Residual Wage Disparity. in Directed Search Equilibrium

Transcription

1 Rsdual Wag Dsar Drcd Sarch qulbrum Joh Ks, Ia Kg ad Boî Jul* Smbr 7, Absrac W xam how much of h obsrvd wag dsrso amog smlar worrs ca b xlad as a cosquc of a lac of coordao amog mlors. To do hs, w cosruc a drcd sarch modl wh homogous worrs bu whr frms ca cra hr good or bad obs, amd a hr mlod or umlod worrs. Worrs our modl ca also sll hr labor o h hghs bddr. Th saoar qulbrum has boh cholog dsrso dffr wags du o dffr ob quals, ad corac dsrso dffr wags du o dffr mar xrcs for worrs. Th qulbrum s also cosrad-ffc sar coras o udrcd sarch modls wh cholog dsrso. W h calbra h modl o h US coom ad show ha h mld dsrso masurs ar qu clos o hos h daa. JL cods: 4, 5, J3, J4, J64 Ths ar was rsd a h Soc for coomc Damcs mgs Socholm, h Ausralasa mgs of coomrc Soc Auclad, h Caada coomcs Assocao mg Moral, h BR summr su, ad a h Uvrs of Sd. Comms b Dbass Badoadha, K Burd, Marcl Jas, Klaus Kul, Sholh Maa, Tm Malo, Dal Mors, Chrsohr Pssards, Ala Rogrs, ad Radall Wrgh ar grafull acowldgd. * Boî Jul, Uvrs of Mam, USA, Ia Kg, Uvrs of Auclad, Z, ad Joh Ks, Uvrs of Mam Vsg.

2 ITRODUCTIO I has log b sablshd ha a larg rooro of wag dsar cao b xlad b dffrcs h obsrvd characrscs of worrs. I fac, h mrcal labor lraur, s grall agrd ha aroxmal wo hrds of wag dsrso s rsdual occurs wh arrowl dfd grous of worrs. S, for xaml, Kaz ad Auor 999. Ths has alwas osd a challg o hor arcularl h lgh of Damod s 97 crqu of wag dsrso, qulbrum, wh homogous worrs. For hs raso, svral rsarchrs hav arbud hs dsrso o uobsrvd hrog amog worrs, wh h mlcao ha fr obsrvaos could ulmal rsolv h ssu. Sarch horss, o h ohr had, hav sough o xla hs homo as a qulbrum oucom wh worrs who ar, fac, homogous. Burd ad Judd 983, for xaml, xlor wo varas of sarch ha allow for qulbrum dsrso: o-squal sarch ad os squal sarch. Boh varas, howvr, rl o x os worr hrog ordr o suor h rsul. Mor rcl, Burd ad Mors 998 argu ha, h rsc of o-h-ob sarch ad Posso arrval ras, dsrso mus occur qulbrum. Thr modl has a couous dsrbuo of wag offrs qulbrum, for homogous worrs. Ths rsul s ssv o som of h udrlg assumos, howvr. For xaml, s mora ha h assum ha cumb frms cao rsod b adusg wags wh bg radd b ohr frms. I s also o clar how hs rsul would chag f arrval ras wr o aramrc bu, sad, drmd b h chocs of ags h modl. Aohr srad of sarch hor has mrgd rcl, whch focuss rcsl o hs ssu of whr burs would choos o sarch, wh gudd b som formao abou sllrs. Ths has com o b ow as drcd sarch hor. Followg Mogomr 99, mos drcd sarch modls, h sarch frco s movad b a sml coordao roblm h rsc of caac cosras. Sllrs ar caac-cosrad, a rod, b h fac ha h hav a fxd Cols cosdrs cass whr hr rsul s robus o chags hs assumo. o all drcd sarch ars modl hs as a coordao roblm. S, for xaml, Mo 997.

