《宏观经济学》课程教学资源（英文版）Lecture 3-8 Economic Growth II

Worth: Mankiw Economics 5e CHAPTER EIGHT Economic growth‖ Is there some action a government of India could take that would lead the Indian economy to grow like Indonesia's or Egypt's? If so, what, exactly? If not, what is it about the "nature of India that makes it so? The conse- quences for human welfare involved in questions like these are simply stag- gering: Once one starts to think about them, it is hard to think about Robert E. Lucas, Jr. This chapter continues our analysis of the forces governing long-run economic rowth. With the basic version of the Solow growth model as our starting point, we take on four new tasks Our first task is to make the Solow model more general and more realistic. In Chapter 3 we saw that capital, labor, and technology are the key determinants of a nations production of goods and services. In Chapter 7 we developed the Solow model to show how changes in capital (saving and investment)and changes in the labor force(population growth) affect the economy s output. We are now ready to add the third source of growth--changes in technology--into the mix Our second task is to examine how a nations public policies can influence the evel and growth of its standard of living. In particular, we address four questions: Should our society save more or save less? How can policy influence the rate of saving? Are there some types of investment that policy should especially encour- age? How can policy increase the rate of technological progress? The Solow growth model provides the theoretical framework within which we consider each of these policy issues. Our third task is to move from theory to empirics. That is, we consider how well the Solow model fits the facts. During the 1990s, a large literature examined the predictions of the Solow model and other models of economic growth. It turns out that the glass is both half full and half empty. The Solow model can shed much light on international growth experiences, but it is far from the last word on the subject. Our fourth and final task is to consider what the solow model leaves out we have discussed previously, models help us understand the world by simplifying it. After completing an analysis of a model, therefore, it is important to consider 207 User JoENA: Job EFFo1424: 6264_ch08: Pg 207: 27096#/eps at 100sl ed,Feb13,20029:584M

User JOEWA:Job EFF01424:6264_ch08:Pg 207:27096#/eps at 100% *27096* Wed, Feb 13, 2002 9:58 AM This chapter continues our analysis of the forces governing long-run economic growth.With the basic version of the Solow growth model as our starting point, we take on four new tasks. Our first task is to make the Solow model more general and more realistic. In Chapter 3 we saw that capital, labor, and technology are the key determinants of a nation’s production of goods and services. In Chapter 7 we developed the Solow model to show how changes in capital (saving and investment) and changes in the labor force (population growth) affect the economy’s output.We are now ready to add the third source of growth—changes in technology—into the mix. Our second task is to examine how a nation’s public policies can influence the level and growth of its standard of living. In particular, we address four questions: Should our society save more or save less? How can policy influence the rate of saving? Are there some types of investment that policy should especially encour￾age? How can policy increase the rate of technological progress? The Solow growth model provides the theoretical framework within which we consider each of these policy issues. Our third task is to move from theory to empirics.That is, we consider how well the Solow model fits the facts. During the 1990s, a large literature examined the predictions of the Solow model and other models of economic growth. It turns out that the glass is both half full and half empty. The Solow model can shed much light on international growth experiences, but it is far from the last word on the subject. Our fourth and final task is to consider what the Solow model leaves out. As we have discussed previously, models help us understand the world by simplifying it. After completing an analysis of a model, therefore, it is important to consider | 207 Economic Growth II 8CHAPTER Is there some action a government of India could take that would lead the Indian economy to grow like Indonesia’s or Egypt’s? If so,what,exactly? If not, what is it about the “nature of India” that makes it so? The conse￾quences for human welfare involved in questions like these are simply stag￾gering: Once one starts to think about them, it is hard to think about anything else. — Robert E. Lucas, Jr. EIGHT

Worth: Mankiw Economics 5e 208 PART I11 Growth Theory: The Economy in the Very Long Run whether we have oversimplified matters. In the last section, we examine a new set of theories, called endogenous growth theories, that hope to explain the technological progress that the Solow model takes as exogenous 8-1 Technological Progress in the solow model ar, our presentation of the Solow model has assumed an unchanging rela- tionship between the inputs of capital and labor and the output of goods and ser- vices. Yet the model can be modified to include exogenous technological progress, which over time expands society's ability to produce The Efficiency of Labor To incorporate technological progress, we must return to the production func- tion that relates total capital K and total labor L to total output Y. Thus far, the production function has been F(K, L We now write the ction function as Y=F(K, where E is a new(and somewhat abstract) variable called the efficiency of labor. The efficiency of labor is meant to reflect society's knowledge about pro- duction methods: as the available technology improves, the efficiency of labor rises. For instance, the efficiency of labor rose when assembly-line production transformed manufacturing in the early twentieth century, and it rose again when computerization was introduced in the the late twentieth century. The ef- ficiency of labor also rises when there are improvements in the health, education, or skills of the labor force The term L X E measures the number of effective workers. It takes into account the number of workers L and the efficiency of each worker E. This new produc tion function states that total output Y depends on the number of units of capital K and on the number of effective workers L X E Increases in the efficiency of labor e are in effect. like increases in the labor force L. The simplest assumption about technological progress is that it causes the effi ciency of labor e to grow at some constant rate g. For example, if g=0.02, then each unit of labor becomes 2 percent more efficient each year: output increases as if the labor force had increased by an additional 2 percent. This form of tech nological progress is called labor augmenting, and g is called the rate of labor augmenting technological progress. Because the labor force L is growing at rate n,and the efficiency of each unit of labor E is growing at rate g, the number of effective workers LX E is growing at rate n+g. User JoENA: Job EFFo1424: 6264_ ch08: Pg 208: 27097#/eps at 100s ed,Feb13,20029:584M

