, t = 10, t = 25, and t = 50. (c) Make a graph of population versus time (on a standard scale). (d) Now make the same graph on a ratio scale. 27 / 28 Exercises Exercise 3: Computing growth rates (I): Suppose xt = (1.04)t and yt = (1.02)t. Calculate the growth rate of zt in each of the following cases: (a) z = xy (b) z = x/y (c) z = y /x (d) z = x 1/2 y 1/2 (e) z = (x/y )2 (f ) z = x 1/3 y 2/3 28 / 28 1 Development economics 1 Lecture 5: Growth and production function VUONG Hung Cuong AEI International School Université Paris-Est Créteil October 10, 2024 1 / 28 Economic models ”If we understand the process of economic growth — or of anything else — we ought to be capable of demonstrating this knowledge by creating it in these pen and paper (and computer-equipped) laboratories of ours. If we know what an economic miracle is, we ought to be able to make one.” — Robert E. Lucas, Jr. ”What I cannot create, I do not understand.”— Richard P. Feynman Economics model is a set of mathematical equations with assumptions to describe the economic phenomena. The theoretical models are then verified by empirical evidence with data Economic models often provide intuitive recommendations 2 / 28 The Economy of Shangri La The people of Shangri La love to eat ice cream Production of ice cream Y = F (K , L) = ĀK 1/3 L2/3 K = Number of ice cream machines (capital) L = Number of workers Y = Number of ice cream produced during the year Ā = A parameter of the production function GPT > This is a Cobb-Douglas production function, where outputs depend on capital and labor with specific weights (exponents). 3 / 28 An Example Y = F (K , L) = ĀK 1/3 L2/3 K = 8 machines L = 27 workers Ā = 2000 Then 2000 x 8^1/3 x 27^2/3 Y = 2000 × 2 × 9 = 36,000 ice cream. 4 / 28 What is the Name of this Production Function? Y = ĀK αLβ 5 / 28 What is the Name of this Production Function? A Cobb-Douglas production function: Y = ĀK αLβ 6 / 28 Returns to Scale Y = F (K , L) = ĀK 1/3 L2/3 Does this production function exhibit increasing, constant, or decreasing returns to scale? GPT > Simplifiying shows that doubling K and L doubles Y: F(2K, 2L) = 2F(K,L) Conclu: The production function exhibits constant returns to scale because (1/3 + 2/3 =1) 7 / 28 Returns to Scale Y = F (K , L) = ĀK 1/3 L2/3 Does this production function exhibit increasing, constant, or decreasing returns to scale? Y = F (K , L) = ĀK α Lβ Constant returns: Doubling inputs will double output (α + β = 1) Increasing returns: Doubling inputs more than doubles output (α + β > 1) Decreasing returns: Doubling inputs less than doubles output (α + β < 1) 8 / 28 Returns to Scale Y = F (K , L) = ĀK 1/3 L2/3 Does this production function exhibit increasing, constant, or decreasing returns to scale? F (2K , 2L) = Ā(2K )1/3 (2L)2/3 F (2K , 2L) = Ā21/3 K 1/3 22/3 L2/3 F (2K , 2L) = 21/3 22/3 ĀK 1/3 L2/3 F (2K , 2L) = 2ĀK 1/3 L2/3 F (2K , 2L) = 2F (K , L) 9 / 28 What is the Standard Replication Argument? 10 / 28 What is the Standard Replication Argument? How can a firm in Shangri La double its production of ice cream? One natural way is to double the number of machines and the number of workers That is, we replicate the firm... The standard replication argument is a key argument that leads us to focus often on constant returns to scale: if you double all the inputs of production, you double output. GPT > The idea that doubling all inputs (e.g., machines and workers) leads to double the output is the "replication argument." Why might returns to scale differ? Increasing Returns: Efficiency improves as scale grows. Decreasing Returns: Constraints (like space or coordination) reduce efficiency. 11 / 28 What is the Standard Replication Argument? How can a firm in Shangri La double its production of ice cream? One natural way is to double the number of machines and the number of workers That is, we replicate the firm... The standard replication argument is a key argument that leads us to focus often on constant returns to scale: if you double all the inputs of production, you double output. Why might returns to scale not be constant? Decreasing? Increasing? 12 / 28 Very Important Distinction: Overall returns to scale By the standard replication argument, we often argue that production functions exhibit constant returns to scale to all inputs. Diminishing returns to a particular input If there are constant returns to all inputs together, then there are diminishing returns to each input by itself. Holding labor constant, the production function exhibits diminishing returns to capital. Adding more ice cream machines to Shangri La has a smaller and smaller effect on the total number of ice creams produced (as there is a limit to how effectively the workers can produce). 