Essays on Macroeconomic Growth: The Role of Human Capital. Aditi Mitra. A dissertation. submitted in partial fulfillment of the

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1 Essays on Macroeconomc Growh: The Role of Human Capal Ad Mra A dsseraon submed n paral fulfllmen of he requremens for he degree of Docor of Phlosophy Unversy of Washngon 2012 Readng Commee: Sephen J. Turnovsky, Char Phlp L. Brock Yu-chn Chen Program Auhorzed o Offer Degree: Economcs

2 Unversy of Washngon Absrac Ths paper analyzes he effecs of echnologcal change on growh and nequaly n a wo-secor endogenous growh model. The frs wo chapers consder wo varaons of he me pah of he shock dscree and gradual. We fnd ha he effecs on nequaly depend upon: () wheher he underlyng source of nequaly sems from dfferenal nal endowmens of human capal or physcal capal, () he me horzon over whch he producvy ncrease occurs. Our resuls sugges ha an ncrease n he growh rae resulng from producvy enhancemen n he human capal secor wll ncrease nequaly. Producvy enhancemen n he fnal oupu secor, hough does no have permanen growh effecs, wll reduce nequaly. In eher case he responses of nequaly ncrease, he more gradually he producvy ncrease akes place. In he hrd chaper, we sudy hs radeoff n he conex of fscal polcy. Where-as a subsdy o he human capal secor unambguously ncreases growh and reduces nequaly, he magnude of he radeoff depends on wheher hs subsdy s fnanced by axes on ncome from physcal capal, or from human capal. We fnd ha, n general, a ax on human capal s preferable o one on physcal capal, snce generaes a more favorable radeoff. Once agan, he resuls evenually depend on he nal source of heerogeney. The model can generae a posve or negave relaonshp beween nequaly and growh, dependng upon he relave sze of hese effecs, conssen wh he dverse emprcal evdence. Essays on Macroeconomc Growh: The Role of Human Capal Ad Mra Char of he Supervsory Commee: Professor Sephen J. Turnovsky Deparmen of Economcs

3 TABLE OF CONTENTS Ls of Fgures.. Ls of Tables... v Chaper I: Growh Inequaly Trade-off n he Presence of Insananeous Shocks Inroducon Analycal Framework Evoluon of Wealh, Income and Welfare Inequaly Wealh Inequaly Income Inequaly Welfare Inequaly Numercal Smulaons Analyss of Resuls Insananeous Shock o he Oupu Secor Insananeous Shock o he Human Capal Secor Concluson Chaper II: Effec of he Tme Pah on he Growh Inequaly Trade-off Inroducon Analycal Framework Evoluon of Wealh, Income and Welfare Inequaly Wealh Inequaly Income Inequaly Welfare Inequaly. 48

4 4. Numercal Smulaons Analyss of Resuls Gradual Shock o he Oupu Secor Gradual Shock o he Human Capal Secor Concluson Chaper III: Fscal Polcy and he Growh Inequaly Trade-off Inroducon Analycal Framework Evoluon of Wealh, Income and Welfare Inequaly Wealh Inequaly Income Inequaly Welfare Inequaly Numercal Smulaons Analyss of Resuls Subsdy Fnanced by a Physcal Capal Tax Subsdy Fnanced by a Human Capal Tax Concluson References 101 Appendx.. 106

5 LIST OF FIGURES Fgure Number Page 1. Fgure 1.1A/B-1.4A/B: Aggregaes: Response o Dscree Shocks Fgure 2.1A/B-2.4A/B: Aggregaes: Response o Dscree Shocks Fgure 3.1A/B-3.3A/B: Aggregae Growh Raes: Response o Dscree Shocks Fgure 4.1A/B-4.3A/B: Dsrbuon of Relave Wealh: Response o Dscree Shocks Fgure 5.1A/B-5.3A/B: Dsrbuon of Relave Income: Response o Dscree Shocks Fgure 6.1A/B-16.2A/B: Aggregaes: Dscree vs. Gradual Shocks Fgure 7.1A/B-7.3A/B: Aggregaes: Dscree vs. Gradual Shocks Fgure 8.1A/B-8.3A/B: Aggregae Prces: Dscree vs. Gradual Shocks Fgure 9.1A/B-9.4A/B: Aggregae Growh Raes: Dscree vs. Gradual Shocks Fgure 10.1A/B-10.3A/B: Dsrbuon of Relave Wealh: Dscree vs. Gradual Shocks Fgure 11.1A/B-11.3A/B: Dsrbuon of Relave Income: Dscree vs. Gradual Shocks Fgure 12.1A/B-12.8A/B: Aggregaes: Fscal Polcy Mx Fgure 13.1A/B-13.3A/B: Aggregae Prces: Fscal Polcy Mx Fgure 14.1A/B-14.3A/B: Aggregae Growh Raes: Fscal Polcy Mx Fgure 15.1A/B-15.3A/B: Dsrbuon of Relave Wealh: Fscal Polcy Mx Fgure 16.1A/B-16.3A/B: Dsrbuon of Pre-ax Relave Income: Fscal Polcy Mx. 100

6 LIST OF TABLES Table Number Page 1.1 Srucural Changes A Aggregaes: Responses o Dscree Shocks B Dsrbuon: Responses o Dscree Shocks A Aggregaes: Responses o Gradual Shocks B Dsrbuon: Responses o Gradual Shocks A Aggregaes: Responses o Fscal Polcy Shocks B Dsrbuon: Responses o Fscal Polcy Shocks. 83 v

7 1 Chaper I: Growh Inequaly Trade-off n he presence of Insananeous Shocks Absrac Ths paper analyzes he effecs of echnologcal change on growh and nequaly n a wo-secor endogenous growh model. I focuses on he echnologcal aspecs raher han he demographc aspecs, hghlghng he role of he secoral producon characerscs whch need no be unform across he economy as poenally mporan deermnans of long run growh and assocaed nequaly. We fnd ha he effecs on nequaly depend upon: () wheher he underlyng source of nequaly sems from dfferenal nal endowmens of human capal or physcal capal, () he secor ha experences he producvy shock. Our resuls sugges ha an ncrease n he growh rae resulng from producvy enhancemen n he human capal secor wll ncrease nequaly. Producvy enhancemen n he fnal oupu secor, alhough no havng permanen growh effecs, wll reduce nequaly. The model can generae posve or negave rade-offs, dependng on hese effecs, conssen wh he dverse emprcal evdence.

