MACROECONOMICS I UPF

Transcription

1 MACROECONOMICS I UPF LECTURE SLIDES SET 2 Professor Anonio Ciccone UPF Macroeconomics I, Slide SET 2 Slide 1

2 5. SAVINGS, INVESTMENT AND THE CREDIT MARKET EQUILIBRIUM OR FROM THE RENTAL PRICE OF CAPITAL TO THE REAL INTEREST RATE 1. Invesmen and savings mee in he credi (also loan) marke Households may have a PREFERENCE o save for consumpion omorrow. This is capured by he following exremely simple SAVINGS FUNCTION: (E19) S () = sy () Households simply save a consan fracion s of heir oal income Y (his includes labor and capial income). Savings are deposied in banks ha use hem o make loans o firms. Firms use credi o buy NEW machines. INVESTMENT refers o he oal purchases of NEW MACHINES and ALSO TO THE VOLUME OF LOANS IN THE ECONOMY. Firms can herefore buy machines or insead ren hem. This will give rise o he ren-or-buy decision which deermines he real ineres rae. UPF Macroeconomics I, Slide SET 2 Slide 2

3 FIGURE 7 HOUSEHOLDS (aggregae labor endowmen L() plus propery righs in firms; preferences for consumpion oday and savings) CREDIT/LOAN MARKET (credi/loans for ineres) GOODS MARKET (consumpion and invesmen goods) LABOR MARKET FIRMS (echnology of producion; capial owned a he beginning of he period K())). RENTAL MARKET FOR CAPITAL GOODS UPF Macroeconomics I, Slide SET 2 Slide 3

4 How firms finance purchase of new machinery (1) Loans: firms ask banks for loans and banks make hese loans wih he savings of households (2) Reained earnings: firms ask heir owners wheher hey can reain some of heir earnings in order o fund purchases of new machinery (3) Issues of new shares: hey purchases new machines and issue propery iles o he machines (shares) direcly o households In he Solow environmen hese ways of financing machinery are all EQUIVALENT. We can herefore jus hink of firms financing he purchase of new machinery by asking banks for loans. UPF Macroeconomics I, Slide SET 2 Slide 4

5 2. The ren or buy decision 1. The user cos of capial definiion in discree ime Firm can demand credi/loans o purchase capial goods: - in principle, his gives hem an alernaive o he renal marke for capial - insead of rening he capial good nex year, for example, you could buy i on credi oday, use i for one year and hen sell i off. The cos of doing so is he USER COST OF CAPITAL User Cos One-year-Period = 1 + r( + 1) * p ( ) 1 p ( + 1) [ ] [ δ ] K K -higher real ineres rae and depreciaion rae increase user cos -high fuure price for capial goods relaive o curren price reduces user cos UPF Macroeconomics I, Slide SET 2 Slide 5

6 2. The user cos in one-secor growh models (which includes, among many, he Solow model) Assume ha consumpion goods and invesmen goods can be produced wih idenical echnologies. In his case, he price of he invesmen goods relaive o he capial good is always uniy. If invesmen goods were more expensive only invesmen goods would be produced by profi maximizing firms. And vice versa. (E21) User Cos One-year-Period [ 1 r ( 1) ] [ 1 δ ] = + + = r ( + 1) + δ UPF Macroeconomics I, Slide SET 2 Slide 6

7 3. The credi/loan marke equilibrium The CREDIT/LOAN MARKET is in equilibrium a ime when: SAVINGS()=INVESTMENT() S()=I() As we will see, he CREDIT/LOAN marke is brough ino equilibrium by adjusmens of he REAL INTEREST RATE. The ren or buy decision and he credi/loan marke equilibrium: -firms can eiher buy capial goods oday (inves) for fuure use, or go o he renal marke for capial in he nex period. R+ ( 1) -he cos of rening nex period is he cos of buying he invesmen goods use i and resell wha is lef is r ( + 1) + δ UPF Macroeconomics I, Slide SET 2 Slide 7

8 We will now show ha in a CREDIT MARKET EQUILIBRIUM where INVESTMENT=SAVINGS>0: (E22) R ( + 1) = r ( + 1) + δ PART 1 OF THE ARGUMENT: R ( + 1) < r ( + 1) + δ Can i be ha and ha, a he same ime he credi marke is in equilibrium? No: in his case no firm wans o inves and I<S. Given he expeced renal cos of capial, firms find i cheaper o ren some of his exising capial raher han inves in new one. Hence, he savings of HH are greaer han he invesmen (which is 0). This siuaion will be eliminaed by a fall in he real ineres rae. UPF Macroeconomics I, Slide SET 2 Slide 8

9 PART 2 OF THE ARGUMENT: R ( + 1) > r ( + 1) + δ Can i be ha credi marke is in equilibrium? and ha, a he same ime he No: in his case firms wan infinie invesmen because hey can earn a profi by buying capial oday and ren i ou omorrow. Hence, he desired invesmen by firms will be greaer han he desired savings by firms, I>S. Hence, for he credi marke o be in equilibrium firms mus be indifferen by buying oday and expecing o ren nex period R ( + 1) = r ( + 1) + δ UPF Macroeconomics I, Slide SET 2 Slide 9

10 Because he expeced renal price of capial nex period is equal o he expeced equilibrium MPK, see he saic equilibrium condiion, we obain: (E23) MPK( + 1) = r( + 1) + δ -in equilibrium firms inves o he poin where he MPK is equal o he real ineres rae plus depreciaion MPK( + 1) δ = r( + 1) - he equilibrium real ineres rae is equal o he ne MPK of he capial a sociey has accumulae up o ime UPF Macroeconomics I, Slide SET 2 Slide 10

