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1、Lecture 6Economic Growthslide 1Economic GrowthExplain improvements in standards of living (GDP per capital) along timeExplain differences across countrieslearn how our own growth rate is affected by shocks and our governments policiesSolow Growth Modelslide 2some statisticsIn Uganda, 96% of people l
2、ive on less than $2/day. (data link)2.8 billion people live on less than $2/day (1.1 billion under $1/day)GDP per capitalChad in 1960: $1212, in 2000: $908lVenezuela in 1960: $7840, in 2000: $6420lKorea in 1960: $1495, in 2000: $15875lH.K. in 1960: $3090, in 2000: $26698slide 3Huge effects from tiny
3、 differences1,081.4%243.7%85.4%624.5%169.2%64.0%2.5%2.0%100 years50 years25 yearspercentage increase in standard of living afterannual growth rate of income per capitaslide 4Long term growth effectRule of 72: 1% growth rate, approximately takes 72 years to double GDPWhat will happen if China keeps 1
4、0% growth rate and US keeps 3% growth rate (US per capita GDP $42,000 China $6800) slide 5World Distribution of Income5slide 6World Income Map6slide 7South vs. North7slide 88slide 9Real GDP per capita, 197520039slide 10Life Expectancy and Income (Preston, 1976)10slide 1111slide 12Heights of Males an
5、d Females in China12slide 13Happiness and Income13slide 14The Solow Modeldue to Robert Solow,won Nobel Prize for contributions to the study of economic growtha major paradigm:lwidely used in policy makinglbenchmark against which most recent growth theories are comparedlooks at the determinants of ec
6、onomic growth and the standard of living in the long runslide 15How Solow model is different from Chapter 3s model1.K is no longer fixed:investment causes it to grow, depreciation causes it to shrink.2.L is no longer fixed:population growth causes it to grow. 3.The consumption function is simpler.4.
7、No G and Tslide 16ProductionInitially assume constant population (L) and no technology changeProduction of goods and services:Constant Returns to Scale: slide 17ProductionLetting z = 1/L, we get the production function in per capita terms: y = Y/L = output per workerk = K/L = capital per workerConst
8、ant Returns to Scale size of the economy does not affect the relationship between capital per worker and output per worker slide 18Production Decreasing MPK: This implies the following shape for the production function:slide 19ProductionMPK is the slope of this curve.kyf(k)Low MPKHigh MPKslide 20Pro
9、ductionCobb-Douglas case: slide 21DemandAssume a closed economy with no government: NX = G = 0Assume that people save a fraction s of their income (and therefore consume 1 s), slide 22DemandSubstituting:In equilibrium: slide 23Capital AccumulationTwo elements determine how the capital stock changes
10、over time:lInvestment: addition of new plants and equipment (makes capital stock rise)lDepreciation: wearing out of existing capital stock (makes capital stock fall)slide 24Capital AccumulationIn other words:slide 25Capital Accumulationkf(k)sf(k)ciyslide 26Capital Accumulation Investment higher than
11、 depreciation capital stock increases Depreciation higher than investment capital stock decreasesslide 27Capital AccumulationSteady-state capital stock (k*):Steady state output, consumption, investment:slide 28Determining the capitallabor ratio in the steady state28slide 29Capital AccumulationLow k
12、high MPK high returns from investment capital stock grows High k low MPK low returns from investment capital stock decreasesIn both cases, the economy converges to the steady state (long-run equilibrium) slide 30Capital AccumulationCobb-Douglas:In steady state:slide 31Increase in Savings Rateks1f(k)
13、ks2f(k)slide 32Increase in Savings RateHigher s means that more resources will be dedicated to investment higher capital stock in steady stateTherefore, output per capita will be also higherslide 33Golden RuleWhat is the relationship between steady-state consumption and savings rate?Two conflicting
14、forces:lHigher s higher output higher the amount of resources available for consumption c* lHigher s lower the proportion of income allocated to consumption c* slide 34Golden RuleFor low values of s, c* increases with sFor high values of s, c* decreases with sGolden Rule: capital stock implied by th
15、e savings rate such that c* is maximizedslide 35Golden RuleMore formally:But in steady state: slide 36Golden RuleGolden Rule: find k* such that c* is maximized slide 37Golden Rulekkf(k)MPK = slide 38Golden Rulesg is the savings rate that implies kg*:kkf(k)MPK = sgf(k)slide 39The relationship of cons
16、umption per worker to the capitallabor ratio in the steady state39slide 40Golden RuleCobb-Douglas case:Golden Rule: MPK = slide 41Golden RuleIn steady state:slide 42Transition to Golden RuleCase 1: s sg, i.e., steady-state capital too high. Decrease s in order to reach sgksgf(k)s2f(k)kslide 43Transi
17、tion to Golden Ruletttkyck*kg*y*yg*c*cg*i*ig*tislide 44Transition to Golden RuleCase 2: s sg, i.e., steady-state capital too low. Increase s in order to reach sgksf(k)sgf(k)kslide 45Transition to Golden Rulettkyck*kg*y*yg*c*cg*i*ig*ittslide 46Transition to Golden RuleIf the economy begins above the
18、golden rule (s too high), consumption increases in all future periods decrease in s leads to welfare improvementIf the economy begins below the golden rule (s too low), consumption falls during transition there is a tradeoff between consuming today or in the future slide 47International Evidence on
