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FIN 30220: Macroeconomic Analysis Long Run Growth

FIN 30220: Macroeconomic Analysis

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FIN 30220: Macroeconomic Analysis. Long Run Growth. The World Economy. Total GDP (2013): $87T Population (2013):7.1B GDP per Capita (2013): $13,100 Population Growth (2013): 1.0% GDP Growth (2013): 2.9%. GDP per capita is probably the best measure of a country’s overall well being. - PowerPoint PPT Presentation

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Page 1: FIN 30220: Macroeconomic Analysis

FIN 30220: Macroeconomic Analysis

Long Run Growth

Page 2: FIN 30220: Macroeconomic Analysis

The World Economy

Total GDP (2013): $87T Population (2013):7.1B GDP per Capita (2013): $13,100 Population Growth (2013): 1.0% GDP Growth (2013): 2.9%

GDP per capita is probably the best measure of a country’s overall well being

Page 3: FIN 30220: Macroeconomic Analysis

Region GDP % of World GDP

GDP Per Capita

Real GDP Growth

United States $17T 20% $53,000 1.6%

European Union $16T 18% $35,000 0.1%

Japan $4.7T 5% $36,300 2.0%

China $13T 15% $9,800 7.7%

Ghana $90B .1% $3,500 7.9%

Ethiopia $118.2B .13% $1,300 7.0%

Note. However, that growth rates vary significantly across countries/regions. Do you see a pattern here?

Source: CIA World Factbook (2013 Estimates)

Page 4: FIN 30220: Macroeconomic Analysis

At the current trends, the standard of living in China will surpass that of the US in 25 years! Or, will they?

Per

Cap

ita

Inco

me

That is, can China maintain it’s current growth rate?

Page 5: FIN 30220: Macroeconomic Analysis

Income GDP/Capita GDP Growth

Low < $1,045 6.3%

Middle $1,045 - $12,746 4.8%

High >$12,746 3.2%

As a general rule, low income (developing) countries tend to have higher average rates of growth than do high income countries

The implication here is that eventually, poorer countries should eventually “catch up” to wealthier countries in terms of per capita income – a concept known as “convergence”

Source: World Bank (2013 estimates)

Page 6: FIN 30220: Macroeconomic Analysis

Some countries, however, don’t fit the normal pattern of development

SudanGDP: $107B (#73)GDP Per Capita: $5,100 (#159)GDP Growth: -2.3% (#213)

MacauGDP: $51.6B (#98)GDP Per Capita: $88,700 (#3)GDP Growth: 11.9% (#5)

So, what is Sudan doing wrong? (Or, what is Macau doing right?)

At current trends, Per capita income in Macau will triple to $273,000 over the next decade. Over the same time period, per capita GDP in Sudan will drop by roughly 25%to $4,000!!!

Page 7: FIN 30220: Macroeconomic Analysis

To understand this, let’s look at the sources of economic growth….where does production come from?

LKAFY ,,Real GDP

“is a function of”

Productivity Capital Stock

Labor

Real GDP = Constant Dollar (Inflation adjusted) value of all goods and services produced in the United States

Capital Stock = Constant dollar value of private, non-residential fixed assets

Labor = Private Sector Employment

Productivity = Production unaccounted for by capital or labor

Page 8: FIN 30220: Macroeconomic Analysis

A convenient functional form for growth accounting is the Cobb-Douglas production function. It takes the form:

LAKY where 1

With the Cobb-Douglas production function, the parameters have clear interpretations:

Capital’s share of income (what % of total income in the US accrues to owners of capital)

Labor’s share of income (what % of total income in the US accrues to owners of labor)

Elasticity of output with respect to capital (% increase in output resulting from a 1% increase in capital)

Elasticity of output with respect to labor (% increase in output resulting from a 1% increase in labor)

Page 9: FIN 30220: Macroeconomic Analysis

3

2

3

1

LAKY

Suppose we have the following Cobb-Douglas production function:

A 1% rise in employment raises GDP by 2/3%

A 1% rise in capital raises GDP by 1/3%

We can rewrite the production function in terms of growth rates to decompose GDP growth into growth of factors:

LKAY %3

2%

3

1%%

Real GDP Growth (observable) Employment

Growth (observable)