13 / 28 I The Marginal Product The marginal product of capital (MPK) is the extra amount of output that is produced when one unit of capital is added, holding all the other inputs constant. Suppose we have five workers. The first five ice cream machines are thus very valuable, as each worker can be matched with a single machine. The next five machines are less valuable — it’s hard for a worker to oversee two machines simultaneously. The marginal product of labor (MPL) is the extra amount of output that is produced when one unit of labor is added, holding all the other inputs constant Suppose we have five ice cream machines, the first five people we hire are very productive. But as we add more and more workers, there is less for them to do with only five machines among them Intuitively, if we hold an input, i, constant, the marginal product of the other input, j, declines as we increase the number of j 14 / 28 The Diminishing Marginal Product of Capital Partial derivative 15 / 28  The Diminishing Marginal Product of Capital The marginal product of capital is given by MPK = 1/3 (L/K)2/3 = 1/3(Y /K ) Similarly, the marginal product of labor is MPL = 2/3 (K/L)1/3 = 2/3(Y /L) Marginal product of labor is proportional to the average amount each worker produces, Y/L, where the factor of proportionality is the Cobb-Douglas exponent, 2/3. 16 / 28 The model Firms hire workers and rent machines to produce ice cream and then sell them to consumers There are three markets here: (1) Ice cream ; (2) Labor ; (3) Capital General equilibrium: we have more than a single market that is clearing. (2) and (3) Labor and Capital markets Supply: The supply labor supply is exogenously given Demand: If firm’s demand for labor is higher, it has to pay a higher wage The same is true regarding the capital market 17 / 28 The model 18 / 28 The model (1) Market for ice cream Supply: There is only one firm in the market Demand: Price per ice cream is fixed at 1, thus it is called ”numéraire”. Consumers buy all the ice cream produced. The firm determines the number of workers and machines to maximize its profit: Π = Y.(1) − rK − wL = ĀK α Lβ − rK − wL 19 / 28 The model First order conditions: (DΠ/Di) = 0 where i is input i = L,K First partial derivative with respect to input i is zero Thus, it is optimal for the firm to hire capital and labor until their marginal products fall to equal r and w, respectively. 20 / 28 The model: General equilibrium 21 / 28 Interpretations First, we will be adding elements to this basic framework to create more sophisticated models in subsequent sessions Second, the equilibrium wage is proportional to output per worker. Similarly, the equilibrium return on capital is proportional to output per unit of capital Third, what makes a country rich or poor ? If the economy is endowed with more machines and/or more people, it will achieve a higher level of production Or, output per worker is likely to be a key indicator of how “happy” individuals are in this economy Note that: “per capita” means per person - consumption per person in the economy, while “per worker” means per member of the labor force - production process efficiency 22 / 28 Interpretations The output per person is The value of A indicates the productivity parameter: a higher value of A means the economy is more productive, or higher output per person, often referred to as total factor productivity, or TFP The second term is capital per person raised to the power 1/3: Renting more ice cream machines for the workers raises output per person. However, increasing capital per person leads to diminishing returns: if we were to double the amount of capital per person, the equilibrium quantity of output per person would less than double 23 / 28 Interpretations What makes a country rich or poor: Answer: Output per person tends to be higher when (1) the productivity parameter is higher and (2) the amount of capital per person is higher 24 / 28 Evidence With a TFP level equal to about 1/3 the U.S. level, China’s production function is shifted down substantially relative to the U.S. production function: at any given level of capital per person, Chinese workers produce only 1/3 the output of their U.S. counterparts 25 / 28 Evidence There is a high correlation between per capita GDP and TFP. Rich countries tend to have high levels of TFP, and poor countries tend to have low levels. Also, the differences in TFP across countries are great 26 / 28 Understanding TFP Differences Three possible sources of differences in efficiency: human capital, technology, and institutions (1) Physical capital is the stock of machines and buildings that an economy accumulates to help in production. Human capital is the stock of skills that individuals accumulate to make them more productive (2) Technology: Goods such as state-of-the-art computer chips, software, new pharmaceuticals, supersonic military jets, skyscrapers, and production techniques (just-in-time inventory methods, information technology, and tightly integrated transport networks) are much more prevalent in rich countries than in poor. Institutions: the differences in government policies and in the rules and regulations including corruption and bribes, property rights, the rule of law, contract enforcement, and the separation of powers. For instance: North vs South Korea 27 / 28 Exercises 28 / 28 1 aterials for this slides are taken from Charles I. Jones and his textbook Development economics 1 Lecture 6: Solow model VUONG Hung Cuong AEI International School Université Paris-Est Créteil October 10, 2024 1 / 25 South Korea and the Philippines In 1960, South Korea and the Philippines were quite similar Per capita GDP: Both around $1500 Population: Both about 25 million, 1/2 working age Similar sectoral composition (industry, agriculture) College enrollment: S. Korea=5%, Philippines=13% Between 1960 and 2017, macroeconomic performance diverged sharply Growth: S. Korea=6.5%, Philippines=2.5% Per capita GDP in 2017: S. Korea=$36,000, Philippines=$7,500 Why? 2 / 25 The Solow Growth Model Robert Solow in 1950s, Nobel prize in 1987 Build on production function, endogenize capital Can the accumulation of capital — computers, machine tools, factories — explain sustained economic growth, like U.S. 2%? Story: A Corn Farm Farm has a silo containing bushels of seed corn Farmers plant the seed, tend the crop, and harvest They eat 3/4ths of the harvest and save the remaining 1/4th in the silo for next year’s planting every years Key: each seed kernel produces ten ears of corn, each with hundreds of kernels, so harvest grows 3 / 25 The Economy of Solovia 1/3 2/3 Production function Yt = ĀKt Lt Capital accumulation ¯ t Kt+1 = Kt + It − dK Capital accumulation ¯ t ∆Kt+1 ≡ Kt+1 − Kt = It − dK Labor force Lt = L̄ Resource constraint Ct + It = Yt Allocation of resources It = s̄Yt Unknowns: Yt , Kt , Lt , Ct , It 4 / 25 The Economy of Solovia We’ve left prices — the wage and the rental price of capital — out of the model. Just a simplification, could add them back easily Real interest rate: the (real) amount someone can earn by saving one unit of output for a year Measured in units of output, or constant dollars What is the real interest rate equal to in the Solow world? The real interest rate equals the rental price of capital = return on investment = marginal product of capital Saving equals investment in this Solow economy Save one unit ⇒ invest one unit ⇒ earn the marginal product of capital, which equals the rental price 5 / 25 Solving the Solow Model The equations can be combined and simplified significantly, yielding ∆Kt+1 = s̄| Yt {z ¯ t − dK | {z } } change in capital net investment 1/3 Yt = ĀKt L̄2/3 These two equations govern the dynamics of the Solow model. Analyze in a Solow diagram 6 / 25 The Solow Diagram ¯ t 1/3 2/3 ∆Kt+1 = s̄Yt − dK Yt = ĀKt L̄ 7 / 25 The Solow Diagram with Output and Consumption 8 / 25 The Capital-Output Ratio The key addition of the Solow model is that it explains where the capital stock comes from. ¯ ∗ , which implies Recall that in steady state s̄Y ∗ = dK K∗ s̄ ∗ = ¯ Y d Different countries have different investment rates (measured as investment divided by GDP). The Solow framework predicts that these should show up as different capital-output ratios (“capital intensities”). 9 / 25 Explaining Capital in the Solow model Countries with high investment rates have high capital-output ratios 10 / 25 Economic Growth in the Solow Model What is the growth rate of the economy in the long run according to the Solow model? 