Growth and Unemployment: towards a theoretical integration

Transcription

1 Growh and Unemploymen: owards a heorecal negraon Fabo R. Arcò Deparmen of Economcs and Quanave Mehods Unversy of Pava Va San Felce, Pava Ialy Fax f.arco@unpv. Sepember 21 ABSTRACT We observe n he leraure of he pas decade some nnovave conrbuons denfed a relaon beween economc growh and long run unemploymen. Ths se of conrbuons s composed of very few elemens, all characerzed by a hgh degree of heerogeney abou her feaures and abou her fnal resuls. In he frs par of he survey we provde a classfcaon of hese early conrbuons. In he second par we explore some alernave formulaons of he problem and we presen a wder se of models dsplayng neresng feaures, able o promoe furher sudes abou he perssence of unemploymen n a growng economy. Keywords: growh, unemploymen, job-search, human capal, sraegc complemenares, co-ordnaon falure. JEL classfcaon: E24, J21, J64, O41. I. Inroducon Economc growh and Labour economcs have been regarded so far as wo separae felds of nvesgaon, dealng wh dfferen ssues and developed wh dfferen ools. In spe of hs general saemen recenly seems ha a heorecal negraon beween growh and unemploymen mgh be consdered somehng possble and even desrable. The revoluon of Endogenous growh heory, sared a he end of he 8s, has no ye exhaused s poenales n producng new conrbuons. Deparng from he Solow-Ramsey paradgm hs process of dffuson generaed a heerogeneous se of models. These models allowed o produce a ferle ground o grow new deas and o develop new ools for he economc analyss. A smlar sory can be old abou developmens n Labour economcs. The debaes amongs Monears and Keynesan vews of unemploymen, as well as new conrbuons of Lucas approach and he New Keynesan Economcs, have generally assumed a sac perspecve n respec of he producve capacy of he sysem. I s obvous ha, under hs assumpon, here was no pon o accoun for growh n a model of unemploymen. A sgnfcan nnovaon occurred wh Pssardes (199) formulaon of an unemploymen heory n equlbrum. He formalzed n a unque framework many prevous aemps o sudy he labour marke n a dynamc perspecve, provdng useful ools o analyse boh long run and shor run unemploymen. Pssardes also nroduced a frs lnk beween 1

2 long run unemploymen and growh (see Pssardes (199), Ch. II), machng hs model wh he neoclasscal framework of economc growh. The man resul founded by Pssardes s a posve correlaon beween growh and unemploymen based on a capalzaon effec. When he labour marke s no frconless hs effec reles on he fac ha frms are much more wllng o nves n new vacances durng he perod of hgh growh. An alernave vew was suggesed by Aghon s and How s (1994). They presened a model based on he Schumpeeran dea of creave desrucon, o show ha he relaon among growh and unemploymen s acually much more complex han n Pssardes framework. Ther general saemen clams ha, because of he nerplay of compeng effecs, he sgn of he relaon beween growh and unemploymen can be eher posve or negave. Ther model conssenly predcs ha hgh raes of growh are negavely correlaed wh unemploymen, whle low raes of growh are posvely correlaed wh unemploymen. In a dfferen conrbuon, based on sraegcal neracon among he agens, Acemoglu (1997) suggess a hrd way o explan he presence of unemploymen n a model of echnologcal change, whch reles on he concep of sraegc complemenares and co-ordnaon falure. The leraure abou growh and unemploymen formalzed n a dynamc general equlbrum envronmen s sll based on very few conrbuons. Ths jus seems o be he very begnnng of an neresng and mporan debae. The perssence of unemploymen as a long run phenomenon sll represens (especally for European counres) a core ssue ha needs o be solved hrough a convncng explanaon and an opporune se of remedes. Acually he urge for furher sudes s self-evden. Ths survey means o presen he mos mporan conrbuons abou he presence of unemploymen n a growng economy, suggesng furher alernave and possble explanaons for hs phenomenon. For hs reason he arcle can be deally dvded n wo pars. In he frs par we wll nroduce he recen leraure abou he opc of growh and unemploymen, whch wll be summarzed n Secon II. In he second par we wll provde a classfcaon of some early conrbuons n he feld of Growh heory, whch seem able o generae a ferle ground for furher research. In Secon III we wll focus on he characerscs of he labour supply and on he heerogeneous dsrbuon of sklls among dfferen workers. In Secon IV we wll sress he relevance of complemenares of facors, processes and sraeges as a possble cause of unemploymen. The man resuls and observaons wll be summarzed n Secons V. 2

3 II. Technologcal change, growh and unemploymen The research abou he opc of growh and unemploymen ook place n he mddle of he las cenury, hanks o he semnal works of Harrod (1939) and Domar (1947). These were mporan bu solaed conrbuons n growh heory snce hey have no been followed by any relevan debae n leraure. The affrmaon of Solow s (1956) model and of s Ramsey-Cass- Koopmans formulaon was based, n spe of earler descrpons of he growh process, on subsuably among facors, flexble coeffcens of he producon funcon and nelasc supply of npus. These core assumpons of he neoclasscal paradgm led growh heorss o focus on models based on a balanced pah wh effcen allocaon of resources. Technologcal progress was nroduced as exogenous varable and he seady sae of he model was ofen deermned ndependenly n respec o he degree of embodmen of echnologcal progress. Ths fac dsplaced any neres regardng any form of heerogeney nsde he economy, allowng o buld aggregae models whou loss of generaly. These common feaures clarfy he reason why long run unemploymen was oally ruled ou by neoclasscal growh models, whch have represened for a long perod he leadng, f no unque, ool o nvesgae economc expanson. For he reasons explaned above he leraure abou growh and unemploymen s new and no exensve. Afer almos ffy years seems ha he ssues rased by he Harrod-Domar model reurned back o he economss aenon. The nroducon of dynamc ools for he analyss of he labour marke and he dffuson of he Endogenous growh research programme represened wo basc seps ha allowed esablshng a frs lnk beween hese wo felds. A he end of he 198s Endogenous growh models sared o develop ncreasng neres abou he specfc feaures of he cumulave facors, showng ha he seady sae may be no unque, neher effcen. In he same me Labour economcs abandoned s sac, shor run perspecve, n order o re-defne conceps and ools ap o nvesgae he perssence of unemploymen n he long run. The concurrng effecs of hese wo processes generaed a ferle ground o develop furher sudes abou he presence of unemploymen n a growng economy, sarng a process whch s jus a he very begnnng, bu ha dsplays hgh poenales for producng more fruful resuls n he fuure. We can denfy wo man ses of conrbuons abou he opc of growh and unemploymen. In he frs se he ssue s developed devong much more aenon o he nsuonal cones of he economy, buldng models ha are defnely more polcy-orened. In he second se of conrbuons we observe models ha are more specfcally concerned wh echnologcal processes and wh he nerplay of mulple heerogeneous facors. In our opnon hese models 3

