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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 CI 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 CI 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