Economics 302 Growth 1 The Facts of Growth – The Long Run

Economics 302 Growth 1 The Facts of Growth – The Long Run Annual Growth RateReal Output per Capita Output per Capita (%)(1992 dollars) Ratio of Real Ouput Per Capita /1950 France ,15019, Germany ,35620, Japan ,82019, United Kingdom ,87019, United States ,17025, Average ,87220,8043.5

Economics 302 Growth 1 The Facts of Growth – The Long Run Constructing Output Numbers Output Per Capita = Purchasing Power Parity: Adjusts for differences in exchange rates and prices

Economics 302 Growth 1 The Facts of Growth – The Long Run Observations Strong growth Growth rates have decreased since the mid 1970s % (GDP/capita doubles every 16 years) % (GDP/capita doubles every 37 years) Convergence in output/capita across countries

Economics 302 Growth 1 The Facts of Growth – The Long Run Convergence in Output/Capita

Economics 302 Growth 1 The Facts of Growth – The Long Run What do you think… Could the finding of convergence be influenced by the way the countries are selected?

Economics 302 Growth 1 The Facts of Growth – The Long Run A Broader Look Across Time and Space Looking across two millennia From the end of the Roman Empire to 1500, no output per capita growth in Europe Small growth in output per capita (0.1%/year and 0.2%/year 1700 to 1820) Modest growth (U.S. = 1.5%) The high-growth of the 1950s and 1960s is unusual

Economics 302 Growth 1 The Facts of Growth – The Long Run A Broader Look Across Time and Space Looking across two millennia (Continued) 1st Millennium to the 15th century, China had the highest output/capita Leaders in output/capita change frequently: Italy Netherlands U.K.

Economics 302 Growth 1 The Facts of Growth – The Long Run The Reality of Growth: A Workingman’s Budget in 1851 AmountPercent of Item of Expenditure(Dollars)Total Butcher’s meat (2 lb a day) Flour (6 1/2 lb a year) Butter (2 lb a week) Potatoes (2 pk a week) Sugar (4 lb a week) Coffee and tea Milk Salt, pepper, vinegar, starch, soap, yeast, cheese, eggs Total expenditure for food Rent Coal (3 tons a year) Charcoal, chips, matches Candles and oil Household articles (wear, tear, and breakage) Bedclothes and bedding Wearing apparel Newspapers Total expenditures other than food

Economics 302 Growth 1 The Facts of Growth – The Long Run Looking Across Countries – Convergence Not the Rule

Economics 302 Growth 1 The Facts of Growth – The Long Run Looking Across Countries – A Closer Look

Economics 302 Growth 1 The Facts of Growth – The Long Run Looking Across Countries – A Closer Look OECD countries are converging Asian countries are converging African countries are not converging Three Conclusions:

Economics 302 Growth 1 The Facts of Growth – The Long Run Looking Across Countries – A Closer Look Miracles: Japan + Asian Tigers (South Korea, Taiwan, Singapore, Hong Kong) (average annual growth of over 5% ) Disasters: Argentina (average income in 1900 Similar to those of world leaders; now middle of World income distribution) Disaster: Sub-saharan Africa (Chad, Ghana, Mozambique) extremely poor throughout history Growth Miracles vs Growth Disasters

Economics 302 Growth 1 The Facts of Growth – The Long Run A Summary 1.Growth is not a historical necessity 2.Convergence of OECD countries to the U.S. may be the prelude to leapfrogging 3.The rapid post WWII growth was atypical

Economics 302 Growth 1 The Facts of Growth – The Long Run Thinking About Growth: A Primer (The Solow Model) The Aggregate Production Function Y = F (K, N) Y = Aggregate Output K = Capital N = Labor

Economics 302 Growth 1 The Facts of Growth – The Long Run The Aggregate Production Function Y = F (K, N) F: Depends on technology

