1. FIN 30220: Macroeconomic Analysis
Long Run Growth

2. The World Economy Total GDP (2012): $83T Population (2012):7B
GDP per Capita (2012): $12,500
Population Growth (2012): 1.1%
GDP Growth (2012): 3.3%
GDP per capita is probably the best measure of a country’s overall well being

3. Region GDP % of World GDP GDP Per Capita Real GDP Growth
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
$15T
18%
$48,000
1.3%
European Union
$16T
19%
$33,000
1.0%
Japan
$4.3T 6%
$34,200
-.4%
China
$7.8T
11%
$6,000
9.8%
India
$3.2T 5%
$2,800
6.6%
Ethiopia
$66.3B
.09%
$800
8.5%
Source: CIA World Factbook

4. At the current trends, the standard of living in China will surpass that of the US in 25 years! Or, will they?
Per Capita Income
That is, can China maintain it’s current growth rate?

5. Income GDP/Capita GDP Growth Low $510 6.3% Middle $2,190 7.0% High
As a general rule, low income (developing) countries tend to have higher average rates of growth than do high income countries
Income
GDP/Capita
GDP Growth
Low
$510
6.3%
Middle
$2,190
7.0%
High
$32,040
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”

6. Some countries, however, don’t fit the normal pattern of development
Sudan
GDP: $80B (#80)
GDP Per Capita: $2,400 (#184)
GDP Growth: -11.2% (#219)
Qatar
GDP: $150B (#59)
GDP Per Capita: $179,000 (#1)
GDP Growth: 16.3% (#1)
At current trends, Per capita income in Qatar will quadruple to $716,000 over the next decade. Over the same time period, per capita GDP in Sudan will drop by roughly 40%to $670!!!
So, what is Sudan doing wrong? (Or, what is Qatar doing right?)

7. To understand this, let’s look at the sources of economic growth…
To understand this, let’s look at the 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

8. 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)

9. Suppose we have the following Cobb-Douglas production function:
A 1% rise in capital raises GDP by 1/3%
A 1% rise in employment raises GDP by 2/3%
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)

10. Lets decompose some recent data first…
Year
Real GDP (Billions of 2000 dollars)
Real Capital Stock (Billions of 2000 dollars)
Employment (thousands)
1939
1,142
1,440
29,923
2006
11,257
12,632
135,155
2007
11,467
12,883
137,180
Lets decompose some recent data first…
Note that capital is growing faster than employment

11. Now, lets look at long term averages
Year
Real GDP (Billions of 2000 dollars)
Real Capital Stock (Billions of 2000 dollars)
Employment (thousands)
1939
1,142
1,440
29,923
2006
11,257
12,632
135,155
2007
11,467
12,883
137,180
Now, lets look at long term averages

12. Contributions to growth from capital, labor, and technology vary across time period
Output
5.79
4.10
1.96
2.63
Capital
3.34
4.24
2.10
2.94
Labor
4.46
1.86
1.60
Productivity
1.71
1.28
0.02
0.59
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!

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

14. 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)

15. An economy can’t grow through capital accumulation alone forever!
Our simple model of economic growth begins with a production function with one key property – diminishing marginal product of capital
Change in Production
Change in Capital Stock
As the capital stock increases (given a fixed level of employment), the productivity of capital declines!!
An economy can’t grow through capital accumulation alone forever!

16. Everything in this model is in per capita terms
Divide both sides by labor to represent our variables in per capita terms
Per capita output
Capital Per Capita
Productivity
In general, let’s assume lower case letters refer to per capita variables

17. 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
Output per capita
Capital stock per capita

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

19. Next, assume that households save a constant fraction of their disposable income
Income Less Taxes
Constant between zero and one
Savings
Again, convert everything to per capital terms by dividing through by the labor force

20. Savings = Household income that hasn’t been spent
KEY POINT:
Savings = Household income that hasn’t been spent
Investment = 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
Firms access these funds by taking out loans, issuing stocks and bonds, etc. and use the funds for investment activities
S = I
Investment per capita

21. Continuing with our example:

22. Investment represents the purchase of new capital equipment
Investment represents the purchase of new capital equipment. This will affect the capital stock in the future
Annual Depreciation Rate
Investment Expenditures
Future capital stock
current capital stock
We need to write this out in per capita terms as well…

23. We need to write this out in per capita terms as well…
Divide through by labor to get things in per capita terms
Multiply and divide the left hand side by future labor supply
Recall that labor grows at a constant rate

24. In our example… The evolution of capital per capita… Given Calculated
Current capital per capita
Annual depreciation rate
Investment per capita
Annual population growth rate
Future capital stock per capita
In our example…
Given
Calculated

25. 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…
Given
Calculated

26. In our example… Just to make sure, lets check our numbers…
The evolution of capital per capita…

27. Let’s update our diagram…
“break even” investment
Actual investment

28. Now we have all the components to calculate next years output per capita and the rate of growth
Given
Calculated
Output per capita growth

29. Let’s update our diagram…

30. Let’s repeat that process again…
Savings = Investment
Capital
Output
Evolution of Capital
New Output
Output Growth
Growth is slowing down…why?

31. The rate of growth depends on the level of investment relative to the “break even” level of investment.
Actual investment based on current savings
Level of investment needed to maintain current capital stock

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

33. 2 1 3 The steady state has three conditions….
Savings per capita is a constant fraction of output per capita
Output is a function of capital per capita
Recall that, in equilibrium, savings equals investment 3
Investment is sufficient to maintain a constant capital/labor ratio

34. With a little algebra, we can solve for the steady state in our example.
Start with condition 3
Use condition 2 and the fact that savings equals investment
Substitute condition 1
Recall that taxes are zero in our example
Solve for k

35. Plugging in our parameters gives us steady state values.
Steady state per capita capital
Steady state per capita output
Steady state per capita savings/investment
Steady state per capita consumption
Constant per capita capital!!!