4 are sll characerzed by a descrpve aude, raher han suggesons abou he polcymakng. On he oher sde, hey are beer mcro-founded and flexble for developng furher sudes. Belongng o he frs se of conrbuons we remark on he work by Gordon (1995), who mean o provde a common explanaon o he producvy slowdown and hgh employmen of he US and he relavely hgh growh, hgh employmen of European counres. Gordon clams ha he rade-off beween growh and unemploymen may occur n he shor run, generaed by srucural shocks, lke wage shocks. The rade-off dsappears n he long run, hrough o a process of dynamc adjusmen. Anoher famous conrbuon dealng wh he effec of fscal polcy n a growng economy was provded by Daver and Tabelln (2). The auhors presen a heorecal model suppored by a wde se of emprcal evdence, ap o nvesgae he relaon beween growh, unemploymen and axaon n he ndusralzed counres. Daver and Tabelln clam ha f he wage-seng mechansm s affeced by any form of rgdes, such as he presence of a monopolsc unon, he role of fscal polcy s deermnan for he denfcaon of a rade off beween growh and unemploymen. The man dea reles on he fac ha, when wages are proeced by a monopolsc unon, axng labour ncome deermnes an ncrease n he real wage rae. An ncrease n he cos of labour gves ncenve o frms o subsue capal for labour, lowerng he margnal producvy of capal. Tha dsplaces nvesmens, hus slowng down economc growh. The emprcal evdence provded by Daver and Tabelln shows ha he ax-effec on he level of unemploymen can be permanen even when he effec on he wage rae s jus emporary. In anoher neresng conrbuon, Cahuc and Mchel (1996) nvesgae he role of mnmum wage n a model of endogenous growh. Lke Daver and Tabelln (2) hey develop a model of overlappng generaons. In her model he labour force s composed of a group of sklled workers and a group of unsklled workers. The echnology dsplays consan reurn o scale and s nfluenced by he presence of a socal exernaly generaed by he process of human capal accumulaon, followng Lucas (1988). The presence of a mnmum wage, usually denfed as one of he causes of unemploymen, plays an mporan role n hs model, deermnng a hgh relave demand for sklled labour. Snce a hgher relave prce for unsklled labour ncreases he demand for sklled labour, raonal workers fnd an ncenve o nves n human capal n order o avod unemploymen. Ths enhances he posve effec of he socal exernaly, supporng boh growh and employmen. 4

5 As a las example we repor he presence n leraure of a conrbuon by Van Schack and De Groo (1998). The auhors mach growh and unemploymen hrough a re-nerpreaon of he Solow s condon n a model of endogenous growh wh effcency-wages 1. The modfed verson of he Solow s condon nerpres he level of labour effcency as he resul of R&D acves performed n a hgh-ech secor, deermnng a lnk beween he nvenon acvy and he unemploymen equlbrum deermned on he labour marke. In all he prevous examples he role of he nsuons s deermnan o denfy he lnk beween economc expanson and he labour marke. We wll now urn o he second se of models of growh and unemploymen. Removng all of he consderaons concerned wh he srucure of axaon and he rgdy of wages, s n our nenon o show ha one can sll denfy many oher dfferen lnks beween growh and unemploymen. These lnks are nmaely relaed wh he characerscs of he accumulaon process and wh he sraegc behavour of he agens. We wll focus our aenon n deeper deal abou hese ssues. We wll depar from he heory of job-search, developed by Pssardes (199) n hs semnal work, and we wll subsequenly consder some of he developmens and conrbuons ha followed hs approach, whch s he closes o he neoclasscal radon. We wll hen analyse he neo-schumpeeran approach of Aghon and How (1994) and her aemp o provde some mcro-foundaons of labour marke dynamcs, relaed wh he effec of creave desrucon emergng from he nvenon process. We wll fnally consder a hrd approach by Acemoglu (1997), whch wll be compleely based on he sraegc neracon of frms and workers. 2.1 Pssardes and he job-search heory The basc framework The semnal work by Charles Pssardes (199) represens a frs and complee collecon of job-search models 2. Chaper II of hs book s compleely dedcaed o job-search and growh and consss of one of he frs aemps o explan he presence of unemploymen n a growng economy. The model adoped s an exenson of he Neoclasscal growh model wh exogenous echnologcal progress. A hs frs sage here s no am o endogenze changes n echnology. 1 For an nroducon abou he leraure on effcency-wages consder n example: Sglz (1976), Shapro and Sglz (1984), Akerlof and Yellen (1986). 2 See also Pssardes (2). The new edon presens some developmens abou he basc ssues nroduced n Pssardes (199) and collecs an exensve bblography of he mos recen works relaed wh job-search. 5

6 Search-heory assumes ha acvy on he labour marke s uncoordnaed, me-consumng and cosly. A proper machng funcon represens he resul of hs acvy as he number of maches n funcon of he number U=uN of unemployed workers and he number V=vN of vacances avalable n he economy a a ceran pon n me. mn = m( un,vn ) [2.1.1] The funcon m s concave, homogeneous of degree one and ncreasng n boh argumens. Concavy s assumed n order o represen a congeson exernaly ha akes place n he labour marke. The more vacances opened by he frms, he shorer he search-effor of unemployed workers; he more unemployed workers on-search n he labour marke, he faser mach avalable for each frm. Saed ha θ=v/u, we can express: q(θ)=m(un,vn)/vn=m(v/u,1) as he rae of recrumen by he frms. Workers flows move ou of and no unemploymen. Job-specfc shocks occur accordng wh a Posson process of rae λ and deermne he end of a mach wh a frm. We can wre he dynamc evoluon of unemploymen n he followng form: u! = λ( 1 u ) θq( θ )u [2.1.2] On he rgh sde of equaon [2.1.2] he frs erm represens he flow of workers no unemploymen and he second erm he flow of workers ou of unemploymen. In seady sae we can express he rae of unemploymen n funcon of he parameer λ and of he labour marke ghness θ. u = λ /[ λ + θq( θ )] [2.1.3] Equaon [2.1.3] s he Beverdge-curve, usually represened as a convex o he orgn and downward-slopng relaon on he (U,V) space of he labour marke. Pssardes assumes ha frms produce he fnal good usng capal and labour hrough a cosan reurn o scale (CRS) echnology, concave and ncreasng n boh facors: y = F K, AL ) [2.1.4] ( Equaon [2.1.4] can be expressed n s nensve form: y=f(k). We assume a frs ha each frm can open only one vacancy. The frm engages a research acvy for machng hs vacancy wh a worker affordng a hrng cos per un of labour denoed by z. When he vacancy s mached, he frm rens capal a rae r and produces oupu y. Frms evaluae he presendscouned revenue of a vacan job W and he presen dscouned revenue of a mached job J, n order o sasfy he Bellman equaon: rw = z + q( θ )( J W ) [2.1.5] On he lef sde expressed he capal cos, where r ndcaes he neres rae. On he rgh sde he value of he rae of reurn s obaned by summng he hrng cos and he expeced ne 6

