Presentation on theme: "FIN 30220: Macroeconomic Analysis"— Presentation transcript:
1FIN 30220: Macroeconomic Analysis Long Run Growth
2The World Economy Total GDP (2012): $83T Population (2012):7B GDP per Capita (2012): $12,500Population Growth (2012): 1.1%GDP Growth (2012): 3.3%GDP per capita is probably the best measure of a country’s overall well being
3Region 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?RegionGDP% of World GDPGDP Per CapitaReal GDP GrowthUnited 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%Source: CIA World Factbook
4At the current trends, the standard of living in China will surpass that of the US in 25 years! Or, will they?Per Capita IncomeThat is, can China maintain it’s current growth rate?
5Income GDP/Capita GDP Growth Low $510 6.3% Middle $2,190 7.0% High As a general rule, low income (developing) countries tend to have higher average rates of growth than do high income countriesIncomeGDP/CapitaGDP GrowthLow$5106.3%Middle$2,1907.0%High$32,0403.2%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”
6Some countries, however, don’t fit the normal pattern of development SudanGDP: $80B (#80)GDP Per Capita: $2,400 (#184)GDP Growth: -11.2% (#219)QatarGDP: $150B (#59)GDP Per Capita: $179,000 (#1)GDP Growth: 16.3% (#1)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!!!So, what is Sudan doing wrong? (Or, what is Qatar doing right?)
7To understand this, let’s look at the sources of economic growth… To understand this, let’s look at the sources of economic growth….where does production come from?“is a function of”Real GDPLaborProductivityCapital StockReal GDP = Constant Dollar (Inflation adjusted) value of all goods and services produced in the United StatesCapital Stock = Constant dollar value of private, non-residential fixed assetsLabor = Private Sector EmploymentProductivity = Production unaccounted for by capital or labor
8A convenient functional form for growth accounting is the Cobb-Douglas production function. It takes the form:whereWith 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)
9Suppose 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%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)
10Lets decompose some recent data first… YearReal GDP (Billions of 2000 dollars)Real Capital Stock (Billions of 2000 dollars)Employment (thousands)19391,1421,44029,923200611,25712,632135,155200711,46712,883137,180Lets decompose some recent data first…Note that capital is growing faster than employment
11Now, lets look at long term averages YearReal GDP (Billions of 2000 dollars)Real Capital Stock (Billions of 2000 dollars)Employment (thousands)19391,1421,44029,923200611,25712,632135,155200711,46712,883137,180Now, lets look at long term averages
12Contributions to growth from capital, labor, and technology vary across time period Output5.794.101.962.63Capital3.3188.8.131.52Labor4.461.861.60Productivity1.711.280.020.59A few things to notice:Real GDP growth is declining over time.Capital has been growing faster than laborThe contribution of productivity is diminishing!
13Our model of economic growth begins with a production function Real GDPLaborProductivityCapital StockGiven our production function, economic growth can result fromGrowth in laborGrowth in the capital stockGrowth in productivity
14We are concerned with capital based growth We are concerned with capital based growth. Therefore, growth in productivity and employment will be taken as givenPopulation grows at rateProductivity grows at rateEmployment= Employment RatioLabor ForceLabor Force= Participation ratePopulation( Assumed Constant)( Assumed Constant)
15An economy can’t grow through capital accumulation alone forever! Our simple model of economic growth begins with a production function with one key property – diminishing marginal product of capitalChange in ProductionChange in Capital StockAs the capital stock increases (given a fixed level of employment), the productivity of capital declines!!An economy can’t grow through capital accumulation alone forever!
