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Growth and Development LECTURE SLIDES SET 2 Professor Antonio Ciccone Slide 1 5. SAVINGS, INVESTMENT AND THE CREDIT MARKET EQUILIBRIUM— OR FROM THE RENTAL PRICE OF CAPITAL TO THE REAL INTEREST RATE 5.1. Investment and savings meet in the credit (also loan) market •Households may not want to consume all their current income •Instead households may want to save some of their current income for future consumption This gives rise to a dynamic economy, as the future (future consumption) is linked to current economic behavior (savings) •In the Solow model this is captured by am extremely simple savings function (E19) S = Aggregate Savings = (savings rate)*(Aggregate Income)=s*Y • Households are assumed to deposit savings in banks • Banks use household savings to make loans to firms that buy investment goods Slide 2 FIGURE HOUSEHOLDS (aggregate labor endowment L(t) plus property rights in firms; preferences for consumption today and savings) CREDIT/LOAN MARKET (credit/loans for interest) GOODS MARKET (consumption and investment goods) LABOR MARKET FIRMS (technology of production; capital owned at the beginning of the period K(t))). RENTAL MARKET FOR CAPITAL GOODS Slide 3 How firms finance purchase of new machinery and how households save (1) Banks: firms ask banks for loans and household deposit savings in banks (2) Debt obligations: firms issue debt directly and households buy debt (3) Retained earnings (stock market): firms ask their owners whether they can retain some of their earnings in order to fund purchases of new machinery and household save by reinvesting their earnings (4) Issues of new shares (stock market): firms issue new shares and households save by buying shares In the Solow environment (and wider economic environments as explained in Modigliani-Miller theorem) these ways of financing machinery are all EQUIVALENT We can therefore just think of savings/financing occuring through bank loans only Slide 4 5.2. Neoclassical investment theory 5.2.1. The decision to buy investment goods: a one-step-at-a-time approach 5.2.2. The user cost of capital definition in discrete time 5.2.3. The user cost of capital in one-sector growth models 5.2.4. The user cost of capital and the desired future capital 5.2.5. The user cost of capital, investment, and the demand for credit/loans 5.2.6. Investment, the demand for credit/loans, and the real interest rate Slide 5 5.2.1. The decision to buy investment goods: a onestep-at-a-time approach Invest or not invest? •To decide whether to buy an investment good, you can compare the cost of the loan you need to buy this good to the future extra revenue generated by the good •To do that, you need to look into the future quite a bit, to forecast revenue A one-step-at-a-time approach •Instead you can look at it this way •Invest of next year’s extra revenue generated by an investment good exceeds the cost of 1)Get a loan, buy the investment good 2)Produce for a year 3)Sell the investment good, liquidate the loan The cost of (1)-(3) is called the user cost of capital Slide 6 One step at a time investment Extra revenue from producing with one more investment good for year On 1 January: - Get loan - Buy investment good On 31 December: - Pay off loan - Sell (used) investment good User cost of capital Invest if: USER COST OF CAPITAL <= EXTRA REVENUE Slide 7 5.2.2. The user cost of capital definition in discrete time The annualized cost of buying investment goods in terms of consumption goods is the user cost of capital User Cost One-year-Period t 1 r (t 1) * pK (t ) 1 pK (t 1) • • r is the real interest rate pK is the price of capital good relative to consumption goods higher real interest rate and depreciation rate increase user cost high