503 Applied Macroeconomics Chapter 4. Economic Growth 2004 Kevin D. Hoover

1. 503 Applied Macroeconomics Chapter 4. Economic Growth 2004 Kevin D. Hoover Applied Intermediate Macroeconomics Prof. M. El-Sakka Dept of Economics Kuwait University

2. Economic Growth what makes GDP grow over time? Our analysis allows us to address questions like: Is it more factor inputs or using them better (technological progress) that explains the growth of the economy? How fast can the economy hope to grow in the long run? What effect will growth have on personal incomes? What factors promote or retard growth? Why have some economies grown rapidly and others stagnated?

3. Why Growth is Important The following figure shows the real GNP per capita of the United States from 1790 to 2003. Two features stand out: the pronounced business cycle and the secular trend, reflecting two centuries of strong ECONOMIC GROWTH. In 1790 GNP per capita was about $613 (2002 constant dollars), which stands midway between the 2002 level of Burundi ($500) and Ethiopia ($700) – two of the poorest countries in the world. The poverty line for a single person in the United States in 2002 was just over $9,000 – about the per capita income of Russia.

5. A central question for macroeconomics is: how can we explain economic growth? Of course, this growth was not uniform across the world. Great Britain industrialized first; the United States followed in close order. Western Europe and Japan grew rapidly by the end of the 19th century, while the so-called Newly Industrializing Countries (for example, Taiwan, Korea, Malaysia, Brazil) began to grow rapidly only after World War II. Some, such as Singapore and Hong Kong, have caught up to U.S. and European levels of income per capita. Others are far behind but growing rapidly. Still others – many of them in sub-Saharan Africa – remain desperately poor.

6. Australia, Canada, New Zealand and USA

7. Accounting for Growth PRODUCTION AT A POINT IN TIME AND PRODUCTION OVER TIME To understand the factors behind economic growth, it helps to look at the aggregate production function over time. Equation (7.1), describes aggregate supply in 1998. (7.1) Y = 8.15L0.69K0.31. Figure 7.3 represents this equation. Only the one combination of labor and capital, one point on the graph of equation (7.1) – the point at which L and K take their measured values for 1998 – describes the actual economy in that year. Every other point says what output would have been had the values of the factors of production been different.

8. Figure 7.3

9. Growth occurs when labor or capital increase or technology advances. If the growth of factors of production could by itself explain the growth of GDP, then equation (7.1) would be adequate. Growth would be modeled simply by plugging higher numbers L and K into the equation. In practice, technology changes too. For example, we can use, equation (7.1) to calculate total factor productivity for 1948: A = 4.40. In other words, technology improved by 85 percent over 50 years ((8.15-4.4)/4.4). The production function for 1948 can be written as: (7.2) Y = 4.40L0.69K0.31. Not only do the factors of production change over time, the production function itself shifts.

10. Figure 7.4 shows the relationship between the time series for GDP, labor and capital and snapshots of their production functions. Panel (A) shows the time series for the three variables, and the heavy vertical segments indicate one year “slices” of the time series at 1948 and 1998. The value for the coefficient A for 1948 is calculated from the first slice and the resulting production function is shown as the lower curves in panels (B) and (C). Similarly, panels (D) and (E) show the production function for 1998. (Panels (D) and (E) are identical to Figure 7.3.) Figure 7.4 illustrates that the history of GDP over time is better described as a jumping from one point on a production function to another point on a different production function than as an upward movement along the same production function.

12. DECOMPOSING ECONOMIC GROWTH How much of the growth in GDP between 1948 and 1998 can be attributed to each factor of production and to technology? Some thought experiments help us answer the question. The overall change in GDP can be decomposed into three parts. The basic data are given in Table 7.3. The 1948 aggregate production function is shown as the lower (heavy) curves in the two panels of Figure 7.5. (These correspond to panels (B) and (C) in Figure 7.4.) The actual input/production points are marked as points A. Thought experiment 1. What would GDP have been in 1948 if ceteris paribus the 1998 labor input had been available?