11 3. Summarizing he credi marke equilibrium (E24) MPK() = r() + δ (E25) I () = S () The STATIC EQUILIBRIUM CONDITIONS, -in he LABOR MARKET and he RENTAL CAPITAL MARKET and -he CREDIT MARKET EQUILIBRIUM CONDITIONS DYNAMIC GENERAL EQUILIBRIUM UPF Macroeconomics I, Slide SET 2 Slide 11

12 4. The credi marke equilibrium and he link beween presen and fuure (or he capial accumulaion equaion in equilibrium) As far as he economics of he Solow model are concerned we are done! -We know how o deermine oupu a a given momen in ime given L and K; we also how o obain facor prices and he real ineres rae. - Now we know how o deermine omorrow s capial sock given oday s capial sock and employmen: Depreciaion (E26) K() K& () = I() δk() = S() δk() Ne Invesmen Gross Invesmen UPF Macroeconomics I, Slide SET 2 Slide 12

13 Making use of HH SAVINGS behavior in (E19) S()=sY() (E27) K& () = sy() δ K() Making use of he fac ha aggregae income=aggregae oupu: Y = F( K, AL) (E28) K& () = sf( K(), A() L()) δ K() his is he EQUILIBRIUM CAPITAL ACCUMULATION EQUATION UPF Macroeconomics I, Slide SET 2 Slide 13

14 6. THE DYNAMICS OF THE SOLOW MODEL 1. The dynamics of capial accumulaion To solve he Solow model compleely, we need o specify he evoluion over ime of some EXOGENOUS facors like EFFICIENCY A and LABOR SUPPLY L We will assume ha labor supply grows a (exogenous) rae n: (E29) L () = L(0) e n (E30) L &() = nl () (E31) L &() L () = n UPF Macroeconomics I, Slide SET 2 Slide 14

15 Similarly, we will assume ha exogenous efficiency A we will assume growh a (exogenous) rae a: (E32) A() = A(0) e a (E33) A& () = aa() (E34) A &() A () = a UPF Macroeconomics I, Slide SET 2 Slide 15

16 SUMMARIZING THE DYNAMIC EQUATIONS OF THE SOLOW MODEL (E35) K& = sf( K, AL ) δ K A& = aa (E36) L& = nl (E37) Following all 3 (so-called sae) variables separaely over ime is somewha cumbersome and inconvenien. And WE DO NOT HAVE TO, because as we have seen many hings depend on capial per efficiency worker, NOT separaely on K, L, and A. UPF Macroeconomics I, Slide SET 2 Slide 16

17 More convenien o focus on he change over ime of CAPITAL PER EFFICIENCY WORKER WHY? k% = K A L - deermines oupu per efficiency worker hrough he producion funcion in efficiency form Y y% ( ) = = f k% AL - geing o he quaniies we are ineresed in is simple (E38) y = y% A (E39) r + δ = f '( k% ) w (E40) f( k) k f '( k) A = % % % UPF Macroeconomics I, Slide SET 2 Slide 17

18 From TIME CHANGES OF K,L,A o TIME CHANGES in capial per efficiency worker k% K = AL K K K k% = L A AL AL A L 2 2 k% K K L K A = A L AL L AL A (E41) K k% k% n k% a = AL UPF Macroeconomics I, Slide SET 2 Slide 18

19 Using he equilibrium capial accumulaion equaion (E28): (E42) K sf( K, AL ) K k% δ = k% n k% a= k% n k % a AL AL (E43) sf( K, AL ) k% = k% δ kn % ka % AL (E44) k% = sf ( k% ) ( ) { δ + n+ a k% ACTUAL SAVINGS AND INVESTMENT BREAK-EVEN INVESTMENT UPF Macroeconomics I, Slide SET 2 Slide 19

20 This equaion gives us he change in k% as a funcion of he presen k% Therefore, given a saring poin k% (0), i allows o sudy he whole ime pah of k%. SO NOW WE ARE DONE WITH THE MECHANICAL DYNAMIC ASPECTS OF THE SOLOW MODEL TOO. Now is he ime o remember: Wha is i we wan o know abou? UPF Macroeconomics I, Slide SET 2 Slide 20

21 Wha we wan o know: INTERMEDIATE QUESTIONS - Will capial per efficiency worker INCREASE or FALL over ime? - Will capial per efficiency worker GROW FOREVER? - Will he GROWTH RATE of capial per efficiency worker INCREASE or DECREASE in ime? FINAL QUESTIONS - Wha does his imply for INCOME, WAGES, and INTEREST RATES. The quesions are mos easily approached graphically. UPF Macroeconomics I, Slide SET 2 Slide 21

22 FIGURE 8a Following capial per efficiency worker in ime: THE PRODUCTION FUNCTION y% ( ) = f k% 0 k %() UPF Macroeconomics I, Slide SET 2 Slide 22

23 FIGURE 8b Following capial per efficiency worker in ime: SAVINGS AND THEREFORE INVESTMENT y% ( ) = f k% sf ( k% ) 0 k %() UPF Macroeconomics I, Slide SET 2 Slide 23

24 FIGURE 8c Following capial per efficiency worker in ime: THE EFFECTIVE DEPRECIATION LINE ( n+ δ + a) k% sf ( k% ) 0 UPF Macroeconomics I, Slide SET 2 Slide 24 k %()

25 FIGURE 8d Following capial per efficiency worker in ime: CAPITAL GROWTH ( n+ δ + a) k% sf ( k% ) k % > 0 0 k%(0) UPF Macroeconomics I, Slide SET 2 Slide 25 k %()