future price for investment goods relative to current price reduces user cost Slide 8 5.2.3. The user cost in one-sector growth models (which includes, among many, the Solow model) •In one-sector models, consumption goods and investment goods are the same type of goods (or more generally can be produced with identical technologies) •Example: cars used both for consumption and for production •In this case, the price of the investment goods relative to the capital good is always unity •Follows from a law of one price in models with perfect competition: identical goods cost everybody the same. Therefore the relative price of investment relative to consumption goods is 1, pK=1. And User Cost One-year-Period t (E21) 1 r (t 1) 1 r (t 1) Slide 9 5.2.4. The user cost of capital and the desired future capital stock Consider a firm that faces a user cost of capital r+ How much does the firm want to invest for producing next year? Depends on extra revenue of investment goods In our model this extra revenue is given by the MPK next year This is because the MPK next year gives us how much more given workforce can produce if given one more unit of capital Slide 10 EXTRA REVENUE FROM INVESTMENT NEXT YEAR = MPK NEXT YEAR MPK(t+1) MPK NEXT YEAR = MPK(t+1) Extra revenue from one more investment good of a firm that has future capital stock K1 MPK1 0 K1 K(t+1) Slide 11 THE DESIRED (PROFIT MAXIMIZING) FUTURE CAPITAL STOCK MPK(t+1)=MARGINAL REVENUE FROM INVESTMENT r(t+1)+δ 0 K*(t+1) K(t+1) Slide 12 5.2.5. The user cost of capital, investment, and the demand for credit/loans MPK(t+1) r(t+1)+δ (1- δ )K(t) 0 K*(t+1) Investment demand K(t+1) = Demand for credit/loans ITFD Growth and Development Slide SET 2 Slide 13 5.2.6. Investment, the demand for credit/loans, and the real interest rate INVESTMENT DEMAND AS WELL AS DEMAND FOR CREDIT/LOANS r(t+1) 0 INVESTMENT, DEMAND FOR CREDIT/LOANS Slide 14 5.3. INVESTMENT AND THE CREDIT/LOAN MARKET EQUILIBRIUM INVESTMENT, DEMAND FOR CREDIT/LOANS r(t+1) SAVINGS, SUPPLY OF CREDIT/LOANS EQUILIBRIUM EQUILIBRIUM INTEREST RATE 0 INVESTMENT, SAVINGS S*=I* Slide 15 5.3.1. Summarizing the credit market equilibrium Investment to point where MPK equals user cost of capital (E24) (E25) MPK r I S Links equilibrium real interest rate to the agggregate capital stock Investment financed by credit/loans whose supply is given by savings Slide 16 Summarizing ALL equilibrium conditions at time t (E24) (E25) MPK (t ) r (t ) I (t ) S (t ) PLUS EQUILIBRIUM CONDITIONS, -in the LABOR MARKET MPL(t ) w(t ) - in RENTAL CAPITAL MARKET MPK (t ) R(t ) GENERAL EQUILIBRIUM AT TIME t Slide 17 5.3.2. The equilibrium capital accumulation equation -- We already knew how to determine output at a given moment in time given L and K -- Now we can also determine the future equilibrium capital stock Step 1) The capital accumulation equation (capital accounting not equilibrium) Depreciation (E26) K (t ) Net Investment K (t ) I (t ) K (t ) S (t ) K (t ) t Gross Investment Slide 18 Step 2) Equilibrium and savings behavior 1) Equilibrium: Investment=Savings (I=S) 2) Savings behavior: S=sY 3) Income=Output: Y=F(K,EL) Slide 19 Equilibrium capital accumulation equation (E27) K (t ) sY (t ) K (t ) Making use of the fact that aggregate income=aggregate output: Y F ( K , EL) (E28) K sF ( K , EL) K • This is the EQUILIBRIUM CAPITAL ACCUMULATION EQUATION • It links the future capital stock to current capital stock, labor force and technology, as well as savings and depreciation rates • This is the key dynamic equation of the Solow model Slide 20 6.1. THE DYNAMICS OF THE SOLOW MODEL 6.1.1. The three main state variables, exogenous (E,L) and endogenous (K) There are 3 variables in the Solow growth model that 1)Change over time 2) If one knows the value of these