14. To answer this question, we plug in the labor value for 1998, along with all the other values for 1948 into equation (7.2):

15. In Figure 7.5, the first thought experiment is shown as the movement from point A to point B along the original labor production function in panel (A), which raises GDP to $2,588. Of course, the capital production function in panel (B) must shift up so that production occurs at the original level of capital and the new level of GDP (point B on the lighter, middle curve of panel (B)).It would be easy to conduct a similar thought experiment:

16. Thought experiment 3. What would GDP have been in 1948 if ceteris paribus both the 1998 labor and capital inputs had been available? Using the appropriate values from Table 7.3: Using both the labor and the capital inputs from 1998, GDP in 1948 would have been $4,079 billion (173 percent) higher in 1948.

17. ACCOUNTING FOR GROWTH RATES The three thought experiments help to clarify what we mean when we ask how much the three factors – labor, capital, and technology – contributed to economic growth. But the analysis is clumsy and can be greatly simplified. In 1957, Robert Solow, provided a classic analysis of this question. Solow’s approach is easily implemented with the Cobb-Douglas production function. Start with the production function: Y = ALαK1– α Using the algebra of growth rates and the notation that a hat (^) over a variable indicates the percentage rate of growth, the production function can be rewritten as:

18. The equation says that the growth rate of output can be decomposed into a weighted average of three parts: the rate of technological change (Aˆ entering with a weight of one), the rate of growth of labor (Lˆ , entering with a weight equal to labor’s share of GDP, α), and the growth rate of capital (Kˆ , entering with a weight equal to capital’s share of GDP, 1 – α). We can compute each of the terms on the right-hand side of equation (7.2) to find out how many percentage points each of the factors contributes to the total rate of growth of GDP. Equally, we can divide both sides by Yˆ to yield (7.6)

19. Each term on the right-hand side now gives the fraction of the total change attributable to one of the elements of the production function. To account for the importance of each element in explaining growth over the 50 years 1948-98, use the data in Table 7.3 to calculate the average growth rates of each factor and of GDP. Then plug these into equation (7.6). The results are shown in Table 7.4. Although a substantial proportion of the growth in output in the period after World War II can be attributed to the direct effect of increased inputs, the largest single factor is the fact that the technology used to convert those inputs into output improved by nearly 40 percent overall.

21. The Sources of Economic Growth The decomposition of GDP growth rates into parts attributed to labor, capital, and technology tells us what. We next consider the how and the why behind each of the main determinants of economic growth, considering improvements in technology and the growth of the labor and capital inputs in turn

22. PRODUCTIVITY AND TECHNOLOGICAL PROGRESS The first determinant of economic growth, technological change, is the least well understood. There is no doubt that it is happening, we can measure its effects. But the exact mechanisms through which technological progress affects growth are notclearly understood and are widely debated. Product Innovation Technical change is evident. At the beginning of the 20th century, steam and water ran factories, railroads and ships dominated long-distance transportation, and the telegraph was the premier mode of communication. The automobile, the airplane, and radio were in their infancies. Electric power and the telephone were barely in their adolescence. Nuclear power, television, and the electronic computer were not even the stuff of dreams. Within one lifetime, the technological landscape has changed almost beyond recognition.

23. Yet, despite the dramatic changes, the effects of technological development have been steady and incremental rather than revolutionary. Economic historians report that new inventions were typically introduced over many years, so that the new technology and the evidently inferior old technologies worked side-by-side for decades. The electric motor co-existed with steam-powered and water-powered, belt-driven tools. The tractor, available from earlier in the 20th century, did not fully replace horses on American farms until after World War II. The laser, one of the fundamental discoveries of the early 1960’s, is now found in bar code readers, fiber optic communication systems, medical instruments, and compact disk drives. Yet it was never patented, because for thirty years it did not appear to have economic applications.

24. The greatest puzzle of all is the computer itself. It clearly led to a qualitative change in modern life and opened up enormous possibilities in many areas. Yet it is hard to find a measurable increase in the productive capacity that could be directly attributed to the computer. Technological progress makes it possible to do more with less. However we measure it, technological progress shows up as an upward shift of the production function. Typically we think of technological progress as reflected in different kinds of machinery. On the one hand, there has been a succession of innovative machinery, either doing entirely new jobs (the radio) or doing old jobs better (the automobile). On the other hand, each of these technologies has been improved – often by many orders of magnitude.

