Lecture 2: Intermediate macroeconomics, autumn Lars Calmfors

Transcription

1 Lecture 2: Intermediate macroeconomics, autumn 2008 Lars Calmfors

2 1 GDP per capita, percent of OECD average, PPP-adjusted Position 1970 Index Position 1980 Index 1 Switzerland USA USA Switzerland Luxembourg Canada Sweden 113 (105*) 4 Luxembourg Canada Iceland Denmark France France Norway Australia Sweden 107 (98*) 9 Netherlands Denmark New Zeeland Belgium Great Britain Australia Belgium Netherlands Germany Austria Italy Italy Austria Germany Norway Japan Japan Great Britain Finland Finland Iceland New Zeeland Spain Spain Ireland Greece Greece Ireland Portugal Portugal Mexico Mexico Turkey Turkey 27 * If Mexico and Turkey are excluded.

3 2 GDP per capita, percent of OECD average, PPP-adjusted Position 1990 Index Position 1998 Index 1 Luxembourg Luxembourg USA USA Switzerland Norway Canada Switzerland Japan Denmark Norway Iceland France Canada Iceland Belgium Denmark Japan Sweden 105 (94*) 10 Austria Belgium Netherlands Austria Australia Finland Germany Italy Ireland Australia France Germany Finland Netherlands Italy Great Britain Great Britain New Zeeland Sweden 96 (85*) 20 Spain New Zeeland Ireland Spain Portugal Portugal Greece Greece Mexico Mexico Turkey Turkey 30 * If Mexico and Turkey are excluded.

4 3 GDP per capita, US dollars, PPP-adjusted, percent of OECD average, ranking by country Luxembourg Norway United States Ireland Switzerland Canada Iceland Netherlands Austria Australia Denmark Sweden Belgium United Kingdom Finland Japan Germany France Euro area Spain Italy Greece New Zealand Korea Czech Republic Portugal Hungary Slovak Republic Poland Mexico Turkey 36 Source: OECD

5 4 Y F( K, L) MPL F( K, L + 1) F( K, L) MPL dy df( K, L) dl dl F L MPK F( K + 1, L) F( K, L) MPK dy df( K, L) dk dk F K First -order condition for maximum If y f( x, z) dy dx f x 0 dy dz f z 0 Profit maximisation π PY RK WL PF( K, L) RK WL dπ PFL W 0 F dl L dπ PFK R 0 F dk K W P R P

6 Figure 3-3: The production function 5

7 Figure 3-4: The marginal product of labour schedule 6

8 7 Production function Y F( K, L) Y AF( K, L) A total factor productivity It holds that: ΔY ΔA ΔK ΔL + α + (1 α) Y A K L α capital income share 1- α labour income share GDP growth total factor productivity growth + contribution from growth of the capital stock + contribution from growth of the labour force Growth accounting The Solow-residual: Δ A Y K L Δ α Δ (1 α) Δ A Y K L

9 Figure 3-5: The ration of labour income to total income in the US and the UK 8

10 9 Mathematics to derive growth equation in the case of Cobb- Douglas production function Logarithms nx is the natural logarithm of x. If x ea, then a n x. nxy nx+ ny nx/ y nx ny nx β β nx Rules of differentiation If y f( g) and g dy fggx dx gx ( ), i.e. if y f( gx ( )), then d( n x) 1 dx x Maximisation If y f( x, z), then the first-order conditions for a maximum are: dy dx dy dz f x f z 0 0

11 10 Another rule of differentiation If then dy dx y xz, zxz 1

12 11 Cobb-Douglas production function Y AF( K, L) AK L α 1 α K, L and Aand thus also Y are functions of time. Yt ( ) AtKt ( ) ( ) αlt ( ) 1 α Taking logarithms: ny( t) nat ( ) + nkt ( ) α + nlt ( ) 1 α ny( t) nat ( ) + α nkt () + (1 α) nlt () Differentiation w.r.t. time gives: d n Y() t d n A() t + α d n K() t + (1 α) d n L() t dt dt dt dt dy i 1 da i 1 + α dk i 1 + (1 α) dl i 1 dt Y dt A dt K dt L Call dy dt i, da i Y A, dk i K och dl i L dt dt dt i i i i Y A + α K + (1 α) L Y A K L α profit share 1- α wage share We thus have: ΔY ΔA ΔK ΔL + α + (1 α) Y A K L

13 12 Profit maximisation π PY RK WL PAKα L1 α RK WL dπ dk PAKα 1L1 α R α 0 dπ dl (1- α) PAKαL α W 0 α R RK RK PAKα 1L1 α PAKαL1 α PY 1 α W WL WL PAKαL α PAKαL1 α PY

