The Facts of Growth The Long Run

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The Facts of Growth The Long Run
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The Facts of Growth The Long Run

• Annual Growth Rate Real Output per
  Capita Output per Capita () (1992 dollars)

Ratio of Real Ouput Per Capita
1950-1973 1973-1998 1950 1998 1998/1950
France 4.2 1.6 5,150 19,158 3.7 Germany 4.9 1.8 4,
356 20,059 4.6 Japan 8.1 2.5 1,820 19,907 10.9 Uni
ted Kingdom 2.5 1.9 6,870 19,005 2.8 United
States 2.2 1.5 11,170 25,890 2.3 Average 4.4 1.9 5
,872 20,804 3.5
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The Facts of Growth The Long Run
Constructing Output Numbers
Purchasing Power Parity Adjusts for differences
in exchange rates and prices
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The Facts of Growth The Long Run
Observations

• Strong growth 1950-2001
• Growth rates have decreased since the mid
  1970s 1950-1978 4.4 (GDP/capita doubles every
  16 years) 1973-2001 1.9 (GDP/capita doubles
  every 37 years)
• Convergence in output/capita across countries

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The Facts of Growth The Long Run
Convergence in Output/Capita
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The Facts of Growth The Long Run
What do you think
Could the finding of convergence beinfluenced by
the way the countries areselected?
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The Facts of Growth The Long Run
A Broader Look Across Time and Space

• Looking across two millennia
• From the end of the Roman Empire to 1500, no
  output per capita growth in Europe
• 1500-1700 -- Small growth in output per capita
  (0.1/year and 0.2/year 1700 to 1820)
• 1820-1950 -- Modest growth (U.S. 1.5)
• The high-growth of the 1950s and 1960s is unusual

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The Facts of Growth The Long Run
A Broader Look Across Time and Space

• Looking across two millennia (Continued)
• 1st Millennium to the 15th century, China had the
  highest output/capita
• Leaders in output/capita change
  frequently Italy Netherlands U.K.

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The Facts of Growth The Long Run
The Reality of Growth A Workingmans Budget in
1851
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The Facts of Growth The Long Run
Looking Across Countries Convergence Not the
Rule
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The Facts of Growth The Long Run
Looking Across Countries A Closer Look
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The Facts of Growth The Long Run
Looking Across Countries A Closer Look
Three Conclusions

• OECD countries are converging
• Asian countries are converging
• African countries are not converging

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The Facts of Growth The Long Run
Looking Across Countries A Closer Look
Growth Miracles vs Growth Disasters

• Miracles Japan Asian Tigers
• (South Korea, Taiwan, Singapore, Hong Kong)
• (average annual growth of over 5 1960-1990)
• Disasters Argentina (average income in 1900
• Similar to those of world leaders now middle of
• World income distribution)
• Disaster Sub-saharan Africa (Chad, Ghana,
• Mozambique) extremely poor throughout history

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The Facts of Growth The Long Run
A Summary
1. Growth is not a historical necessity 2. Conver
gence of OECD countries to the U.S. may be the
prelude to leapfrogging 3. The rapid post WWII
growth was atypical
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The Facts of Growth The Long Run
Thinking About Growth A Primer (The Solow Model)
The Aggregate Production Function
Y F (K, N) Y Aggregate Output K Capital N
Labor
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The Facts of Growth The Long Run
The Aggregate Production Function
Y F (K, N)
F Depends on technology
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The Facts of Growth The Long Run
Returns to Scale and Returns to Factors
Constant returns to scale 2Y F(2K,2N) xY
F(xK,xN)

• Decreasing returns to factors (capital labor)
• Increases in K and N lead to smaller and smaller
  increases in output

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The Facts of Growth The Long Run
Output and Capital per worker
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The Facts of Growth The Long Run
Output and Capital per worker
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The Facts of Growth The Long Run
Output and Capital per worker
Output per worker, Y/N
Capital per worker, K/N
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The Facts of Growth The Long Run
The Sources of Growth

• An improvement in technology shifts
• the production function up

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The Facts of Growth The Long Run
The Sources of Growth
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The Facts of Growth The Long Run
The Sources of Growth

• Capital Accumulation
• Cannot sustain growth because of diminishing
  returns to capital
• Capital accumulation requires savings, therefore,
  what is the appropriate savings rate?