3 umbr of obcs o sll. Burs, v wh awar of h locaos ad rcs of all h sllrs, fac a frco f h all mov smulaousl: oo ma burs ma arrv a a o sllr. If hs sllr has fwr us of h good o sll ha dmadd b h burs, som burs wll b uabl o urchas h good. A h sam m, hr ma b ohr sllrs ha hav oo fw burs aroach hm, so som of h good ma b lf usold. Thus, h fac of hs coordao roblm, som burs ad som sllrs ma d u frusrad v f h umbr of us for sal h aggrga s h sam as h umbr of us ha burs would l o urchas. I hs modls, h ol smmrc qulbrum s o whch all burs radomz wh choosg whch sllr o aroach. Ths radomzao mls a dogous machg fuco ha rsmbls, svral mora was, h fuco usd h machg lraur for xaml, Pssards. Ths basc srucur has b xlord rcl svral ars. Wh, hr dffr sourcs of qulbrum wag dsrso amog homogous worrs hav b dfd. Jul, Ks, ad Kg show ha, wh worrs auco hr labor, sc som worrs wll rcv mor bddrs ha ohrs, som worrs wll o hghr wags ha ohrs. Thus, wags ca dffr sml du o h radomzao hr h coordao roblm. W wll rfr o hs of dsrso hr as corac dsrso. Scodl, as show Acmoglu ad Shmr, f dffr obs hav dffr roducvs, hs ca lad o homogous worrs bg ad dffrl dffr obs. W wll rfr o hs as cholog dsrso. 3 Th hrd sourc of wag dsrso, xlord Burd, Sh ad Wrgh ad Sh a coms from h fac ha rcs chargd wll, gral, b a fuco of h svr of h caac cosra. Ths draws o Prs 984 sgh ha, caac-cosrad sgs, burs fac a rad-off bw rcs ad robabl of sal. W ca h of hs as caac dsrso. Th coc of caac dsrso forcs us o h abou whch s of ags ar o whch sd of h mar ad wha, xacl, s bg sold h labor mar. Acmoglu ad Shmr, Burd, Sh, ad Wrgh ad Sh a,b follow h rado sarch hor whr frms ac as sllrs sllg obs 3 Acmoglu ad Shmr s modl also has h addd frco of o-squal sarch: worrs cao s osd wags ulss h a a cos o rcv a saml of hm.

4 o worrs. I Jul, Ks, ad Kg, w modl worrs as bg h mor radoal rol as sllrs hs mar. Whl sms rasoabl o cosdr ha caac dsrso ma la a maor rol wh dffr szs of frms sll obs, sms clar ha hs rol would b sgfcal dmshd wh dvdual worrs ar sllrs. 4 I hs ar w argu ha a larg rooro of h obsrvd rsdual wag dsrso ca b xlad as a cosquc of h basc coordao roblm ha udrls hs drcd sarch modls. To do hs, w cosruc h smls ossbl modl of hs, whch dogous corac ad cholog dsrso ar obad qulbrum. W modl worrs as sllrs of labor, ad allow frms o cra vacacs of dffr s: hgh ad low roducv wh dffr assocad coss. Th su s sgfcal smlr ha Acmoglu ad Shmr s ar, largl bcaus w do o hav h addd comlcao of osqual sarch. 5 Ths allows us o drv xlc soluos for h dogous varabls. I also allows us o sola h ffcs of h coordao roblm alo. W sar b frs xamg h rors of a sac modl, ad drv cssar ad suffc codos for cholog dsrso o xs qulbrum, wh frms ar fr o r ad choos hr chologs. W h xd h modl o a damc f horzo vrom whch allows for sarch, boh o ad off h ob, ad saraos. W solv for valus of h dogous varabls h saoar qulbrum, ad show ha hs qulbrum s cosrad-ffc. Paramr valus ar h chos so ha h modl machs h ma wl wag ad umlom ra of h US coom 995. K sascs of h umrcal wag dsrbuo grad b h modl ar h comard wh hos from mrcal suds. Amog h rsuls, w fd ha h sadard dvao of h log of hs wags s aroxmal 54% of h fgur gv, h Kaz ad Auor 999 sud, for h r wag dsrbuo 995. Prhas mor srgl, wh cosdrg h 9- rcls of h log wag dsrbuo, h modl rdcs a fgur of.8, whch s qu clos o h aroxma.5 fgur rord, b Kaz ad Auor, for rsdual wag dsrso ha ar. 4 I Jul, Ks, ad Kg, w rovd a mor dald comarso of hs framwors. 5 Aohr dffrc s ha w allow for frm r hr, rahr ha fxg h umbr of frms. 3

5 Th cosrad-ffcc rsul s coss wh smlar rsuls h drcd sarch lraur wh homog for xaml: Mo 997 ad Jul, Ks ad Kg. Howvr, sads sar coras wh hos h udrcd sarch lraur. For xaml, Sarg ad Lugqus coclud: 6 I h cas of hrogous obs h sam labor mar wh a sgl machg fuco w sablsh h mossbl of ffcc whou govrm rvo. Ths s clarl a cas whr h mlcaos of drc ad udrcd sarch hor dffr subsaall. Th assumo ha machg robabls ar uaffcd b bhavour, hr udrcd sarch, lads o a cogso ha dsors h wlfar rors of h qulbrum. Wh ags ca choos machg robabls, hs dsoro s rmovd. Th ar s orgazd as follows. Sco rss ad aalss h sac modl. Sco h rss h srucur of h damc modl. Sco 3 rss aalcal rsuls cocrg h saoar qulbrum. Th quaav aalss of h modl s rsd Sco 4. Th coclusos of h sud ar gv Sco 5, alog wh a gral dscusso. Th roofs of all h roosos h ar ar coad h Adx. 6 Acmoglu ad Davs rach smlar coclusos. 4

