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

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!

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

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

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)

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

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.

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”

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

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

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

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

Returns to capital are constant over time Average Nominal Return = ~5% Average Real Return = ~1% US Annual Returns to Capital (1948-2014)

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

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)

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

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!

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

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 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

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

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

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%

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)

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)

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

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

Declining Average Product of Capital Around the World

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

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

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

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

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 = - 25.6% Growth in Population = 2.5% Growth in GDP Per Capita = -28.1% Average = .6%

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

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)

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

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

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….

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

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

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%

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%

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)

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 0.78 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

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)

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%

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

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

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

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 = 1.71 - .78 = .93%) (Per capita growth = 5.49 - .50 = 4.99%)

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

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

Let’s look at historical data for the US and Europe. Real Per Capita GDP, Europe and the United States: 1820 - 2000 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 (1989 -2000) Productivity Growth (2000-2005) 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: 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 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