The Romer Model: Policy Implications

Transcription

1 The Romer Model: Policy Implications Prof. Lutz Hendricks Econ520 February 16, / 29

2 Policies have level effects What are the effects of government policies? We may expect policies to affect saving (s K ), R&D (s A ), or population growth (n). Consider the case of φ < 1, where growth is g(a) = λ n 1 φ (1) Main result: Policies that affect only saving or investment in R&D (s A ) do not affect long-run growth. Note: For policies that do not affect R&D the model behaves exactly like the Solow model. 2 / 29

3 R&D Subsidies Consider a permanent increase in s A. We must consider two equations: g(a) = B (s A L) λ A φ 1 (2) K = s K Y d K (3) Note: Behavior of A is independent of K and Y. Simplify by assuming λ = 1 and φ = 0 so that g(a) = B s A L / A (4) Balanced growth rate: g(a) = n 3 / 29

4 R&D Subsidies g(a) = δ s A A/L n (A/L)* A/L 4 / 29

5 R&D Subsidies On a BGP, (4) determines A/L: g(a) = n = Bs A L/A (5) implies (A/L) = B s A n (6) Transition: As long as L/A is above BGP, g(a) > n is above BGP. Therefore, g(a) declines over time until it reaches n. The BGP is stable. 5 / 29

6 Transition path after an increase in s A g(a) = δ s A A/L n (A/L)* A/L 6 / 29

7 Time path of the growth rate of ideas. A period of faster innovation builds up more ideas. 7 / 29

8 Time path of A. Eventually growth levels off, but the higher level of A remains forever. 8 / 29

9 Policy implications Patent protection, R&D subsidies, and other policies affect s A. These policies can raise the growth rate of output, although not in the long run. Policies do affect long-run levels of Y/L. 9 / 29

10 Gains From Openness Traditional trade theory implies that gains from trade are small. The Romer model has a new channel for gains from trade. The idea: each firm invests in technology capital A closed economy: A can be used in all domestic locations open economy: A can be used in more locations productivity rises due to increasing returns to scale 10 / 29

11 Evidence: Gains From Openness Idea: Fig. do 1. EU-6 countries labor productivity thatasopen a percentage upofgrow U.S. ( ). faster? Fig joiners labor productivity as a percentage of EU-6 ( ). Source: McGrattan and Prescott (2009) other group of three countries Austria, Finland, and Sweden joined the EU in shows that collectively, the productivity of these countries relative to that of the EU-6 was lling until the countries joined the EU; then it turned around and gained ground. 11 / 29

12 Evidence: Gains From Openness E.R. McGrattan, E.C. Prescott / Journal of Economic Theory 144 (2009) Fig. 5. CE-8 labor productivity as a percentage of EU-6 ( ). Source: McGrattan and Prescott (2009) 12 / 29

13 Evidence: Gains From Openness Lucas (2009): open economies converge to the frontier country. 13 / 29

14 Outlook for U.S. growth VOL. 92 NO. 1 JONES: SOURCES OF U.S. ECONOMIC GROWTH IN A WORLD OF IDEAS FIGURE 1. U.S. GDP PER CAPITA, LOG SCALE argue against many endogenous growth models. Such models suggest that the long-run growth U.S. share growth of the has labor been constant force dev for must a longlevel time. off. Over the post Butmost are we likely on aeven balanced before, thes been rising steadily. Each incr growth path? transition path growth effect a on income, and the series of the last 50 or 100 years have stant growth path with a growth the long-run, sustainable growt economy. This appears to be th way to reconcile the facts th paper. A number of authors, most Klenow and Andrés Rodrígu and Ellen R. McGrattan and Ja Jr. (1999), have observed that large number of candidate grow literature, there has been surp 14 / 29

15 Inputs that increase productivity are rising CONOMIC GROWTH IN A WORLD OF IDEAS THE AMERICAN ECONOMIC REVIEW MARCH 2002 STATES esidual econstanies is et al. ics of popu- constant. 7 Also, we will measure h directly as educational attainment and incorporate this constant term in the coefficient. The last term in equation (10) is the effective number of researchers in the world. Recall from equation (6) that this number is given by a weighted sum of research labor. To provide a rough empirical measure of H A, we will make two assumptions. First, we assume that only researchers in the G-5 countries (France, West Germany, Japan, the United Kingdom, and the United States) are capable of extending the frontier of knowledge. This is motivated primarily FIGURE 3. byaverage the lack U.S. ofeducational data for other ATTAINMENT, countries PERSONS AGED 25 AND OVER prior to the 1980 s and by the fact that the majority of world research effort is conducted in these countries. Second, we assume that the quality of these researchers is the same across sponding the advanced to thecountries quantitiesand in equation has remained (9). 6 constant over The quantities appear time; this to grow can be at implemented roughly constant artificially rates, although by setting a slight productivity 0. This seems slowdown like a in reasonable both output assumption per hour and if one multifactor thinks that productivity is apparent. The capital-output ratio is to be hired in the first place, a researcher must have a certain level of education. The rise in average fairly stable, as is commonly accepted, and human capital per worker rises because of educational attainment, then, would not have an the What happens when these inputs stop growing? FIGURE 4. RESEARCH INTENSITY IN THE G-5 COUNTRIES Notes: The dashed line indicates data that have been estimated by the author. See Appendix B. G-5 employment at a rate of 1.2 percent per year. 8 The magnitude of research intensity is also worth noting. In the United States and throughout the G-5 countries, less than 1 percent of the labor force is engaged in research according to the definition employed by the National Science 15 / 29