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The Facts of Growth The Long Run
The Sources of Growth

• Technological Progress
• Required for sustained growth
• What determines the rate of technological progres
  s?

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Saving, Capital Accumulation, and OutputThe Long
Run
Observation
U.S. 18.6Germany 24.6Japan 33.7
What do you think
Would increasing the U.S. savings rate lead to
sustained higher U.S. growth in the future?
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Interactions between Output and Capital
Two long-run relations between output and capital

• The amount of capital determines the amount of
  output being produced
• The amount of output determines the amount of
  savings and investment and, thus, the amount of
  capital

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Interactions between Output and Capital
Capital, Output, and Saving/Investment
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Interactions between Output and Capital
The Effects of Capital on Output
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Interactions between Output and Capital
The Effects of Capital on Output
Two assumptions

• Employment (N) is constant
• There is no technological progress (f is constant)

Therefore
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Interactions between Output and Capital
The Effects of Output on Capital Accumulation
Output Investment
Three assumptions

• Closed economy I S (G-T)
• I S if G T 0, therefore (G-T)0
• S sY Private saving is proportional
  to income s Savings rate (between 0 1)

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Interactions between Output and Capital
The Effects of Output on Capital Accumulation
Observations

• The savings rate does not appear to
  systematically increase or decrease as Y
  increases
• Richer countries do not appear to have
  systematically higher savings rates than poorer
  ones
• Investment is proportional to output

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Interactions between Output and Capital
The Effects of Output on Capital Accumulation
Investment and Capital Accumulation
The evolution of the capital stock
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Interactions between Output and Capital
The Effects of Output on Capital Accumulation
Investment and Capital Accumulation
The relation between output and capital
accumulation
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Interactions between Output and Capital
The Effects of Output on Capital Accumulation
Investment and Capital Accumulation
The relation between output and capital
accumulation
Capital/worker in t1 Capital/Worker in t,
adjusted for depreciation and
investmentInvestment/worker Savings rate x
Output/worker in t
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Interactions between Output and Capital
The Effects of Output on Capital Accumulation
Investment and Capital Accumulation
The relation between output and capital
accumulation
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Interactions between Output and Capital
A Summary
The Production Side
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Implications of Alternative Saving Rates
Dynamics of Capital and Output
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Implications of Alternative Saving Rates
Dynamics of Capital and Output
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Implications of Alternative Saving Rates
Dynamics of Capital and Output
The change in capital/worker from t to t1
depends on the difference between
Investment/Worker Depreciation/Worker
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Implications of Alternative Saving Rates
Dynamics of Capital and Output
Capital/Worker increases Investment/Worker gt
Depreciation/Worker
Capital/Worker decreases Investment/Worker lt
Depreciation/Worker
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Implications of Alternative Saving Rates
Dynamics of Capital and Output Graphically
Output per worker, Y/N
AB Output/worker
AC Investment/worker
AD Depreciation
AC gt AD
K/N
(Ko/N)
Capital per worker, K/N
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Implications of Alternative Saving Rates
Dynamics of Capital and Output
Assume
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Implications of Alternative Saving Rates
Steady-State Capital and Output
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Implications of Alternative Saving Rates
The Saving Rate and Output
What are the effects of the saving rate on the
rate of output per worker?

• The saving rate has no effect on the long run
  growth rate of output/worker, this is equal to
  zero.
• The saving rate determines the level of
  output/worker in the long run.
• An increase in the saving rate will lead to a
  higher growth of output/worker for some time, but
  not forever.