16Everything in this model is in per capita terms Divide both sides by labor to represent our variables in per capita termsPer capita outputCapital Per CapitaProductivityIn general, let’s assume lower case letters refer to per capita variables
17Again, 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 shrinksOutput per capitaCapital stock per capita
18Lets use an example. The current level of capital per capita will determine the current standard of living (output per capita = income per capita)
19Next, assume that households save a constant fraction of their disposable income Income Less TaxesConstant between zero and oneSavingsAgain, convert everything to per capital terms by dividing through by the labor force
20Savings = Household income that hasn’t been spent KEY POINT:Savings = Household income that hasn’t been spentInvestment = 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 activitiesHouseholds save their income by opening savings accounts, buying stocks and bonds, etcFirms access these funds by taking out loans, issuing stocks and bonds, etc. and use the funds for investment activitiesS = IInvestment per capita
22Investment represents the purchase of new capital equipment Investment represents the purchase of new capital equipment. This will affect the capital stock in the futureAnnual Depreciation RateInvestment ExpendituresFuture capital stockcurrent capital stockWe need to write this out in per capita terms as well…
23We need to write this out in per capita terms as well… Divide through by labor to get things in per capita termsMultiply and divide the left hand side by future labor supplyRecall that labor grows at a constant rate
24In our example… The evolution of capital per capita… Given Calculated Current capital per capitaAnnual depreciation rateInvestment per capitaAnnual population growth rateFuture capital stock per capitaIn our example…GivenCalculated
25Just as a reference, lets figure out how much investment per capita would be required to maintain a constant level of capital per capitaEvolution of per capita capitalAssume constant capital per capitaSolve for investmentIn our example…GivenCalculated
26In our example… Just to make sure, lets check our numbers… The evolution of capital per capita…
30Let’s repeat that process again… Savings = InvestmentCapitalOutputEvolution of CapitalNew OutputOutput GrowthGrowth is slowing down…why?
31The rate of growth depends on the level of investment relative to the “break even” level of investment.Actual investment based on current savingsLevel of investment needed to maintain current capital stock
32Eventually, actual investment will equal “break even” investment and growth ceases (in per capita terms). This is what we call the steady state.
332 1 3 The steady state has three conditions…. Savings per capita is a constant fraction of output per capitaOutput is a function of capital per capitaRecall that, in equilibrium, savings equals investment3Investment is sufficient to maintain a constant capital/labor ratio
34With a little algebra, we can solve for the steady state in our example. Start with condition 3Use condition 2 and the fact that savings equals investmentSubstitute condition 1Recall that taxes are zero in our exampleSolve for k
35Plugging in our parameters gives us steady state values. Steady state per capita capitalSteady state per capita outputSteady state per capita savings/investmentSteady state per capita consumptionConstant per capita capital!!!
36Eventually, 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!
37Suppose we started out example economy above it’s eventual steady state… An economy above its steady state shrinks (in per capita terms) towards its steady state.
38An economy above its steady state shrinks (in per capita terms) towards its steady state. An economy above its steady state can’t generate enough savings to support its capital stock!
39Countries above their eventual steady state will shrink towards it “Absolute convergence” refers to the premise that every country will converge towards a common steady stateInvestment needed to maintain current capital/labor ratioActual investment (equals savings)Actual investment (equals savings)Investment needed to maintain current capital/labor ratioSteady StateCountries above their eventual steady state will shrink towards itCountries below their eventual steady state will grown towards itCountries at their eventual steady state will stay there
401 2 3 Most countries follow the “usual” pattern of development Developing countries have very little capital, but A LOT of labor. Hence, the price of labor is low, the return to capital is very high12High returns to capital attract a lot of investment. As the capital stock grows relative to the labor force, output, consumption, and real wages grow while interest rates (returns to capital fall)3Eventually, a country “matures” (i.e. reaches its steady state level of capital). At this point, growth can no longer be achieved by investment in capital. Growth must be “knowledge based” – improving productivity!Productivity
41Does the economy have a “speed limit”? Economic Growth can be broken into three components:GDP Growth= Productivity Growth + (2/3)Labor Growth + (1/3)Capital GrowthIn the Steady State, Capital Growth = Labor GrowthGDP Growth= Productivity Growth + Employment Growth
42Developing 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 convergenceExamples 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%)
43Some countries, however, don’t fit the traditional pattern. Developing Countries with Low GrowthMadagascar(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 GrowthHong 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%)
44Consider two countries… Country ACountry BWe already calculated this!Even though Country B is poorer, it is growing slower than country A (in per capita terms)!
45With a higher rate of population growth, country B has a much lower steady state than country A!!!