7 revenue n he occurrence of a job mach. In equlbrum here are no rens for vacan jobs, so ha f W=: J = z / q( θ ) [2.1.6] The job-creaon equaon [2.1.6], expresses ha he prof belongng o a new job s equal o he expeced cos of hrng a worker. A smlar evaluaon s performed for each mached job, by usng he Bellman equaon: r( J + k) = f ( k) δk w λj [2.1.7] The lef sde represens he asse value of a mached vacancy plus he value of rened capal. The rgh sde expresses he prof emergng from a flled job, where w s he cos of labour and δ s he rae of deprecaon of capal. Subsung equaon [2.1.6] n equaon [2.1.7] we oban ha 3 : ( r + λ) z f ( k) ( r + δ ) w = [2.1.8] q( θ ) In order o derve a complee specfcaon of he seady sae, a descrpon of he wage-seng mechansm s requred. Pssardes observes ha n a labour marke descrbed as an uncoordnaed and cosly acvy, he sum of expeced reurns of a searchng frm and expeced reurns of a searchng worker s srcly nferor o he reurns emergng from a job mach. There s presence of rens generaed by each mached job ha are o be shared beween profs and wages. The soluon suggesed s he adopon of a Nash-bargan mechansm, whch leads o he followng resul: [ f ( k ) ( r + δ )k θz] w = π z + (1 π ) + [2.1.9] The equlbrum wage equaon expressed n [2.1.9] s he soluon of he barganng problem. I resuls o be a weghed average beween he benef for unemploymen b and he margnal producvy of labour, augmened of he average hrng cos θz. Parameer π ndcaes he prof share. The congeson exernaly n he labour marke dsplays s lnear effecs on he equlbrum wage hrough parameer θ. Equaons [2.1.3], [2.1.8], [2.1.9] deermne he seady sae confguraon for (u,θ,w). Ths basc model can now be exended n order o oban exogenous growh. Exogenous dsemboded echnologcal progress can occur, assumng ha he producvy parameer A n equaon [2.1.4] ncreases over he me and for all he frms n a classcal labour-augmenng fashon. A γ = A e [2.1.1] 7

8 Each frm can now open a wder number of vacances, denoed by V. I s assumed ha he number of frms s large enough o elmnae uncerany abou labour flows. The wage seng mechansm follows he same Nash-barganng mechansm descrbed by equaon [2.1.9]. Ths assumpon abou wage-seng mechansm s conssen wh resuls f a marke for capal does exs and here are no long-erm conracs. In fac each frm decdes how many jobs are o be creaed by ancpang he correc wage, bu he same frm assumes he wage as gven when he number of jobs s acually saed. The sream of frm ' s expeced profs s expressed by: r Π = e [ F( K,AL ) wl zav K! δk ]d [2.1.11] The dynamcs of he labour force for each frm s descrbed by: L! = q( θ )V λl [2.1.12] Profs are maxmzed n respec o capal and number of vacances opened, subjec o he consran expressed by [2.1.12]. For gven pahs of A and θ, Euler s condons guaranee he exsence of an opmal pah for K and L. The seady sae s obaned seng o zero equaon [2.1.12], when: V λl = [2.1.13] q( θ ) To oban conssency n seady sae, we assume ha he unemploymen benef b and he hrng cos z are boh ndexed wh he level of wages: b=b w, z=z w. The new wage-equaon urns no he followng expresson: 1 π w = A[ f ( k ) ( r + δ )k ] [2.1.14] 1 πz ( 1 π )b θ Solvng he neremporal opmsaon problem for equaon [2.1.12], condons for he seady sae are derved. As long as F(K,AL ) s homogeneous of degree one can express hese condons n erms of uns of effcen labour, hrough he use of he nensve form: f ' ( k) = r + δ [2.1.15] [ f ( k ) kf ' ( k )] ( r + λ γ ) A = w + z w [2.1.16] q( θ ) The margnal producvy of labour equals he wage pad o he workers, plus a erm whch accouns for he frcons of he labour marke. Subsung equaon [2.1.16] n equaon [2.1.14] we denfy a fnal condon for he labour marke ghness θ: 3 Equaon [2.1.8] can be regarded as a labour demand relaon, whch s downward slopng n he space (w,θ), even when he producvy of labour s consan. 8

9 r + λ γ π b ( 1 π ) zθ (1 π ) z = [2.1.17] q( θ ) From equaon [2.1.17] we fnd ha γ and θ are, ceers parbus, posvely relaed. Tha s due o he dynamcs whch le behnd he frm s prof maxmzaon process. Consderng Euler s condons for maxmzng equaon [2.1.11] can be shown ha each frm s supposed o afford hrng coss oday for he sream of profs wll earn omorrow. We assumed ha profs and hrng coss boh grow a he same rae n seady sae so, wh hgher growh raes, frms wll fnd raonal o open more vacances oday n order o save hrng coss of omorrow, hus obanng an ncrease n he sream of profs. Ths denfes he capalzaon effec whch s based on he forward-lookng behavour of frms ha are supposed o maxmze her profs. A change n he rae of growh deermnes a change n he opmal choce of frms abou he number of vacances o be opened, reflecng s effecs on he labour marke. The model sll lacks he means o deermne he rae of neres, whch s denfed by he demand-sde of he economy. Pssardes follows a radonal dynamc IS-LM approach. The law of accumulaon of capal s defned from: K! = Y δk C [2.1.18] The aggregae consumpon s defned as a fxed amoun β of he dsposable ncome: ( Y δk + ( p )M / P ) C = β µ! [2.1.19] Where: µ s he rae of growh for money, p! s he rae of nflaon and M/P expresses he real balances. The LM balance condon closes he model: M / P = g( r + p! ) Y g < [2.1.2] From he demand-sde se of equaon one can derve he followng seady-sae condon: [ 1 βγg( r + µ γ )] f ( k) [(1 β ) δ + γ ] k = β [2.1.21] Equaon [2.1.21], ogeher wh equaon [2.1.15], deermnes r and k n seady-sae. We have already observed ha he rae of growh s negavely relaed wh he rae of unemploymen from he supply sde s perspecve. From equaon [2.1.21] we noe ha an ncrease n he growh rae lowers he capal rao per un of effcen labour, deermnng an ncrease n he rae of neres r. Through equaon [2.1.17] hs affecs he labour marke ghness and he effec can be eher posve or negave, dependng on he sgn of he dfference r-γ. Whle he supply-sde of he model deermnes a unvocal relaon among growh and unemploymen, he fnal effec can be eher posve or negave when one consders he demand-sde dynamcs. 9