11 / 25 Economic Growth in the Solow Model What is the growth rate of the economy in the long run according to the Solow model? Zero! There is no long-run growth in Solow!! Why? 12 / 25 Understanding the Steady State Result Why does the economy settle down to a steady state? ¯ ∗ — investment equals depreciation. s̄Y ∗ = dK The new investment we make is just enough to offset the wear-and-tear that depreciates the existing capital Because investment — the s̄Y curve — exhibits diminishing returns. As we increase capital, output rises by a smaller and smaller amount. But a constant fraction of capital depreciates. 13 / 25 Understanding the Steady State Result Why does the economy settle down to a steady state? ¯ ∗ — investment equals depreciation. s̄Y ∗ = dK The new investment we make is just enough to offset the wear-and-tear that depreciates the existing capital Because investment — the s̄Y curve — exhibits diminishing returns. As we increase capital, output rises by a smaller and smaller amount. But a constant fraction of capital depreciates. So diminishing returns to capital is at the heart of why growth eventually ceases in the Solow model. — A huge, disappointing failure... 14 / 25 Growth and Transition Dynamics Despite this negative result on long-run growth, the Solow framework is extraordinarily useful The reason is related to Transition Dynamics And this is most easily studied by considering an “experiment” in Solovia: Suppose Solovia begins in steady state in the year 2000 with an investment rate of 10%. What happens if the investment rate then increases permanently in the year 2020 to 15%? 15 / 25 A Permanent Increase in the Investment Rate 16 / 25 The Response of Output to a Rise in Investment 17 / 25 The Principle of Transition Dynamics As suggested by the Solow Diagram and by the last example, a key prediction of the Solow framework is The Principle of Transition Dynamics: the farther below its steady state an economy is, the faster it will grow; similarly, the farther above its steady state, the faster it will decline (the slower it will grow). Differences in growth rates across countries largely reflect how near or far countries are from their steady state. 18 / 25 Examples: The United States and China United States Growth at a constant rate of 2% per year for more than a century In some sense, this reflects the fact that the U.S. is close to its steady state. China Rapid growth at more than 8% per year during the last 25 years Suggests China is below its steady state and therefore growing rapidly Think about Japan after World War II... 19 / 25 Per capita GDP in Several Countries 20 / 25 Growth Rates in the OECD, 1960–2017 () In the OECD, the poor countries grew most rapidly and the rich countries grew 21 / 25 Growth Rates around the World, 1960–2017 For the world as a whole, however, growth rates are unrelated to initial GDP... Why? Answser: Investment rate and TFP 22 / 25 Investment in South Korea and the Philippines 23 / 25 What we learn from the Solow Framework In the long run, a country is rich or poor in part based on what fraction of its output it invests for the future. Similar reasoning suggests that the fraction of the population employed, the number of hours worked per person, and investment in human capital play a similar role. Through the principle of transition dynamics, the model helps us understand why some countries grow rapidly and others slowly. Capital accumulation — the accumulation of more machine tools, computers, and factories per worker — is not a mechanism that leads to sustained long-run growth. Shortcomings of the Solow Framework: (1) We still do not know: why countries have different investment rates (2) How do we understand long run economic growth? 24 / 25 Questions for Review What is the mechanism in the Solow model that generates growth? Why does it fail to sustain growth in the long run? What determines the real interest rate in an economy? How does the Solow framework explain differences in growth rates across countries? Why do poor countries in the OECD grow faster than rich countries in the OECD, but poor countries in the world do not grow faster than rich countries in the world? What is the principle of transition dynamics? 