Chapter 5: Long-Run Economic Growth After reading this chapter, you should be able to: 5.1 Discuss the connection between labor productivity and the standard of living (pages x – x) 5.2 Use the Solow Growth Model to Explain the Effect of Capital Accumulation on Labor Productivity (pages x – x) 5.3 Explain how total factor productivity affects labor productivity (pages x – x) 5.4 Explain the balanced growth path and convergence and the long-run equilibrium (pages x – x) Chapter Opener: Labor Productivity and the Standard of Living in China and the United States In 2008 China had a population of 1.3 billion people and its economy employed 772.8 million workers while the United States has a population of just 301.3 million people and the U.S. economy employs 156.3 million workers. Given these differences in population and growth rates of real GDP, you might conclude that China had a much larger economy and a higher standard of living than the United States. However, the opposite is true; the standard of living was 5.5 times higher in the United States than China. How was this possible? The average worker in the United States produced 6.4 times as many goods and services than the average worker in China. Productivity is the key to understanding the standard of living. Understanding 1 why these productivity differences exist is the key to understanding why the standard of living varies across countries. Even though the standard of living is higher in the United States, the Chinese economy has been growing much more rapidly than the U.S. economy. The growth rate of real GDP in China has averaged 8.5 percent per year from 1980 to 2008 while the growth rate of real GDP in the United States has averaged just 2.9 percent over the same time period. Furthermore, the Chinese Premier Wen Jiabao on March 5, 2010 reaffirmed his country’s commitment to achieve 8 percent real GDP growth for 2010 and China is expected to aim for similarly high growth rates in the future. The rapid Chinese growth rates mean that the Chinese economy is growing larger relative to the U.S. economy. However, as we just saw the standard of living is still higher in the United States than in China. SOURCE: Penn World Tables. Poon, Terrence; Back, Aaron; and Wu, J.R. “China Economy Still Needs Support,” Wall Street Journal, March 5, 2010. An Inside Look [or An Inside Look at Policy] on page xx explores……. Big Question for This Chapter: In Chapter 1, we introduced 10 big questions in macroeconomics. Here are the big questions we return to in this chapter: Big Question 1: Why has the standard of living increased over the last two hundred years? Big Question 2: Why have some countries failed to achieve sustained economic growth? 2 We start by explaining the connection between labor productivity and the standard of living. As you read this chapter, see if you can answer these questions. You can check your answers against those we provide at the end of the chapter. Continued on page xx [Transition statement] In Chapter 4, we learned that capital per worker hour and Total Factor Productivity (TFP) are the key determinants of potential real GDP per worker hour. In this chapter, we explain the determinants of capital per worker hour and total factor productivity. Real GDP per worker hour is important because both potential real GDP and potential real GDP per worker hour are closely tied to labor productivity. [End transition statement] 5.1 Discuss the Connection between Labor Productivity and the Standard of Living The circular flow diagram in Figure 2-1 showed us that real GDP equals the income generated in an economy. So, real GDP per person is a measure of both the income available to the average person in the country and how many goods and services the average person can purchase. Economists assume that people are rational and purchase goods and services that make themselves better off. For example, if you are hungry then you buy food. If you are cold, then you buy shelter. As your income increases, you use the extra income to purchase goods and services that make you better off. For this reason, economists often use real GDP per person as a measure of the standard of living. 3 Figure 5-1 shows real GDP per person from 1820 to 2008 for several countries and Figure 5-1 Real GDP per Person, 1820-2008 SOURCE: Angus Maddison. Data available at: http://www.ggdc.net/maddison/. Caption: The levels of real GDP per person varied significantly in 1820 with Africa at $420 per person and the United Kingdom at $1,706. However, the relative rankings of countries by real GDP per person have changed because the growth rates of real GDP per person have varied. For example, the growth rate of real GDP per person averaged just 0.8 percent per year in Africa. This is an extremely low growth rate and in 2008 real GDP per person was just $1,780 in Africa. Some African countries such as Malawi, Niger, and Zambia still have real GDP per persons of 4 $744, $514, and $845. For all intents and purposes, growth has not come to many countries in Africa. In contrast, Japan’s growth rate averaged 1.9 percent per year so real GDP per person in Japan rose from $669 in 1820 to $22,816 in 2008. Real GDP per person in China was stagnant until the 1970s and then accelerated rapidly from essentially zero percent to over eight percent per year. As a result, of these differences in growth rates, the relative rankings of regions by real GDP per person have also changed. In 1820, the United Kingdom had the highest real GDP per person, but now the United States has a higher and Japan has the same real GDP per person. End Caption regions around the world. The levels of real GDP per person varied significantly in 1820 with Africa at $420 per person and the United Kingdom at $1,706. However, the relative rankings of countries by real GDP per person have changed because the growth rates of real GDP per person have varied. For example, the growth rate of real GDP per person averaged just 0.8 percent per year in Africa. This is an extremely low growth rate and in 2008 real GDP per person was just $1,780 in Africa. Some African countries such as Malawi, Niger, and Zambia still have real GDP per persons of $744, $514, and $845. For all intents and purposes, growth has not come to many countries in Africa. In contrast, Japan’s growth rate averaged 1.9 percent per year so real GDP per person in Japan rose from $669 in 1820 to $22,816 in 2008. Real GDP per person in China was stagnant until the 1970s and then accelerated rapidly from essentially zero percent to over eight percent per year. As a result, of these differences in growth rates, the relative rankings of regions by real GDP per person have also changed. In 1820, the United Kingdom had the highest real GDP per person, but now the United States has a higher and Japan has the same real GDP per person. 5 The standard of living is related to labor productivity through the following equation: (5.1) ππππ πΊπ·π (ππππ’πππ‘πππ) = ( ππππ πΊπ·π π»ππ’ππ π»ππ’ππ ) (ππππ’πππ‘πππ), ππππ πΊπ·π so the standard of living equals labor productivity, ( π»ππ’ππ π»ππ’ππ ), times labor input, (ππππ’πππ‘πππ). Both labor productivity and labor inputs influence the standard of living, but the most important determinant of the standard of living is labor productivity. Even if every man, woman, and child in a country worked 24 hours a day 365 days a year, each person can work no more than 8,760 hours per year because people need sleep and eat, children go to school, and older people retire. Although there is a clear limit to how much the labor input can increase real GDP per person, there is no limit to labor productivity — as long as productivity increases, real GDP per person can also increase. Once we have explained labor productivity, we have explained most of real GDP per person and the standard of living. Labor productivity rose from $13.47 per worker hour in 1949 to $47.26 per worker hour in 2008, but labor inputs actually decreased somewhat from 837.3 hours per person in 1949 to 830.0 hours per person in 2008 for reasons that we will discuss in Chapter 7. The decrease in labor inputs should reduce the potential real GDP per person. So, the entire increase in potential real GDP per person is due to increased productivity. We can use equation (5.1) to calculate what potential real GDP per person would have been if labor productivity had remained at 1949 levels and if labor inputs had remained at 1949 levels. Figure 5-2 shows these two series along with the actual level of potential real GDP Figure 5-2 Influence of Labor Productivity and Labor Inputs on Real GDP per Person, 1949 - 2008 6 SOURCE: Bureau of Economic Analysis, Bureau of the Census, and Congressional Budget Office. Caption: The blue line represents potential real GDP per person, the green line represents real GDP per person if hours per person remained at 1949 levels, and the red line represents potential real GDP per person if labor productivity remained at 1949 levels. If labor productivity remains constant at the 1949 level, then potential real GDP per person barely changes and is just $11,177 by 2007. However, if labor inputs remain constant at the 1949 level, then potential real GDP per person rises all the way to $39,574 by 2007. Clearly, labor productivity is the main determinant of the increase in potential real GDP per person. 7 End Caption per person. The blue line represents potential real GDP per person, the green line represents real GDP per person if hours per person remained at 1949 levels, and the red line represents potential real GDP per person if labor productivity remained at 1949 levels. If labor productivity remains constant at the 1949 level, then potential real GDP per person barely changes and is just $11,177 by 2007. However, if labor inputs remain constant at the 1949 level, then potential real GDP per person rises all the way to $39,574 by 2007. Clearly, labor productivity is the main determinant of the increase in potential real GDP per person. Problems with Real GDP per person as a Measure of the Standard of Living Real GDP per person is not a perfect measure of the standard of living, but it is likely the best measure that we have. As long as people use their income to purchase goods and services that make them better off, then the standard of living should increase with real GDP per person. Nevertheless, there are several objections to using real GDP per person as a measure of the standard of living that we consider in more detail: ο· Distribution of income ο· Value of leisure time ο· Happiness ο· Life Expectancy Distribution of Income 8 Real GDP per person is just an average — it tells you what the average person in the economy can consume. However, an average can be misleading because it does not tell you about the distribution of income. Table 5-2 illustrates this problem using an example of two people in two countries. Table 5-2 Income Distribution and Real GDP per Person Country 1 Country 2 Person 1 $50,000 $99,000 Person 2 $50,000 $1,000 GDP per Person $50,000 $50,000 In country 1, each person earns exactly $50,000 so GDP per person is $50,000 and tells you how many goods and services the typical person can consume. In this case, real GDP per person is a very good measure of the standard of living for the typical person. However, this approximation is not very good for country 2. In country 2, person 1 has an income of $99,000, and person 2 has an income of just $1,000. GDP per person is still $50,000, but person 1 can consume much more than that amount and person 2 can consume much less. Person 1 has a higher standard of living and person 2 has a lower standard of living than GDP per person indicates. Uneven distribution of income is important to keep in mind when using GDP per person as a measure of the standard of living for the typical person. However, also keep in mind that two analyses suggest that increases in real GDP per person make the poor better off. First, as real GDP per person for the world rose by 1.8 percent per year from 1981 to 2005, the number of 9 people living on less than $1.25 per day fell from 1.9 billion in 1981 to 1.4 billion in 2005.1 That represents a 26 percent decrease in the number of extremely poor individuals in just 24 years. Even if economic growth did not cause the decrease in poverty, economic growth and substantial decreases in poverty are compatible. Second, if all the gains from economic growth went to only those individuals at the top of the income distribution, then increases in GDP per person would have little benefit for those at the bottom of the income distribution. However, there is some evidence that the poor do benefit from economic growth just as much as the rest of society. David Dollar and Aart Kraay, economists with the World Bank, found that as real GDP per person increased by about one percent, the income of the individuals in the bottom 20 percent of the income distribution also increased by one percent.2 As an economy grows, there is a tendency for the incomes of the individuals in the bottom of the income distribution to rise. Therefore, the rich do not get richer at the expense of the poor. Figure 5-3 shows the relationship between the Figure 5-3 Relationship between Real GDP per Person and Average Income of Individuals in the Lower 20 Percent of the Income Distribution 1 Data come from the World Bank’s PovcalNet and are available at http://web.worldbank.org/WBSITE/EXTERNAL/EXTDEC/EXTRESEARCH/EXTPROG RAMS/EXTPOVRES/EXTPOVCALNET/0,,contentMDK:21867101~pagePK:64168427~pi PK:64168435~theSitePK:5280443,00.html. Data downloaded on May 6, 2009. 2 “Growth is Good for the Poor,” Journal of Economic Growth vol.7, no.3, (2002) pp.195-225. 10 SOURCE: Dollar and Kraay (2002). Data is available on the web at: http://econ.worldbank.org/WBSITE/EXTERNAL/EXTDEC/0,,contentMDK:20311740~pagePK: 64165401~piPK:64165026~theSitePK:469372,00.html#Growth__inequality_and_poverty Caption: As real GDP per person increases, the average income for individuals in the bottom 20 percent of the income distribution also increases. On average, when real GDP per person increases by one percentage point, the average income for individuals in the bottom 20 percent of the income distribution also increases by about one percentage point. Therefore, there is no tendency for inequality to increase as real GDP per person increases. We see a similar pattern when we look at individual countries and regions such as Africa, China, Japan, the United Kingdom and the United States. 