10 Endogenous consumer s behavour Pssardes (199) defnes he aggregae consumpon as a fxed amoun of dsposable ncome. Erksson (1997) presens a slghly dfferen verson of he model, developng he demand-sde on he lne of he Ramsey-model. Ths modfcaon can urn no an neresng ool o nvesgae he feedback mpac generaed by he labour marke on he rae of growh of he economy. Assumng ha each consumer dsplays a consan neremporal elascy of subsuon (CIES) nsananeous uly funcon: 1 σ ( C 1) / 1 σ U j = j [2.2.22] The household s budge consran s defned by: K! = ( 1 τ ) rk + w(1 u) L + b wul C + VI [2.2.23] j j Households are all dencal. Each household accouns for he me spen n producon ( 1 u)l j and he me spen n unemploymen ul j as well as needs o consder he renal ncome derved from pung ou vacances VI j. The parameer τ represens he ax rae on capal ncome. Re-expressng he consumpon n un of effcen labour and solvng he neremporal opmsaon problem for he households one fnds ha: c = σ 1! ( f '( k) ρ σγ )c [2.2.24] From equaons [2.1.15], [2.2.24] and [2.2.23], expressed n effcency uns, one can deermne he responsveness of k, c and he new endogenous varable r n respec of he parameers of he model. The rae of neres becomes posvely varyng n respec of he ax rae τ, he elascy of subsuon σ, he rae of neremporal subsuon ρ and of he rae of growh γ. Compung he effec of a varaon of he growh rae on he marke ghness and of a varaon of he marke ghness on unemploymen, Erksson deermnes a posve relaon beween growh and unemploymen, under he assumpon ha he elascy of neremporal subsuon s small enough. Techncally, Erksson showed ha dr/dγ=σ/(1-τ), so ha f σ<1- τ, hen an ncrease n γ decreases he dfference (r-γ). From equaon [2.1.17] hs urns no a lower level of he marke ghness and a subsequen ncrease n unemploymen. Snce all he parameers of he model dsplay a posve relaon wh he rae of neres, one can even focus on he demand sde of he model, concludng ha f eher σ or ρ ncrease, he rae of neres ncreases, sressng he rade-off beween growh and unemploymen. Erksson shows how an apparenly slgh change of he orgnal model deermnes an oppose resul n respec o wha was obaned by Pssardes (199). Endogenzng he rae of neres 1 j o j j j

11 allows o explore n deal he nerplay of he labour marke wh he mechancs of growh. The rae of neres assumes a key role n Erksson s specfcaon of he model. Every knd of nervenon whch s mean o lower he rae of neres deermnes hgher employmen. A smlar resul s obaned when he rae of growh s endogenously deermned by some cumulave facor whch susans he fall of he producvy of capal n equaon [2.2.24]. The rae of growh becomes much more responsve o a change of he parameers, and he rade-off beween growh and unemploymen can be sll denfed. Endogenous growh and unemploymen: Neoclasscal and Keynesan feaures Bean and Pssardes (1993) presened furher developmens of he basc model of job-search. They bul an overlappng generaon model where boh growh and unemploymen are endogenous varables: hs allows us o analyse anoher knd of feedback effec ha unemploymen generaes on growh. Ther framework s based on an exenson of he basc overlappng generaon model by Damond (1965), where hey nroduce a echnology whch dsplays decreasng reurns o capal a he frm level, bu consan reurns a he aggregae level, followng he benchmark case of Romer (1986). As a second assumpon, he auhors nroduce a cosly process of machng beween workers and frms. In a frs phase, he model smply dsplays n seady sae endogenous growh wh posve rae of unemploymen. In a second phase, Keynesan feaures are nroduced nsde he model, assumng mperfec compeon n he goods marke. The model s enrched wh many dfferen parameers whch can accoun for polcy nervenon. The auhors are parcularly focused on he effec of changes n aggregae savngs. They argue ha unemploymen can reduce he pool of savngs and, subsequenly, he nvesmens necessary o enhance accumulaon of capal. Deparng from hs observaon, hey use her model o nvesgae how dfferen knds of polcy nervenon can affec he endogenous varable hrough he mechansm descrbed above 4. In he model a reducon of he hrng coss deermnes an ncrease n he number of vacances creaed by frms. Ths enhances unemploymen and generaes an ncrease n he pool of savngs, whch smulaes accumulaon of capal and enhances growh. In hs case an nervenon orened o he labour marke deermnes posve effec for boh growh and unemploymen. When he nervenon s dreced o ncrease he workers barganng power, he resuls are much more ambguous. A hgher wage dscourages frms from openng new 4 We wll refer here o Caballero s commens o Bean and Pssardes (1993), whch are enclosed a he end of her paper. Caballero summarzes he man resuls and presens some frs consderaons abou he emprcal evdence of he lnk beween growh and unemploymen. 11