variables one can a) determine the static equilibrium (given model parameters like s, , a etc.) b) determine where the economy is going next (Such variables of a dynamic system are often called STATE VARIABLES) These variables are 1)Size of the labor force or aggregate labor supply (L) 2)Level of labor-augmenting technology (E) 3)Capital stock (K) Slide 21 • Of these 3 state variables, 2 change exogenously • These are labor force/supply L and technology E • Both are taken to grow at constant rates, called n and a Labor force L (aggregate labor supply) grows at growth rate n Labor augmenting technology E grows at growth rate a nt (E32) E (t ) E (0)eat (E30) L(t ) nL(t ) (E33) E (t ) aE (t ) (E31) L(t ) n L(t ) (E29) L(t ) L(0)e (E34) E (t ) a E (t ) Slide 22 The third state variable is the most interesting one, as it is endogenous Equilibrium capital accumulation equation (E35) Kt sF ( Kt , Et Lt ) Kt Slide 23 • Hard to believe, but now we are done with the ‘economics’ of the Solow model • Still some work required to get the ‘mechanics’ in a form so that we can analyze the economics in a insightful way • This involves identifying the key variables of the dynamic system (there turn out to be 3) • And simplify that dynamic system (turns out we can simplify to 1 state variable Slide 24 The 3 state variables together define a DYNAMIC SYSTEM •Given a point in space (K,L,E) •We know where the system goes next •And can therefore calculate all state variables going forward forever (E35) Kt sF ( Kt , Et Lt ) Kt (E36) Et aEt (E37) Lt nLt • But following all 3 (so-called state) variables separately over time is difficult • Solow was the first to realize that we can avoid this complication when we focus on capital per efficiency worker K/(EL) • Rather than looking separately on K, L, and E Slide 25 More convenient to focus on the change over time of CAPITAL PER EFFICIENCY WORKER Kt kt Et Lt WHY? determines output per efficiency worker through the production function in efficiency form Yt a yt Et Lt f kt kt getting to the quantities we are interested in is simple (E38) (E39) (E40) yt yt Et rt f '(kt ) a (kt )a 1 wt a (1 a ) f (kt ) (1 a ) kt Et Slide 26 6.1.3. The simple math of percentage changes Or if you know the growth rate of and the growth rate of variables x and of z, what is the growth rate of x*z and of x/z? Slide 27 Growth of a product of two variables and growth of a ratio of two variables Slide 28 From TIME CHANGES of K,L,E to TIME CHANGES in capital per efficiency worker k t Kt kt Kt Et Lt E L t t The growth rule for ratios as K/(EL) is K divided by EL k t K t Lt E t Lt Et kt Kt The growth rule for products as EL is E times L kt Kt (n a ) kt Kt Substitute n and a for growth rates of L and o E respectively Kt kt (n a )kt Et Lt Multiply both sides of equation by k_tilde=K/(EL) Slide 29 6.1.4. The equilibrium capital accumulation equation for capital per efficiency worker K/(LE) Slide 30 • Gives us the future change in • Therefore, given a starting point kt as a function of the present k (0) kt it allows to study the whole time path of • Mathematically, this is the simplest possible dynamic equation system: a one-dimensional differential equation • This is a dynamic equation that just moves along a line • Now we are done with the ‘mechanics’ of the dynamics • Time to recall what it is we want to know about? • And find a intuitive way to answering these questions Slide 31 kt 6.1.5. Key questions about the dynamics of economic growth and how to answer them ‘INTERMEDIATE’ QUESTIONS (about K/(EL)) •Will capital per efficiency worker INCREASE or FALL over time? •Will capital per efficiency worker GROW FOREVER? •Will the GROWTH RATE of capital per efficiency worker INCREASE or DECREASE in time? ‘FINAL’ OR ‘ULTIMATE’ QUESTIONS (about economic variables of interest) •- What does this imply for INCOME, WAGES, and INTEREST RATES? Slide 32 A graphical analysis of the implication of the equilibrium capital accumulation equation for K/(EL) Slide 33 6.1.6. A graphical analysis of the dynamics of economic growth: the ‘SOLOW A’ GRAPH y f k 0 k Slide 34 FIGURE Following capital per efficiency worker in time: SAVINGS AND THEREFORE INVESTMENT y f k sf k 0 k Slide 35 FIGURE Following capital per efficiency worker in time: THE EFFECTIVE DEPRECIATION LINE (n a )k sf k 0 k Slide 36 FIGURE Following capital per efficiency worker in time: CAPITAL PER EFFICIENCY WORKER GROWTH (n a )k sf k kt 0 0 k k (0) Slide 37 FIGURE Following capital per efficiency worker in time: THE CAPITAL GROWTH ZONE (n a )k sf k 0 k BGP k Slide 38 FIGURE Following capital per efficiency worker in time: FALLING CAPITAL ZONE (n a )k sf k 0 k BGP k (0) Slide 39 k FIGURE Following capital per efficiency worker in time (n a )k sf k 0 k BGP k Slide 40 Some useful terminology • BALANCED GROWTH PATH (BGP) also called STEADY STATE (SS) sometimes An equilibrium where all variables grow at constant rates (growth rate can be 0) • GLOBALLY STABLE BGP OR SS A BGP or SS is globally stable if the economy ends up in the BGP in the long run NO MATTER WHERE THE ECONOMY STARTS OUT (in terms of K,L,E). ‘History doesn’t matter’ in the long run • GLOBAL CONVERGENCE to BGP or SS If the BGP or SS is globally stable there is global convergence •ECONOMY STARTING BELOW/ABOVE THE BGP OR SS An economy starts below the BGP or SS if it has less capital per efficiency worker than it will have in the BGP/SS. It starts above the BGP or SS if it has higher capital per efficiency worker than in BGP/SS Slide 41 6.1.6. A graphical analysis of the dynamics of economic growth: the ‘SOLOW B’ GRAPH for the ANALYSIS OF GROWTH RATES Obtaining the growth rate of capital per efficiency worker over time: (E45) kt sf (kt ) ACTUAL SAVINGS AND INVESTMENT ( n a)kt BREAK-EVEN INVESTMENT (E46) f (kt ) kt s ( n a ) kt kt AVERAGE PRODUCT OF CAPITAL Slide 42 The ‘SOLOW B’ GRAPH FOR THE GROWTH RATE OF CAPITAL PER EFFICIENCY WORKER K/EL (E46) kt s kt f (kt ) kt ( n a ) AVERAGE PRODUCT OF CAPITAL Slide 43 f k s k 0 k Slide 44 f k s k n a 0 k Slide 45 f k s k kt kt 0 n a k (0) k Slide 46 f k s k kt kt 0 n a k (0) k (t1 ) k Slide 47 f k s k kt kt 0 n a k BGP k (0) Slide 48 k 6.1.7. Three main results Result 1: Over time capital per efficiency worker tends to a balanced growth path (BGP) or steady state (SS) value. The BGP/SS does not depend on the initial values of K,L,E (the BGP/SS does depend on model parameters like s,n, etc.) economy is globally stable (history doesn’t matter in the long run) Result 2: The closer capital per efficiency worker to its BGP value, the lower the growth rate of K/(EL) and therefore the growth rate of K (recall that E,L grow at constant rates) in the absence of changes to preference or technology parameters, the growth rate of capital (per efficiency worker) is therefore falling over time, as economy approaches its BGP/SS over time Result 3: In the BGP/SS, growth of capital per efficiency worker is zero. In economies starting below BGP/SS the growth of K/(EL) is positive. In economies starting above BGP/SS the growth of K/(EL) is negative Slide 49 6.2. From capital accumulation to growth of output per worker 6.2.1. More simple math of percentage changes with application to Cobb-Douglas production function Once we know the growth of K,E,L, and therefore the growth rate of K/(EL), we can determine the growth rate of Y,Y/L, and Y/(EL) using the production function a (E47) where 0 a 1 Yt Kt 1a Et Lt is the elasticity of output with respect to capital To do so, some more simple math of percentage changes is useful. Growth