11 End Caption real GDP per person and average income for the bottom 20 percent of the income distribution. As real GDP per person increases, the average income for individuals in the bottom 20 percent of the income distribution also increases. On average, when real GDP per person increases by one percentage point, the average income for individuals in the bottom 20 percent of the income distribution also increases by about one percentage point. Therefore, there is no tendency for inequality to increase as real GDP per person increases. We see a similar pattern when we look at individual countries and regions such as Africa, China, Japan, the United Kingdom and the United States. Value of Leisure Time Because real GDP per person measures the income of the average person in a country, it tells us how many goods and services the average person can consume. But people care about more than the goods and services they can purchase. For example, people want time to spend with their friends, their spouses, or their children. In other words, individuals also care about leisure time. If the large increases in the standard of living shown in Figure 5-1 came solely from increases in labor inputs, then the increase in real GDP per person would have come at the expense of less leisure time. Whether individuals are better off would therefore depend on the value of the lost leisure time relative to the value of the goods and services that individuals gained. 12 As we saw earlier, all of the increase in potential real GDP per person has come from increased productivity and average annual hours worked per person has remained essentially constant for the United States. Figure 5-4 shows average annual Figure 5-4 Annual Average Hours per worker hour in Western Countries, 1870 - 2000 SOURCE: Huberman and Minns (2007). Caption: As real GDP per person has increased, annual average hours per worker hour tends to decrease. So, leisure time tends to rise as real GDP per person increases. Hours per year for the average worker in the United States decreased from 3,096 hours per year in 1870 to 1,878 hours per year in 2000. That is, a 39.3 percent decrease in the amount of time working and a significant amount of extra time available for leisure activities such as being with friends and 13 family. All western nations experienced a similar decrease in average hours per worker hour. For example, hours per year for the average worker in France decreased from 3,168 in 1870 to 1,443 in 2000. The decrease in hours worked was larger outside of the United States, but average annual hours worked did decrease in the United States for reasons that we will explain in Chapter 7. End Caption hours of work per worker hour for several western countries: France, Germany, Italy, the United Kingdom, and the United States. Hours per year for the average worker in the United States decreased from 3,096 hours per year in 1870 to 1,878 hours per year in 2000. That is, a 39.3 percent decrease in the amount of time working and a significant amount of extra time available for leisure activities such as being with friends and family. All western nations experienced a similar decrease in average hours per worker hour. For example, hours per year for the average worker in France decreased from 3,168 in 1870 to 1,443 in 2000. The decrease in hours worked was larger outside of the United States, but average annual hours worked did decrease in the United States for reasons that we will explain in Chapter 7. Happiness Richard Easterlin of the University of Pennsylvania looks at results from nineteen different countries and concludes that there is little relationship between self-reported happiness in surveys and real GDP per person across countries or within a country.3 This lack of 3 “Does Economic Growth Improve the Human Lot? Some Empirical Evidence,” (1974) In Nation’s and Households in Economic Growth: Essays in Honor of Moses Abramowitz edited by Paul David and Melvin Reder. Academic Press. 14 correlation is called the Easterlin Paradox because happiness does not necessarily increase with incomes. Why the lack of relationship? Easterlin argues that individuals judge themselves relative to their peer groups. Therefore, if your income increases by 10 percent, but the income of all your peers also increases by 10 percent then you will not report yourself as any happier because you have not improved relative to your peers. However, if your income increases by 10 percent while everyone else’s income remains constant then you have improved relative to your peers so you will report yourself as happier.4 Because the increased real GDP per person does not lead to increased happiness, Easterlin argues that economists and policymakers place too much emphasis on economic growth. Richard Layard of the London School of Economics notes that at low levels of real GDP per person an increase in income does lead to increased happiness.5 However, he also argues that there is little relationship between average income and happiness once real GDP per person exceeds $15,000 per year. At low levels of income, economic growth produces vital goods and services like food, shelter, and clothing. However, once these basic necessities are met economic growth tends to produce luxuries that do not necessarily make individuals better off. For example, investment bankers and lawyers often work long hours and neglect their personal lives. They have little time to interact with spouses, children, or friends. In this example, the extra goods and services may come at the cost of less fulfilling personal lives. Once individuals reach a certain level of income, they begin to make judgments about their happiness based on their income relative to their peers rather than their absolute level of income. Therefore, an increase in income will not make a person happier if 4 “Will Raising the Incomes of All Increase the Happiness of All?” Journal of Economic Behavior and Organization (1995) pp.35-47. 5 “Happiness: Has Social Science a Clue?” Lionel Robbins Memorial Lecture 2002/2003, London School of Economics. Available at: http://cep.lse.ac.uk/events/lectures/layard/RL030303.pdf. 15 everyone else’s income increases by just as much. Absolute income is no longer important, but relative income is important. The Easterlin Paradox shows that money cannot buy happiness as the saying goes. Or does it? Justin Wolfers and Betsey Stevenson of the Wharton School at the University of Pennsylvania reexamined this issue using a wider range of countries.6 They find a robust positive relationship between self-reported happiness and GDP per person across 131 countries. In addition, Wolfers and Stevenson also find a positive relationship between economic growth and happiness within a country. Their work suggests that economic growth and higher absolute levels of income do make individuals happier. Life Expectancy Modern economic growth generates pollution. Consumers create air pollution by burning gasoline to power their cars and natural gas to heat their homes. Firms create air pollution when they produce electricity, pesticides, or plastics. This pollution affects the air we breathe, the water we drink, and the food we eat. Sometimes pollution is a minor irritant that spoils scenic views, but pollution can also contribute to dangerous diseases such as cancer. In addition, busy workers have less leisure time, which can create stress and negative health consequences, potentially shortening life spans. Therefore, the costs to higher real GDP per person might offset the benefits of the increase in the amount of goods and services that individuals can purchase. Does life expectancy decrease with real GDP per person? No. In fact, as real GDP per person 6 “Economic Growth and Subjective Well-Being: Reassessing the Easterlin Paradox” in Brookings Paper on Economic Activity (Spring 2008), 1-102. 16 increases, life expectancy at birth increases suggesting that health outcomes actually improve as real GDP per person increases. Figure 5-5 shows the relationship Figure 5-5 Relationship between Real GDP per Person and Life Expectancy at Birth, 2007 SOURCE: World Bank’s World Development Indicators Caption: There is a clear tendency for life expectancy to increase as GDP per person increases. When real GDP per person is $5,000 the life expectancy is 66.9 years and this rises to 74.1 years as real GDP per person increases to $15,000. However, if real GDP per person increases by another ten thousand dollars to $25,000 then life expectancy only increases to 77.4. Therefore, life expectancy increases at a decreasing rate with real GDP per person. Despite the pollution 17 costs associated with economic growth, the higher real GDP per person the longer the average person can expect to live. End Caption between life expectancy at birth and GDP per person for 185 countries in 2007. There is a clear tendency for life expectancy to increase as GDP per person increases. When real GDP per person is $5,000 the life expectancy is 66.9 years and this rises to 74.1 years as real GDP per person increases to $15,000. However, if real GDP per person increases by another ten thousand dollars to $25,000 then life expectancy only increases to 77.4. Therefore, life expectancy increases at a decreasing rate with real GDP per person. Despite the pollution costs associated with economic growth, the higher real GDP per person the longer the average person can expect to live. Part of the reason that pollution costs do not shorten life spans as real GDP per person increases is that a clean environment is a normal good, which means that individuals purchase more of it as their incomes increase. This idea lies behind the environmental Kuznets curve. The relationship depicted by the curve states that as an economy expands, pollution initially increases, reaches a maximum, and then begins to decline as individuals choose to spend more of their income on a cleaner environment. Therefore, rather than destroying the environment and reducing life expectancy, economic growth may improve the environment and increase life expectancy. As real GDP per person increases, individuals can also purchase more health care which should also increase life expectancy. 18 5.2 Use the Solow Growth Model to Explain the Effect of Capital Accumulation onLabor Productivity Labor productivity is the key determinant of real GDP per person and, therefore, the standard of living. In Chapter 4, we learned that capital accumulation and total factor productivity (TFP) are the primary determinants of the labor productivity. Therefore, if we want to understand why the standard of living increases over time, we need to understand capital accumulation and the determinants of total factor productivity. In this section, we discuss capital accumulation and assume that total factor productivity remains constant. Economists use the Solow growth model to explain how capital accumulation influences labor productivity. The model is named after Nobel Laureate Robert Solow of the Massachusetts Institute of Technology who developed the model during the 1950s.7 His work and this model has become the foundation for how economists think about economic growth. We work with the intensive form of the aggregate production function that we described in Chapter 4, in which y is potential real GDP per worker hour and k is capital per worker hour. Economists also call k the capital-labor ratio. As we saw in Chapter 4, potential real GDP per worker hour and the capital-labor ratio are related through the aggregate production function: (5.2) π¦ = π΄π πΌ , where α is capital’s share of income and A is total factor productivity. We learned in Chapter 4 that for the United States capital’s share of income equals 0.32 and that total factor productivity in 2007 was 9.4. Figure 5-6 shows: 7 Solow, Robert. “A Contribution to the Theory of Economic Growth,” Quarterly Journal of Economics, 70, (February 1956) pp.65-94. 19 Figure 5-6 The Aggregate Production Function for the United States, 2007 Caption: The capital-labor ratio for the United States was $144.94 per hour in 2007, and potential real GDP per worker hour was $46.36 per hour. The production function shows us what happens to labor productivity as the capital-labor ratio increases while keeping total factor productivity constant. If the capital-labor ratio increases to $174.94 per hour, then labor productivity increases to $49.24. The marginal product of the extra capital is $2.88 per hour. If the capital-labor ratio increases again by $30 to $204.94 per hour, then labor productivity also increases to $51.79 per hour. The marginal product of the extra capital is still positive but decreases to $2.56 per hour. Why does the marginal product of capital decrease? The marginal product of capital decreases due to diminishing marginal returns when total factor productivity is constant, so the contribution of capital accumulation to labor productivity growth eventually becomes zero. The fact that capital experiences diminishing marginal returns means that the 20 sustained increase in labor productivity and the standard of living that the United States and other countries have experienced must be due to factors other than capital accumulation such as total factor productivity growth. We will return to this issue later in the chapter. End Caption the aggregate production function for the United States. The capital-labor ratio for the United States was $144.94 per hour in 2007, and potential real GDP per worker hour was $46.36 per hour. The production function shows us what happens to labor productivity as the capital-labor ratio increases while keeping total factor productivity constant. If the capital-labor ratio increases to $174.94 per hour, then labor productivity increases to $49.24. The marginal product of the extra capital is $2.88 per hour. If the capital-labor ratio increases again by $30 to $204.94 per hour, then labor productivity also increases to $51.79 per hour. The marginal product of the extra capital is still positive but decreases to $2.56 per hour. Why does the marginal product of capital decrease? The marginal product of capital decreases due to diminishing marginal returns when total factor productivity is constant, so the contribution of capital accumulation to labor productivity growth eventually becomes zero. The fact that capital experiences diminishing marginal returns means that the sustained increase in labor productivity and the standard of living that the United States and