Capital Growth (observable)

Productivity Growth (unobservable)

Page 10: FIN 30220: Macroeconomic Analysis

Year Real GDP (Billions of 2009 dollars)

Real Capital Stock (Billions of 2005 dollars)

Employment (thousands)

2010 14,939 40,615 130,745

2011 15,190 40,926 132,828

Lets decompose some recent data first…

% ln 15,190 ln 14,939 *100 1.67Y

% ln 132,828 ln 130,745 *100 1.58L

1 2% 1.67 .76 1.58 .36

3 3A

% ln 40,926 ln 40,615 *100 .76K

*Source: Penn World Tables

Page 11: FIN 30220: Macroeconomic Analysis

Year Real GDP (Billions of 2009 dollars)

Real Capital Stock (Billions of 2005 dollars)

Employment (thousands)

1950 2,273 6,328 46,855

2011 15,190 40,926 132,828

Now, lets look at long term averages

ln 15,190 ln 2,273% *100 3.11

61Y

ln 40,926 ln 6,328% *100 3.06

61K

ln 132,828 ln 46,855% *100 1.70

61L

1 2% 3.11 3.06 1.70 .98

3 3A

Page 12: FIN 30220: Macroeconomic Analysis

1939 - 1948

1948 - 1973

1973-1990

1990-2007

2007-2013

Output 5.79 4.00 3.10 3.60 1.1

Capital 3.34 3.70 4.20 4.10 1.4

Labor 4.46 1.00 1.90 1.60 -0.1

Productivity 1.71 2.1 0.5 1.2 0.7

A few things to notice:

Real GDP growth is declining over time.

Capital has been growing faster than labor

The contribution of productivity is diminishing!

Contributions to growth from capital, labor, and technology vary across time period

Page 13: FIN 30220: Macroeconomic Analysis

Generally speaking, productivity growth has been declining since WWIIA

nnua

l Gro

wth

Page 14: FIN 30220: Macroeconomic Analysis

Our model of economic growth begins with a production function

Real GDP

Productivity Capital Stock

Labor

Given our production function, economic growth can result from

• Growth in labor• Growth in the capital stock• Growth in productivity

3

2

3

1

LAKY

Page 15: FIN 30220: Macroeconomic Analysis

We are concerned with capital based growth. Therefore, growth in productivity and employment will be taken as given

Productivity grows at rate

AgPop

Pop

LF

LF

LL

Population grows at rate

Lg

Employment

Labor Force= Employment Ratio

( Assumed Constant)

Labor Force

Population= Participation rate

( Assumed Constant)

3

2

3

1

LAKY

Page 16: FIN 30220: Macroeconomic Analysis

Our simple model of economic growth begins with a production function with one key property – diminishing marginal product of capital

Y

K

),,( LKAF

As the capital stock increases (given a fixed level of employment), the productivity of capital declines!!

K

YMPK

Change in Capital Stock

Change in Production

An economy can’t grow through capital accumulation alone forever!

3

2

3

1

LAKY

K

Y

K

Y

Page 17: FIN 30220: Macroeconomic Analysis

Everything in this model is in per capita terms

3

2

3

1

LAKY Divide both sides by labor to represent our variables in per capita terms

3

13

1

3

2

3

1

3

2

3

1

AkL

KA

LL

LAK

L

Yy

Capital Per Capita

Productivity

Per capita output

In general, let’s assume lower case letters refer to per capita variables

Page 18: FIN 30220: Macroeconomic Analysis

3

1

Aky

Again, the key property of production is that capital exhibits diminishing marginal productivity – that is as capital rises relative to labor , its contribution to production of per capita output shrinks

y

k

Capital stock per capita

Output per capita

Page 19: FIN 30220: Macroeconomic Analysis

3

1

Aky

Lets use an example. The current level of capital per capita will determine the current standard of living (output per capita = income per capita)

y

k

000,1

000,8

6

%2

0

L

K

A

g

g

L

A

8k

1286 3

1

y

Page 20: FIN 30220: Macroeconomic Analysis

Next, assume that households save a constant fraction of their disposable income

TYS

Savings

Income Less Taxes

Constant between zero and one

Again, convert everything to per capital terms by dividing through by the labor force

