Human Capital in the Solow Model

Transcription

1 Week 4 57 Week 4 Human Capital in the Slw Mdel Distinctin between knwledge capital and human capital Latter is rival and embdied in wrker Frmer relates t nnrival ideas that all share (cstlessly) Mdel is mtivated by the dminant questin: Why are sme cuntries richer than thers? Slw mdel says differences in k Nt plausible (as Rmer shws late in Ch 1) Mankiw, Rmer, & Weil: differences in physical and human capital They argue this is plausible; thers disagree Differences in A Why wuld technlgy be different acrss cuntries? Barriers (legal and therwise) t adptin Nn-applicability f advanced technlgies in pr cuntries (climate, unreliable physical infrastructure, etc.) Differences in scial infrastructure We ll have mre t say abut this sn Hw t incrprate human capital int mdel? Many alternative ways; Rmer des ne (and thers in prblems 4.8 and 4.9) Hw des ecnmy prduce human capital? Prcess f educatin r training has tw majr csts: teachers time (fr which they are paid) and students time (fr which they are nt paid) Can use a tw-sectr mdel with a prductin functin fr educatin using labr (teachers) and capital (schls) like the ne fr knwledge in the R&D mdel Can just deduct sme amunt f a cnglmerate utput as being educatin in a ne-sectr mdel (like sme utput is physical capital rather than cnsumptin). This is Rmer s 4.8. Can mdel the prcess as hlding peple ut f the labr frce during an educatin perid. This is Rmer s Sectin 4.1. This desn t mdel the cst f teachers and schls. Nte that frgne earnings may be higher than teacher/schl csts at mst schls (if maybe nt at Reed)

2 58 Human Capital in the Slw Mdel Simple human-capital mdel setup Let H t LtGE wrkers Lt times the amunt f human capital per wrker GE be the amunt f human capital, which is the number f average educatin level f current wrkers. G E 0 E G E e is a cmmnly used functinal frm, where E is the We assume that in a steady state with educatin level E, peple live T years, ging t schl fr E years and wrking fr T E years. In general (but nt in this mdel), human capital includes nt just educatin but training, health and ther acquired characteristics that affect labr prductivity. 1 Y t K t A t H t K t sy t K t A t gat L t nlt Slving the mdel This mdel lks (and behaves) similarly t Slw mdel K K Define k AH ALG E k tsf ktn gkt s k 0 k k* n g 1 1 Hw will a change in E affect the steady-state grwth path? Effects f E (r G ) n K and Y are equivalent t increase in L Ecnmy mves t higher, parallel steady-state path Level effect, but n grwth effect Y and Y/L are higher in steady-state But the imprtant variable (living standards) here is Y/N, where N is ttal ppulatin * * Y t y * AtGE L t n the steady-state path N t N t Increase in E des nt affect y* r A(t) Increase in E raises G(E) Increase in E lwers L/N because mre peple are in schl and fewer in the labr frce What will be the net effect? What is L/N?

3 Grwth Accunting 59 It seems like it shuld be T E / T since that is the rati f wrking years t ttal life years fr each individual That is crrect if n = 0 If the ppulatin is grwing, then the chrt in educatin is larger than the chrt that is wrking. Rmer (and Cursebk) shws that in steady state ne nt Lt e e nt N t e 1 It is intuitively clear (and mathematically easy) that Dynamics f increase in E L/ N E 0 Initial effect lwers Y because fewer peple in labr frce but n immediate increase in the educatin f thse wh are wrking In steady state, the tw effects nted abve are in cnflict and we dn t knw which will dminate Y / N Y / N Y / N L/ N E E L/ N E The first term depends mstly n G E If G E and the secnd is negative. is large, then Y/N is likely t rise with an increase in E This makes intuitive sense: if educatin is highly prductive it will raise percapita incme; if it is nt, then it drains peple wh culd be wrking int useless educatin. Grwth Accunting Origins and framewrk Effrt first tried by Slw in late 1950s t decmpse grwth f GDP int cmpnents attributable t labr-frce grwth, capital-stck grwth, and grwth in ttal-factr prductivity. We have n direct data n prductivity, s it must be inferred as the part f GDP grwth that cannt be explained thrugh grwth in inputs. This is called the Slw residual. Cnsider Cbb-Duglas apprximatin t prductin functin with A brught utside f L term Y ne t the 1/(1 ) pwer t recncile with the usual Harrd-neutral frm 1 AK L (With Cbb-Duglas, we can just define this A t be the ld lny ln A ln K 1 ln L

4 60 Grwth Accunting Y K L A 1 Y K L A defines Slw residual A Y K L 1 A Y K L We can apprximate as capital s share f GDP We can estimate the grwth rates f GDP and f capital and labr input Nte the difficulty f measuring the capital stck Shuld labr-frce grwth be adjusted fr increase in human capital? (Prbably) Grwth accunting is the prcess f estimating all f these grwth factrs and calculating a Slw residual, which is unexplained increase in TFP. Examples f grwth accunting Denisn s table (Cursebk Ch 6, Table 1, p. 6-5) Emphasize general magnitudes f capital, labr, and TFP cntributins Dramatic decline in TFP grwth after 1973 Oil embarg and price increase Glbalizatin, rise f Japanese imprts and decline f US manufacturing Cmmn t ther Western cuntries (as we will see) Led t endgenus-grwth thery as ecnmists tried t explain the decline in TFP grwth Maddisn s table (Cursebk Ch 6, Table 2, p. 6-6) Differences and similarities acrss 6 advanced cuntries Pst-WWII Glden Age (cnvergence) Where did Japan s grwth cme frm? All except UK had large decline after Other cuntries (Cursebk Ch 6, Table 3, p. 6-7) Nte differences in TFP grwth acrss cuntries Peru and Venezuela vs. ther Latin American cuntries Singapre vs. ther Asian tigers Impact f infrmatin technlgy (Cursebk Ch 6, Table 4, p. 6-8) Slw quip: Cmputers are everywhere except in the prductivity statistics. Recvery in TFP grwth since 1995 fueled by IT Typical technlgical prgressin: Prductivity effects cme decades after the technlgy is first implemented S curve f adptin and prductivity effect