6 . TH STATIC MODL Cosdr a sml coom wh a larg umbr of dcal, rs ural, ob caddas whr ach cadda has o dvsbl u of labor o sll. Thr ar M vacacs of wo s: {, }, whr, ad ar drmd b fr r. Th roducv of a worr s f umlod ad > f mlod a ob of, whr >.Icoss o cra a vacac, whr > ad. ach vacac ca aroach ol o cadda. Th ordr of la s as follows. Gv, M vacacs of ach r h mar. Oc h umbr of ras has b sablshd, vacacs choos whch cadda o aroach. Oc vacacs hav b assgd o caddas, wags ar drmd hrough a ascdg-bd glsh auco. 7 W solv h modl usg bacwards duco. Wag Drmao ach worr coducs a ascdg-bd auco, whr hs rsrv wag s sml hs ousd oo. I qulbrum, h wag w of a worr who s mlod a ob of roducv, ad who had a scod bs offr from a ob of roducv s gv b: w. for all {, } ad {,, }. 7 W usf h usag of a auco hs of vrom Jul, Ks, ad Kg. Th form of auco s rrlva, sc rvu quvalc holds hr. S, for xaml, McAf ad McMlla

7 6 Th Assgm of Vacacs o Worrs As s sadard drcd sarch vroms, 8 wh cosdrg h locao choc of burs, ao s rsrcd o h uqu smmrc mxd srag qulbrum whch ach bur of ach radomzs ovr sllrs. Cosqul, a larg mar, h robabl ha a worr s aroachd b a vacac of maxmum roducv s gv b:. I also follows ha, a larg mar, from h ool of vaca obs of roducv, a cadda obas hr o offr, o offr, ad mull offrs wh robabls, ad, rscvl. Thrfor, h robabl dsrbuo of wags s gv b:,,,,,,, w w w w w w w.3 whr dos h robabl ha worr obas a wag w. If h umbrs of vacacs wr gv xogousl.., ad wr aramrs h.3 would rrs h fal soluo of h modl. xamg.3, s clar ha wag dsrso has wo sourcs: corac dsrso ad roducv dsrso. For xaml, h dffrc h wags w ad w s du rl o corac dsrso: boh cass, h roducv of h ob s low, 8 S, for xaml, Burd, Sh ad Wrgh ad Sh a,b.

8 bu worrs who ar w had a ousd offr from aohr low roducv ob whras worrs who ar w dd o. I ordr o rcv h hghs wag w, worrs d o b o h rgh d of boh corac ad roducv dsrso: h rsc of a las o hgh roducv vacac s rqurd o ma hs wag chcall fasbl, ad h rsc of a las o ohr hgh roducv vacac, as a ousd offr s rqurd o ma hs wag a qulbrum oucom. I s also clar ha corac dsrso ca b a las as mora o worrs as roducv dsrso. For xaml, a worr a hgh roducv ob ars a wag qual o w wh robabl wag of w wh robabl whl a worr low roducv ob ars a hghr, >. W ow ur o h drmao of ad.. Boh of hs robabls ar osv f Vacac r Th rof of a frm s qual o s ouu mus s vacac crao cos ad h wag as o h worr. Thrfor, h rof π of a vaca ob of roducv ha mas a offr o a worr who has a bs rval offr of roducv s gv b: π max{,}.4 Th xcd rof π of a vaca ob of roducv s gv b: π max{ q,}.5 π max{ q q,}.6 whr q s h robabl ha a frm ars a rof qual o π. Th robabl ha a vaca ob dos o fac offr como from a rval ob of roducv s gv b. Thrfor q q s h robabl ha h vaca ob dos o fac a rval vaca ob of hr roducv, ad q s h 7

