The fundamentals of economic growth MK 8

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The fundamentals of economic growth

MK 8

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THE GROWTH QUESTION

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Figure 1.1: GDP p.c. and Life Satisfaction

Fig. 1.1

GDP per Capita and Life Satisfaction in 2006

Sources: World Economic Outlook, IMF; Wikipedia

Satisfactionwithlifeindex

GDP per capita 2006

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Figure 4.3: Life Expectancy and Income

Source: Heston, Summers and Aten (2006) Fig. 4.3

Life expectancy

per capitaGDP

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Miracles and disasters

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Issues on Macroeconomics

Long – run growth

• Why are some countries richer than other?

• Why are some countries growing faster than other?

• Are per capita incomes converging?

• Is there something government policies can do about?

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MIRACLES AND DISASTERS

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KALDOR FACTS

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The Kaldor’ facts

1. Output per worker grows over time at a sustained rate

2. The capital stock per worker grows over time at a sustained rate

3. The capital-output ratio exhibits no clear trend over time

4. The real return to capital is relatively constant over 5. The shares of labour and of capital on national time

income are roughly constant over time

6. There are wide differences in the growth rate of productivity across countries

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Capital output ratios

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The basic Solow model

“A thrifty society will, in the long run, be wealthier than an impatient one, but it

will not grow faster” [Robert Lucas Jr.]

.

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The basic model

• Production function with CRS on capital (K) and labour (N)

• TFP (A) constant

• Perfect competition

• Keynesian consumption function with exogenous savings rate

• Population expanding at a constant rate

• Constant depreciation rate

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Factor income shares

• Perfect competition and CRS imply constant factor income shares

• The share of labour income in national income is equal to 1-b the elasticity of labour in the production function

• The share of capital is b.

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Output-labour ratio (y=Y/N)

0

y= Af k( )

A

s f k( )

 

ⁿ^^ ^k

B

A D

C

k1

0

 k 

^{ }^k ⁰

k2

Capital-labour ratio (k=K/N)

Dynamics and Equilibrium

k*

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THE BASIC SOLOW MODEL AND THE FACTS

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Saving rate and per capita GDP

5 6 7 8 9 10 11

0 5 10 15 20 25 30 35

Investment as a percentage of GDP (average 1950-2000) Real GDP per capita in 2000 (logs, 1996 US dolars)

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Population growth and per capita GDP

5.5 6.5 7.5 8.5 9.5 10.5

-1% 0% 1% 1% 2% 2% 3% 3% 4% 4% 5%

Average population growth (1950-2000) Log of GDP per capita in 2000 (1996 US dolars)

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0

A

s f k( )



ⁿ ^^



^k

A

s f k( )

Capital-labour ratio (k=K/N)

Fig. 3.8 (a)

y=Af k( )

A

B

The

productivity of capital (and r) declines

What happens when s increases?

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What happens when A increases?

N Y

y = /

*

k1 ^k ⁼ ^K ^/ ^N

(n+)k

sy sy

*

k0

*

y1

*

y0

(Y/K)₀

kb

A

y = ₁ _b

k A y = ₀

0

1

The productivity of capital (and r) is constant

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Growth effects ?

Investment Rate and Growth of Real GDP per

capita

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The Solow model and the Kaldor’ facts

1. Output per worker grows over time at a sustained rate - Not OK

2. The capital stock per worker grows over time at a sustained rate – Not OK

3. The capital-output ratio exhibits no clear trend over time – OK

4. The real return to capital is relatively constant over time – OK

5. The shares of labour and of capital on national income are roughly constant over time - OK

6. There are wide differences in the growth rate of productivity across countries – Not OK.

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GOLDEN RULE

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Constant fraction (n) of capital per worker is used up in production each period.

0

y=Af k( )

 

ⁿ^^

= k

depreciation

 ^

-  Net output

( )

= Af k n k

 k = replacement investment needed

to maintain constant capital intensity Gross output

( )

= Af k

k

The Steady State: Gross Vs. Net Output

k Capital-labour ratio

(k=K/N)

Fig. 3.5 (a)

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Raising Steady State Consumption

Fig. 3.10

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How efficient is a move towards the golden rule?

• If s>s_G a free lunch is available (dynamic inefficiency)

• But if s<s_G, the move towards the golden rule obeys to a trade off. Without a social welfare function, one cannot evaluate this move.

• Why would a decentralized economy deliver too much savings? Distortions?

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SOLOW RESIDUAL

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The Solow residual

• Measures the contribution of factors other

than labour and physical capital to the change in per capita GDP

• The contribution of capital and labour is assessed taking into account the

corresponding income shares

• TFP change is computed as the difference

between the actual growth of output and the growth implied by factor accumulation.

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The Solow Decomposition 1913-1987

The Solow Decomposition 1913-1987*

(avg. annual growth rates)

*An adjustment has been made for the modernization of productive capital

Table 3.6 (a)

Source: Maddison (1991)

Country GDP Contribution

of inputs

Residual

France 2.6 1.1 1.0

Germany 2.8 1.4 0.8

Netherlands 3.0 2.0 0.4

UK 1.9 1.2 0.5

USA 3.0 2.0 0.7

Japan 4.7 3.0 0.5

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Discussion

• The Solow model accounts for the fact that historical ratios of capital to output and real interest rates tend to be relatively stable in the long run.

• It also offers the credible suggestion that countries with high savings rates and low population growth rates should enjoy higher per capita incomes.

• In its current formulation the model fails, however, to explain the most basic fact of modern economic growth: that per capita income tends to increase over time.

• Continuous growth of per capita income could be obtained in the context of the Solow model if saving rates rose continuously over time. But then,

interest rates should exhibit declining trends, and this does not happen in reality.

• The obvious solution is to allow technology to expand over time: as we just saw, with technological progress, per capita output expansion does not imply a declining interest rate.