User JOEWA:Job EFF01424:6264_ch08:Pg 208:27097#/eps at 100% *27097* Wed, Feb 13, 2002 9:58 AM whether we have oversimplified matters. In the last section, we examine a new set of theories, called endogenous growth theories, that hope to explain the technological progress that the Solow model takes as exogenous. 8-1 Technological Progress in the Solow Model So far, our presentation of the Solow model has assumed an unchanging rela￾tionship between the inputs of capital and labor and the output of goods and ser￾vices. Yet the model can be modified to include exogenous technological progress, which over time expands society’s ability to produce. The Efficiency of Labor To incorporate technological progress, we must return to the production func￾tion that relates total capital K and total labor L to total output Y.Thus far, the production function has been Y = F(K, L). We now write the production function as Y = F(K, L × E), where E is a new (and somewhat abstract) variable called the efficiency of labor.The efficiency of labor is meant to reflect society’s knowledge about pro￾duction methods: as the available technology improves, the efficiency of labor rises. For instance, the efficiency of labor rose when assembly-line production transformed manufacturing in the early twentieth century, and it rose again when computerization was introduced in the the late twentieth century. The ef- ficiency of labor also rises when there are improvements in the health, education, or skills of the labor force. The term L × E measures the number of effective workers. It takes into account the number of workers L and the efficiency of each worker E.This new produc￾tion function states that total output Y depends on the number of units of capital K and on the number of effective workers L × E. Increases in the efficiency of labor E are, in effect, like increases in the labor force L. The simplest assumption about technological progress is that it causes the effi- ciency of labor E to grow at some constant rate g. For example, if g = 0.02, then each unit of labor becomes 2 percent more efficient each year: output increases as if the labor force had increased by an additional 2 percent.This form of tech￾nological progress is called labor augmenting, and g is called the rate of labor￾augmenting technological progress. Because the labor force L is growing at rate n, and the efficiency of each unit of labor E is growing at rate g, the number of effective workers L × E is growing at rate n + g. 208 | PART III Growth Theory: The Economy in the Very Long Run

Worth: Mankiw Economics 5e CHAPTER 8 Economic Growth Il 209 The Steady State With Technological Progres Expressing technological progress as labor augmenting makes it analogous to population growth. In Chapter 7 we analyzed the economy in terms of quanti- ties per worker and allowed the number of workers to rise over time. now we analyze the economy in terms of quantities per effective worker and allow the number of effective workers to rise To do this, we need to reconsider our notation We now let k= K/(L X E) stand for capital per effective worker and y=Y/(L X E)stand for output per ef- fective worker. With these definitions, we can again write y=f(l) t This notation is not really as new as it seems. If we hold the efficiency of labor constant at the arbitrary value of 1, as we have done implicitly up to now, the these new definitions of k and y reduce to our old ones. When the efficiency of labor is growing, however, we must keep in mind that k and y now refer to quan tities per effective worker(not per actual worker) Our analysis of the economy proceeds just as it did when we examined popu- lation growth. The equation showing the evolution of k over time now changes to △k=$f(k)-(6+n+g)k As before, the change in the capital stock Ak equals investment sf(k)minus break-even investment(8+n+gk. Now, however, because k=K/EL, break even investment includes three terms: to keep k constant, &k is needed to replace depreciating capital, nk is needed to provide capital for new workers, and gk is needed to provide capital for the new "effective workers "created by technologi- As shown in Figure 8-1, the inclusion of technological progress does not sub stantially alter our analysis of the steady state. There is one level of k, denoted figure 8-1 nvestment, Technological Progress and the break-even Break-even investment, (8+n+ g)k Solow Growth Model Labor Investment augmenting technological progress at rate g affects the Solow growth model in much the same way as did population growth at rate n. Now that k is Investment, sf(k) defined as the amount of capital per effective worker, increases in the number of effective workers because of technological progress tend to decrease k In the steady state investment sf(k) exactly offsets the reductions in k attributable k* Capital per effective worker, k to depreciation, population The steady growth, and technological progress User JoENA: Job EFFo1424: 6264_ ch08: Pg 209: 27098#/eps at 100s ed,Feb13,20029:584M

User JOEWA:Job EFF01424:6264_ch08:Pg 209:27098#/eps at 100% *27098* Wed, Feb 13, 2002 9:58 AM The Steady State With Technological Progress Expressing technological progress as labor augmenting makes it analogous to population growth. In Chapter 7 we analyzed the economy in terms of quanti￾ties per worker and allowed the number of workers to rise over time. Now we analyze the economy in terms of quantities per effective worker and allow the number of effective workers to rise. To do this, we need to reconsider our notation.We now let k = K/(L × E) stand for capital per effective worker and y = Y/(L × E) stand for output per ef￾fective worker.With these definitions, we can again write y = f(k). This notation is not really as new as it seems. If we hold the efficiency of labor E constant at the arbitrary value of 1, as we have done implicitly up to now, then these new definitions of k and y reduce to our old ones.When the efficiency of labor is growing, however, we must keep in mind that k and y now refer to quan￾tities per effective worker (not per actual worker). Our analysis of the economy proceeds just as it did when we examined popu￾lation growth.The equation showing the evolution of k over time now changes to Dk = sf(k) − ( d + n + g)k. As before, the change in the capital stock Dk equals investment sf(k) minus break-even investment (d + n + g)k. Now, however, because k = K/EL, break￾even investment includes three terms: to keep k constant,d k is needed to replace depreciating capital, nk is needed to provide capital for new workers, and gk is needed to provide capital for the new “effective workers” created by technologi￾cal progress. As shown in Figure 8-1, the inclusion of technological progress does not sub￾stantially alter our analysis of the steady state. There is one level of k, denoted CHAPTER 8 Economic Growth II | 209 figure 8-1 Investment, break-even investment k* Capital per effective worker, k Break-even investment, (d n g)k Investment, sf(k) The steady state Technological Progress and the Solow Growth Model Labor￾augmenting technological progress at rate g affects the Solow growth model in much the same way as did population growth at rate n. Now that k is defined as the amount of capital per effective worker, increases in the number of effective workers because of technological progress tend to decrease k. In the steady state, investment sf(k) exactly offsets the reductions in k attributable to depreciation, population growth, and technological progress.

