Helmu-Scmd-Unversä Unversä der Bundeswer Hamburg Unversy of e Federal Armed Forces Hamburg Fäcergruppe Volkswrscafslere Deparmen of Economcs Dscusson Paper Nr. January 005 36 Mddle-Class Consensus, Socal Capal and e Mecancs of Economc Developmen Sefan Derc Josen
Mddle-Class Consensus, Socal Capal and e Mecancs of Economc Developmen Sefan Derc JOSTEN Insue of Publc Fnance, Helmu-Scmd-Unversy Hamburg, Germany. Absrac Ts paper analyzes a eerogeneous-agens endogenous-grow model ncorporang bo ransacon coss and socal capal. An ndvdual can eer become an acve par of e socey s mddle-class neworks of rus and muual cooperaon, us makng a posve conrbuon o overall socal capal. Alernavely, e ndvdual can say socally dsnegraed and free-rde on e communy s socal capal. Due o e exsence of asymmerc nformaon, agens face a moral-azard problem on e cred marke wc gves rse o ransacon coss and can be allevaed by prvae, governmenal or socal governance srucures. An ncrease n nequaly and srnkng of e mddle class depresses e communy s socal capal, wc, n urn, weakens e nformal socal governance sysem and ncreases economy-wde ransacon coss. As a resul a more unequal dsrbuon lowers e economy s grow rae. JEL Classfcaon: D3, O4, Z3 Keywords: Socal Capal; Inequaly; Mddle Class; Economc Grow ; Dsrbuon. Correspondence o: Dr. Sefan D. Josen, Insu für Fnanzwssenscaf, Facberec WOW, Helmu-Scmd- Unversä, Unversä der Bundeswer Hamburg, Holsenofweg 85, D-043 Hamburg, F. R. G. Pone and e-mal: Tel.: + 040 654-38, Fax: + 040 654-069 e-mal: sefan.osen@unbw-amburg.de.
Mddle-Class Consensus, Socal Capal and e Mecancs of Economc Developmen * By e problem of economc developmen I mean smply e problem of accounng for e observed paern, across counres and across me, n levels and raes of grow of per capa ncome. Ts may seem oo narrow a defnon, and peraps s, bu nkng abou ncome paerns wll necessarly nvolve us n nkng abou many oer aspecs of socees oo... (Rober E. Lucas (988, p. 3)). Inroducon One of e mos mporan ssues n economcs s e problem of economc developmen as defned by Lucas (988) n e quoe gven above. Wa causes economc grow and us prospery for e people of e world?, n parcular: Were do e uge dfferences n economc grow and developmen wc can be observed across counres n e real world come from? Neoclasscal grow eory ells us a f all economes were nrnscally e same excep for er sarng capal nenses, en convergence would apply n an absolue sense;.e., poor counres would end o grow faser per capa an rc ones. If, on e oer and, economes dffer n varous respecs e.g. propenses o save, propenses o ave cldren, wllngness o work, access o ecnology, and governmen polces en e convergence force apples only n a condonal sense: Te grow rae ends o be g f e sarng per capa GDP s low n relaon o s longrun (seady-sae) poson. As can be seen, many of ese convenonal, exbook explanaons of cross-counry dfferences n economc grow and developmen merely move e ssue o anoer, more fundamenal level. If, e.g., dfferences n savng raes across counres deermne cross- * Ts paper as benefed from several commens made by parcpans of e Annual Conference of e European Publc Coce Socey (EPCS) 004 n Berln and e 004 Annual Congresses of e Inernaonal Insue of Publc Fnance (IIPF) n Mlano and e Veren für Socalpolk n Dresden. Te usual dsclamer apples.
