Download Long Run Growth

FIN 30220:
Macroeconomics
Long Term Economic Growth
Now, we want to take a look at the trend component.
GDP
“Business Cycle” (deviations from
average growth)
Trend (Average growth)
Time
This set of notes focuses solely on the trend!
Let’s Take a look at the global economy…
• Total GDP (2014): $107T
• Population (2014):7.1B
• GDP per Capita (2014): $16,100
• Population Growth (2013): 1.0%
• GDP Growth (2014): 3.3%
* Source: CIA World Factbook
Note. However, that growth rates vary significantly across countries/regions. Do
you see a pattern here?
Region
GDP
% of
World
GDP
GDP Per
Capita
Real GDP
Growth
United States
$18T
17%
$54,000
2.4%
European Union
$18T
17%
$39,000
1.4%
Japan
$4.7T
4%
$37,500
-0.1%
China
$18T
17%
$13,200
7.3%
Ghana
$109B
.1%
$4,100
7.3%
South Sudan
$24B
.03%
$2,000
24.7%
Mozambique
$31B
.03%
$1,200
7.4%
* Source: CIA World Factbook (2014 Estimates)
Global Economic Growth = 3.3%
United States
2.4%
Japan: -0.1%
China
7.3%
South Sudan
24.7%
Ghana
7.3%
Mozambique
7.5%
*Source: World Bank
As a general rule, low income countries tend to have higher average rates of growth than do high income countries
Income Class
GDP/Capita
GDP Growth
Low
< $1,045
6.3%
Middle
$1,045 - $12,746
4.8%
High
>$12,746
3.2%
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)
Some countries, however, don’t fit the normal pattern of development
Syria
GDP: $55.8B (#108)
GDP Per Capita: $2,900 (#194)
GDP Growth: -9.9% (#221)
Monaco
GDP: $6.8B (#166)
GDP Per Capita: $78,700 (#9)
GDP Growth: 9.3% (#3)
So, what is Syria doing wrong? (Or, what is Monaco doing right?)
There are regularities in long term growth in the US
Nicholas Kaldor developed in 1957 what have come to be known as the “Kaldor Facts”
of growth.
Nicholas Kaldor
1908-1986







The growth rate of GDP per capita is (fairly) constant
The ratio of capital to GDP is constant
The ratio of capital to labor is growing
Labor’s share of income (and, hence, capital’s share) is constant
The rate return to capital is constant (interest rate)
The real wage rate grows at a constant rate
The ratio of consumption to GDP and Investment to GDP are constant
These facts seem to be consistent across many countries and time periods, suggesting that there are a small number of
common forces which give rise to long term growth and that there may be a coherent theoretical explanation to its origin.
Real GDP per capita grows at a (fairly) constant long term average rate of 2% for developed countries (like the US)
8
Annual GDP Per Capita Growth
6
4
2%/yr.
2
0
1961-01-01
-2
-4
-6
1971-01-01
1981-01-01
1991-01-01
2001-01-01
2011-01-01
The ratio of capital to output is constant…
2.8
2.6
Capital Stock/GDP
2.4
2.2
2.2
2
1.8
1.6
1948
1963
1978
1993
The “great ratios” are constant over time
0.8
0.2
Consumption to Output Ratio
0.18
0.7
0.6
0.14
0.5
0.12
0.4
0.3
0.1
0.08
Investment to output ratio
0.06
0.2
0.04
0.1
0.02
0
1947
0
1963
1979
1995
2011
Investment to output ratio
Consumption to Output Ratio
0.16
The capital/labor ratio is growing….
0.25
1.5% per year
Capital Stock/Employment
0.2
0.15
0.1
0.05
0
1948
1963
1978
1993
Real wages generally rise at the rate of productivity growth (at least, until recently)
Index: 1947 = 100
450
400
2% per year
350
300
250
200
150
From the early 1980’s
on, we have developed
a “wage gap”
100
50
0
1947
1952
1957
1962
1967
1972
Real GDP Per Hour
1977
1982
1987
1992
Real Compensation Per Hour
1997
2002
2007
2012
Historically, labor’s share of income has been constant at around 65%, but has decreased since the 1980s.
Percent
70
68
66
65%
64
?
62
60
58
56
1947
1952
1957
1962
1967
1972
1977
1982
1987
1992
1997
Note: Capital’s share of income = 1 – Labor’s share of income
2002
2007
2012
Returns to capital have no trend
17
12
7
Average = ~5%
2
1948
1958
1968
1978
1988
1998
-3
US Nominal Returns (1948-2014)
-8
2008
Returns to capital have no trend
8
6
4
Average Nominal =
~5%
2
Minus Average
Inflation = ~4%
Average = ~1%
0
1948
1958
1968
1978
1988
1998
-2
-4
-6
-8
US Real Returns (1948-2014)
2008
To begin with, let’s look at the potential sources of economic growth….where does production come from?
“is a function of”
Real GDP
Y  F  A, K , L
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
A convenient functional form for growth accounting is the Cobb-Douglas production function. It takes the form:


Y  AK L
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)
Using factor income shares, we can identify the parameters of a Cobb-Douglas production function :
A 1% rise in capital
raises GDP by 1/3%
A 1% rise in
employment raises
GDP by 2/3%
1
3
2
3
Y  AK L
Now, we can rewrite the production function in terms of growth rates to decompose GDP growth into growth
of factors:
1
2
%Y  %A  %K   %L 
3
3
Real GDP Growth
(observable)
Productivity Growth
(unobservable)
Capital Growth
(observable)
Employment
Growth
(observable)
Year
Real GDP (Billions of 2000
dollars)
Real Capital Stock (Billions of
2000 dollars)
Employment (thousands)
2010
14,939
40,615
130,745
2011
15,190
40,926
132,828
Lets decompose some recent data first…
%Y  ln 15,190   ln 14,939   *100  1.67
%K  ln  40,926   ln  40, 615   *100  .76
%L  ln 132,828   ln 130, 745   *100  1.58
%A  1.67 
1
2
.76   1.58  .36
3
3
*Source: Penn World Tables
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 
%Y 
*100  3.11
61
ln  40,926   ln  6,328  
%K 
*100  3.06
61
ln 132,828   ln  46,855  
%L 
*100  1.70
61
%A  3.11 
1
2
 3.06   1.70   .98
3
3
Contributions to growth from capital, labor, and technology vary across time period in the United States
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 regularities, however:
Real GDP growth is declining over time.
Capital has been growing faster than labor
Productivity growth is diminishing!
Annual Growth
In fact, productivity growth has been declining since WWII
"You can see the computer age
everywhere but in the productivity
statistics."
Robert Solow*
*Nobel Prize, 1987
Our model of economic growth begins with a production function
Y  F  A, K , L 
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
We are concerned with capital based growth. Therefore, growth in productivity and employment will be taken
as given
Y  F  A, K , L 
Population
grows at rate
gL
Productivity
grows at rate
 L  LF 
 Pop
L

 LF  Pop 
gA
Employment
Labor Force
= Employment Ratio
( Assumed Constant)
Labor Force
Population
= Participation rate
( Assumed Constant)
Think of the economy as an apple orchard…
Y  F  A, K , L 
Labor
Real GDP
Productivity
Capital Stock
Apples
Weather
Farmers
Apple Trees
Combined with your labor and productivity,
you produce apples
At some point in time, you have a fixed
number of apple trees
50 Workers
Lets say, 100 trees
Note: Your current
capital/labor ratio is
100/50 = 2
Let’s say you produce 500 Apples
(Note, that’s 10 apples per worker)
Note: Let’s leave out
government or the rest of
the world for now
Now, where does your output go?
You produced 500 Apples
480 Apples get consumed
(96% Consumption rate)
Y CI
20 Apples get planted in the
ground to become new apple
trees next year
(4% Investment rate)
20 Apples
20 New Trees Next
Year
Now, what happens next year?
10 Dead trees
Trees don’t last forever…lets say
that 10% of your trees die each
year. (10% annual depreciation of
capital)
Let’s assume your
population (workforce)
grows at 2% per year
20 New trees from
invested apples
Next your you have an orchard
with 110 trees (10% capital
growth)
Next year you have 51
workers (2% population
growth)
Combined with your labor and productivity,
you produce apples
Now, repeat…
51 Workers
110 trees
Let’s say you produce 540 Apples
Note: Your current
capital/labor ratio is
110/51 = 2.15
(Note, that’s 10.6 apples per
worker)
Let’s take stock…
Year
GDP
Real Capital Stock
Employment
Year 0
500
100
50
Year 1
540
110
51
8% GDP
Growth
Assuming
10% Capital
Growth
2% Labor
Growth
Productivity Growth
1
3
2
3
Y  AK L
%A  8 
1
2
10    2   3.36
3
3
Can this process continue forever? NO!
Y
Output
2Y
The key assumed
property of production
is that capital exhibits
diminishing marginal
productivity – that is
as capital rises
relative to labor , its
contribution to
production of output
shrinks
Y  F  A, K , L 
Y
Capital
K
2K
K
Lets take this step by step….
Labor’s share
of income
Capital’s share
of income
Your capital, labor,
and productivity
determine your
ability to produce
output
 1
Y  AK L
Investment Rate
You choose how to
allocate that
output across two
activities:
consumption and
investment
Investment today
determines your
capital stock
tomorrow
I  Y
C  1    Y
Y CI
K  1    K  I
'
Depreciation Rate
Given this, we can
calculate the
growth in your
capital stock
K  1    K  I
'
Subtract K from both sides
K'  K  I  K
Divide each side by K
K'  K
I
 gK   
K
K
Y 
gK      
K
Recall that Investment is a constant
fraction of output
I  Y
Capital Per capita is
K
k
L
Growth in capital per capita
gk  g K  g L
So, from the previous expression, we have
Average product of
capital (GDP divided
by the capital stock)
Investment
Rate
Rate of population growth
Y 
gk        g L
K
Growth of
capital per
capita
Rate of depreciation
The key assumed property of production is that capital exhibits diminishing marginal productivity –
that is as capital rises relative to labor , its contribution to production of output shrinks.
Y
Y  F  A, K , L 
So, absent productivity
growth, increasing
capital will lower the
average product of
capital
Y
2K
K
3K
K
Y 
gk        g L  0
K
 Y    gL
  