L

T

L

Y

L

S tys

Page 21: FIN 30220: Macroeconomic Analysis

KEY POINT:

Savings = Household income that hasn’t been spentInvestment = Corporate purchases of capital goods (plant, equipment, etc)

The role of the financial sector is to make funds saved by households available for firms to borrow for investment activities

Households save their income by opening savings accounts, buying stocks and bonds, etc

tys S = I

Firms access these funds by taking out loans, issuing stocks and bonds, etc. and use the funds for investment activities

iL

I

Investment per capita

Page 22: FIN 30220: Macroeconomic Analysis

3

1

Aky sy,

k

i s y t

Continuing with our example:

0

%10

t

8k

1286 3

1

y

.10 12 0 1.2i

Page 23: FIN 30220: Macroeconomic Analysis

Investment represents the purchase of new capital equipment. This will affect the capital stock in the future

IKK )1('

Future capital stock current capital stock

Annual Depreciation Rate

Investment Expenditures

We need to write this out in per capita terms as well…

Page 24: FIN 30220: Macroeconomic Analysis

L

I

L

K

L

K )1(

' Divide through by labor to get things in per capita terms

L

I

L

K

LL

LK )1(

'

'' Multiply and divide the left hand side by future labor supply

L

I

L

K

L

L

L

K

)1('

'

'

Recall that labor grows at a constant rate

)1('

LgL

L

ikgk L )1(1' Lg

ikk

1

)1('

We need to write this out in per capita terms as well…

Page 25: FIN 30220: Macroeconomic Analysis

lg

ikk

1

)1('

Future capital stock per capita

Annual depreciation rateCurrent capital per capita

Investment per capita

In our example…

10%

2%

8

1.2

Lg

k

i s

Given

Calculated

The evolution of capital per capita…

Annual population growth rate

24.802.1

2.18)10.1('

k

Page 26: FIN 30220: Macroeconomic Analysis

ikgk L

~)1(1'

kk '

kgi L ~

Just as a reference, lets figure out how much investment per capita would be required to maintain a constant level of capital per capita

Evolution of per capita capital

Assume constant capital per capita

Solve for investment

In our example…

200,1

000,8

000,1

%2

%10

SI

K

L

gL

Given

Calculated

96.802.10.~ i

Page 27: FIN 30220: Macroeconomic Analysis

Just to make sure, lets check our numbers…

In our example…

96.802.10.~ i

000,8

000,1

%2

%10

K

L

gL

lg

ikk

1

)1('

The evolution of capital per capita…

kk

8

02.1

96.8)10.1('

Page 28: FIN 30220: Macroeconomic Analysis

3

1

Aky iiy~

,,

k

tysi

kgi L ~

1286 3

1

y

2.1si

96.~ i

8k

Let’s update our diagram…

Actual investment

“break even” investment

Page 29: FIN 30220: Macroeconomic Analysis

Now we have all the components to calculate next years output per capita and the rate of growth

3

1

''' kAy

0

2%

6

8

1.2

' 8.24

A

L

g

g

A

k

i

k

Given

Calculated 11.1224.86' 3

1

y

%91.100*12ln11.12ln ygOutput per capita growth

24.802.1

2.18)10.1('

k

Page 30: FIN 30220: Macroeconomic Analysis

3

1

Aky iiy~

,,

k

tysi

kgi L ~

12y

2.1si

96.~ i

8k

Let’s update our diagram…

24.8'k

11.12y

Page 31: FIN 30220: Macroeconomic Analysis

020,1

405,8

6

%2

0

L

K

A

g

g

L

A

Let’s repeat that process again…

24.8'k 11.1224.86 3

1

y

0

%10

tT

211.1011.1210. s

46.8

02.1

211.124.810.1

1

)1('

Lg

ikk

Capital Savings = Investment

Evolution of Capital

Output

New Output

22.1246.86' 3

1

y

Output Growth

%90.100*11.12ln22.12ln yg

Growth is slowing down…why?