Worth: Mankiw Economics 5e 210 PART I11 Growth Theory: The Economy in the Very Long Run k, at which capital per effective worker and output per effective worker are constant. As before, this steady state represents the long-run equilibrium of th e econom The Effects of Technological Progress able 8-1 shows how four key variables behave in the steady state with technolog ical progress As we have just seen, capital per effective worker k is constant in the steady state. Because y=f(k), output per effective worker is also constant Remem- ber,though, that the efficiency of each actual worker is growing at rate g. Hence, output per worker(Y/L=yXE)also grows at rate g Total output Y=yX(EX LI With the addition of technological progress, our model can finally explain the sustained increases in standards of living that we observe. That is, we have shown that technological progress can lead to sustained growth in output per worker. B contrast, a high rate of saving leads to a high rate of growth only until the steady state is reached. Once the economy is in steady state, the rate of growth of output per worker depends only on the rate of technological progress. Acording to the Solow model, only technological progress can explain persistently rising living standards The introduction of technological progress also modifies the criterion for the Golden Rule. The Golden Rule level of capital is now defined as the steady state chat maximizes consumption per effective worker. Following the same argu ments that we have used before, we can show that steady-state consumption per effective worker is *=f(k*)-(6+n+g)k Steady-state consumption is maximized if MPk=δ+n+g, MPK-6=n+ That is, at the Golden Rule level of capital, the net marginal product of capital, MPK-6, equals the rate of growth of total output, n g. Because actual Steady-State Growth Rates in the Solow Model With Technological Progress Variable Symbol eady-State Growth Rate Output per effective worker y=Y/(EXL)=f(k) Output pe g g User JoENA: Job EFFo1424: 6264_ ch08: Pg 210: 27099#/eps at 100sl ed,Feb13,20029:584M

User JOEWA:Job EFF01424:6264_ch08:Pg 210:27099#/eps at 100% *27099* Wed, Feb 13, 2002 9:58 AM k*, at which capital per effective worker and output per effective worker are constant. As before, this steady state represents the long-run equilibrium of the economy. The Effects of Technological Progress Table 8-1 shows how four key variables behave in the steady state with technolog￾ical progress.As we have just seen, capital per effective worker k is constant in the steady state. Because y = f(k), output per effective worker is also constant. Remem￾ber, though, that the efficiency of each actual worker is growing at rate g. Hence, output per worker (Y/L = y × E) also grows at rate g.Total output [Y = y × (E × L)] grows at rate n + g. With the addition of technological progress, our model can finally explain the sustained increases in standards of living that we observe.That is, we have shown that technological progress can lead to sustained growth in output per worker. By contrast, a high rate of saving leads to a high rate of growth only until the steady state is reached. Once the economy is in steady state, the rate of growth of output per worker depends only on the rate of technological progress. According to the Solow model, only technological progress can explain persistently rising living standards. The introduction of technological progress also modifies the criterion for the Golden Rule.The Golden Rule level of capital is now defined as the steady state that maximizes consumption per effective worker. Following the same argu￾ments that we have used before, we can show that steady-state consumption per effective worker is c* = f(k*) − ( d + n + g)k*. Steady-state consumption is maximized if MPK = d + n + g, or MPK − d = n + g. That is, at the Golden Rule level of capital, the net marginal product of capital, MPK − d , equals the rate of growth of total output, n + g. Because actual 210 | PART III Growth Theory: The Economy in the Very Long Run Variable Symbol Steady-State Growth Rate Capital per effective worker k = K/(E × L) 0 Output per effective worker y = Y/(E × L) = f(k) 0 Output per worker Y/L = y × E g Total output Y = y × (E × L) n + g Steady-State Growth Rates in the Solow Model With Technological Progress table 8-1

Worth: Mankiw Economics 5e CHAPTER 8 Economic Growth Il 211 economies experience both population growth and technological progress, we must use this criterion to evaluate whether they have more or less capital than at the golden rule steady state 8-2 Policies to Promote growth Having used the Solow model to uncover the relationships among the different sources of economic growth, we can now use the theory to help guide our hinking about economic polie Evaluating the Rate of Saving According to the Solow growth model, how much a nation saves and invests is a key determinant of its citizens'standard of living. So let's begin our policy discus sion with a natural question: Is the rate of saving in the U.S. economy too low, too high, or about right? As we have seen, the saving rate determines the steady-state levels of capital and output. One particular saving rate produces the Golden Rule steady state, which maximizes consumption per worker and thus economic well-being. The Golden Rule provides the benchmark against which we can compare the U.S. economy. To decide whether the U.S. economy is at, above, or below the Golden Rule steady state, we need to compare the marginal product of capital net of deprecia tion(MPK-8) with the growth rate of total output(n+g). As we just estab- lished, at the Golden Rule steady state, MPK-8=n+g. If the economy is operating with less capital than in the Golden Rule steady state, then diminish lls us that MPK-8>n+g In this Ite of saving will eventually lead to a steady state with higher consumption However, if the economy is operating with too much capital, then MPK-8<n +8, and the rate of saving should be reduced. To make this comparison for a real economy, such as the U.S. economy, we need an estimate of the growth rate (n+g) and an estimate of the net marginal product of capital (MPK-8) Real GDP in the United States grows an average of 3 percent per year, so +g=0.03. We can estimate the net marginal product of capital from the following three facts 1. The capital stock is about 2.5 times one years GDP. 2. Depreciation of capital is about 10 percent of GDP. 3. Capital income is about 30 percent of GDP. Using the notation of our model (and the result from Chapter 3 that capital owners earn income of MPK for each unit of capital), we can write these facts as 2.6k=0.1 3.MPK×k=0.3y User JOENA: Job EFF01424: 6264_ch08: Pg 211: 27100 #/eps at 100s ed,Feb13,20029:584M