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Implications of Alternative Saving Rates
The Effects of Different Saving Rate
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Implications of Alternative Saving Rates
The Effects of Different Saving Rate
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Implications of Alternative Saving Rates
The Effects of Different Saving Rate
(No technological progress)
Associated with saving rate s1 gt s0
Associated with saving rate s0
t
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Implications of Alternative Saving Rates
The Effects of Different Saving Rate
(Technological progress)
t
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Implications of Alternative Saving Rates
The Savings Rate and the Golden Rule
Does an increase in saving lead to an increase
inconsumption in the long run?
Two Scenarios

• Saving Rate 0
• Capital 0
• Output 0
• Consumption 0

• Saving Rate 1
• Consumption 0
• Output replaces depreciation

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Implications of Alternative Saving Rates
The Savings Rate and the Golden Rule
The Golden-Rule Level of Capital
The value of saving that yields the highestlevel
of consumption in steady state.
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Implications of Alternative Saving Rates
sG
0
1
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Getting a Sense of Magnitudes
Question for Discussion
Can a low saving/investment rate explain why the
U.S. growth rate has been so low since 1950?
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Implications of Alternative Saving Rates
The Savings Rate and the Golden Rule
What do you think
Are countries likely to have too muchcapital?
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Getting a Sense of Magnitudes
Some Questions

• How large is the effect of a change in the saving
  rate on output in the long run?
• For how long and by how much does an increase in
  the saving rate affect growth?
• How far is the U.S. from the Golden Rule of Level
  of Capital?

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Getting a Sense of Magnitudes
Calculating the Answers
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Getting a Sense of Magnitudes
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Getting a Sense of Magnitudes
The Effects of the Saving Rate on Steady-State
Output
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Implications of Alternative Saving Rates
The Effects of the Saving Rate on Steady-State
Output
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Getting a Sense of Magnitudes
The Effects of the Saving Rate on Steady-State
Output
Steady-State Output/Worker
Observation
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Getting a Sense of Magnitudes
The Effects of the Saving Rate on Steady-State
Output
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Getting a Sense of Magnitudes
The Dynamic Effects of an Increase in the Saving
Rate
Assume

• The saving rate has always been equal to 0.1
• Then the saving rate increases to 0.2 forever

Then
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Getting a Sense of Magnitudes
The Dynamic Effects of an Increase in the Saving
Rate
Continuing for each year yields
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Getting a Sense of Magnitudes
The Dynamic Effects of an Increase in the Saving
Rate
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Getting a Sense of Magnitudes
The Dynamic Effects of an Increase in the Saving
Rate
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Getting a Sense of Magnitudes
The U.S. Saving Rate and the Golden Rule
What saving rate that would maximize steady-state
consumption?
In Steady-State
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Getting a Sense of Magnitudes
The Saving Rate and the Steady-State Levels of
Capital, Output, and Consumption per Worker
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Getting a Sense of Magnitudes
The U.S. Saving Rate and the Golden Rule
Observation
If s lt .50 increasing s will increase
long-run consumption
In the U.S., s lt 20
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Physical Versus Human Capital
Human Capital
The set of skills of the workers in theeconomy.
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Physical Versus Human Capital
Observations
OECD Countries

• 100 of children get a primary education
• 90 of children get a secondary education
• 38 of children get a higher education
• Literacy rate above 95

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Physical Versus Human Capital
Extending the Production Function
Measuring the Impact of Human Capital
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Physical Versus Human Capital
Human Capital, Physical Capital, and Output
How does including human capital impact our
analysis?
Investment now includes physical and humancapital
In the U.S.
Education spending 6.5 of GDP Investment
16.0 of GDP
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Physical Versus Human Capital
Human Capital, Physical Capital, and Output
Some Complications

• Education is partly consumption
• Education cost should include the
  opportunitycost
• On-the-job training is not included
• Should compare investment rates net
  ofdepreciation

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Physical Versus Human Capital
Endogenous Growth
What do you think
To what extent does growth depend on the savings
rate, education, and technological change?