Chapter 6 LongRun Economic Growth Table 6 1

Chapter 6 Long-Run Economic Growth

Table 6. 1 Economic Growth in Eight Major Countries, 1870– 1998 Copyright © 2005

Goals of Chapter 6 n Identify forces that determine the growth rate of an economy u. Changes in productivity are key u. Saving and investment decisions are also important n Examine policies governments may use to influence the rate of growth Copyright © 2005 Pearson Addison-Wesley. All rights reserved. 3

6. 1 The Sources of Economic Growth n Production function Y = AF(K, N) (6. 1) u. Decompose into growth rate form: the growth accounting equation ΔY/Y = ΔA/A + a. K ΔK/K + a. N ΔN/N (6. 2) u. The a terms are the elasticities of output with respect to the inputs (capital and labor) u. Interpretation l A rise of 10% in A raises output by 10% l A rise of 10% in K raises output by a. K times 10% l A rise of 10% in N raises output by a. N times 10% u. Both a. K and a. N are less than 1 due to diminishing marginal productivity Copyright © 2005 Pearson Addison-Wesley. All rights reserved. 4

6. 1 The Sources of Economic Growth n Growth accounting u. Four steps in breaking output growth into its causes (productivity growth, capital input growth, labor input growth) l. Get data on ΔY/Y, ΔK/K, and ΔN/N, adjusting for quality changes l. Estimate a. K and a. N from historical data l. Calculate the contributions of K and N as a. K ΔK/K and a. N ΔN/N, respectively l. Calculate productivity growth as the residual: ΔA/A = ΔY/Y - a. K ΔK/K - a. N ΔN/N Copyright © 2005 Pearson Addison-Wesley. All rights reserved. 5

Table 6. 2 The Steps of Growth Accounting: A Numerical Example 6

Table 6. 2 The Steps of Growth Accounting: A Numerical Example (cont’d) Copyright ©

6. 1 The Sources of Economic Growth u. Application: growth accounting and the east Asian “miracle” (in 4 th edition) l. The east Asian "tigers" (Taiwan, Hong Kong, Singapore, and South Korea) grew over 7% per year for 25 years l. Alwyn Young's research found that their rapid growth resulted from capital and labor growth, not productivity growth (total factor productivity, TFP) l. TFP growth rates: TW (2. 6%), HK (2. 3%), SG (0. 2%) SK (1. 7%) l. The implication is that such rapid growth can't be sustained, since growth in inputs is hard to maintain permanently Copyright © 2005 Pearson Addison-Wesley. All rights reserved. 8

6. 1 The Sources of Economic Growth u. Growth accounting and the productivity slowdown l. Denison's results for 1929– 1982 (Table 6. 3) Ø Entire period output growth 2. 92%; due to labor 1. 34%; due to capital 0. 56%; due to productivity 1. 02% Ø Pre-1948 capital growth was much slower than post-1948 Ø Post-1973 labor growth slightly slower than pre-1973 Ø Productivity growth is major difference ü Entire period: 1. 02% ü 1929– 1948: 1. 01% ü 1948– 1973: 1. 53% ü 1973– 1982: -0. 27% ü 1982 -1997: 0. 76% (Bureau of Labor Statistics) l. Productivity growth slowdown occurred in all major developed countries Copyright © 2005 Pearson Addison-Wesley. All rights reserved. 9

Table 6. 3 Sources of Economic Growth in the United States (Denison) (Percent per

6. 1 The Sources of Economic Growth u. Application: the post-1973 slowdown in productivity growth: What caused the decline in productivity? l Measurement—inadequate accounting for quality improvements l The legal and human environment—regulations for pollution control and worker safety, crime, and declines in educational quality l Technological depletion and slow commercial adaptation— Nordhaus suggests that technological innovation has temporarily dried up; also, companies may be slow to adapt new technology l Oil prices—huge increase in oil prices reduced productivity of capital and labor, especially in basic industries l New industrial revolution—learning process for information technology from 1973 to 1990 meant slower growth Copyright © 2005 Pearson Addison-Wesley. All rights reserved. 11

6. 1 The Sources of Economic Growth u. Application: a U. S. productivity miracle? l. Labor productivity growth increased sharply in the second half of the 1990 s l. The increase in labor productivity can be traced to the ICT (information and communications technologies) revolution ØComputer technology improved very rapidly after 1995 ØFirms invested heavily in ICT because of increased marginal productivity ØAdvances in computer technology spilled over into other industries Copyright © 2005 Pearson Addison-Wesley. All rights reserved. 12

Table 6. 4 Growth in Average Labor Productivity Copyright © 2005 Pearson Addison-Wesley. All

6. 2 Growth Dynamics: The Solow Model n. Three basic questions about growth u. What's the relationship between the long -run standard of living and the saving rate, population growth rate, and rate of technical progress? u. How does economic growth change over time? Will it speed up, slow down, or stabilize? u. Are there economic forces that will allow poorer countries to catch up to richer countries? Copyright © 2005 Pearson Addison-Wesley. All rights reserved. 14

