1. Long Term Economic Growth
FIN 30220: Macroeconomics
Long Term Economic Growth

2. This set of notes focuses solely on the trend!
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!

3. The Global Economy GDP(2016): $119T Population: 7.1B
$39,200
$26,100
$42,500
$57,300
$14,600
$38,900
$18,900
$6,700
$14,800
$48,800
GDP(2016): $119T
Population: 7.1B
GDP Per Capita: $16,300
* Source: CIA World Factbook

4. Growth Rates around the World
1.6%
0.7%
3.1%
2.4%
7.3%
0.0%
2.2%
7.2%
0.1%
2.7%
GDP Growth (2016): 2.6%
Population Growth: 1.4%
GDP Growth Per Capita: 1.2%
*Source: World Bank

5. As a general rule, low income countries tend to have higher average rates of growth than do high income countries
Example: Rwanda
GDP Per Capita: $697
GDP Growth: 3.6%
Country Type (# of Countries)
GDP Growth (PPP)
GDP Per Capita Growth (PPP)
Low Income (30)
3.42%
0.97%
Low Middle Income (52)
3.52%
1.95%
Upper Middle Income (56)
2.45%
1.43%
High Income (78)
2.25%
1.35%
Global Average (216)
2.63%
1.26%
Example: Sudan
GDP Per Capita: $2,414
GDP Growth: 4.9%
Example: Mexico
GDP Per Capita: $9,005
GDP Growth: 2.46%
Example: Portugal
GDP Per Capita: $19,222
GDP Growth: 1.59%
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 (2015 estimates)

6. Every rule has exceptions!
Ireland
GDP = $322B
GDP Per Capita = $69,400
GDP Growth = 26.3%
Can we explain the outliers?
Yemen
GDP = $73.5B
GDP Per Capita = $2,500
GDP Growth = -4.2%
*Source: CIA Factbook

7. 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
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.

8. 2% Long term growth seems to have a “speed limit”
Real GDP per capita growth in the United States 2%
~2%
Long term growth seems to have a “speed limit”

9. Capital Per Worker in the United States
1.6% per year
Capital Stock Per Worker (2001 Dollars)

10. The ratio of capital to output in the United States
Capital Stock/GDP
3.2

11. The “great ratios” are constant over time
Consumption as a percentage of GDP
63%
17%
Investment as a percentage of GDP
Consumption as a percentage of GDP
Investment as a percentage of GDP

12. Real wages generally rise at the rate of productivity growth (at least, until recently)
Index: 1947 = 100
2% per year

13. Returns to capital are constant over time
Average Nominal Return = ~5%
Average Real Return = ~1%
US Annual Returns to Capital ( )

14. Historically, labor’s share of income has been constant at around 65%, but has decreased since the 1980s.
Percent
65% ?
Note: Capital’s share of income = 1 – Labor’s share of income

15. To begin with, let’s look at the potential sources of economic growth…
To begin with, let’s look at the potential sources of economic growth….where does production come from?
“is a function of”
Real GDP
Labor
Productivity
Capital Stock
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

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

17. 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%
Now, we can rewrite the production function in terms of growth rates to decompose GDP growth into growth of factors:
Real GDP Growth (observable)
Productivity Growth (unobservable)
Capital Growth (observable)
Employment Growth (observable)

18. Now, lets look at long term averages
Year
Real GDP (Billions of 2009 dollars)
Real Capital Stock (Billions of 2011 dollars)
Employment (thousands)
1954
2,566
7,925
49,087
2014
15,900
51,190
138,937
Now, lets look at long term averages

19. Contributions to growth from capital, labor, and technology vary across time period in the United States
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!

20. In fact, productivity growth has been declining since WWII
Annual Growth
"You can see the computer age everywhere but in the productivity statistics."
Robert Solow*
*Nobel Prize, 1987

21. Our model of economic growth begins with a production function
Real GDP
Productivity
Labor
Capital Stock
Given our production function, economic growth can result from
Growth in labor
Growth in the capital stock
Growth in productivity

22. We are concerned with capital based growth
We are concerned with capital based growth. Therefore, growth in productivity and employment will be taken as given
Population grows at rate
Productivity grows at rate
Employment
= Employment Ratio
Labor Force
Labor Force
= Participation rate
Population
( Assumed Constant)
( Assumed Constant)

23. Think of the economy as an apple orchard…
Labor
Productivity
Real GDP
Capital Stock
Apples
Weather
Farmers
Apple Trees

24. 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
Let’s say you produce 500 Apples
Note: Your current capital/labor ratio is 100/50 = 2
(Note, that’s 10 apples per worker)

25. Now, where does your output go?
Note: Let’s leave out government or the rest of the world for now
You produced 500 Apples
480 Apples get consumed
20 Apples get planted in the ground to become new apple trees next year
(96% Consumption rate)
(4% Investment rate)
20 Apples
20 New Trees Next Year

26. 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)
Next your you have an orchard with 110 trees (10% capital growth)
20 New trees from invested apples
Let’s assume your population (workforce) grows at 2% per year
Next year you have 51 workers (2% population growth)