25 / 25 1 aterials for this slides are taken from Charles I. Jones and his textbook Development economics 1 Lecture 7: Romer model VUONG Hung Cuong AEI International School Université Paris-Est Créteil October 10, 2024 1 / 20 Solow and Romer Robert Solow (1950s) Capital versus Labor Cannot sustain long-run growth Nobel prize, 1987 Paul Romer (1990s) Objects versus Ideas Sustains long-run growth Wide-ranging implications for intellectual property, antitrust policy, international trade, the limits to growth, sources of “catch-up” growth Nobel prize, 2018 2 / 20 Objects versus Ideas Objects : raw materials Most goods: iPads, houses, oil, computers, capital, labor The amount of raw material available — oil, sand, atoms of carbon, oxygen, and so on — is finite The economics of objects underlies Adam Smith’s invisible hand theorem Ideas : instructions Instructions or recipes — designs for making/using objects Sand: from beaches/glass to computer chips Other examples: design of iPad, architectural plan for a house, method for turning oil into plastic, management techniques of Walmart, oral rehydration therapy While resources are scare, the number of ways of arranging these raw materials is virtually infinite Romer’s insight: Economic growth is sustained by discovering better and better ways to use the finite resources available to us 3 / 20 The Idea Diagram 4 / 20 Nonrivalry Objects (most goods) are rival Your use of a container ship to deliver Lenovo laptops means I cannot use that same container ship to deliver microwave ovens Gives rise to scarcity, a central focus of economics Ideas are nonrival = infinitely usable Mrs. Fields use of a famous recipe for making chocolate chip cookies does not reduce the ”amount” of the recipe available to me One architect’s use of the Pythagorean Theorem in designing a building does not reduce the “amount” of the theorem available to anyone else The PCR (polymerase chain reaction) technique for replicating strands of DNA can be used by 1 lab, 10 labs, or 1000 labs simultaneously 5 / 20 Excludability The extent to which someone has property rights over a good and can legally restrict its use Nonrivalry says ideas can be used by many people simultaneously. But society may provide property rights that lead to legal restrictions on this Nonrivalry vs. Excludability Nonrivalry is an intrinsic characteristic — from nature Excludability (the extent of property rights) is a feature of the institutions chosen by society Overall benefit to society, but did the inventor capture anything close to the social returns from the invention? Social value of 10 trillion dollars vs. 50 billion dollars cost of COVID vaccine according to OECD Chief Economist Laurence Boone 6 / 20 Increasing Returns Suppose Asthma Inc. is developing a new drug for treating asthma (affects about 10% of the population) Coming up with the successful, new chemical formula is the hard part — rough estimates suggest an average cost of $2 billion to develop a new drug Once developed, just an object, subject to standard CRS production Example: $2 billion R&D cost, then $1 per dose in manufacturing costs Constant returns after invention implies increasing returns including invention $2 billion dollars → 1 dose $4 billion dollars → about 2 billion doses! Doubling inputs far more than doubles output! 7 / 20 Revisit our standard Production Function Familiar notation, but now let At denote the “stock of knowledge” (i.e. the cookbook of recipes) 1/3 2/3 Yt = F (Kt , Lt , At ) = At Kt Lt Constant returns to scale in K and L holding knowledge fixed. Why? F (2K , 2L, A) = 2 × F (K , L, A) But therefore increasing returns in K , L, and A together! F (2K , 2L, 2A) > F (2K , 2L, A) Economics is quite straightforward: Replication argument + Nonrivalry → CRS to objects Therefore there must be IRS to objects and ideas 8 / 20 Problems with Perfect Competition Adam Smith’s fundamental Invisible Hand result Under perfect competition, markets lead to the best of all possible worlds (Pareto optimal outcome) Marginal benefits = marginal costs via the price system Prices allocate scarce resources to their best uses Why do increasing returns pose a problem? What if Asthma Inc. charges marginal cost? Covers the variable cost but not the fixed cost of R&D → negative profits → no research What if Asthma Inc. charges $100 per dose? Many people who would purchase the drug at marginal cost ($1) will not purchase at the higher price → inefficiency (deadweight loss) Ideas of above cost pricing and price discriminiation!!! 9 / 20 How to Address Problems with Perfect Competition? What do firms do to address these issues with perfect competition? Trade secrets to keep monopoly and sell at markup Fixed cost to produce ideas vs. fixed costs to produce objects Price discrimination (e.g., by country, by income of customer) Attempt to minimize deadweight loss What do govt’s do to address these issues with perfect competition? Patents grant monopoly profits for a time to allow firm to recoup initial investment How long to grant monopoly? Innovation vs. restricted supply R&D subsidies and public-private joint ventures How to know which ideas to subsidize? 