rule for variables raised to a power: Slide 50 For our Cobb-Douglas production function the growth rules imply 1) When the capital stock K grows but L and E are constant ALPHA tells us the percentage growth in Y when K grows by 1% This is called the ELASTICITY OF OUTPUT with respect to CAPITAL Slide 51 For our Cobb-Douglas production function the growth rules imply 2) When the labor force L grows but K and E are constant 1 MINUS ALPHA tells us the percentage growth in Y when L grows by 1% This is called the ELASTICITY OF OUTPUT with respect to LABOR Slide 52 For our Cobb-Douglas production function the growth rules imply 3) When the labor force L and capital both grow but E is constant Slide 53 6.2.2. The Cobb-Douglas production function in per worker form a (E49) (E50) Kt Yt Et Lt Et Lt yt Et yt Et kta Slide 54 Our growth rules therefore yield the following expression for output per worker growth yt Et yt Et kta (E51) yt E t yt a yt Et yt EFFICIENCY GROWTH Apply growth rule for products ELASTICITY OF OUTPUT TO CAPITAL kt kt a CAPITAL PER EFFICIENCY GROWTH Apply growth rule for variables raised to power Slide 55 FIGURE growth of output per worker for economy starting below BGP/SS y (t ) y (t ) a 0 Time t Slide 56 FIGURE Evolution of output per worker on LN scale (or ratio scale) for economy starting below BGP/SS BGP/SS output per worker ln y (t ) ln y (t ) ln y (0) 0 Slide 57 Time t 6.3. Real wage growth and changes in the real interest rate The real wage is determined by w=MPL a (E52) (E53) (E54) wt MPLt a wt (1 a ) Et Kt Kt 1a Et Lt Lt Et Lt a (1 a ) Kt a Et Lt 1a Lt Yt wt (1 a ) (1 a ) yt Lt product rule for growth rates wt yt wt yt The real wage is simply A CONSTANT FRACTION of income per capita and real wage growth is therefore EQUAL TO output per worker growth Slide 58 The real interest rate is determined by r+=MPK (E55) (E56) rt MPKt a 1 rt a Kt a Kt Et Lt rt a kt Et Lt Lt 1a a 1 1a a 1 Kt a E L t t NEGATIVE NUMBER! the real interest rate FALLS as capital per efficiency worker increases the real interest rate INCREASES as capital per efficiency worker falls Slide 59 FIGURE: real interest rate over time for economy starting below BGP/SS r (t ) rBGP 0 Time t Slide 60 7. THE EFFECTS OF AN INCREASE IN SAVINGS ON INCOME 7.1. Growth in the long run (in the balanced growth path) This was the dynamics of economic growth Now let’s see where the economy ends up in the long run But when does the long run start? It is when the economy has reached the BGP/SS The economy is in the BGP/SS when there is no longer growth per efficiency worker (E57) yt yt kt kt BGP 0 BGP This is the condition we need to work with to find out about the long run economics Slide 61 Key result about the determinants of long run growth of capital per worker and output per worker (the rate of economic growth of the economy once it has reached the BGP/SS) yt yt kt kt BGP 0 BGP Implies once we recognize that K/(EL)=(K/L)*E and that Y/(EL)=(Y/L)*E and apply the growth rule for products (E58) yt yt kt kt BGP a GROWTH LABOR-EFFICIENCY BGP Slide 62 Key result for long run economic growth: The long-run growth rate of output per worker of a country is determined by the GROWTH RATE OF LABOR EFFICIENCY ONLY This implies in particular that the long-run growth rate of output per worker does NOT depend on the SAVINGS RATE at all INTUITION: The result is driven by DECREASING RETURNS TO CAPITAL IN PRODUCTION. Recall that (E59) Because of decreasing returns to capital, SAVINGS per efficiency worker rises less than proportionally with capital. But BREAK-EVEN INVESTMENT rises proportionally. So they will be eventually equal NO MATTER what the SAVINGS RATE may be. At that point growth in income per capita is equal to growth in labor-efficiency. Slide 63 FIGURE: Effect of SAVINGS RATE on capital per efficiency worker (n a )k s HIGH f k s LOW f k 0 LOW SAVINGS BGP HIGH SAVING BGP Slide 64 k (t ) FIGURE: Effect of SAVINGS RATE INCREASE on output per worker growth starting from in a BGP y (t ) y (t ) a 0 Time t INCREASE IN SAVINGS RATE Slide 65 7.2. Output per worker in the long run (in the BGP/SS) The savings rate does, however, affect the LEVEL OF OUTPUT PER WORKER This came out in the previous slides as the growth rate of output per worker increased for a while when the savings rate increased To determine the effect of the savings rate on BGP/SS output per worker, we have to work with the equation that defines the BGP/SS 0 (E60) ( n a)kt sf (kt ) ACTUAL SAVINGS AND INVESTMENT BREAK-EVEN INVESTMENT An immediate implication of the equation is the that BGP/SS capital/output ratio is increasing in the savings rate (E61) kt yt BGP s na Slide 66 For the Cobb-Douglas production function we can work things out in more detail (E62) kt kta BGP s na Solving for the BGP amount of capital per efficiency worker yields (E63) k BGP 1 1a s n a Hence a higher savings rate implies a higher K/(EL) in the BGP/SS The amount of capital per worker can be obtained by multiplying by efficiency E (E64) kt , BGP 1 1a s n a Et Slide 67 Substituting in the production function yields output per efficiency worker and output per worker (E65) (E66) yBGP a 1a s n a yt , BGP a 1a s n a Et Hence a higher savings rate implies a higher Y/(EL) and Y/L in the BGP/SS Slide 68 8. QUANTITATIVE FEATURES OF THE SOLOW MODEL 8.1. Effect of savings on long run income We have seen that the effect of the savings rate on long run output per worker can be obtained very easily when the production function is Cobb-Douglas (E67) yt , BGP a 1a s n a Et Using the growth rule for variables raised to a power we therefore get (E68) Elasticity of long-run income level with respect to savings rate Slide 69 Quantitative effect of savings on long run income growth long-run output increase in savings rate growth savings rate alpha=0.33 alpha=0.66 elasticity=0.5 elasticity=2 15% to 16% 0.07 0.03 0.13 15% to 17% 0.13 0.07 0.27 15% to 18% 0.20 0.10 0.40 15% to 19% 0.27 0.13 0.53 15% to 20% 0.33 0.17 0.67 Slide 70 How large is a and therefore the ELASTICITY OF LONG-RUN OUTPUT WITH RESPECT TO THE SAVINGS RATE? a In the Solow model is the ELASTICITY OF OUTPUT WITH RESPECT TO THE CAPITAL STOCK. Formally Yt Kt Kt a MPKt Kt Yt Yt Equilibrium in the capital market implies that rt Hence MPK t (rt ) Kt a share of CAPITAL in income Yt Slide 71 In practice one usually doesn’t measure the capital income share directly Instead one measures the labor income share and uses the formula CAPITAL INCOME SHARE=1 minus LABOR INCOME SHARE We have seen that the CAPITAL SHARE IN INCOME in industrialized countries is around 1/3 (and labor share around 2/3). Hence (E70) a 1 2 / 3 1/ 3 1 1 a 1 (1 2 / 3) 2 / 3 2 Slide 72 NEXT QUESTION ABOUT SAVINGS RATES: How much of cross-country differences in output per worker can be explained by cross-country differences in savings/investment rates? Back to our equation for output per worker in BGP/SS (E71) yt , BGP a 1a s n a Et Take two countries, country1 and country2, that are identical in everything except their savings rates s1 and s2. What is the long-run output per worker difference? Slide 73 In this case we get that output of country1 relative to country1 in the BGP/SS is (E72) (E73) yCOUNTRY 1, BGP yCOUNTRY 2, BGP yCOUNTRY 1, BGP yCOUNTRY 2, BGP a s1 1a s2 1/ 2 0.27 0.03 93 Hence rather small output difference given the enormous differences in savings rates differences in savings rates alone cannot explain enormous differences in income between rich and poor countries Slide 74 8.2. The speed of convergence to the BGP/SS How