Economics 302 Growth 1 The Facts of Growth – The Long Run Returns to Scale and Returns to Factors Constant returns to scale:2Y = F(2K,2N) xY = F(xK,xN) Decreasing returns to factors (capital & labor): Increases in K and N lead to smaller and smaller increases in output

Economics 302 Growth 1 The Facts of Growth – The Long Run Output and Capital per worker

Economics 302 Growth 1 The Facts of Growth – The Long Run Output and Capital per worker

Economics 302 Growth 1 The Facts of Growth – The Long Run Output and Capital per worker Output per worker, Y/N Capital per worker, K/N Y/N = (K/N, 1) A A´ B´ B C´ C D´ D

Economics 302 Growth 1 F(K/N, 1) The Facts of Growth – The Long Run The Sources of Growth An improvement in technology shifts the production function up Output per worker, Y/N Capital per worker, K/N A A´ B´

Economics 302 Growth 1 The Facts of Growth – The Long Run The Sources of Growth Increases in occur when technology shifts the production functions

Economics 302 Growth 1 The Facts of Growth – The Long Run The Sources of Growth Capital Accumulation Cannot sustain growth because of diminishing returns to capital Capital accumulation requires savings, therefore, what is the appropriate savings rate?

Economics 302 Growth 1 The Facts of Growth – The Long Run The Sources of Growth Technological Progress Required for sustained growth What determines the rate of technological progress?

Economics 302 Growth 1 Saving, Capital Accumulation, and Output The Long Run Observation: The savings rate since 1950 U.S.18.6% Germany24.6% Japan33.7% What do you think… Would increasing the U.S. savings rate lead to sustained higher U.S. growth in the future?

Economics 302 Growth 1 Interactions between Output and Capital Two long-run relations between output and capital  The amount of capital determines the amount of output being produced  The amount of output determines the amount of savings and investment and, thus, the amount of capital

Economics 302 Growth 1 Interactions between Output and Capital Capital, Output, and Saving/Investment

Economics 302 Growth 1 Interactions between Output and Capital The Effects of Capital on Output output per worker capital per worker

Economics 302 Growth 1 Interactions between Output and Capital The Effects of Capital on Output Therefore: Two assumptions: 1.Employment (N) is constant 2.There is no technological progress (f is constant)

Economics 302 Growth 1 Interactions between Output and Capital The Effects of Output on Capital Accumulation Three assumptions: 1.Closed economy: I = S + (G-T) 2.I = S if G = T = 0, therefore (G-T)=0 3.S = sY: Private saving is proportional to income s = Savings rate (between 0 & 1) Output & Investment

Economics 302 Growth 1 Interactions between Output and Capital The Effects of Output on Capital Accumulation Observations 1.The savings rate does not appear to systematically increase or decrease as Y increases 2.Richer countries do not appear to have systematically higher savings rates than poorer ones 3.Investment is proportional to output Output & Investment I t = sY t

Economics 302 Growth 1 Interactions between Output and Capital The Effects of Output on Capital Accumulation The evolution of the capital stock: Investment and Capital Accumulation K t+1 = (1- ) K t + I t = the depreciation rate

Economics 302 Growth 1 Interactions between Output and Capital The Effects of Output on Capital Accumulation The relation between output and capital accumulation Investment and Capital Accumulation K t+1 = (1- ) K t + I t and I t = sY t K t+1 = (1- ) K t + sY t and ÷ N

Economics 302 Growth 1 Interactions between Output and Capital The Effects of Output on Capital Accumulation The relation between output and capital accumulation Investment and Capital Accumulation Capital/worker in t+1 = Capital/Worker in t, adjusted for depreciation and investment Investment/worker = Savings rate x Output/worker in t

Economics 302 Growth 1 Interactions between Output and Capital The Effects of Output on Capital Accumulation The relation between output and capital accumulation Investment and Capital Accumulation Reorganizing: Savings/worker - depreciation Change in