25. Process Innovation Processes are important. In the early 19th century, Eli Whitney the inventor, of the idea of interchangeable parts. Henry Ford combined the idea of interchangeable parts with that of the assembly line to produce the Model T – the first automobile cheap enough for ordinary workers to afford. Ford and Whitney changed the way in which the machinery was used. Similarly, Frederick Winslow Taylor observed, measured, and timed the smallest tasks involved in production processes and then tried to design “the one best way” for workers to perform each task. In some contexts, it produces impressive gains in productivity and quality control.

26. In the 1980’s American businesses became interested in Japanese methods of production that were almost the opposite of Taylorism, in which workers took more responsibility for the whole production process. These were reflected in ideas such as “quality circles” and “total quality management,” in which workers were usually less specialized; and their own experience on the job, rather than the rules of an outside expert, guided process development. Similarly, “just-in-time inventory management” and new arrangements between firms and their suppliers were aimed at achieving productivity gains.

27. Research and Development Some aspects of technological progress can occur nearly accidentally, as when a discovery in pure science or a casual observation turns out to have important economic uses. Economists refer to such cases as exogenous technological progress: a new technology arises independently of economic considerations. More important, however, is endogenous technological progress: a new technology is developed in response to economic incentives. The development of antibiotic drugs after the war was largely the result of targeted, large-scale RESEARCH AND DEVELOPMENT (R&D)– partly by universities and non-profit research institutes, but largely by pharmaceutical companies in search of profits.

28. R&D creates a new idea without immediate economic payoff (as happened at Bell Laboratories with the laser); but often R&D borrows the root ideas from other sources and works to develop them in ways that will turn out to be profitable. Thomas Edison’s famous laboratory in New Jersey is an early example of systematic research and development of technology for profit. There he invented the light bulb, the phonograph, the stock-market ticker, the carbon-button telephone microphone, and many other products. Other businesses include their R&D arms within the productive enterprise. Either way, the central point is that much of the innovation in the modern economy is an intentional and focused response to profit opportunities, and not simple good luck – endogenous rather than exogenous technological progress.

29. THE GROWTH OF LABOR The Law of Motion of Labor. How fast the labor force grows depends on how fast the population was growing sixteen to twenty years before and how fast the rate of participation of potential workers in actual employment is changing. The English economist Sir Roy Harrod(1900-78), a pioneer of the economics of growth, referred to the long-term rate of growth of the labor force that resulted from population growth, rather than from temporary changes in participation rates, as the NATURAL RATE OF GROWTH – indicated by the constant n. A LAW OF MOTION describesthe development of a quantity through time. The law of motion for labor can be written in terms of the natural rate of growth: (7.7) Lt = (1 + n)Lt-1.

30. The stock of labor each period is n percent higher than the period before. If we pick a starting point, call it time 0, at which the stock of labor takes a known value, L0, then the law of motion can also be written: (7.8) Lt = L0(1 + n)t, where time tis measured as the number of periods after time 0. The equation shows that labor grows exponentially at rate n. In many cases in macroeconomic analysis we are concerned about time horizons over which we can take the rate of population growth (and potential labor force) as outside of the influence of economic considerations. Although such an assumption is often a reasonable approximation, it may prove a poor one if we wish to explain growth in the long term or why different countries have grown at different rates.

31. Malthusianism David Ricardo (1772-1823) and T. Robert Malthus (1766-1834) argued that the rate of population growth is a function of the real wage. Their idea was that when the real wage was high, workers were well-nourished and could support larger families. The increased number of workers increased the competition for work and drove the real wage back down. Now workers found themselves with inadequate resources. They and their families were likely to be malnourished and to become the victims of disease and early death. They might delay marriage or otherwise reduce the number of children conceived, and the population would fall. An equilibrium would be established at which the real wage was just large enough that the workers and the productive resources were in balance. The wage that maintains such an equilibrium is called the subsistence wage.

32. It was, in all probability, a poverty wage. Malthus’s and Ricardo’s pessimistic view of the economy was often called the iron law of wages. Malthus argued that, unchecked, population tends to grow exponentially, while food and other resources grow, at best, arithmetically. Consequently, population constantly threatens to outstrip resources. But, of course, it cannot actually outstrip resources, so one way or another population growth must be checked. Malthus was not predicting future disaster. Instead, he was trying to explain current misery. Malthus recognized two sorts of checks to population growth. Positive checks: malnutrition, disease, and the resulting early death. He also recognized a prudential check: people wishing to maintain a standard of living taking steps to prevent their families from growing too large to support.