27. 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)

28. Let’s take stock… 8% GDP Growth 10% Capital Growth 2% Labor Growth
Year
GDP
Real Capital Stock
Employment
Year 0
500
100 50
Year 1
540
110 51
8% GDP Growth
10% Capital Growth
2% Labor Growth
Assuming
Productivity Growth

29. Can this process continue forever? NO!
Output per capita
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
Capital per capita

30. 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
Investment Rate
You choose how to allocate that output across two activities: consumption and investment
Investment today determines your capital stock tomorrow
Depreciation Rate

31. Given this, we can calculate the growth in your capital stock
Subtract K from both sides
Divide each side by K
Recall that Investment is a constant fraction of output

32. So, the growth of capital in a country is affected by: Investment rate
Average product of capital (GDP divided by the capital stock)
So, the growth of capital in a country is affected by:
Investment rate
Rate of depreciation
Average product of capital
Growth of capital
Rate of depreciation
Given the growth in capital above, GDP growth is affected by
Productivity growth
Population growth

33. VS. Nigeria USA Investment Rate: 20% Average Product of Capital: .60
Depreciation Rate: 5% (WAG)
Investment Rate: 20%
Average Product of Capital: .31
Depreciation Rate: 5% (WAG)
(7%)
(1.2%)
Population Growth: 1%
Productivity Growth: 1.1%
Population Growth: 1%
Productivity Growth: .78%
GDP Per Capita Growth = 3.10%
GDP Per Capita Growth = 0.85%

34. Capital Exhibits Diminishing Marginal Productivity
GDP Per Capita
e.g. USA
High GDP Per capita
($52,000)
Low Marginal product of capital
e.g. Nigeria
High Marginal product of capital
Low GDP Per capita
($5,200)
Capital Per Capita
Low Capital Per capita ($8,600)
High Capital Per capita
($167,000)

35. What happens at the margin affects the average
Average Product of Capital
Average Product of Capital
e.g. USA
GDP Per Capita
High GDP Per capita
($52,000)
e.g. Nigeria
Low GDP Per capita
($5,200)
Capital Per Capita
Low Capital Per capita ($8,600)
High Capital Per capita
($167,000)

36. For a given investment rate, as a country develops (capital per capita expands), the average product of capital declines and that slows the economy down
GDP Per capita
GDP Per capita
Slope = Y/K
Slope = Y/K
Slope = Y/K
Slope = Y/K
Capital Per Capita
Capital Per Capita
Now
Future

37. Average Product of Capital in the US and Nigeria
.60
.31
Source: Penn World Tables

38. Declining Average Product of Capital Around the World

39. Assumption: In the “Steady State”, the Average Product of capital is constant
Real GDP Growth
Productivity Growth
Capital Growth
Employment Growth
In the steady state, is constant so
In the “Steady State” growth depends only on productivity growth

40. Transition towards Steady State Steady State
Case #1: Zero productivity growth – all per capita variables are constant!
Transition towards Steady State
Steady State
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

41. Transition towards Steady State Steady State
Case #2: Positive productivity growth – all per capita grow at a rate proportional to productivity growth!
Transition towards Steady State
Steady State
GDP per capita grows as a rate proportional to productivity growth
Developing Countries
Low GDP per capita
Low capital per capita
High average product of capital
Fast growth of GDP per capita
Developed Countries
High GDP per capita
High capital per capita
Low average product of capital
Slow/zero growth of GDP per capita

42. So, we can explain the basic rule…
Country Type (# of Countries)
(Average) GDP Per Capita (PPP)
GDP Growth (PPP)
Low Income (30)
$600
2.12%
Low Middle Income (52)
$2,364
3.52%
Upper Middle Income (56)
$7,198
2.45%
High Income (78)
$33,776
2.25%
Global Average (216)
$13,155
2.63%
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

43. Yemen So, what the heck is wrong with Yemen? GDP = $20.1B
GDP Per Capita = $774
Employment: 10.7M
Capital Stock Per Capita = $20,415
Growth in GDP = %
Growth in Population = 2.5%
Growth in GDP Per Capita = -28.1%
Average = .6%

44. For the time being, leave out productivity growth…
Growth in capital per capita
Constant in the steady state
The steady state level for the average product of capital is determined by a country’s structural parameters

45. Note that a countries long term level of average capital productivity is determined by some structural parameters
A low/high level for the average product of capital means a high/low level for capital per capita and GDP per capita (due to diminishing returns to capital)

46. With zero productivity growth, we would have something like this…
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
Note that in the shaded area, country B will be growing faster even though it is wealthier

47. It will look similar with positive steady state growth
Some countries have characteristics that lead it to a long term average product of capital that is low – hence a higher level of capital and GDP
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 and GDP
High population growth
Low investment rates

48. Yemen So, productivity growth determines the long term growth
Productivity Growth: Average = -.9%
If Yemen could reach the same long run rate of productivity growth as the US, they could catch us in terms of long term growth, but….