6. 2 Growth Dynamics: The Solow Model u. Setup of the Solow model l. Basic assumptions and variables ØPopulation and work force grow at same rate n ØEconomy is closed and G = 0 ØCt = Yt - It (6. 3) ØRewrite everything in per-worker terms: yt = Yt/Nt; ct = Ct/Nt; kt = Kt/Nt Økt is also called the capital-labor ratio Copyright © 2005 Pearson Addison-Wesley. All rights reserved. 15

6. 2 Growth Dynamics: The Solow Model u. The per-worker production function lyt = f(kt) (6. 4) l. Assume no productivity growth for now (add it later) l. Plot of per-worker production function —Fig. 6. 1 l. Same shape as aggregate production function Copyright © 2005 Pearson Addison-Wesley. All rights reserved. 16

Figure 6. 1 The per-worker production function Copyright © 2005 Pearson Addison-Wesley. All rights

6. 2 Growth Dynamics: The Solow Model u. Steady states l Steady state: yt, ct, and kt are constant over time l Gross investment must Ø Replace worn out capital, d. Kt Ø Expand so the capital stock grows as the economy grows, n. Kt l It = (n + d)Kt (6. 5) l From Eq. (6. 3), Ct = Yt - It = Yt - (n + d)Kt (6. 6) l In per-worker terms, in steady state c = f(k) - (n + d)k l Plot of c, f(k), and (n + d)k (Fig. 6. 2) l Increasing k will increase c up to a point (6. 7) Ø This is k 1 in the figure, the Golden Rule capital stock Ø For k beyond this point, c will decline Ø But we assume henceforth that k is less than k 1, so c always rises as k rises Copyright © 2005 Pearson Addison-Wesley. All rights reserved. 18

Figure 6. 2 The relationship of consumption per worker to the capital–labor ratio in

6. 2 Growth Dynamics: The Solow Model u. Reaching the steady state l. Suppose saving is proportional to current income: St = s. Yt (6. 8) , where s is the saving rate, which is between 0 and 1 l. Equating saving to investment gives s. Yt = (n + d)Kt (6. 9) l. Putting this in per-worker terms gives sf(k) = (n + d)k (6. 10) l. Plot of sf(k) and (n + d)k (Fig. 6. 3) l. The only possible steady-state capital-labor ratio is k* Copyright © 2005 Pearson Addison-Wesley. All rights reserved. 21

Figure 6. 3 Determining the capital–labor ratio in the steady state Copyright © 2005

6. 2 Growth Dynamics: The Solow Model l. Output at that point is y* = f(k*); consumption is c* = f(k*) - (n + d)k* l. If k begins at some level other than k*, it will move toward k* ØFor k below k*, saving > the amount of investment needed to keep k constant, so k rises ØFor k above k*, saving < the amount of investment needed to keep k constant, so k falls l. To summarize, with no productivity growth, the economy reaches a steady state, with constant capital-labor ratio, output per worker, and consumption per worker Copyright © 2005 Pearson Addison-Wesley. All rights reserved. 23

6. 2 Growth Dynamics: The Solow Model u. The fundamental determinants of longrun living standards l. The saving rate ØHigher saving rate means higher capital-labor ratio, higher output per worker, and higher consumption per worker (shown in Fig. 6. 4) ØShould a policy goal be to raise the saving rate? üNot necessarily, since the cost is lower consumption in the short run üThere is a trade-off between present and future consumption Copyright © 2005 Pearson Addison-Wesley. All rights reserved. 24

Figure 6. 4 The effect of an increased saving rate on the steady-state capital–labor

6. 2 Growth Dynamics: The Solow Model l. Population growth Ø Higher population growth means a lower capital-labor ratio, lower output per worker, and lower consumption per worker (shown in Fig. 6. 5) Ø Should a policy goal be to reduce population growth? ü Doing so will raise consumption per worker ü But it will reduce total output and consumption, affecting a nation's ability to defend itself or influence world events Ø The Solow model also assumes that the proportion of the population of working age is fixed ü But when population growth changes dramatically this may not be true ü Changes in cohort sizes may cause problems for social security systems and areas like health care Copyright © 2005 Pearson Addison-Wesley. All rights reserved. 26

Figure 6. 5 The effect of a higher population growth rate on the steady-state

6. 2 Growth Dynamics: The Solow Model l Productivity growth Ø The key factor in economic growth is productivity improvement Ø Productivity improvement raises output per worker for a given level of the capital-labor ratio Ø In equilibrium, productivity improvement increases the capitallabor ratio, output per worker, and consumption per worker ü Productivity improvement directly improves the amount that can be produced at any capital-labor ratio ü The increase in output per worker increases the supply of saving, causing the long-run capital-labor ratio to rise Ø Can consumption per worker grow indefinitely? ü The saving rate can't rise forever (it peaks at 100%) and the population growth rate can't fall forever ü But productivity and innovation can always occur, so living standards can rise continuously Ø Summary: The rate of productivity improvement is the dominant factor determining how quickly living standards rise Copyright © 2005 Pearson Addison-Wesley. All rights reserved. 28