33. Population could grow rapidly only if some extraordinary circumstance released these checks. The European discovery of the Americas, for example, made rapid population growth possible. Economic Development and the Stabilization of Population Many modern commentators take the spectacular growth of population and real GDP over the past 200 years as proof that Malthus was wrong. But they misunderstand his analysis. True, the technological progress over these two centuries, especially the progress in agriculture, would have surprised Malthus – as indeed it has persistently surprised many. But given that progress, which removed the positive checks, Malthus would himself have predicted the population growth.

34. A cliché in economic development is that prosperity is the best birth control. Richer countries tend to have lower population growth rates. For example, India is growing at 1.68 percent per year; while the population of Italy is growing at 0.24 percent per year. Figure 7.6 shows a strong negative relationship (correlation coefficient R = -0.73) between GDP per capita in 2000 and the average rate of population growth over the period 1960-2000. Still, Malthus is ultimately correct that population must stabilize, whether at a high or low level of income per capita. As the world becomes richer, the overall growth rate of population is slowing. Demographers predict that the world population growth rate, 1.27% in 1999, will fall to less than 0.5% by 2050. And one way or another various checks must operate to bring population growth to a halt.

36. THE GROWTH OF CAPITAL While the growth of labor respond to economic forces only in the long run, the factors that govern the growth of capital are the result of more immediate macroeconomic decisions. Recall that “investment” is the production of new physical means of production. Investment adds to the stock of capital. The relationship can also be represented as a simple law of motion: (7.9) Kt = Kt-1 + It-1 – Depreciationt-1. I is sometimes referred to as gross investment. Net investment (It-1 – Depreciationt-1) defined the amount that investment adds to the stock of capital. Subtracting Kt-1 from each side allows us to relate investment to the change in the capital stock: (7.10) ΔKt = Kt – Kt-1 = It-1 – Depreciationt-1 = net It-1.

37. What is the rate of growth of capital? Divide both sides of (7.10) by Kt-1: (7.11) Kˆt = ΔKt/Kt-1 = net It-1/Kt-1 Multiplying the right-hand side of (7.11) by Yt-1/Yt-1 gives: The first factor on the right-hand side is the share of net investment in GDP, and second term is capital productivity (φ). So, we can rewrite equation (7.11’) as:

38. The equation shows that the rate of growth of capital depends on the available technology (the capital productivity coefficient φ) and the economic choice of how much to invest. An increase in capital productivity or an increase in the rate of investment ceteris paribus boosts the rate of growth of capital; while an increase in the depreciation rate lowers net investment and, therefore, lowers the rate of growth of capital. There is some evidence, however, that all things cannot in reality be held equal. More productive computer technology has been associated with a faster rate of economic obsolescence. The gain to capital growth from increased productivity would in that case be partly offset by the fall in net investment owing to higher depreciation rates. The key economic variable is the rate of investment (I).

39. The Neoclassical Growth Model Models in which aggregate production is described by a constant-returns-to-scale production function, and in which the use of the factors of production can be adjusted quickly and flexibly to changes in relative prices so that full employment of resources is maintained at all times. THE PROCESS OF GROWTH Assume that technology is not changing. Since aggregate production can be well described using a constant-returns-to-scale production function, one possible path for economic growth is to expand smoothly, so that the economy of 2005 is just a scaled-up version of the economy in 1905: labor, capital, and output are all bigger by exactly the same proportion. This idea of smooth or balanced growth is shown in Figure 7.7.

41. Under constant returns to scale and equal proportional increases in factors of production, the productivities of labor and capital remain constant. Notice that the capital-labor ratio κ = K/L = θ/φ. Since both labor productivity (θ) and capital productivity (φ) are constant, κ is also constant. As the economy grows, there is more capital, but it is spread out over more workers. This is called CAPITAL WIDENING. Since the rule for profit maximization says that the marginal product of each factor is equal to its real price, the real wage (w/p) and the real rental rate (ν /p) must also be constant. Nowdefine BALANCED GROWTH. An economy displays balanced growth without technological progress when all real aggregates grow at the same constant rate and when the marginal products of the factors of production and, therefore, factor prices remain constant.