other countries have experienced must be due to factors other than capital accumulation such as total factor productivity growth. We will return to this issue later in the chapter. Capital Accumulation and the Bath Tub Analogy 21 Labor productivity is the critical determinant of the standard of living. We learned in Chapter 4 that 41.7 percent of the labor productivity growth is due to capital accumulation. The Solow growth model helps explain capital accumulation. If you understand a bath tub, then you understand the essential elements of this model. Figure 5-7 shows a bath tub with water flowing into the tub through the faucet Figure 5-7 Capital Accumulation and the Bath Tub Analogy Water flowing into the bath tub Level of water in the bath tub Water flowing out of the bath tub Caption: Understanding the basics of capital accumulation are as simple as understanding why the level of water rises and falls in a bath tub. Investment per worker hour is the water flowing into the bath tub and the amount of investment necessary to keep the capital-labor ratio constant is water flowing out of the bath tub. The level of water in the bath tub is the capital-labor ratio. End Caption and water flowing out of the bath tub through the drain. The level of water is a stock variable because we measure it at a point in time, while the water flowing into and flowing out of the tub 22 are flow variables that are measured per time period. When is the level of water in the bath tub constant? The answer is simple. The level of the water in the tub is constant when the water flowing into the bath tub is exactly equal to the water flowing out of the bath tub. How does the level of water in the tub change? The level of water in the tub increases when the water flowing into the tub is greater than the water flowing out of the tub, and the level of water in the tub decreases when the water flowing out of the tub is greater than the water flowing into the tub. To apply the bath tub analogy to labor productivity, we just need to identify the stock and flow variables in the Solow growth model. The capital-labor ratio is the stock variable because we measure it at a point in time as the amount of capital goods per worker. As a reminder, the capital-labor ratio is defined as: πΎ π = πΏ, where K is the stock of capital goods and L is the labor force. The capital-labor ratio can change for one two reasons: either the capital stock changes or labor force changes. Investment and Water Flowing into the Bath Tub The level of water in the bath tub increases when water flows into the tub, but what causes the capital-labor ratio to increase? The capital-labor ratio increases when the stock of machines, tools, buildings, and roads increases. In other words, when households, firms, or the government purchase investment goods. For simplicity, we assume that the investment rate of for the economy, s, is a constant ratio between zero and one. Investment per worker hour, i, equals: (5.3) π = π π¦. 23 Figure 5-8 shows the investment rate for the United States from 1949 to 2008. During this Figure 5-8 The Investment Rate for the United States, 1949 - 2008 SOURCE: Bureau of Economic Analysis and Congressional Budget Office Caption: the private sector conducts the vast majority of investment activity in the United States. From 1949 to 2008, private sector investment averaged 16.0 percent of potential GDP while government investment averaged just 4.1 percent of potential real GDP. You should also notice a distinct decrease in the rate of government investment after the 1960s, from 6.5 percent in 1953 to 3.4 percent in 2008. End Caption period, the investment rate averaged 0.201 of potential GDP, so: 24 i = 0.201y for the United States. Figure 5-9 shows that the private sector conducts the vast majority of investment activity in the United States. From 1949 to 2008, private sector investment averaged 16.0 percent of potential GDP while government investment averaged just 4.1 percent of potential real GDP. You should also notice a distinct decrease in the rate of government investment after the 1960s, from 6.5 percent in 1953 to 3.4 percent in 2008. Remember that π¦ = π΄π πΌ , so: π = π (π΄π πΌ ), and for the United States, π = (0.201)(9.4π 0.32 ) = 1.89π 0.32 . Figure 5-9 shows how investment per worker hour changes as the capital-labor ratio increases. Figure 5-9 Investment per worker hour, Real GDP per worker hour, and the CapitalLabor Ratio 25 Caption: Notice that the investment function has the same general shape as the production function from Figure 4.6 (a) in Chapter 4. This similarity occurs because we have assumed a constant investment rate for the economy. Therefore, as the capital-labor ratio increases real GDP per worker hour also increases and that causes investment per worker hour to increase. However, because of diminishing marginal returns, the increase in investment per worker hour gets smaller and smaller as the capital-labor ratio increases. End Caption Notice that the investment function has the same general shape as the production function from Figure 4.6 (a) in Chapter 4. This similarity occurs because we have assumed a constant investment rate for the economy. Therefore, as the capital-labor ratio increases real GDP per 26 worker hour also increases and that causes investment per worker hour to increase. However, because of diminishing marginal returns, the increase in investment per worker hour gets smaller and smaller as the capital-labor ratio increases. The Role of the Financial Sector in Capital Accumulation Capital accumulation plays an important role in explaining labor productivity. But how do households, firms, and the government finance the purchase of new capital goods? This question highlights the importance of the financial sector because investment is often financed by funds obtained in financial markets. If Ford wants to build a new factory in the United States, then it is likely to obtain the funds in financial market by either borrowing or issuing new stock. Where do financial markets obtain the funds to finance Ford’s investment? Other individuals in the household, government, and foreign sectors have decided to save. When you save by putting some of your income in a savings account, this saving allows the bank to lend those funds toa household or a firm, like Ford, that wants to invest. Therefore, a well functioning financial market is essential for allowing households, firms, and the government to finance the investment expenditures that lead to higher labor productivity. Investment is the purchase of capital goods by households and firms, πΌ ππππ£ππ‘π , and the government, πΌ πΊππ£πππππππ‘ . Therefore, the total amount of capital goods purchased in an economy, I, is: πΌ ≡ πΌ ππππ£ππ‘π + πΌ πΊππ£πππππππ‘ . 27 The funds for purchasing these investment goods come from private savings, π ππππ£ππ‘π , government savings, π πΊππ£πππππππ‘ , and foreign sector savings, ππΉππππππ . Therefore, national savings, S, is: π ≡ π ππππ£ππ‘π + π πΊππ£πππππππ‘ + ππΉππππππ . Private saving equals household disposable income minus consumption expenditures. Therefore, a tax increase, a decrease in income, or an increase in consumption all lead to less private savings. If government saving is positive then the government runs a budget surplus, but if government saving is negative then the government runs a budget deficit. A budget surplus, like the United States had in the late 1990s, leads to higher national saving, all else equal. In contrast, the large budget deficits that the government expects to run from 2010 to 2019 means that national saving is lower. Foreign sector saving is the sum of saving by foreign households and foreign governments. When individuals in these sectors save, then there is a larger pool of funds available to finance investment expenditures. When we discussed the loanable funds model in Chapter 3, we learned that saving equals investment, so: πΌ = π, and πΌ ππππ£ππ‘π + πΌ πΊππ£πππππππ‘ = π ππππ£ππ‘π + π πΊππ£πππππππ‘ + ππΉππππππ . The results here are very similar to the results with the loanable funds model in Chapter 3. A budget deficit means government savings becomes negative. Unless private or foreign savings 28 increases to compensate, investment expenditures must decrease. Whether the budget deficit causes private or government investment expenditures to decrease depends on the circumstances. Similarly, if the household sector saves more and government and foreign savings remain constant, then investment expenditures must increase. Again, whether private or government investment expenditures increase depends on the circumstances. Break-Even Investment and Water Flowing out of the Bath Tub Break-even investment is the level of investment necessary to keep the capital-labor ratio constant. When investment is greater than the break-even level, the capital-labor ratio increases and when investment is less than the break-even level, the capital-labor ratio decreases. Two factors determine the break-even level of investment. First, the capital stock depreciates over time. We assume that the depreciation rate, d, is a constant fraction of the capital-labor ratio and that the depreciation rate is between zero and one, so: π·ππππππππ‘πππ = ππ. Second, the capital-labor ratio can decrease when the capital stock is constant and the number of workers increases. The capital-labor ratio decreases because the existing capital stock is spread across a larger labor force. You can think of this as the dilution of the existing capital stock. We use n to represent the growth rate of the labor force and n takes a value between zero and one, so: π·πππ’π‘πππ = ππ. Therefore, we can think of break-even investment as: (5.4) π΅ππππ πΈπ£ππ πΌππ£ππ π‘ππππ‘ = π·ππππππππ‘πππ + π·πππ’π‘πππ 29 = ππ + ππ = (π + π)π. Notice that break-even investment is just a constant fraction of the capital-labor ratio, so at higher levels of the capital-labor ratio the break-even investment is higher. For the United States, the growth rate of potential labor hours has averaged 1.2 percent or 0.012 per year from 1949 - 2008. The depreciation rate depends on the type of capital good. For example, buildings can last for decades while computers may only be useful for a few years so computers depreciate much more quickly than buildings. However, a depreciation rate of 10 percent or 0.10 is a common value to use. Hence, break-even investment for the United States is: Break-Even Investment = (0.10 + 0.012)k = 0.112k. When we graph the break-even investment line in Figure 5-10, we see that it is a straight line with Figure 5-10 Break-Even Investment and the Capital-Labor Ratio 30 Caption: The break-even investment line has a slope equal to the sum of the depreciation rate and the labor force growth rate. At higher levels of the capital-labor ratio, more investment is required to keep the capital-labor ratio constant, so the break-even level of investment is also higher. An increase in the depreciation or labor force growth rates leads to a steeper break-even investment line, while a decrease in the depreciation rate or labor force growth rates leads to a flatter break-even investment line. End Caption a positive slope equal to (d + n); at higher levels of the capital-labor ratio, more investment is required to keep the capital-labor ratio constant, so the break-even level of investment is also higher. An increase in the depreciation or labor force growth rates leads to a steeper break-even investment line, while a decrease in the depreciation rate or labor force growth rates leads to a flatter break-even investment line. 31 Equilibrium and the Steady State The change in the level of water in the bath tub equals the water flowing into the bath tub minus the water flowing out of the bath tub. For the level of water in the bath tub to remain constant, the water flowing into the tub must equal the water flowing out of the tub. Think of this as the equilibrium for the bath tub. In terms of the Solow growth model, the level of water is the capital-labor ratio so equilibrium occurs when the capital-labor ratio is constant. Economists call this equilibrium a steady state. A steady state is an equilibrium in which the capital-labor ratio and output per worker hour are constant, but capital, labor, and output are growing. The steady-state is the long-run equilibrium so if an economy is not at the steady-state then the economy will gradually move toward the steady state. To find the steady state, we first need to find an equation for the change in the capital-labor ratio and the change in the capital-labor ratio equals investment minus break-even investment: πΆβππππ ππ πππ£ππ ππ π€ππ‘ππ = πππ‘ππ ππππ€πππ ππ − π€ππ‘ππ ππππ€πππ ππ’π‘ πΆβππππ ππ πΆππππ‘ππ πΏππππ π ππ‘ππ = πΌππ£ππ π‘ππππ‘ − π΅ππππ ππ£ππ πΌππ£ππ π‘ππππ‘. We can express this relationship as, βπ = π − (π + π)π. If we plug in the relationship for investment per worker hour in equation (5.4) we get (5.5) βπ = π π¦ − (π + π)π = π (π΄π πΌ ) − (π + π)π. Equation (5.14) is the key equation for the Solow growth model because it tells us how the capital-labor ratio evolves over time and allows us to determine the equilibrium. We know that 32 βπ = 0 in the steady state. We can plug this fact into equation (5.10) to solve for the steadystate capital-labor ratio k* as: (5.6) π π΄ π ∗ = [π+π] 1⁄ (1−πΌ) . Using the aggregate production function, the steady state real GDP per worker hour is: (5.7) π¦∗ = π΄ πΌ⁄ 1⁄ (1−πΌ) [ π ] (1−πΌ) . π+π For the United States, the formula for the steady state values is 0.201π΄ 1.47 π ∗ = [ 0.112 ] = 2.36π΄1.47 and π¦ ∗ = 1.32π΄1.47 . (MD: Steady State An equilibrium in which the capital-labor ratio and output per worker hour are constant, but capital, labor, and output are growing. The steady-state is the long-run equilibrium so if an economy is not at the steady-state then the economy will gradually move toward the steady state.) Figure 5-11 shows both the investment and break-even Figure 5-11 Equilibrium in the Solow Growth Model 33 Caption: The investment curve and the break-even investment line intersect at point A. In the steady state, the capital-labor ratio is constant, so that the change in the capital-labor ratio is zero. This point occurs where the investment line intersects the break-even investment line at point A in Figure 5-12. At point A, the capital-labor ratio is $63.8 per worker hour and the levels of investment and break-even investment are $7.1 per worker hour. Suppose that the initial