26 FIGURE 8e Following capial per efficiency worker in ime: THE CAPITAL GROWTH ZONE ( n+ δ + a) k% sf ( k% ) 0 k% BGP UPF Macroeconomics I, Slide SET 2 Slide 26 k %()

27 FIGURE 8f Following capial per efficiency worker in ime: FALLING CAPITAL ZONE ( n+ δ + a) k% sf ( k% ) 0 k%(0) UPF Macroeconomics I, Slide SET 2 Slide 27 k %()

28 FIGURE 8g Following capial per efficiency worker in ime ( n+ δ + a) k% sf ( k% ) 0 k% BGP UPF Macroeconomics I, Slide SET 2 Slide 28 k %()

29 Some imporan erminology - BALANCED GROWTH PATH (also called STEADY STATE someimes) An equilibrium where all variables grow a consan raes (his growh rae can be 0) - GLOBALLY STABLE BGP A BGP is globally sable if he economy ends up in he BGP in he long run NO MATTER WHERE THE ECONOMY STARTS. - CONVERGENCE A somewha fuzzy concep. Many people seem o say ha here is convergence if he growh rae of income per capial decreases as he counry grows richer. UPF Macroeconomics I, Slide SET 2 Slide 29

30 The growh rae of capial per efficiency worker over ime (E45) k% = sf ( k% ) ( ) { δ + n+ a k% ACTUAL SAVINGS AND INVESTMENT BREAK-EVEN INVESTMENT (E46) k% f( k% ) = s ( δ + n+ a) k% k% { AVERAGE PRODUCT OF CAPITAL UPF Macroeconomics I, Slide SET 2 Slide 30

31 y %() y% ( ) = f k% MPK 0 k%(0) k %() UPF Macroeconomics I, Slide SET 2 Slide 31

32 y %() y% ( ) = f k% 0 k% (0) k %( ) k %( 2) 1 UPF Macroeconomics I, Slide SET 2 Slide 32 k %()

33 y %() y% ( ) = f k% APK= AVERAGE PRODUCT OF CAPITAL 0 k%(0) UPF Macroeconomics I, Slide SET 2 Slide 33 k %()

34 y %() y% ( ) = f k% APK 0 k%(0) UPF Macroeconomics I, Slide SET 2 Slide 34 k %()

35 The growh rae of capial per efficiency worker over ime (E46) k% f( k% ) = s ( δ + n+ a) k% k% { AVERAGE PRODUCT OF CAPITAL UPF Macroeconomics I, Slide SET 2 Slide 35

36 s f k% k% ( ) 0 k %() UPF Macroeconomics I, Slide SET 2 Slide 36

37 s f k% k% ( ) n + δ + a 0 UPF Macroeconomics I, Slide SET 2 Slide 37 k %()

38 s f k% k% ( ) k% k% n + δ + a 0 k%(0) UPF Macroeconomics I, Slide SET 2 Slide 38 k %()

39 s f k% k% ( ) k% k% n + δ + a 0 k%(0) k %( ) 1 UPF Macroeconomics I, Slide SET 2 Slide 39

40 s f k% k% ( ) k% k% n + δ + a 0 k% BGP k%(0) UPF Macroeconomics I, Slide SET 2 Slide 40

41 We have herefore shown he hree following resuls: - Resul 1: Over ime capial per efficiency worker ends o is balanced growh pah value, which we have denoed by k% BGP (as long as he iniial capial sock is sricly posiive) - hence, he economy will end up a he same level of capial per efficiency worker, no maer wha he iniial values for A,K,L - Resul 2: The closer capial per efficiency worker o is BGP value, he lower is growh rae -in he absence of SHOCKS o preferences or echnology, he GROWTH RATE of capial per efficiency workers is herefore falling over ime Resul 3: In he balanced growh pah, growh of capial per efficiency worker is ZERO UPF Macroeconomics I, Slide SET 2 Slide 41

42 k %() FIGURE 11 RESULT 1: over ime capial per efficiency worker ends o is balanced growh pah value k% BGP k%(0) 0 Time UPF Macroeconomics I, Slide SET 2 Slide 42

43 FIGURE 12 RESULT 2 and 3: he closer capial per efficiency worker o is BGP value, he lower is growh rae; in he long-run he growh rae is ZERO k %() k %() 0 Time UPF Macroeconomics I, Slide SET 2 Slide 43

44 2. From capial accumulaion o growh of oupu per worker The easies way o make he link is o assume he producion funcion akes he so-called Cobb-Douglas form α (E47) Y = ( K ) ( AL ) 1 where 0< α < 1 is he elasiciy of oupu wih respec o capial: α (E48) Y K K Y or = α Percenage increase in = α *Percenage increase in K Y UPF Macroeconomics I, Slide SET 2 Slide 44

45 The Cobb-Douglas producion funcion in efficiency uni form is (E49) Y A L K = AL α or (E50) y% = % k α 0< α < 1 hence is also he elasiciy of oupu per efficiency worker wih respec o capial per efficiency worker. UPF Macroeconomics I, Slide SET 2 Slide 45

46 Growh in oupu per worker - oupu per worker is oupu per efficiency worker imes efficiency y = A y% = Ak% α (E51) (E51) - differeniaing herefore yields ELASTICITY OF OUTPUT TO CAPITAL y } A y% k% = + = a{ + α y A y% EFFICIENCY k% { GROWTH CAPITAL PER EFFICIENCY GROWTH UPF Macroeconomics I, Slide SET 2 Slide 46

47 FIGURE 13 Evoluion of oupu per worker (on LN scale) ln y ( ) ln y*( ) = y A( ) BGP ln y ( ) ln y(0) 0 UPF Macroeconomics I, Slide SET 2 Slide 47 Time