8 2 1 Inroducon Mos developed economes have seen a rend of rsng earnngs nequaly n he las wo decades of he 20h cenury (Aknson 1999). Evdence of hs can be seen n he rsng skll premum ha has been emergng, an ncrease n he reurns o sklled versus unsklled labor (Mchell 2005). As a resul of hese developmens, he role of human capal has receved ncreasng aenon boh as a source of economc growh and of he observed rsng ncome nequaly. Several specfc channels lnkng he accumulaon of human capal and nequaly have been denfed. I s well esablshed n leraure ha wage dfferenals (Mncer Wage Equaon) 1 arse from dfferenals n skll aanmen, va human capal accumulaon. Dspares n educaonal aanmen have been seen as one mporan cause of greaer ncome nequaly. [see Becker and Tomes (1986), Galor and Zera (1993), Fernandez and Rogerson (1998), Vaene and Zlcha (2001)]. San-Paul and Verder (1991) analyze he relaonshp beween publc educaon, growh and ncome dsrbuon n an OLG model. Durlauf (1991), also uses human capal formaon and earnngs o show he perssence of nequaly n an OLG framework. Ehrlch and Lu(1991) and Ehrlc and Km(2007) focus on he role of ferly dfeferences as a source of ncome nequaly. Hang and Mullgan (2000) use human capal heerogeney o sudy nergeneraonal mobly. We aemp o sudy he growh-nequaly radeoff n a framework of heerogeney n boh physcal and human capal endowmen. Our model follows closely on he lnes of he semnal Lucas (1988) and Uzawa (1965) represenave agen model, wh exernales n human capal. We employ a Romer model o consder he mpac of one of he major deermnans of he growh-nequaly relaonshp, namely an ncrease n producvy 2. The key elemen of our model s ha an ndvdual's personal dsposable ncome depends on her ncome from he accumulaon of human capal and her ncome from physcal capal. Hence, nequaly n nal endowmens of boh physcal as well as human capal, affec fnal levels of ncome nequaly. 1 Human capal has posve and sgnfcan effecs on growh, esmaed o be as much as 6%, whch concdes wh he mcroeconomc evdence va he Mncer Wage Equaon. In he class of regressons called he Macro Mncer equaons, he growh of per capa GDP s regressed on he growh and level of he sock of human capal. Our resuls are largely conssen wh he Mnceran earnngs funcon leraure n labor economcs whch assumes ha growh s drven by he accumulaon of human capal. 2 Ths s one of he key facors nfluencng he growh-nequaly relaonshp denfed by Solmano (1998)

9 3 We also assume ha physcal capal s specfc o he producon of fnal oupu, n whch case he human capal producon secor becomes he fundamenal engne of growh, conssen wh much of he emprcal evdence. Ths model focuses on he echnologcal aspecs raher han he demographc aspecs, hghlghng he role of he secoral producon characerscs whch need no be unform across he economy as poenally mporan deermnans of long run growh and assocaed nequaly. As Lucas argued, hs exenson of he Uzawa (1965) model and he nroducon of nersecoral facor mobly provdes mporan nsghs and yelds a subsanal mprovemen over he sandard one-secor neoclasscal model n explanng he process of economc developmen. We show he exsence of a sharp conras beween he effecs of a producvy ncrease n he fnal oupu secor on he one hand, and a correspondng ncrease n he human capal producng secor, on he oher, drven by dfferences n nal endowmens of physcal and human capal. In he former case, here s no mpac on growh where-as ncome nequaly falls. The oppose occurs when he nal producvy ncrease s n he educaon secor. Whle growh rae ncreases unambguously, s mpac on ncome nequaly depends on relave secoral nenses. In he more plausble case where he human capal secor s relavely more nensve n human capal, here s an ncrease n ncome nequaly reflecng a posve rade-off. The key deermnan of wealh nequaly, s he behavour of he consumpon-wage rao along he ransonal pah and s mplcaons for he dfferenal savngs rae across agens. Ths may be mporan n explanng why oherwse smlar economes dffer largely n her levels of nequaly. The evoluon of ncome nequaly, s hen deermned by he neracon of hs changng wealh nequaly along wh he changng fracon of ncome from asses as a share of personal ncome. In relaed leraure, Galor and Moav (2004) use a one secor model o sudy he effec of nequaly on he process of developmen, va accumulaon of physcal and human capal. Vaene and Zlcha (2009), consder a wo secor model wh boh physcal as well as human capal, and he mpac on nequaly n an overlappng generaons model. In conras o our paper hough, hey consder heerogeney only n human capal and no n physcal capal. They fnd ha he effec of ncome nequaly on growh s ambguous and depends on he naure of educaon echnology. In conras o our model, hey clam ha f he echnology shock s neural, here s no mpac on growh. Ecksen and Zlcha (1994) sudy nequaly usng a one secor OLG model wh boh

10 4 human and physcal capal, where heerogeney n human capal s generaed va heerogeney n parenal nvesmen n her chldren's educaon(or he home componen). They buld on he dea ha heerogeney n hs 'home componen' s a major source of he observed ncome dsrbuon [see Becker and Tomes (1979), Loury (1981)]. The relaonshp beween growh and nequaly has been subjec o a grea deal of conroversy. I has been dffcul o reconcle he dfferen heores, especally snce emprcal evdence has been nconclusve. Vaene and Zlcha (2007) clam ha he relaonshp beween growh and ncome nequaly s ambguous and depends on he source of change n he human capal formaon process. Our resuls show, ha he growh-nequaly rade-off depends crucally on he nal endowmen of human capal vs. ha of physcal capal, n he conex of producvy shocks. There s a class of leraure ha sudes he properes of alernave numercal echnques o model ssues of heerogeney. Infac, he focus s shfng on he accuracy of hese numercal algorhms n her ably o solve complex and analycally nracable models. Krussel and Smh (1998), nclude heerogeney n ncome and wealh arsng from parally unnsurable dosyncrac ncome shocks. Den Haan, Judd and Jullard (2010) buld on he work by Krussel and Smh (1998), and use DSGE modelng o descrbe he very frs model ha consders dfferen numercal algorhms. In he face of hghly complex non lnear models, one needs o be more careful n he choce of he soluon algorhm used and n parcular n he evaluaon of he accuracy of he numercal soluon so generaed. Krussel and Smh (2006) focus on he mehodologcal aspecs of nequaly deermnaon n he presence of heerogeney. The key nsgh s ha approxmae aggregaon allows one o solve he problems of forward lookng agens wh a very small se of sae varables (aggregae capal only) and aan noneheless a very hgh degree of accuracy 3. All he same, hey go on o show usng a wo perod model, ha, n he presence of addonal frcons lke cred marke mperfecons used o model heerogeney, approxmae aggregaons of he represenave agen model mgh no be robus. When he equlbrum growh rae and ncome dsrbuon are muually dependen, her jon deermnaon and he analyss of her relaonshp becomes nracable; see e.g. Sorger 3 Quanave Macro Models wh Heerogeneous Agens', Per Krussel, Anhony Smh (2006)

