lecture 8: history and causes of growthwbrooks/lecture8.pdf · lecture 8: history and causes of...
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Lecture 8: History and Causes of Growth
1
11 February 2020
Prof. Wyatt Brooks
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Causes of Growth Before: Looked at special cases and tried to
qualitatively understand causes of growth
Now evaluate causes of growth quantitatively
Motivating question: How important is history? That is, if a country has always been poor, are they at a
disadvantage relative to one that has been rich?
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Solow Growth Model
Robert Solow Macroeconomist Professor at MIT Nobel Prize (1987)
Important Contributions: Developed a macroeconomic
model that allows for a decomposition of GDP into factors of production (capital, labor, productivity) Showed that capital
accumulation is relatively unimportant for growth Contrasts with the thinking of
the majority of economists before (Smith, Marx, etc.)
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Macroeconomic Models Models: A theoretical construct designed to represent a
complex system. Economists use these models to predict the effects of
policy, such as: If taxes are raised, what will happen to
unemployment? Who will gain and lose from a free trade
agreement? What happens to unemployment if the Federal
Reserve increases the supply of money in the economy? What policies can increase growth in developing
countries?
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Key Features of a Macroeconomic Model
Consumers: Represent households who supply labor, make investments and consume
Firms: Represent all businesses who use factors of production (labor, capital, land, etc.) to produce output
Equilibrium: The outcome of the model.
A prediction about how firms and consumers interact through markets
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Solow Growth Model Observation: Richer countries have more capital
(more machines, factories, etc.)
Is this the cause or the result of their greater income?
Two possibilities considered:
Countries have more capital because they save a greater part of their income
Countries have more capital because the return on investing in capital is higher
The whole model is beyond the scope of this class, so we will consider a greatly simplified version
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Simplified Solow Growth ModelConsumers: Consume a constant fraction of GDP and own
all the capital in the economy Not modeling: Unemployment (everyone always works) Lifecycle (no children, students or retirees) Within-country income inequality
Consumers described by one equation:
I = s Ywhere s, a number between 0 and 1, is the
fraction of output that gets invested.
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Simplified Solow Growth ModelFirms: Use the capital to produce output Not modeling: Labor markets (searching for workers) Finance (borrowing to take on projects) Executive compensation
Firms described by one equation:
Y = A K0.3
where Y is GDP, A is productivity and K is the capital stock
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Simplified Solow Growth ModelEquilibrium: All output is used either in investment or
consumption (no trade, no government):
Y = C + I
How the stock of capital changes over time:
K’ = I + (1- δ)Kwhere K’ is the capital stock next year,
K is the capital stock this year, I is investment this year, and δ is the depreciation rate
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Simplified Solow Growth ModelSo the entire model is described by four equations:
Households: I = s Y Firms: Y = A K0.3
Capital Accumulation: K’ = I + (1- δ)K GDP: Y = C + I
Rearranging terms:
I = s Y = s A K0.3
K’ = I + (1- δ)K = s A K0.3 + (1- δ)K
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How does the capital stock change over time?
K’
K
K’= K
How are capital this year, and capital next year related?
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How does the capital stock change over time?
K’
K
K’= K
K’ = s A K0.3 + (1- δ)K
The equation above tells you how much capital there will be next year
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How does the capital stock change over time?
K’
K
K’= K
K’ = s A K0.3 + (1- δ)K
Suppose the economy starts with some low capital level K0
K0
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How does the capital stock change over time?
K’
K
K’= K
K’ = s A K0.3 + (1- δ)K
Then the equation says that next year’s capital stock will be K1
K0
K1
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How does the capital stock change over time?
K’
K
K’= K
K’ = s A K0.3 + (1- δ)K
Using the red 45 degree line as a reference, we can find K1 on the horizontal axis.
K0
K1
K1
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How does the capital stock change over time?
K’
K
K’= K
K’ = s A K0.3 + (1- δ)K
Then we can find K2
K0
K1
K1
K2
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How does the capital stock change over time?
K’
K
K’= K
K’ = s A K0.3 + (1- δ)K
Repeating these steps, we can find the capital stock in any future year
K0
K1
K1
K2
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How does the capital stock change over time?
K’
K
K’= K
K’ = s A K0.3 + (1- δ)K
Repeating these steps, we can find the capital stock in any future year
K0
K1
K1
K2
K2
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How does the capital stock change over time?
K’
K
K’= K
K’ = s A K0.3 + (1- δ)K
Repeating these steps, we can find the capital stock in any future year
K0
K1
K1
K2
K2
K3
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How does the capital stock change over time?
