# Economic Growth II: Technology, Empirics, and Policy

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1 CHAPTER9 : Technology, Empirics, and Policy Modified for ECON 2204 by Bob Murphy 2016 Worth Publishers, all rights reserved

2 IN THIS CHAPTER, YOU WILL LEARN: how to incorporate technological progress in the Solow model about policies to promote growth about growth empirics: confronting the theory with facts two simple models in which the rate of technological progress is endogenous 1

3 Introduction In the Solow model of Chapter 8, the production technology is held constant. income per capita is constant in the steady state. Neither point is true in the real world: : U.S. real GDP per person grew by a factor of 8.3, or 1.9% per year. examples of technological progress abound (see next slide). 2

4 Examples of technological progress U.S. farm sector productivity nearly tripled from 1950 to The real price of computer power has fallen an average of 30% per year over the past three decades. 2000: 361 million Internet users, 740 million cell phone users 2015: 3.1 billion Internet users, 4.9 billion cell phone users 2001: ipod capacity = 5gb, 1000 songs. Not capable of playing episodes of Game of Thrones. 2015: ipod touch capacity = 64gb, 16,000 songs. Can play episodes of Game of Thrones. 3

5 Technological progress in the Solow model A new variable: E = labor efficiency Assume: Technological progress is labor-augmenting: it increases labor efficiency at the exogenous rate g: g = ΔE E 4

6 Technological progress in the Solow model We now write the production function as: Y = F( K, L E ) where L E = the number of effective workers. Increases in labor efficiency have the same effect on output as increases in the labor force. 5

7 Technological progress in the Solow model Notation: y = Y /LE = output per effective worker k = K /LE = capital per effective worker Production function per effective worker: y = f(k) Saving and investment per effective worker: sy = sf(k) 6

8 Technological progress in the Solow model (δ +n + g)k = break-even investment: the amount of investment necessary to keep k constant. Consists of: δ k to replace depreciating capital n k to provide capital for new workers gk to provide capital for the new effective workers created by technological progress 7

9 Technological progress in the Solow model Investment, break-even investment Δk = s f(k) (δ +n +g)k (δ+n +g )k sf(k) k * Capital per worker, k 8

10 Steady-state growth rates in the Solow model with tech. progress Variable Capital per effective worker Output per effective worker Output per worker Symbol k = K /(L E ) y = Y /(L E ) (Y/L) = y E Steady-state growth rate 0 0 g Total output Y = y E L n + g 9

11 The Golden Rule with technological progress To find the Golden Rule capital stock, express c * in terms of k * : c * = y * i * = f (k * ) (δ +n +g) k * c * is maximized when MPK = δ + n + g or equivalently, MPK δ = n + g In the Golden Rule steady state, the marginal product of capital net of depreciation equals the pop. growth rate plus the rate of tech progress. 10

12 Growth empirics: Balanced growth Solow model s steady state exhibits balanced growth many variables grow at the same rate. Solow model predicts Y/L and K/L grow at the same rate (g), so K/Y should be constant. This is true in the real world. Solow model predicts real wage grows at same rate as Y/L, while real rental price is constant. Also true in the real world. 11

13 Growth empirics: Convergence Solow model predicts that, other things equal, poor countries (with lower Y/L and K/L) should grow faster than rich ones. If true, then the income gap between rich & poor countries would shrink over time, causing living standards to converge. In real world, many poor countries do NOT grow faster than rich ones. Does this mean the Solow model fails? 12

14 Growth empirics: Convergence Solow model predicts that, other things equal, poor countries (with lower Y/L and K/L) should grow faster than rich ones. No, because other things aren t equal: In samples of countries with similar savings & pop. growth rates, income gaps shrink about 2% per year. In larger samples, after controlling for differences in saving, pop. growth, and human capital, incomes converge by about 2% per year. 13

15 Growth empirics: Convergence What the Solow model really predicts is conditional convergence countries converge to their own steady states, which are determined by saving, population growth, and education. This prediction comes true in the real world. 14

16 Growth empirics: Convergence Figure 1 Figure 2 Growth rate: 1960& &1 & &1 & Log output per working-age adult: 1960 Log output per working-age adult: 1960 Growth rate: 1960& Source: Figures 1 and 2: G. Mankiw, D. Romer, and D. Weil, A Contribution to the Empirics of Economic Growth, Quarterly Journal of Economics 107, no. 2 (May 1992): See Supplement