11 5 (2000). Casell and Venura (2000), and more recenly Garcίa Peñalosa and Turnovsky (2006, 2007, 2008), provde a sysemac analyss of he dsrbuonal consequences of he represenave agen model, where here exss a source of heerogeney. They explo he fac ha f he uly funcon s homogeneous n s relevan argumens (whch ncludes he consan elascy uly funcon ha seemngly domnaes conemporary macrodynamc heory), he aggregae economy can be summarzed by a represenave agen. As a resul, aggregae behavor becomes ndependen of he economy's dsrbuonal characerscs, and he analyss becomes racable. Bu he racably of he aggregaon also depends upon he source of he heerogeney. The model here ses ou a framework n whch boh growh and dsrbuon are jonly deermned and where he heerogeney of agens, whch s he source of ncome nequaly, sems from an her nal dsrbuon of endowmens of physcal as well as human capal. In he model we presen a sequenal equlbrum srucure ha may be exended o analyze alernave nequaly measures. Alhough he varous nequaly measures are srucurally relaed n hs sraghforward way, we conduc our analyss by numercally smulang a wo-secor, hree-facor producon model. 2 Analycal Framework The analyss exends he radonal wo secor model o nroduce agens who are heerogeneous n her nal endowmens of physcal as well as human capal. 2.1 Technology and Facor Paymens There s a sngle represenave frm producng fnal oupu, usng he aggregae neo-classcal producon funcon (1). X F K, H, L A K H L H 1 (1) X X X X where all facors have posve bu dmnshng margnal physcal producs and are subjec o consan reurns o scale. A any pon of me, he economy has accumulaed uns of physcal capal and uns of human capal. Boh human capal and labor can move nsananeously and coslessly from one secor o anoher. Followng Lucas and Uzawa (1988), we assume ha

12 6 physcal capal s employed only n he fnal oupu secor 4.The secoral allocaons of are consraned by: and L X L 1 (2) Y H H H (3) X Y We defne he followng varables whch are used hroughou he res of he paper : L / ( H / H) and L / ( H / H) X X X Y Y And, X, LX, H / H X, and Y, LY, H / HY, We wll prove n (a3) laer ha z, z, j z for all z XY, Our procedure s o follow Bond, Wang, and Yp (1996) and o express he macroeconomc dynamc equlbrum n erms of he rao of physcal capal o human capal, k K H, he rao of consumpon o human capal, c C H, and he rao of he shadow value, q, augmened by he dynamcs of A, B. To do so s convenen o le u H X H denoe he allocaon of human capal o he producon of fnal oupu. The aggregae frm makes s producve decsons o maxmze prof, so ha he reurns o physcal capal, r K, human capal, r H, and labor,w, are as below: Y r r K H W H k A u 1 k A u X X k w A u 1 X (4a) (4b) (4c) From (4a-c) we see ha he equlbrum real wage s proporonal o he economy-wde sock of human capal and a decreasng funcon of he rao of raw labor o human capal employed n he 4 Mechancs of Economc Developmen n an opmal model of economc growh', H. Uzawa (1965)

13 7 fnal oupu secor, whle he raes of reurn on human and physcal capal are boh ncreasng funcons of ha same rao. In conras, he rae of reurn on physcal capal (human capal) s a decreasng (ncreasng) funcon of he rao of physcal capal o human capal employed n he fnal oupu secor. 2.2 Heerogeneous Consumers There s a connuum of agens, each ndexed by, dencal n all respecs excep her nal endowmens of physcal capal K,0 and human capal H,0. Snce we consder a growng economy, we are neresed n he shares of ndvdual I n he accumulang oal socks of human capal, * H () h () and physcal capal, H () * K () k (), where H () and K () denoe he K () correspondng economy-wde average quanes. The nal relave endowmens are dsrbued wh mean one and sandard devaons h,0, k,0 and may or may no be correlaed 5. The analyss makes wo mporan assumpons regardng he underlyng source and naure of he heerogeney. Frs, here are clearly many sources of heerogeney of whch nal endowmens are arguably he mos sgnfcan. Compellng emprcal evdence supporng hs, s provded by Pkey (2010) 6 Second, he nal dsrbuon of endowmens can be perfecly arbrary and herefore conssen wh any requred non-negavy consrans 7. As wll become apparen n due course, he dsrbuon of he nal endowmens wll be refleced n he evolvng dsrbuons of wealh and ncome. Each agen s endowed wh a un of raw labor ha can be allocaed eher o employmen n he fnal oupu secor, L X, or o acqurng more human capal, L Y, hus, L X, LY, 1 (6a) 5 Beng he sandard devaon of he relave capal sock, s n fac he coeffcen of varaon. 6 On he Long Run Evoluon of Inherance - France ', Thomas Pkey (2010) 7 There s an exensve leraure generang heerogeney from agens' nal endowmens of wealh; see e.g. Chaerjee (1994), Chaerjee and Ravkumar (1999), Sorger (2000), Casell and Venura (2000), Malar and Malar (2001), Alvarez-Pel a' ez and Daz (2005) and Obols-Homs and Urrua (2005). An alernave source of heerogeney n he earler leraure was he rae of me preference as e.g. n Becker (1980) where he mos paen agen ends up holdng all capal.

14 8 A any pon of me, he agen has accumulaed a sock of human capal, H ha smlarly can be allocaed eher o he fnal oupu secor or o he furher accumulaon of human capal H H H (6b) X, Y, Physcal capal, however, s employed only n he fnal oupu secor and herefore does no nvolve an allocaon decson. We assume ha he wage rae earned by raw (unsklled) labor s W, whle he reurns o human capal and human capal are r, H r K, respecvely, all hree beng expressed n uns of fnal oupu. Each agen produces human capal usng he followng Cobb-Douglas producon funcon: We can hnk of 1,, H B H L H (6c) Y Y, as a combnaon of boh echnologcal change and he average number of years of educaon n he labor force 8. Ths funcon s of he sandard Romer (1986) form, n ha s homogeneous of degree one n he accumulang asse (human capal), wh he economy-wde average sock of human capal provdng an exernaly ha rases he producvy of each ndvdual s raw labor. The only way an agen can accumulae human capal s by devong hs own physcal resources o hs acvy; here s no marke where human capal can be purchased. The agen s budge consran, descrbng hs marke acves, assers ha he ncome earned from hs hree producve facors may be spen eher on consumpon or on accumulang physcal capal K r K r H WL C (6d) K H X, X, Each agen has a lfeme uly ha s assumed o be an soelasc funcon of he sngle consumpon good : 1 MaxU Ce d wh 1 (6) 0 8 'Inequaly and Growh', Cecela Garc ' a Pe n alosa (2008)

15 9 where 1/ (1 ) represens he neremporal elascy of subsuon. The nsananeous uly funcon s aken o be concave, he consumpon good s assumed o be a normal good, whle he agen's rae of me preference s aken o be consan for he analyss. Performng he maxmzaon of (6) s.. (6a) hrough (6d) yelds he followng frs order opmaly condons: 1 C (7a) r H 2, k A u X (7b) 1 2, B Y, (7c) W k HA u 1 X (7d) 1, B(1 ) H Y, (7e) 2, (7f) r K (7g) where s he agen s shadow value of wealh assocaed wh value of wealh assocaed wh K and s agen s shadow H. Equaons (7f) and (7g) when combned gve he neremporal no arbrage condon whch ensures ha he reurn on educaon (n erms of uns of fnal goods) and he reurn on physcal capal mus be equalzed a each pon n me. In addon, he followng ransversaly condons mus hold o ensure ha he ndvdual agen s neremporal budge consran s me lm Ke 0 lm He 0