36. Eventually, actual investment will equal “break even” investment and growth ceases (in per capita terms). This is what we call the steady state.
In the steady state (with no productivity growth), all per capita variables have zero growth!

37. Suppose we started out example economy above it’s eventual steady state…
An economy above its steady state shrinks (in per capita terms) towards its steady state.

38. An economy above its steady state shrinks (in per capita terms) towards its steady state.
An economy above its steady state can’t generate enough savings to support its capital stock!

39. Countries above their eventual steady state will shrink towards it
“Absolute convergence” refers to the premise that every country will converge towards a common steady state
Investment needed to maintain current capital/labor ratio
Actual investment (equals savings)
Actual investment (equals savings)
Investment needed to maintain current capital/labor ratio
Steady State
Countries above their eventual steady state will shrink towards it
Countries below their eventual steady state will grown towards it
Countries at their eventual steady state will stay there

40. 1 2 3 Most countries follow the “usual” pattern of development
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 1 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

41. 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 + Employment Growth

42. 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%)

43. 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%)

44. Consider two countries…
Country A
Country B
We already calculated this!
Even though Country B is poorer, it is growing slower than country A (in per capita terms)!

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

46. 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.
High Population Growth (Haiti)
Haiti
Population Growth: 2.3%
GDP/Capita: $1,600
GDP Growth: -1.5%
Low Population Growth (Argentina)
Argentina
Population Growth: .96%
GDP/Capita: $13,700
GDP Growth: 8.7%
Steady State
(Haiti)
Steady State
(Argentina)
Argentina, with its low population growth is well below its steady state growing rapidly towards it
Haiti is currently ABOVE its steady state (GDP per capita is falling due to a high population growth rate

47. Zimbabwe (until recently)
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.
Zimbabwe (until recently)
GDP/Capita: $2,100
GDP Growth: -7%
Investment Rate (%0f GDP): 7%
High Savings Rate (Hong Kong)
Hong Kong
GDP/Capita: $37,400
GDP Growth: 6.9%
Investment Rate (% of GDP): 21.2%
Low Savings Rate (Zimbabwe)
Steady State
(Zimbabwe)
Steady State
(Hong Kong)
Hong Kong, with its high investment rate is well below its steady state growing rapidly towards it
Zimbabwe is currently ABOVE its steady state (GDP per capita is falling due to low investment rate

48. 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.
France
GDP/Capita: $30,000
GDP Growth: 1.6%
Government (%0f GDP): 55%
Small Government (US)
Large Government (France)
USA
GDP/Capita: $48,000
GDP Growth: 2.5%
Government (% of GDP): 18%
Steady State
(France)
Steady State
(USA)
The smaller government of the US increases the steady state and, hence, economic growth
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

49. 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).

50. Question: Is maximizing growth a policy we should be striving for?
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)
In the steady state, investment simply maintains the existing steady state
Maybe we should be choosing a steady state with the highest level of consumption!

51. Steady state consumption is a function of steady state capital
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
Change in consumption per unit change in steady state capital
Change in capital maintenance costs per unit change in steady state capital
Change in production per unit change in steady state capital

52. Consumption equals zero – capital maintenance requires all of production
Steady state consumption is maximized!!!
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

53. Let’s go back to our example…
We can solve for the steady state capital that maximizes consumption

54. Maximum sustainable capital stock – consumption equals zero
Steady state capital that maximizes consumption
Steady state with a 10% investment rate

55. Using our example, lets compare consumption levels…
Steady State with Savings Rate = 10%
“Optimal” Steady State
In this example, we could increase consumption by 30% by altering the savings rate!!

56. By comparing steady states, we can find the savings rate associated with maximum consumption
Steady State with a given Savings Rate
“Optimal” Steady State
To maximize steady state consumption, we need a 33% savings/investment rate!!

57. So, where does the US stand?
Production (2008)
Consumption (2008)
Investment (2008)
Government Purchases (2008)
$14,264B
$10,057B
$1,994B
$2,882B
The savings rate in the US is currently around 4%, but what we really want is the investment rate
At our steady state, GDP growth should be 3-3.5% (Per capita GDP will grow at 1-1.5%)

58. We need to calibrate the model to the data…
Production (2008)
Consumption (2008)
Investment (2008)
Government Purchases (2008)
$14,264B
$10,057B
$1,994B
$2,882B
In the steady state…
We know everything but the value for productivity
GDP Per Capita (2008) = $47,000

59. Investment expenditures would be 33%, or $22,464.
Now, suppose that we could increase the investment rate to 33% as our model prescribes
Production (2008)
Consumption (2008)
Investment (2008)
Government Purchases (2008)
$14,264B
$10,057B
$1,994B
$2,882B
In the steady state…
We could raise per capita income to close to $70,000
Investment expenditures would be 33%, or $22,464.
Currently, government plus private consumption per capita is around $43,000
Private consumption per capita
government purchases per capita

60. Should we pursue policies to raise the investment rate in the US?
Current Steady State (y = $47,000)
Projected Steady State (y=$68,000)

61. Is a higher steady state worth the transition?
Immediate drop in consumption as economy responds to policy change
Growth of per capita consumption under old policy regime = 1.5%
Growth of per capita consumption increases during transition period
Growth of per capita consumption returns to 1.5%