Transcript Week 13
The Solow model Stylised facts of growth The Solow model Steady state and convergence The Solow model Until now, when output was changing, it was due to economic fluctuations in the IS-LM or AS-AD models. Long run growth, however, determines the capacity of the economy to produce goods and services, and ultimately welfare: 1913 : Argentina’s GDP is 70% larger than Spain’s. 2000 : Spain’s GDP is 50% larger than Argentina’s. 1945 : Ghana’s GDP is 60% larger than Korea ’s. 2000 : South Korea’s GDP is 100% larger than Ghana’s. 1970 : Italy’s GDP is 50% larger than Ireland’s. 2000 : Ireland’s GDP passes Italy’s GDP. What are the causes of economic growth? How can one maintain growth? The Solow model 5 Stylised facts The Solow model Convergence to the steady state Stylised fact 1 : Sudden acceleration of output 2500 2000 1500 1000 500 0 US Industrial production index (Source: NBER) Stylised fact 2 : Medium run fluctuations in growth 1200 CAN FRA GBR ITA JPN USA 1000 800 600 400 200 19 50 19 53 19 56 19 59 19 62 19 65 19 68 19 71 19 74 19 77 19 80 19 83 19 86 19 89 19 92 19 95 19 98 0 Real GDP per capita (1950 =100) Source: Penn Tables 6.1 Stylised fact 3 : Persistent lags and catch-up 30000 USA NOR IRL 20000 JPN AUT ITA ESP PRT FIN ISL BEL FRA DNK CAN AUS NLD CHE GBR NZL ISR 10000 MUS TTO ZAF THA BRA TUR PAN CRI COL PER SLV EGY GTM MAR PHL LKA BOL IND PAK HND NIC KEN UGA ETH NGA 0 2000 ARG URY MEX 0 GDP per capita 2000 40000 LUX 4000 VEN 6000 GDP per capita 1950 8000 10000 Stylised fact 3 : Persistent lags (USA=100) 100 90 Cameroon Ivory Coast Gabon Rwanda 80 70 60 50 40 30 20 10 0 Real GDP per capita Source: Penn Tables 6.1 Senegal Stylised fact 3 : Catch-up (USA=100) 100 90 China India Japan Singapore Thailand 80 70 60 50 40 30 20 10 19 50 19 52 19 54 19 56 19 58 19 60 19 62 19 64 19 66 19 68 19 70 19 72 19 74 19 76 19 78 19 80 19 82 19 84 19 86 19 88 19 90 19 92 19 94 19 96 19 98 20 00 0 Real GDP per capita (1950 =100) Source: Penn Tables 6.1 Stylised fact 4 : Increased inequality between countries 1,0 0,9 Inequality between countries Inequality within countries 0,8 0,7 0,6 0,5 0,4 0,3 0,2 0,1 0,0 1820 1850 1870 1890 1910 Source: Bourguignon & Morrison (2003) 1929 1950 1960 1970 1980 1992 Stylised fact 5 : Biased technical change The technological evolutions linked to growth seem to favour skilled labour, leading to a loss of jobs in traditional sectors This is called “skill-biased technical change”. This increases income inequality because it changes the structure of the demand for labour. Keeping labour supply unchanged this leads to either An increase in unemployment A fall in relative wage between skilled/unskilled labour This phenomenon is neither universal or permanent The post-war boom did not affect unskilled labour negatively 5 Stylised facts 1. World output has seen an abrupt acceleration over the long run. 2. GDP per capita and productivity can fluctuate significantly in the medium run. These fluctuations are not necessarily synchronised across countries. 3. Some countries have been able to catch up with the living standards of the richest countries, while other countries have stagnated relative to rich countries. 4. Inequalities have increased and shifted from inequalities within countries to inequalities between countries. This has slowed down since the 90’s, mainly because of the take-off of the Chinese and Indian economies. 5. Technical progress is biased as in increases income inequalities, either by reducing the wages of the unskilled labourers, either by increasing unemployment (i.e. By reducing their employability). The Solow model 5 Stylised facts The Solow model Convergence to the steady state The Solow model The Solow model is based on several simplifying assumptions Joan Robinson ironically referred to the lack of realism of these assumptions by referring to the “Kingdom of Solovia” A1 Factors of production are substitutes and not complements. A2 Savings generate investments, which is consistent with the neoclassical interpretation of the savings/investment balance. A3 The interest rate is perfectly flexible and instantaneously adjusts investment and savings. A4 Wages adjust so that the supply of labour (set exogenously by the growth rate of the population) and the demand for labour adjust perfectly The Solow model The macroeconomic production function Production is a function of capital K and L (with exogenous growth rate n ) It exhibits constant returns to scale Y F K , L Simplification : By dividing by the amount of labour L, one can express the variables “per capita”: Y K F ,1 L L Y y L y f k K k L The Solow model Output per worker y Output y = f(k) Decreasing marginal returns: each extra unit of capital per worker reduces the marginal productivity of capital 1 Capital per worker k The Solow model y Income is either spent or saved : Output y = f(k) y ci Output per worker Output per worker Consumption per worker Additionally, savings are equal to investment : c Investment i= s × f(k) y i s y y f k Therefore: i Capital per worker i s f k Investment per worker k The Solow model This tells us that given a production technology and a level of population, the level of output will depend only on the available stock of capital. This stock is determined by two flows: Investment : the capital stock increases when firms purchase new equipment . We have just seen how this is determined. Capital consumptions, which reduce the stock of capital available to workers. This