10 / 20 Population Growth in the Solow Model Suppose the population grows at 1% per year in Solow What is the long-run growth rate of GDP per person? What is the long-run growth rate of GDP? Answers: In a Constant Returns to Scale world such as Solow, scale = population does not matter. We can have a billion people or one person, and the results for GDP per person are essentially the same → each farmer with more seed to plant still runs into diminishing returns (y = k 1/3 ) But since L grows at 1% and Y /L is constant, Y grows at 1% also 11 / 20 The Romer Model: Our Corn Farm Again Farmers can use their labor (and capital) to produce corn ∼ Or... they can use their labor to invent new technologies for growing corn more productively New tractors and combines New fertilizer, irrigation systems, and drought-resistant seed Model here is slightly different from that in textbook Textbook: ∆At+1 = Lt At Focus on ideas versus objects; drop capital to keep simple 12 / 20 The Key Insight: Nonrivalry Production function for goods Yt = Aβt Lt where β is degree of increasing returns Dividing by Lt , output per person is Yt yt ≡ = Aβt Lt Because of nonrivalry, output per person depends on the total stock of ideas, not on “ideas per person” — contrast with capital! If you add one new computer, you make one worker more productive: y = k 1/3 (need 1m computers for 1m workers) If you add one new idea (e.g. better spreadsheet or the internet itself), you can make any number of workers more productive. 13 / 20 Where do ideas come from? What is the simplest model of idea growth? Each person produces 1 new idea per year At+1 − At = Lt ⇒ ∆At+1 = Lt Then, ∆At+1 Lt gAt = = At At Now solve for At to get 1 At = Lt gAt Intepretation: More people means more ideas 14 / 20 What is the long-run growth rate of At ? In the LR, gAt = gA is constant. Apply our growth rules to 1 At = Lt gA Obviously At and Lt will grow at the same rate when gA is constant: gA = n̄ The growth rate of ideas equals the growth rate of researchers = population growth 15 / 20 Growth in the Romer Model Recall: yt = Aβt and gA = n̄ Applying our growth rules, what is the growth rate of yt ? gy = βgA = β n̄ Growth in per capita GDP is proportional to the growth rate of ideas. People produce ideas, so the growth rate of ideas equals the growth rate of people! The long-run growth rate is the product of β — the strength of increasing returns — and n̄ the growth rate of “scale”. 16 / 20 From IRS to Growth Why does the Solow model fail to deliver growth whereas the Romer model successfully grows per capita income in the long run? Objects (Solow): Add 1 computer make 1 worker more productive. Output per worker ∼ # of computers per worker (diminishing returns) Ideas (Romer): Add 1 new idea make unlimited # more productive. E.g. cure for lung cancer or drought-resistant seeds Income per person depends on aggregate stock of knowledge, not on the number of ideas per person. Example: The invention of antibiotics, electricity, the semiconductor, and the WWW makes all of us richer today 17 / 20 Example Solow on Mobiphone Suppose each worker can make 100 cellphones per day More workers → more production, but also more people who need phones → no long run growth in phones per person Romer on Mobilphone Suppose workers can also invent better phones and discover ways to make phones more cheaply More workers → more phones and better phones → this can sustain growth 18 / 20 World Growth over the Very Long Run Population growth and per capita GDP growth over 10,000 years People produce ideas, and... More ideas leads to more people! 