16 Aggregaon We now have he basc componens, and he nex ask s o aggregae hem o derve he economy-wde equlbrum. Equang he across secors by dvdng (7e) by (7c) and (7d) by (7b) we ge: 1, 1 H 2, Y, (a1) 1, H 2, X (a2) Equang (a1) and (a2) 1, , Y, X Ths mples Y, Y, j Y and so, X Y, 1 1, 1, j 2, 2, j Also, from he Euler condon (7g) we know 2, 1 BY And so mus be he same for all ndvduals. 1, 1, j j and 2, 2, j j and so, j j

17 11 Defnng q, he above mples ha j q q q where q s he un prce of human capal defned n erms of uns of goods. The relevan pon here s, ha wh all ndvduals followng he same Euler equaon, he aggregae economy evolves ndependenly of dsrbuonal consderaons. Under que general condons, he economy proceeds as f here s a sngle represenave agen 9. Ths s he case as long as he producon funcon has he sandard neoclasscal properes, and agens have he same ases represened by a uly funcon homogeneous n s sngle argumen, consumpon. Ths condon s crucal n faclang he aggregaon ha perms us o derve he macroeconomc equlbrum. Usng q hus defned, he opmaly condons (5b), (5c) and (7c), (7e) gve us he followng resuls: r H qb (8a) 1 Y w qb(1 ) Y ε (8b) q q r q H r (8c) K Takng me dervave of (7a) C C 1 r 1 1 K (9) Therefore, each agen wll choose he same growh rae for consumpon regardless of nal endowmen of asses. In parcular, C C (9 ) C C C and herefore equal o he average. We may hen wre C C where 1 d =1 and s 0 consan for each and wll be deermned n he sysem. Thus defned, denoes he agen's oal consumpon relave o economy wde average consumpon, and, as we wll show laer, wll 9 Gorman (1953)

18 12 deermne relave welfare. Snce real raes of reurn are equalzed across secors for boh labor as well as human capal, a every pon of me, we ge he followng relaonshp beween be expressed n erms of qa, and B as below 1 εη1 X and Y, whch can k q m (10) X u where Then, 1 B (1 ) m A and m s some consan for gven values of AB,,, and. X Γ Y where Γ (1 ) whch s he sandard resul ha for gven producve elasces,,,, he relave nenses of raw labor o human capal wll move proporonaely n he wo secors. The quany measures he relave nenses of sklled o unsklled labor n he wo secors. If 1, human capal s relavely more nensve han unsklled labor n he human capal secor and vce versa. So we have Γ (, ) and hence, r r ( q, k), r r ( q, k) and w w( q, k) X Y qk K K From he full employmen condon (3), we can also solve for u whch ges deermned whn he sysem, as a funcon of k and q H H u 1Y X Y (11) u u( q, k) Equaons (10) and (11) are crcal n deermnng he mpac effecs of producvy changes. dx dy dq dk da db X Y u[ 1] q k A B 1 (10 ) du u dy 1 1 Y u[ 1] (11 )

19 13 One varable of parcular neres s he skll premum. The reason for hs s ha he supply of raw labor s fxed, whereas human capal grows ndefnely over me, as a resul of whch n he long run he reurn o human capal s consan, whle he reurn o raw labor grows a he equlbrum rae. We herefore defne he skll premum as he rao of ncome earned by human capal o he ncome earned by raw labor. Thus, a crucal deermnan s he equlbrum rao of raw o sklled labor employed n he human capal secor. rh rh 1 S Y X W / H w The sandard effec of relave labor supples s capured by he nverse relaonshp beween skll premum and he rao of unsklled o sklled labor. 2.4 Macro Economc Equlbrum The lnear homogeney of he producon funcons n he prvae facors allows us o express relaons n erms of effecve labor uns. Defnng K H effecve labor un and C H k o be he physcal capal per c o be he consumpon per effecve labor un, we can descrbe he dynamcs n erms of hese varables. Combnng (9) and (9 ), he equlbrum dynamcs of aggregae consumpon s: C C r K 1 (12a) C C C rk 1 (12a ) Aggregang over ndvduals, fnal goods marke equlbrum mples ha he fnal oupu n excess of oal consumpon wll be accumulaed as capal: k K A( H X) X C u 1 K k c K A X K u k (12b) (12b )

20 14 Smlarly, aggregang over each agen's human capal accumulaon equaon, (2), H B( 1u) H 1 Y (12c) H H 1 H B(1 u) Y (12c ) The arbrage equaons (7f) and (7g) gve us he fnal aggregae dynamc equaon (8c) q q r q H rk (12d) The macro dynamc equlbrum s a modfcaon of ha analyzed by Bond e al. (1996), he dfferences beng () he dsncon beween sklled and unsklled labor, and () he assumpon ha physcal capal s specfc o he fnal oupu secor. Bu he key observaon s ha he evoluon of he aggregae economy s ndependen of any dsrbuonal measures. As k, c, and q evolve, hs wll generae adjusmen pahs for he raes of reurn and he secoral allocaon of resources. The aggregaon shown n equaons (12) above allows us o represen he equlbrum dynamcs of he economy as a whole as follows () Labor Marke Clearance L L 1 (13a) X Y () () Human capal marke clearance k Goods marke clearance K A( uh ) X C u (13b) (13c) (v) Human capal accumulaon 1 H B u H (1 ) Y (13d) Ths macroeconomc equlbrum has a smple srucure. Equaons (13) deermne he secoral facor allocaons and he dynamc evoluon of he sysem. Due o he homogeney of he underlyng uly funcon, equaon (6), he macro-economc equlbrum s ndependen of any dsrbuonal aspecs.

21 15 Transonal Dynamcs In erms of our prevously defned varables, core dynamcs can be represened by he followng dfferenal equaons n k, c and q k k Au (, ) X c k H q k u r ( K q, k) c c H ( q, k) 1 q qr ( q, k) r ( q, k) K H (14a) (14b) (14c) Ths sysem has many of he characerscs of a ypcal wo secor economy as poneered by Lucas (1988) and exended by Bond, Wang and Yp (1996) 10, where he (local) dynamcs are dscussed n deal by lnearsng hs sysem around he seady sae. There s no need o pursue ha dscusson here, excep o noe ha he dynamcs s a saddle pon, wh a one dmensonal sable manfold. Seady sae equlbrum wll have he characerscs k c q 0. We can show ha he sysem has a saddle pon f and only f he expresson: [ ( )( ) ( )( ) ] ( ) Ths ensures sably (non ndeermnacy) of he sysem. The sysem has wo one sluggsh varable ( ) and wo jump varables. Thus, he above condons ensure he presence of wo negave and one posve egen values, hence assurng sably of he saddle pah.we show numercally ha he sysem s saddle pah sable wh one negave roo 0. Along he sable pah, physcal capal per effecve labor un evolves gradually, whle consumpon per effecve labor un and he relave prce q, may jump n response o new nformaon as comes avalable. Deals of he lnearzaon and he assocaed jacoban have been gven n Appendx A1 and A2. 10 'A General Two-Secor Model of Endogenous Growh wh Human and Physcal Capal: Balanced Growh and Transonal Dynamcs', Erc W. Bond, Png Wang, Chong K Yp (1996)

