SGPE Summer School: Macroeconomics Lecture 5

SGPE Summer School: Macroeconomics Lecture 5

Recap: The natural levels of production and interest rate Y n = C( Y,Y e,r, A) + I ( r,y e, K) where Y n = F(K, E(1- u n )L) Capital stock was taken as exogenous 2

Recap: The natural rate of interest for given K r ( n e,,, ) S Y Y r A r n e I r, Y, K S,I 3

Introduction Presentation Outline: Capital accumulation and growth Wage determination and unemployment Money and inflation in the long run 4

Growth (Chapter 5) Question: What factors determine the capital stock, production and the real interest rate in the very long run? Analysis of two cases: Constant population and technology Constant population growth and technical development We also examine income differences between countries 5

Growth: Given population & technology Optimal capital stock: but what determines the real interest rate? u'(c t ) u'(c t+1 ) / (1+ r) =1+ r t MPK 1+ m -d = r In a closed economy, long-run equilibrium, without growth in population or technology, consumption must be constant, so we must have r = r 6

Growth: Given population & technology Thus we have, in long-run equilibrium without growth in population or technology: MPK 1+ m -d = r Þ K * We call long-run equilibrium steady state (this term will be explained later) 7

Growth: Given population & technology 8

Growth: Given population & technology What happens if we start with K<K *? MPK is high so companies want to invest and the real interest is high: With high real interest, consumers want to consume less today than in the future; they save and accumulate assets (= capital in a closed economy) The capital stock grows until it reaches equilibrium As the equilibrium level is reached, MPK falls and growth returns to zero If we start out with K>K * the opposite occurs 9

Growth: Given population & technology We can also illustrate the adjustment in the diagram with savings and investment. In the long-run equilibrium (steady state) : S(Y *,Y *,r, A) = I(r,Y *,K) where Y * = F(K *,EN n ) If we start out with a lower capital K then investments are higher and income and savings are lower for a given real interest rate, so the real interest has to be higher 10

Growth: Given population & technology 11

Growth: Given population & technology What happens if the consumer starts to care more about the future (lower )? 12

Growth: Given population & technology What happens if the consumer starts to care more about the future (lower )? 13

Growth: Given population & technology Convergence Using CRS we can express the model in terms of capital and income per effective worker CRS means that We can choose F( zk, zen ) = zy z = 1 EN for any z Production function: Y EN = F æ ç K è EN,1 ö ø 14

Growth: Given population & technology Let y º Y EN, k º K EN Production function: and Production per effective worker depends only upon capital per effective worker, regardless of the size of the population. This is a consequence of CRS. Marginal product of capital: æ K ö f (k) = f ç è EN ø º F æ ç K è EN,1 ö ø y = f ( k) MPK = F K ( k,1) = f '( k) Condition for long-run equilibrium: f '(k * ) 1+ m -d = r 15

Growth: Given population & technology K* = k *EN Y* = f ( k *)EN 16

Growth: Given population & technology For given population and technology: The capital stock and production reach their long-run equilibrium levels over time In long-run equilibrium we have no growth If different countries have the same technology and same subjective discount rate, they will in the long run have the same real GDP per capita convergence! 17

Growth: Population growth and technical development With given population and technology there is growth only during the adjustment period if you start out from low capital stock. To explain growth in the very long run we have to have population growth and technical development. Assume that the population is growing and technology is improving at constant rates: r DE E = g 18

Growth: Population growth and technical development Let us guess that real interest is constant on the long-term growth path: r = r. The optimal capital stock per effective worker is determined by the same condition as before: f '(k * ) 1+ m -d = r 19

Growth: Population growth and technical development But what factors determine the real interest rate? To see this we assume a logarithmic utility function: u( C ) t = ln( C ) t u'(c t ) u'(c t+1 ) / (1+ r) =1+ r t r» r + g Þ Þ u' ( C ) t =1/ C t 1+ r t = ( 1+ r) C t+1 C t = ( 1+ r) ( 1+ g) Real interest is determined by the subjective discount rate ( r) and the pace of technological development (g). Consumers must be bribed not to consume more today. 20

Growth: Population growth and technical development In steady state: K EN = k * Þ K = k * EN Þ DK K = DE E + DN N = g + n Y EN = f k * ( ) Þ Y = f k * ( ) EN Þ DY Y = DE E + DN N = g + n K/EN and Y/EN are constant K and Y grow at the rate g+n K/N and Y/N grow at the rate g 21

Growth: The golden rule Does a larger capital stock always mean more consumption? Which capital stock maximises consumption in steady state? 22

