FIN 30220: Macroeconomic Analysis Long Run Growth

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FIN 30220: Macroeconomic Analysis Long Run Growth Slide 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 countrys overall well being Slide 3 RegionGDP% of World GDP GDP Per Capita Real GDP Growth United States$15T18%$48,0001.3% European Union$16T19%$33,0001.0% Japan$4.3T6%$34,200-.4% China$7.8T11%$6,0009.8% India$3.2T5%$2,8006.6% Ethiopia$66.3B.09%$8008.5% Note. However, that growth rates vary significantly across countries/regions. Do you see a pattern here? Source: CIA World Factbook Slide 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 its current growth rate? Slide 5 IncomeGDP/CapitaGDP Growth Low$5106.3% Middle$2,1907.0% High$32,0403.2% As a general rule, low income (developing) countries tend to have higher average rates of growth than do high income countries 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 Slide 6 Some countries, however, dont 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) So, what is Sudan doing wrong? (Or, what is Qatar doing right?) 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!!! Slide 7 To understand this, lets look at the sources of economic growth.where does production come from? Real GDP is a function of 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 Slide 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: Capitals share of income (what % of total income in the US accrues to owners of capital) Labors 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) Slide 9 Suppose we have the following Cobb-Douglas production function: A 1% rise in employment raises GDP by 2/3% A 1% rise in capital raises GDP by 1/3% We can rewrite the production function in terms of growth rates to decompose GDP growth into growth of factors: Real GDP Growth (observable) Employment Growth (observable) Capital Growth (observable) Productivity Growth (unobservable) Slide 10 YearReal GDP (Billions of 2000 dollars) Real Capital Stock (Billions of 2000 dollars) Employment (thousands) 19391,1421,44029,923 200611,25712,632135,155 200711,46712,883137,180 Lets decompose some recent data first Note that capital is growing faster than employment Slide 11 YearReal GDP (Billions of 2000 dollars) Real Capital Stock (Billions of 2000 dollars) Employment (thousands) 19391,1421,44029,923 200611,25712,632135,155 200711,46712,883137,180 Now, lets look at long term averages Slide 12 1939 - 19481948 - 19731973-19931993-2007 Output 5.794.101.962.63 Capital 3.344.242.102.94 Labor 4.462.101.861.60 Productivity 1.711.280.020.59 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! Contributions to growth from capital, labor, and technology vary across time period Slide 13 Our model of economic growth begins with a production function 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 Slide 14 We are concerned with capital based growth. Therefore, growth in productivity and employment will be taken as given Productivity grows at rate Population grows at rate Employment Labor Force = Employment Ratio ( Assumed Constant) Labor Force Population = Participation rate ( Assumed Constant) Slide 15 Our simple model of economic growth begins with a production function with one key property diminishing marginal product of capital As the capital stock increases (given a fixed level of employment), the productivity of capital declines!! Change in Capital Stock Change in Production An economy cant grow through capital accumulation alone forever! Slide 16 Everything in this model is in per capita terms Divide both sides by labor to represent our variables in per capita terms Capital Per Capita Productivity Per capita output In general, lets assume lower case letters refer to per capita variables Slide 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 Capital stock per capita Output per capita Slide 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) Slide 19 Next, assume that households save a constant fraction of their disposable income Savings Income Less Taxes Constant between zero and one Again, convert everything to per capital terms by dividing through by the labor force Slide 20 KEY POINT: Savings = Household income that hasnt 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 S = I Firms access these funds by taking out loans, issuing stocks and bonds, etc. and use the funds for investment activities Investment per capita Slide 21 Continuing with our example: Slide 22 Investment represents the purchase of new capital equipment. This will affect the capital stock in the future Future capital stock current capital stock Annual Depreciation Rate Investment Expenditures We need to write this out in per capita terms as well Slide 23 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 We need to write this out in per capita terms as well Slide 24 Future capital stock per capita Annual depreciation rate Current capital per capita Investment per capita In our example Given Calculated The evolution of capital per capita Annual population growth rate Slide 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 Slide 26 Just to make sure, lets check our numbers In our example The evolution of capital per capita Slide 27 Lets update our diagram Actual investment break even investment Slide 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 Slide 29 Lets update our diagram Slide 30 Lets repeat that process again Capital Savings = Investment Evolution of Capital Output New Output Output Growth Growth is slowing downwhy? Slide 31 The rate of growth depends on the level of investment relative to the break even level of investment. Level of investment needed to maintain current capital stock Actual investment based on current savings Slide 32 Eventually, actual investment will equal break even investment and growth ceases (in per capita terms). This is what we call the steady state. Slide 33 The steady state has three conditions. 1 Investment is sufficient to maintain a constant capital/labor ratio 2 Savings per capita is a constant fraction of output per capita Output is a function of capital per capita 3 Recall that, in equilibrium, savings equals investment Slide 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 Slide 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!!! Slide 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! Slide 37 Suppose we started out example economy above its eventual steady state An economy above its steady state shrinks (in per capita terms) towards its steady state. Slide 38 An economy above its steady state cant generate enough savings to support its capital stock! Slide 39 Steady State Countries below their eventual steady state will grown towards it Investment needed to maintain current capital/labor ratio Actual investment (equals savings) Countries above their eventual steady state will shrink towards it Investment needed to maintain current capital/labor ratio Actual investment (equals savings) Countries at their eventual steady state will stay there Absolute convergence refers to the premise that eve