22 16 Balanced growh equlbrum The seady sae balanced growh equlbrum s reached when summarzed by he followng condons and s Secoral allocaon of raw labor Secoral allocaon of human capal: ( ) Full Employmen ( ) ( ) ( ) ( )( ) ( ) Equlbrum Growh: ( ) [ ( ) ( )( ) ] ( )( ) Equlbrum raes of reurn: ( ) ( ) Gven he fnal values of reurn, hese equaons deermne he equlbrum values of whch hen mply he correspondng equlbrum facor raes of, skll premum,, and equlbrum growh rae Two crcal condons consran he equlbrum value of and. The frs s he ransversaly condon, ha each agen mus sasfy. Ths wll be me f and only f, [ ] [ ] Whch n seady sae s equvalen o. Ths s urn s equvalen o The oher condon s ha wh no deprecaon o human capal, he equlbrum growh rae s always posve, whch n urn mples ha 1 u. Combnng hese wo condons, ogeher wh he full employmen condon, yelds he followng bounds on Y for a feasble soluon o exs: If ( ) If ( )

23 Long run effecs of producvy ncreases on aggregae equlbrum The producvy ncreases n he wo secors have dramacally dfferen long-run effecs on he aggregae economy [Equaons (10 ) and (11 )]. These resuls are summarzed n Table a Producvy ncrease n fnal oupu secor, A Proposon 1: A producvy ncrease n he fnal oupu secor: I. Leads o a equ-proporonae ncreases n () he rao of physcal o human capal, () he prce of human capal, () he raes of reurn o human capal, (v) he reurn o raw labor, and (v) he consumpon o human capal rao. Ths proporonae ncrease exceeds uny by an amoun ha reflecs he producvy of physcal capal n fnal oupu. II. I has no effec on () he secoral raos of sklled o unsklled labor, () human capal across secors, () he reurn o physcal capal, (v) he equlbrum growh rae, or (v) he skll premum. The nuon underlyng hese responses s sraghforward. An ncrease n producvy, A, of he fnal oupu secor aracs resources o ha secor. Ths rases he producvy of raw labor and human capal proporonaely n ha secor, ncreasng her relave raes of reurn as measured n erms of fnal oupu. Wh lnear homogeneous producon funcons, for proporonae ncreases n facor prces, here s no ncenve o subsue; hus here s no movemen of human capal and raw labor. Accordngly facor marke equlbrum s mananed by a proporonae rse n he relave prce of human capal, so ha he skll premum, measured n erms of educaon remans unchanged b Producvy ncrease n he human capal secor, B In hs case he producvy ncrease s n he growh-generang secor, and as a resul he effecs are more complex and depend upon he relave secoral facor nenses. Proposon 2: A producvy ncrease n he human capal secor has he followng long-run effecs: () I leads o an unambguous ncrease n he equlbrum growh rae and a

24 18 lkely less han proporonae declne n he prce of human capal. () If he human capal secor s relavely more nensve n sklled labor han s he fnal oupu secor ( 1), he rae of reurn on human capal wll fall and ha on raw labor wll decrease oo, hough by relavely more, rasng he skll premum. If Γ < 1, he responses are reversed. The followng nuon apples. An ncrease n producvy of human capal B aracs resources o ha secor. Suppose 1, so ha he human capal secor s relavely more nensve n human capal. As a resul of he shock, he reurn o human capal wll end o rse and ha of raw labor fall hus resulng n an ncrease n he skll premum. There s, however, anoher effec n operaon. The producvy of raw labor and human capal are enhanced by her neracon wh physcal capal n he fnal oupu secor. As resources move away from hs secor hs effec s reduced, as represened by he erm (1 ) for he correspondng expressons n Table 1. Ths renforces he declne n he wage of raw labor and offses he ncrease n he reurn o human capal, causng skll premum o evenually fall, hough remans hgher han s pre-shock levels. The mos srkng conras beween he producvy ncreases n he wo secors s n he mpac on he long-run growh rae. To see he reason behnd hs s consrucve o subsue (19b), (19c), and (19f) no (19e), rewrng as 1 1 B ( 1) Y B Y Y 1 1 (19e ) From he lef-hand sde equaly, we may solve for long-run rao of raw labor o human capal n he form ( ). We may hen wre ( B, ( B)), from he rgh hand sde equaly, Y Y B hghlghng how, boh drecly and hrough Y Y, he producvy of he human capal secor s he crucal long-run deermnan of growh, whch by he same oken s ndependen of he producvy n he fnal oupu secor. 11 The reason ha B wll ncrease he growh rae s because of he lmed subsuon possbles n he producon funcon for human capal. 11 Through, he producve elasces n he fnal oupu secor play a role n deermnng he equlbrum growh rae.

25 19 3 Evoluon of Wealh, Income and Welfare Inequaly We now proceed o consder he consequences of changes n producvy for he evoluon of wealh and ncome nequaly, as well as he overall level of neremporal welfare nequaly. 3.1 Wealh Inequaly The wealh of agen s defned by V ( ) K ( ) q( ) H ( ) (15) where we assume ha V 0 so ha he agen has ne posve wealh and s herefore solven. Takng me dervave of (15) and usng (14c) we have: V ( ) r ( ) V ( ) W() C () (15 ) K Boh (15) and (15 ) ndcae ha n he absence of any marke mpedmens, he shadow value of human capal, q (), behaves lke a prce n a compeve marke. Summng (15 ) over all agens n he economy, gves us he aggregae wealh equaon: V ( ) r () K V( ) W( ) C( ) (16) where 0 V ensures he solvency of he aggregae economy V 0. We defne ndvdual ' s share of aggregae wealh as v ( V ( ) V ( ) ). Takng me dervave of v and combnng (15 ) ogeher wh (16), along wh he fac ha C C we ge: 1 v ( ) W ( ) C( ) (1 v ( )) C( )(1 ) (17) V ( ) Equaon (17) hghlghs how he evoluon of an ndvdual agen's share of relave wealh depends on he evoluon of aggregae consumpon, wage, as well as hs own specfc endowmen as refleced n v and. Before solvng for v (), we see from (17) ha agen ' s seady sae share of wealh sasfes