14 13 Accounting for growth in labour productivity ΔY α ΔK + (1- α) ΔL + ΔA Y K L A GDP growth contribution from growth of capital stock + contribution from growth of labour + total factor productivity growth Labour productivity: Y/L Δ Y L Y L Δ Y Y Δ L L ΔY ΔL α ΔK + (1- α) ΔL + ΔA ΔL Y L K L A L ΔY L ( K L ) + Y Δ α L Δ K Δ L ΔA A Growth in labour productivity contribution from capital deepening + total factor productivity growth Capital deepening: Increase in capital intensity (capital relative to labour) Capital deepening can be decomposed into ICT capital deepening and non-ict capital deepening

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17 16 Annual growth of total factor productivity in OECD countries, Irland ( ) Finland ( ) Grekland ( ) Sverige ( ) USA Australien ( ) Storbritannien ( ) Portugal ( ) Frankrike Japan ( ) Tyskland Kanada Österrike ( ) Nya Zeeland ( ) Belgien ( ) Nederländerna ( ) Danmark ( ) Italien ( ) Spanien ( )

18 17 Explanations of high productivity growth in Sweden Large contributions from both ICT-producing and ICT-using sectors Encompassing deregulations of product and service markets - low level of regulation - early deregulations High educational level (complementarity between ICT technology and high-skilled labour) High R&D expenditures (Research and development) Creative destruction in the 1990s

19 18 Constant returns to scale Y F(K, L) zy zf(k, L) F(zK, zl) 10 % larger input of capital and labour raises output also by 10 %. z 1 L Y L F K L (, 1) Y L y output per capita K L k capital intensity (capital stock per capita) y F(, k 1) f() k Output per capita is a function of capital intensity y Y/ L Kα L1 α/ L KαL α ( K/ L) α kα y Y/ L AKα L1 α/ L AKαL α A( K/ L) α Akα

20 19 The Solow model (1) y c + i Goods market equilibrium (2) c (1-s) y Consumption function, s is the savings rate (3) y f(k) Production function (4) d δk Capital depreciation, δ is the rate of depreciation (5) k i δk Change in the capital stock Change in the capital stock Gross investment Depreciation y (1-s)y + i i sy Investment Saving i sf(k)

21 20 k i δk sf(k) δk In a steady state, the capital stock is unchanged from period to period, i.e. k 0 and thus: sf(k) δk Convergence of GDP per capita Countries with different initial GDP per capita will converge (if they have the same production function, the same savings rate and the same depreciation rate). The catch-up factor Strong empirical support for the hypothesis that GDP growth is higher the lower is initial GDP per capita

22 Figure 7-2: Output, consumption and investment 21

23 Figure 7-3: Depreciation 22

24 Figure 7-4: Investment, depreciation and the steady state 23

25 Figure 7-5: An increase in the saving rate 24

26 Figure 7-6: International evidence on investment rates and income per person 25

27 26 Golden rule of capital accumulation Which savings rate gives the highest per capita consumption in the steady state? y c + i c y i In a steady state, gross investment equals depreciation: i δk Hence: c f(k) - δk Consumption is maximised if the marginal product of capital equals the rate of depreciation, i.e. MPC δ Mathematical derivation Differentiate c function w.r.t. k: c/ k f δ 0 f k δ k

28 Figure 7-7: Steady-state consumption 27

29 Figure 7-8: The saving rate and the golden rule 28

30 Figure 7-9: Reducing saving when starting with more capital than in the golden rule steady state 29

31 Figure 7-10: Increasing saving when starting with less capital than in the golden rule steady state 30

32 31 A steady state with population growth n ΔL L population growth Δ k i δ k nk Change in capital intensity (k K/L) Gross investment Depreciation Reduction in capital intensity due to population growth In a steady state: Δ k i δ k nk 0, i.e. i ( δ + n) k 0

33 32 Derivation K capital stock, I gross investment, L population k K/ L capital stock per worker (capital intensity) i I/ L gross investment per worker Δ K I δ K ΔK K I K δ Use that: Δk ΔK ΔL and k K L Δ L L n Δk I δ k K n Hence: Δk I i L δ k L K n Δk i δ k k n Δk i δk nk i ( δ + n) k