counry ncome or grow-rae dfferences, en wy do some socees save more an oers? If muc of e nernaonal dfferences n grow raes are explaned by dverse governmen polces, en wy do publc nsuons n some counres perform sysemacally beer an ose n oer counres? Te dssasfacon w explanaons of cross-counry dfferences n grow and developmen by endogenous varables as led o a recen searc n e leraure for more fundamenal caracerscs of socees a deermne developmen oucomes. Te presen paper pus forward e exsence of a broad mddle class e members of wc sare w eac oer a farly omogenous se of socal orenaons ( mddle-class consensus ) and e socal capal bul by socal neracons and nformal relaonsps wn s mddle class as crcal deermnans of an economy s grow and developmen. Accordngly, s paper s movaed by and relaed o wo recen srands of leraure: Frs, ere s e leraure on e economcs of socal capal wc wll be deal w n some deal n secon below. Secondly, ere s e leraure on e role of e mddle class or, more generally, of nequaly for economc grow and developmen. W respec o e role of e mddle class for economc developmen ere exss an odd dcoomy n economcs beween s sorcal and s analycal brances. On e one and, economc sorans ave long been empaszng e mporance of a large mddle class for economc developmen. E.g. Landes (998) reflecng on England s leadng role n e process of ndusralzaon pons ou a e deal grow and developmen socey would be caracerzed, among oer ngs, by a relavely large mddle class (pp. 7f.). Te developmen leraure and economss, on e oer and, ave been vrually slen on e mddle class. Only recenly, Easerly (00) pus forward e exsence of a mddle-class consensus as a crcal deermnan of nernaonal developmen dfferences. Defnng a mddle-class consensus as a suaon of
relave equaly and enc omogeney, e goes on o sow emprcally a suc a mddle-class consensus faclaes ger levels of ncome and grow, as well as ger levels of publc goods. Snce mddle class s bo n s general meanng and as defned n e model presened below essenally a dsrbuve caegory, e presen paper s also nexrcably lnked o e large (and ye sll growng) leraure on nequaly and grow. A number of emprcal cross-counry sudes fnd g nequaly measured n several sudes by e sare of qunles 3 and 4,.e. by e sare of e mddle class lnked o poor grow performances. Smulaed by bo e emprcal evdence and e emergence of endogenous grow eory, e eorecal leraure as, n urn, worked ou ree basc ses of ransmsson cannels roug wc nequaly n ncome and/or weal dsrbuon mg acually slow down economc grow: Frs, ere are economc cannels. For example n Agon and Bolon (997), capal marke mperfecons deny e poor o e effcen amoun of nvesmen; w decreasng reurns a e ndvdual level, redsrbuon o e less endowed wll be grow enancng snce e laer s margnal produc s ger. 3 A second economc cannel sems from e fac a nequaly affecs an economy s demand srucure and may erefore nfluence nnovaon ncenves (see Zwemüller (000) or Masuyama (000)) and economc developmen (see Murpy e.al. (989)). In addon, ere are polco-economc cannels. In models endogenzng bo economc grow and publc polcy, ncome nequaly 3 A noable excepon are Adelman and Morrs (967, p.30) wo noe a n e economc developmen of Wesern Europe, e mddle class were a drvng force and, accordngly, e grow of a robus mddle class remans of crucal mporance n conemporary low-ncome naons. A survey and overall assessmen of early sudes can be found n Bénabou (996). Noe, owever, a snce e emergence of Dennger s and Squre s (996) new daa se on ncome nequaly e overall emprcal evaluaon of e effecs of nequaly on grow as become muc more blurred. In parcular, Forbes (000) and Barro (000) fundamenally callange prevous fndngs of a negave nequaly-grow relaonsp. However, bo Forbes (000) and Barro (000) use panel daa and esmaon meods, us removng couny-specfc effecs and focusng on sor-erm neremporal varaons, wle e argumen of bo e presen paper and mos of e prevous leraure on nequaly and grow refers o long-run grow effecs of nequaly. Furermore, Dennger and Olno (000) fnd a even n Forbe s (000) and Barro s (000) economerc meodology weal nequaly, as measured by e dsrbuon of land, sll as a causal negave effec on grow. Furer semnal papers wn s subse of eory nclude Galor and Zera (993); Baneree and Newman (993); and Bénabou (996). 3
