Chapter 6

Long-Run Economic Growth

Introduction (Table 6.1)

• A nation’s ability to provide improving standard of living for its people depends on its long-run rate of economic growth.

• e.g. (1) Australia v.s. Japan (2) US (Between 1947~1973, GDP

growth=4%; 1973~2002, GDP growth=2.9%)

Goals of this chapter

• To identify the force that determine the growth rate of an economy over long periods of time.

• To examine various policies that governments may use to try to influence the rate of growth.

• To identify forces that determine the growth rate of an economy1. Changes in productivity are key2. Saving and investment decisions are also important

6.1 The Sources of Economic Growth

• (A) Production function• Y = AF(K, N) (6.1)• 1. Decompose into growth rate form: the growth accounting

equation

• DY/Y = DA/A + aK DK/K + aN DN/N (6.2)• 2. The a terms are the elasticities of output with respect to the

inputs (capital and labor)

B) Growth accounting

• 1. Four steps in breaking output growth into its causes (productivity growth, capital input growth, labor input growth)

• a. Get data on DY/Y, DK/K, and DN/N, adjusting for quality changes

• b. Estimate aK and aN from historical data• c. Calculate the contributions of K and N as

aK DK/K and aN DN/N, respectively• d. Calculate productivity growth as the

residual: DA/A = DY/Y – aK DK/K – aN DN/N

2. Growth accounting and the productivity slowdown

• a. Denison’s results for 1929–1982 (text Table 6.3)• (1) Entire period output growth 2.92%; due to labor

1.34%; due to capital 0.56%; due to productivity 1.02%• (2) Pre-1948 capital growth was much slower than

post-1948• (3) Post-1973 labor growth slightly slower than pre-

1973• (4) Productivity growth is major difference• b. Productivity growth slowdown occurred in all

major developed countries

3. Application: the post-1973 slowdown in productivity growth

What caused the decline in productivity?• a. Measurement• b. The legal and human environment• c. Technological depletion and slow

commercial adaptation• d. Oil prices• e. New industrial revolution

4. Application: a U.S. productivity miracle?

• a. Labor productivity growth increased sharply in the second half of the 1990s

• b. The increase in labor productivity can be traced to the ICT (information and communications technologies) revolution

• (1) Computer technology improved very rapidly after 1995

• (2) Firms invested heavily in ICT because of increased marginal productivity

• (3) Advances in computer technology spilled over into other industries

6.2 Growth Dynamics: The Solow Model

• Recall that the economy’s rate of input growth as given in the growth accounting equation

Why do capital and labor grow at the rate that they do?

Three basic questions about growth?

Setup of the Solow model

• 1. Basic assumptions and variables

• a. Population and work force grow at same rate n

• b. Economy is closed and G = 0

• c. Ct = Yt – It (6.3)

• d. Rewrite everything in per-worker terms: yt = Yt/Nt; ct = Ct/Nt; kt = Kt/Nt

• e. kt is also called the capital-labor ratio

2. The per-worker production function

• a. yt = f(kt) (6.4)

• b. Assume no productivity growth for now (add it later)

• c. Plot of per-worker production function—text Figure 6.1

• d. Same shape as aggregate production function

3. Steady states

• a. Steady state: yt, ct, and kt are constant over time• b. Gross investment must• (1) Replace worn out capital, dKt• (2) Expand so the capital stock grows as the

economy grows, nKt• c. It = (n + d)Kt (6.5)• d. From Eq. (6.3),• Ct = Yt – It = Yt – (n + d)Kt (6.6)• e. In per-worker terms, in steady state• c = f(k) - (n + d)k (6.7)• f. Plot of c, f(k), and (n + d)k (Figure 6.1; identical to

text Figure 6.2)

Conclusions from Figure 6.2

• g. Increasing k will increase c up to a point

• (1) This is kG in the figure, the Golden Rule capital stock

• (2) For k beyond this point, c will decline

• (3) But we assume henceforth that k is less than kG, so c always rises as k rises

4. Reaching the steady state

• a. Suppose saving is proportional to current income:• St = sYt, (6.8)• where s is the saving rate, which is between 0

and 1• b. Equating saving to investment gives• sYt = (n + d)Kt (6.9)•

c. Putting this in per-worker terms gives• sf(k) = (n + d)k (6.10)• d. Plot of sf(k) and (n + d)k (Figure 6.2; identical to

text Figure 6.3)