9 robabl ha a vaca ob facs a low roducv rval bu o a hgh roducv rval. Th sul of vaca obs of roducv xcd rof π of a vaca ob of roducv s drmd b fr r, so h s qual o zro qulbrum: π π.7 Th assumo ha h ouu of a arcular of ob s grar ha h cos of h ob vacac dos o guara ha h sul of obs of ha s osv. For xaml, s as o s ha q ca b gav f suffcl larg mag q suffcl small. Thrfor w do o ow, basd o our rs assumos, whhr or o h wo dffr obs wll xs qulbrum. Th followg rooso rss cssar ad suffc codos for hs of roducv dsrso. s Prooso : Boh s of obs xs qulbrum > followg codos hold: f ad ol f h ad / > /. > Morovr, wh hs codos hold, h h qulbrum valus of ad ar gv b: l / l /.8 l /.9 Th frs codo Prooso surs ha h sul of hgh roducv obs s alwas osv f h ouu of a good ob of s caal cos xcds h ouu of a bad ob of s caal cos. Th scod codo mls ha h sul of low roducv obs s alwas osv f h ouu of a bad ob 8

10 r u of caal s grar ha h ouu of a good ob r u of caal. Ths wo codos ar sasfd b h sml assumo of a dmshg margal roduc of caal. Udr hs codos, quaos.3,.7,.8, ad.9 comll solv for h qulbrum aoff srucur h sac modl. Cosrad ffcc W ow cosdr h roblm of a socal lar ha s abl o corol r, bu sll facs h sam coordao frco as rva ags. Th lar chooss ad o maxmz oal xcd surlus S: S max { }, Prooso : Th dcralzd qulbrum s cosrad ffc. Th rasog bhd h ffcc rsul s as follows. Cosdr h choc of whhr or o o add o mor low qual vacac. Wh som robabl, h mlor wh hs w vacac wll aroach a cadda ha s also aroachd b som ohr vacac, of hr of hgh or low qual. I hs cas, f hs ohr vacac s also low qual, h wh som robabl, h rg vacac wll hr h worr, so h gas o h mach wh h ohr mlor wll b los. Ths s a xral cos assocad wh h w vacac. Howvr, hr s also a bf crad: h mach of h rg vacac ad h worr. Clarl, hs cos ad hs bf xacl cacl ach ohr. Thus, h socal rur from such a w vacac s zro. Du o h auco mchasm, hs s rcsl h rva rur ha a w low qual vacac gs hs cas. If, howvr, h ohr vacac s of hgh qual, h, aga, h socal valu of h rg low qual vacac s zro ad h aoff wll b zro, hough h auco mchasm. If h rg low qual vacac aroachs a worr whom ohrws would o b machd, h a socal bf s grad: h valu of h 9

11 mach. Th xcd margal socal bf of h w vacac s hrfor h robabl ha h w vacac wll b alo wh aroachs a worr, mulld b. Th margal socal cos of grag a w vacac s sml h cos of crag h vacac. A socal lar quas hs wo, ad so dos a rva ra. A smlar l of rasog holds for h crao of a w hgh qual vacac. I hs cas, howvr, f h ohr vacac s of low qual, h h w hgh qual vacac wll hr h worr wh robabl o. Hr, h gas o h mach wh h ohr vacac wll b los, bu h gas o h w mach wll b, so h socal gas ar. Oc aga, hrough h auco mchasm, hs s rcsl h rva rur ha a w hgh qual vacac rcvs. I all cass h rva ad socal rurs ar quad. I s also worhwhl o o ha h rol of h worr as sllr s crucal hr. I a smlar modl, bu whr frms la h rol of sllr of obs, Jas 999 shows ha ol o of ob ca xs qulbrum.. TH DYAMIC MODL Thr s larg umbr,, of dcal rs ural worrs facg a f horzo, rfc caal mars, ad a commo dscou facor β >. I ach m rod, ach worr has o dvsbl u of labor o sll. A h sar of ach rod,,,3,...,hrxs umlod worrs, of roducv,ad worrs obs of roducv > whr {, }. Also, a h bgg of ach rod, hr xs M vaca obs of ach roducv drcd a umlod worrs ad hgh roducv vaca obs M drcd a mlod worrs obs of roducv. 9 I ach rod a vaca ob has a caal cos of such ha ad. Also, a mach 9 o ha o low roducv vaca ob ar drcd a mlod worrs hgh roducv obs.