K
*
The average product of capital is
declining
Eventually, growth in capital per capita ceases (capital grows at the same rate as labor) and the capital stock per capita is
constant. We call this the “steady state”
Y
K
 gL   


  
Y
K
K
*
Y 
 
K
Eventually, growth in capital per capita ceases (capital grows at the same rate as labor) and the capital stock per capita is
constant
Y
Y  F  A, 2 K , 2 L 
2Y
Y  F  A, K , L 
Y
As capital and labor
grow at the same
pace, the average
product of capital
(Y/K) remains constant
K
K
2K
Therefore, in an economy with no productivity growth, sustainable long term growth will imply a growth in the capital stock
that equals growth in population (really, workforce)
So, if we take our growth accounting expression….
1
2
%Y  %A  %K   %L 
3
3
Real GDP Growth
Productivity Growth
Capital Growth
=0
Capital Growth equals labor
growth eventually
%Y  %L
Employment
Growth
%K   %L 
Eventually, GDP growth equals population growth
OR
Y 
%    0
L
Eventually, GDP per capital growth equals zero
So, consider this idea of convergence (rich countries grow slow, poor countries grow fast)
Y
L
Transition towards Steady State
Steady State
Y 
%    0
L
Time
Developing Countries
• Low GDP per capita
• Low capital per capita
• High average product of capital
• Low average product of labor
• Fast growth of GDP per capita
Developed Countries
• High GDP per capita
• High capital per capita
• Low average product of capital
• High average product of labor
• Slow/zero growth of GDP per capita
Note that a countries long term level of average capital productivity is determined by some structural
parameters
Y 
gk        g L  0
K
 Y    gL
  

K
*
The long term average product of capital will determine the long term position of a country
Y
K
 gL   


  A
 gL   


  B
*
Y 
 
 K A
Y 
 
 K B
*
k
The long term average product of capital will determine the long term position of a country
 Y    gL
  