nfluences e balance of power n e polcal sysem n suc a way as o generae pressure o governmen o ncrease ncome redsrbuon a, n urn, reduces ncenves and, ereby, slows down economc grow. 4 Te presen paper ams a glgng a rd se of cannels lnkng nequaly and grow a as receved muc less aenon n e leraure: soco-economc ransmsson mecansms. 5 To do so, s paper adds o e exsng leraure n wo sgnfcan ways. Frs, presens an endogenous grow model n wc eerogeneous agens ransac under asymmerc nformaon, wc gves rse o a moral azard problem and economy-wde ransacon coss. 6 Secondly, supplemens e model s economc secor by an endogenous, raonal- coce dervaon of socal negraon, mddleclass formaon and socal capal buldng. An ndvdual can eer become an negral par of e socey s neworks of rus and muual co-operaon, us makng a posve conrbuon o overall socal capal. Alernavely, e ndvdual can say socally dsnegraed, parcpae n e socey s economc ransacons bu no conrbue o e communy s socal capal, us freerdng on oers nvesmens n soco-srucural resources. Wn s formal framework, e presen paper sows a, wen e gap beween e rc and e poor wdens n a socey, e sze of e mddle class wose members make posve conrbuons o e value of resources embedded n e socey s nformal relaonsps srnks, wle e sare of socal drop-ous n e populaon ncreases. Te economy s socal capal wll be depressed wc, n urn, ncreases economy-wde ransacon coss and, ereby, slows down capal accumulaon. As a resul, nequaly and economc grow are nversely relaed. 4 5 Imporan conrbuons o s feld of sudy nclude Berola (993); Alesna and Rodrk (994) as well as Persson and Tabelln (994). Pero (993), as well as San-Paul and Verder (993), combne asse marke ncompleeness w e polcs of redsrbuon. Noable conrbuons o s feld of sudy nclude Alesna and Pero (996), Benabb and Ruscn (996), as well as Knell (999). Accordng o e former wo, nequaly may lead o soco-polcal nsably and may us ave a dermenal effec on economc grow. Knell (999) consders e grow effecs of nequaly and sausseekng n a socal comparson model w dfferen degrees of saus preferences for young and old ndvduals. Te basc resul s a e negave mpac of nequaly on grow s aggravaed f ndvduals are more saus-orened. 4
Te res of e paper proceeds as follows. Secon provdes a defnon of socal capal and dsls from e emergng economc eory of socal capal four sylzed facs wc are relevan for e curren analyss. Secons 3 and 4 develop e formal framework of analyss, sarng w decenral opmzng decsons of ndvdual agens and en movng o aggregae varables descrbng macroeconomc beavour and e economy s equlbrum grow pa. Secon 5 explores e effecs of ncreased nequaly on e economy s grow rae and secon 6 concludes by provdng a summary of resuls.. On e Economcs of Socal Capal: A Defnon and Four Sylzed Facs Te soco-economc explanaon of e nequaly-grow lnk proposed n e presen paper s based on e general dea a resources embedded n socal neworks of muual rus and cooperaon reduce ransacon coss and are, us, an mporan deermnan of long-run economc performance. Te concep of socal capal provdes a useful umbrella erm o capure e nuon and growng awareness among some (oug no all) economss a socey maers. 7 Tere s no sngle defnon of socal capal, bu raer varous approaces o e concep exs. For e purpose of s paper, I coose a defnon wc s closely relaed o Coleman s (988, 990) orgnal concep and defne socal capal as e se of soco-srucural (symbolc) resources lke values, norms, roles and moral oblgaons a nere n sysems of socal relaons, or socal aggregaes, and a faclae co-operave beavour wn or beween ese socal aggregaes. Wle as sad varous approaces o e noon of socal capal exs, one can denfy ceran sylzed facs abou socal capal on wc mos socal capal eorss seem o agree. Four of 6 7 Te basc ransacon-coss se-up follows Zak and Knack (00) wo, owever, do no make use of an endogenous grow model bu ulze a neoclasscal producon funcon. For nsance, Gradsen and Jusman (000) presen a polcal economy framework n wc publc scoolng conrbues o economc grow no only by buldng uman capal bu also by nsllng common norms a ncrease socal coeson. See also Gradsen and Jusman (00). Temple and Jonson (998) empasze a socey 5
em wc are of parcular relevance for e ssues dscussed n e presen paper wll be oulned more closely n e followng: () Socal capal exbs publc good caracerscs. Coleman (988, 990), among oers, empaszes e publc-good caracerscs of soco-relaonal feaures a are useful o ndvduals for specfc acons. Once provded, ese collecve asses and feaures are nonrval n consumpon and ey are avalable o all members of e communy, regardless of wc members acually promoe, susan, or conrbue o suc resources (non-excludably). 8 () Socal capal s produced by ndvdual nvesmen of me and effor, bu n a less drec way an s uman or pyscal capal. As an arbue of e socal srucure n wc a person s embedded, socal capal s no e prvae propery of any of e persons wo benef from. Accordngly, many of e benefs of acons a brng socal capal no beng are experenced by persons oer an e person so acng,.e. ere are posve exernales, and, us, ndvdual ncenves o nves n socal capal are sysemacally depressed. However, many forms of socal neracons and neworks also eer ave nrnsc value or are nexrcably nerwned w prvae, nsrumenal benefs for sngle agens. 