User JOEWA:Job EFF01424:6264_ch08:Pg 211:27100#/eps at 100% *27100* Wed, Feb 13, 2002 9:58 AM economies experience both population growth and technological progress, we must use this criterion to evaluate whether they have more or less capital than at the Golden Rule steady state. 8-2 Policies to Promote Growth Having used the Solow model to uncover the relationships among the different sources of economic growth, we can now use the theory to help guide our thinking about economic policy. Evaluating the Rate of Saving According to the Solow growth model, how much a nation saves and invests is a key determinant of its citizens’standard of living. So let’s begin our policy discus￾sion with a natural question: Is the rate of saving in the U.S. economy too low, too high, or about right? As we have seen,the saving rate determines the steady-state levels of capital and output. One particular saving rate produces the Golden Rule steady state, which maximizes consumption per worker and thus economic well-being.The Golden Rule provides the benchmark against which we can compare the U.S. economy. To decide whether the U.S. economy is at, above, or below the Golden Rule steady state, we need to compare the marginal product of capital net of deprecia￾tion (MPK − d ) with the growth rate of total output (n + g). As we just estab￾lished, at the Golden Rule steady state, MPK − d = n + g. If the economy is operating with less capital than in the Golden Rule steady state, then diminish￾ing marginal product tells us that MPK − d > n + g. In this case, increasing the rate of saving will eventually lead to a steady state with higher consumption. However, if the economy is operating with too much capital, then MPK − d < n + g, and the rate of saving should be reduced. To make this comparison for a real economy, such as the U.S. economy, we need an estimate of the growth rate (n + g) and an estimate of the net marginal product of capital (MPK − d ). Real GDP in the United States grows an average of 3 percent per year, so n + g = 0.03.We can estimate the net marginal product of capital from the following three facts: 1. The capital stock is about 2.5 times one year’s GDP. 2. Depreciation of capital is about 10 percent of GDP. 3. Capital income is about 30 percent of GDP. Using the notation of our model (and the result from Chapter 3 that capital owners earn income of MPK for each unit of capital), we can write these facts as 1. k = 2.5y. 2. d k = 0.1y. 3. MPK × k = 0.3y CHAPTER 8 Economic Growth II | 211

Worth: Mankiw Economics 5e 212 PART I11 Growth Theory: The Economy in the Very Long Run preciation 8 by dividing 2 by equation 1 6k/k=0.1y)/(25y) And we solve for the marginal product of capital MPK by dividing equation 3 by (MPK×k)/k=(0.3y)/(2.5y) MPK=0.12 Thus, about 4 percent of the capital stock depreciates each year, and the marginal product of capital is about 12 percent per year. The net marginal ital, MPK-8, is about 8 percent per year: We can now see that the return to capital (MPK-8=8 percent per year) ell in excess of the economy's average growth rate (n+g=3 percent per year) This fact, together with our previous analysis, indicates that the capital stock in he U.S. economy is well below the Golden Rule level. In other words, if th United States saved and invested a higher fraction of its income, it w more rapidly and eventually reach a steady state with higher consumption. This finding suggests that policymakers should want to increase the rate of saving and investment. In fact, for many years, increasing capital formation has been a high priority of economic policy. Changing the Rate of Saving The preceding calculations show that to move the U.S. economy toward the Golden Rule steady state, policymakers should increase national saving. But how can they do that? We saw in Chapter 3 that, as a matter of sheer accounting, gher ving means higher public saving, higher private saving, or some combination of the two. Much of the debate over policies to increase growth centers on which of these options is likely to be most effective. The most direct way in which the government affects national saving is hrough public saving-the difference between what the government receives in tax revenue and what it spends. When the government's spending exceeds its rev enue, the government is said to run a budget deficit, which represents negative lbic saving. As we saw in Chapter 3, a budget deficit raises interest rates and crowds out investment; the resulting reduction in the capital stock is part of the burden of the national debt on future generations. Conversely, if the government spends less than it raises in revenue, it is said to run a budget surplus. It can then re tire some of the national debt and stimulate investment The government also affects national saving by influencing private saving- he saving done by households and firms. In particular, how much people decide to save depends on the incentives they face, and these incentives are altered by variety of public policies. Many economists argue that high tax rates on capital cluding the corporate income tax, the federal income tax, the estate tax, Inc many state income and estate taxes-discourage private saving by reducing User JoENA: Job EFFo1424: 6264_ ch08: Pg 212: 27101#/eps at 100s ed,Feb13,20029:584M