16 A Model Extend the Romer model to incorporate: 1. Human capital in the production of output. 2. Human capital in R&D. Output production: Y t = A σ t K α t (h t L Yt ) 1 α (7) Then y t = Y t /L t = (K t /Y t ) α/(1 α) l Yt h t A σ/(1 α) t (8) 16 / 29

17 Output growth Along the transition: g(y) = α 1 α g(k/y) + g(l Y) + g(h) + σ g(a) (9) 1 α Balanced growth rate: K/Y and l y must be constant over time g(y) = g(h) + σ g(a) (10) 1 α In addition: g(a) will slow down when R&D inputs stop growing. We expect the balanced growth rate to be lower even than past TFP growth. 17 / 29

18 R&D sector Ȧ t = B(l At h t L t ) λ A φ t (11) so that Balanced growth: g(a) = (h tl At L t ) λ g(a) = A 1 φ t λ (g(h) + n) 1 φ (12) (13) Assume long-run g(h) = 0 because schooling levels off (strong assumption). Then (just like in our textbook model): g(a) = λ 1 φ n (14) 18 / 29

19 BGP output growth g(y) = Normalize σ = 1 α. Then γ = λ/(1 φ). Key point σ 1 α g(a) = σ λ n (15) 1 α 1 φ }{{} γ Transitional growth has several sources: g(h), growth of A in excess of γn, and balanced A growth of γn. Only the γn part is sustainable! 19 / 29

20 Quantifying the slowdown We observe: g(y) = 2% per year Balanced growth: γn where n = 1.2% per year. So the value of γ determines the slowdown. 20 / 29

21 How big is γ? Key idea (roughly): g(a) = (h tl At L t ) λ A 1 φ t (16) We observe g(a),h,l A. If g(a) was constant over time (roughly true), the we can estimate γ = λ/(1 φ). Result: γ 1/3. Key implication Only 1/3 of past TFP growth is sustainable once transitory increases of h and l A comes to an end. 21 / 29

22 Growth accounting implications Post-war average growth g(y) = 0.02 n = Balanced growth = γn = (1/3) 1.2% = 0.4% 22 / 29

23 n Transition dynamics We82.3 can simulate 51.4the model13.5 path to find out how rapidly growth slows down. tion (17) assuming x and n Result: Growth slows by half (relative to γn) every 40 years. te of rea- -life ized ctor ould e 4 eter tion an e of 950 d of near iven FIGURE 5. THE TRANSITION OF MULTIFACTOR PRODUCTIVITY TO STEADY STATE Notes: Log scale. A t is calculated using equation (18) as- 23 / 29

24 Discussion Thoughts? 24 / 29

25 Summary Innovations are produced just like regular goods, but they are non-rival. Therefore, we have scale effects: larger markets support more rapid innovation. The growth rate of Y/L is proportional to the population growth rate. A one-time increase in R&D effort (higher L A ) raises the rate of innovation permanently. But this is not enough to sustain higher long-run growth. Policies only have level effects. 25 / 29

26 Final Example What is the effect of a permanent increase in 1. research productivity (easy) 2. population (holding k fixed or not) 3. population growth (Europe) 26 / 29

27 Reading Jones (2013b), ch. 5. The section on the outlook for US growth is based on Jones (2002). Optional: Romer (2011), ch Jones (2013a), ch / 29

28 Advanced Reading Jones (2005) talks in some detail about the economics of ideas. Lucas (2009) and McGrattan and Prescott (2009) on openness and growth 28 / 29

29 References I Jones, C. I. (2002): Sources of US economic growth in a world of ideas, The American Economic Review, 92, (2005): Growth and ideas, Handbook of economic growth, 1, (2013a): Macroeconomics, W W Norton, 3rd ed. Jones, Charles; Vollrath, D. (2013b): Introduction To Economic Growth, W W Norton, 3rd ed. Lucas, R. E. (2009): Trade and the Diffusion of the Industrial Revolution, American Economic Journal: Macroeconomics, McGrattan, E. R. and E. C. Prescott (2009): Openness, technology capital, and development, Journal of Economic Theory, 144, Romer, D. (2011): Advanced macroeconomics, McGraw-Hill/Irwin. 29 / 29