9 As a resul, mos forms of socal capal are bul as a by-produc of varous socal acves no necessarly underaken w a vew o srengen socal capal. Punam (993) gves e example a members of Florenne coral socees parcpae because ey lke o sng, no because er parcpaon srengens e Tuscan socal fabrc. () An essenal par of e nsrumenal value of socal capal les n e fac a reduces ransacon coss by provdng an nformal governance srucure agans opporunsc beavor. In 8 9 maers for grow for reasons oer an rus or socal capal. However, ey also sow a one of er ndexes of socal capably may be a useful proxy for socal capal n developng counres. An mporan example s onesy. If eac communy member s ones n commercal ransacons, all of socey benefs due o e reducon of e coss of dong busness. Suc cos reducons are caracerzed bo by nonexcludably and non-rvalness. E.g., accordng o Bur (99) nformaon and nfluence (over one s own auonomy or a of oers) are wo ypes of prvae benefs flowng from socal neworks. However, a rd ype of benef may be denfed n e form of socal soldary nvolvng co-operaon, a sense of socal duy and recprocy no founded on any mmedae payback for ose conrbung o e welfare of oers. 6
a world of bounded raonaly, posve ransacon coss and mperfec foresg, conracs are necessarly ncomplee, ncompleely self-enforcng and ncapable of dealng w all relevan aspecs of uman acon and conngences. Furermore, ere exs sysemac ncenves for opporunsc beavor bo before (ex ane) and afer (ex pos) a ransacon akes place. In suc a seng, socal capal can work o reduce ransacon coss by embeddng sngle economc ransacons n a sysem of socal relaons, us acng as an nformal governance srucure agans opporunsc beavor. Among oer ngs, soco-srucural resources a nere n sysems of socal relaons generae expecaons, nformal rules of umb and common undersandngs a allow agens o conduc er personal neracons und busness dealngs effcenly. Welldeveloped neworks are also lkely o reduce ransacon coss bo by reducng searc coss and by renforcng complance w group norms. Fnally, e g levels of rus assocaed w socal capal are crcal for many ransacons a ake place n e conex of an ndvdual formng expecaons abou acons of oers a ave a bearng on s ndvdual s coce of acon, wen a acon mus be cosen before e or se can observe e acons of oers ( Dasgupa (000), p. 330). (v) Growng nequaly of ncome and weal leads o a declne n socal capal. Knack and Keefer (997), Knack (999) and Zak and Knack (00) all fnd rus and ncome equaly o be posvely correlaed a e cross-counry level. Usng US sae-level daa, Kawac e. al. (997) also argue a ncome nequaly lowers socal capal. Based on a broad survey of relevan emprcal sudes, Punam (000, p. 359) concludes a bo across space and across me, equaly and fraerny are srongly posvely correlaed ; e goes on o clam a e recen declne n socal capal n e US s lnked o growng nequaly of ncome and weal. 7
3. Socal Capal, Transacon Coss, and Economc Grow. A Smple Model To llusrae e basc neracons beween socal capal, ransacon coss and economc grow, le us consder an economy w a connuum of nfnely-lved consumers wo dffer only n er respecve ownersp sares n e economy s aggregae socks of capal and labor. Eac consumer seeks o smoo s consumpon over me by savng. However, o access e capal marke consumers ave o ulze nvesmen brokers. Only e brokers know e acual reurn earned on an nvesmen and us face a moral-azard problem. Te brokers ncenves and opporuny o cea er clens are couneraced by ree poenal governance mecansms: Frs of all, consumers can spend me nvesgang er brokers n order o reduce e laer s ably o cea (prvae governance srucure). Secondly, ere exs formal nsuons, ncludng among oers: fnancal regulaons, nvesgave agences a oversee brokers, and e udcal sysem a enforces conracs and prosecues ceaers (governmenal governance srucure). Trd and fnally, a broker s opporunsm can be sanconed by nformal nsuons (socal governance srucure). Informal sancons depend on, or are faclaed by, a sysem of socal relaons a ranscends e sngle ransacon. Economc ransacons are us embedded n a socal srucure a deermnes e rewards for co-operaon or penales for devaon. Accordngly, nformal sancons wll be e more effecve, e ger an economy s socal capal. Te closed economy modelled below consss of four secors of economc agens: a secor of frms producng e economy s sngle good; an (mplc) governmen secor provdng a governmenal governance srucure wc s fnanced va lump-sum axes pad by prvae ouseolds; a secor of eerogeneous nfnely-lved prvae consumers; and fnally a secor of nvesmen brokers wo are dsnc from consumers and dencal o eac oer n all relevan respecs. Economc agens nerac on a goods marke, a labor marke and a capal marke. 8