42. Balanced Growth with Technological Progress On average, labor productivity grows at the same rate as labor augmenting technological progress and capital productivity at the same rate as capital-augmenting technological progress . A factor-augmentingimprovementin technology has exactly the same effect on GDP as increase the factor itself by the same proportion. For example, if the labor force grows at nand the rate of improvement in labor productivity due to labor-augmenting technological progress is , then we can analyze the growth of GDP as if the labor force grew at . Similarly, if the growth in capital productivity were due to capital-augmenting technological progress, GDP would grow as if the capital stock grew at . Balanced growth now requires that GDP grows at the same rate as labor and capital adjusted for technologically induced improvements in productivity.

43. In that case, balanced growth requires the capital stock to grow rapidly to keep up with the growth both of labor and labor productivity – so the capital-labor ratio must rise at a trend rate approximately equal to . Similarly, once there is technological progress, marginal products and factor prices will no longer remain constant. The marginal product of labor for the Cobb-Douglas production function can be written as: The growth rate of the marginal product of labor can be written:

44. Equation (7.13) shows that the marginal product of labor must grow at the same rate as labor productivity. Since the real wage and the marginal product of labor are equal under perfect competition, the real wage should also grow at the same rate. A parallel argument can be made to show that the marginal product of capital and the real rental rate should grow at the same rate as capital productivity.

45. Putting the considerations of this section together leads to a modification of our earlier definition: An economy displays balanced growth with technological progress when real GDP grows at the same constant rate as labor and capital adjusted for factor augmenting technological progress, such that the marginal products and prices of the each factors of production grow at constant (but perhaps different) rates consistent with the relationship

46. Unbalanced Growth Consider the case in which labor grows faster than capital. In Figure 7.8 labor is governed by the law of motion for labor so that at period t labor is Lt and one period later it is Lt+1 = (1 + n)Lt. Capital grows so that Kt+1=(1+Kˆ )K, but by proportionally less than labor: Kˆ < n . The increase in GDP is greater than it would have been had both factors had grown at the slower rate Kˆ and smaller than if both had grown at the faster rate n. In period t+1, labor has become relatively more abundant. If firms could not adjust their production techniques in response to changing conditions, then the extra labor would simply remain unemployed – constrained by the fact that there is not enough capital, using the current technique, to outfit the new workers. But when, as we assume in the long run, firms can adjust, they respond to changing factor prices.

48. When the supply of labor rises, its relative price falls. Firms want to hire more labor. Their response to changing relative prices, moves the production point along the labor production function to point B. Here, not only is the marginal product of labor lower, the average product of labor has fallen to θ2. In contrast, capital has become relatively scarce, so that the real rental rate rises. Firms economize on the now relatively more expensive capital moving the production point to a steeper part of the curve at point D, where the marginal product of capital is higher to match the higher real rental rate. As a result, the average product of capital rises to φ2.

49. There is no unemployment or excess capital capacity in this example precisely because the market responds to the changing factor prices by choosing a technique more appropriate to the new relative factor supplies. Notice that as we move from period t to period t+1, the capital labor ratio κ = (K/L = θ/φ) falls, since θ falls and φ rises. We could just as well have considered the case in which capital grew faster than labor. It is intuitively obvious that the capital-labor ratio would rise in this case. The capital-labor ratio provides a measure of capital intensity defined as the amount of capital per unit of labor. Along a balanced growth path, the economy experiences capital widening, but capital intensity remains constant. Along an unbalanced growth path, firms respond to changes in relative factor supplies, so capital intensity changes.

50. When capital grows faster than labor, capital intensity increases, which is known as CAPITAL DEEPENING: there is more capital available for each worker to use. We have already seen that capital deepening will occur when the rate of labor augmenting technological progress exceeds the rate of capital-augmenting technological progress. It is not just the mix of broad categories such as capital and labor that change in response to changing prices, but the detailed mix of all the inputs to the production process and the technologies needed to support that mix change as well. This process of adjusting the mix of inputs to changing supplies is essential to keeping the economy growing smoothly.