26 20 C C W ( k, q) V V 1 (18) C C V C C ( rk) ( rk) v 1 V V V 1 1 (18 ) Thus f ndvdual ' s wealh places hm above average, s.. v 1, hen hs long run margnal propensy o consume ou of hs above average wealh s gven, by ( r ) K 0 1 To analyze he evoluon of relave wealh, we lnearse (17) around he seady sae, mposng C W c, w H H and V v. Ths leads o an equaon of he form H ( rk) c ( rk) c() c v 1 v ( v ( ) v ) ( v 1) ( w( ) w) 1 v 1 c v Snce he coeffcen of v () s posve, (19) hghlghs how he dynamcs of v () are drven by he (forward-lookng) ransonal me pah of c( ) / w( ). For noaonal convenence we shall denoe ( ) ( ) by ( ). We can hen express (17) n he form: 12. (19) ( ) ( ) ( ) [( ( ) )( ( ) ) ( ) ( ) ( )] (17 ) Lnearzed around seady sae, we can express (19) as: ( ) [( )( ( ) ) ( ) ( ( ) )] (19 ) Suppose ha he economy s nally n seady sae and a me 0 experences a permanen ncrease n he producvy of he oupu secor A. The mmedae effec of hs s o generae a jump n q as par of he adjusmen o ensure ha he economy les on s new sable saddle pah. 12 ( r ) From (18 ) we can compue K V 1 ( v 1) (1 ) C consan hroughou he ranson.. Ths mples ha he agen s relave consumpon s

27 21 Ths n urn causes a jump n agen 's nal relave wealh v (0) ( K q(0) H ) / ( K q(0) H ),0,0 0 0 dv (0) q(0) H,0 q(0) H(0) dq(0) v (0) K,0 q(0) H,0 K0 q(0) H0 q(0) (20) The naure of he jump depends upon () he devaon n he agen's nal relave asse endowmen from he economy-wde average, and () he relave prce : sgn ( dq (0)). Thereafer, v () wll evolve n accordance wh (19), gven he nal jumps and consequen ransonal pahs of boh c () as well as w (). The key pon o observe abou (19 ) s ha he coeffcen of ( ) In order for he relave wealh o reman bounded he soluon for expresson ( ) ( ) [ ( ) ( ( ) ) ( ) s gven by he forward lookng ( )( ) ] (19 a) and has he propery ha lm ( ) 1 hus ensurng ha lm v ( ) v. Seng 0 n (19 a) ( ) ( ) [ ( ) ( ( ) ) ( )( ) ] (19 b) We can show ha he soluon s of he qualave form v ( ) 1 ( )( v 1) ( ) ( ) v v (21) where () represens he me pahs of aggregae varables, ( ) and ( ). Seng n (21), v(0) 1 (0)( v 1) v,0 (0) v The above equaon, (22), gves he seady sae dsrbuon of agen ' s relave wealh ( v 1), gven agen ' s dsrbuon of nal wealh ( v (0) 1) along wh he nal jump n z () Ths, ogeher wh (19 a) and (19 b) hen gves he me pah for agen 's relave wealh v (). In (22)

28 22 he smulaons we conduc, he jump n nal wealh (20) s small and has neglgble dsrbuonal consequences. For smplcy we shall assume ha all agens nally hold he same relave shares of physcal o human capal whch are equal o he average. Tha s, K,0 K j,0 K0 k(0) k0 n whch case dv (0) 0. On mpac, he nal dsrbuon of H H H,0 j,0 0 wealh remans unchanged, so ha v (0) 1 v 1 k 1 h 1 * *,0,0,0 H K where h and k *,0 *,0,0,0 H0 K0 Because of he lneary of (20) and (21) we can readly ransform hese equaons descrbng a specfc agen's relave asse poson no correspondng relaonshps for he sandard devaon of he dsrbuon of wealh across agens, whch herefore serves as a convenen measure of wealh nequaly. ( ) ( ) v v (21 ) (0) (0) v v (22 ) Gven v,0, he seady sae wealh dsrbuon s deermned by (0), whch n urn depends on he expeced changes n ( ), along he subsequen ransonal adjusmen pah. The soluons (19 ) and (20) hghlgh how agen s relave wealh a each pon of me,, and herefore he enre dsrbuon of wealh s drven by he (expeced) fuure me pah of he consumpon o wage rao from me forward, as hese respond o he underlyng srucural change, n hs case he ncrease n he level of echnology. As a resul, he pah followed by z () wll have a permanen effec on he relave sock of wealh and herefore on s dsrbuon across agens. In he presen case, followng s nal jump, he evoluon of wealh nequaly durng he ranson wll depend upon he relave speeds of adjusmen of consumpon and wage. A hs pon we can sae he followng proposon: Proposon 3: If consumpon adjuss more (less) rapdly han do wages along

29 23 he ransonal pah, so ha z approaches z from below (above), hen wealh nequaly wll declne (ncrease) durng he ranson. The nuon for hs resul s sraghforward. If consumpon grows faser han do wages on raw labor, savngs grow a a slower rae. Snce wealher people end o save more, her relave rae of wealh accumulaon declnes and wealh nequaly declnes as well. 3.2 Income Inequaly: Dsrbuon of Income Usng (13f) of he macro economc equlbrum as derved from he arbrage condons, ndvdual ' s personal ncome s Y ( ) rk ( ) V ( ) W() (23) and summng over all agens gves us he average economy wde personal ncome Y( ) r ( ) V( ) W( ) K (23 ) Dvdng (23) by (23 ) gves us he relave ncome of agen y, rk( ) V( ) W ( ) y () r ( ) V ( ) W ( ) K Y Y (24) The lneary of (24) allows us o express he relaonshp beween relave ncome and relave wealh n erms of he correspondng sandard devaons of her respecve dsrbuons, () and (), namely y v rk ( ) V ( ) y ( ) v( ) s( ) v( ); s( ) 1 r ( ) V ( ) W( ) K (25) ( ) ( ) y So, ncome s more equally dsrbued han wealh a any pon of me. The me pah of ncome nequaly reflecs ha of wealh nequaly and he share of ncome from wealh ( ). y () s () v() ( ) s( ) ( ) y v v

30 24 rk () V ( ) W ( ) W ( ) v() rk ( ) V ( ) W ( ) rk ( ) V ( ) W ( ) v( ) v (25 ) where he rgh hand sde depends upon he evoluon of V ( ), rk ( ) and W () and (), as hey respond o he shock. Usng he smplfyng assumpon ha k * *,0,0 * * v,0 k,0 h,0 1 h 1 such ha and nal values are gven, we see ha he nal pre shock seady sae ncome nequaly s whle n he new seady sae, rk (0)( q(0) H0 K0) y(0) r (0)( q(0) H K ) W K v,0 (26) ( ) ( ) (26 ) From equaon (26 ) we see ha ncome nequaly wll rse relave o s nal equlbrum level, f: () he dscouned value of effecve wealh, v, rses; () he real reurn o labor, w, decreases. Wheher hs happens wll depend on wheher he shock o producvy mpacs he oupu or he educaon secor. 3.3 Welfare Inequaly Recallng (6) agen ' s welfare a me s Subsung C C no hs expresson yelds 1 Z() C (29) 1 Z ( ) ( C( )) ( ) Z ( ) (30) where Z () s he average welfare level a me. Subsung (29) no (6) yelds an analogous relaonshp for he relave neremporal welfare evaluaed along he equlbrum growh pah. U U Z() (31) Z() A each nsan of me, agen ' s relave welfare remans consan, so ha hs neremporal

31 25 C relave welfare, z Z / Z remans consan as well. Usng (18 ) and he fac ha c H V and v we can express relave welfare n he form H ( r K ) v U 1 Z() Ω 1 ( v 1) z ( ) U c Z() (32) We can now compue a measure of welfare nequaly. A naural merc for hs s obaned by applyng he followng monoonc ransformaon of relave uly. Ths enables us o express he relave uly of ndvdual as z ( r K ) v 1 c 1/ Ω Ω ( ) 1 ( v 1) (32 ) Boh nsananeous and neremporal welfare nequaly, expressed n erms of equvalen uns of wealh, can be measured by he sandard devaon of relave uly and are consan and dencal o he seady sae level of ncome nequaly ( ) ( ) ( ) (33) 4 Numercal Smulaons Gven he complexy of he model, o analyze he consequences of a producvy shock, on he dynamcs of wealh and ncome dsrbuon s necessary o employ numercal smulaons. We begn by calbrang a benchmark economy usng he followng sandard parameer values represenng a ypcal economy.