12 a rod ma dssolv h subsqu rod wh fxd robabl ρ,. I ach rod, a vaca ob ca r goaos wh a mos o worr. Wh ach rod, h ordr of la s as follows. A h bgg of h rod, gv h sa, w vacacs r. Oc h umbr of ras has b sablshd, vacacs choos whch worrs o aroach. Oc w vacacs hav b assgd o caddas, wags ar drmd hrough h auco mchasm. Wag Drmao L do h xcd dscoud valu of a mach bw a umlod worr ad a ob of roducv a h sar of a rod. Through h auco, h worrs shar W of h xcd dscoud valu s qual o h xcd dscoud valu scod bs avalabl ob offr: of a mach bw h worr ad h worr s W. Th Assgm of Vacacs o Worrs Umlod worrs advrs aucos wh a rsrv rc of whl worrs low roducv obs advrs aucos wh a rsrv rc of.th worrs ar dsgushabl ol b hr mlom sa. As h sac modl, w rsrc ao o h uqu smmrc mxd srag qulbrum whch ach vacac radomss ovr ach rlva grou of worrs. Cosqul, h w hrs of rscvl b: H hgh roducv worrs ad H low roducv worrs ar gv H. H.3

13 whr, ad. Th fraco ρ of all obs dssolv h x rod, hrfor, h sul of worr of ach volvs accordg o h followg raso quaos: ρ H {, }.4 Th radomss of ob offrs mls ha a worr ca oba hr o, mull or o ob offrs from vacacs of hr. Thrfor, follows ha h xcd rs valu of a umachd worr sasfs: V.5 whr s h robabl ha a worr has o or fwr offrs, s h robabl of mull offrs ol o of whch s ossbl good, ad s h robabl of mull good offrs. Vacac r Th xcd rof umlod worr sasfs: Π of a ob of roducv mag a offr o a Π max{,}.6 Π max{,}.7 whr s h robabl ha a low or hgh roducv ob dos o fac a rval, ad s h robabl ha a hgh roducv ob facs ol a low roducv rval. Th xcd rof of a offr b a hgh roducv o a worr a low roducv ob s gv b:

14 Π max{,}.8 whr s h robabl ha hgh roducv ob dos o fac a comg offr from a rval hgh roducv ob. Th sul of vaca obs of roducv s drmd b fr r. Thus Π Π Π.9 Th valu of a umachd worr h x rod drms h ousd oo of a umachd worr h curr rod, so β V. Th oal surlus of a hgh roducv ob s qual o h ouu of a hgh roducv ob lus h dscoud fuur flow of com from such a ob wghd b h robabl of a xogous ob sarao o umlom: [ β ρv ρ ] β ρ[ ρv ρ ].... Wags low roducv obs ar bargad wh h udrsadg ha h worr wll g h cras of surlus assocad wh a oal favourabl fuur barga bw h worr ad a hgh roducv ob durg h worr's ur a a low roducv ob. Thrfor, h xcd rs valu of bg a worr a low roducv ob mus corora h robabl of movg o a hghr ag hgh roducv ob a subsqu rod. Hc β ρv ρ X β ρ ρv ρ X.... whr X summarzs hr ossbl oucoms: s h robabl ha h mlod worr s o rcrud, T,sh robabl ha h mlod worr s rcrud b o good ob, ad 3

15 s h robabl ha h worr s rcrud b o or mor hgh roducv obs. I hs ar w wll, for h mos ar, rsrc our ao o h saoar qulbrum. Howvr, h followg rooso sablshs ha cra valus ar saoar a qulbrum of hs modl. Prooso 3: Th qulbrum valus of {,,, Π, Π, Π, V, b {,,, Π, Π, Π,V,,, }, ar saoar. }, dod For h rmadr of h ar, w rsrc our ao o h saoar qulbrum. 3. TH STATIOARY QUILIBRIUM Th followg roosos characrz som of h mora faurs of h saoar qulbrum. Th frs cocrs h fracos of h worforc ha ar assgd, a h d of vr rod, o h dffr s of obs. Prooso 4: I h saoar qulbrum, h fraco of worrs ach roducv sa s gv b: ρ ρ 3. ρ ρ ρ

16 whr h s ar gv b quao. ad. oc ha h saoar srucur allows us o us som of h rsuls dvlod Sco, whch cosdrs h sac modl. Th x rooso sablshs a suffc codo for o-h-ob sarch o xs qulbrum. Prooso 5: Vaca good obs ar drcd a worrs mlod bad obs f, whch cas h sul of hs obs > β ρ s drmd b: 3.4 β ρ Ths codo surs ha good obs wll o u rsos o h xsc of bad obs. I arcular, surs ha frms wll rcru worrs bad obs. Howvr, dos o sur ha good ob vacacs wll b od u had o had como wh bad obs h rcrum of umlod worrs. I ohr words, w sll hav o drm whhr s srcl osv. I also dos o addrss h xsc of bad obs qulbrum. Ths wo cocrs ar cosdrd h followg wo roosos. Prooso 6: Umlod worrs rcv mor good offrs o avrag ha worrs bad obs. Th sul of good obs amd a umlod worrssdrmdb: 3.5 whr < mls >. Th x rooso sablshs h xsc of a qulbrum wh o-h-ob sarch. 5