is what we look at next. Investment Capital stock per worker Capital consumptions The Solow model Capital consumptions 1: Discounting Capital stock is reduced by depreciation. As the capital stock grows older, its value is discounted The amount of discounting is given by the discount rate δ. For example, if the expected life of a piece of equipment is 20 years, the discount rate is around 5%. This gives δ≃0,05. With a capital stock k, the size of the discount is equal to δk The Solow model Capital consumptions 2: Population growth In the long run, populations are not constant. This creates a second capital consumption, as one needs to provide capital to the new workers: Lets assume a fixed capital stock K : K k L If the population grows at a rate n, the expenditure required to keep the the capital stock per worker equal to k is equal to nk The Solow model Capital consumptions 3: Technical progress If new technologies are introduced, workers become more productive. Less labour is required to produce the same amount of output ⇒ Some workers become available for other uses Technical progress is therefore equivalent to an increase in the number of workers, in other words to population growth (we shall call this growth g). The net variation of the capital stock per worker is therefore given by the following equation : Δk = i – (δ+n+g)k The Solow model ( g n)k Capital consumption Capital consumption (δ+n+g)k Expenditure required to maintain this level of capital per worker Capital per worker k The Solow model 5 Stylised facts The Solow model Convergence to the steady state Convergence to the steady state Investment & consumption flows Capital consumptions (δ+n+g)×k (δ+n+g) ×k2 i2 (δ+n+g)×k*=i* Investment i = s×f(k) i1 (δ+n+g) × k1 k1 The capital stock increases as investment is higher than capital consumptions k* Steady-state level of capital per worker k2 Capital per worker (k) The capital stock falls as consumptions are higher than investment Convergence to the steady state Investment & consumption flows Capital consumptions (δ+n+g)k An increase in the savings ratio… s2×f(k) s1×f(k) …increases the steady-state capital stock k1* Initial steadystate k2* New steadystate Capital per worker (k) LUX 30000 USA 20000 IRL MAC GBR ATG BRB 10000 MUS ESP PRT SVN CZE K NOR CAN DNK AUS CHE HKG ISL JPN NLD SWE AUTFIN BEL GER FRAITA NZL ISR KOR GRC SVK ARG SYC URY HUN CHL MYS EST POL GAB HRVMEX BWA BLR ZAF LVA RUS LTU BRA KAZ VCT TUN TUR BLZ VEN THA PAN GRD GEO IRN LBNCRI LCA FJI BGR COL SWZ MKD DOM PRY DZA UKR M PER SLVGTM ROM EGY SYR JOR MAR JAM IDN GUY PHL CHNCPV ECU ALB KGZLKABOL GIN PNG ARM AZE INDPAK MDA GNQ CMR CIVTJK HNDKEN LSO COG COM SEN NIC NPL KHM MRT GHA GMB BEN UGA MOZ MLI TGO BFA BGD TCD MDG RWA YEM NGA NER MWI ZMB ETH BDI GNB TZA TTO 0 Income per capita in 1999 40000 Convergence to the steady state 0 10 20 Investment as a percentage of output (1960-1999) 30 ZWE 40 Convergence to the steady state Investment & consumption flows 2... Reduces the capital stock per worker… (δ+n2+g) ×k (δ+n1+g) ×k s×f(k) k2* 3. …And therefore reduces the steady-state capital stock. k1* k Capital per worker 1. A higher growth rate of the population… The Solow model predicts that countries with high demographic growth rates should have a lower level of per-capita income, ceteris paribus. Convergence to the steady state 30000 USA 20000 DNK IRL NOR CHE JPN NLD BEL FIN AUT FRA GBR ITA ISL CAN AUS NZL ESP ISR PRT 10000 MUS TTOARG URY 0 Income per capita 2000 40000 LUX 0 1 MEX BRA THAZAF TUR VEN PAN CRI COL PER SLV EGY GTM MAR PHL LKA IND BOL HND PAK NIC KEN ETHNGA UGA 2 Demographic growth rate (average annual growth rate) 3 Convergence to the steady state The concept of steady-state has three central implications : An economy at steady state no longer changes. An economy that isn’t at the steady-state will tends to move towards it. It therefore defines the long run equilibrium of the economy. However: the steady state depends on the savings ratio, therefore there is space for an economic growth policy. Convergence to the steady state Output, investment, and consumption flows Capital consumption (δ+n+g)k The savings ratio and the golden rule Production y = f(k) Investment i2= s2 × f(k) c2 Investment i1= s1 × f(k) c1 i2 i1 Capital stock per worker k Which of the 2 steady states is socially preferable ? Convergence to the steady state Output, investment, and consumption flows Capital consumption (δ+n+g)k The savings ratio and the golden rule Production y = f(k) c1 Investment i1= s1 × f(k) Investment i2= s2 × f(k) c2 i1 i2 Capital stock per worker k Which of the 2 steady states is socially preferable ? Convergence to the steady state Output, investment, and consumption flows Capital consumption (δ+n+g)k The savings ratio and the golden rule Production y = f(k) The optimal steadystate maximises consumption Investment i*= s* × f(k*) c* This occurs when the slope of the production function is equal to the slope of the capital consumption function y n g k i* pmk n g Capital stock per worker k Convergence to the steady state Transition to the golden rule steady-state Starting off with too much Capital Production (y) Consumption (c) Investment (i) t0 Fall in the savings ratio t Convergence to the steady state Transition to the golden rule steady-state Starting off with too little Capital Production (y) Consumption (c) Transition crisis, which requires political intervention and arbitrage Investment (i) t0 Increase in the savings ratio t