capitallabor ratio is $22 per worker hour which we label as π1 in Figure 5-12. At that capital-labor ratio, the level of investment, π1 , is $5.1 per worker hour and is greater than break-even investment, (π + π)π1, of $2.5 per worker hour. According to equation (5.8), βπ > 0 and the capital-labor ratio increases toward the steady state capital-labor ratio, π ∗ . Now suppose the initial capital-labor ratio is $125 per worker hour which we label as π2 in Figure 5-12. At that capital-labor ratio, the level of investment, π2 , is $8.9 per worker hour and is greater than break- 34 even investment, (π + π)π2 , of $14.0 per worker hour. According to equation (5.8), βπ < 0, and the capital-labor ratio decreases toward the steady-state capital-labor ratio, π ∗ . End Caption investment lines. In the steady state, the capital-labor ratio is constant, so that the change in the capital-labor ratio is zero. This point occurs where the investment line intersects the break-even investment line at point A in Figure 5-12. At point A, the capital-labor ratio is $63.8 per worker hour and the levels of investment and break-even investment are $7.1 per worker hour. The steady state at point A is stable because there is a built-in tendency for the economy to move toward the equilibrium. For example, suppose that the initial capital-labor ratio is $22 per worker hour which we label as π1 in Figure 5-12. At that capital-labor ratio, the level of investment, π1 , is $5.1 per worker hour and is greater than break-even investment, (π + π)π1, of $2.5 per worker hour. According to equation (5.8), βπ > 0 and the capital-labor ratio increases toward the steady state capital-labor ratio, π ∗ . The increase in the capital-labor ratio is the vertical distance between the investment and break-even investment lines. Notice that this vertical distance decreases as the capital-labor ratio increases. Why does this happen? As the economy accumulates more capital goods per worker hour, capital goods become less productive because of diminishing marginal returns. As a result, the extra output and investment that the economy receives from additional capital decreases as the economy accumulates more capital. The increase in the capital-labor ratio continues until βπ = 0, and that does not occur until the capital-labor ratio equals π ∗ . 35 Now suppose the initial capital-labor ratio is $125 per worker hour which we label as π2 in Figure 5-12. At that capital-labor ratio, the level of investment, π2 , is $8.9 per worker hour and is greater than break-even investment, (π + π)π2 , of $14.0 per worker hour. According to equation (5.8), βπ < 0, and the capital-labor ratio decreases toward the steady-state capital-labor ratio, π ∗ . The decrease in the capital-labor ratio is the vertical distance between the investment and break-even investment lines. Notice that this vertical distance decreases as the capital-labor ratio decreases due to diminishing marginal returns. Why does this happen? Once again it is due to diminishing marginal returns. As the economy reduces capital goods per worker hour, capital goods become more productive. As a result, the extra output and investment that the economy receives from additional capital increases as the economy reduces the capital-labor ratio. The decrease in the capital-labor ratio continues until βπ = 0, and that does not occur until the capital-labor ratio equals π ∗ . So, the steady-state is the equilibrium for the economy. We will come back to this point when we discuss the balanced growth path in the next section. The Investment Rate and Real GDP Per Worker Hour Now that we have an equilibrium model for the capital-labor ratio and real GDP per worker hour, we can ask what causes the equilibrium to change. Figure 5-12 shows what happens when the investment rate increases from 0.201, π 1 , to 0.302, π 2 . First, Figure 5-12 An Increase in the Investment Rate 36 Caption: An increase in the investment rate from 0.201 to 0.302 shifts the investment curve shifts upward from π 1 π¦ to π 2 π¦, so the economy is now producing more investment goods for any given level of the capital-labor ratio. Next, the capital-labor ratio increases. The level of investment is now greater than the level necessary to replace depreciation and provide the new workers with just as much capital as the existing workers. As a result, the capital-labor ratio begins to rise from the original steady-state value of $63.8, π1∗ , to the new steady-state value of $115.8, π2∗ . Because the capital-labor ratio is one of the inputs of the production function, the higher capital-labor ratio increases real GDP per worker-hour. So, the Solow growth model predicts that a higher investment rate will increase labor productivity from $35.5 dollars per worker hour, π¦1∗ , to $43.0 dollars per worker hour, π¦2∗ , and a higher standard of living. Notice that the increase in real GDP per worker hour eventually decreases to zero due to diminishing marginal returns to capital goods. 37 End Caption the investment curve shifts upward from π 1 π¦ to π 2 π¦, so the economy is now producing more investment goods for any given level of the capital-labor ratio. Next, the capital-labor ratio increases. The level of investment is now greater than the level necessary to replace depreciation and provide the new workers with just as much capital as the existing workers. As a result, the capital-labor ratio begins to rise from the original steady-state value of $63.8, π1∗ , to the new steady-state value of $115.8, π2∗ . Because the capital-labor ratio is one of the inputs of the production function, the higher capital-labor ratio increases real GDP per worker-hour. So, the Solow growth model predicts that a higher investment rate will increase labor productivity from $35.5 dollars per worker hour, π¦1∗ , to $43.0 dollars per worker hour, π¦2∗ , and a higher standard of living. Notice that the increase in real GDP per worker hour eventually decreases to zero due to diminishing marginal returns to capital goods. [Box Begins] Macro Data: The American Reinvestment and Recovery Act and Real GDP Per Person Congress passed and President Obama signed into law the American Reinvestment and Recovery Act in February 2009. The Act is designed to stimulate the economy in the short run, but it may have a negative long-run effect on labor productivity and the standard of living. The Congressional Budget Office estimates that the Act will reduce real GDP by between 0.0 percent 38 and 0.2 percent in 2019.8 Why is that? The Act will increase the budget deficit by $787 billion dollars, which the government is likely to pay for by borrowing. In other words, the government will run a budget deficit and government savings will decrease. Because investment expenditures equal saving, the investment rate should fall and the decrease in the investment rate should lead to a lower capital-labor ratio and a lower level of potential real GDP per worker hour. Figure 5-13 shows the effect of the decrease in the investment due to the borrowing Figure 5-13 The Long-Run Effect of the American Reinvestment and Recovery Act 8 ”Estimated Macroeconomic Impacts of the American Recovery and Reinvestment Act of 2009.” Letter from Douglas Elmendorf Director of the Congressional Budget Office to Senator Charles E. Grassley (Iowa). March 2, 2009. Available at: http://www.cbo.gov/ftpdocs/100xx/doc10008/03-02-Macro_Effects_of_ARRA.pdf. 39 Caption: The budget deficits will reduce government savings which will reduce the funds available to the private sector to invest. As a result the investment rate will decrease from s1 to s2 and the investment curve will shift downward from s1y to s2y. As a result, the steady-state capital-labor ratio will decrease from π1∗ to π2∗ and output per worker hour will decrease from π¦1∗ to π¦2∗ . Because workers will be less productive, potential real GDP will also decrease. End Caption associated with the American Reinvestment and Recovery Act. The budget deficits will reduce government savings which will reduce the funds available to the private sector to invest. As a result the investment rate will decrease from s1 to s2 and the investment curve will shift downward from s1y to s2y. As a result, the steady-state capital-labor ratio will decrease from π1∗ to π2∗ and output per worker hour will decrease from π¦1∗ to π¦2∗ . Because workers will be less productive, potential real GDP will also decrease. However, part of the funds from the Act will go to infrastructure and other investment projects for which the government is responsible. If the Act adds government investment dollars to balance off falling private investment dollars, the overall investment rate in the economy, and the investment curve, will shift down only slightly. The end result will be a relatively small decrease in potential real GDP per worker hour and potential real GDP. However, if the Act finances government consumption or investment projects with little or no value, then the investment rate for the economy will decrease and so will labor productivity and potential real GDP. The key point is that a deficit may reduce potential real GDP depending upon what the government does with the funds it borrows. See related problem XXX on page XXX. 40 [End Box] Depreciation, Labor Force Growth Rate, and Real GDP per worker hour Figure 5-14 shows what happens when the depreciation rate decreases. First, the breakFigure 5-14 A Decrease in the Depreciation Rate Caption: A decrease in the depreciation rate flattens the break-even investment line. Next, the capital-labor ratio increases for the same reason as we found when the investment rate increases; the level of investment is now greater than the level necessary to replace depreciation and provide the new workers with just as much capital as the existing workers. As a result, the capital-labor ratio begins to rise from the original steady-state value of π1∗ to the new steady-state value of π2∗ . Because the capital-labor ratio is one of the inputs of the production function, the higher capital-labor ratio increases potential real GDP per worker hour. Therefore, the Solow 41 growth model predicts that a lower depreciation rate will lead to higher productivity and higher standard of living. End Caption even investment line flattens. Next, the capital-labor ratio increases for the same reason as we found when the investment rate increases; the level of investment is now greater than the level necessary to replace depreciation and provide the new workers with just as much capital as the existing workers. As a result, the capital-labor ratio begins to rise from the original steady-state value of π1∗ to the new steady-state value of π2∗ . Because the capital-labor ratio is one of the inputs of the production function, the higher capital-labor ratio increases potential real GDP per worker hour. Therefore, the Solow growth model predicts that a lower depreciation rate will lead to higher productivity and higher standard of living. What about the growth rate of the labor force? Notice that the growth rate of the labor force and the depreciation rate both influence the slope of the break-even investment line in the same way. Therefore, a decrease in the labor force growth rate will have exactly the same effect on the standard of living as a decrease in the depreciation rate. Therefore, the Solow growth model predicts that a lower labor force growth rate will lead to higher productivity and higher standard of living. Solved Problem 5.1: A Decrease in the Labor Force Growth Rate and Real GDP per worker hour. According to the United Nation’s Population Division, the population growth rate 42 averaged 1.7 percent per year between 1950 and 2005. The following table shows the Population Division forecasts that the population growth rates for different regions in the world. Population Growth Rates across the World Period Africa Asia Europe North America South America World 1950 to 2005 2.6 1.9 0.5 2.2 1.2 1.7 2005 to 2050 1.7 0.6 -0.1 0.6 0.6 0.8 -1.3 -0.6 -1.6 -0.6 -0.9 Change in the Population Growth Rate -0.9 SOURCE: United Nations Population Division. The calculations are based upon the Median Variant forecast. The slower population growth rate should also reduce the growth rate of the labor force. What effect will this reduction have on labor productivity and the standard of living in the world? Solving the Problem: Step 1: Review the chapter material. The problem asks you to determine the effect of a decrease in the labor force growth rate on labor productivity and the standard of living, so you may want to review the section “Depreciation, Labor Force Growth Rate, and Real GDP per worker hour, “ which begins on page x. 43 Step 2: Use a graph to determine how a decrease in labor force growth rate influences the Solow growth model. The Solow growth model consists of three curves: the aggregate production function, the investment curve, and the break-even investment line. To determine the effect of a decrease in the labor force growth rate, we must determine which, if any, of these curves the labor force growth rate influences. Earlier we learned that the break-even investment line is (π + π)π so the slope of the break-even investment depends on the depreciation rate and the labor force growth rate. When the labor force growth rate decreases, the slope of the break-even investment line will decrease and the line will flatten or pivot downwards. The equation for the aggregate production function is π¦ = π΄π πΌ and equation the equation for the investment curve is π π¦ then you will see so that the labor force growth rate does not influence either of these curves. Therefore, the labor force growth rate influences only break-even investment. Your graph showing the effect of the decrease in the labor force growth rate should look like this: 44 Step 3: Determine the effect on the capital-labor ratio. The break-even investment line shifts downwards. At the initial capital-labor ratio, π1∗ , the level of investment, π π¦1∗ is greater than the new level of break-even investment, (π + π2 )π1∗ . Equation (5.14) tells us how the capital-labor ratio evolves over time. Using that equation and what we know about the current levels of investment and break-even investment: βπ = π π¦1∗ − (π + π2 )π1∗ > 0. As a result, the capital-labor ratio begins to increase towards the new steady-state capital-labor ratio, π2∗ . The change in the capital-labor ratio is the vertical distance between the investment curve and the break-even investment line. The vertical distance gets smaller as the capital-labor ratio increases due to diminishing marginal returns, so the increase in the capital-labor ratio gets 45 smaller and smaller as the world approaches the new steady state. Growth stops when the economy reaches the new steady state at point B. The steady state level of labor productivity has increased from π¦1∗ to π¦2∗ . Step 4: Determine the effect of the capital-labor ratio on the standard of living. Economists use real GDP per person to measure the standard of living, and equation (5.1) tells us that real GDP per person equals labor productivity multiplied by labor input. We measure labor input as average annual hours worked per person. If labor input remains constant, then the increase in labor productivity from π¦1∗ to π¦2∗ will increase the standard of living. The ultimate effect of the decrease in the population growth rate is to increase the standard of living for the average person in the world. The United Nations predicts that the population growth rate will decrease during the 2005 to 2050 period for all regions of the world. However, the table at the beginning of this Solved Problems shows that the decrease in the population growth rate will vary across regions of the world. For example, Africa is expected to have a population growth rate of 1.7 percent per year. Asia, North America, and South America are expected to have population growth rates of about 0.6 percent per year, but Europe is expected to have a negative population growth rate of -0.1 percent per year. The largest decrease in the population growth rate will occur in North America so, all else equal, you should expect that labor productivity and the standard of living increases from slower labor force growth rates will be highest in North America. 