12 vacances, ncreasng unemploymen. On he oher sde hgher ncome for workers urns no an ncrease n he pool of savngs, whch could smulae growh. The ne effec on he pool of savngs canno be deermned a pror. Adopng mperfec compeon n he goods marke, when he mark-up margn s suffcenly hgh, one observes ha an ncrease of he margnal propensy o consume can ncrease he pool of savngs and smulae growh despe wha could be predced under Classcal assumpons. The auhors assume ha hrng coss are valued n erms of consumpon. If he prce for consumpon goods rses, hrng coss rse and unemploymen also rses. A reducon n he propensy o save rases he employmen level. In hs case he effec s so srong ha also generaes an ncrease n he pool of savngs, enhancng growh hrough accumulaon of capal. Ths new framework by Bean and Pssardes (1993) can urn no an useful ool o nvesgae he mpac of dfferen polces on boh he endogenous varables. The model s based on a wder se of assumpon, such as expressng all he coss n erms of consumpon and assumng sandard condons for deermnacy of he seady sae n he overlappng generaon model. Of course resuls become more precse, bu less robus. Workers on acve search In he basc framework of he job-search model only frms are assumed o ncur n a cos o mach workers wh her opened vacances. Workers are jus supposed o be passvely wang for a mach, comparng her perspecve ncome wh he opporuny cos of beng unemployed. Kng and Wellng (1995), on he conrary, assume ha workers need o bear a drec cos when hey decde o acvely search for a new job, whle frms can creae vacances whou any cos. The auhors develop a model where frms belongng o dfferen spaal locaons can receve dfferen locaon-specfc shocks. The frms are also affeced by economy-wde exogenous echnologcal progress. Under raonal expecaon hypohess, workers fnd an ncenve o move o hgh-producvy dsrcs snce hey can ncrease her expeced ncome n erms of wage. In seady sae one fnds ha, n he presence of acve cos of search for workers, he rae of search s an ncreasng funcon of he growh rae and oal unemploymen s a decreasng funcon of he growh rae. Ths resul allows us o show a dfferen mechansm of deermnaon of equlbrum unemploymen. In boh Pssardes (199) and Kng and Wellng (1995) here s a negave correlaon beween growh and unemploymen, bu n Pssardes (199) he amoun of search 12

13 s decreasng wh he sze of nnovaons, snce more vacances are opened hrough he capalzaon effec. In Kng and Wellng (1995) he rae of search s ncreasng snce workers ry o move o more producve dsrcs. In he model he concep of wang-me unemploymen s also nroduced, and hs occurs when he worker does no move, bu jus was for an mprovemen of he condon of her/hs own dsrc. Wang-me unemploymen, as well as oal unemploymen, s a decreasng funcon of he rae of growh. The key assumpon on whch Kng and Wellng (1995) derved her resuls s based on he presence of a drec cos for acve search for workers ha does no seem o fnd much suppor n leraure. Neverheless Kng and Wellng (1995) show ha he presence of asymmery beween he raonal choce of workers and frms s a basc assumpon for he resul derved abou he rae of search. More, we fnd neresng he dea of developng he presence of spaally dsnc locaons affeced by dfferen shocks. The auhors clam ha hs assumpon can be even nerpreed as he presence n he economy of dfferen producve opporunes, o be mached wh specfc ypes of human capal by heerogeneous workers. The posve relaon beween he rae of search and he rae of growh could be nerpreed as an ncenve for workers o devoe much me o human capal accumulaon when he nnovaons are larger. Ths would mply ha n perods of expanson here s less search whn a professon and more swchng beween professons. We wll develop hs ssue n he nex secons. 2.2 The neo-schumpeeran approach o growh and unemploymen Aghon and How (1994) presened one frs neresng reply o Pssardes (199) aemps o consder growh and unemploymen n a jon way. They exended her basc model of creave desrucon o ake no accoun he problem of labour reallocaon across he frms. A few years laer furher exensons have been brough o hs model n her conrbuon on endogenous growh heory (See Aghon and How (1998)). Aghon s and How s (1994) model s based on an economy consued by a connuum of nfnely lved agens, ndexed on he space [,1]. Each household s endowed wh a flow of one un of labour servce ha s/he supples o frms. S/he s also endowed wh a sock of h unes of human capal. All he households dsplay he same preferences and he same neremporal uly funcon over he fnal good y: U( c ) = E ρ c ( y )e d [2.2.1] 13

14 The number of frms s endogenously deermned n seady sae. Aghon and How defne he frm as: [ ] an nsuonal embodmen of knowledge, n oher words [ ] a research facles for producng new knowledge, for generang new deas. [Aghon and How (1994), p.479]. Seng up a new plan requres a sunk cos D, whch rses a he seady sae growh rae: D =D e γ. Once seled, each plan produces a sream of nnovaon, followng a Posson process of rae λ. Producon of he fnal good s performed combnng a machne ha embodes a specfc echnology, an approprae worker o be mached wh he machne and a varable amoun of human capal: y = A f ( h h ) [2.2.2] mn The funcon f(.) dsplays all he neoclasscal feaures and Inada condons are assumed as well. In he basc framework he producvy parameer A s exogenously deermned and followng he sandard exponenal rule: A =A e -γ. The Posson process descrbes he flow of nnovaons for he frm. If a frm decdes o conver he nnovaon projec n new echnology, wll afford an mplemenaon cos C and he new process wll be avalable a me. Unemploymen s generaed n he model by labour-reallocaon across frms. In fac, as long as a frm does no nnovae, wll no be able o cover s fxed cos and wll be forced o close forcng he worker no unemploymen. The worker wll sar lookng for a new mach wh anoher frm. The machng process s deermnsc and s descrbed followng a machng funcon of he ype adoped by Damond and Blanchard (1989) and Pssardes (199). The machng funcon s assumed o dsplay all he neoclasscal sandard feaures. The recrumen rae q(v) for a frm searchng a new worker wll be a decreasng funcon of he number of vacances n he economy. For each worker lookng for a new mach he jobfndng rae υ wll be an ncreasng funcon of he whole number of vacances. Assume ha he duraon of each mach akes S un of me. A worker forced no unemploymen wll wa 1/υ(V) uns of me before fndng a new job. On he oher sde a frm ryng o assocae a worker wh a new machne, wll wa 1/q(V) uns of me before obanng a proper mach. Aghon and How denfy a suaon of nvolunary unemploymen f workers spend more me lookng for a job han workng: 1/υ(V)>S. Denong by u he rae of unemploymen we can sae he equlbrum condon for flows ou o and no unemploymen: ( 1 u )( 1/ S ) = υ(v ) [2.2.3] If we assume S consan and echnologcally deermned, equaon [2.2.3] can be re-wren as: u = 1 Sυ(V ) [2.2.4] 14