Page 32: FIN 30220: Macroeconomic Analysis

3

1

Aky iiy~

,,

k

tysi

kgi L ~

i~

The rate of growth depends on the level of investment relative to the “break even” level of investment.

k

si

y

Level of investment needed to maintain current capital stock

Actual investment based on current savings

Page 33: FIN 30220: Macroeconomic Analysis

3

1

Aky iiy~

,,

k

tysi

kgi L ~

Eventually, actual investment will equal “break even” investment and growth ceases (in per capita terms). This is what we call the steady state.

ssk

isi~

ssy

Page 34: FIN 30220: Macroeconomic Analysis

The steady state has three conditions….

1

kgi L

Investment is sufficient to maintain a constant capital/labor ratio

2

Savings per capita is a constant fraction of output per capita

tys 3

1

Aky Output is a function of capital per capita

3

Recall that, in equilibrium, savings equals investment

is

Page 35: FIN 30220: Macroeconomic Analysis

With a little algebra, we can solve for the steady state in our example.

%10

%10

0

6

%2

0

t

A

g

g

L

A kgi L Start with condition 3

kgty L Use condition 2 and the fact that savings equals investment

kgtAk L

3

1

Substitute condition 1

kgAk L 3

1Recall that taxes are zero in our example

2

3

Lg

Ak

Solve for k

Page 36: FIN 30220: Macroeconomic Analysis

Plugging in our parameters gives us steady state values.

%10

%10

0

6

%2

0

t

A

g

g

L

A

18.1102.10.

6*10. 2

32

3

Lg

Ak

Steady state per

capita capital

40.1318.116 3

13

1

AkySteady state per capita output

34.1040.1310. tys Steady state per capita savings/investment

18.11

02.1

34.118.1110.1

1

)1('

Lg

ikk

06.12040.139.1 tyc Steady state per capita consumption

Constant per capita capital!!!

Page 37: FIN 30220: Macroeconomic Analysis

Eventually, actual investment will equal “break even” investment and growth ceases (in per capita terms). This is what we call the steady state.

3

1

Aky iiy~

,,

k

tysi

kgi L ~

18.11ssk

34.1si

40.13ssy

In the steady state (with no productivity growth), all per capita variables have zero growth!

Page 38: FIN 30220: Macroeconomic Analysis

Suppose we started out example economy above it’s eventual steady state…

%10

%10

0

000,1

000,15

6

%2

0

t

L

K

A

g

g

L

A

15k

8.14156 3

13

1

Aky

48.108.1410. tysi

7.14

02.1

48.11510.1

1

)1('

Lg

ikk

7.147.146'' 3

13

1

Aky

%68.100*8.14ln7.14ln% y

An economy above its steady state shrinks (in per capita terms) towards its steady state.

Page 39: FIN 30220: Macroeconomic Analysis

3

1

Aky

iiy~

,,

k

tysi

kgi L ~

15k

48.1i

8.14y

An economy above its steady state shrinks (in per capita terms) towards its steady state.

8.1~ i

An economy above its steady state can’t generate enough savings to support its capital stock!

Page 40: FIN 30220: Macroeconomic Analysis

y

kSteady State

Countries below their eventual steady state will grown towards it

Investment needed to maintain current capital/labor ratio

Actual investment (equals savings)

Countries above their eventual steady state will shrink towards it

Investment needed to maintain current capital/labor ratio

Actual investment (equals savings)

Countries at their eventual steady state will stay there

“Absolute convergence” refers to the premise that every country will converge towards a common steady state

Page 41: FIN 30220: Macroeconomic Analysis

Most countries follow the “usual” pattern of development

1 Developing countries have very little capital, but A LOT of labor. Hence, the price of labor is low, the return to capital is very high

2 High returns to capital attract a lot of investment. As the capital stock grows relative to the labor force, output, consumption, and real wages grow while interest rates (returns to capital fall)

3 Eventually, a country “matures” (i.e. reaches its steady state level of capital). At this point, growth can no longer be achieved by investment in capital. Growth must be “knowledge based” – improving productivity!

Productivity

3

1

Aky

Page 42: FIN 30220: Macroeconomic Analysis

Does the economy have a “speed limit”?