Frms and Facor Paymens Te key o endogenous grow of e modelled economy s e neracon of learnng-by-dong and knowledge spllovers. Accordng o Arrow (96), e creaon and adopon of knowledge s mos closely relaed o experence. In parcular, e consders a frm s nvesmen a good measure for s frm s ncrease n experence and knowledge, snce eac new macne produced and pu no use s capable of cangng e envronmen n wc producon akes place, so a learnng akes place w connuous new smul (Arrow (96), p. 57). Romer (986) uses Arrow s se-up and combnes w e second key assumpon a eac frm s knowledge s a publc good a any oer frm can access a zero coss. In oer words, once dscovered, a pece of knowledge splls over nsanly across e wole economy. More formally, consder a neoclasscal producon funcon w labor-augmenng ecnology for frm, Y = F K, W L ), () ( were Y denoes e frm s oupu wc s a funcon of e frm s sock of pyscal capal, K, e frm s labor npu, L, and e ndex of knowledge avalable o e frm. Funcon F ( ) sasfes e usual neoclasscal properes and pyscal capal deprecaes a rae δ wc s dencal for all frms. Combnng e assumpons of learnng-by-dong and knowledge spllovers oulned above, A can be replaced by economy-wde capal K n equaon (). Assumng, furermore, a e producon funcon akes e Cobb-Douglas form, e producon funcon for frm can be wren as Y = A K KL, 0 < α <. () α α Y ( ) ( ) Le us assume a eac frm s small enoug o neglec s own conrbuon o e aggregae capal sock and erefore reas K as gven. Denoe by ~ ~ y : = Y L, k : = K L, ~ y : = Y L and ~ k : = K L e usual nensve varables, were L gves aggregae labor npu. In equlbrum, all frms make 9
e same coces, so a ~ y ~ ~ ~ = y and k = k. Economy-wde producon n nensve form s us gven by ~ ~ K α α y = AY k, (3) and e average produc of capal amouns o ~ y ~ = A k α Y L. (4) Accordng o (4), e average produc of capal s ncreasng n e sze of e aggregae labor npu. On e oer and, s average npu s nvaran w respec o e capal sock k because e learnng-by-dong and spllover effecs elmnae a e socal level e dmnsng reurns o pyscal capal wc eac sngle frm faces. Assumng, as usual, a eac compeve frm akes facor prces as gven, prof maxmzaon and e zero-prof condon mply producve facor npus o be pad er respecve prvae margnal produc: Y r + δ = K = αa L Y α (5a) Y w = = α KL L α ( ) AY, (5b) were r denoes e ne neres rae (renal prce of capal) and w s e wage rae per labor un. Te prvae margnal produc of capal s nvaran w respec o e capal sock, s less an e average produc and s ncreasng n L. Houseolds and Facor Accumulaon Te economy s ouseold secor consss of a connuum of eerogeneous nfnely-lved consumers, ndexed by [0,], wo dffer only n er respecve relave endowmen w 0
producon facors labor,, and capal, k. For analycal racably, le us assume a all consumers are endowed w e same amoun of pyscal capal,.e. a ; k0 = k0. 0 Tus a me ey dffer only n er ndvdual endowmens w e non-accumulaed facor labor. Te aggregae labor endowmen of e economy s normalzed o uny: ; H : = d. Eac ndvdual can earn ncome from bo capal and labor. However, o access e capal marke consumers ave o ulze nvesmen brokers. Only e brokers know e acual reurn r earned on an nvesmen and, due o s asymmerc nformaon, ey are able o approprae a ceran fracon of a reurn on nvesmens. Consumers ave access o an nvesmen nvesgaon ecnology: + η [ e, p, S]:[0,] [0,], w η e > 0, η p > 0 and η S > 0 (6) wc perms agens o deermne e fealy of brokers n reporng nvesmen ncome. Tecnology (6) gves e fracon of e acual reurn o an nvesmen a e consumer receves from s broker. Ta fracon s deermned by ree alernave governance srucures agans e 0 broker s opporunsm: A prvae ouseold devoes a fracon e of s ndvdual labor endowmen o nvesgae e acual reurn on s or er nvesmens. Secondly, formal nsuons, provded by e governmen and funded by a lump-sum ax τ pad by consumers, seek o deec and puns ceang brokers; le er effecveness be denoed by p. Trd and fnally, a broker s opporunsm can be sanconed by nformal nsuons, e effecveness of wc s deermned by e economy s socal capal S. All ree governance srucures ac o consran e brokers 0 Snce capal s an accumulaed facor, ndvdual capal socks may, n prncple, dverge over me; owever, wll urn ou a s s no e case n e presen model.
opporunsm, us paral dervaves n (6) are posve. Snce, furermore, e governance srucures are alernaves o eac oer, le us assume a second-order cross paral dervaves are negave. Ta par of er labor endowmen an agen devoes o nvesgang er broker se can no longer allocae o workng n goods producon. Accordngly, labor supply of consumer, l, s, a any pon n me, resrced by e + l. (7) Afer-ax ncome of consumer s us gven by y [ e, p S ] k τ = w ( e ) + rη,. (8) Le us assume a all ndvduals ave e same CIES uly funcon. Allocave decsons of e ndvdual are deermned by solvng e followng problem: θ ( c ) U = c, e 0 Max e θ ρ d dk η τ d, (P) s..: k : = = w( e ) + [ e, p, S ] r k c were θ > 0, so a e elascy of margnal uly w respec o consumpon equals e consan θ, and ρ > 0 s e subecve dscoun rae (or rae of me preference). Te necessary and suffcen condons for a consumer opmum are c c θ ( η r ρ) = (9) w = η r k e. (0) Ts model of moral azard on capal markes s adoped from Zak and Knack (00).