46 Your Turn: See related problem XXX on page XXX. ********************************************************************** Table 5-3 summarizes how changes in the Solow growth model change the steady-state Table 5-3 Summary of Changes in the Steady-State An increase in… will… …leading to …and the investment rate shift the investment curve up… an increase in the capital-labor ratio increase potential real GDP per worker hour. the level of total factor productivity … shift the investment curve up… an increase in the capital-labor ratio increase potential real GDP per worker hour. the depreciation rate… shift the break-even investment live up a decrease in the capital-labor ratio a decrease in potential real GDP per worker hour. the labor force growth rate… shift the break-even investment live up a decrease in the capital-labor ratio a decrease in potential real GDP per worker hour. potential real GDP per worker hour. Increases in the investment rate and total factor productivity lead to higher real GDP per worker hour in the steady-state while increases in the depreciation rate and the growth rate of the labor force lead to lower real GDP per worker hour in the steady state. 5.3 Explain how Total Factor Productivity Affects Labor Productivity 47 Total factor productivity measures the overall efficiency of the economy in transforming capital and labor into final goods and services that households can consume. Total factor productivity growth, along with capital accumulation are the two sources for increases in labor productivity. We just learned that increases in labor productivity from capital accumulation eventually decrease to zero due to diminishing marginal returns. As a consequence, total factor productivity is the ultimate source of labor productivity growth and, hence, the increase in the standard of living. Total Factor Productivity and Real GDP per worker hour Figure 5-15 shows the effect of an increase in total factor productivity for the United Figure 5-15 An Increase in Total Factor Productivity 48 Caption: For the United States in 2007, total factor productivity is initially 9.4 and the capitallabor ratio is $144.9 per hour so potential real GDP per worker hour is $46.4 and the economy is at point A in Figure 5-16. If the capital-labor ratio remains constant and total factor productivity increases by one point to 10.4 then the production function shifts up and the economy is now at point B, so that at any given capital-labor ratio, real GDP per worker hour increases to $51.3 per hour. In this example, an increase in total factor productivity has a similar effect as an increase in the investment rate. But there is an important difference. The marginal product of capital decreases as the economy accumulates more capital holding all else constant, but the extra output from increasing total factor productivity does not. If total factor productivity increases to by another point to 11.4 then the economy moves to point C and potential real GDP per worker hour increases to $56.2. Therefore, each time total factor productivity increases by one point, potential real GDP per worker hour increases by $4.9. In contrast to capital goods, there are no diminishing marginal returns for total factor productivity. Therefore, there is no limit to growth from increases in total factor productivity and total factor productivity growth must be the explanation for increases in labor productivity and the standard of living. End Caption States in 2007 assuming that the capital-labor ratio equals $144.9 per hour. Total factor productivity is initially 9.4 so potential real GDP per worker hour is $46.4 and the economy is at point A in Figure 5-16. If the capital-labor ratio remains constant and total factor productivity increases by one point to 10.4 then the production function shifts up and the economy is now at point B, so that at any given capital-labor ratio, real GDP per worker hour increases to $51.3 per hour. In this example, an increase in total factor productivity has a similar effect as an increase 49 in the investment rate. But there is an important difference. The marginal product of capital decreases as the economy accumulates more capital holding all else constant, but the extra output from increasing total factor productivity does not. If total factor productivity increases to by another point to 11.4 then the economy moves to point C and potential real GDP per worker hour increases to $56.2. Therefore, each time total factor productivity increases by one point, potential real GDP per worker hour increases by $4.9. In contrast to capital goods, there are no diminishing marginal returns for total factor productivity. Therefore, there is no limit to growth from increases in total factor productivity and total factor productivity growth must be the explanation for increases in labor productivity and the standard of living. New technology is one source of higher total factor productivity. If a new technology is discovered that increases the processing power of computers, then total factor productivity would increase from A1 to A2. The production function would shift upward and real GDP per worker hour would increase. Similarly, if a second technology is discovered that reduces congestion on the internet, then the productivity of all existing computers would increase so total factor productivity would increase from A2 to A3. The production function would again pivot upward and real GDP per worker hour would increase again. What effect does an increase in total factor productivity have on the steady-state values of the capital-labor ratio and potential real GDP per worker hour? Figure 5-16 shows the effect of a one-time Figure 5-16 A One-Time Increase in Total Factor Productivity 50 Caption: The one-time increase in total factor productivity shifts the production function from π΄1 π 0.32 to π΄2 π 0.32 . At the initial capital-labor ratio, investment, π΄2 (π1∗ )0.32 , is now greater than break-even investment. As a result, the capital-labor ratio increases and this causes potential real GDP per worker hour to increase and the steady state to move from point A to point B. End Caption increase in total factor productivity. The one-time increase in total factor productivity shifts the production function from π΄1 π 0.32 to π΄2 π 0.32 . At the initial capital-labor ratio, investment, π΄2 (π1∗ )0.32 , is now greater than break-even investment. As a result, the capital-labor ratio increases and this causes potential real GDP per worker hour to increase and the steady state to move from point A to point B. 51 In fact, the growth rate of total factor productivity, gA, is the key determinant for labor productivity growth and the growth rate of the standard of living when labor inputs per person are constant. Table 5-4 Table 5-4 Steady-State Growth Rates Variable Symbol Capital-labor ratio Potential real GDP per worker hour Steady-State Growth Rate π≡ πΎ πΏ 1 ( )π 1−πΌ π΄ π¦≡ π πΏ 1 ( )π 1−πΌ π΄ Capital Stock πΎ≡ππ₯πΏ 1 ( )π + π 1−πΌ π΄ Potential real GDP π≡π¦π₯πΏ 1 ( )π + π 1−πΌ π΄ shows the steady-state growth rates for the capital-labor ratio and potential real GDP per worker hour when the hours per person (labor input) is constant. The appendix at the end of the chapter shows the how to derive the steady-state growth rates. For the United States, capital’s share of income, α, is 0.32. TFP growth has averaged 0.0125 or 1.25 percent per year and the growth rate of potential labor hours, n, averaged 0.0121 or 1.21 percent per year. So, for the United States: 1 ππ = ππ¦ = (1−0.32) 0.0125 = 0.0184 or 1.84 percent per year, and 1 ππΎ = ππ = (1−0.32) 0.0125 + 0.0121 = 0.0305 or 3.05 percent per year. 52 Labor productivity increases by about 1.84 percent per year, and if labor inputs per person are constant, then potential real GDP per person also grows at about 1.84 percent per year. Similarly, when labor inputs per person are constant, potential labor hours grow at about 1.21 percent per year so potential real GDP grows at about 3.05 percent per year. What Explains Differences in TFP? Now that we know that TFP growth is the key factor behind labor productivity growth and the growth rate of the standard of living, we need to determine why TFP increases over time. Economists have spent a tremendous amount of time trying to answer this question. Although no single theory has emerged, economists have identified several important factors, which we discuss next. Research and Development and the Level of Technology As we mentioned in Chapter 4, total factor productivity measures the overall efficiency of the economy in transforming inputs into real GDP. One of the most important factors influencing total factor productivity is the stock of knowledge that the world possess and the associated level of technology. The invention of computers made workers more productive by giving them new and better types of capital goods to work with. For example, word processors allow one administrative assistant today to do work that would have taken a team of administrative assistants in 1949. Assembly line workers in automobile plants now operate and oversee robots rather than doing the manual labor themselves. As a result, one worker today can produce many more automobiles than a team of workers could in 1949. In both examples, the new capital goods has made labor more productive. 53 New capital goods do not just appear out of thin air. Private firms and the government devote a significant amount of resources to research and development (R&D) activities to come up with ideas for new capital goods or new goods and services for consumption. A considerable amount of the economy’s resources are devoted to discovering and testing these new ideas. The Commerce Department calculates that the United States conducted $317 billion worth of R&D in 2004, with the private sector responsible for $209 billion of R&D and the government responsible for the remaining $108 billion of R&D. [Begin Box] Research and Development Expenditures and Labor Productivity Differences between China and the United States On page xx we saw that labor productivity in the United States was 6.3 times higher than in China. Because of the higher labor productivity, the United States is able to maintain a higher standard of living. Part of the reason the United States has a higher level of labor productivity is that the United States devotes more resources to develop new technology and accumulate human capital. For example, in 2004 (the most recent year data is available for both countries) the United States devoted 2.6 percent of GDP to research and development while China devoted just 1.2 percent and as recently as 1996 China devoted just 0.6 percent of GDP research and development. The higher level of investment in new technology helps increase knowledge and total factor productivity so U.S. workers remain more productive. SOURCE: World Development Indicators, the World Bank. [End Box] 54 H3: Quality of Labor The quality of labor, like the quality of capital goods, can change over time. Workers become more skilled as they acquire human capital. Human capital is the accumulated knowledge and skills that workers acquire from education and training or from life experiences. There are two basic ways for workers to acquire human capital. (MD: Human Capital The accumulated knowledge and skills that workers acquire from education and training or from life experiences.) First, a worker can go to school for formal training to learn basic skills that are useful in the workplace. Students go to school to learn science, math, and other subjects that make them better workers. And as students learn and acquire new skills, their human capital increases, and they become more productive workers. Through this learning, education transforms low-skilled high school graduates into high-skilled engineers and scientists. Second, as Nobel Laureate Kenneth Arrow of Stanford University points out, workers can accumulate skills through learning by doing.9 Arrow argued that the more workers perform a task, the more they learn about how to do the task quickly — thereby improving their productivity in doing the task. Arrow cited evidence from engineering studies showing that the amount of time it takes to build an airplane decreases as workers build more airplanes. This relationship emerges because the workers have acquired knowledge and skills through building the previous airplanes, making them more productive. 9 “Economic Implications of Learning by Doing,” The Review of Economic Studies (June 1962), pp.155-173. 