48 FIGURE 14: growh of oupu per worker y() y() a 0 Time UPF Macroeconomics I, Slide SET 2 Slide 48

49 3. Real wage growh and changes in he real ineres rae Again, he easies case is o assume he producion funcion akes he so-called Cobb-Douglas form α ( ) ( ) 1 α K - he real wage is AL w = MPL = L α (E53) w α A ( K ) ( AL ) = (1 ) = (1 α) Y (E54) w = (1 α) = (1 α) y L w = (1 α) y α α ( K ) ( AL ) 1 w& = w y y& L α he real wage is simply A CONSTANT FRACTION of income per capia and real wage growh is EQUAL TO oupu per worker growh UPF Macroeconomics I, Slide SET 2 Slide 49

50 FIGURE 15a Evoluion of REAL WAGE (on LN scale) ln w*( ) = w A( ) BGP ln w ( ) ln w ( ) ln w(0) 0 UPF Macroeconomics I, Slide SET 2 Slide 50 Time

51 - he real ineres rae is he ne marginal produc of capial (E55) r = MPK δ = α ( K ) ( AL ) 1 L α hence α (E56) r ( K ) ( AL ) 1 1 α AL α 1 K = α δ = α δ r 1 k α % ( ) = α δ NEGATIVE NUMBER! he real ineres rae FALLS as capial per efficiency worker increases UPF Macroeconomics I, Slide SET 2 Slide 51

52 FIGURE 15b real ineres rae over ime r () r BGP 0 Time UPF Macroeconomics I, Slide SET 2 Slide 52

53 7. THE EFFECTS OF AN INCREASE IN SAVINGS ON INCOME 1. Growh in he long run (in he balanced growh pah) Afer having analyzed he DYNAMICS of growh for all momens in ime we will now focus on he long-run, i.e. he balanced growh pah - we already have shown ha (E57) k% y% = = 0 k% y% BGP BGP and herefore (E58) k k BGP y = = a = GROWTH LABOR-EFFICIENCY y BGP UPF Macroeconomics I, Slide SET 2 Slide 53

54 Resul: The long-run growh rae oupu per worker of a counry is deermined by he GROWTH RATE OF LABOR EFFICIENCY ONLY. -In paricular, he long-run growh rae of oupu per worker does NOT depend on he SAVINGS RATE a all. -This is because of DECREASING RETURNS TO CAPITAL IN PRODUCTION. Recall ha k% = sf ( k% ) ( δ + n+ a) k% (E59) { ACTUAL SAVINGS BREAK-EVEN AND INVESTMENT INVESTMENT f ''( k % ) < 0 Because of decreasing reurns o capial, SAVINGS per efficiency worker rises less han proporionally wih capial. Bu BREAK-EVEN INVESTMENT rises proporionally. So hey will be evenually equal NO MATTER wha he SAVINGS RATE may be. A ha poin growh in income per capia is equal o growh in labor-efficiency. UPF Macroeconomics I, Slide SET 2 Slide 54

55 2. Oupu per worker in he long run (in he balanced growh pah) The savings rae does, however, affec he LEVEL OF OUTPUT PER WORKER - having a simple expression for oupu per worker in he BGP is easies wih a Cobb-Douglas producion funcion - noe ha in he BGP: (E60) 0 = sf ( k% ) ( ) { δ + n+ a k% ACTUAL SAVINGS AND INVESTMENT BREAK-EVEN INVESTMENT (E61) k% k s y = % % f( k% ) = δ + n + a BGP BGP UPF Macroeconomics I, Slide SET 2 Slide 55

56 - he Cobb-Douglas producion funcion in inensive forms is y% k α which yields: (E62) k% k% α BGP s = δ + n + a solving for he BGP amoun of capial per efficiency worker: (E63) k% BGP s = δ + n+ a 1 1 α = % he amoun of capial per worker can be obained by muliplying by efficiency A (E64) k BGP, s = δ + n+ a 1 1 α A UPF Macroeconomics I, Slide SET 2 Slide 56

57 - subsiuing in he producion funcion yields oupu per efficiency worker and oupu per worker (E65) y% BGP s = δ + n+ a α 1 α (E66) y BGP, s = δ + n+ a α 1 α A kbgp, s = y δ + n + a BGP, UPF Macroeconomics I, Slide SET 2 Slide 57

58 Hence, if efficiency growh is consan in ime, as assumed, we ge ha income per capia growh in he BGP is consan in ime. We also ge ha he CAPITAL-OUTPUT (k/y) raio is consan in ime. A consan capial-oupu raio and seady growh of income per capia is ofen seen o describe he U.S. well, especially for a longer ime period. (Solow developed his model hinking of he U.S. economy.) UPF Macroeconomics I, Slide SET 2 Slide 58

59 JONES Slide1: US IN BGP? UPF Macroeconomics I, Slide SET 2 Slide 59

60 FIGURE 16 Effec of SAVINGS RATE on capial per efficiency worker HIGH ( ) s f k% ( n+ δ + a) k% LOW s f k% ( ) 0 LOW SAVINGS HIGH SAVINGS UPF Macroeconomics I, Slide SET 2 Slide 60 k% ()

61 FIGURE 17 Effec of SAVINGS RATE INCREASE on growh (saring from BGP) y() y() a 0 INCREASE IN SAVINGS RATE Time UPF Macroeconomics I, Slide SET 2 Slide 61

62 y () y () a 0 INCREASE IN SAVINGS RATE Time UPF Macroeconomics I, Slide SET 2 Slide 62