17 Prooso 7: A qulbrum wh,, > xss. Th sul of bad obs hs qulbrum s drmd b: β ρ 3.6 ad h sul of good obs s drmd b quaos 3.4 ad 3.5. quaos 3.4, 3.5 ad 3.6 drm h saoar qulbrum valus of,,ad. Tha s, h drm h umbrs of vacacs of h dffr s qulbrum. Comuaoall, h ssm s rcursv: 3.4 drms, h 3.5 drms, h 3.6 solvs for. Whl sml aalcal soluos ar o avalabl, s sraghforward o comu hs valus umrcall, for a gv vcor of aramrs,,,, β, ρ ha sasfs h rsrco Prooso 5. Bfor rocdg o h umrcal aalss, howvr, s usful o draw ou som mor aalcal rsuls. Prooso 8: Th xcd valus of worrs h dffr sas ar gv b: V β ρ β 3.7 βv 3.8 βρv β ρ 3.9 Wh,,ad β ρv ρ β ρ 3. drmd quaos 3.4, 3.5 ad 3.6, h valus of V,,, ad ca ow b drmd b h quaos Prooso 8. Oc 6

18 aga, hs s a rcursv ssm, wh V drmd 3.7, h ad drmd quaos 3.8 ad 3.9. Wh V ad drmd, 3. drms. W ca ow solv for h rod wags h saoar qulbrum. Ths ar drmd b: w 3. w βρv β ρ {,,} w V β ρ ρ β ρ {,} whr w dos h wag r rod of a worr sa W. Th followg rooso ow rss h r wag dsrbuo h saoar qulbrum. Prooso 9: Th wag dsrbuo h saoar qulbrum s as gv h followg abls. Wags w w βρv β ρ w w β ρ βρv w β ρ βρv w 7

19 Fraco of worforc arg ach wag / [ ρ / ρ] [ ρ / ρ] ρ / ρ Gv h aramrs,,,, β, ρ ad quaos 3.-3., h quaos Prooso 9 drm h wag srucur h saoar qulbrum. A hs o, s usful o comar hs srucur wh ha of h sac modl gv quao.3. Clarl, w,, ad w ar h sam h wo modls. Whl h w rasog wh w s sraghforward boh modls, w ad w ma d som xlaao. Th s ha, ach rod, h xcd valu of rofs for h ach frm s drv dow o zro. If wo or mor vacacs of h sam bu o of h ohr lad a h doors of h sam worr, a chac of a osv x os rof for hs frms dsaars. Th cos h ad o gra h vacac, s alrad su. Th ar, ffc, us l frms h sac gam. Th valu of holdg h ob o o h x rod s zro. As h sac gam, Brrad como bw h wo dcal frms drvs h curr aoff o zro. Th valu of w low qual ob. s also drmd, as h sac modl, b h surlus assocad wh a Ul h valu of frms, h valu of worrs s o drv o zro h damc modl. Whras, h sac modl, ach worr s ousd oo s zro; h damc modl, a umlod worr s ousd oo s >.Ifaworr rcvs ol o low qual vacac, h auco mchasm drms ha hs worr wll rcv xacl hs ousd oo. Th valu of w Prooso 9 s 8

20 sml h rod wag coss wh ha. Th drmao of aalogous. w s rl Bfor urg o h umrcal aalss of hs modl, w frs cosdr, oc aga, h quso of cosrad ffcc, whr h socal lar chooss o maxmz h oal xcd surlus S max {,, H, H, M, M } β { H H M M M } subc o quaos.,.3 ad.4. Prooso : Th saoar qulbrum s cosrad-ffc. 4. QUATITATIV AALYSIS Thr ar sx aramrs hs modl:,,,, β, ρ. To assss h quaav sgfcac of h dsrso hs hor, as our basl, w cd aramr valus o aroxma h US coom 995. W chos hs ar for wo rasos. Frs, hs hor absracs from a cclcal faurs, ad s ssall a hor of a coom ha s rformg wll h ol frco bg h basc coordao roblm. Arguabl, hs was h cas h US a ha m. Scod, 995 s h las ar cosdrd Kaz ad Auor s 999 sud, whch rss ma sascs ha ar rlva for hs hor. Paramr Valus Th Kaz ad Auor 999 sud aalss wl daa. Wh a aual dscou ra of 5%, hs mls a wl dscou facor of β.999. Usg Kuh ad Swma s 998 sma of a 4% mohl sarao ra, w s h wl ρ.. To focus o a qulbrum wh o-h-ob sarch, gv h valus of β ad ρ, w rsrcd our chocs of,, ad o sasf h codo sad 9

