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 economy
1. Changes in productivity are key
2. 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 post1948
• (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.
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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.
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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 capitallabor 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 capitallabor 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)
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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 capital
a.
There’s a strong connection between productivity and
human capital
b.
Government can encourage human capital formation
through educational policies, worker training and relocation
programs, and health programs
c.
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