Economics 302 Growth 1 Interactions between Output and Capital A Summary The Production Side Capital-Output Relation: Output-Capital Relation:

Economics 302 Growth 1 Implications of Alternative Saving Rates Dynamics of Capital and Output Given: And:

Economics 302 Growth 1 Implications of Alternative Saving Rates Dynamics of Capital and Output Given: - Change in capital from year t to year t+1 = Invest- ment during year t depreciation during year t

Economics 302 Growth 1 Implications of Alternative Saving Rates Dynamics of Capital and Output The change in capital/worker from t to t+1 depends on the difference between: Investment/Worker & Depreciation/Worker

Economics 302 Growth 1 Implications of Alternative Saving Rates Dynamics of Capital and Output Capital/Worker increases: Investment/Worker > Depreciation/Worker Capital/Worker decreases: Investment/Worker < Depreciation/Worker

Economics 302 Growth 1 Output per worker f(K t /N) Depreciation per worker K t /N Investment per worker sf(K t /N) Implications of Alternative Saving Rates Dynamics of Capital and Output Graphically Output per worker, Y/N Capital per worker, K/N A B Y*/N C K*/N D (K o /N) AB = Output/worker AC = Investment/worker AD = Depreciation AC > AD

Economics 302 Growth 1 Implications of Alternative Saving Rates Dynamics of Capital and Output The evolution of & over time Assume: is low, therefore I > depreciation ( ) If I >, increases until I = When I = : & remain Long-run equilibrium

Economics 302 Growth 1 Implications of Alternative Saving Rates Steady-State Capital and Output Steady-State Value of Capital/Worker Steady-State Value of Output/Work

Economics 302 Growth 1 Implications of Alternative Saving Rates The Saving Rate and Output What are the effects of the saving rate on the rate of output per worker? 1.The saving rate has no effect on the long run growth rate of output/worker, this is equal to zero. 2.The saving rate determines the level of output/worker in the long run. 3.An increase in the saving rate will lead to a higher growth of output/worker for some time, but not forever.

Economics 302 Growth 1 Investment s 0 f(K t /N) (K 0 /N) Implications of Alternative Saving Rates The Effects of Different Saving Rate Depreciation per worker K t /N Output per worker, Y/N Capital per worker, K/N Investment s 1 f(K t /N) K 1 /N

Economics 302 Growth 1 Investment s 0 f(K t /N) Investment s 1 f(K t /N) Output per worker, Y/N Capital per worker, K/N Depreciation per worker K t /N Implications of Alternative Saving Rates The Effects of Different Saving Rate Output per worker f(K t /N) Y 1 /N B A K 1 /N (K 0 /N) Y 0 /N D C I >

Economics 302 Growth 1 Output per worker, Y/N Time Implications of Alternative Saving Rates The Effects of Different Saving Rate Y 1 /N Y 0 /N t Associated with saving rate s 0 Associated with saving rate s 1 > s 0 (No technological progress)

Economics 302 Growth 1 Output per worker, Y/N (log scale) Time Implications of Alternative Saving Rates The Effects of Different Saving Rate t Associated with saving rate s 0 Associated with saving rate s 1 > s 0 (Technological progress)

Economics 302 Growth 1 Implications of Alternative Saving Rates The Savings Rate and the Golden Rule Does an increase in saving lead to an increase in consumption in the long run? Two Scenarios: Saving Rate = 0 Capital = 0 Output = 0 Consumption = 0 Saving Rate = 1 Consumption = 0 Output replaces depreciation

Economics 302 Growth 1 Implications of Alternative Saving Rates The Savings Rate and the Golden Rule The Golden-Rule Level of Capital: The value of saving that yields the highest level of consumption in steady state.