21 Prooso 5. W s 5, whch s a h lowr d of h obsrvd dsrbuo. W chos h valus of, ad o mach h avrag wl wag 98 dollars $55, h aural ra of umlom 3.9% ad h vacac ra.6%. Ths valus wr 3. 3, 5, ad 76. Rsuls Tabl 4., blow, rss h qulbrum wag dsrbuo, for hs s of aramrs. Wags qulbrum Wag Dsrbuo Fraco of Worforc w. 393 w w w w w Tabl 4. I s qu clar from hs abl ha boh roducv dsrso ad corac dsrso la mora rols wag drmao. For xaml, amog worrs ha rcv ol o ob offr, hos ha rcv hs offr from a hgh roducv vacac rcv a wag of w 3. 3, whl hos ha rcv h offr from a low Th acual umlom ra 995 was 5.6%. W chos 3.9% as our aroxma arg for h umlom ra bcaus h umlom ra sld dow o ha umbr subsqu ars, ad hs hor s rall a hor of h aural ra. Th.6% fgur for h vacac ra was xraolad from Blachard ad Damod 989, usg labor forc fgurs from h BLS ad h vacac dx from h Cofrc Board. Th valus of ad ma sm qu hgh, wh cosdrg wl coss. Howvr, w hav modlld hs so ha hs coss rma oc a vacac s flld ad vacacs ar flld qu qucl qulbrum. I ral, hr fxd coss wh crag obs, ad hs ca b qu larg wh cosdrg h caal ha s usd o mach wh a worr. Followg Pssards, o h sa vcor as small as ossbl, w modl hs coss as flow coss.

22 roducv vacac rcv ol w 7.. Ths dffrc s du rl o roducv dsrso. Howvr, amog hos worrs ha a obs wh hgh roducv vacacs, hos ha had o ohr offr rcv w 3. 3, hos whos scod-bs offr cam from a low-roducv vacac rcv w 5. 83, whl hos whos scod-bs offr cam from aohr hgh roducv vacac rcv w Th dffrc of hs hr wags s drv url b corac dsrso. Tabl 4. also shows ha, h saoar qulbrum, mos worrs ar good obs. Addg ad, w ca s ha ol.4% of worrs ar bad obs. Aloghr, 85.65% of worrs ar good obs. Howvr, vr fw.5% ar ad h o wag of w Du o corac dsrso, 8.% ar ol w 3.3, whl 55.% ar w Ths lavs 3.93% umlod. Tabl 4. shows h saoar qulbrum valus of som of h ohr varabls. Ohr K Varabls qulbrum Good Vacacs Amd a Worrs Bad Jobs. 56 Good Vacacs Amd a Umlod Worrs. 75 Bad Vacacs Amd a Umlod Worrs. 47 Valu of Umlod Worr 33, 649 Valu of a Bad Job Mach 35, 55 Valu of a Good Job Mach 35, 54 Tabl 4. From hs abl, ca b s ha h robabl of a worr rcvg a good ob offr, wh umlod.69 s hghr ha h rcvg o wh alradmlodabadob.53. Ths occurs bcaus of h xra

23 bargag owr a worr a bad ob has: f succssfull rcrud, h mus b ad w 5.83, rahr h wag w 3. 3 ad o a worr ha was rvousl umlod. Ovrall, h robabl of a worr lavg a curr ob o a aohr.53 o s aroxmal o quarr h robabl of a currl umlod worr fdg a ob.964. Rhrasg hs, qulbrum, h offr arrval ra for umlod worrs s sgfcal hghr ha h offr arrval ra of mlod worrs. Ths s somhg ha has b obsrvd mrcall, ad s call assumd udrcd sarch modls wh o-h-ob sarch. From Tabls 4. ad 4., aohr faur of h qulbrum ca b s. Alhough h vacac/umlom raos for good ad bad obs ar qu smlar magud, h saoar qulbrum, h vas maor of worrs ar good obs. O-h-ob-sarch s sgfca ough o drv hs rsul. Worrs bad obs ow ha h wll o sa hr for vr log. Ths s also rflcd h fac ha h rao. 34 s sgfcal smallr ha h valu of Th / / valus of h machs clud all xcd rurs o boh h frm ad h worr. Thus, as ca b s from quao 3., h valu of as o accou h fac ha h worr wll, mos ll, mov o o a good ob h fuur. Th x abl, Tabl 4.3, comars som of h sascs from hs xaml wh hos from US daa. S, for xaml, Pssards 994.