Economic Growth can be broken into three components:

GDP Growth

= Productivity Growth + (2/3)Labor Growth + (1/3)Capital Growth

In the Steady State, Capital Growth = Labor Growth

GDP Growth

= Productivity Growth + Labor Growth

( GDP Per Capita Growth = Productivity Growth)

Page 43: FIN 30220: Macroeconomic Analysis

Developing countries are well below their steady state and, hence should grow faster than developed countries who are at or near their steady states – a concept known as absolute convergence

Examples of Absolute Convergence (Developing Countries)

China (GDP per capita = $6,300, GDP Growth = 9.3%)

Armenia (GDP per capita = $5,300, GDP Growth = 13.9%)

Chad (GDP per capita = $1,800, GDP Growth = 18.0%)

Angola (GDP per capita = $3,200, GDP Growth = 19.1%)

Examples of Absolute Convergence (Mature Countries)

Canada (GDP per capita = $32,900, GDP Growth = 2.9%)

United Kingdom (GDP per capita = $30,900, GDP Growth = 1.7%)

Japan (GDP per capita = $30,700, GDP Growth = 2.4%)

Australia (GDP per capita = $32,000, GDP Growth = 2.6%)

Page 44: FIN 30220: Macroeconomic Analysis

Some countries, however, don’t fit the traditional pattern.

Developing Countries with Low Growth

Madagascar(GDP per capita = $900, GDP Growth = - 2.0%)

Iraq (GDP per capita = $3,400, GDP Growth = - 3.0%)

North Korea (GDP per capita = $1,800, GDP Growth = 1.0%)

Haiti (GDP per capita = $1,200, GDP Growth = -5.1%)

Developed Countries with high Growth

Hong Kong (GDP per capita = $37,400, GDP Growth = 6.9%)

Iceland (GDP per capita = $34,900, GDP Growth = 6.5%)

Singapore (GDP per capita = $29,900, GDP Growth = 5.7%)

Qatar (GDP Per Capita = $179,000, GDP Growth = 16.3%)

Page 45: FIN 30220: Macroeconomic Analysis

Consider two countries…

Country A

000,1

000,4

%10

%10

0

6

%15

0

L

K

t

A

g

g

L

A

000,1

000,8

%10

%10

0

6

%2

0

L

K

t

A

g

g

L

A

Country B

We already calculated this!

12y%91.yg

52.946 3

13

1

Aky

952.052.910. tysi

95.3

15.1

952.410.1

1

)1('

Lg

ikk

48.995.36'' 3

13

1

Aky

41.100*52.9ln48.9ln yg

Even though Country B is poorer, it is growing slower than country A (in per capita terms)!

Page 46: FIN 30220: Macroeconomic Analysis

iiy~

,,

k

itys

kiA 10.02.~

18.11ssAk

With a higher rate of population growth, country B has a much lower steady state than country A!!!

kiB 10.15.~

3

2

3

2.10*6 3.71

.10 .15

Bss

L

Ak

g

4Bk 8Ak

Page 47: FIN 30220: Macroeconomic Analysis

Conditional convergence suggests that every country converges to its own unique steady state. Countries that are close to their unique steady state will grow slowly while those far away will grow rapidly.

y

Steady State

(Haiti)

High Population Growth (Haiti)

Low Population Growth (Argentina)

Haiti

Population Growth: 2.3%

GDP/Capita: $1,600

GDP Growth: -1.5%

Argentina

Population Growth: .96%

GDP/Capita: $13,700

GDP Growth: 8.7%Steady State

(Argentina)

Haiti is currently ABOVE its steady state (GDP per capita is falling due to a high population growth rate

Argentina, with its low population growth is well below its steady state growing rapidly towards it

Page 48: FIN 30220: Macroeconomic Analysis

Conditional convergence suggests that every country converges to its own unique steady state. Countries that are close to their unique steady state will grow slowly while those far away will grow rapidly.

y

Steady State

(Zimbabwe)

High Savings Rate (Hong Kong)

Low Savings Rate (Zimbabwe)

Zimbabwe (until recently)

GDP/Capita: $2,100

GDP Growth: -7%

Investment Rate (%0f GDP): 7%

Hong Kong

GDP/Capita: $37,400

GDP Growth: 6.9%

Investment Rate (% of GDP): 21.2%Steady State

(Hong Kong)

Zimbabwe is currently ABOVE its steady state (GDP per capita is falling due to low investment rate