5 Crss-Cuntry Studies f Grwth and Incme Differences 61 Crss-Cuntry Studies f Grwth and Incme Differences Abslute vs. cnditinal cnvergence Slw and Ramsey mdels predict that (ceteris paribus) prer cuntries will grw faster than rich nes and that cuntries will same parameters will end up with same level f per-capita incme. Endgenus grwth mdels ften predict n cnvergence: gaps in per-capital incme will remain ver time even between cuntries with same parameters. g 0, t y 0 Abslute cnvergence: i i Cuntries that start with higher incme at 0 will grw mre slwly between 0 and t Pltting grwth against initial per-capita incme shuld yield dwnwardslping curve. Shw states, regins frm Barr & Sala-i-Martin (Cursebk, Ch 6, Figure 4, p and fllwing figures) Barr diagram fr all cuntries: p. 21/242 f JPE paper N evidence f cnvergence fr large, hetergeneus sample f cuntries Pritchett s evidence frm extraplating U.S. grwth (1.5%) backward t 1870 frm current level f per-capita incme fr pr cuntries: peple culd nt have survived at the implied levels f incme (<$100 per-capita GDP cmpared with $250 estimate fr current cst f sufficient calric intake t survive)

6 62 Crss-Cuntry Studies f Grwth and Incme Differences Cnditinal cnvergence: g 0, ty 0 X i i i Cuntries with different values f X variables will cnverge t higher r lwer grwth paths, s cnvergence is cnditinal n having the same X What variables shuld be in X? Table 7 f Cursebk Ch 6 (p. 35) summarizes Sala-i-Martin s evidence frm millins f regressins using a large pl f variables that thers have prpsed. Institutins as determinants f grwth Demcracy, rule f law, absence f crruptin, prices reflect scarcity, absence f war, revlutins, cups, and assassinatins, educated labr frce, etc. Abramvitz s scial capability r what thers have called scial infrastructure Des grwth wealth gd institutins r d gd institutins grwth? Acemglu et al.: Instrumental variable f clnial survival rates t examine causality Cuntries in which clnists survived in 1500 gt gd institutins and strng grwth Grwth culd nt have caused the gd institutins that far back Other interesting hyptheses: Ashraf & Galr: Genetic diversity encurages grwth Cmin, Easterly, & Gng: Strng intertempral persistence in technlgy adptin: 1000BC 0AD, 0AD 1500AD, and mst f

7 Crss-Cuntry Studies f Grwth and Incme Differences 63 the cuntries with mst advanced technlgy in 1500AD are richest tday.

8 64 Mney in Grwth Mdels Mney in Grwth Mdels Hw can we build a macr mdel withut mney? Classical dichtmy says that real side perates independently f mnetary frces: mney is a veil Hw wuld we add mney? Need a reasn t hld it Balancing cst f making transactins with less mney against frgne interest Definitin f mney Means f payment r medium f exchange M1 = narrw mney (checking accunts and currency) M2 = brader mney (savings accunts, small CDs, etc.) Supply f mney Central bank cntrls issue f mnetary base Rati f mney supply t mnetary base is mney multiplier that depends n public s prpensity t hld currency and banks prpensity t hld reserves Central bank cntrls B and thus attempts t cntrl M Demand fr mney Balancing benefits (cheaper transactins) against csts (frgne interest) d,, M P L Y i TC PY i TC Mnetary equilibrium in a grwth mdel Suppse that Y grws at n + g Central bank increases mney supply at rate s d M M P Y i TC In equilibrium: s d M M P Y i TC In steady state: P P g n Y n g Y i and TC are unchanging Sme evidence that = 1, s n g If grwth f mney supply exceeds grwth f mney demand, inflatin makes up the difference Steady-state prperties: 1 gn 1

9 Mney in Grwth Mdels 65 Nte that we assume that the real ecnmy affects mnetary cnditins (inflatin) but nt vice versa Change in interest rate? If r then (given ) i, s M d, M d < M s, P and W Similar kind f adjustment ccurs t raise r lwer prices and wages after change in Y r M s Nte that Y implies P, which means that prices are cuntercyclical in RBC framewrk Rles f price in ecnmy Mnetary rle: aggregate P balances M s and M d Resurce allcatin rle: relative prices signal scarcity This rle is masked in RBC because there is nly ne gd, but it is crucially imprtant in micrecnmics Can all prices adjust at nce? Our mdel suggests that it is a simple matter fr P t mve up r dwn In a wrld with perfect infrmatin and perfect crdinatin, all prices culd instantly adjust upward r dwnward In the real wrld, there is n such crdinatin Prices and wages may be sticky Sme may be stickier than thers This can lead t relative prices changes that alter resurce allcatin and cause inefficiency Keynesian mdels: stickiness f P and/r W Prices in different markets adjust at different speeds Stck market: very fast Gds market: much slwer Labr market: prbably very slw If P cannt establish M s = M d quickly, then ther variables are likely t respnd t this imbalance in the shrt run Fr example, a change the interest rate culd re-establish equilibrium between M s and M d immediately, whereas a change in P and W culd take mnths r years This is the essence f Keynesian mdel Mdeling strategy fr secnd half f curse: Start by examining behavir f ecnmy with fixed prices/wages Examine micrecnmic basis fr price/wage stickiness (Cnsider empirical evidence n stickiness)