Chapter 6
Long-Run
Economic
Growth
Table 6.1 Economic Growth in Eight Major
Countries, 1870–1998
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Goals of Chapter 6
Identify forces that determine the growth
rate of an economy
Changes in productivity are key
Saving and investment decisions are also
important
Examine policies governments may use to
influence the rate of growth
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6.1 The Sources of Economic Growth
Production function
Y = AF(K,N)
(6.1)
Decompose into growth rate form: the growth
accounting equation
ΔY/Y = ΔA/A + aK ΔK/K + aN ΔN/N
(6.2)
The a terms are the elasticities of output with respect to
the inputs (capital and labor)
Interpretation
 A rise of 10% in A raises output by 10%
 A rise of 10% in K raises output by aK times 10%
 A rise of 10% in N raises output by aN times 10%
Both aK and aN are less than 1 due to diminishing
marginal productivity
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6.1 The Sources of Economic Growth
Growth accounting
Four steps in breaking output growth into its
causes (productivity growth, capital input
growth, labor input growth)
Get data on ΔY/Y, ΔK/K, and ΔN/N, adjusting for
quality changes
Estimate aK and aN from historical data
Calculate the contributions of K and N as aK ΔK/K
and aN ΔN/N, respectively
Calculate productivity growth as the residual:
ΔA/A = ΔY/Y - aK ΔK/K - aN ΔN/N
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Table 6.2 The Steps of Growth Accounting:
A Numerical Example
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Table 6.2 The Steps of Growth Accounting:
A Numerical Example (cont’d)
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6.1 The Sources of Economic Growth
Application: growth accounting and the east
Asian “miracle” (in 4th edition)
The east Asian "tigers" (Taiwan, Hong Kong,
Singapore, and South Korea) grew over 7% per
year for 25 years
Alwyn Young's research found that their rapid
growth resulted from capital and labor growth, not
productivity growth (total factor productivity, TFP)
TFP growth rates: TW (2.6%), HK (2.3%), SG (0.2%)
SK (1.7%)
The implication is that such rapid growth can't be
sustained, since growth in inputs is hard to maintain
permanently
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6.1 The Sources of Economic Growth
Growth accounting and the productivity
slowdown
Denison's results for 1929–1982 (Table 6.3)
 Entire period output growth 2.92%; due to labor 1.34%;
due to capital 0.56%; due to productivity 1.02%
 Pre-1948 capital growth was much slower than post-1948
 Post-1973 labor growth slightly slower than pre-1973
 Productivity growth is major difference
 Entire period: 1.02%
 1929–1948: 1.01%
 1948–1973: 1.53%
 1973–1982: -0.27%
 1982-1997: 0.76% (Bureau of Labor Statistics)
Productivity growth slowdown occurred in all major
developed countries
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Table 6.3 Sources of Economic Growth in the
United States (Denison) (Percent per Year)
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6.1 The Sources of Economic Growth
Application: the post-1973 slowdown in productivity
growth: What caused the decline in productivity?
 Measurement—inadequate accounting for quality improvements
 The legal and human environment—regulations for pollution
control and worker safety, crime, and declines in educational
quality
 Technological depletion and slow commercial adaptation—
Nordhaus suggests that technological innovation has temporarily
dried up; also, companies may be slow to adapt new technology
 Oil prices—huge increase in oil prices reduced productivity of
capital and labor, especially in basic industries
 New industrial revolution—learning process for information
technology from 1973 to 1990 meant slower growth
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6.1 The Sources of Economic Growth
Application: a U.S. productivity miracle?
Labor productivity growth increased sharply
in the second half of the 1990s
The increase in labor productivity can be
traced to the ICT (information and
communications technologies) revolution
Computer technology improved very rapidly after
1995
Firms invested heavily in ICT because of
increased marginal productivity
Advances in computer technology spilled over
into other industries
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Table 6.4 Growth in Average Labor Productivity
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6.2 Growth Dynamics: The Solow Model
Three basic questions about growth
What's the relationship between the
long-run standard of living and the saving
rate, population growth rate, and rate of
technical progress?