15 Ths s a Beverdge curve, represenng he ypcal negave relaon beween vacances and unemploymen. Aghon s and How s man purpose consss on expressng he Beverdge curve n funcon of echnologcal change. Through a progressve process of specfcaon hey nes growh generaed by nnovaon no he labour marke s seady sae condon expressed by [2.2.4]. Whenever a frm decdes o nnovae, say a me, sars lookng for a specalzed worker. A mach s obaned a me +1/q(V) and he producon process can begn. The maxmzaon condon for each frm s: max h hmn { A f ( h h ) p h} = A Π ( p / A ) mn 15 [2.2.5] The prce for human capal grows, as well as he oher prces and coss, a he seady sae rae: p =p o e γ. I follows ha he frm needs o nnovae o survve n he long-run. In fac, f he level of A does no grow, he prof wll decrease and fnally falls o zero a me +S, forcng he worker no unemploymen. If no nnovaons are nroduced, a me +S human capal reaches a rgger value p max whch deermnes null profs for he frm. We can express he duraon of a mach n he followng way: p S p + γs A = A e = p max [2.2.6] S = Γ / γ Γ = log (p max ) log (p o /A ) > [2.2.7] Subsung equaon [2.2.7] no equaon [2.2.4] we oban: u = 1 Γ υ(v ) / γ [2.2.8] Ths shows ha growh generaes a drec creave desrucon effec on unemploymen, acng hrough a reducon of he duraon of he job mach. Aghon and How denoe ha oher compeng effecs of growh on unemploymen are o be aken no accoun. These effecs work ndrecly hrough he dynamc mechansm of enrance of new frms no he economy and hrough he clearng equaon on he human capal marke. Consder he flow of dscouned expeced profs for a frm ha s gong o ener no he marke: rε W = WA = E [(V W )e ] [2.2.9] ε + ε + + ε Where +ε denoes he dae of he frs nnovaon for he frm whch eners a and V +ε =VA +ε s he presen value of he sream of profs generaed by he nnovaon occurred a +ε. Solvng equaon [2.2.9] one obans ha: W = λv /( r γ ) [2.2.1]

16 Denong by d he sunk cos he frm has o afford, he free-enry condon wll be: d = λv /( r γ ) [2.2.11] Equaon [2.2.5] represens he sream of profs ha an nnovaon provdes durng he mach [, +S]. As n Pssardes (199), frms and marke se he wage hrough a barganng mechansm. Frms oban a prof-share π: π 1. Each mach requres an mplemenaon cos, denoed by Z =za. An nnovaon nroduced a me a, sars o generae profs a me 1+1/q(V), when an approprae mach wh a worker occurs. A hs me he mplemenaon cos s pad and he frm obans a sream of profs lasng a me 1+1/q(V)+S. Consderng wha saed wh equaons [2.2.5], [2.2.6] and [2.2.7] we can fnally express he dscouned sream of profs generaed by a frm: Γ / γ / τ = / s max γs Γ V e r π e r Π ( p e )ds z [2.2.12] obanng a defnve formulaon for he free-enry condon: λ / Γ γ r / τ r / s max γs Γ d = e π e Π ( p e )ds z [2.2.13] r γ If he growh rae γ ncreases wo compeng effecs wll emerge: I wll decrease he ne rae a whch he sream of profs s dscouned. For each frm he enry wll resul less cosly. More vacances wll be creaed, reducng he unemploymen rae. (Capalsaon effec). I wll reduce he lfe-me of each frm (see equaon [2.2.8]), by ncreasng he prce for human capal. Each nnovaon wll generae fewer vacances han before. Tha wll be refleced n an ncrease of he rae of unemploymen. (Indrec creave desrucon effec). Consderng equaon [2.2.8] we can observe ha creave desrucon deermnes a drec negave effec on unemploymen hrough he duraon of each mach and he parameer Γ. I also deermnes an ndrec effec hrough he reducon of V, whch lowers he job-fndng rae υ(v). To close he model we fnally consder he clearng condon for human capal marke: Γ 1 max χ Γ H = (1 u ) h( p e )dχ [2.2.14] Γ The lef sde represens he aggregae supply of human capal n he economy. The rgh sde s he demand sde, obaned by mulplyng he labour force for he demand of human capal of each frm, where χ=γs: χ [,Γ] s he echnologcal age of he plan. From equaon [2.2.14] 16

17 we can deduce ha Γ, maxmum echnologcal age for a plan s an ncreasng funcon of he rae of unemploymen and a decreasng funcon of he aggregae sock of human capal n he economy. The seady sae for he sysem s a confguraon (u *,V *,Γ * ) ha guaranee: clearng on human capal marke, a consan unemploymen rae, a consan number of vacances, fxed a he level ha ses o zero he profably on he free-enry condon. Dfferenly parameersed smulaons for he model refleced only wo possble resuls: a reverse U-shaped relaon beween growh and unemploymen or a monoone ncreasng relaon beween growh and unemploymen. The presence of many parameers drves o a complex explanaon of he effecs of growh on unemploymen, bu smulaons seemed o f wha happens n realy. Aghon and How exended her framework o accoun for flexble rae of neres, endogenous growh, and learnng by dong. Endogenous growh was nroduced adopng he resuls presened n Aghon and How (1992). Learnng by dong effecs seem o be he mos neresng feaure of hese new exensons. Suppose nroducng a learnng mechansm, whch depends on he level of workers employed n producon: γ = γ + α(1 u ) α u >, γ > [2.2.15] The new defnon for he rae of growh affecs he free-enry condon expressed n [2.2.13]. The producvy of each mach wll depend on he consan rae of growh γ and on he share of growh based upon he learnng process. The fnal effec urns o be ambguous. An ncrease n unemploymen deermnes an ncrease of he echnologcal age of each machne Γ, as seen n he human capal marke clearng equaon. Tha ncreases he number of vacances V wh a posve effec, reducng fuure unemploymen. An ncrease n unemploymen also deermnes an ncrease n he dscoun rae for he sream of expeced profs and a reducon of learnng-by-dong on each mach. The laer effec occurs as long as less workers n acve labour force generae less aggregae learnng spllovers. The auhors assume ha learnng s a process ha nvolves all he producve uns, so ha does no generae creave desrucon effecs. An ncrease n he learnng performance of households wll no deermne reallocaon, bu only unemploymen reducon. On he oher hand he learnng process generaes a feedback effec ha mgh also generae sraegc complemenares n he sense of Cooper and John (1988) and hen mulple equlbra. The economy could be rapped n a suaon of low growh, low learnng and hgh-unemploymen. 17