46Conditional 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.High Population Growth (Haiti)HaitiPopulation Growth: 2.3%GDP/Capita: $1,600GDP Growth: -1.5%Low Population Growth (Argentina)ArgentinaPopulation Growth: .96%GDP/Capita: $13,700GDP Growth: 8.7%Steady State(Haiti)Steady State(Argentina)Argentina, with its low population growth is well below its steady state growing rapidly towards itHaiti is currently ABOVE its steady state (GDP per capita is falling due to a high population growth rate
47Zimbabwe (until recently) 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: $2,100GDP Growth: -7%Investment Rate (%0f GDP): 7%High Savings Rate (Hong Kong)Hong KongGDP/Capita: $37,400GDP Growth: 6.9%Investment Rate (% of GDP): 21.2%Low Savings Rate (Zimbabwe)Steady State(Zimbabwe)Steady State(Hong Kong)Hong Kong, with its high investment rate is well below its steady state growing rapidly towards itZimbabwe is currently ABOVE its steady state (GDP per capita is falling due to low investment rate
48Conditional 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.FranceGDP/Capita: $30,000GDP Growth: 1.6%Government (%0f GDP): 55%Small Government (US)Large Government (France)USAGDP/Capita: $48,000GDP Growth: 2.5%Government (% of GDP): 18%Steady State(France)Steady State(USA)The smaller government of the US increases the steady state and, hence, economic growthFrance 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
49Suggestions 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 stateConsider 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).
50Question: Is maximizing growth a policy we should be striving for? Our model begins with a relationship between the capital stock and productionThese goods and services that we produce can either be consumed or used for investment purposes (note: taxes are zero)In the steady state, investment simply maintains the existing steady stateMaybe we should be choosing a steady state with the highest level of consumption!
51Steady state consumption is a function of steady state capital 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 changesChange in consumption per unit change in steady state capitalChange in capital maintenance costs per unit change in steady state capitalChange in production per unit change in steady state capital
52Consumption equals zero – capital maintenance requires all of production Steady state consumption is maximized!!!In this region, an increase in capital increases production by more than the increase in maintenance costs – consumption increasesIn this region, an increase in capital increases production by less than the increase in maintenance costs – consumption decreases
53Let’s go back to our example… We can solve for the steady state capital that maximizes consumption
54Maximum sustainable capital stock – consumption equals zero Steady state capital that maximizes consumptionSteady state with a 10% investment rate
55Using our example, lets compare consumption levels… Steady State with Savings Rate = 10%“Optimal” Steady StateIn this example, we could increase consumption by 30% by altering the savings rate!!
56By comparing steady states, we can find the savings rate associated with maximum consumption Steady State with a given Savings Rate“Optimal” Steady StateTo maximize steady state consumption, we need a 33% savings/investment rate!!
57So, where does the US stand? Production (2008)Consumption (2008)Investment (2008)Government Purchases (2008)$14,264B$10,057B$1,994B$2,882BThe savings rate in the US is currently around 4%, but what we really want is the investment rateAt our steady state, GDP growth should be 3-3.5% (Per capita GDP will grow at 1-1.5%)
58We need to calibrate the model to the data… Production (2008)Consumption (2008)Investment (2008)Government Purchases (2008)$14,264B$10,057B$1,994B$2,882BIn the steady state…We know everything but the value for productivityGDP Per Capita (2008) = $47,000
59Investment expenditures would be 33%, or $22,464. Now, suppose that we could increase the investment rate to 33% as our model prescribesProduction (2008)Consumption (2008)Investment (2008)Government Purchases (2008)$14,264B$10,057B$1,994B$2,882BIn the steady state…We could raise per capita income to close to $70,000Investment expenditures would be 33%, or $22,464.Currently, government plus private consumption per capita is around $43,000Private consumption per capitagovernment purchases per capita
60Should we pursue policies to raise the investment rate in the US? Current Steady State (y = $47,000)Projected Steady State (y=$68,000)
61Is a higher steady state worth the transition? Immediate drop in consumption as economy responds to policy changeGrowth of per capita consumption under old policy regime = 1.5%Growth of per capita consumption increases during transition periodGrowth of per capita consumption returns to 1.5%