Economics 302 Growth 1 Implications of Alternative Saving Rates Consumption per worker, C/N Saving rate, s sGsG 01 Maximum steady state Consumption per worker

Economics 302 Growth 1 Question for Discussion Can a low saving/investment rate explain why the U.S. growth rate has been so low since 1950? Getting a Sense of Magnitudes

Economics 302 Growth 1 Implications of Alternative Saving Rates The Savings Rate and the Golden Rule Are countries likely to have too much capital? The value of saving that yields the highest level of consumption in steady state. Consider: What do you think…

Economics 302 Growth 1 Getting a Sense of Magnitudes Some Questions: 1.How large is the effect of a change in the saving rate on output in the long run? 2.For how long and by how much does an increase in the saving rate affect growth? 3.How far is the U.S. from the Golden Rule of Level of Capital?

Economics 302 Growth 1 Calculating the Answers Assume: (Constant return to scale and decreasing returns to either capital or labor) Getting a Sense of Magnitudes

Economics 302 Growth 1 Replace with Recall: Getting a Sense of Magnitudes

Economics 302 Growth 1 The Effects of the Saving Rate on Steady-State Output In steady-state is constant and the left side = 0 and: Getting a Sense of Magnitudes

Economics 302 Growth 1 Implications of Alternative Saving Rates The Effects of the Saving Rate on Steady-State Output : square both sides : Divide by and reorganize

Economics 302 Growth 1 The Effects of the Saving Rate on Steady-State Output Steady-State Output/Worker: Observation Higher saving rate and lower depreciation both lead to higher and in the long run. Getting a Sense of Magnitudes

Economics 302 Growth 1 The Effects of the Saving Rate on Steady-State Output Assume: Getting a Sense of Magnitudes

Economics 302 Growth 1 The Dynamic Effects of an Increase in the Saving Rate Assume: Getting a Sense of Magnitudes The saving rate has always been equal to 0.1 Then the saving rate increases to 0.2 forever Then:

Economics 302 Growth 1 The Dynamic Effects of an Increase in the Saving Rate Continuing for each year yields… Getting a Sense of Magnitudes

Economics 302 Growth 1 The Dynamic Effects of an Increase in the Saving Rate Getting a Sense of Magnitudes

Economics 302 Growth 1 The Dynamic Effects of an Increase in the Saving Rate Getting a Sense of Magnitudes

Economics 302 Growth 1 Getting a Sense of Magnitudes The U.S. Saving Rate and the Golden Rule What saving rate that would maximize steady-state consumption? In Steady-State:

Economics 302 Growth 1 Getting a Sense of Magnitudes The Saving Rate and the Steady-State Levels of Capital, Output, and Consumption per Worker CapitalOutputConsumption Saving Rate,per Worker,per Worker,per Worker, sK/NY/NC/N

Economics 302 Growth 1 Getting a Sense of Magnitudes The U.S. Saving Rate and the Golden Rule Observation If s <.50: increasing s will increase long-run consumption In the U.S., s < 20%

Economics 302 Growth 1 Physical Versus Human Capital Human Capital: The set of skills of the workers in the economy.

Economics 302 Growth 1 Physical Versus Human Capital Observations OECD Countries: 100% of children get a primary education 90% of children get a secondary education 38% of children get a higher education Literacy rate above 95%

Economics 302 Growth 1 Physical Versus Human Capital Extending the Production Function Measuring the Impact of Human Capital:

Economics 302 Growth 1 Physical Versus Human Capital Human Capital, Physical Capital, and Output How does including human capital impact our analysis? Investment now includes physical and human capital In the U.S.: Education spending =6.5% of GDP Investment =16.0% of GDP

Economics 302 Growth 1 Physical Versus Human Capital Human Capital, Physical Capital, and Output Some Complications: Education is partly consumption Education cost should include the opportunity cost On-the-job training is not included Should compare investment rates net of depreciation

Economics 302 Growth 1 Physical Versus Human Capital Endogenous Growth What do you think… To what extent does growth depend on the savings rate, education, and technological change?