K
*
Y
L
Y 
 
 L B
Y 
 
 L A
Country B has structural parameters that lead it
to a long term average product of capital that is
lower – hence a higher level of capital per capita
and GDP per capita
Country A has structural parameters that lead it
to a long term average product of capital that is
higher – hence a lower level of capital per capita
and GDP per capita
Time
Note that in the shaded area, country B will be growing faster even though it is wealthier
Point #1:
All else equal poor countries
grow faster that rich countries
due to the diminishing returns
to capital
Point #2:
All is not always equal across
countries…differences in
structural parameters will
effect a country’s development
• Low productivity inhibits
growth
• High population growth
inhibits growth
• Low investment rates inhibit
growth
So, we can explain the basic rule…
Income Class
GDP/Capita
GDP Growth
Low
< $1,045
6.3%
Middle
$1,045 - $12,746
4.8%
High
>$12,746
3.2%
This observation is driven entirely by the diminishing returns to capital. As a
country develops and it’s capital per capita increases, diminishing returns start to
kick in and the country slows down because increases in capital are providing
smaller and smaller increases in production
High Investment Countries
China
Investment (% GDP Per
of GDP)
Capita
Real GDP
Growth
46%
$15,400
6.6%
Indonesia
33.2%
$11,700
4.9%
Qatar
30.6%
$129,700
2.6%
India
30%
$6,700
7.6%
26.4%
$58,100
1.4%
China
Hong Kong
#1: Republic of Congo
• GDP Per Capita: $6,800
• GDP Growth: 3.9%
• Investment Rate: 51%
• Population Growth: 2.5%
Low Investment Countries
China
Investment (% GDP Per
of GDP)
Capita
Real GDP
Growth
Montenegro
8.3%
$17,000
5.1%
Cuba
9.6%
$11,600
1.3%
Iraq
10.1%
$16,500
10.3%
Pakistan
10.9%
$5,100
4.7%
Greece
12.6%
$26,800
.10%
#225: Libya
• GDP Per Capita: $14,200
• GDP Growth: -3.3%
• Investment Rate: 4.7%
• Population Growth: 3%
High Population Growth Countries
China
Population
growth
GDP Per
Capita
Real GDP
Growth
Zimbabwe
4.36%
$2,000
-0.3%
Jordan
3.86%
$11,100
2.8%
Malawi
3.58%
$1,100
2.7%
Niger
3.28%
$1,100
5.2%
Mali
3.00%
$2,300
5.3%
#1: Lebanon
• GDP Per Capita: $18,500
• GDP Growth: 1.0%
• Investment Rate: 32.9%
• Population Growth: 9.37%
Low Population Growth Countries
China
Population
Growth
GDP Per
Capita
Real GDP
Growth
Sri Lanka
0.86%
$11,200
5.00%
Namibia
0.67%
$11,800
4.2%
China
0.44%
$15,400
6.6%
Japan
-0.13%
$38,900
0.5%
Germany
-0.18%
$48,200
1.7%
#225: Syria
• GDP Per Capita: $2,900
• GDP Growth: -9.9%
• Investment Rate: 20.5%
• Population Growth: -9.73%
Recall the empirical regularities we want to match..
The growth rate of
GDP per capita is
constant (around 2%)
The ratio of capital to
output is constant
The ratio of capital to
labor is growing
So far, we have GDP per
capita is constant in the
steady state
Nicholas Kaldor
1908-1986
Labor’s share of income (and,
hence, capital’s share) is
constant
By assumption
The real wage rate
grows at a constant
rate
Due to constant
average product
of labor
The rate return to
capital is constant
(interest rate)
Due to constant
average product
of capital
The ratio of consumption
to GDP and Investment to
GDP are constant
By assumption
We can resolve these factual problems with productivity growth
Y
y
L
y

k
Y
L
K
L

With productivity
growth, capital can
grow relative to labor
and the average
product can remain
constant!
Y
K
GDP Per
Capita
Productivity
growth
Y  F  A, k 
y
Capital per
capita
k
k
K
L
So, with productivity growth,
Y 
gk        g L  0
K
The average product of capital is
CONSTANT!!
For that to happen, the growth of capital is equal to the growth in output
%Y   %A     %K   1    %L 
Growth in output equals growth in capital
%Y  %K
%A
%Y 
 %L
1
GDP per capita grows at a rate proportional to
productivity growth plus population growth
 Y  %A
%   
 L  1
GDP per capita grows at a rate proportional to
productivity growth
The idea of convergence will be the same except that there will be long run growth in GDP per capita
Y
L
 Y  %A
%   
 L  1
Time
GDP per capita
grows as a rate
proportional to
productivity
growth
All countries will grow at the rate of productivity growth in the long term, but at different levels, depending on their
characteristics
Y
L
Some countries have structural parameters that
lead it to a long term average product of capital
that is higher – hence a higher level of capital per
capita and GDP per capita
• High productivity
• Low population growth
• High investment rates
Some countries have structural parameters that
lead it to a long term average product of capital
that is lower – hence a lower level of capital per
capita and GDP per capita
• Low productivity
• High population growth
• Low investment rates
K
L
Let’s look at the US for a minute…
Growth
2007-2013
GDP
1.1
Capital
1.4
Labor
-0.1
GDP Per Capita
1.2
Productivity
0.7
Let’s predict GDP per Capita growth in the
US in the steady state
This model predicts that the rate of growth
in GDP per capita will be proportional to the
rate of productivity growth
 Y  %A
%   
 L  1
Capital’s share of income
(For the US, around .40)
.7
 Y  %A
%   