Conclusions from Figure 6.3

• e. The only possible steady-state capital-labor ratio is k*

• f. Output at that point is y* = f(k*); consumption is c* = f(k*) - (n + d)k*

• g. If k begins at some level other than k*, it will move toward k*

• h. To summarize, with no productivity growth, the economy reaches a steady state, with constant capital-labor ratio, output per worker, and consumption per worker

C) The fundamental determinants of long-run living standards

• 1. The saving rate• a. Higher saving rate means higher capital-

labor ratio, higher output per worker, and higher consumption per worker (shown in text Figure 6.4)

• b. Should a policy goal be to raise the saving rate?

• (1) Not necessarily• (2) There is a trade-off between present and

future consumption

2. Population growth

• a. Higher population growth means a lower capital-labor ratio, lower output per worker, and lower consumption per worker (shown in text Figure 6.5)

• b. Should a policy goal be to reduce population growth?

3. Productivity growth

• a. The key factor in economic growth is productivity improvement

• b. Productivity improvement raises output per worker for a given level of the capital-labor ratio

• c. In equilibrium, productivity improvement increases the capital-labor ratio, output per worker, and consumption per worker

• d. Can consumption per worker grow indefinitely?• e. Summary: The rate of productivity improvement is

the dominant factor determining how quickly living standards rise

4. Application: Do economies converge?

• a. Unconditional convergence: Poor countries eventually catch up to rich countries

If there is international borrowing and lending, there is more support for unconditional convergence

• (a) Capital should flow from rich to poor countries, as it will have a higher marginal product there

• (b) So investment wouldn’t be limited by domestic saving

b. Conditional convergence: • Living standards will converge in countries

with similar characteristics [s, n, d, f(k)]

• (1) Countries with different fundamental characteristics will not converge

• (2) 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

c. No convergence: Poor countries don’t catch up over time; this is inconsistent with the Solow model

• d. What is the evidence?

• (1) Little support for unconditional convergence

• (2) Mankiw, Romer, and Weil, 1992

• (3) Barro and Sala-i-Martin, 1992

D) Endogenous growth theory—explaining the sources of productivity growth

• Solow model assumes the rate of productivity growth as given.

• 1. Aggregate production function• Y = AK (6.11)• a. Constant MPK, why not diminishing?• (1) Human capital• (2) Research and development programs• (3) Increases in capital and output generate

increased technical knowledge

2. Implications of endogenous growth

• a. Suppose saving is a constant fraction of output: S = sAK

• b. Since investment = net investment + depreciation, I = DK + dK

• c. Setting investment equal to saving implies:• DK + dK = sAK (6.12)• d. Rearrange (6.12):• DK/K = sA – d (6.13)• e. Since output is proportional to capital, DY/Y =

DK/K, so• DY/Y = sA – d (6.14)• f. Thus the saving rate affects the long-run growth

rate (not true in Solow model)

3. Summary

• a. Endogenous growth theory attempts to explain, rather than assume, the economy’s growth rate

• b. The growth rate depends on many things, such as the saving rate, that can be affected by government policies

II. Government Policies to Raise Long-Run Living Standards (Sec. 6.3)

• A) Policies to affect the saving rate• 1. If the private market is efficient, the government

shouldn’t try to change the saving rate

•2. How can saving be increased?

• a. 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

• b. Another way is to increase government saving

B) Policies to raise the rate of productivity growth

• 1. Improving infrastructure• a. Infrastructure: highways, bridges, utilities,

dams, airports• b. Empirical studies suggest a link between

infrastructure and productivity• c. U.S. infrastructure spending has declined

in the last two decades• d. Would increased infrastructure spending

increase productivity?• (1) There might be reverse causation • (2) Infrastructure investments by government

may be inefficient

2. Building human capitala. There’s a strong connection between productivity and

human capitalb. Government can encourage human capital formation through educational policies, worker training and relocation

programs, and health programsc. Another form of human capital is entrepreneurial skill

Government could help by removing barriers like red tape

• 3. Encouraging research and development• Government can encourage R and D

through direct aid to research