User JOEWA:Job EFF01424:6264_ch08:Pg 212:27101#/eps at 100% *27101* Wed, Feb 13, 2002 9:58 AM We solve for the rate of depreciation d by dividing equation 2 by equation 1: d k/k = (0.1y)/(2.5y) d = 0.04. And we solve for the marginal product of capital MPK by dividing equation 3 by equation 1: (MPK × k)/k = (0.3y)/(2.5y) MPK = 0.12 Thus, about 4 percent of the capital stock depreciates each year, and the marginal product of capital is about 12 percent per year.The net marginal product of cap￾ital, MPK − d , is about 8 percent per year. We can now see that the return to capital (MPK − d = 8 percent per year) is well in excess of the economy’s average growth rate (n + g = 3 percent per year). This fact, together with our previous analysis, indicates that the capital stock in the U.S. economy is well below the Golden Rule level. In other words, if the United States saved and invested a higher fraction of its income, it would grow more rapidly and eventually reach a steady state with higher consumption.This finding suggests that policymakers should want to increase the rate of saving and investment. In fact, for many years, increasing capital formation has been a high priority of economic policy. Changing the Rate of Saving The preceding calculations show that to move the U.S. economy toward the Golden Rule steady state, policymakers should increase national saving. But how can they do that? We saw in Chapter 3 that, as a matter of sheer accounting, higher national saving means higher public saving, higher private saving, or some combination of the two. Much of the debate over policies to increase growth centers on which of these options is likely to be most effective. The most direct way in which the government affects national saving is through public saving—the difference between what the government receives in tax revenue and what it spends.When the government’s spending exceeds its rev￾enue, the government is said to run a budget deficit, which represents negative public saving. As we saw in Chapter 3, a budget deficit raises interest rates and crowds out investment; the resulting reduction in the capital stock is part of the burden of the national debt on future generations. Conversely, if the government spends less than it raises in revenue, it is said to run a budget surplus. It can then re￾tire some of the national debt and stimulate investment. The government also affects national saving by influencing private saving— the saving done by households and firms. In particular, how much people decide to save depends on the incentives they face, and these incentives are altered by a variety of public policies. Many economists argue that high tax rates on capital— including the corporate income tax, the federal income tax, the estate tax, and many state income and estate taxes—discourage private saving by reducing the 212 | PART III Growth Theory: The Economy in the Very Long Run

Worth: Mankiw Economics 5e CHAPTER 8 Economic Growth Il 213 rate of return that savers earn. However, tax-exempt retirement accounts, such as IRAs, are designed to encourage private saving by giving preferential treatment to income saved in these accounts Many disagreements among economists over public policy are rooted in dif- ferent views about how much private saving responds to incentives. For example, suppose that the government were to expand the amount that people could put into tax-exempt retirement accounts Would people respond to the increased in- entive to save by saving more? Or would people merely transfer saving done in other forms into these accounts--reducing tax revenue and thus public saving without any stimulus to private saving? Clearly, the desirability of the policy de- pends on the answers to these questions. Unfortunately, despite much research on this issue, no consensus has emerged. Should the Social Security System Be Reformed? Although many government policies are designed to encourage saving, such as the preferential tax treatment given to pension plans and other retirement ac- counts, one important policy is often thought to reduce saving: the Social Secu rity system. Social Security is a transfer system designed to maintain individuals income in their old age. These transfers to the elderly are financed with a payroll ax on the working-age population. This system is thought to reduce private sav- ing because it reduces individuals'need to provide for their own retirement To counteract the reduction in national saving attributed to Social Security many economists have proposed reforms of the Social Security system. The sys tem is now largely pay-as-you-go: most of the current tax receipts are paid out to the current elderly population. One suggestion is that Social Security should be fully funded. Under this plan, the government would put aside in a trust fund the payments a generation makes when it is young and working; the government would then pay out the principal and accumulated interest to this same genera tion when it is older and retired. Under a fully funded Social Security system, an increase in public saving would offset the reduction in private saving a closely related proposal is privatization, which means turning this govern- ment program for the elderly into a system of mandatory private savings ac- counts, much like private pension plans. In principle, the issues of funding and privatization are distinct. A fully funded system could be either public(in which case the government holds the funds) or private(in which case private financial institutions hold the funds). In practice, however, the issues are often linked. Some economists have argued that a fully funded public system is problematic They note that such a system would end up holding a large share of the nations wealth, which would increase the role of the government in allocating capital. In addition, they fear that a large publicly controlled fund would tempt politicians to cut taxes or increase spending, which could deplete the fund and cause the system to revert to pay-as-you-go status. History gives some support to this fear the initial architects of Social Security wanted the system to accumulate a much larger trust fund than ever materialized User JoENA: Job EFFo1424: 6264_ ch08: Pg 213: 27102#/eps at 100s ed,Feb13,20029:584M