K’
K
K’= K
K’ = s A K0.3 + (1- δ)K
Repeating these steps, we can find the capital stock in any future year
K0
K1
K1
K2
K2
K3
K3
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How does the capital stock change over time?
K’
K
K’= K
K’ = s A K0.3 + (1- δ)K
Repeating these steps, we can find the capital stock in any future year
K0
K1
K1
K2
K2
K3
K3
K4
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How does the capital stock change over time?
K’
K
K’= K
K’ = s A K0.3 + (1- δ)K
Notice that the capital stock is approaching the point where the two lines meet
K0
K1
K1
K2
K2
K3
….
K10
K10
….
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How does the capital stock change over time?
K’
K
K’= K
K’ = s A K0.3 + (1- δ)K
The point where the two lines meet is the steady state level of capital. Once the economy is at this level, the capital level does not change.
K*
K*
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Some Things to Notice The further the economy starts below the steady
state level of capital, the faster the economy initially grows
Referred to as the “catch-up” effect
This is due to the effect of “diminishing returns”
The amount of extra output from each additional unit of capital goes down as the capital stock gets larger
Growth slows over time until the capital stock reaches the steady state level
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Savings and Productivity
What happens if the savings rate of the country changes? Increase s from its initial level to a higher level
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Increase in the Savings Rate
K’
K
K’= K
K’ = s A K0.3 + (1- δ)K
Suppose the economy is in a steady state with savings rate s.
K*
K*
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Increase in the Savings Rate
K’
K
K’= K
K’ = s’ A K0.3 + (1- δ)K
Then the savings rate increases to s’.
K*
K*
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Increase in the Savings Rate
K’
K
K’= K
K’ = s’ A K0.3 + (1- δ)K
Now capital accumulates according to the new equation with the higher savings rate
K1
K*
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Increase in the Savings Rate
K’
K
K’= K
K’ = s’ A K0.3 + (1- δ)K
And we proceed exactly like before.
K1
K*
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Increase in the Savings Rate
K’
K
K’= K
K’ = s’ A K0.3 + (1- δ)K
Eventually a new, higher steady state capital stock is reached.
K0
K0 K*
K*
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Savings and Productivity What happens if instead productivity is
increased?
Same thing.
Income goes up, so consumers have more to invest, which increases the capital stock.
How are they different?
Higher savings: Decreases consumption today, increases it (maybe) in the future
Higher productivity: Increases consumption both today and in the future
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0
20000
40000
60000
80000
100000
120000
-20 -10 0 10 20 30 40 50 60 70
GD
P pe
r Cap
ita
Savings Rate
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Savings and ProductivityBack to what Solow found: Savings rates (even historical) have little
relationship to relative wealth Apparently the wealth of countries that are
now rich is not because of long term savings and investment per se
That is, clearly the fact that rich countries are rich is partly because they have more capital. BUT they have more capital becausethey have high productivity.
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Savings and Productivity This is an extremely important finding. Suggests that a long history of capital
accumulation is not necessary to be wealthy If a country is able to increase its productivity,
capital will “catch up” quite quickly This shifted the emphasis in the study of
promoting development in low income countries away from trying to send them capital, and towardtrying to make their economies more efficient How do you do that? Perhaps the most important open question in
economics.
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Sources of Growth? Growth through savings: Increases in GDP driven by higher K/Y
Growth through productivity: Increases in GDP driven by higher A K/Y is roughly constant (as in Solow)
Other possibilities: Labor: L/N Human capital: h
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Last Topic: Growth Accounting
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USA Growth Accounting
50
100
200
400
1950 1960 1970 1980 1990 2000 2010
Y/NK/Y^(1/2)hL/NA^(3/2)
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China Growth Accounting
50
100
200
400
800
1600
3200
1950 1960 1970 1980 1990 2000 2010
Y/NK/Y^(1/2)hL/NA^(3/2)
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South Korea Growth Accounting
50
100
200
400
800
1600
3200
1960 1970 1980 1990 2000 2010
Y/NK/Y^(1/2)hL/NA^(3/2)
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Argentina Growth Accounting
50
100
200
400
1950 1960 1970 1980 1990 2000 2010
Y/NK/Y^(1/2)hL/NA^(3/2)
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Zimbabwe Growth Accounting
25
50
100
200
400
1960 1970 1980 1990 2000 2010
Y/NK/Y^(1/2)hL/NA^(3/2)
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Findings In growing countries, growth is not driven by K/Y,
it’s driven by A In non-growing countries, big fluctuations in all of
the factors Why does A go up in growing countries? Look to histories Improvements in technology Improvements in institutions