Macroeconomic analysis Economic growth

FIN 30220: Macroeconomic Analysis Long Run Growth The World 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% GDP per capita is probably the best measure of a country’s overall well being 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% Ethiopia $118.2B 13% $1,300 7.0% Source: CIA World Factbook (2013 Estimates) Per Capita Income At the current trends, the standard of living in China will surpass that of the US in 25 years! Or, will they? That is, can China maintain it’s current growth rate? As a general rule, low income (developing) countries tend to have higher average rates of growth than high income countries Income 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 Sudan GDP: $107B (#73) GDP Per Capita: $5,100 (#159) GDP Growth: -2.3% (#213) Macau GDP: $51.6B (#98) GDP Per Capita: $88,700 (#3) GDP Growth: 11.9% (#5) At current trends, Per capita income in Macau will triple to $273,000 over the next decade Over the same time period, per capita GDP in Sudan will drop by roughly 25%to $4,000!!! So, what is Sudan doing wrong? (Or, what is Macau doing right?) To understand this, let’s look at the 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: α β Y = AK L where α + β =1 With the Cobb-Douglas production function, the parameters have clear interpretations: α β 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) 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% 3 Y = AK L We can rewrite the production function in terms of growth rates to decompose GDP growth into growth of factors: %∆Y = ( %∆A) + ( %∆K ) + ( %∆L ) 3 Real GDP Growth (observable) Productivity Growth (unobservable) Capital Growth (observable) Employment Growth (observable) Year Real GDP (Billions of 2009 dollars) Real Capital Stock (Billions of 2005 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 − ( 76 ) − ( 1.58 ) = 36 3 *Source: Penn World Tables 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%) 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%) Consider two countries… We already calculated this! Country A Country B gA = gA = g L = 2% g L = 15% A=6 t =0 θ = 10% A=6 t =0 θ = 10% δ = 10% K = 8,000 L = 1,000 δ = 10% K = 4,000 L = 1,000 3 y = Ak = 6( ) = 9.52 i = s = θ ( y − t ) = 10( 9.52 − ) = 952 k'= (1 − δ )k + i (1 − 10 ) + 952 = = 3.95 1+ gL + 15 3 y ' = Ak ' = 6( 3.95) = 9.48 g y = [ ln ( 9.48) − ln ( 9.52 ) ] *100 = −.41 y = 12 g y = 91% Even though Country B is poorer, it is growing slower than country A (in per capita terms)! With a higher rate of population growth, country B has a much lower steady state than country A!!! ~ y , i, i ~ iB = ( 15 + 10 ) k ~ iA = ( 02 + 10 ) k s = θ ( y − t) = i k =4 B  θA  k B ss =  ÷  δ + gL   10*6  = ÷ = 3.71 10 + 15   k =8 A k A ss = 11.18 k 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 Haiti Population Growth: 2.3% High Population Growth (Haiti) y Low Population Growth (Argentina) GDP/Capita: $1,600 GDP Growth: -1.5% Argentina Population Growth: 96% GDP/Capita: $13,700 GDP Growth: 8.7% Steady State Steady State (Argentina) (Haiti) Haiti is currently ABOVE its steady state (GDP per capita is falling due to a high population growth rate Argentina, with its low population growth is well below its steady state growing rapidly towards it 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 y GDP Growth: -7% High Savings Rate (Hong Kong) Investment Rate (%0f GDP): 7% Hong Kong Low Savings Rate (Zimbabwe) GDP/Capita: $37,400 GDP Growth: 6.9% Investment Rate (% of GDP): 21.2% Steady State Steady State (Zimbabwe) (Hong Kong) Zimbabwe is currently ABOVE its steady state (GDP per capita is falling due to low investment rate Hong Kong, with its high investment rate is well below its steady state growing rapidly towards it 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 y GDP Growth: 1.6% Small Government (US) Government (%0f GDP): 55% Large Government (France) USA GDP/Capita: $48,000 GDP Growth: 2.5% Government (% of GDP): 18% Steady State Steady State (France) 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 (USA) The smaller government of the US increases the steady state and, hence, economic growth 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) Question: Is maximizing growth a policy we should be striving for? y = Ak y = c+i 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) y = c + (δ + g L ) k In the steady state, investment simply maintains the existing steady state c = y − ( δ + g L ) k = Ak − ( δ + g L ) k Maybe we should be choosing a steady state with the highest level of consumption! 