55 H3: Government and Social Institutions Nobel Laureate Douglass North of Stanford University and economist Robert Thomas of the University of Washington have emphasized the importance of government and social institutions in explaining differences in labor productivity and the standard of living across countries.10 North and Thomas, and many other economists, believe that markets and property rights are important institutions that lead to economic growth. Individuals and firms are unlikely to risk their own funds, and investors are unlikely to lend their funds to individuals and firms, unless they can keep the profits from risky investment projects. In other words, property rights must be secure to encourage investment and capital accumulation. In some countries, property rights are not secure due to government corruption because it is impossible for individuals and firms to start or expand businesses without paying bribes to at least one government official. Historical evidence suggests that government institutions and property rights do matter. After Germany’s defeat in World War II and the onset of the Cold War between the United States and the Soviet Union, Germany was divided into West Germany which was a parliamentary democracy with a market economy and secure property rights and East Germany which was a communist dictatorship without a strong market or secure property rights. Both East and West Germany were devastated by World War II. The two countries were reunified into a single country in 1990 and at the time of reunification real GDP per person in then West Germany was 2.6 times the level of real GDP per person in East Germany. The case of North and South Korea provides a second example of the importance of government institutions. Japan had occupied the Korean peninsula during World War II, but after Japan’s surrender Soviet 10 The Rise of the Western World: A New Economic History. Cambridge University Press (1973). 56 troops occupied what would become North Korea while U.S. troops occupied what would become South Korea. Just like East Germany, North Korea was a communist dictatorship without strong markets or secure property rights while South Korea had strong markets and secure property rights. While economic data for North Korea are unreliable because the North Korean government does not make official data available, the CIA Fact Book estimates that real GDP per person for South Korea was 14.4 times the level in North Korea in 2008. Economists Daron Acemoglu of MIT, Simon Johnson of MIT, and James Robinson of the University of California at Berkeley tried to find systematic evidence showing the effect of government and social institutions on real GDP per person.11 European countries colonized large regions of the world between the 1600s and the 1800s. In countries such as the United States, Australia and New Zealand, Europeans came as settlers and established institutions that enforced the rule of law. These favorable institutions encouraged investment which led to faster economic growth and higher real GDP per person. However, in Africa and other areas European countries did not come as settlers. Instead, the Europeans came to extract natural resources and so did not establish government institutions that favored investment. The areas of the world in which the Europeans established strong property rights are generally rich today while the regions in which Europeans did not establish strong property rights are generally not rich. The experiences of the Germany, Korea, and the former European colonies have convinced many economists that government institutions play a critical role in encouraging economic growth. 11 “The Colonial Origins of Comparative Development: An Empirical Investigation,” American Economic Review (December 2001), pp. 1369-1401. 57 Geography Not all economists today agree with the primary importance of institutions for explaining the standard of living. In fact, as long ago as Adam Smith’s 1776 book An Inquiry into the Nature and Causes of the Wealth of Nations, economists have pointed out that geography influences a nation’s natural resources. For example, access to navigable rivers and coast line makes trade easier and should increase labor productivity and the standard of living. For example, the United States has a large coast line and extensive navigable rivers while countries such as Bolivia and Tibet are landlocked and mountainous so transportation is difficult. However, Jeffrey Sachs of Columbia University argues that geography plays an important role in economic growth for another reason. Sachs, along with economists Andrew Mellinger and John Gallup, argues that tropical climates experience higher rates of infectious disease such as malaria.12 The countries that are poor today are often the countries with high rates of infectious disease, such as malaria, in the past. Infectious disease influence health especially for infants and young children, and these health problems can influence the labor productivity later in life. For example, children with serious childhood illnesses often grow up to be shorter than other children. If someone is short due to extensive childhood illness or nutritional deficiency as a child then they are often not as physically strong as they otherwise would have been. As a result, workers who are shorter due to physical illness often make them less productive agricultural workers. This adverse link may explain why agricultural productivity is lower in tropical areas, such as Burundi, Malawi, Uganda and Zambia. Low agricultural productivity makes famines 12 “Climate, Coastal Proximity, and Development,” in Oxford Handbook of Economic Geography. Oxford University Press (2000). 58 more likely, with a further negative effect on health, labor productivity, and the standard of living. The Financial System The role of the financial system is to match borrowers with lenders and so the financial system helps the economy allocate resources. When the financial system works well, individuals who want to borrow to finance the accumulation of physical or human capital can find someone willing to lend them funds. To the extent that firms and the government fund R&D with funds obtained in the financial system, a well-functioning financial system also supports R&D activities and can therefore lead to more investment in physical capital, human capital, and R&D. The financial system can also influence the efficiency of the economy, which means can influence total factor productivity. The financial system allocates funds to the individuals who are willing to pay the most to obtain the funds in the form of interest. These individuals are also those whose investment projects have the best likelihood of success. Therefore, a good financial system ensures that resources flow to their most productive uses, and total factor productivity for the economy increases. As a consequence, labor productivity and the standard of living are higher. Research by Thorsten Beck of the World Bank, Ross Levine of the University of Minnesota, and Norman Loayza of Central Bank of Chile concludes that the financial system does have a significant effect on total factor productivity growth.13 Interestingly, it is not just banks that matter for economic growth. Ross Levine and Sara Zervos of the World Bank find 13 “Finance and the Sources of Growth,” Journal of Financial Economics (2000) pp. 261-300. 59 that stock market liquidity also influences productivity and capital accumulation.14 The more liquid a stock market, the easier it is for investors to sell stocks in a company that they no longer want. Because stocks are easier to sell when people do not want to hold them, they are more likely to purchase the stock in the first place. As a consequence, stock prices are higher, and it is less costly for firms to issue new stock to pay for investment projects. The research by Ross Levine and others on financial markets tells us that the development of financial markets plays an important role in sustaining economic growth in both developed and developing economies. [Begin Box] Chinese Economic Reforms of 1978 Economic research and history tells us that government institutions are important determinants of economic growth and the standard of living. Figure 5-1 on page xx shows that economic growth accelerated in China starting in the late 1970s at about the time that China instituted a number of major economic reforms in 1978. Prior to the reforms China was a communist nation without secure property rights so markets in China were relatively limited and unimportant. For example, agricultural workers had to turn over everything that they produced to the Chinese government which then distributed the food to its citizens. The Chinese government also placed severe restrictions on foreign firms and individuals that wanted to purchase financial assets or physical assets in China. The economic reforms changed this. The initial reforms opened China to international trade and investment which allowed foreign technology to flow into China more easily and so should have increased total factor productivity. The initial reforms also allowed 14 “Stock Markets, Banks, and Economic Growth,” American Economic Review (June 1998) pp.537-558. 60 agricultural farmers to sell some of their crops in a market and keep the proceeds from the sales. This reform provided agricultural workers with a financial incentive to worker harder and so should have increased total factor productivity. The reforms accelerated in the 1980s and 1990s to allow a greater role for the market which has allowed total factor productivity and real GDP per person to increase rapidly in China since the late 1970s. [End Box] 5.4 Explain the Balanced Growth Path and Convergence and the Long-Run Equilibrium The steady-state is the equilibrium for the economy; however, it is an equilibrium in which the key economic quantities such as potential real GDP and potential real GDP per worker hour are growing. Therefore, you can think of an economy as having an equilibrium time path for key quantities such as potential real GDP and potential real GDP per worker hour. When the economy is in the steady state it is on the balanced growth path. The balanced growth path is the time path for the economy when it is in the steady state. Therefore, along the balanced growth path the capital-labor ratio and potential real GDP per worker grow at the same rate and the capital stock and potential real GDP grow at the same rate. Understanding the equilibrium time path is critical for understanding the long-run behavior of potential real GDP and potential real GDP per worker hour. 61 (MD: Balanced Growth Path The time path for the economy when it is in the steady state. Therefore, along the balanced growth path the capital-labor ratio and potential real GDP per worker grow at the same rate and the capital stock and potential real GDP grow at the same rate.) When the economy is on the balanced growth path, the economy is also in the steady state. Therefore, to determine the growth rate of potential real GDP per worker hour and potential real GDP along the balanced growth path, we start by looking at the steady state. π π΄ Equations (5.6) and (5.7) tell us that the steady-state value capital-labor equals [π+π] that the steady-state potential real GDP per worker hour is πΌ⁄ 1⁄ π (1−πΌ) (1−πΌ) π΄ [π+π] . 1⁄ (1−πΌ) and In the steady state, the rates of investment, depreciation, and labor force growth along with capital’s share of income are all constant. However, if total factor productivity is growing then the capital-labor ratio and potential real GDP per worker hour are growing. Table 5-4 on page xx shows they both 1 1 grow at the rate of (1−πΌ) ππ΄ in the steady state which means they grow at the rate of (1−πΌ) ππ΄ 1 along the balanced growth path. Since (1−πΌ) ππ΄ is the growth rate along the balanced growth 1 path, (1−πΌ) ππ΄ is also the slope of the balanced growth path for potential real GDP per worker hour and real GDP per person. The capital stock is just the capital-labor ratio times the amount of worker hours in the economy and potential real GDP is just potential real GDP per worker hour times the amount of worker hours the economy employs. Therefore, the steady-state capital stock equals π π΄ πΏ [π+π] 1⁄ (1−πΌ) and the steady-state potential real GDP equals 62 πΌ⁄ 1⁄ π (1−πΌ) (1−πΌ) πΏπ΄ [π+π] . As Table 5-4 on page xx shows the steady-state growth rates of the capital stock and potential real GDP depends on the growth rates of the labor force and the total factor productivity. Table 5-4 on 1 page xx shows they both grow at the rate of [(1−πΌ) ππ΄ + π ] in the steady state which means they 1 1 grow at the rate of [(1−πΌ) ππ΄ + π ] along the balanced growth path. Since [(1−πΌ) ππ΄ + π ]is the 1 growth rate along the balanced growth path, [(1−πΌ) ππ΄ + π ] is also the slope of the balanced growth path for potential real GDP. Figure 5-1 on page xx shows that the growth rates for the United Kingdom, the United States and the entire world have been roughly constant since 1820 which suggests these countries and the world are on or near the balanced growth path. Just as the steady state is the equilibrium for the economy, the balanced growth path is the equilibrium for the economy so there is a built in tendency for the economy to return to the balanced growth path after an event pushes the economy off the balanced growth path. However, some countries such as Japan and China look like they are off the balanced growth path for extended periods of time. This can occur when either the balanced growth path changes or when the balanced growth path is constant, but some event knocks the economy off the balanced growth path. When the economy is in the steadystate, the economy is also on the balanced growth path. Therefore, if the steady-state is constant, then the balanced growth path has not changed. However, when the steady-state changes the balanced growth path will change. The experiences of Germany and Japan after World War II provide a good example of how an economy that is off its balanced growth path eventually converges back to the balanced growth path. During the end of World War II, both Germany and Japan experienced a large 63 decrease in the capital-labor ratio as the United States and its allies bombed the factories, bridges, and transportation networks in both countries. Figure 5-17 shows real GDP per person over time for both Germany Figure 5-17 Post World War II Convergence in Germany and Japan SOURCE: Angus Maddison Caption: Germany and Japan experience a large decrease in real GDP per person at the end