19、Investment Rates and Income per Personslide 48Population GrowthAssume that the population-and labor force- grow at rate n. (n is exogenous)EX: Suppose L = 1000 in year 1 and the population is growing at 2%/year (n = 0.02). Then L = n L = 0.02 1000 = 20,so L = 1020 in year 2.slide 49Break-even invest
20、ment( + n)k = break-even investment, the amount of investment necessary to keep k constant. Break-even investment includes: k to replace capital as it wears outn k to equip new workers with capital(otherwise, k would fall as the existing capital stock would be spread more thinly over a larger popula
21、tion of workers)slide 50The equation of motion for kWith population growth, the equation of motion for k is k = s f(k) ( + n) k break-even investmentactual investmentslide 51The Solow Model diagramInvestment, break-even investmentCapital per worker, k sf(k)( + n ) kk* k = s f(k) ( +n)kslide 52The im
22、pact of population growthInvestment, break-even investmentCapital per worker, k sf(k)( +n1) kk1* ( +n2) kk2* An increase in n causes an increase in break-even investment,leading to a lower steady-state level of k.slide 53Prediction:Higher n lower k*. And since y = f(k) , lower k* lower y* . Thus, th
23、e Solow model predicts that countries with higher population growth rates will have lower levels of capital and income per worker in the long run. slide 54International Evidence on Population Growth and Income per Personslide 5555slide 56Clark 2005, p1308 Fig 1slide 57The Golden Rule with Population
24、 GrowthTo find the Golden Rule capital stock, we again express c* in terms of k*:c* = y* i*= f (k* ) ( + n) k* c* is maximized when MPK = + n or equivalently, MPK = nslide 58Technology ProgressRewrite the production function to incorporate technology change:E = efficiency of laborE L = effective wor
25、kersAssume: Technological progress is labor-augmenting: it increases labor efficiency at the exogenous rate g: slide 5959Technology ProgressAssume that E grows at rate gTherefore E L grows at rate n + gRedefine all variables in terms of effective workers: k = K/EL = capital per effective workerslide
26、 6060Technology ProgressThen y = Y/EL (= output per effective worker) is given by:Similarly for consumption and investment:slide 6161Technology ProgressTherefore, the equations are the same as beforeThe only change is in the law of motion for k. Capital per effective worker:lIncreases with investmen
27、tlDecreases with physical depreciationlAlso decreases because there are more effective workers to share the existing capital (higher L and E)slide 6262Technology ProgressThen:In steady-state, capital per effective worker is fixed: slide 6363Technology Progressksf(k)( +n+g)kk*k1k2slide 6464Technology
28、 ProgressIn steady state, income, consumption and investment per effective worker are also constant over time: slide 6565Technology ProgressTherefore capital, income, consumption and investment per worker grow at the rate g in steady-state: slide 66slide 66Steady-State Growth Rates in the Solow Mode
29、l with Tech. Progressn + gY = y E L Total outputg(Y/ L ) = y E Output per worker0y = Y/ (L E )Output per effective worker0k = K/ (L E )Capital per effective workerSteady-state growth rateSymbolVariableslide 6767Technology ProgressThis follows since steady-state variables are constant and E is growin
30、g at the rate gTherefore, the inclusion of technology progress in the Solow model can generate sustained long-run growthslide 6868Technology ProgressMoreover, total capital, output, consumption and investment grow at the rate n+g in steady state:Given that steady-state variables are constant and EL
31、is growing at the rate n+gslide 6969Consumption per effective worker in steady state:Golden Rule: find k* s.t. c* is maximized:Golden Ruleslide 70Government Policies to raise the rate of productivity growthlImproving infrastructurelWould increased infrastructure spending increase productivity?There
32、might be reverse causation: Richer countries with higher productivity spend more on infrastructure, rather than vice versaInfrastructure investments by government may be inefficient, since politics, not economic efficiency, is often the main determinantslide 71Government Policies to raise the rate o
33、f productivity growthlBuilding human capitalTheres a strong connection between productivity and human capitalGovernment can encourage human capital formation through educational policies, worker training and relocation programs, and health programsAnother form of human capital is entrepreneurial ski
34、llGovernment could help by removing barriers like red tapelEncouraging research and developmentGovernment can encourage R and D through direct aid to researchslide 72Why is technological breakthroughs progress so unequal across countries?What determined whether/when new technology adopted?lGeography
35、 view: importance of ecology, climate, disease environment, geography, in short, factors outside human control.lInstitutions view: importance of man-made factors; especially organization of society that provide incentives to individuals and firms.lHistorys accidents: some countries are unlucky and t