 1.17%
 L  1   1  .40
China (9.8%)
Investment Rate: 35-45%
Population Growth: 0.5%
United States (1.6%)
Investment Rate: 15%
Population Growth: 0.7%
S. Korea (4%)
Investment Rate: 30-35%
Population Growth: 0.4%
Annual Growth Rate
India (7.2%)
Investment Rate: 30-40%
Population Growth: 1.2%
Lets look at some other
countries
Thailand (4%)
Investment Rate: 25-30%
Population Growth: 0.3%
* Source: Penn World Tables
2000 – 2011 Average Annual Growth Rates
Country
US
China
India
S. Korea
Thailand
Real GDP Growth
1.64
9.84
7.21
4.02
4.04
Real GDP Per Capita Growth
.99
9.03
5.08
2.68
1.98
Real Capital Growth
1.93
11.12
8.62
5.30
2.66
Labor Growth
.65
.81
2.13
1.34
2.06
Productivity Growth
.56
5.63
2.93
1.37
1.77
GDP Per Capita
• US: 52,800
• China: 9,800
• India: 4,010
• S. Korea: 33,200
• Thailand: 9,900
Capital Stock Per Capita
• US: 128,296
• China: 56,910
• India: 20,773
• S. Korea: 218,240
• Thailand: 57,468
Let’s compare the model results with the facts…
#1
#2
#3
#4
#5
GDP Per Capita
United States
South Korea
Thailand
China
India
Capital Per Capita
South Korea
United States
Thailand
China
India
Growth Predicted from model
India
China
Thailand
United States
South Korea
Actual Growth
China
India
South Korea
Thailand
United States
•
•
•
High rate of Chinese productivity growth
relative to China could explain this
India’s higher rate of population growth could
explain this
India’s lower investment rate could explain this
•
•
•
High rate of productivity growth
High Investment rate
Low population growth
•
•
•
Low rate of productivity growth
Low Investment Rate
High rate of population growth
European Union
•GDP: $15.8T
•GDP Per Capita: $34,500
•Real GDP Growth: 1.6%
•Inflation Rate: 1.5%
United States
•GDP: $17.0T
•GDP Per Capita: $53,000
•Real GDP Growth: 1.7%
•Inflation Rate: 1.6%
Capital Stock Per Capita: $128,296
Population Growth: 0.7%
Investment Rate: 15-20%
Government (% of GDP): 40%
Capital Stock Per Capita: ~$128,000
Population Growth: 0.16%
Investment Rate: 15-20%
Government (% of GDP): 50-60%
Capital Stock Per Capita
Let’s look at historical data for the US and Europe.
GDP Per
Capita
Real Per Capita GDP, Europe and the United States: 1820 - 2000
WWI
US Outpaces Europe
WWII
Europe Outpaces US
Europe and US Grow at roughly
the same pace
Here’s American productivity relative to European productivity.
Country
Labor
Productivity
(2004) *
Productivity Growth
(1989 -2000)
Productivity Growth
(2000-2005)
USA
100
1.7%
2.5%
Germany
92
1.7%
1.0%
France
107
1.5%
1.3%
Italy
92
1.7%
0.0%
England
87
1.8%
2.0%
* USA = 100
** Source: OECD
Real GDP per Hour, Europe and the United States: 1870 - 2000
US productivity Outpaces
Europe
European productivity
Outpaces US
European and US productivity grow at
roughly the same pace
So we have that productivity in Europe has caught up to that of the United States, yet GDP per
capita still lags the US…why?
Ratio of Europe to the United States: 1820 - 2000
European Productivity
roughly equal to that of the
US (~95%)
European GDP per capita
roughly equal to 75% of the
US
Primarily, it seems that it is labor effort
When we compare the US with Europe…
Country
Unemployment
Rate (Average)
Average annual hours
USA
5.0%
1,794 (34.5 hrs per wk)
Germany
10.0%
1,426 (27.4 hrs per wk)
France
9.0%
1,441 (27.7 hrs per wk)
Italy
9.0%
1,585 (30.4 hrs per wk)
England
5.5%
1,669 (32.0 hrs per wk)
Y  F  A, K , L 
• Same level
• Same growth
• Same level
• Same growth
• lower level
• Lower growth
growth
The smaller number of workers (lower aggregate hours worked) seems to put the European Union on a permanently
lower level to that of the US
Y  F  A, K , L 
USA
Y
L
Europe
(75% of the US)
Same as US
Same as US
~79% of US
K
L