18 The nervenon of a planner would be requred o move he sysem on a Pareo-preferred equlbrum. In he earles verson of he model (see Aghon and How (1998a)) he perfec subsuably hypohess among nermedae good has been removed 5 bu nohng was old abou he demand of fnal goods. The demand sde of he model s reduced o a very smple problem of uly maxmzaon, where he uly funcon s assumed o be lnear. Consumers do no perform consumpon-smoohng. More, households can be eher employed or unemployed, bu hey are assumed o consume he same amoun of good n each perod. Tha s less lkely o be rue, as long as he same feedback effec ha was presened for learnng-by-dong can be expermened regardng he demand for he fnal good. Inroducng a demand-sde no he model could lead us o conclude ha as long as less workers are n he acve labour force, here wll be less consumpon and ha wll reduce he ncenve o frms o ener and creae new vacances. Even n hs case sraegc complemenares could arse. 2.3 Coordnaon falures, growh and unemploymen Acemoglu (1997) crczes he recen leraure abou he problem of growh and unemploymen, ponng ou ha none of he conrbuons presened consders he problem of labour supply. Labour s carefully descrbed n erms of demand, bu no many consderaons are spen regardng worker sklls n relaon o specfc echnologes. Acemoglu focuses on hs aspec, presenng a model wh wo compeng echnologes and poenal heerogeney among workers endowed wh dfferen sklls. The frs exsng echnology requres a fxed cos, normalzed o, whle he second echnology requres a new machne a he fxed cos d>. The new machne needs o be mached wh a sklled worker o produce a sream of producvy y+α. Boh he frs echnology and he second, f no properly mached wh a sklled worker, produce a sream of producvy equal o y. Suppose ha he labour marke allocaon mechansm s descrbed by a sandard random machng funcon. If he proporon of sklled workers n he unemploymen pool s u skll, he probably ha a sklled worker wll be mached wh a vacancy wll also be u skll. Job-specfc shocks occur a he exogenous rae λ, and deermne he end of a mach. 5 Inroducng mperfec subsuably o produce he fnal goods allows emphaszng he role of he capalzaon effec. In fac, n a sysem wh low degree of subsuably among nermedae goods an nnovaon ha occurs n one secor wll reflec posve effecs n many oher secors and employmen wll rse. The creave desrucon effec wll be lower. 18

19 Assume ha he sysem s n seady sae when he new echnology becomes avalable. In any pon n me each frm may decde abou openng a new vacancy a flow cos c, adopng he new echnology for producon. Invesng n he new echnology, he frm may also choose wheher o ran an unsklled worker a cos χ. Assumng ha θ represens he ghness on he labour marke, he seady sae condon a me = s expressed by equaon [2.1.3]. The value of a frm adopng a new echnology wh a flled job s denoed by J N. The value s denoed V N, when he vacancy s sll avalable. Values J and V wll denoe he same quanes when he frm has no adoped he new echnology. Le us now consder he followng se of Bellman equaons: rj rv N N J! V! N N N N N = y + α w + λ(v J ) ( 1 u skll )max = c + q( θ ) N + u skll ( J V N N ON N { J V χ; J V,} N ) [2.3.1] Where r s he fxed neres rae, he frs equaons sae ha he perod value of a frm wh a N flled job s equal o he nsananeous capal gan J!, plus he ne produc y+α-w N, plus he opporuny cos of he sream of prof obaned n he case a job-specfc shock occurs, expressed by λ. The second equaon saes ha he perod value of a frm wh an open vacancy s equal o he nsananeous capal gan, mnus he cos of openng a vacancy and plus a weghed average of he dfferen profs he frm can earn f fllng up he vacancy a probably q(θ). The worker mached wh he frm can be sklled and so able o generae he sream of profs: J N -V N. In he case ha he worker s unsklled, he frm wll decde f s worh o ran hm, a he cos χ, leavng hm unsklled obanng he sream of profs J ON -J N, or leavng he vacancy unflled wh a null prof. A second se of Bellman equaons descrbes smlar condons for a frm ha does no adop he new echnology: rj rv J! 1 V! = y + α w + λ(v J ) ( 1 u skll )max = c + q( θ ) + u skll max + N { J V ; J V d χ} + { } N N J V ; J V d; Assume ha: m denoes he number of frms adopng he new echnology, [2.3.2] nskll he number of sklled workers employed n frms adopng he radonal echnology, n 1 unskll he number of unsklled workers employed n frms adopng he new echnology. Acemoglu derves he 19

20 dynamcs for he pool of unemployed sklled workers, obanng he followng dfferenal equaon: Quanes m and n 1 u! = θq( θ )[ m(1 n ) + ( 1 m )n u ] [2.3.3] skll 1 unskll unskll skll are deermned by equaons [2.3.1] and [2.3.2] and hey consequenly deermne he flow of sklled workers no and ou of unemploymen. Wages are seled hrough a Nash-bargan game, where workers are assumed o dsplay a bargan power of (1-π). No-arbrage condons are also assumed for equlbrum: V =, V N =δ. Under he above assumpons from equaon [2.3.1] and [2.3.2] we can oban he followng condons: J N ( ) = J ( ) = [(1 π )( y + α ) + λd] /[ r + λ] [(1 π )y]/[ r + λ] skll [2.3.4] A new echnology s adoped when: J N J + d + χ. Ths condon depends on he marke ghness θ and can be re-wren as: [ rd + ( r + λ ) χ] /( 1 β ) 1 α α θ ) [2.3.5] ( If he condon expressed n equaon [2.3.5] holds, Acemoglu shows ha he sysem wll move owards an equlbrum where he new echnology wll be adoped progressvely by all he frms and where frms wll decde o ran all he workers. The dynamcs are deermned hrough he marke ghness θ, whch shfs from an nal value θ o a fnal value θ 1, where u θ1 ( θ ) u( ). Acemoglu observes ha a coordnaon falure could arse f we assume ha each frm expecs ha no oher frms wll adop he new echnology. In hs case one of he wo no-arbrage condons does no hold any more (V N d). Frms ha loose her workers because of a random shock wll no be able o sell he machne embodyng he new echnology. They wll also expec no possbles n fndng a new sklled worker (u skll =), snce all he workers sll wll be sll unsklled on he labour marke. The new condon o nves n he nnovave echnology wll be: α 1 α ( θ ), where: α ( θ ) α ( θ ) [2.3.6] The effecve cos for nvesng n he new echnology wll be hgher n respec o he case 1 expressed by condon [2.3.5]. The auhor demonsraes ha f ( α θ ), α ( θ )) α here ( wll exs wo pure sraegy symmerc equlbra for hs game beween frms. In one equlbrum here wll be no nnovaon and hgh unemploymen, n he oher equlbrum here wll be nnovaon and lower unemploymen. 2