36、rapped in underdevelopment.72slide 73The Geography Factor73slide 74The Institutions Factor74slide 75Institutions and Economic Performances75slide 76Institutions and Economic Performances76slide 77But institutions are complicated: identification problemGood institutions are correlated with many other
37、 good things. Theories about institutions are thus very difficult to test.The study of the causal role of institutions on economic growth is therefore complicated by concerns about endogeneity.For example, the United States is rich; it has good institutions; it has high levels of education; it has a
38、 common law heritage; it has a temperate climate.Good institutions are difficult to pin down precisely. We want to be very careful to disentangle different causal effects and isolate the effect of interest.77slide 78But institutions are also endogenousInstitutions could vary because underlying facto
39、rs differ across countries: Geography, ecology, climateMontesquieus story: Geography determines “human attitudes” Human attitudes determine both economic performance and political system. Institutions potentially influenced by the determinants of income78slide 7979Factor PricesSo far, we solved the
40、model without any reference to wages and rental rates (factor prices)We just focused on how income is generated, but not on how it is distributedAssume that a competitive firm hires capital and labor to generate outputslide 8080Factor PricesAssuming Cobb-Douglas technology: Then the problem for this
41、 firm is given by:slide 8181Factor PricesFirst-order condition for K implies that:In steady-state, the real rental rate is fixed (since k is fixed)slide 8282Factor PricesFirst-order condition for L implies that:In steady-state, the real wages increase at the rate g (since k is fixed and E grows at t
42、he rate g)slide 8383Factor PricesAssume that capital is initially below the steady-state. Then k will evolve according to the following path:tkk*slide 8484Factor PricesRental rate:linitially high (low k implies high MPK)ldecreases over time as capital accumulates and MPK decreasestR/Pslide 8585Facto
43、r PricesDefine wage in terms of efficiency units as:Then :linitially low (low k implies low MPL labor abundant relative to capital)lincreases over time as capital accumulates and MPL increaseslconstant in steady stateslide 8686Factor PricesThis means that real wages (w/P):lGrow faster than g during
44、the transitionlGrow at the rate g in steady-statetslide 87Growth AccountingWant to be able to explain why and how countries growThere are many sources of growthFirst step is to decompose aggregate growth into its components:lGrowth in the labor forcelGrowth in capitallGrowth in productivity87slide 8
45、888Sources of Economic GrowthAssume Cobb-Douglas Production FunctionTake log and differentiatingslide 89Computing TFPz: Total Factor Productivity (TFP) or “Solow Residual”Y is GDP, K is aggregate capital, N is number of workersNeed to know 89slide 9090What is “z”Human Capital (Education)Technologica
46、l ProgressExternality: environmental IssuesInstitutional EffectlFirm OrganizationlPatent ProtectionlCorruptionsslide 91Labor Share in the Cobb-Douglas Production FunctionFirm optimization:First-order condition with respect to N:Labor share is wN/Y. Here:91slide 92ResultCan use average labor share as
47、 measure of lLabor share (total wages divided by GDP) in the U.S. is about 64%lEstimate to be 0.36Can now compute TFP as: 92slide 93Total Factor Productivity in the U.S.93slide 94Decomposing Growth RatesTaking logs of production function:The same applies to log differences:Log differences are approx
48、imately equal to percentage changes:94slide 95Growth Decomposition for the U.S.95slide 96Growth Decomposition for the Asian Tigers96slide 97Growth Accounting for Chinaslide 98Human Capital in China98slide 99Human Capital in China99slide 100InnovationNew GoodsPatentsTechnology in China100slide 101101
49、Management and ProductivityPatents 1996-2004Management ScoreNote: European firms only as uses the European Patent Office databaseslide 102102Policies to promote growthSaving RateHuman capital investmentEncouraging technological progressRight Institutionsslide 103103Growth empirics: Confronting the S
50、olow model with the factsSolow models steady state exhibits balanced growth - many variables grow at the same rate. Solow model predicts Y/L and K/L grow at same rate (g), so that K/Y should be constant. This is true in the real world. Solow model predicts real wage grows at same rate as Y/L, while
51、real rental price is constant. Also true in the real world. slide 104104ConvergenceSolow model predicts that, other things equal, “poor” countries (with lower Y/L and K/L ) should grow faster than “rich” ones.If true, then the income gap between rich & poor countries would shrink over time, and livi
52、ng standards “converge.” In real world, many poor countries do NOT grow faster than rich ones. Does this mean the Solow model fails? slide 105105ConvergenceNo, because “other things” arent equal. In samples of countries with similar savings & pop. growth rates, income gaps shrink about 2%/year.In la
53、rger samples, if one controls for differences in saving, population growth, and human capital, incomes converge by about 2%/year. slide 106106ConvergenceWhat the Solow model really predicts is conditional convergence - countries converge to their own steady states, which are determined by saving, population growth, and education. And this prediction comes true in the real world.