63 8. QUANTITATIVE IMPLICATIONS OF THE SOLOW MODEL 1. Effec of savings on long run income We have seen ha he effec of he savings rae on long run oupu per worker can be obained very easily when he producion funcion is Cobb-Douglas (E67) y BGP, s = δ + n+ a α 1 α A -- he PERCENTAGE INCREASE in long-run income ha comes from a ONE- PERCENT INCREASE in he savings rae is he (E68) α = 1 α y BGP, s y s BGP, UPF Macroeconomics I, Slide SET 2 Slide 63

64 - he greaer he elasiciy of oupu wih respec o capial, α he greaer he effec of savings on long run income -- HOW LARGE IS THIS ELASTICITY? I urns ou ha under he assumpion of he Solow model here is a simple way o esimae α Y K - he definiion of α is: α = = MPK K Y Y - equilibrium in he capial marke implies ha - hence r K + δ = MPK ( r + δ ) K α = = share of CAPITAL in income Y - consan reurns o scale implies ha all income is paid o capial or labor; herefore (E69) α = 1 share of LABOR in income UPF Macroeconomics I, Slide SET 2 Slide 64

65 - he LABOR INCOME SHARE in indusrialized counries is around 1/3: (E70) α 1 2/3 1/3 1 = = = 1 α 1 (1 2/3) 2/ hence, increasing he savings rae by 1% raises long-run income per capia by only 0.5% under he assumpions of he Solow model -- HOW MUCH CAN DIFFERENCES IN SAVINGS RATE OF CAPITAL EXPLAIN? (E71) y BGP, s = δ + n+ a α 1 α A UPF Macroeconomics I, Slide SET 2 Slide 65

66 - ake wo counries ha are idenical in everyhing bu SAVINGS/INVESTMENT raes -denoe heir savings raes by s1 and s2 respecively; wha is hen he difference in long-run incomes beween he wo counries? (E72) (E73) y y y y COUNTRY1, BGP COUNTRY 2, BGP COUNTRY1, BGP COUNTRY 2, BGP s1 = s2 α 1 α 1/ = = 9= raher small given he enormous differences in savings raes differences in savings raes alone canno explain enormous differences in income beween rich and poor counries UPF Macroeconomics I, Slide SET 2 Slide 66

67 2. Income per capia versus oupu per worker The Solow model is abou OUTPUT PER WORKER; how do we ge from here o OUTPUT PER CAPITA? As L=NUMBER OF WORKER, we ge (E74) Y WORKER Y = POPULATION POPULATION L his can be wrien furher as ((E75)) Y = POP WORKINGAGE POP LABORFORCE EMPLOYMENT Y POP WORKINGAGE POP LABORFORCE L UPF Macroeconomics I, Slide SET 2 Slide 67

68 hence (E76) INCOME or OUTPUT per CAPITA = DEMOGRAPHIC FACTOR X LABOR FORCE PARTICIPATION RATE X (1-UNEMPLOYMENT RATE) X OUTPUT PER WORKER Income or oupu per capia may herefore be low because of - LOW oupu per worker - HIGH unemploymen among hose who do paricipae - LOW paricipaion of he populaion in he labor marke - HIGH share of children and reired persons UPF Macroeconomics I, Slide SET 2 Slide 68

69 Wih informaion on OUTPUT PER HOUR WORKED, we can do even beer and decompose oupu per worker ino: (E80) Y HOURS Y = L WORKERS HOURS where Hours= oal hours worked in he economy Hours/Workers= hours worked per employed person UPF Macroeconomics I, Slide SET 2 Slide 69

70 The nex able, from Inernaional comparisons of labor produciviy and per capia income by van Ark and McGuckin, Monhly Labor Review, July 1999 illusraes he effec of he differen componens for he US, Japan, and he EU (all relaive o he OECD average) UPF Macroeconomics I, Slide SET 2 Slide 70

71 TABLE 1 US EU JAPAN OUTPUT PER HOUR OUTPUT PER WORKER OUTPUT PER PERSON IN LABOR FORCE OUTPUT PER WORKING-AGE PERSON (age 15-64) OUTPUT PER PERSON FIGURES ARE RELATIVE TO OECD AVERAGE, daa refer o Hence facors oher han oupu per hour play an imporan role in explaining differences in income per capia beween hese rich counries/regions. UPF Macroeconomics I, Slide SET 2 Slide 71

72 FIGURE 18 Bu he main explanaion for differences in INCOME PER CAPITA are differences in OUTPUT PER WORKER (counry or region relaive o US) 100 G a p in G D P p e r C a p ia d e c o m p o s e d in P a ric ip a io n Gap and Labour Produciviy Gap, W orld W es ern Europe Norh America Oceania Eas Europe/ Cenral Asia A sia Lain America Middle Eas Produciviy gap Africa Paricipaion gap UPF Macroeconomics I, Slide SET 2 Slide 72

73 9. EMPIRICAL APPLICATIONS 1. Growh accouning The aggregae producion funcion makes clear ha GROWTH in OUTPUT can be wrien in erms of GROWTH in INPUTS plus GROWTH OF EFFICIENCY (E81) α ( ) ( ) Y = K AL 1 α ( ) ( ) ( ) 1 α α 1 α = Y A K L EFFICIENCY OF ALL INPUTS ALL INPUTS The EFFICIENCY FACTOR muliplying all inpus is called TOTAL FACTOR PRODUCTIVITY (TFP) α (E82) Y = TFP ( K ) ( L ) 1 α UPF Macroeconomics I, Slide SET 2 Slide 73