Equaon (9) s a sandard Ramsey rule of opmal savngs w e expeced ne yeld on savngs beng η r. Accordng o (0), e uly-maxmzng allocaon of ndvdual labor npu balances e margnal ncome earned by workng w e exra ncome one can generae by nvesgang one s broker. Snce ndvdual endowmen w pyscal capal s e same for all consumers, equaon (0) mples a n = 0 all consumers make dencal coces of nvesgave labor, e. Taken (6) * 0 no accoun, en follows from (9) a ndvdual grow raes of consumpon a me 0 are also e same for all consumers. Furermore, usng e ouseolds flow budge consran n (P) along w e ransversaly condon of (P), one can sow a all ndvduals n = 0 accumulae capal a a very same rae. Tus, nerndvdual deny of capal endowmens s preserved over me and we ave for any laer pon n me: ; k = k, e = e, η = η. * Invesmen brokers As menoned above, o access cred markes consumers mus ulze nvesmen brokers wo are dsrbued over e same nerval bu are dsnc from consumers. Brokers ake a poron of e nvesmen prncple and neres as er wage w I. For smplcy, brokers are assumed o be rsk neural and do no save. Consumpon of a represenave nvesmen broker n s, us, gven by I I { η [ e, p S ]} r k c = w =,. () See Barro and Sala--Marn (995), pp. 4f., 49 for a formal dervaon of s resul n a learnng-by-dong model w knowledge spllovers and omogenous consumers. 3
Equlbrum grow pa For e labor marke o clear n any gven perod, overall labor npu no goods producon mus equal e sum of ndvdual labor supples: L * * l d = ( e ) d = H e d = 0 0 0 = e. () Equlbrum n e capal marke requres: K ~ = k d = k = k ( e ). (3) 0 W populaon normalzed o uny, economy-wde and ndvdual capal socks concde,.e. k = K. Ulzng s normalzaon, as well as facor paymen rules (5), (0) can be wren as η = α ( e ). (4) e α For any consan values of p and S, labor spen by eac consumer on nvesgang er broker s also nvaran over me. Le us assume from now on a bo e effecveness of publc governance srucures p and e economy s socal capal S are ndeed consan over me. Accordngly, e economy s grow rae s gven by: PROPOSITION (Long-erm grow) For a gven level of socal capal, economy-wde oupu, pyscal capal sock and consumpon all grow a e common and me-nvaran rae of Y γ : = Y K = K C = C = ( αayη ( e) θ α δ ρ). (5) Proof. Acordng o (9), dynamc evoluon of consumpon and pyscal capal sock of any ndvdual consumer s caracerzed by e followng grow rae k c ; = = ( rη ρ). k c θ 4
As s grow rae s e same for all consumers, ecoomy-wde consumpon and pyscal capal sock, as well as aggregae goods producon, also grow a s rae. Takng no accoun (5a) and e me-nvarances derved above, one fnally ends up w (5). q.e.d. Accordng o (5), e economc grow rae s e ger, e ger s e fracon η of e acual reurn o an nvesmen a e consumer receves from s broker and e less labor e consumers ave o spend on nvesgang er brokers. Transacon Coss Te model economy presened so far mples a smple measure of e economy s overall ransacon coss caused by asymmerc nformaon and opporunsc beavor n e capal marke. Economy-wde ransacon coss can be expressed as e aggregae amoun of labor a agens spend on verfyng er brokers acons. Ta s, aggregae ransacon coss are gven by TC = L = * e d e. (6) 0 = 4. Socal Capal, Inequaly and Mddle-Class Consensus Socal Capal In order o formalze e nuve deas and sylzed facs presened n secon, le us assume a n perod an economy s socal capal, S, smply consss of e sum of symbolc resources, s, a eac of s ndvdual young members s wllng o embed no e socal srucure: S = s d. 3 (7) 0 3 Te followng raonal-coce dervaon of socal negraon and socal capal buldng s closely relaed o e one oulned n Josen (004). 5
Due o e publc-good caracerscs of socal capal, no ndvdual as an ncenve o drecly nves me and/or effor n s accumulaon. However, every young ndvdual raonally decdes weer se wans o become an negral par of e socal communy sarng a general socal orenaon (norms, values, language, culure, ec.) or no. If an ndvdual ops for socal dsnegraon se does no acvely promoe or susan socal neracons and neworks and, us, does no conrbue o e economy s socal capal. If, nsead, an ndvdual cooses o become an acve par of e socey s neworks of rus and co-operaon, se makes a posve conrbuon o e value of resources embedded n ese socal aggregaes. Accordngly, socal capal produced by any consumer s gven by s = > 0, f 0, f ssocally dsnegraed s socally negraed. Indvdual negraon decson Every consumer bases er raonal-coce decson on weer o socally negrae or dssocae erself on a comparson of er own advanages and dsadvanages. On e one and, beng par of a communy w sared norms, values, language, ec. wll mprove one s own appness and wellbeng. 