Long Term Economic Growth

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

This set of notes focuses solely on the trend!
Recall that we can take GDP for the US and decompose it into “Trend” and “Cycle” 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 (2013): $87T Population (2013):7.1B GDP per Capita (2013): $13,100 Population Growth (2013): 1.0% GDP Growth (2013): 2.9% * Source: CIA World Factbook

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 $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% South Sudan $14B .01% $1,400 24.7% Mozambique $28.2B .03% $1,200 7.0% * Source: CIA World Factbook (2013 Estimates)

*Source: World Bank South Sudan 24.7% United States 1.6% Japan: 2.0%
China 7.7% South Sudan 24.7% Ghana 7.9% Mozambique 7.0% *Source: World Bank

Income Class GDP/Capita GDP Growth Low < $1,045 6.3% Middle
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
Central African Republic GDP: $3.36B (#178) GDP Per Capita: $700 (#224) GDP Growth: -14.5% (#221) Macau GDP: $51.6B (#98) GDP Per Capita: $88,700 (#3) GDP Growth: 11.9% (#5) If current trends continue, per capita GDP in Macau will triple to $273,000 over the next decade. Over the same time period, per capita GDP in the Central African Republic will drop by roughly 80% to $146!!! So, what is the Central African Republic doing wrong? (Or, what is Macau 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 The growth rate of GDP per capita is (fairly) constant The ratio of capital to output 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%
2%/yr. Annual GDP Per Capita Growth

The ratio of capital to output is constant…
Capital Stock/GDP 2.2

? The “great ratios” are constant over time
Consumption to Output Ratio Consumption to Output Ratio Investment to output ratio ?

The capital/labor ratio is growing….
1.5% per year Capital Stock/Employment

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

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

US Nominal Returns (1948-2014) Returns to capital have no trend
Average = ~5% US Nominal Returns ( )

US Real Returns (1948-2014) Returns to capital have no trend
Average Nominal = ~5% Minus Average Inflation = ~4% Average = ~1% US Real Returns ( )

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

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)

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)

Lets decompose some recent data first…
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… *Source: Penn World Tables

Now, lets look at long term averages
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

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!

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, 1987 Nobel Prize, 1987

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

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)

Think of the economy as an apple orchard…
Labor Productivity Real GDP 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 Let’s say you produce 500 Apples Note: Your current capital/labor ratio is 100/50 = 2 (Note, that’s 10 apples per worker)

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

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)

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… 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

Can this process continue forever? NO!
Output 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

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

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

Growth in capital per capita
Capital Per capita is Growth in capital per capita Average product of capital (GDP divided by the capital stock) So, from the previous expression, we have Investment Rate Rate of population growth 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. So, absent productivity growth, increasing capital will lower the average product of capital

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”

Eventually, growth in capital per capita ceases (capital grows at the same rate as labor) and the capital stock per capita is constant As capital and labor grow at the same pace, the average product of capital (Y/K) remains constant

So, if we take our growth accounting expression….
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…. Real GDP Growth Productivity Growth Capital Growth Employment Growth =0 Capital Growth equals labor growth eventually Eventually, GDP growth equals population growth OR Eventually, GDP per capital growth equals zero

Transition towards Steady State Steady State
So, consider this idea of convergence (rich countries grow slow, poor countries grow fast) 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

Note that a countries long term level of average capital productivity is determined by some structural parameters The long term average product of capital will determine the long term position of a country

The long term average product of capital will determine the long term position of a country
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

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

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

Remember the outliers pointed out earlier?
Central African Republic GDP: $3.36B (#178) GDP Per Capita: $700 (#224) GDP Growth: -14.5% (#221) Macau GDP: $51.6B (#98) GDP Per Capita: $88,700 (#3) GDP Growth: 11.9% (#5) Investment rate = 8.3% Population Growth = 2% Investment rate = 12.3% Population Growth = 1.7%

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 The real wage rate grows at a constant rate The rate return to capital is constant (interest rate) The ratio of consumption to GDP and Investment to GDP are constant Labor’s share of income (and, hence, capital’s share) is constant By assumption Due to constant average product of capital By assumption Due to constant average product of labor

We can resolve these factual problems with productivity growth
With productivity growth, capital can grow relative to labor and the average product can remain constant!

So, with productivity growth,
The average product of capital is CONSTANT!! For that to happen, the growth of capital is equal to the growth in output Growth in output equals growth in capital GDP per capita and capital per capita grow at a rate proportional to productivity growth plus population growth GDP per capita and capital per capita grow 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
GDP per capita grows as a rate proportional to productivity growth

Growth 2007-2013 GDP 1.1 Capital 1.4 Labor -0.1 GDP Per Capita 1.2
Let’s look at the US for a minute… This model predicts that the rate of growth in GDP per capita will be proportional to the rate of productivity growth Growth GDP 1.1 Capital 1.4 Labor -0.1 GDP Per Capita 1.2 Productivity 0.7 Capital’s share of income (For the US, around .33) Let’s predict GDP per Capita growth in the US

All countries will grow at the rate of productivity growth in the long term, but at different levels, depending on their characteristics 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

Lets look at some other countries
China Investment Rate: 35-45% Population Growth: 0.5% Government (% of GDP): 24% United States Investment Rate: 15-20% Population Growth: 0.7% Government (% of GDP): 41% S. Korea Investment Rate: 30-35% Population Growth: 0.4% Government (% of GDP): 30% Annual Growth Rate India Investment Rate: 30-40% Population Growth: 1.2% Government (% of GDP): 27% Thailand Investment Rate: 25-30% Population Growth: 0.3% Government (% of GDP): 23% Lets look at some other countries * Source: Penn World Tables

2000 – 2011 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 Growth Predicted from model Actual Growth High rate of productivity growth High Investment rate Low population growth Low rate of productivity growth Low Investment Rate 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 population growth

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% United States GDP: $17.0T GDP Per Capita: $53,000 Real GDP Growth: 2.0% 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

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

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

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

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

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

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

Long Term Economic Growth

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