of World War II that you would expect due to the destruction of the capital stock. However, after the War both countries grew much more rapidly than before the War. Germany grew rapidly from the end of the War until about 1960. After 1960, Germany appears to grow at the same rate 64 as it was prior to the War. In fact, Germany appears to be on the same growth path after 1960 as it was before World War II. Japan had a similar experience. Japan grew rapidly from the end of the War until the mid 1970s, but appears to move to a higher balanced growth path compared to the one it was on before World War II. End Caption and Japan. Both countries experience a large decrease in real GDP per person at the end of World War II that you would expect due to the destruction of the capital stock. However, after the War both countries grew much more rapidly than before the War. Germany grew rapidly from the end of the War until about 1960. After 1960, Germany appears to grow at the same rate as it was prior to the War. In fact, Germany appears to be on the same growth path after 1960 as it was before World War II. Japan had a similar experience. Japan grew rapidly from the end of the War until the mid 1970s, but appears to move to a higher balanced growth path compared to the one it was on before World War II. Because Japan moved to a higher balanced growth path, the steady-state capital-labor ratio and potential real GDP per worker hour must have increased. Why do countries return to the balanced growth path? We can use the Solow growth and the experiences of Germany and Japan to explain why. Using Germany as our example, Figure 5-18 shows the effect of the Figure 5-18 The Solow Growth Model and Post-World War II Convergence in Germany 65 3. As a result, investment is greater than the break-even level of investment so the capitallabor ratio and real GDP per worker hour converge to the steady-state values. Production Function π¦∗ Break-Even Investment Line A π¦1945 Investment Function π π¦1945 1. Prior to World War II Germany is in the steady state so it is on the balanced growth path. 2. The United States and its allies bomb Germany which decreases the capital-labor ratio and causes potential real GDP per worker hour to decrease. (π + π)π1945 π∗ π1945 Capital-Labor Ratio Caption: Germany starts off in the steady state at point A prior to World War II. Since Germany is in the steady state, Germany is also on the balanced growth path so the capital-labor ratio and 1 potential real GDP per worker hour both grow at rate (1−πΌ ) ππ΄ . Towards the end of the War, the Soviet Union, United Kingdom, and United States bombed German factories, bridges and transportation networks which destroyed large portions of the German capital stock. As a result, the capital-labor ratio decreased from π ∗ to π1945 and real GDP per worker hour decreased from π¦ ∗ to π¦1945 . The decrease in labor productivity caused the decrease in potential real GDP per person at the end of World War II that we see in Figure 5-17. Total factor productivity 66 continued to grow in Germany which caused potential real GDP per worker hour and real GDP per person to grow. However, now that the capital-labor ratio had fallen to π1945 , the German economy grew for an additional reason: it accumulated capital more quickly than along the balanced growth path. At π1945 , the level of investment, π π¦1945, was greater than the break-even level of investment, (π + π)π1945 so the capital-labor ratio increased towards the steady state value of π ∗ . From 1945 to 1960, the capital-labor ratio in Germany was increasing for two reasons. First, total factor productivity growth was positive so the growth rate of the capitallabor ratio along the balanced growth path was positive. Second, Germany was converging from the capital-labor ratio of π1945 towards the steady-state capital-labor ratio of π ∗ . Since the growth rate of the capital-labor ratio determines the growth rate of potential real GDP per worker hour, the growth rate of real GDP per worker hour also had two sources: balanced growth due to total factor productivity growth and growth due to the convergence of π¦1945 to π¦ ∗ . End Caption destruction of the capital stock on potential real GDP per worker hour. Germany starts off in the steady state at point A prior to World War II. Since Germany is in the steady state, Germany is also on the balanced growth path so the capital-labor ratio and potential real GDP per worker 1 hour both grow at rate (1−πΌ ) ππ΄ . Towards the end of the War, the Soviet Union, United Kingdom, and United States bombed German factories, bridges and transportation networks which destroyed large portions of the German capital stock. As a result, the capital-labor ratio decreased from π ∗ to π1945 and real GDP per worker hour decreased from π¦ ∗ to π¦1945 . The decrease in labor productivity caused the decrease in potential real GDP per person at the end of World War II that we see in Figure 5-17. Total factor productivity continued to grow in 67 Germany which caused potential real GDP per worker hour and real GDP per person to grow. However, now that the capital-labor ratio had fallen to π1945 , the German economy grew for an additional reason: it accumulated capital more quickly than along the balanced growth path. At π1945 , the level of investment, π π¦1945 , was greater than the break-even level of investment, (π + π)π1945 so the capital-labor ratio increased towards the steady state value of π ∗ . From 1945 to 1960, the capital-labor ratio in Germany was increasing for two reasons. First, total factor productivity growth was positive so the growth rate of the capital-labor ratio along the balanced growth path was positive. Second, Germany was converging from the capital-labor ratio of π1945 towards the steady-state capital-labor ratio of π ∗ . Since the growth rate of the capital-labor ratio determines the growth rate of potential real GDP per worker hour, the growth rate of real GDP per worker hour also had two sources: balanced growth due to total factor productivity growth and growth due to the convergence of π¦1945 to π¦ ∗ . In general, we can think of the growth rate of potential real GDP per worker hour as: ππ¦ = (ππππππππ ππππ€π‘β πππ‘π) + (ππππ€π‘β ππππ ππππ£πππππππ) As long as the capital-labor ratio is less than π ∗ growth from convergence is positive so the German economy is growing more rapidly than it does along the balanced growth path. Therefore, potential real GDP per worker hour converged towards π¦ ∗ so real GDP per person converged towards the balanced growth path. However, if an economy starts off with a capitallabor ratio that is greater than π ∗ then the capital-labor ratio will decrease over time so growth from convergence will be negative. As a result, the economy will grow more slowly than along the balanced growth path so potential real GDP per worker will converge to the balanced growth path. 68 The experience of Germany is consistent with Germany returning to the pre-World War II steady state and so the pre-World War II balanced growth path. However, Japan looks like it converged toward a higher balanced growth path. This is consistent with an increase in the steady-state capital-labor ratio and potential real GDP per worker hour in Japan. Question xx on page xxx asks you to explain how this could occur. [Begin Box] Making the Connection: When will China’s Standard of Living Exceed the U.S. Standard of Living In 2008, the real GDP per person was 5.5 times higher than that of China’s. However, the growth rate of real GDP per person has averaged 7.0 percent per year in China since the start of economic reforms in 1978 while the growth rate of real GDP per person in the United States has averaged just 1.9 percent per year over the same time period. Since China the standard of living in China is growing more rapidly than in the United States, eventually China’s standard of living will catch up to and exceed the U.S. standard of living. At those rates of growth, the Chinese standard of living will exceed the U.S. standard of living in the year 2043. However, what we have learned about economic growth gives us very good reasons to think that, just like Germany and Japan, China will not be able to sustain these rapid growth rates for the indefinite future. The growth rate of real GDP per person along the balanced growth path is determined by the growth rate of total factor productivity. For China to maintain its high rates of growth in real GDP per person, China would have to maintain high rates of growth for total factor productivity, but that is unlikely. First, the United States investments more in activities such as research and 69 development which result in new technologies and increase total factor productivity. Second, much of China’s growth is likely due to the transition from a communist to a market economy so China’s growth rate is likely to decrease as the transition is completed. It is probably best to think of the transition to a market economy as moving China’s balanced growth path higher. The high rates of growth in real GDP per person are due to convergence to the higher growth path. As China approaches the new higher balanced growth path, we would expect China’s growth rate to decrease to a more sustainable rate. SOURCE: Penn World Tables [End Box] Figure 5-19 shows what the time paths of real GDP per person would look like for an Figure 5-19 Potential Time Paths for Real GDP per Person Natural logarithm of real GDP per person Time path for a country initially above the balanced growth path Balanced growth path Time path for a country initially below the balanced growth path Time 70 Caption: If an economy is on the balanced growth path then it remains on the path until an event moves the economy off the path. When the economy is on the balanced growth path, the growth rate of potential real GDP per person is determined by the growth rate of total factor productivity. If an economy starts off below the balanced growth path then growth from convergence is positive so the economy grows faster than it would along the balanced growth path and eventually converges to the balanced growth path. If an economy starts off above the balanced growth path then growth from convergence is negative so the economy grows slower than it would along the balanced growth path and eventually converges to the balanced growth path. End Caption economy on the balanced growth path initially, an economy initially below the balanced growth path, and for an economy initially above the balanced growth path. If an economy is on the balanced growth path then it remains on the path until an event moves the economy off the path. When the economy is on the balanced growth path, the growth rate of potential real GDP per person is determined by the growth rate of total factor productivity. If an economy starts off below the balanced growth path then growth from convergence is positive so the economy grows faster than it would along the balanced growth path and eventually converges to the balanced growth path. If an economy starts off above the balanced growth path then growth from convergence is negative so the economy grows slower than it would along the balanced growth path and eventually converges to the balanced growth path. 71 Answering the Big Question What we learned in this chapter helps answer two Big Questions from Chapter 1: Big Question 1: Why has the standard of living increased over the last two hundred years? Big Question 2: Why have some countries failed to achieve sustained economic growth? The standard of living has increased because increases in TFP have driven labor productivity higher. Higher labor productivity then leads to a higher standard of living. A well-functioning financial system and a government that protects property rights increase the likelihood of a country achieving sustained economic growth. Conclusion In this chapter, we showed that the growth rate of total factor productivity is the key factor in explaining the long-run equilibrium growth rates of labor productivity and the standard of living. Economists do not have a definitive explanation for why total factor productivity differs across countries. However, we do know some of the factors that are important in explaining differences in total factor productivity and labor productivity. Especially in advanced nations the amount of resources devoted to R&D and the discovery of new knowledge should influence the capital goods are important. In addition, the quality of government institutions and the quality of financial markets play an important role in determining total factor productivity. 72 Economists do know that the growth rate of total factor productivity determines the growth rate of labor productivity and the standard of living in equilibrium. Economists also know that an economy tends to converge towards its equilibrium growth path. Convergences helps explain why Germany and Japan grew so rapidly in the first decade or two after World War II, but have grown more slowly since then. In Chapter 6, we will cover money to understand how the inflation rate is determined in the long run. Before moving on to that chapter, read An Inside Look on the next page to learn how…..” Summary 5.1 Discuss the Connection between Labor Productivity and the Standard of Living Real GDP per person tells us the amount of goods and services that the average person in an economy can consume. If an individual is rational, then he will purchase goods and services that make himself better off. So, real GDP per person is a useful measure of the standard of living. The standard of living is labor productivity multiplied by labor input measured as average hours worked per person. The population is finite and there are just 24 hours in a day, so there is a limit to how much increasing labor inputs can increase the standard of living. However, labor productivity can increase indefinitely and as long as labor productivity increases the standard of living can increase. Real GDP per person is not a perfect measure of the standard of living because it ignores the distribution of income, the value of leisure time, whether people are happy or not, and life expectancy. However, the incomes of the poor, leisure time, self- 73 reported happiness and life expectancy all tend to increase as real GDP per person increases. Although imperfect, real GDP per person remains a very good measure of the standard of living. 