4 To keep e exposon racable, le us smply assume a socal negraon gves any ndvdual member of socey a warm-glow uly denoed by e srcly posve consan + u S > 0. On e oer and, owever, socal negraon does no come wou coss. For one o become an negral par of e communy, one as o adap oneself o e group s common audes and socal orenaon wc, probably, wll devae from one s own. In erms of Coleman s (990) raonal-coce socology, by onng a socal communy an ndvdual gves up e rgs o conrol 4 W reference o emprcal sudes on e assocaon beween supporve relaonsps and self-repored appness and well-beng, Punam (000, p. 33) sums up a n sudy afer sudy, people emselves repor a good 6
ceran of er own acons and ransfers ese rgs o e collecvy. Ts ransfer of rgs mposes coss on e ndvdual wc are ndcaed by e dfference beween e uly level acually secured and e level wc would ave been secured under full manenance of ndvdual rgs o conrol one s own acons. As oulned n Coleman (990, 34f.), ese coss wll be all e ger, e less e ndvdual s preferred beavor s congruen w e communy s prevalen norms or expecaons. Snce, n e model above, ndvduals dffer only w respec o er labor endowmens, s naural o assume a ndvdual socal orenaon s (perfecly) correlaed w s ndvdual labor endowmen. Accordngly, e culural dsance beween consumer and e communy s socal orenaon s measured by, were : = d = H 0 denoes e communy members average labor endowmen. Furermore, Coleman s (990) reasonng mples a e larger s dsance, e ger s ndvdual s dsuly from socal negraon, as ndcaed by e followng dsuly funcon: were (, ) = 0 S S ( ) d = d,, (8) d S d S, 0, lm d (, ) = S, lm d S (, ) = 0. 5 Accordng o (8), anyone w labor endowmen equal o average wll be able o comply o e socal reference norm wou any loss of ndvdual well-beng. On e oer and, any ndvdual w wll sll be allowed o on e communy, bu wll suffer from er non-complance w e socal norms. Terefore, er aderence o e communy s socal orenaon comes a a loss of ndvdual well-beng. Wle sll enoyng e warm-glow effec of beng a par of a relaonsps w famly members, frends, or romanc parners far more an money or fame are prerequses for er appness. 7
communy, non-average ndvduals, us, ave o weg u + S agans e dsuly d S caused by er socal negraon. For any ndvdual, overall ne uly from socal negraon wll be gven by u S = u + d, S S and agen cooses socal negraon as long as er ne uly s posve. Gven e assumpons made abou (8), ere exs exacly wo crcal values, denoed by < and >, respecvely, for wc e respecve consumer wll be us ndfferen beween socal negraon and socal dsnegraon, for wc n oer words + S S (, ) = d ( ) u = d, S. (9) All ndvduals w labor endowmen beween and consue e socey s mddle class: Tey sare a common se of relavely omogenous socal orenaons ( mddle class consensus ) and acvely engage n socal neracons and neworkng, us makng a posve conrbuon o e economy s socal capal. On e oer and, ndvduals w labor endowmen below ( lower class ) or above ( upper class ) op for socal dssocaon. Tey parcpae n e socey s economc ransacons, bu ey do no conrbue o e communy s socal capal. Due o e publc-goods aspecs of socal capal, ey are, nevereless, able o capure e nsrumenal benefs of economy-wde socal capal, us free-rdng on oers nvesmens n soco-srucural resources. 5 A smlar dsuly funcon can be found n Gradsen and Jusman (000) referng o e culural dsance beween parens and cld n an encally dvded socey w publc scoolng. 8
Inequaly and Socal Capal Te connuum of ndvduals s defned over e nervall [0,]. Terefore, e fracon of consumers wo are socally dsnegraed can be expressed n erms of e value of e cumulave dsrbuon funcon of e varable, denoed by F ) (, as ( ) = F ( ) + ( F ( ) = +. (0) Due o s smple relaonsp, e effecs of an ncrease n ncome nequaly on an economy s socal capal can be derved as: LEMMA. A more unequal dsrbuon, n e sense of a smple mean-preservng spread n, s assocaed w a srnkng mddle class, wle e sare of e populaon a does no conrbue o e economy s soco-srucural resources ncreases. Accordngly, a more unequal dsrbuon lowers economy-wde socal capal. Proof. See appendx q.e.d. 5. Inequaly and Ineremporal Allocaon As sown by LEMMA, e sare of socally dsnegraed consumers and, us, e sze of e mddle class depend on e exen of nequaly prevalen n an economy. Terefore, a smple meanpreservng spread n e dsrbuon of labor endowmens nfluences e economy s grow rae by s adverse effec on socal capal: PROPOSITION (Grow effecs of nequaly) An ncrease n nequaly reduces socal capal, ncreases economy-wde ransacon coss and, us, lowers an economy s grow rae. Proof. Accordng o (5), an economy s grow rae s gven by 9