Hong Kong, with its high investment rate is well below its steady state growing rapidly towards it

Page 49: FIN 30220: Macroeconomic Analysis

Conditional convergence suggests that every country converges to its own unique steady state. Countries that are close to their unique steady state will grow slowly while those far away will grow rapidly.

y

Steady State

(France)

Small Government (US)

Large Government (France)

France

GDP/Capita: $30,000

GDP Growth: 1.6%

Government (%0f GDP): 55%

USA

GDP/Capita: $48,000

GDP Growth: 2.5%

Government (% of GDP): 18%Steady State

(USA)

France has a lower steady state due to its larger public sector. Even though its per capita income is lower than the US, its growth is slower

The smaller government of the US increases the steady state and, hence, economic growth

Page 50: FIN 30220: Macroeconomic Analysis

Suggestions for growth….

High income countries with low growth are at or near their steady state. Policies that increase capital investment will not be useful due to the diminishing marginal product of capital.

Consider investments in technology and human capital to increase your steady state.

Consider limiting the size of your government to shift resources to more productive uses (efficiency vs. equity)

Low income countries with low growth either have a low steady state or are having trouble reaching their steady state

Consider policies to lower your population growth.

Try to increase your pool of savings (open up to international capital markets)

Policies aimed at capital formation (property rights, tax credits, etc).

Page 51: FIN 30220: Macroeconomic Analysis

Question: Is maximizing growth a policy we should be striving for?

3

1

Aky

icy

Our model begins with a relationship between the capital stock and production

These goods and services that we produce can either be consumed or used for investment purposes (note: taxes are zero)

kgcy L In the steady state, investment simply maintains the existing steady state

kgAkkgyc LL 3

1 Maybe we should be choosing a steady state with the highest level of consumption!

Page 52: FIN 30220: Macroeconomic Analysis

kgAkc L 3

1

Steady state consumption is a function of steady state capital. If we want to maximize steady state consumption, we need to look at how consumption changes when the capital stock changes

LgAkdk

dc

3

2

3

1

Change in consumption per unit change in steady state capital

Change in production per unit change in steady state capital

Change in capital maintenance costs per unit change in steady state capital

Page 53: FIN 30220: Macroeconomic Analysis

3

1

Aky iy~

,

k

kgi L ~

*k

03

1 3

2

LgAkdk

dc

In this region, an increase in capital increases production by more than the increase in maintenance costs – consumption increases

In this region, an increase in capital increases production by less than the increase in maintenance costs – consumption decreases

Consumption equals zero – capital maintenance requires all of production

Steady state consumption is maximized!!!

Page 54: FIN 30220: Macroeconomic Analysis

03

1 3

2

LgAk

Let’s go back to our example…

2

3

3*

Lg

Ak

%10

%10

0

6

%2

0

t

A

g

g

L

A

We can solve for the steady state capital that maximizes consumption

6802.10.3

6*

2

3

k

Page 55: FIN 30220: Macroeconomic Analysis

3

1

Aky

iiy~

,,

k

tysi 10.

kgi L ~

353max k

Maximum sustainable capital stock – consumption equals zero

68* k11* k

Steady state capital that maximizes consumption

Steady state with a 10% investment rate

Page 56: FIN 30220: Macroeconomic Analysis

%10

%10

0

6

%2

0

t

A

g

g

L

A

Using our example, lets compare consumption levels…

6802.10.3

6*

2

3

k18.1102.10.

6*10. 2

3

k

40.1318.116 3

1

y 5.24686 3

1

y

34.118.1110.02. i 16.86810.02. i

06.1234.140.13 c

Steady State with Savings Rate = 10% “Optimal” Steady State

34.1616.85.24 c

In this example, we could increase consumption by 30% by altering the savings rate!!

Page 57: FIN 30220: Macroeconomic Analysis

%10

%10

0

6

%2

0

t

A

g

g

L

A

By comparing steady states, we can find the savings rate associated with maximum consumption

2

3

31

*

Lg

Ak

2

3

Lg

Ak

Steady State with a given Savings Rate “Optimal” Steady State

To maximize steady state consumption, we need a 33% savings/investment rate!!

3

1*