How does economic growth change over
time? Will it speed up, slow down, or
stabilize?
Are there economic forces that will allow
poorer countries to catch up to richer
countries?
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6.2 Growth Dynamics: The Solow Model
Setup of the Solow model
Basic assumptions and variables
Population and work force grow at same rate n
Economy is closed and G = 0
Ct = Yt - It (6.3)
Rewrite everything in per-worker terms:
yt = Yt/Nt; ct = Ct/Nt; kt = Kt/Nt
kt is also called the capital-labor ratio
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6.2 Growth Dynamics: The Solow Model
The per-worker production function
yt = f(kt) (6.4)
Assume no productivity growth for now
(add it later)
Plot of per-worker production
function—Fig. 6.1
Same shape as aggregate production
function
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Figure 6.1 The per-worker production function
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6.2 Growth Dynamics: The Solow Model
Steady states
 Steady state: yt, ct, and kt are constant over time
 Gross investment must
 Replace worn out capital, dKt
 Expand so the capital stock grows as the economy grows, nKt
 It = (n + d)Kt (6.5)
 From Eq. (6.3), Ct = Yt - It = Yt - (n + d)Kt (6.6)
 In per-worker terms, in steady state c = f(k) - (n + d)k
 Plot of c, f(k), and (n + d)k (Fig. 6.2)
 Increasing k will increase c up to a point
(6.7)
 This is k1 in the figure, the Golden Rule capital stock
 For k beyond this point, c will decline
 But we assume henceforth that k is less than k1, so c always rises
as k rises
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Figure 6.2 The relationship of consumption per
worker to the capital–labor ratio in the steady state
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Figure 6.2 The relationship of consumption per
worker to the capital–labor ratio in the steady state
(cont’d)
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6.2 Growth Dynamics: The Solow Model
Reaching the steady state
Suppose saving is proportional to current income:
St = sYt
(6.8)
, where s is the saving rate, which is between 0 and 1
Equating saving to investment gives
sYt = (n + d)Kt
(6.9)
Putting this in per-worker terms gives
sf(k) = (n + d)k
(6.10)
Plot of sf(k) and (n + d)k (Fig. 6.3)
The only possible steady-state capital-labor ratio is k*
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Figure 6.3 Determining the capital–labor ratio
in the steady state
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6.2 Growth Dynamics: The Solow Model
Output at that point is y* = f(k*); consumption is c* =
f(k*) - (n + d)k*
If k begins at some level other than k*, it will move
toward k*
For k below k*, saving > the amount of investment
needed to keep k constant, so k rises
For k above k*, saving < the amount of investment
needed to keep k constant, so k falls
To summarize, with no productivity growth, the
economy reaches a steady state, with constant
capital-labor ratio, output per worker, and
consumption per worker
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6.2 Growth Dynamics: The Solow Model
The fundamental determinants of longrun living standards
The saving rate
Higher saving rate means higher capital-labor
ratio, higher output per worker, and higher
consumption per worker (shown in Fig. 6.4)
Should a policy goal be to raise the saving rate?
Not necessarily, since the cost is lower
consumption in the short run
There is a trade-off between present and future
consumption
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Figure 6.4 The effect of an increased saving rate
on the steady-state capital–labor ratio
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6.2 Growth Dynamics: The Solow Model
Population growth
 Higher population growth means a lower capital-labor ratio,
lower output per worker, and lower consumption per
worker (shown in Fig. 6.5)
 Should a policy goal be to reduce population growth?
 Doing so will raise consumption per worker
 But it will reduce total output and consumption,
affecting a nation's ability to defend itself or influence
world events
 The Solow model also assumes that the proportion of the
population of working age is fixed
 But when population growth changes dramatically this
may not be true
 Changes in cohort sizes may cause problems for
social security systems and areas like health care
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Figure 6.5 The effect of a higher population growth
rate on the steady-state capital–labor ratio
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6.2 Growth Dynamics: The Solow Model
 Productivity growth
 The key factor in economic growth is productivity improvement
 Productivity improvement raises output per worker for a given
level of the capital-labor ratio
 In equilibrium, productivity improvement increases the capitallabor ratio, output per worker, and consumption per worker
 Productivity improvement directly improves the amount that
can be produced at any capital-labor ratio
 The increase in output per worker increases the supply of
saving, causing the long-run capital-labor ratio to rise
 Can consumption per worker grow indefinitely?