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 c = Ak − ( δ + g L ) k − dc = Ak − ( δ + g L ) dk Change in consumption per unit change in steady state capital Change in production per unit change in steady state capital Change in capital maintenance costs per unit change in steady state capital − dc = Ak − ( δ + g L ) = dk ~ y, i ~ i = ( gL + δ )k y = Ak Consumption equals zero – capital maintenance requires all of production Steady state consumption is maximized!!! k k* 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 Let’s go back to our example… − Ak − ( δ + g L ) =   A  k * =   3( δ + g L )  We can solve for the steady state capital that maximizes consumption gA = g L = 2% A=6 t =0 θ = 10% δ = 10%    = 68 k * =   3( 10 + 02 )  ~ y , i, i ~ i = ( gL + δ )k y = Ak i = s = 10( y − t ) k * = 11 Steady state with a 10% investment rate k * = 68 Steady state capital that maximizes consumption k max = 353 k Maximum sustainable capital stock – consumption equals zero Using our example, lets compare consumption levels… gA = Steady State with Savings Rate = 10% g L = 2% A=6 t =0 θ = 10% δ = 10%  10 *  k =  = 11.18  10 + 02  “Optimal” Steady State    = 68 k * =   3( 10 + 02 )  y = 6(11.18) = 13.40 y = 6( 68) = 24.5 i = ( 02 + 10 )11.18 = 1.34 i = ( 02 + 10 ) 68 = 8.16 c = 13.40 − 1.34 = 12.06 c = 24.5 − 8.16 = 16.34 In this example, we could increase consumption by 30% by altering the savings rate!! By comparing steady states, we can find the savings rate associated with maximum consumption gA = Steady State with a given Savings Rate g L = 2% A=6 t =0 θ = 10% δ = 10%  θA   k =   δ + gL  “Optimal” Steady State ( )  A k* =   δ + g  L   θ* = To maximize steady state consumption, we need a 33% savings/investment rate!! [...]... Annual Growth Generally speaking, productivity growth has been declining since WWII Our model of economic growth begins with a production function 1 3 Real GDP 2 3 Y = AK L 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. .. Evolution of Capital (1 − δ )k + i (1 − 10 ) 8.24 + 1.211 k' = = = 8.46 1+ gL 1.02 s = 10(12.11 − 0 ) = 1.211 New Output 1 3 y ' = 6( 8.46 ) = 12.22 Output Growth g y = [ ln (12.22 ) − ln (12.11) ] *100 = 90% Growth is slowing down…why? The rate of growth depends on the level of investment relative to the “break even” level of investment Actual investment based on current savings ~ y , i, i ~ i = ( gL...   LF  Pop  gA Employment Labor Force Population grows at rate = Employment Ratio ( Assumed Constant) Labor Force Population = Participation rate ( Assumed Constant) 1 3 Our simple model of economic growth begins with a production function with one key property – diminishing marginal product of capital Change in Production Y = AK L Y F ( A, K , L ) ∆Y ∆Y MPK = ∆K ∆K Change in Capital Stock As... = 6( 8) 3 = 12 Actual investment i = s = 1 2 ~ i = 96 k =8 k Now we have all the components to calculate next years output per capita and the rate of growth (1 − 10)8 + 1.2 k'= = 8.24 1 + 02 gA = 0 g L = 2% A=6 k =8 i = 1.2 k ' = 8.24 Output per capita growth Given Calculated y ' = A' k ' 1 3 1 3 y ' = 6( 8.24 ) = 12.11 g y = [ ln (12.11) − ln (12 ) ] *100 = 91% Let’s update our diagram… ~ i = ( gL... %∆A = 3.11 − 1 2 ( 3.06 ) − ( 1.70 ) = 98 3 3 Contributions to growth from capital, labor, and technology vary across time period 1939 1948 1948 1973 19731990 19902007 20072013 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 notice: Real GDP growth is declining over time Capital has been growing faster... i k = 1+ gL ' The evolution of capital per capita… Annual depreciation rate Current capital per capita (1 − δ )k + i k'= 1 + gl Future capital stock per capita Investment per capita Annual population growth rate In our example… δ = 10% g L = 2% k =8 i = s = 1.2 Given Calculated (1 − 10)8 + 1.2 k'= = 8.24 1 + 02 Just as a reference, lets figure out how much investment per capita would be required to... y , i, i ~ i = ( gL + δ )k y = Ak 1 3 i = s = θ ( y − t) y i=s ~ i Level of investment needed to maintain current capital stock k k Eventually, actual investment will equal “break even” investment and growth ceases (in per capita terms) This is what we call the steady state ~ i = ( gL + δ )k ~ y , i, i y = Ak y ss 1 3 i = s = θ ( y − t) ~ i=s=i k ss k The steady state has three conditions… 1 y = Ak