User JOEWA:Job EFF01424:6264_ch08:Pg 213:27102#/eps at 100% *27102* Wed, Feb 13, 2002 9:58 AM rate of return that savers earn. However, tax-exempt retirement accounts, such as IRAs, are designed to encourage private saving by giving preferential treatment to income saved in these accounts. Many disagreements among economists over public policy are rooted in dif￾ferent views about how much private saving responds to incentives. For example, suppose that the government were to expand the amount that people could put into tax-exempt retirement accounts.Would people respond to the increased in￾centive to save by saving more? Or would people merely transfer saving done in other forms into these accounts—reducing tax revenue and thus public saving without any stimulus to private saving? Clearly, the desirability of the policy de￾pends on the answers to these questions. Unfortunately, despite much research on this issue, no consensus has emerged. CHAPTER 8 Economic Growth II | 213 CASE STUDY Should the Social Security System Be Reformed? Although many government policies are designed to encourage saving, such as the preferential tax treatment given to pension plans and other retirement ac￾counts, one important policy is often thought to reduce saving: the Social Secu￾rity system. Social Security is a transfer system designed to maintain individuals’ income in their old age.These transfers to the elderly are financed with a payroll tax on the working-age population.This system is thought to reduce private sav￾ing because it reduces individuals’ need to provide for their own retirement. To counteract the reduction in national saving attributed to Social Security, many economists have proposed reforms of the Social Security system.The sys￾tem is now largely pay-as-you-go: most of the current tax receipts are paid out to the current elderly population. One suggestion is that Social Security should be fully funded. Under this plan, the government would put aside in a trust fund the payments a generation makes when it is young and working; the government would then pay out the principal and accumulated interest to this same genera￾tion when it is older and retired. Under a fully funded Social Security system, an increase in public saving would offset the reduction in private saving. A closely related proposal is privatization, which means turning this govern￾ment program for the elderly into a system of mandatory private savings ac￾counts, much like private pension plans. In principle, the issues of funding and privatization are distinct.A fully funded system could be either public (in which case the government holds the funds) or private (in which case private financial institutions hold the funds). In practice, however, the issues are often linked. Some economists have argued that a fully funded public system is problematic. They note that such a system would end up holding a large share of the nation’s wealth, which would increase the role of the government in allocating capital. In addition, they fear that a large publicly controlled fund would tempt politicians to cut taxes or increase spending, which could deplete the fund and cause the system to revert to pay-as-you-go status. History gives some support to this fear: the initial architects of Social Security wanted the system to accumulate a much larger trust fund than ever materialized

Worth: Mankiw Economics 5e 214 PART I11 Growth Theory: The Economy in the Very Long Run lil. hese issues rose to prominence in the late 1990s as policymakers became re that the current Social Security system was not sustainable. That is, the mount of revenue being raised by the payroll tax appeared insufficient to pay all the benefits being promised. According to most projections, this problem was to become acute as the large baby-boom generation retired during the early decades of the twenty-first century. Various solutions were proposed. One poss bility was to maintain the current system with some combination of smaller ben efits and higher taxes. Other possibilities included movements toward a fully funded system, perhaps also including private accounts. This issue was prominent in the presidential campaign of 2000, with candidate George W. Bush advocating a reform including private accounts. As this book was going to press, it was still unclear whether this reform would come to pass Allocating the Economy's Investment The Solow model makes the simplifying assumption that there is only one type of capital. In the world, of course, there are many types. Private businesses invest in traditional types of capital, such as bulldozers and steel plants, and newer types of capital, such as computers and robots. The government invests in various forms of public capital, called infrastructure, such as roads, bridges, and sewer systems In addition, there is human capital the knowledge and skills that workers through education, from early childhood programs such as Head Start to on-the-job training for adults in the labor force. Although the basic Solow model includes only physical capital and does not try to explain the efficiency of labor, in many ways human capital is analogous to physical capital. Like physical capital, human capital raises our ability to produce goods and services. Raising the level of human capital requires investment in the form of teachers, libraries, and student time. Recent re- search on economic growth has emphasized that human capital is at least as impor tant as physical capital in explaining international differences in standards of living Policymakers trying to stimulate economic growth must confront the issue of what kinds of capital the economy needs most. In other words, what kinds of capital yield the highest marginal products? To a large extent, policymakers can rely on the marketplace to allocate the pool of saving to alternative types of in vestment. Those industries with the highest marginal products of capital will nat urally be most willing to borrow at market interest rates to finance new investment. Many economists advocate that the government should merely cre- ate a"level playing field"for different types of capital-for example, by ensuring that the tax system treats all forms of capital equally. The government can then rely on the market to allocate capital efficiently To learn more about the debate over Social Security, see Social Security Reform: Links to Saving, In- estment and Growth. Steven A. Sass and Robert K. Triest. eds. Conference Series No 41. Federal Reserve Bank of Boston, June 1997 2N. Gregory Mankiw, David Romer, and David N Weil, " A Contribution to the Empirics of Eco- nomic Growth, "Quarterly Journal of Economics(May 1992): 407-437. User JoENA: Job EFFo1424: 6264_ch08: Pg 214: 27103#/eps at 100sl ed,Feb13,20029:584M

User JOEWA:Job EFF01424:6264_ch08:Pg 214:27103#/eps at 100% *27103* Wed, Feb 13, 2002 9:58 AM 214 | PART III Growth Theory: The Economy in the Very Long Run These issues rose to prominence in the late 1990s as policymakers became aware that the current Social Security system was not sustainable. That is, the amount of revenue being raised by the payroll tax appeared insufficient to pay all the benefits being promised.According to most projections, this problem was to become acute as the large baby-boom generation retired during the early decades of the twenty-first century.Various solutions were proposed. One possi￾bility was to maintain the current system with some combination of smaller ben￾efits and higher taxes. Other possibilities included movements toward a fully funded system, perhaps also including private accounts.This issue was prominent in the presidential campaign of 2000, with candidate George W. Bush advocating a reform including private accounts. As this book was going to press, it was still unclear whether this reform would come to pass.1 1To learn more about the debate over Social Security, see Social Security Reform: Links to Saving, In￾vestment, and Growth, Steven A. Sass and Robert K.Triest, eds., Conference Series No. 41, Federal Reserve Bank of Boston, June 1997. 2 N. Gregory Mankiw, David Romer, and David N.Weil,“A Contribution to the Empirics of Eco￾nomic Growth,’’ Quarterly Journal of Economics (May 1992): 407–437. Allocating the Economy’s Investment The Solow model makes the simplifying assumption that there is only one type of capital. In the world, of course, there are many types. Private businesses invest in traditional types of capital, such as bulldozers and steel plants, and newer types of capital, such as computers and robots.The government invests in various forms of public capital, called infrastructure, such as roads, bridges, and sewer systems. In addition,there is human capital—the knowledge and skills that workers acquire through education,from early childhood programs such as Head Start to on-the-job training for adults in the labor force.Although the basic Solow model includes only physical capital and does not try to explain the efficiency of labor, in many ways human capital is analogous to physical capital. Like physical capital, human capital raises our ability to produce goods and services. Raising the level of human capital requires investment in the form of teachers, libraries, and student time. Recent re￾search on economic growth has emphasized that human capital is at least as impor￾tant as physical capital in explaining international differences in standards of living.2 Policymakers trying to stimulate economic growth must confront the issue of what kinds of capital the economy needs most. In other words, what kinds of capital yield the highest marginal products? To a large extent, policymakers can rely on the marketplace to allocate the pool of saving to alternative types of in￾vestment.Those industries with the highest marginal products of capital will nat￾urally be most willing to borrow at market interest rates to finance new investment. Many economists advocate that the government should merely cre￾ate a “level playing field” for different types of capital—for example, by ensuring that the tax system treats all forms of capital equally.The government can then rely on the market to allocate capital efficiently