74 (E83) ELASTICITY ELASTICITY OF OUTPUT OF OUTPUT TO CAPITAL TO LABOR Y } TFP K 678 L = + α + (1 α) Y TFP K { L { AGGREGATE CAPITAL GROWTH AGGREGATE LABOR GROWTH Re-arranging allows us o see how TFP growh can be esimaed: TFP Y K L (E84) = α + (1 α) TFP Y K L - OUTPUT (Y), CAPITAL (K), and EMPLOYMENT (L) are easy o esimae for many counries UPF Macroeconomics I, Slide SET 2 Slide 74

75 - bu o calculae TFP growh we ALSO need o know he ELASTICITY OF OUTPUT TO CAPITAL AND TO LABOR - we know ha, in equilibrium, he MARGINAL PRODUCT of a facor is equal o he PRICE OF THAT FACTOR and herefore (E85) Y K K α = = = K Y MPK Y CAPITAL SHARE OF INCOME (E86) 1 YL L α = = = LY MPL Y LABOR SHARE OF INCOME - daa on hese INCOME SHARE is available for many counries UPF Macroeconomics I, Slide SET 2 Slide 75

76 TFP growh and he SOLOW RESIDUAL We can herefore esimae TFP growh as TFP Y K L TFP Y K L (E87) = ( K_SHARE ) + ( L_SHARE) SOLOW RESIDUAL under CONSTANT RETURNS TO SCALE, K_SHARE+L_SHARE=1 and TFP Y L K L = TFP Y L K L (E88) ( 1 L _SHARE) GROWTH OF OUTPUT PER WORKER GROWTH OF CAPITAL PER WORKER UPF Macroeconomics I, Slide SET 2 Slide 76

77 TABLE 2 macroeconomic growh daa for 2 counries TECHNOLISTAN SAVISTAN AVERAGE ANNUAL GROWTH (OVER PERIOD) GDP 8% 8% CAPITAL STOCK 10% 12% EMPLOYMENT 4% 4% SHARE OF LABOR IN INCOME noe ha in boh counries oupu per worker was growing a 8%-4%=4% Suppose ha based on his figures you are asked o make bes possible forecas of LONG-RUN INCOME PER WORKER GROWTH in SAVISTAN relaive o TECHNOLISTAN UPF Macroeconomics I, Slide SET 2 Slide 77

78 TABLE 3 ANNUAL CONTRIBUTION OF ANNUAL GDP GROWTH CAPITAL STOCK EMPLOYMENT TFP TECHNOLISTAN 8% 5% 2% 1% SAVISTAN 8% 6% 2% 0% Wha implicaions for long-run growh does his TFP growh difference have according o he SOLOW MODEL? (E89) y A = y A COUNTRY, BGP COUNTRY, BGP UPF Macroeconomics I, Slide SET 2 Slide 78

79 (E90) TFP = ( A ) 1 α 123 EFFICIENCY OF ALL INPUTS (E91) TFP A = LABOR SHARE TFP A (E92) TFP TFP y = y LABOUR SHARE COUNTRY, BGP UPF Macroeconomics I, Slide SET 2 Slide 79

80 TABLE 4 LONG-RUN OUTPUT PER WORKER FORECAST ANNUAL CONTRIBUTION OF ANNUAL TFP GROWTH SHARE OF LABOR IN INCOME LONG-RUN OUTPUT PER WORKER FORECAST TECHNOLISTA N 1% 0.5 2% SAVISTAN 0% 0.5 0% - one would expec TECHNOLISTAN o grow faser because i has proven capable o improve efficiency (adop or inven beer echnologies) - SAVISTAN has been growing by brue force--hey were savings a lo and herefore accumulaing capial rapidly; he SOLOW model says ha his canno lead o growh in he long run because of decreasing reurns o capial UPF Macroeconomics I, Slide SET 2 Slide 80

81 1. Oupu and TFP growh of he Asian Tigers The Asian Tigers, Souh Korea, Taiwan, Hong Kong, and Singapore have had very rapid growh of OUTPUT and OUTPUT PER CAPITA Wha are he PROXIMATE CAUSES of ha?: - increases in labor force paricipaion - capial accumulaion - TFP IMPORTANT TO KNOW because increases in paricipaion and capial inensiy CANNOT FUEL GROWTH FOREVER. Alwyn Young has analyzed his issue in The Tyranny of Numbers: Confroning he Saisical Realiies of he Eas-Asian Growh Experience Quarerly Journal of Economics, 1995 UPF Macroeconomics I, Slide SET 2 Slide 81

82 Young esimaes: GDP per CAPITA GROWTH = GDP GROWTH POP GROWTH " N" in nex figures " D" in nex figures GDP per WORKER GROWTH = GDP GROWTH EMPLOYMENT GROWTH " N " in nex figures " D" in nex figures GROWTH ON INPUTS, OFTEN WEIGHTED BY QUALITY TFP GROWTH UPF Macroeconomics I, Slide SET 2 Slide 82

83 YOUNG SLIDE 1: growh of income and oupu all 4 counries UPF Macroeconomics I, Slide SET 2 Slide 83

84 YOUNG SLIDE 2: TFP growh HK UPF Macroeconomics I, Slide SET 2 Slide 84

85 YOUNG SLIDE 3: TFP growh SINGAPORE UPF Macroeconomics I, Slide SET 2 Slide 85

86 YOUNG SLIDE 4: TFP growh in oher counries UPF Macroeconomics I, Slide SET 2 Slide 86

87 2. US versus EU growh: when did he EU sop o cach up (and why)? The US has higher levels of oupu per worker han he EU, bu he EU has been CATCHING UP for mos over he pos World-War II period. This process of CATCHING-UP has sopped in he lae 1990s Has he EU sopped caching up because of: - TFP growh? - CAPITAL ACCUMULATION? Rober Gordon from Norhwesern Universiy and co-auhors have researched his in much deail; hey argue ha he process sopped because of boh TFP and capial growh and ha new INFORMATION and COMMUNICATION TECHNOLOGIES (ICT) played a role UPF Macroeconomics I, Slide SET 2 Slide 87

