Technology and the Solow Model

Transcription

1 Technology and the Solow Model Extra credt assgnment You have the opton to make an n-class presentaton 15 mnutes, wll answer questons Some papers cover topcs that go (slghtly) beyond ths course. Counts for a 7 pont (%) bonus. Presentatons f any wll begn n 3-4 weeks Papers are allocated on an FCFS bass. 1

2 Dscusson questons from last lecture What does the basc Solow Model say about Ad for Afrca? What modfcaton do you need to make to alter ths concluson? Suppose we relax Inada condton 1: F(0,L)>0. How does that affect the steady states? Overvew: Introducng Technologcal Growth Prevously, we saw that ncreasng savngs rate does not lead to long-run growth. There s only transtonal growth. In ths lecture, we wll add TFP growth whch wll generate long-run growth. But before we do that: Queston: Is t possble that the transton s very very long, so that the past 200 years countres have been gong through one long transton wthout any technologcal progress? If the answer s yes, Solow model could be an nterestng model of growth (and vce versa f no). 2

3 Can Transtonal Dynamcs Be Important for Long Run? In prncple, one can choose s, n, d, and especally α to make the transton last as long as 400 years! Solow Dagram for dfferent Alfa values 3

4 Solow Dagram for dfferent Alfa values Can Transtonal Dynamcs Be Important for Long Run? In prncple, one can choose s, n, d, and especally α to make the transton last as long as 400 years! Although ths seems lke an explanaton, t fals mserably n an mportant respect: If TFP dd not grow, then all the growth s due to captal accumulaton. For ncome per-capta to grow by 4 fold (beng very conservatve), captal-labor rato must have grown by: y k k y k k a / a = = 4 Þ = 4» takng a=0.3 a What s wrong wth ths? 4

5 Can Transtonal Dynamcs Be Important for Long Run? Captal s dffcult to measure (for several reasons), so t s dffcult to mmedately reject that t could have gone up by 100 fold. But, there s another mplcaton: a a a 1850 ( d) ( ) R ak (1- a ) 1 =»( ) = R k + 1-d 25 So, f the nterest rate s 5 percent n 2005, t must have been 5 x 25 = 125% n 1850! Strongly contradcts Kaldor fact #1 Therefore, we do need TFP growth to make sense of the data Introducng TFP Growth Recall that TFP s a catch-all term that ncludes not only the technology level, but also the mpact of regulatons, fscal polcy, commodty prces, etc. on producton. a The producton functon s: ( ) 1 - Y = F( K, AL) = K AL a Assume that A grows at a constant rate: A = A 0 e gt A A = g Output per-person s: y= k a A Captal accumulaton mples: 1 -a. K = s Y K K d Dfferentate y: y ( ) A y = α k k + 1 α A (2.9) 5

6 Balanced Growth Notce that K wll grow at a constant rate only f Y/K s. constant: K Y = s -d K K But moreover, f Y/K s constant, so s y/k, so y and k wll be growng at the same rate. Balanced Growth Path (BGP): s a stuaton where y, k, c, (and n) all grow at a constant rate. Use g X to denote the growth rate of varable x. Along BGP, gy = gk. Substtute nto (2.9): gy = gk = g All varables grow at the same rate as TFP! Solow Dagram wth TFP Growth Now varables wll grow forever as long as TFP grows forever. We need to modfy the notaton to account for ths. Defne the captal-technology rato: k K / AL Notce that captal-labor rato (K/L) s not constant over tme. It grows at the same rate as TFP Rewrte the per-person producton functon: y = k α Usng the same dervaton as before, we get:. k = s y n + g + d ( ) k 6

7 Fg. 2.9 Solvng for the Balanced Growth Path (BGP) As we dd for a steady state, a BGP s obtaned by settng the growth rate of the captal-technology rato to zero:. k = sk α 1 ( n + g + d) = 0 1/ k ( 1 α ) s * = n + g + d α /( 1 α ) s and y * = n + g + d Notng that y = y / A we can solve for output per worker a/1 along the BGP: ( -a) * æ s ö y ( t) = A( t) ç èn+ g+ d ø So, accordng to Solow s model, only TFP growth s the engne of economc growth n the long-run 7

8 Increase n Investment Rate and Growth Suppose the economy s growng along the BGP. A new polcy (e.g., elmnatng dvdend taxaton) ncreases nvestment rate permanently. What s the mpact on growth n the shortrun and n the long-run? 8

9 9

10 Level versus Growth Rate Effects If a comparatve statc exercse results n a permanent shft n the level of output, we call ths a level effect. If t permanently ncreases the growth rate, we call ths a growth rate effect. Whch one s more mportant (or better)? It generally depends: do you prefer your ncome to double tomorrow or ts growth rate to change by 0.1%? Among other thngs t also depends on tme preference or patence. But growth rate effects compound over tme and can potentally have huge effects n the long-run, so the dstncton between the two types of effects should be kept n mnd GROWTH ACCOUNTING 10

11 Growth Accountng Use the same dentty we derved before. Defne 1 For total output: B= A -a Y Y = B B +α K K + 1 α L For output per person: y y = B B +α k k Both versons wll come n handy dependng on the queston we have n mnd ( ) L FIGURE 4-11a Contrbuton to total output growth

12 FIGURE 4-11b Growth accountng FIGURE 4-11c Growth accountng

13 FIGURE 4-12 Growth accountng n emergng markets, Growth Accountng for the Unted States Output Labor Captal TFP 60 s 70 s 80 s 90 s 4.1% % % % For labor and captal contrbutons to growth n output multply by shares Global Busness Envronment 26 13

14 In The News Whte House Struggles to Halt Flap Over Jobs Report (Reuters, Feb 19 th, 2004) The Whte House on Thursday struggled anew to contan the fallout over an overly optmstc forecast that 2.6 mllon jobs wll be created ths year and some Republcans expressed concern about the damage beng done to Presdent Bush We are eager for some reassurance that your economc projectons and estmates are based n realty, not poltcal fcton, sad the letter, sgned by House Democratc leader Nancy Pelos and others. Global Busness Envronment 27 The Presdent s Forecast 28 14

15 Mankw s calculaton: He s usng the growth accountng formula: g = g + ag + 1 -a g ( ) Y A K L Plugs n: (a) 2.1% for TFP growth (long-run average), (b) 1.8% for K growth (long-run average): a g K = = 0.6% Forecasts 3.7% growth n next 5 years, based on past trend growth. Leaves: 3.7%-2.1%-0.6% = 1% to be explaned by employment growth: 1- a g = 1% Þ g = 1.5% = 2.6 mllon jobs ( ) Hs logc: Untl now, we ve seen bg ncreases n TFP, slow ncreases n employment. Snce macro varables revert to ther long-run trends (.e., Balanced growth ), we should see lower TFP growth and faster employment growth n the future. L L 15