lecture 8: history and causes of growthwbrooks/lecture8.pdf · lecture 8: history and causes of...

Lecture 8: History and Causes of Growth

1

11 February 2020

Prof. Wyatt Brooks

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?

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.)

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?

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

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

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.

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

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

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

How does the capital stock change over time?

K’

K

K’= K

How are capital this year, and capital next year related?


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


K’

K

K’= K

K’ = s A K0.3 + (1- δ)K

Suppose the economy starts with some low capital level K0

K0


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


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


K’

K

K’= K

K’ = s A K0.3 + (1- δ)K

Then we can find K2

K0

K1

K1

K2


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


K’

K

K’= K

K’ = s A K0.3 + (1- δ)K


K0

K1

K1

K2

K2


K’

K

K’= K

K’ = s A K0.3 + (1- δ)K


K0

K1

K1

K2

K2

K3


K’

K

K’= K

K’ = s A K0.3 + (1- δ)K


K0

K1

K1

K2

K2

K3

K3


K’

K

K’= K

K’ = s A K0.3 + (1- δ)K


K0

K1

K1

K2

K2

K3

K3

K4


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

….


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*

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

Savings and Productivity

What happens if the savings rate of the country changes? Increase s from its initial level to a higher level

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*


K’

K

K’= K

K’ = s’ A K0.3 + (1- δ)K

Then the savings rate increases to s’.

K*

K*


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*


K’

K

K’= K

K’ = s’ A K0.3 + (1- δ)K

And we proceed exactly like before.

K1

K*


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*

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

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

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.

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.

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

Last Topic: Growth Accounting

USA Growth Accounting

50

100

200

400

1950 1960 1970 1980 1990 2000 2010

Y/NK/Y^(1/2)hL/NA^(3/2)

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)

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)

Argentina Growth Accounting

50

100

200

400

1950 1960 1970 1980 1990 2000 2010

Y/NK/Y^(1/2)hL/NA^(3/2)

Zimbabwe Growth Accounting

25

50

100

200

400

1960 1970 1980 1990 2000 2010

Y/NK/Y^(1/2)hL/NA^(3/2)

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

lecture 8: history and causes of growthwbrooks/lecture8.pdf · lecture 8: history and causes of...

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