88 GORDON SLIDE 1 cach up of GDP per worker sops in 1998 UPF Macroeconomics I, Slide SET 2 Slide 88

89 GORDON SLIDE 2 cach up TFP also sops in 1998 UPF Macroeconomics I, Slide SET 2 Slide 89

90 GORDON SLIDE 3 cach up capial inensiy also sops in 1998 UPF Macroeconomics I, Slide SET 2 Slide 90

91 2. Produciviy level accouning I is also ineresing o ask how much of he difference in he LEVEL of OUTPUT PER WORKER (AVERAGE LABOR PRODUCTIVITY) are driven by: - CAPITAL (physical and human) - TFP This can be done working wih he Cobb-Douglas producion funcion α ( ) ( ) 1 α = or Y K AL Y L α K = TFP L implies ha we can esimae he level of TFP as TFP y = = k α Oupu per Worker a CAP SHARE a (Oupu per Worker a ) UPF Macroeconomics I, Slide SET 2 Slide 91

92 Labour Produciviy gaps (Oupu per hour, Marke economy 2001) 140 US UK GER FR UPF Macroeconomics I, Slide SET 2 Slide 92

93 Explanaions for labour produciviy gaps Capial per hour, marke economy US GER FR UK UPF Macroeconomics I, Slide SET 2 Slide 93

94 Table 5 For US, UK, FRANCE, and GERMANY we ge US FRANCE& GERMANY UK OUTPUT per HOUR BENCHMARK Minus 20% approximaely Minus 30-35% approximaely CAPITAL per HOUR BENCHMARK Similar o US Minus 30% approximaely UPF Macroeconomics I, Slide SET 2 Slide 94

95 Hence: US versus France & Germany - he produciviy gap beween US on one hand and France and Germany on he oher CANNOT be explained by PHYSICAL CAPITAL - bigges par of he gap is due o TFP UK - appears o be behind in TFP and PHYSICAL CAPITAL relaive o boh US and France and Germany UPF Macroeconomics I, Slide SET 2 Slide 95

96 3. Convergence 1. Definiion and mechanisms Convergence: - When poorer counries grow faser han rich counries. Mechanisms: - Higher average and marginal produciviy of capial in poor counries (he flip side of decreasing reurns o capial) - Technological convergence UPF Macroeconomics I, Slide SET 2 Slide 96

97 2. Was here convergence among oday s rich counries? Many of oday s rich counries have daa on oupu per person going back o he 19h cenury. This allows us o ask: Did hose ha sared poorer grow faser since he 19h cenury? For he period , his is he quesion asked by Baumol Produciviy, Convergence, and Welfare American Economic Review, 1986 UPF Macroeconomics I, Slide SET 2 Slide 97

98 Baumol Slide1: Convergence among ex-pos rich UPF Macroeconomics I, Slide SET 2 Slide 98

99 The figure suggess a clear paern of convergence among oday s rich counries. BUT here are problems wih his approach: Problem 1: The sample we have are only counries ha evenually became rich. Maybe here were some counries ha were as rich as, say, Finland, in he 19h cenury, bu hen did poorly. These counries would hen BREAK he paern of convergence of he figure. Wha counries would ha be? -Chile -Argenina -Porugal - DeLong considers a sample consising of he riches counries in he 19h cenury (no oday) and follows hem over he same ime period. DeLong Have Produciviy Levels Convergence? American Economic Review, UPF Macroeconomics I, Slide SET 2 Slide 99

100 UPF Macroeconomics I, Slide SET 2 Slide 100

101 Problem 2: Relaed o daa qualiy. If he daa for he 19h cenury is worse han ha of oday, we may conclude based on his daa ha here is convergence when in realiy here is none. Imagine: - In 1870: all counries really have income he same income, equal o y(1870) - In 1980: all counries have STILL he same income Now imagine ha he daa we have is wrong and underesimaes 1870 income for some counries and overesimaes i for ohers. I.e. here is measuremen error. Then we ge he following figure. UPF Macroeconomics I, Slide SET 2 Slide 101

102 Figure 19: Measuremen error and (ficiious) convergence y* Time UPF Macroeconomics I, Slide SET 2 Slide 102

103 DeLong argues ha if his measuremen problem is aken ino accoun han he paern of growh acually indicaes DIVERGENCE among rich counries in he 19h cenury. Probably no oo surprising because: - he forces of convergence are mos likely sronger in marke economies, i.e. economies wih economic freedom and proeced propery righs - many economies did no conform o his paern over long periods of ime because of communisms, expropriaory dicaorships ec. UPF Macroeconomics I, Slide SET 2 Slide 103

104 3. Convergence among regions We can also look a he paern of convergence across regions of one counry. The following wo figures are abou long-erm income convergence and oupu convergence across he STATES of he UNITED STATES. This quesion is analyzed in Barro and Sala-i-Marin Convergence Journal of Poliical Economy, UPF Macroeconomics I, Slide SET 2 Slide 104