21 Expecaons abou he echnology adoped by frms deermnes a knd of sraegc complemenary whch nfluences he acual rae of unemploymen. Ths resul s acheved whn an neremporal horzon model, where he relave frequency of sklled workers n he unemploymen pool s dynamcally upgraded over he me by equaon [2.3.3]. Ths seems o sugges a way o nroduce he sac concep of Nash-equlbrum n a dynamc envronmen. III. The role of human capal In he prevous secon we presened some resuls already obaned o model unemploymen n a growng economy. We now mean o explore alernave soluons o he problem, referrng o he recen exsng leraure abou growh. I s our purpose o show ha some of he models and mechansms adoped o descrbe he growh process dsplay uncovered poenales o provde an explanaon for he perssence of unemploymen n he economy. We noed ha he models based on Pssardes framework are much more lnked wh he neoclasscal concepon of physcal capal nerpreed as he basc accumulang facor. A slghly dfferen and neresng nerpreaon abou he presence of heerogeneous sklls can be found n he spaal model by Kng and Wellng (1995), even f no deeply developed. The neo-schumpeeran approach, on he oher hand, assumes he presence of heerogeneous workers o be mached wh dfferen echnologes, bu he aenon s focused on he decsonal algorhm of he enrepreneur, leavng he workers o be passvely wang for a mach. The process of mach s hdden nsde he black box, represened by he machng funcon. In Acemoglu s (1997) framework, explc consderaon abou he heerogeney of he labour supply does no rely on a machng funcon, bu he dynamcs of he dsrbuon of sklls s sll analysed as an aggregave resul. The leadng role s sll assgned o frms ha, n hs case, sraegcally nerac n he economy. In hs secon we mean o focus on he role of human capal, devong parcular aenon o he dsrbuon of sklls across he pool of workers. In our opnon, modellng hs knd of heerogeney among agens can urn no an neresng ool o analyse he relaonshp beween growh and unemploymen. The Endogenous growh revoluon ha occurred a he end of 198s, gave a deermnan conrbuon n hs sense. In he neoclasscal framework capal sock has radonally been consdered he mos mporan cumulave facor. In spe of ha a large number of endogenous growh models emphaszed he feaures of he labour force. 21

22 3.1 Educaon and human capal Followng Lucas (1988) re-exposon of human capal heory, some models have nroduced new and more complex defnons of labour as a producve facor, fndng ha could be assgned he leadng role n he accumulaon process. Ths fac can be very useful for our analyss f he dsrbuon of he labour force can lead o a beer explanaon for he perssence of unemploymen n a growng economy. Lucas (1988) arbued o he workers a personal deny hrough he dfferen endowmen of human capal ha hey decde o cumulae before enerng he process of producon. Ths dea was no developed any furher n hs model and all he sgnfcan resuls were derved a he aggregave level. Sokey (1991) followed Lucas conrbuon, nroducng a relaon beween heerogeney of workers and heerogeney of goods. Heerogeney of workers s defned by Sokey n erms of dfferen levels of human capal whch hey decde o cumulae before enerng he process of producon. Each agen ses he quany of me o dedcae o educaon. The agen compares hs nvesmen wh he opporuny cos of a hgher wage durng he me devoed o producon. Invesng me n educaon he agen unconscously deermnes an ncrease of he aggregae sock of knowledge no he sysem. S/he s no able o ake no accoun he exernal effec refleced n he whole economy, whch s deermnan o generae growh. Heerogeney of goods s defned by her echnologcal nenses. Goods provdng a hgher number of Lancaseran characerscs are goods whch requre more specalzed workers o be produced. The echnology adoped consss of a CRS neoclasscal producon funcon, unchangng over me. Technologcal progress s defned n hs framework as droppng lowernensy goods and addng hgher-nensy goods n he producon se of he economy (see also Sokey 6 (1988)). Ths process s generaed by he exernal effec ha allows mprovng echnologcal sklls and expandng he upper bounds of he producon se. Sokey s man goal s provdng an explanaon for he leadng role of nernaonal rade n deermnng dfferen paerns of human capal specalzaon and goods producon. To acheve hs goal, Sokey removes he classcal hypohess of perfec subsuably among sklled and unsklled labour: sklled labour performs hgher-qualy servces o produce echnology-nensve goods dsplayng more characerscs. Even f he man am of Sokey s work s dealng wh pah dependence and nernaonal rade, we can underlne some neresng feaures abou he composon of he labour force. The 6 In Sokey (1988) s presened a formalzaon of hs process, by whch upper and lower bounds over he horzon of characerscs ncrease over he me. The bounds move n funcon of he level of knowledge prevously cumulaed nsde he sysem. 22

23 paper explcly consders he problem of allocang heerogeneous workers over producon of dfferen goods. Removng he hypohess of perfec subsuably among dfferen workers we could nfer a frs cause of unemploymen, whch may arse n a conex of growh. We can even hnk abou hs feaure n a dynamc way. If nernaonal rade has a really srong nfluence on labour specalsaon and producons mgh happen ha he dsrbuon of workers across dfferen lnes of goods could be locked-n by nernaonal marke mechansms. Le us suppose ha one counry dsplays a hgh share of s oupu composon oally devoed o expor. If an exernal shock affecs he demand for he man se of goods produced by ha counry, unemploymen could rse. In fac producon could no be easly swched o dfferen and more profable goods as long as he dsrbuon of workers s locked-n. The conclusons presened are jus conjecures, derved by a smple framework bul wh dfferen purposes, bu hey sress he mporance of core assumpons, (lke labour mperfec subsuably and labour and goods heerogeney) ha may be nroduced o hnk abou unemploymen n a growng economy. 3.2 Learnng-by-dong and human capal The examples presened above nerpre human capal as he resul of nvesmen n educaon. We wll now consder anoher model developed by Lucas (1993). Ths framework collecs Sokey s conrbuons abou lock-n mechansms and maches hem wh a dfferen formulaon of susaned growh dependng on allocaon of labour across dfferen lnes of producon 7. In hs case he man mechansm s no based on educaon, bu on learnng-bydong. Lucas defnes an economy wh a connuum of goods x, ndexed by s, such ha s [,S]. x = A L h [3.2.1] s, s α s, s, Sklled labour hl s he only facor of producon. The level of accumulaed skll s represened by h, where α expresses he effec of prevously accumulaed skll on he acual level of producon. A s a producvy parameer. Learnng-by-dong s he leadng process ha allows cumulang sklls over he me: h! = L h [3.2.2] s, α s, s, A any pon n me, he acual level of ably n producng he good s depends on a sarng level of knowledge referred o me and on he flow of workers who prevously gave her conrbuon o he producon of good s: 7 For anoher smlar example, developed whn a dynamc nerpreaon of he bg-push mechansm of growh, see also Temple and Voh (1998). 23