19 / 20 Combining the Solow and Romer Models Romer: Explains the trend growth of the world frontier (e.g. the United States) – The world frontier grows through the discovery of new ideas – In 2000, 47% of people with PhDs in Sci/Eng in US were immigrants Solow: Countries grow “around” the Romer trend – Principle of transition dynamics explain why countries grow at different rates for long periods of time – Each country has a steady state relative to the world frontier – Steady state is determined by TFP, openness to ideas, institutions, misallocation, investment rates, etc. 20 / 20  NBER WORKING PAPER SERIES THE FACTS OF ECONOMIC GROWTH Charles I. Jones Working Paper 21142 http://www.nber.org/papers/w21142 NATIONAL BUREAU OF ECONOMIC RESEARCH 1050 Massachusetts Avenue Cambridge, MA 02138 May 2015 In preparation for a new volume of the Handbook of Macroeconomics. I am grateful to Kevin Bryan, John Haltiwanger, Jonathan Haskel, Bart Hobijn, Jihee Kim, Pete Klenow, Marti Mestieri, Chris Tonetti, seminar participants at the Stanford Handbook conference, and the editors John Taylor and Harald Uhlig for helpful comments. The views expressed herein are those of the author and do not necessarily reflect the views of the National Bureau of Economic Research. NBER working papers are circulated for discussion and comment purposes. They have not been peer- reviewed or been subject to the review by the NBER Board of Directors that accompanies official NBER publications. © 2015 by Charles I. Jones. All rights reserved. Short sections of text, not to exceed two paragraphs, may be quoted without explicit permission provided that full credit, including © notice, is given to the source. The Facts of Economic Growth Charles I. Jones NBER Working Paper No. 21142 May 2015 JEL No. E0,O4 ABSTRACT Why are people in the richest countries of the world so much richer today than 100 years ago? And why are some countries so much richer than others? Questions such as these define the field of economic growth. This paper documents the facts that underlie these questions. How much richer are we today than 100 years ago, and how large are the income gaps between countries? The purpose of the paper is to provide an encyclopedia of the fundamental facts of economic growth upon which our theories are built, gathering them together in one place and updating the facts with the latest available data. Charles I. Jones Graduate School of Business Stanford University 655 Knight Way Stanford, CA 94305-4800 and NBER [email protected]  THE FACTS OF ECONOMIC GROWTH 1 “[T]he errors which arise from the absence of facts are far more numerous and more durable than those which result from unsound reasoning respect- ing true data.” — Charles Babbage, quoted in Rosenberg (1994), p. 27. “[I]t is quite wrong to try founding a theory on observable magnitudes alone... It is the theory which decides what we can observe.” — Albert Einstein, quoted in Heisenberg (1971), p. 63. Why are people in the United States, Germany, and Japan so much richer today than 100 or 1000 years ago? Why are people in France and the Netherlands today so much richer than people in Haiti and Kenya? Questions like these are at the heart of the study of economic growth. Economics seeks to answer these questions by building quantitative models — mod- els that can be compared with empirical data. That is, we’d like our models to tell us not only that one country will be richer than another, but by how much. Or to explain not only that we should be richer today than a century ago, but that the growth rate should be 2 percent per year rather than 10 percent. Growth economics has only partially achieved these goals, but a critical input into our analysis is knowing where the goalposts lie — that is, knowing the facts of economic growth. The goal of this paper is to lay out as many of these facts as possible. Kaldor (1961) was content with documenting a few key stylized facts that basic growth theory should hope to explain. Jones and Romer (2010) updated his list to reflect what we’ve learned over the last 50 years. The purpose of this paper is different. Rather than highlighting a handful of stylized facts, we draw on the last thirty years of the renaissance of growth economics to lay out what is known empirically about the subject. These facts are updated with the latest data and gathered together in a single place. The hope is that they will be useful to newcomers to the field as well as to experts. The result, I hope, is a fascinating tour of the growth literature from the perspective of the basic data. The paper is divided broadly into two parts. First, I present the facts related to the growth of the “frontier” over time: what are the growth patterns exhibited by the richest countries in the world? Second, I focus on the spread of economic growth throughout  2 CHARLES I. JONES Figure 1: GDP per person in the United States LOG SCALE, CHAINED 2009 DOLLARS 64,000 32,000 16,000 2.0% per year 8,000 4,000 2,000 1880 1900 1920 1940 1960 1980 2000 YEAR Note: Data for 1929