quickly do economies close the gap to their BGP/SS? How quickly does the economic growth rate drop as the economy approach its BGP/SS? How quickly do transitional growth – driven by capital deepening – vanish as the economy approaches its BGP/SS? Slide 75 Closed form solution for Y/(EL) in Solow model with CobbDouglas technology 1,2 1 0,8 0,6 0,4 0,2 0 0 20 40 60 80 100 120 140 Jones 2010 Notes on closed form Solow Slide 76 160 When the economy starts with a level of output per efficiency worker that is PHI (f) times the BGP/SS level Output relative to BGP/SS only a function of relative initial condition and parameters l,a Slide 77 Convergence of BGP/SS and growth illustrated for alpha=0.33 Growth rates of output per worker over time (years) 0,1 0,09 Parameters 0.33 alpha (a) 0.02 a 0.03 delta () 0.02 n 0.5 phi (f) 0,08 0,07 0,06 0,05 0,04 Total growth 0,03 0,02 0,01 Transitional growth 0 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 Closes half the gap to BGP/SS after 12 years Slide 78 Convergence of BGP/SS and growth illustrated for alpha=0.66 Growth rates of output per worker over time (years) 0,1 0,09 Parameters 0.66 alpha (a) 0.02 a 0.03 delta () 0.02 n 0.5 phi (f) 0,08 0,07 0,06 0,05 0,04 Total growth 0,03 0,02 Transitional growth 0,01 0 0 20 40 60 80 100 Closes half the gap to BGP/SS after 33 years Slide 79 120 A slightly different perspective on the rate of convergence (the predicted future growth path) Parameters unknown 0.02 0.03 0.02 unknown alpha (a) a delta () n phi (f) We see a high initial growth rate of around 9%, for example (seen at the moment of ‚take off‘ in China, Taiwan, South Korea, and Singapore for example) Question: What is the path of future growth rates that we would predict based on the Solo model Answer: depends on the value for a Slide 80 Path of future growth based on the Solo model for different vales of alpha (a) 0,1 0,09 0,08 0,07 0,06 alpha=0.9 alpha=0.8 alpha=0.66 alpha=0.33 0,05 0,04 0,03 0,02 0,01 0 0 10 20 30 40 Slide 81 8.3. Income per capita versus output per worker The Solow model is about OUTPUT PER WORKER How do we get from there to OUTPUT PER CAPITA? As L=NUMBER OF WORKER, we get (E74) Y WORKER Y POPULATION POPULATION L This can be written further as (E75) Y POP WORKINGAGE POP LABORFORCE EMPLOYMENT Y POP WORKINGAGE POP LABORFORCE L Slide 82 INCOME or OUTPUT per CAPITA = DEMOGRAPHIC FACTOR X LABOR FORCE PARTICIPATION RATE X (1-UNEMPLOYMENT RATE) X OUTPUT PER WORKER Income or output per capita may therefore be low because of •LOW output per worker •HIGH unemployment among those who do participate •LOW participation of the population in the labor market •HIGH share of children and retired persons Slide 83 With information on OUTPUT PER HOUR WORKED, we can do even better and decompose output per worker into (E76) Y HOURS Y L WORKERS HOURS where •Hours= total hours worked in the economy •Hours/Workers= hours worked per employed person Slide 84 The role of demographics, labor force participation, unemployment, and productivity for income per capita in US, EU, and Japan relative to OECD US rel OECD EU rel OECD JAPAN rel OECD OUTPUT PER HOUR 120 103 82 OUTPUT PER WORKER 118 98 92 OUTPUT PER PERSON IN LABOR FORCE 121 94 96 OUTPUT PER WORKING-AGE PERSON (age 15-64) 130 90 102 OUTPUT PER PERSON 128 90 106 Data from “International comparisons of labor productivity and per capita income” by van Ark and McGuckin, Monthly Labor Review, July 1999 Hence factors other than output per hour play an important role in explaining differences in income per capita between these rich countries/regions Slide 85 FIGURE : Around the world the mai factor accounting for differences in INCOME PER CAPITA (vertical axis) are differences in OUTPUT PER WORKER (horizontal axis) From PWT8.1 Slide 86