Figure 6. 6 An improvement in productivity Copyright © 2005 Pearson Addison-Wesley. All rights

Figure 6. 7 The effect of a productivity improvement on the steady-state capital–labor ratio

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6. 2 Growth Dynamics: The Solow Model l. Application: Do economies converge? ØUnconditional convergence: Poor countries eventually catch up to rich countries üThis should occur if saving rates, population growth rates, and production functions are the same worldwide üThen, even though they start with different capital-labor ratios, all countries should converge with the same capital-labor ratio, output per worker, and consumption per worker üIf there is international borrowing and lending, there is more support for unconditional convergence * Capital should flow from rich to poor countries, as it will have a higher marginal product there * So investment wouldn't be limited by domestic saving Copyright © 2005 Pearson Addison-Wesley. All rights reserved. 32

6. 2 Growth Dynamics: The Solow Model ØConditional convergence: Living standards will converge in countries with similar characteristics [s, n, d, f(k)] ü Countries with different fundamental characteristics will not converge ü So a poor country can catch up to a rich country if both have the same saving rate, but not to a rich country with a higher saving rate ØNo convergence: Poor countries don't catch up over time; this is inconsistent with the Solow model ØWhat is the evidence? ü Little support for unconditional convergence ü Some support for conditional convergence after correcting for differences in saving rates and population growth (Mankiw, Romer, and Weil, 1992) ü Support for conditional convergence among states in the United States (Barro and Sala-i-Martin, 1992) ü Since there's little support for unconditional convergence, international financial markets must be imperfect (due to limits on foreign investment by governments, tariff barriers, and information costs) Copyright © 2005 Pearson Addison-Wesley. All rights reserved. 33

6. 2 Growth Dynamics: The Solow Model n Endogenous growth theory—explaining the sources of productivity growth u. Aggregate production function Y = AK (6. 11) l. Constant MPK ØHuman capital ü Knowledge, skills, and training of individuals ü Human capital tends to increase in same proportion as physical capital ØResearch and development programs ØIncreases in capital and output generate increased technical knowledge, which offsets decline in MPK from having more capital Copyright © 2005 Pearson Addison-Wesley. All rights reserved. 34

6. 2 Growth Dynamics: The Solow Model u. Implications of endogenous growth l. Suppose saving is a constant fraction of output: S = s. AK l. Since investment = net investment + depreciation, I = ΔK + d. K l. Setting investment equal to saving implies: ΔK + d. K= s. AK (6. 12) l. Rearrange (6. 12): ΔK/K = s. A - d (6. 13) l. Since output is proportional to capital, ΔY/Y = ΔK/K, so ΔY/Y = s. A - d (6. 14) l. Thus the saving rate affects the long-run growth rate (not true in Solow model) Copyright © 2005 Pearson Addison-Wesley. All rights reserved. 35

6. 2 Growth Dynamics: The Solow Model u. Summary l. Endogenous growth theory attempts to explain, rather than assume, the economy's growth rate l. The growth rate depends on many things, such as the saving rate, that can be affected by government policies Copyright © 2005 Pearson Addison-Wesley. All rights reserved. 36

6. 3 Government Policies to Raise Long-Run Living Standards n Policies to affect the saving rate u. If the private market is efficient, the government shouldn't try to change the saving rate l The private market's saving rate represents its trade-off of present for future consumption l But if tax laws or myopia cause an inefficiently low level of saving, government policy to raise the saving rate may be justified u. How can saving be increased? l One way is to raise the real interest rate to encourage saving; but the response of saving to changes in the real interest rate seems to be small l Another way is to increase government saving Ø The government could reduce the deficit or run a surplus Ø But under Ricardian equivalence, tax increases to reduce the deficit won't affect national saving Copyright © 2005 Pearson Addison-Wesley. All rights reserved. 37

6. 3 Government Policies to Raise Long-Run Living Standards n Policies to raise the rate of productivity growth u. Improving infrastructure l Infrastructure: highways, bridges, utilities, dams, airports l Empirical studies suggest a link between infrastructure and productivity l U. S. infrastructure spending has declined in the last two decades l Would increased infrastructure spending increase productivity? Ø There might be reverse causation: Richer countries with higher productivity spend more on infrastructure, rather than vice versa Ø Infrastructure investments by government may be inefficient, since politics, not economic efficiency, is often the main determinant Copyright © 2005 Pearson Addison-Wesley. All rights reserved. 38

6. 3 Government Policies to Raise Long-Run Living Standards u. Building human capital l There's a strong connection between productivity and human capital l Government can encourage human capital formation through educational policies, worker training and relocation programs, and health programs l Another form of human capital is entrepreneurial skill. l Government could help by removing barriers like red tape (red tape is the administration of government paperwork and procedures that are time consuming and costly to businesses (particularly small businesses), the term red tape was developed from early business practice when government paperwork was bound with red strands) u. Encouraging research and development l Government can encourage R&D through direct aid to research Copyright © 2005 Pearson Addison-Wesley. All rights reserved. 39