34 Figure 7-11: Population growth in the Solow model 33

35 Figure 7-12: The impact of population growth 34

36 Figure 7-13: International evidence on population growth and income per person 35

37 36 A steady state with population growth Y F( K, L) ΔY α ΔK + (1 α) ΔL Y K L In a steady state, k K/L is constant. Because Δk ΔK ΔL k K L 0, We have ΔK K ΔL L n är ΔY α ΔK + (1 α) ΔL αn + (1 α) n n Y K L GDP growth Population growth

38 37 Golden rule with population growth c y i f(k) (δ + n)k Consumption per capita is maximised if MPC δ + n, i.e. if the marginal product of capital equals the sume of the depreciation rate and population growth Alternative formulation: The net marginal product of capital after depreciation (MPK δ) should equal population growth (n) Mathematical derivation Differentiation of c-function w.r.t k gives: c/ k f ( δ + n) 0 f k δ + n k

39 38 Labour-augmenting technical progress Y F( K, L i E) E labour efficiency L i E efficiency units of labour y Y F( K, 1) F( k, 1) f( k) LE LE k K LE Steady state L grows by n % per year E grows by g % per year Δk sf(k) (δ + n + g)k 0 Gross investment Depreciation + Reduction in capital intensity because of population growth + Reduction in capital intensity because of technological progress

40 Figure 8-1: Technological progress and the Solow growth model 39

41 40 Growth Y Kα ( LE) 1 α ΔY α ΔK + (1 α)( ΔL + ΔE ) Y K L E In a steady state K/LE is constant ( Δ L/ L + Δ E/ E) n + g Δ K/ K n + g. ΔY Y α( n + g) + (1 α)( n + g) n + g GDP growth population growth+ technological progress Δy ΔY ΔL n + g n g y Y L Growth in GDP per capita rate of technological progress

42 41 Table 8-1: Steady-State growth rates in the Solow model with technological progress Variable Capital per effective worker Output per effective worker Output per worker Total output Symbol k K/ (L E ) y Y/ (L E ) (Y/ L ) y E Y y E L Steady-state growth rate 0 0 g n + g

43 42 Golden rule with technological progress c f(k) - (δ + n + g)k Consumption per efficiency unit is maximised if MPK δ + n + g The marginal product of capital should equal the sum of depreciation, population growth and technological progress Alternative formulation: The net marginal product (MPK - δ) should equal GDP growth (n + g). Mathematical derivation Differentiation w.r.t. k: c/ k f ( δ + n+ g) 0 k f k δ + n +g Real world capital stocks are smaller than according to the golden rule. The current generation attaches a larger weight to its own welfare than according to the golden rule.

44 43 Comparison of UK capital stock with golden rule level MPK δ n + g n + g Capital stock is 2.5 times GDP K 2.5Y 2. Depreciation of capital is 10 percent of GDP δk 0.1Y 3. Capital income is 30 percent of GDP MPK K 0.3Y Divide (2) by (1): δk K δ 0.1Y 2.5Y 0.04 Divide (3) by (1) MPK K 0.3Y K 2.5Y MPK 0.12 MPK δ > n + g The capital stock is far below the golden-rule level!

45 44 Endogenous or exogenous growth In the Solow model growth is exogenously determined by population growth and technological progress Recent research has focused on the role of human capital A higher savings rate or investment in human capital do not change the rate of growth in the steady state The explanation is decreasing marginal return of capital (MPK is decreasing in K ) The AK-model Y AK ΔK sy - δk Assume A to be fixed! ΔY/Y ΔK/K ΔK/K sak/k δk/k sa - δ ΔY/Y sa - δ A higher savings rate s implies permanently higher growth Explanation: constant returns to scale for capital Complementarity between human and real capital

46 45 A two-sector growth model Business sector Education sector Y F[K, (1-u)EL] ΔE g(u)e ΔK sy - δk Production function in business sector Production function in education sector Capital accumulation u share of population in education ΔE/E g(u) A higher share of population, u, in education raises the growth rate permanently (cf AK-model here human capital) A higher savings rate, s, raises growth only temporarily as in the Solow model

47 46 Human capital in growth models 1. Broad-based accumulation of knowledge in the system of education 2. Generation of ideas and innovations in research-intensive R&D sector 3. Learning by doing at the work place Policy conclusions 1. Basic education incentives for efficiency in the education system incentives to choose and complete education 2. Put resources in top-quality R&D 3. Life-long learning in working life Technological externalities / knowledge spillovers

48 47 Role of institutions Quality of institutions determine the allocation of scarce resources Legal systems secure property rights - helping hand from government (Europe) - grabbing hand from government Acemoglu / Johnson /Robinson - European settlers in colonies preferred moderate climates (US, Canada, NZ) - European-style institutions - Earlier institutions strongly correlated with today s institutions