17 Growth empirics: Convergence Figure 1 Mideast Great Lakes Per Capita Personal Income as a Percentage of U.S. Average By Region Far West New England 100 Plains Rocky Mt Southwest Southeast Source: U.S. Department of Commerce, Bureau of Economic Analysis. See Supplement

18 Growth empirics: Factor accumulation vs. production efficiency Differences in income per capita among countries can be due to differences in: 1. capital physical or human per worker 2. the efficiency of production (the height of the production function) Studies: Both factors are important. The two factors are correlated: countries with higher physical or human capital per worker also tend to have higher production efficiency. 17

19 Growth empirics: Factor accumulation vs. production efficiency Possible explanations for the correlation between capital per worker and production efficiency: Production efficiency encourages capital accumulation. Capital accumulation has externalities that raise efficiency. A third, unknown variable causes capital accumulation and efficiency to be higher in some countries than others. 18

20 Policy issues Are we saving enough? Too much? What policies might change the saving rate? How should we allocate our investment between privately owned physical capital, public infrastructure, and human capital? How do a country s institutions affect production efficiency and capital accumulation? What policies might encourage faster technological progress? 19

21 Policy issues: Evaluating the rate of saving Use the Golden Rule to determine whether the U.S. saving rate and capital stock are too high, too low, or about right. If (MPK δ) > (n + g ), U.S. economy is below the Golden Rule steady state and should increase s. If (MPK δ) < (n + g ), U.S. economy is above the Golden Rule steady state and should reduce s. 20

22 Policy issues: Evaluating the rate of saving To estimate (MPK δ), use three facts about the U.S. economy: 1. k = 2.5 y The capital stock is about 2.5 times one year s GDP. 2. δk = 0.1 y About 10% of GDP is used to replace depreciating capital. 3. MPK k = 0.3 y Capital income is about 30% of GDP. 21

23 Policy issues: Evaluating the rate of saving 1. k = 2.5 y 2. δk = 0.1 y 3. MPK k = 0.3 y To determine δ, divide 2 by 1: δk k = 0.1 y 2.5y δ 0.1 = =

24 Policy issues: Evaluating the rate of saving 1. k = 2.5 y 2. δk = 0.1 y 3. MPK k = 0.3 y To determine MPK, divide 3 by 1: MPK k 0.3y = k 2.5y 0.3 MPK = = Hence, MPK δ = =

25 Policy issues: Evaluating the rate of saving From the last slide: MPK δ = 0.08 U.S. real GDP grows an average of 3% per year, so n + g = 0.03 Thus, MPK δ = 0.08 > 0.03 = n + g Conclusion: The U.S. is below the Golden Rule steady state: Increasing the U.S. saving rate would increase consumption per capita in the long run. 24

26 Policy issues: How to increase the saving rate Reduce the government budget deficit (or increase the budget surplus). Increase incentives for private saving: Reduce capital gains tax, corporate income tax, estate tax, as they discourage saving. Replace federal income tax with a consumption tax. Expand tax incentives for IRAs (individual retirement accounts) and other retirement savings accounts. 25

27 Policy issues: Allocating the economy s investment In the Solow model, there s one type of capital. In the real world, there are many types, which we can divide into three categories: private capital stock public infrastructure human capital: the knowledge and skills that workers acquire through education How should we allocate investment among these types? 26

28 Policy issues: Allocating the economy s investment Two viewpoints: 1. Equalize tax treatment of all types of capital in all industries, then let the market allocate investment to the type with the highest marginal product. 2. Industrial policy: Government should actively encourage investment in capital of certain types or in certain industries, because they may have positive externalities that private investors don t consider. 27

29 Possible problems with industrial policy The government may not have the ability to pick winners (choose industries with the highest return to capital or biggest externalities). Politics (e.g., campaign contributions) rather than economics may influence which industries get preferential treatment. 28

30 Policy issues: Establishing the right institutions Creating the right institutions is important for ensuring that resources are allocated to their best use. Examples: Legal institutions, to protect property rights. Capital markets, to help financial capital flow to the best investment projects. A corruption-free government, to promote competition, enforce contracts, etc. 29

31 Establishing the right institutions: North vs. South Korea After WW2, Korea split into: North Korea with institutions based on authoritarian communism South Korea with Western-style democratic capitalism Today, GDP per capita is over 10x higher in S. Korea than N. Korea 30