Growth: The golden rule (golden rule capital stock) Investments in steady state where : I = DK +dk = DK K K +dk = ( n + g ) K +dk = ( n + g +d) K Consumption per effective worker: Y EN - I EN = f ( k ) - ( n + g +d)k DY Y = DK K = n + g To get the capital stock that maximises consumption, take the derivative with respect to k: f ' k ( ) = n + g +d 23

Growth: The golden rule (golden rule capital stock) f ' k ( ) = n + g +d Assume K=2Y and, for the sake of simplicity, f '( k) = MPK = ak a-1 N 1-a =a Ka N 1-a K n g 0 0.03 0.07 0.10 Marginal return on capital is higher than m = 0 =a Y K» 1 3 1 2» 0.17 n + g +d Conclusion: the capital stock is lower than the consumption-maximising capital stock Increased saving would increase consumption in the long run. The problem is that we are impatient... 24

Growth: The Solow model Central assumptions: Constant savings rate (s) (no optimising) Closed economy: Investments = savings: I = sf(k,en) 25

Growth: The Solow model Change in capital stock: DK = sf(k,en)-dk sf(k * ) = dk * steady-state sf(k) > dk Þ K grows sf(k) <dk Þ K falls 26

Why are some countries richer than others? GDP per capita in 2010 (PPP, 2005 constant prices, USD) USA 41 365 Sweden 36 132 China 7 130 India 3 477 Zimbabwe 319 27

Why are some countries richer than others? 28

Why are some countries richer than others? Our theory: convergence Two countries with the same E,a,m,u n and d should converge to the same income per capita in the long run If one of the countries is poorer, growth should be higher and over time the country should catch up with the richer country Obviously, this is not happening at least not very quickly. Income differentials are large and persistent 29

Why are some countries richer than others? Capital stocks What does capital do in the model? Contributes to the production of goods and services Is produced and increases through savings/investments Decreases through capital consumption Different kinds of capital are complements in production: Private capital: machinery, buildings Public capital: infrastructure such as roads, airports, telecommunication, schools, courts, admin, buildings Human capital: education, experience Differences in policies, taxes, corruption can lead to different capital stocks per worker 30

Why are some countries richer than others? Can differences in physical capital explain income differences? Y N = K a E 1-a N 1-a = K a E 1-a N -a = K a æ N N a E1-a = ç K è N Compare two counties: Y India / N India Y US / N US 0.08 1.00 = æ = K / N ö India India ç è K US / N US ø æ ç è 0.07 1.8 ö ø 1/3 æ ç è E India E US a ö ø æ ç è 2/3 E India E US Differences in physical capital explain only part of the differences in income ö ø 1-a æ = 0.34 ç è E India E US ö ø 2/3 ö ø a E 1-a 31

Why are some countries richer than others? 32

Why are some countries richer than others? Can differences in human capital explain income differences? Hard to measure One measure is the average number of years the adult population went to school To see how much it can explain we need to measure the effect on productivity of one more year of schooling Empirical estimates: Between 10 and 30% of the differences in income can be explained by differences in human capital 33

Why are some countries richer than others? 34

Why are some countries richer than others? 35

Why are some countries richer than others? Conclusion: At most 50 % of the income differences can be explained by differences in physical capital and schooling At least 50% of the differences in income must be explained by other factors than the differences in physical capital and schooling 36

Why are some countries richer than others? What other factors can explain differences in income? Inadequate access to technology different E Overpopulation, lack of natural resources? No! Inadequate institutions ( social infrastructure ) Corruption and lawlessness Lack of competition Poor public infrastructure Taxes and regulations Poorly functioning labour markets 37

Why are some countries richer than others? 38

Why are some countries richer than others? 39

Why are some countries richer than others? Does income per capita converge? Some convergence in Europe but no general convergence between rich and poor countries The growth funnel: in rich countries, GDP per capita grows by about 2 per cent per year some poorer countries catch up, others fall behind Geographical differences: many Asian countries have had rapid growth while many African countries have fallen behind 40

What determines technical development? In the long run it is technology that drives growth in GDP per capita We have treated E as exogenous our theory did not explain what determines technical development Endogenous growth theory tries to explain what drives technical development These models often contain an explicit sector for research and development 41

What determines technical development? Production function for knowledge DE = an n R E q where N R is the number of staff in R&D Assume N R = ln Þ g = DE E = a(ln)n E q-1 Growth depends on how many people work in R&D Growth depends on the amount of existing knowledge that influences the development of new knowledge: q <1: growth eventually slows down growth goes on forever q =1: g = DE E = a(ln )n We stand on the shoulders of giants 42