Worth: Mankiw Economics 5e CHAPTER 8 Economic Growth Il 215 Other economists have suggested that the government should actively encour ge particular forms of capital. Suppose, for instance, that technological advance ccurs as a by-product of certain economic activities. This would happen if new and improved production processes are devised during the process of building capital (a phenomenon called learning by doing) and if these ideas become part of society's pool of knowledge. Such a by-product is called a technological externality (or a knowledge spillover). In the presence of such externalities, the social returns to capital exceed the private returns, and the benefits of increased capital accumula tion to society are greater than the Solow model suggests. Moreover, some types of capital accumulation may yield greater externalities than others. If, for example, installing robots yields greater technological externalities than building a ner steel mill, then perhaps the government should use the tax laws to encourage in- vestment in robots. The success of such an industrial policy, as it is sometimes called, requires that the government be able to measure the externalities of different eco- nomic activities so it can give the correct incentive to each activity. Most economists are skeptical about industrial policies, for two reasons. First, measuring the externalities from different sectors is so difficult as to be virtually impossible If policy is based on poor measurements, its effects might be close to random and, thus, worse than no policy at all. Second, the political process is far from perfect. Once the government gets in the business of rewarding specific in- dustries with subsidies and tax breaks, the rewards are as likely to be based on po- litical clout as on the magnitude of externalities One type of capital that necessarily involves the government is public capital Local, state, and federal governments are always deciding whether to borrow finance new roads, bridges, and transit systems. During his first presidential cam- paign, Bill Clinton argued that the United States had been investing too little in infrastructure. He claimed that a higher level of infrastructure investment would make the economy substantially more productive. Among economists, this claim d both defenders and critics. Yet all of them agree that measuring the margin duct of public capital is difficult. Private capital generates an easily measured te of profit for the firm owning the capital, whereas the benefits of public cap ital are more diffu Encouraging Technological Progress The Solow model shows that sustained growth in income per worker must come from technological progress. The Solow model, however, takes technological progress as exogenous; it does not explain it. Unfortunately, the determinants of technological progress are not well understoo Despite this limited understanding, many public policies are designed to stim- ulate technological progress. Most of these policies encourage the private sector to devote resources to technological innovation. For example, the patent system Paul Romer, "Crazy Explanations for the Productivity Slowdown, "NBER Macroeconomics Annual 2(1987):163-201 User JOENA: Job EFF01424: 6264_ch08: Pg 215: 27104 #/eps at 100s ed,Feb13,20029:584M

User JOEWA:Job EFF01424:6264_ch08:Pg 215:27104#/eps at 100% *27104* Wed, Feb 13, 2002 9:58 AM Other economists have suggested that the government should actively encour￾age particular forms of capital. Suppose, for instance, that technological advance occurs as a by-product of certain economic activities.This would happen if new and improved production processes are devised during the process of building capital (a phenomenon called learning by doing) and if these ideas become part of society’s pool of knowledge. Such a by-product is called a technological externality (or a knowledge spillover). In the presence of such externalities, the social returns to capital exceed the private returns, and the benefits of increased capital accumula￾tion to society are greater than the Solow model suggests.3 Moreover, some types of capital accumulation may yield greater externalities than others.If,for example, installing robots yields greater technological externalities than building a new steel mill, then perhaps the government should use the tax laws to encourage in￾vestment in robots.The success of such an industrial policy, as it is sometimes called, requires that the government be able to measure the externalities of different eco￾nomic activities so it can give the correct incentive to each activity. Most economists are skeptical about industrial policies, for two reasons. First, measuring the externalities from different sectors is so difficult as to be virtually impossible. If policy is based on poor measurements, its effects might be close to random and, thus, worse than no policy at all. Second, the political process is far from perfect. Once the government gets in the business of rewarding specific in￾dustries with subsidies and tax breaks, the rewards are as likely to be based on po￾litical clout as on the magnitude of externalties. One type of capital that necessarily involves the government is public capital. Local, state, and federal governments are always deciding whether to borrow to finance new roads, bridges, and transit systems. During his first presidential cam￾paign, Bill Clinton argued that the United States had been investing too little in infrastructure. He claimed that a higher level of infrastructure investment would make the economy substantially more productive.Among economists, this claim had both defenders and critics.Yet all of them agree that measuring the marginal product of public capital is difficult. Private capital generates an easily measured rate of profit for the firm owning the capital, whereas the benefits of public cap￾ital are more diffuse. Encouraging Technological Progress The Solow model shows that sustained growth in income per worker must come from technological progress. The Solow model, however, takes technological progress as exogenous; it does not explain it. Unfortunately, the determinants of technological progress are not well understood. Despite this limited understanding, many public policies are designed to stim￾ulate technological progress. Most of these policies encourage the private sector to devote resources to technological innovation. For example, the patent system CHAPTER 8 Economic Growth II | 215 3 Paul Romer,“Crazy Explanations for the Productivity Slowdown,’’ NBER Macroeconomics Annual 2 (1987): 163–201