5.2 Use the Solow Growth Model to Explain the Effect of Capital Accumulation onLabor Productivity Labor productivity depends on the capital-labor ratio and the level of TFP. The capitallabor ratio depends on the level of investment and the break-even level of investment, is the level of investment necessary to keep the capital-labor ratio constant. The steady state occurs when investment equals break-even investment and the capital-labor ratio is constant. An increase in the investment rate leads to a higher capital-labor ratio and a higher level of labor productivity. Because financial markets work to ensure that savings flow into investment, anything that increases saving will lead to a higher investment rate, a higher capital-labor ratio, and a higher level of labor productivity, all else equal. Anything that decreases saving, such as a government budget deficit, will cause the reverse to happen, all else equal. The break-even level of investment is determined by the growth rate of the labor force and the depreciation rate. A decrease in either the depreciation rate or the labor force growth rate decreases the break-even level of investment. As a consequence, the capital-labor ratio and level of labor productivity are higher. Increases in the depreciation rate or labor force growth rate cause the reverse to happen. 5.3 Explain how Total Factor Productivity Affects Labor Productivity 74 TFP measures the overall efficiency of the economy in transforming inputs into goods and services. TFP is not subject to diminishing marginal returns, so increases in TFP can explain sustained increases in labor productivity. Since labor productivity is the key determinant of the standard of living, TFP growth also explains sustained increases in the standard of living. TFP also explains the large differences in labor productivity and the standard of living across countries as well. To understand labor productivity and the standard of living fully, we must understand why TFP changes over time and why TFP is higher in some countries than others. Unfortunately, economists do not have a complete explanation for why TFP differs over time and across countries. However, economists have identified these important factors: (1) Investment in R&D leads to new ideas and new products that make workers more productive. (2) Education and learning by doing increase the skill level of the labor force. (3) Good government and social institutions channel resources toward wealth creating activities and away from wealth redistribution activities. (4) Geography and climate determine a nation’s natural resources and the rate of infectious disease among the population. (5) A well-functioning financial system ensures that savings flow to the individuals with the most productive investment projects and may lead to higher levels of physical and human capital. 5.4 Explain the Balanced Growth Path and Convergence and the Long-Run Equilibrium 75 Potential real GDP and potential real GDP per worker hour grow during equilibrium. The equilibrium growth rate is determined by the growth rate of total factor productivity. When an economy initially has a capital-labor ratio that is below the steady-state value, the capital-labor ratio grows quickly so potential real GDP per worker hour converges to the balanced growth path. When an economy initially has a capital-labor ratio that is above the steady-state value, the capital-labor ratio grows slowly so potential real GDP per worker hour converges to the balanced growth path. AUTHORS WILL ADD PROBLEMS IN NEXT DRAFT Appendix: Describe How Capital Accumulation Causes Endogenous Growth Capital accumulation and total factor productivity growth are the two determinants of labor productivity and the standard of living. Due to diminishing marginal returns, growth from capital accumulation eventually dies out so total factor productivity growth is the ultimate determinant of the growth rate of labor productivity and the standard of living. According to the Solow growth model, a low growth rate of total factor productivity causes a low growth rate of the standard of living. The answer is very clear and precise, but where does total factor productivity growth come from? The Solow model just assumes that total factor productivity growth occurs, so the model just assumes different growth rates of labor productivity and the standard of living. The model doesn’t explain why the growth rate of the standard of living is low in some countries. 76 Endogenous growth theory tries to solve this problem inherent in the Solow growth model. Endogenous growth theory is a theory of economic growth that tries to explain the growth rate of total factor productivity. There are many different endogenous growth models, and we do not intend to explain them all. Instead, we introduce one of the simplest versions of the theory that focuses on the importance of capital accumulation. To highlight how capital accumulation can lead to productivity growth, we assume that the quantity of labor is fixed at 1 and that total factor productivity is also fixed. Given these two assumptions, the only way that labor productivity and the standard of living can increase is if the capital stock increases. A common aggregate production function in endogenous growth models is: (A.1) π = π΄πΎ. (MD: Endogenous Growth Theory A theory of economic growth that tries to explain the growth rate of total factor productivity.) Notice that there are no diminishing marginal returns to capital in this aggregate production function. In fact, the marginal product of capital always equals A so the marginal product of capital is constant. Because the marginal product of capital is constant, capital accumulation can drive productivity growth. In addition, the growth rate of potential real GDP equals the growth rate of the capital stock. Assuming a constant marginal product of capital makes sense if we use a broader interpretation of the “K” term in the aggregate production function.15 For example, K may 15 Paul Romer, “Crazy Explanations for the Productivity Slowdown,” In NBER Macroeconomics Annual 1987, vol 2, ed. Stanley Fischer. Cambridge, Mass.: MIT Press, 1987. Sergio Rebelo, “Long-Run Policy Analysis and Long-Run Growth,” Journal of Political Economy (June 1991) pp. 500-521. 77 include not just physical capital, but also human capital. Recall that human capital is the knowledge and skills that the workers in the economy possess. If an economy accumulates physical and human capital at the same rate, then the ratio of physical to human capital remains constant and the marginal product of capital may not decline. Why would human capital increase with physical capital? As physical capital increases, a country becomes richer and the country may invest more in education and devote more resources to on-the-job training. Increased education and on-the-job training should both lead to more human capital. In addition, as an economy accumulates more capital goods of a given type, learning by doing occurs, so the existing workers become more proficient using the capital goods. The more highly skilled workers can keep the marginal product of capital from declining. Finally, we may consider the stock of knowledge as one type of capital good. As the stock of ideas increases, the economy can produce new and better types of capital goods and, as a consequence, the marginal product of capital does not decline. The aggregate production function with a broader definition of capital has important consequences for our theory of economic growth. To see these consequences, think in terms of the bath tub analogy that we introduced on page xx (add in page proofs). The investment rate, s, is still a constant fraction of output. Given our aggregate production function, water flowing into the bath tub is now: πππ‘ππ ππππ€πππ ππ = π π = π π΄πΎ. We have assumed a constant labor force, so the growth rate of the labor force, n, equals zero and water flowing out of the bath tub is now: 78 πππ‘ππ ππππ€πππ ππ’π‘ = ππΎ. So, the change in the level of water in the bath tub, βπΎ, equals: βπΎ = π π΄πΎ − ππΎ. We can divide each side of the equation by the capital stock to find an expression for the growth rate of the capital stock: βπΎ πΎ = π π΄ − π. Given the new production function in equation (5.18), the growth rate of potential real GDP is (A.2) βπ π = π π΄ − π. Because we have assumed a constant labor force, equation (A.2) also tells us the long-run growth rate of labor productivity. In the Solow growth model, the growth rate of labor productivity depended on an assumed rate of TFP growth. However, equation (A.2) tells us that the growth rate of productivity depends on the investment rate, so the investment rate emerges as an important determinant of the growth rate of labor productivity and the standard of living. In addition, government policies that either increase or decrease the investment rate become important determinants of the standard of living. For example, the U.S. government has special tax credits designed to promote investment in capital goods and research and development. This endogenous growth model provides an answer to why countries experience high or low growth rates of the standard of living: countries with high investment rates experience high growth rates and countries with low investment rates experience low growth rates. 79 The Evidence on Endogenous Growth Theory The endogenous growth model we just described predicts the relationship between the investment rate and the growth rate of labor productivity and the standard of living. Equation (A.2) says that as the investment rate increases, the growth rate of labor productivity also increases. All else equal, the higher investment rate should lead to a higher growth rate of real GDP per person. Charles Jones of Stanford University examined this prediction using data from advanced economies and found that growth rates of real GDP per person are roughly constant over long periods of time, but that the investment rates increased significantly during the postWorld War II era.16 If the endogenous growth model is correct, then Jones should have found that the increase in the investment rates were associated with higher growth rates of real GDP per person. Instead, he found that growth rates of real GDP per person have been constant over time. He interprets this finding as evidence against the simple endogenous growth models. The evidence that Charles Jones presents suggests that the simple model of endogenous growth does not does not explain the long-run performance of advanced economies. However, research on endogenous growth has moved beyond the simple models described here to more advanced models that fit the data better. Mathematical Appendix Solving for the Steady State Capital-Labor Ratio and Real GDP per Worker Hour Equation (5.5) describes how the capital-labor ratio changes over time: 16 “Time Series Tests of Endogenous Growth Models,” Quarterly Journal of Economics (May 1995), pp.495-525. 80 βπ = π (π΄π πΌ ) − (π + π)π. In the steady-state, the capital labor ratio is constant. Therefore, to find the steady-state capitallabor ratio first set βπ = 0 so: 0 = π (π΄π πΌ ) − (π + π)π. Next divide by k on each side of the equation: 0 = π (π΄π πΌ−1 ) − (π + π). Isolating the capital-labor on the right-hand side, we have π+π π π΄ = π πΌ−1 1 Raising each side of the equation to the πΌ−1 power yields: π∗ = [ π+π π π΄ ] 1⁄ πΌ−1 . We can transform this into: π π΄ π ∗ = [π+π] 1⁄ 1−πΌ . To find the steady-state real GDP per worker hour plug this expression into the production intensive form production function π¦ = π΄π πΌ to get: π π΄ π¦ ∗ = π΄ [π+π] πΌ⁄ (1−πΌ) . Now just rearrange terms so that there is just one term representing A, total factor productivity: π¦∗ = π΄ πΌ⁄ 1⁄ (1−πΌ) [ π ] (1−πΌ) . π+π Calculating the Steady-State Growth Rates Capital-Labor Ratio 81 The steady-state capital-labor ratio is π π΄ π ∗ = [π+π] 1⁄ 1−πΌ . In the steady state, capital’s share of income, the investment rate, the depreciation rate and the growth rate of the labor force are all constant. However, total factor productivity may increase. Therefore, it will be helpful to rewrite the equation for the steady-state capital-labor ratio as: ππ‘∗ = 1⁄ 1⁄ 1−πΌ π (1−πΌ) π΄π‘ [π+π] where we include the t subscript to emphasize that the capital-labor ratio and total factor productivity change over time. Following what we learned in the Chapter 4 Appendix we can take the natural logarithm of each side of the above equation to get: 1 1 π ππππ‘∗ = (1−πΌ) πππ΄π‘ + (1−πΌ) [π+π] . The derivative of the natural logarithm of the variable Xt with respect to time is: πππππ‘ ππ‘ 1 πππ‘ =π π‘ ππ‘ = πππ‘⁄ ππ‘ ππ‘ = ππ . Apply this rule and the rules for derivatives that we learned in Chapter 4, we find that the growth rate for the steady-state capital-labor ratio is: 1 ππ ∗ = (1−πΌ) ππ΄ . Real GDP per Worker Hour The steady-state real GDP per worker hour is 82 π¦∗ = π΄ πΌ⁄ 1⁄ (1−πΌ) [ π ] (1−πΌ) . π+π Just as it was helpful to use time subscripts for the expression for the steady-state capital-labor ratio, it is also helpful here to emphasize that real GDP per worker hour and total factor productivity may change over time: π¦π‘∗ = πΌ⁄ 1⁄ 1−πΌ π (1−πΌ) π΄π‘ [π+π] Following what we learned in the Chapter 4 Appendix we can take the natural logarithm of each side of the above equation to get: 1 πΌ π πππ¦π‘∗ = (1−πΌ) πππ΄π‘ + (1−πΌ) [π+π] . Apply the rule for taking the derivative of a variable with respect to time and the rules for derivatives that we learned in Chapter 4, we find that the growth rate for the steady-state capitallabor ratio is: 1 ππ¦ ∗ = (1−πΌ) ππ΄ . Real GDP π Real GDP per worker hour is defined as π¦ = πΏ . We can rewrite this definition by multiplying by labor on each side of the equation to obtain: π = π¦πΏ. The labor force and real GDP per worker hour grow over time so write the above equation as: 83 ππ‘ = π¦π‘ πΏπ‘ Apply the rule for taking the derivative of a variable with respect to time and the rules for derivatives that we learned in Chapter 4, we find that the growth rate for the steady-state capitallabor ratio is: ππ = ππ¦ + ππΏ . The labor force grows at a constant rate of n so the above equation becomes: ππ = ππ¦ + π. When the economy is in the steady-state, the growth rate of real GDP per worker hour is ππ¦ ∗ so the growth rate for real GDP in the steady state is: ππ ∗ = ππ¦ ∗ + π. Now we can substitute in the expression for the steady-state growth rate of real GDP per worker hour to obtain: 1 ππ ∗ = (1−πΌ) ππ΄ + π 84