32 Establishing the right institutions: Corruption and Growth See Supplement

33 Policy issues: Encouraging tech. progress Patent laws: encourage innovation by granting temporary monopolies to inventors of new products. Tax incentives for R&D Grants to fund basic research at universities Industrial policy: encourages specific industries that are key for rapid tech. progress (subject to the preceding concerns). 32

34 CASE STUDY: Is free trade good for economic growth? Since Adam Smith, economists have argued that free trade can increase production efficiency and living standards. Research by Sachs & Warner: Average annual growth rates, developed nations developing nations open 2.3% 4.5% closed 0.7% 0.7% 33

35 CASE STUDY: Is free trade good for economic growth? To determine causation, Frankel and Romer exploit geographic differences among countries: Some nations trade less because they are farther from other nations, or landlocked. Such geographical differences are correlated with trade but not with other determinants of income. Hence, they can be used to isolate the impact of trade on income. Findings: increasing trade/gdp by 2% causes GDP per capita to rise 1%, other things equal. 34

36 Endogenous growth theory Solow model: sustained growth in living standards is due to tech progress. the rate of tech progress is exogenous. Endogenous growth theory: a set of models in which the growth rate of productivity and living standards is endogenous. 35

37 The basic model Production function: Y = AK where A is the amount of output for each unit of capital (A is exogenous & constant) Key difference between this model & Solow: MPK is constant here, diminishes in Solow Investment: sy Depreciation: δk Equation of motion for total capital: ΔK = sy δk 36

38 The basic model ΔK = sy δk Divide through by K and use Y = A K to get: ΔY Y ΔK = = sa δ K If sa > δ, then income will grow forever, and investment is the engine of growth. Here, the permanent growth rate depends on s. In Solow model, it does not. 37

39 Does capital have diminishing returns or not? Depends on definition of capital. If capital is narrowly defined (only plant & equipment), then yes. Advocates of endogenous growth theory argue that knowledge is a type of capital. If so, then constant returns to capital is more plausible, and this model may be a good description of economic growth. 38

40 A two-sector model Two sectors: manufacturing firms produce goods. research universities produce knowledge that increases labor efficiency in manufacturing. u = fraction of labor in research (u is exogenous) Manufacturing: Y = F [K, (1 u)e L] Research: ΔE = g(u)e Capital accumulation: ΔK = sy δk 39

41 A two-sector model In the steady state, manufacturing output per worker and the standard of living grow at rate ΔE / E = g (u). Key variables: s: affects the level of income, but not its growth rate (same as in Solow model) u: affects level and growth rate of income 40

42 DISCUSSION QUESTION The merits of raising u Question: In what ways would raising u (i.e. devoting more labor to research) benefit the economy? What are the costs of raising u? 41

43 Facts about R&D 1. Much research is done by firms seeking profits. 2. Firms profit from research: Patents create a stream of monopoly profits. Extra profit from being first on the market with a new product. 3. Innovation produces externalities that reduce the cost of subsequent innovation. Much of the new endogenous growth theory attempts to incorporate these facts into models to better understand technological progress. 42

44 Is the private sector doing enough R&D? The existence of positive externalities in the creation of knowledge suggests that the private sector is not doing enough R&D. But, there is much duplication of R&D effort among competing firms. Estimates: Social return to R&D 40% per year. Thus, many believe govt should encourage R&D. 43

45 Economic growth as creative destruction Schumpeter (1942) coined term creative destruction to describe displacements resulting from technological progress: the introduction of a new product is good for consumers but often bad for incumbent producers, who may be forced out of the market. Examples: Luddites ( ) destroyed machines that displaced skilled knitting workers in England. Walmart displaces many mom-and-pop stores. 44

46 CHAPTER SUMMARY 1. Key results from Solow model with tech progress: Steady-state growth rate of income per person depends solely on the exogenous rate of tech progress The U.S. has much less capital than the Golden Rule steady state 2. Ways to increase the saving rate Increase public saving (reduce budget deficit) Tax incentives for private saving 45

47 CHAPTER SUMMARY 3. Empirical studies Solow model explains balanced growth, conditional convergence. Cross-country variation in living standards is due to differences in cap. accumulation and in production efficiency. 4. Endogenous growth theory: Models that examine the determinants of the rate of tech. progress, which Solow takes as given. explain decisions that determine the creation of knowledge through R&D. 46

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