Worth: Mankiw Economics 5e 216 PART I11 Growth Theory: The Economy in the Very Long Run gives a temporary monopoly to inventors of new products; the tax code offers tax breaks for firms engaging in research and development; and government agencies such as the National Science Foundation directly subsidize basic re- search in universities. In addition, as discussed above, proponents of industrial policy argue that the government should take a more active role in promoting specific industries that are key for rapid technological progress CASE STUDY The worldwide slowdown in economic growth Beginning in the early 1970s, world policymakers faced a perplexing problem- a global slowdown in economic growth. Table 8-2 presents data on the growth in real GDP per person for the seven major world economies. Growth in the United States fell from 2.2 percent to 1.5 percent, and other countries experi enced similar or more severe declines. Accumulated over many years, even a small hange in the rate of growth has a large effect on economic well-being. Real in- ome in the United States today is about 20 percent lower than it would have been had growth remained at its previous level. Why did this slowdown occur? Studies have shown that it was attributable to a fall in the rate at which the production function was improving over time. The appendix to this chapter explains how economists measure changes in the pro- duction function with a variable called total factor productivity, which is closely re lated to the efficiency of labor in the Solow model. There are, however, many hypotheses to explain this fall in productivity growth. Here are four of them. Measurement Problems One possibility is that the productivity slowdown did not really occur and that it shows up in the data because the data are flawed. As you may recall from Chapter 2, one problem in measuring inflation is correcting for changes in the quality of goods and services. The same issue arises when mea- suring output and productivity. For instance, if technological advance leads to more computers being built, then the increase in output and productivity is easy to measure. But if technological advance leads to faster computers being built, hen output and productivity have increased, but that increase is more subtle and harder to measure. Government statisticians try to correct for changes in quality, but despite their best efforts, the resulting data are far from perfect. Unmeasured quality improvements mean that our standard of living is rising nore rapidly than the official data indicate. This issue should make us suspicious of the data, but by itself it cannot explain the productivity slowdown. To explain a slow- down in growth, one must argue that the measurement problems got worse. There is some indication that this might be so As history passes, fewer people work in indus. tries with tangible and easily measured output, such as agriculture, and more work vices. Yet few economists believe that measurement problems were the full stor, in industries with intangible and less easily measured output, such as medical se Oil Prices When the productivity slowdown began around 1973, the obvious hypothesis to explain it was the large increase in oil prices caused by the actions of the OPEC oil cartel. The primary piece of evidence was the timing: productivity growth slowed at the same time that oil prices skyrocketed. Over time, however, User JoENA: Job EFFo1424: 6264_ ch08: Pg 216: 27105#/eps at 100sl ed,Feb13,20029:584M

User JOEWA:Job EFF01424:6264_ch08:Pg 216:27105#/eps at 100% *27105* Wed, Feb 13, 2002 9:58 AM gives a temporary monopoly to inventors of new products; the tax code offers tax breaks for firms engaging in research and development; and government agencies such as the National Science Foundation directly subsidize basic re￾search in universities. In addition, as discussed above, proponents of industrial policy argue that the government should take a more active role in promoting specific industries that are key for rapid technological progress. 216 | PART III Growth Theory: The Economy in the Very Long Run CASE STUDY The Worldwide Slowdown in Economic Growth Beginning in the early 1970s, world policymakers faced a perplexing problem— a global slowdown in economic growth.Table 8-2 presents data on the growth in real GDP per person for the seven major world economies. Growth in the United States fell from 2.2 percent to 1.5 percent, and other countries experi￾enced similar or more severe declines.Accumulated over many years, even a small change in the rate of growth has a large effect on economic well-being. Real in￾come in the United States today is about 20 percent lower than it would have been had growth remained at its previous level. Why did this slowdown occur? Studies have shown that it was attributable to a fall in the rate at which the production function was improving over time. The appendix to this chapter explains how economists measure changes in the pro￾duction function with a variable called total factor productivity, which is closely re￾lated to the efficiency of labor in the Solow model. There are, however, many hypotheses to explain this fall in productivity growth. Here are four of them. Measurement Problems One possibility is that the productivity slowdown did not really occur and that it shows up in the data because the data are flawed.As you may recall from Chapter 2, one problem in measuring inflation is correcting for changes in the quality of goods and services.The same issue arises when mea￾suring output and productivity. For instance, if technological advance leads to more computers being built, then the increase in output and productivity is easy to measure. But if technological advance leads to faster computers being built, then output and productivity have increased, but that increase is more subtle and harder to measure. Government statisticians try to correct for changes in quality, but despite their best efforts, the resulting data are far from perfect. Unmeasured quality improvements mean that our standard of living is rising more rapidly than the official data indicate.This issue should make us suspicious of the data,but by itself it cannot explain the productivity slowdown.To explain a slow￾down in growth, one must argue that the measurement problems got worse.There is some indication that this might be so.As history passes,fewer people work in indus￾tries with tangible and easily measured output, such as agriculture, and more work in industries with intangible and less easily measured output, such as medical ser￾vices.Yet few economists believe that measurement problems were the full story. Oil Prices When the productivity slowdown began around 1973, the obvious hypothesis to explain it was the large increase in oil prices caused by the actions of the OPEC oil cartel.The primary piece of evidence was the timing: productivity growth slowed at the same time that oil prices skyrocketed. Over time, however