105 UPF Macroeconomics I, Slide SET 2 Slide 105

106 UPF Macroeconomics I, Slide SET 2 Slide 106

107 Advanages and disadvanages of looking for convergence across regions Advanages: Regions in he same counry end o share he same poliical framework. Differences in income are herefore more likely o be driven by economics. Disadvanages: Income of a region is closely relaed o wha he region specializes in (agriculure?, gold mining?, car manufacuring?, financial services?) and o he process of migraion of ciy-formaion (urbanizaion). Growh heory has lile o say abou all ha. UPF Macroeconomics I, Slide SET 2 Slide 107

108 4. Convergence world-wide afer World War II Wha if we look a he relaion beween oupu growh and iniial oupu per worker for as broad a sample as possible in he pos WWII period? As has been documened by many economiss, we ge no indicaion of convergence. Rich counries may on average even have been growing faser han poor counries. UPF Macroeconomics I, Slide SET 2 Slide 108

109 UPF Macroeconomics I, Slide SET 2 Slide 109

110 Or for he period: UPF Macroeconomics I, Slide SET 2 Slide 110

111 I looks like poor counries have been falling behind in oupu per worker Bu does his prove he absence of he wo convergence mechanisms: - decreasing reurns o capial? - echnological convergence? No necessarily, because BAD ECONOMIC POLICIES in many poor counries have hindered growh. For example: no proecing even mos basic human and economic righs no invesing in criical facors like infrasrucure (roads, elecriciy ec.) and human capial (primary and secondary educaion) UPF Macroeconomics I, Slide SET 2 Slide 111

112 1. Cross-counry convergence in he Solow model CASE 1: -- poor counry: poor only because SCARCE CAPITAL: LOW K(0)/L(0) -- rich counry: rich only because ABUNDANT CAPITAL: HIGH K(0)/L(0) in all oher dimensions he wo counries are idenical (s,δ,n,a,a()) UPF Macroeconomics I, Slide SET 2 Slide 112

113 s f k% k% ( ) k% k% n + δ + a poor k rich k k% BGP % k () UPF Macroeconomics I, Slide SET 2 Slide 113

114 CASE 2: -- poor counry: poor because SCARCE CAPITAL and LOW SAVINGS RATE -- rich counry: rich because ABUNDANT CAPITAL and high SAVINGS RATE UPF Macroeconomics I, Slide SET 2 Slide 114

115 LOW s f k % k% k% k% ( ) ( ) s HIGH f k % k% n + δ + a poor k(0) k% BGP, poor rich k(0) k% BGP, rich % k () UPF Macroeconomics I, Slide SET 2 Slide 115

116 2. Condiional convergence The basic idea is ha here is CONDITIONAL CONVERGENCE if poorer counries would have grown faser han richer counries had hey adoped he same ECONOMIC POLICIES. UPF Macroeconomics I, Slide SET 2 Slide 116

117 How could we check in pracice? By running a regression. For example, esimae he parameers a, b, c below ln y ln y = counry,1960 counry, a * SchoolingInvesmen + b* PoliicalSabiliy counry counry + c*ln y counry,1960 GROWTH EXPLAINED BY POLICIES GROWTH EXPLAINED BY CONDITIONAL CONVERGENCE This is done in Barro Economic Growh in a Cross-Secion of Counries, Quarerly Journal of Economics UPF Macroeconomics I, Slide SET 2 Slide 117

118 Growh assuming same schooling and poliical sabiliy in all counries Income in 1960 UPF Macroeconomics I, Slide SET 2 Slide 118

119 Approach makes sense bu also has problems. Because ECONOMIC POLICIES are no exogenous and maybe a leas in par due o low iniial incomes. For example: - The approach says ha low growh in poor counries may be due o low invesmen in schooling. Bu maybe low invesmen in schooling is a consequence (no cause) of he povery of counries. - The approach says ha low growh in poor counries may be due o poliical insabiliy. Bu maybe poliical insabiliy is a consequence (no cause) of he povery of counries. -Ec. UPF Macroeconomics I, Slide SET 2 Slide 119

120 5. Forecasing growh of he BRICS 1. The who? - Brazil, Russia, India, and China - Large counries ha are sill quie poor bu have shown periods of rapid growh in recen imes - Could soon represen a huge par of world GDP, leading o imporan changes in inernaional poliics and economics (which is why Goldman Sachs is ineresed in forecasing heir fuure growh) UPF Macroeconomics I, Slide SET 2 Slide 120

121 2. Forecass Le us consider he Goldman-Sachs forecas of when oal GDP in hese counries will overake he GDP of Germany. UPF Macroeconomics I, Slide SET 2 Slide 121

122 UPF Macroeconomics I, Slide SET 2 Slide 122

123 UPF Macroeconomics I, Slide SET 2 Slide 123

124 As you know here are many hings ha mus analyzed o ge a forecas of oal GDP. Among hem: - working-age populaion and labor-force paricipaion - oupu per worker. UPF Macroeconomics I, Slide SET 2 Slide 124

125 UPF Macroeconomics I, Slide SET 2 Slide 125

126 UPF Macroeconomics I, Slide SET 2 Slide 126

127 Avoid ha by building in a process of convergence (or growh slowdown): ln a + b y counry, 1 counry, * X 0.02*ln counry, + ln y = y counry, This can be done by building he forecass of growh in hese counries around he Solow model. UPF Macroeconomics I, Slide SET 2 Slide 127

128 UPF Macroeconomics I, Slide SET 2 Slide 128

129 Can one check he reliabiliy of hese forecass? One approach is o do WITHIN SAMPLE FORECASTING. - Preend i is Use he approach used o forecas GDP of he BRICs o predic growh of counries Compare o he realized growh raes. UPF Macroeconomics I, Slide SET 2 Slide 129

130 UPF Macroeconomics I, Slide SET 2 Slide 130