 The saving rate can't rise forever (it peaks at 100%) and the
population growth rate can't fall forever
 But productivity and innovation can always occur, so living
standards can rise continuously
 Summary: The rate of productivity improvement is the dominant
factor determining how quickly living standards rise
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Figure 6.6 An improvement in productivity
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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
Application: Do economies converge?
Unconditional convergence: Poor countries
eventually catch up to rich countries
This should occur if saving rates, population growth
rates, and production functions are the same
worldwide
Then, 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
If 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
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6.2 Growth Dynamics: The Solow Model
Conditional convergence: Living standards will converge
in countries with similar characteristics [s, n, d, f(k)]
 Countries with different fundamental characteristics will not
converge
 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
No convergence: Poor countries don't catch up over
time; this is inconsistent with the Solow model
What is the evidence?
 Little support for unconditional convergence
 Some support for conditional convergence after correcting for
differences in saving rates and population growth (Mankiw,
Romer, and Weil, 1992)
 Support for conditional convergence among states in the United
States (Barro and Sala-i-Martin, 1992)
 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)
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6.2 Growth Dynamics: The Solow Model
Endogenous growth theory—explaining the
sources of productivity growth
Aggregate production function Y = AK (6.11)
Constant MPK
Human capital
 Knowledge, skills, and training of individuals
 Human capital tends to increase in same proportion as
physical capital
Research and development programs
Increases in capital and output generate increased
technical knowledge, which offsets decline in MPK
from having more capital
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6.2 Growth Dynamics: The Solow Model
Implications of endogenous growth
Suppose saving is a constant fraction of output:
S = sAK
Since investment = net investment + depreciation,
I = ΔK + dK
Setting investment equal to saving implies:
ΔK + dK= sAK (6.12)
Rearrange (6.12): ΔK/K = sA - d (6.13)
Since output is proportional to capital, ΔY/Y = ΔK/K,
so ΔY/Y = sA - d (6.14)
Thus the saving rate affects the long-run growth rate
(not true in Solow model)
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6.2 Growth Dynamics: The Solow Model
Summary
Endogenous growth theory attempts to
explain, rather than assume, the
economy's growth rate
The growth rate depends on many
things, such as the saving rate, that
can be affected by government policies
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6.3 Government Policies to Raise Long-Run Living Standards
 Policies to affect the saving rate
If the private market is efficient, the government
shouldn't try to change the saving rate
 The private market's saving rate represents its trade-off of
present for future consumption
 But if tax laws or myopia cause an inefficiently low level of
saving, government policy to raise the saving rate may be
justified
How can saving be increased?
 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
 Another way is to increase government saving
 The government could reduce the deficit or run a surplus
 But under Ricardian equivalence, tax increases to reduce the
deficit won't affect national saving
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6.3 Government Policies to Raise Long-Run Living Standards
 Policies to raise the rate of productivity growth
Improving infrastructure
 Infrastructure: highways, bridges, utilities, dams, airports
 Empirical studies suggest a link between infrastructure and
productivity
 U.S. infrastructure spending has declined in the last two
decades
 Would increased infrastructure spending increase productivity?
 There might be reverse causation: Richer countries with higher
productivity spend more on infrastructure, rather than vice versa
 Infrastructure investments by government may be inefficient,
since politics, not economic efficiency, is often the main
determinant
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6.3 Government Policies to Raise Long-Run Living Standards
Building human capital
 There's a strong connection between productivity and
human capital
 Government can encourage human capital formation
through educational policies, worker training and relocation
programs, and health programs
 Another form of human capital is entrepreneurial skill.
 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)
Encouraging research and development
 Government can encourage R&D through direct aid to
research
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