α γ = ( αa Y η( e) δ ρ), θ were, accordng o (6), e depcs aggregae ransacon coss. None of e deermnans of e economc grow rae depends on e economy s dsrbuon n a drec manner. However, bo varable e and e value of funcon η [ e, p, S] are dependen on socal capal, e value of wc, n urn, depends on e nequaly n e dsrbuon of labor endowmens. Tus, we ave were α e + η[ e, p, S] = αa η α Y [ e, p, S]( )( e) ( e) σ θ σ σ γ α, e e S = σ S σ η η S and = σ S σ. Accordng o LEMMA, S σ < 0. Furermore, as been assumed above a η S > 0. Implcly dfferenang opmaly condon (0), e effec of socal capal on e opmal ndvdual amoun of labor allocaed o nvesgaon follows as e S η = e S η e < 0. Terefore, follows a e σ > 0, η σ < 0 and, fnally, γ σ < 0. q.e.d. Te economy s grow rae s reduced by ger nequaly due o e followng soco-economc mecansm: A mean-preservng spread n e dsrbuon of ndvdual labor endowmens wdens e culural gap beween e rc and e poor n a socey. Accordngly, for a ger fracon of ndvduals e coss of complance w e communy s norms ouwegs e advanages of socal negraon. Terefore, e sze of e mddle class wose members make posve conrbuons o e value of resources embedded n e socey s neworks srnks, wle e sare of socal dropous n e populaon ncreases. As a resul, e economy s overall socal capal s depressed. Te reduced level of socal capal, n urn, reduces e effecveness of nformal governance srucures 0
agans opporunsc beavor and, us, lowers e economy s grow rae va wo cannels: Frs, economy-wde ransacon coss rse because ndvdual consumers ry o compensae e lowered effecveness of socal governance srucures by ncreasng e amoun of labor ey allocae o er own nvesgaons. Ts reallocaon of labor nduces a fall n e margnal producvy of pyscal capal and, us, e economy s grow rae. Snce, furermore, e ncrease n prvae nvesgaon agans opporunsc beavor s only an mperfec subsue for e role of socal capal as an nformal governance srucure, e effecve yeld on savngs a e consumers receve s lowered. Houseolds savngs and e rae of prvae capal accumulaon are, erefore, reduced, wc s also dermenal o economc grow. 6. Concluson Ts paper as analyzed a eerogeneous-agens endogenous-grow model ncorporang bo ransacon coss and socal capal. An ndvdual can eer become an acve par of e socey s mddle-class neworks of rus and muual co-operaon, us makng a posve conrbuon o overall socal capal. Alernavely, e ndvdual can socally dssocae erself, parcpae n e socey s economc ransacons, bu no conrbue o e communy s socal capal. Due o e exsence of asymmerc nformaon, agens face a moral-azard problem on e cred marke wc gves rse o ransacon coss and can be allevaed by prvae, governmenal or socal governance srucures. An ncrease n nequaly, as measured by a smple mean-preservng spread n ndvdual labor endowmens, s assocaed w a srnkng mddle class and as been sown o depress e communy s socal capal, wc, n urn, weakens e nformal socal governance sysem and ncreases economy-wde ransacon coss. As a resul a more unequal dsrbuon lowers e economy s rae of capal accumulaon and grow. All n all, e above analyss wle n self farly resrcve serves o llusrae wo pons of more general valdy. Frs, e exsence of a broad mddle class e members of wc sare w eac oer a farly omogenous se of socal orenaons ( mddle-class consensus ) and e socal
capal bul by socal neracons and nformal relaonsps wn s mddle class are mporan deermnans of long-run economc grow and developmen. Secondly, n addon o economc and polco-economc ransmsson cannels medang e relaonsp beween dsrbuon and grow, ere also exs soco-economc ones. As menoned before, e specfc ransmsson mecansm demonsraed n e presen paper sould be seen as merely one of several cannels roug wc nequaly and socal background condons nerac o consran or foser grow cannels remanng o be furer elaboraed on n fuure researc. Appendx: Proof of Lemma. Le from F and F be wo dsrbuon funcons of e random varable. Furermore, le F dffer F by a smple mean-preservng spread (as defned n Roscld and Sglz (970)). Ts s equvalen o sayng a bo dsrbuons ave e same mean and n addon ĥ suc a ˆ ˆ, F ( ) F ( ), and, F ( ) F ( ) (sngle crossng propery). For analycal smplcy, le us assume a e sngle crossng occurs somewere n e open nerval ], [. Ten, e sngle crossng propery of a smple mean-preservng spread mples a : = F ( ) : = F ( ), wle : = F ( ) : = F ( ). Accordng o (7), economy-wde socal capal s gven by: S = s d = 0 s d. Terefore, for any smple mean-preservng spread, we ave s d > S : = S : = s d. q.e.d.
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