49. Productivity growth determines the long term growth, but how about the level
With a high rate of population growth and a low investment rate, Yemen will have a lower capital per capita (and hence GDP per capita in the long term).
Yemen
Again, assume a long term universal productivity growth of 1%
Population Growth: 2.5%
Investment rate = 11%
Even if Yemen can reach the long term productivity of the US, it will always be poorer due to its low investment rate and high population growth

50. Point #2:
Point #1:
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
All else equal poor countries grow faster that rich countries due to the diminishing returns to capital

51. High Investment Countries
China
Investment (% of GDP)
GDP Per 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%
Hong Kong
26.4%
$58,100
1.4%
#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 (% of GDP)
GDP Per 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%

52. 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%
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%
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%

53. Side Note: We have the following long term regularities
Returns to labor grow over time
Labor’s share of income is constant
Returns to capital are constant
capital’s share of income is constant
Hourly compensation
(Grows at a constant rate)
Nominal interest rate (constant)
Labors' share of income in the US (Constant)
Capital’s share of income in the US (Constant)
GDP per hour (average product of labor) grows at a constant rate
Average Product of capital (Assumed Constant in steady state)

54. Let’s look at the US for a minute…
Growth
GDP
1.1
Capital
1.4
Labor
-0.1
GDP Per Capita
1.2
Productivity
0.78
This model predicts that the rate of growth in GDP per capita will be proportional to the rate of productivity growth
Capital’s share of income
(For the US, around .40)
Let’s predict GDP per Capita growth in the US in the steady state

55. Final Note: We have the following long term regularities
Returns to labor grow over time
Labor’s share of income is constant
Returns to capital are constant
capital’s share of income is constant
Labor Productivity per hour = $75/hr. (approx.)
Average product of capital = $0.30 (approx.)
$50 per hour would be the average hourly wage (and its growing at a rate proportional to productivity growth)
10% rate of return on invested capital (constant)

56. VS. Example: Real GDP (2009$): $16,861B Real GDP (2011$): $17,150B
Real GDP Per Capita (2009$): $51,919
Employment: 146M
Real Capital Stock capita (2011$): $167,000
Real GDP Growth: 2.0%
Population Growth: 0.78%
Real GDP Per Capita Growth: 1.22%
Real GDP (2011$): $17,150B
Real GDP Per Capita (2010$): $6,497
Employment: 923M
Real Capital Stock Per Worker (2011$): $49,543
Real GDP Growth: 6.9%
Population Growth: 0.50%
Real GDP Per Capita Growth: 6.4%

57. GDP Per Capita GDP Growth in the US vs. China
13.6%
6.4%
8% Per Year Average
1.9%
2% Per Year Average

58. Average Product of Capital in the US and China
.25
.31

59. Gross Investment Rates in the US and China (% of GDP)
(Private plus public)
46%
20%

60. VS. Based off of Current Numbers Average Product of Capital = .31
Productivity Growth = .79%
Investment Rate = .17%
Population Growth: 0.78%
Average Product of capital = .25
Productivity Growth = 3%
Investment Rate = 46%
Population Growth: 0.50%
(1.2%)
(6.5%)
(Per capita growth = = .93%)
(Per capita growth = = 4.99%)

61. In the Long Term, China should surpass the US, but grow at the same rate
“Steady State”
GDP grows a rate proportional to productivity growth (~1.5%)
Higher investment rate
Lower investment rate
2050

62. VS. European Union United States Capital Stock Per Capita: ~$128,000
GDP: $15.8T
GDP Per Capita: $34,500
Real GDP Growth: 1.6%
Inflation Rate: 1.5%
VS.
United States
GDP: $17.0T
GDP Per Capita: $53,000
Real GDP Growth: 1.7%
Inflation Rate: 1.6%
Capital Stock Per Capita: ~$128,000
Population Growth: 0.16%
Investment Rate: 15-20%
Government (% of GDP): 50-60%
Capital Stock Per Capita: $128,296
Population Growth: 0.7%
Investment Rate: 15-20%
Government (% of GDP): 40%
Capital Stock Per Capita

63. Let’s look at historical data for the US and Europe.
Real Per Capita GDP, Europe and the United States:
GDP Per Capita
WWI
WWII
Europe and US Grow at roughly the same pace
US Outpaces Europe
Europe Outpaces US

64. Here’s American productivity relative to European productivity.
Country
Labor Productivity (2004) *
Productivity Growth ( )
Productivity Growth ( )
USA
100
1.7%
2.5%
Germany 92
1.0%
France
107
1.5%
1.3%
Italy
0.0%
England 87
1.8%
2.0%
* USA = 100
** Source: OECD

65. 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

66. Ratio of Europe to the United States: 1820 - 2000
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:
European Productivity roughly equal to that of the US (~95%)
European GDP per capita roughly equal to 75% of the US

67. 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
1,585 (30.4 hrs per wk)
England
5.5%
1,669 (32.0 hrs per wk)
Same level
Same growth
Same level
Same growth
lower level
Lower growth growth

68. 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
USA
Europe
(75% of the US)
Same as US
Same as US
~79% of US