32 26 Parameer Values Preference Parameers ( ) Producon Parameers => Γ >1 Cases Producvy Parameers Frs he preference parameers correspondng o a rae of me preference of 4% and an neremporal elascy of subsuon of 0.4 are sandard and nonconroversal. The exponens 1/ 3 n he producon funcon for fnal oupu approxmaes he emprcal esmaes of he generalzed Solow producon funcon obaned by Mankw, Romer and Wel (1992) 13. Emprcal evdence on he producon funcon for human capal s far more sparse. We feel ha he mos mporan npu n augmenng he sock of human capal s human capal, followed by raw labor, wh physcal capal beng he leas mporan, and whch we have se o zero. Thus we se 0.60, as a plausble benchmark, whch we may noe s very close o he calbraed value of 0.62 obaned by Manuell and Seshadr (2010). Ths confguraon of producve exponens yelds 1.5, mplyng ha he producon of human capal s more nensve n sklled, raher han unsklled, labor relave o he producon of fnal oupu. The frs row of Table 2.A summarzes he key aggregae varables n hs nal equlbrum. Ths equlbrum s assocaed wh a capal-oupu rao of 3.23, a growh rae of 2.56%, a rae of reurn on physcal capal (gnorng deprecaon) of 10.4%, and a reurn on human capal of 5.47%, wh he skll premum of 105%. Nearly 90% of raw labor and 85% of human capal s allocaed o he fnal oupu secor. Also, as saed earler, we mpose he fac ha he nal dsrbuon of physcal capal and human capal s he same. Ths leads o he fac ha, dv (0) 0 ha s, he nal dsrbuon of relave wealh remans unchanged on mpac, n response o a shock. For he purpose of he smulaons, hs pus 1 where s defned as k h *,0 *, The resuls for hs have been abulaed n Table 2(b). In Table 2(b) we focus on hree polar cases, () equ-proporonae 13 They oban esmaes of 0.43, 0.31, 0.28.

33 27 nequaly across nal asse holdngs,,0,0,0 1, () no nal physcal capal k h kh nequaly,,0,0 0, () no nal human capal nequaly,,0,0 0. k kh Raher han calbrae o a specfc economy, we prefer o ensure ha our calbraon les whn he observed range, so ha may be vewed as beng ypcal of a class of economes raher han a specfc economy. In hs respec, he mpled capal-oupu rao, consumpon-oupu rao and he rao of he value of human capal o physcal capal, summarzed for he basc calbraons are generally whn a plausble range and hus sugges ha he benchmark represens a plausble sarng pon. h kh 5 Analyss of Resuls 5.1 Insananeous shock o he fnal oupu secor The long run effecs of he aggregae economy are descrbed n lne 2 of Table 2.A. An ncrease n producvy specfed as a nsananeous ncrease n by 10%, leads o a long-run ncrease n he rao of physcal o human capal, he relave prce of human capal,he consumpon o human capal rao, he real reurn on human capal and he real wage by 15.4%. The secoral allocaons of sklled and unsklled labor and he reurn on physcal capal, along wh he growh rae, reman unchanged. [see Panel A, Fgure ] The producvy ncrease n he fnal oupu secor draws resources owards hs secor. Gven he relave secoral nenses (Γ >1), we see from equaons (10 ) and (11 ) ha facor marke equlbrum wll requre a declne n he relave demand for sklled labor, so ha and boh fall on mpac. A he same me, forward lookng agens predc ha hs ncrease n producvy wll ncrease. The relave scarcy of human capal causes ( ) o jump up on mpac. The shf n resources oward he producon of fnal oupu (whch s nensve n raw labor) resuls n a shor erm declne n skll premum. On mpac, he producvy ncrease resuls n an ncrease n consumpon, snce consumers adjus her consumpon o he new hgher permanen ncome. Wage oo jumps, hough by a greaer proporonae amoun, causng he consumpon-wage rao o declne. The producvy ncrease causes reurn o physcal capal o ncrease more han he reurn o human capal. Whle hs smulaes he growh of physcal capal, ha of human capal declnes. The rao hus begns o rse.

34 28 The evoluon of wealh nequaly depends crcally on he nal dsrbuon of relave endowmens. If he dsrbuon s proporonal across agens ( ), nal wealh nequaly remans unchanged. If hey are enrely due o dfferences n human capal, he nal ncrease n ( ) wll rase shor run wealh nequaly, whle f hey are due o physcal capal, wealh nequaly wll mmedaely declne [see (20)]. The effec on ncome nequaly depends on he sze of he nal posve effec from he share of ncome from capal ( ( )), relave o he nal response of wealh nequaly( ( )). These wo effecs may be eher re-enforcng or offseng, dependng on he source of heerogeney. These nal responses rgger he ransonal dynamcs. Snce exceeds, hs resuls n a reversal of he nal declne n The ncreasng rao offses hs o some exen, hough on balance, ncrease o he pre-shock levels. As resources move back oward he educaon secor ( ncreases), declnes whle ncreases. Growh raes gradually converge o her orgnal seady sae levels. Dynamcs of dsrbuon are drven by he ranson of he consumpon o wage rao. As he rao of consumpon o wage ( ) ncreases n ranson o s new hgher seady sae, savngs declne [see (19 )]. Ths s key n explanng he declne of wealh nequaly n ranson. Wheher wealh nequaly ends up beng more or less equal han s pre-shock level depends on he source of he heerogeney. In he case ha wealh nequaly s due o varaons n he nal endowmen of human capal, long run wealh nequaly wll ncrease by 2.8%. If nsead s due o dfferenal endowmens n physcal capal, wll declne by 5.6%. [see Table 2.B.]. The ransonal dynamcs of () mrrors ha of wealh nequaly and reflecs a number y of conflcng nfluences. In he shor erm, he ncrease n producvy ncreases capal ncome more han does wage ncome. The ncreasng effecve wealh hus domnaes and ncome nequaly rses on mpac. Overme, capal accumulaon rases he wage rae, whereas he reurn o capal says he same. Snce labor s more equally dsrbued han capal, he reurn o he more equally dsrbued facor ncreases. Ths, coupled wh he fallng wealh nequaly causes long-run ncome nequaly o fall by 0.85% [Panel A, Fgure 1.10 (a)]. I may be noed ha wh he reurn o physcal capal unchanged n he long run, he long run ncome nequaly wll change by he same proporonae amoun as does wealh nequaly ( ( ) ). The same s rue for welfare nequaly.

35 Insananeous Shock o he Human Capal Secor An ncrease n producvy s specfed as an ncrease n B by 10%. These conras from he responses n A above, n ha he producvy ncreases n he human capal secor has a permanen growh effec, whch for hese smulaons rses from 2.56% o 2.99%. There s emprcal evdence ha suppors hs resul. Denson (1985) found ha growh n years of schoolng beween 1929 and 1982 explaned abou 25% of he growh n he U.S. per capa ncome durng he perod. The experences of nearly one hundred counres snce 1960 sugges ha educaon nvesmens n 1960 are an mporan varable explanng subsequen growh n per capa ncomes (Barro 1989). The long run responses have been summarzed n lne 3 of Table 2.A. Ths producvy ncrease draws resources no he human capal secor, shfng boh sklled and unsklled labor oward ha secor. Thus, he share of boh human capal as well as unsklled labor n he oupu secor fall. Snce he educaon secor s more nensve n human capal, equlbrum n boh markes requres small permanen ncreases n and n he long run. Also, he ncrease n he long run rao of human o physcal capal (fall n ) resuls n a reducon n relave scarcy of human capal, hus a fall n ( ). In he long run, he relave ncrease n sklled labor n he fnal oupu secor ( ) rases he reurn on physcal capal and reduces he real wage (reurn o unsklled labor). Whle he ncrease n ncreases he reurn o human capal, he fall n ends o lower. On balance, he laer domnaes and reurn o human capal falls. Bu he reurn o unsklled labor falls by more, causng skll premum o ncrease. The response of he reurn o human capal s also conssen wh emprcal evdence. Teulngs and Rens (2009) show a clear negave relaonshp beween he prvae reurn o educaon and he average level of schoolng n he counry, when workers have dfferen skll levels. Ths s refleced n our analyss as a fall n he reurn o educaon wh ncreasng socks of human capal. Goldn and Kaz (2001) use U.S. daa from o show ha greaer and unversally hgher levels of educaon reduced he rae of reurn o years of educaon relave o her exremely hgh level a he urn of he 20 h cenury. The shor run ransonal responses o an ncrease n B are approxmaely he mrror mages of hose o (n secon above), and may be explaned analogously. Much of he explanaon may be explaned by equaons (10 ) and (11 ) where operaes n he reverse drecon, and ( ) falls on mpac.

36 30 Wh respec o dsrbuon, snce he echnology ncrease now occurs n he human capal secor, he mmedae rse n wage rae s offse. The consumpon-wage rao now rses, bu declnes hrough he subsequen ranson. Ths causes wealh nequaly o ncrease durng ranson as dscussed above (hrough he savngs channel). Once agan, he long-run level of nequaly depends on he nal endowmens. When hs s unform, wealh nequaly ncreases by 1% bu wll declne by 2.5% f he nal heerogeney s due o human capal endowmens alone. Ths mechansm could parly explan he recen ncrease n ncome nequaly n he US. Beween 1975 and 1995 he Gn coeffcen n he US ncreased by 6.4 Gn pons. The perod also wnessed he wdespread adopon of IT echnologes. Adopon of IT echnologes ypcally requres a hgher level of human capal/skll. I has been argued ha he resulng producvy ncrease leads o greaer wage nequaly, and hence greaer ncome nequaly. Our analyss mples ha an ncrease n he echnology parameer would also affec he dsrbuon of ncome hrough s effec on he reurns o capal physcal as well as human and labor. In he long run, real wages of unsklled labour fall. Acemoglu (2002) shows ha real reurns o low-sklled (10 h percenle) have eher sagnaed or fallen n he las 30 years. Capal ncome meanwhle, falls by much more. Ths, coupled wh he fall n effecve wealh uns, causes ncome nequaly o fall on mpac. In he long run hough, he ncreasng wealh nequaly domnaes, causng ncome nequaly o also rse, by 1.0% [Panel B, Fgure 2.10 (a)]. In he case where he nal dsrbuon of physcal capal s he same for all agens (λ =0) and ncome nequaly dynamcs are drven by he nal endowmens of human capal, nequaly falls on mpac and hen rses owards s new lower seady sae, a fall of 2.5% [Panel B, Fgure 2.10 (b)]. In conras, when he nal dsrbuon of human capal s he same for all agens (λ = ), nequaly shows a marked ncrease of 5.2% [Panel B, Fgure 2.10 (c)]. 6 Concluson Human capal, parcularly ha aaned hrough educaon, has replaced physcal capal as he prme engne of growh [see Ehrlc (2007), Galor and Moav (2002)]. Greaer educaon ncreases he skll and producvy of workers, whch ncreases he oupu of goods and servces. Evdence provded by Goldn and Kaz (2001) and Abramovz and Davd (2000) sugges ha over he perod n he Uned Saes he conrbuon of human capal accumulaon o he

37 31 growh process has nearly doubled whereas he conrbuon of physcal capal has declned sgnfcanly. The relaonshp beween growh and nequaly remans largely unresolved, despe he nensve research devoed o over he pas 50 years. Emprcal evdence s nconclusve, some auhors fnd a negave relaonshp beween hese varables, whle ohers oban a posve relaonshp. Alesna and Rodrk (1993) fnd a negave relaonshp beween nequaly and growh. Persson and Tabelln (1994) conduc emprcal analyss for a sample of 56 counres, pos World War II, from and also fnd a negave relaonshp beween growh and nequaly. Caselló and Doménech (2002) fnd a robus negave relaonshp beween growh and nequaly usng nal human capal nequaly raher han ncome nequaly. K.J.Forbes (2000), uses emprcal analyss o predc a posve relaonshp beween economc growh and ncome nequaly, especally when he shor erm mpac s consdered. Gven ha hese varables are smulaneously and endogenously deermned, hey need o be specfed whn he conex of a complee growh model. There are some dfferences beween earler work and relaed leraure, and our model. Whereas earler work has focused on he effec of wealh nequaly on growh, n our framework, he dsrbuon of wealh has no mpac on growh. We look a he mpac of ner-secoral movemens n resources on he growh-nequaly radeoff, raher han demographcs. We fnd ha he nal source of heerogeney and he secoral locaon of he shocks are he prmary deermnans of he fnal level of nequaly. There are mporan polcy mplcaons ha may be drawn from hs. A shock o he oupu secor, whle reducng nequaly, does no rase growh raes. Thus, some sor of a polcy combnaon ha ncreases he producvy of he oupu secor whle encouragng growh n he educaon secor could gve a more favorable radeoff beween nequaly and growh. I explore hs furher n my hrd paper.