24 Comarg Sascs Sasc Modl US Daa Ma Wag Sadard Dvao Log Wag %-% Log Wag Umlom Ra Vacac Ra.6.6 Tabl 4.3 Th valus of h aramrs wr chos so ha h ma wag, h umlom ra, ad h vacac ra wr clos o hos h daa. Th ma wl wag for mals h US was aroxmal $ Th umlom ra 5.6% ovrall, wh a smad aural ra of 3.9%. Th corrsodg fgurs from h modl ar $55.55 ad 3.93%. Kaz ad Auor ror ha h sadard dvao of h log wag h US ovrall 995 was.66. I h modl, h corrsodg fgur s.37 aroxmal 53% of h fgur h daa. Thus, o could argu ha 53% of hs obsrvd dsrso was du o h coordao roblm, whch rsuls boh roducv dsrso ad corac dsrso amog worrs ha ar ffcvl homogous. Ths rsul s rforcd b aohr sasc rord b Kaz ad Auor. Th ror h dffrcs of h 9 h ad h rcls of h log wag dsrbuo, boh ovrall ad for h rsdual wag dsrbuo. I h US, ovrall, 995, hs fgur was aroxmal.54 ovrall ad.5 for h rsdual dsrbuo. I h modl, hs fgur s.8. Thus, b hs masur, hs sml modl ca xla a larg rooro of h rsdual wag dsrso. W ca also us hs modl for local comarav sac xrcss comarg h qulbrum oucoms across saoar qulbra wh dffr aramr valus. Th followg abl rss h rsuls from hs xrcs, for small rurbaos aroud h aramrs h abov bas cas. 3

25 β ρ V w w w - - w - - w w - - σ log w log9 log Tabl 4.4: Comarav Sacs Mos of h sgs hs abl ar qu uv. Two ha ar o mmdal obvous ar ad. Tha s, h umlom ra s a / > / < dcrasg fuco of h roducv, ad a crasg fuco of h cos, of a good ob. Ths s udrsadabl, howvr, wh obsrvg ha s also h cas ha, ad,. I hs cas hghr / < / < / > / > valus of, ad lowr valus of h cos, whl crasg h umbr of good obs, gra a dcras bad obs ad lowr h ovrall mlom ra. 4

26 Aohr rsg faur ha coms ou hs abl s ha hghr valus of h sarao ra ρ lad o hghr umlom ras, bu lss dsrso. Ths lads o a rduco h xcd rs valu of h sram of fuur aoffs, whch affcs h xcd rur from good obs dsrooroal sc h hav hghr coss o b ad u-fro. Ths rducs h umbr of good obs, ad h wag good obs, whl couragg h r of bad obs. Ovrall, umlom gos u, du o h larg drc ffc of saraos o umlom. Howvr, dsrso s rducd b h dmshd rlav valu of good obs. Ths offrs a alrav xlaao for h gav corrlao obsrvd bw hs varabls, ad aalsd, a udrcd sarch modl b Dlacrox. 5. COCLUSIOS From hs aalss, aars ha a larg rooro of h obsrvd wag dsar amog smlar worrs ca b s as a drc cosquc of h lac of coordao amog mlors. Wh ach mlor chooss, ddl, h qual of a ob ad h cadda o offr o, h h hor rdcs ha w wll obsrv boh corac dsrso ad cholog dsrso. I h absc of hs coordao roblm, all mlors would choos h sam of ob, ad would a h sam wag o dcal worrs. Quaavl, wh calbrag h modl o mach obsrvd ma wags ad umlom ras, w foud ha, ds s smlc, ca com rmarabl clos rlcag h dsrso sascs ha hav b calculad, dd suds, for US daa. W also foud ha h qulbrum allocaos ar cosrad-ffc h ss ha a lar could do o br ulss abl o lma h coordao roblm, ad hc, h machg frco. I arcular, h olcs advocad for xaml Acmoglu, whch fluc h rlav comoso of good ad bad obs whou rducg h machg frcos, would ol hur hr. Ths s a xaml of how coclusos ca b qu dffr modls wh drcd ad udrcd sarch. 5

27 O aalg faur of hs modl s ha h masurs of dsrso ar uaffcd b sml scalg u of h roducvs ad coss. Fuur wor, hrfor, could mbd hs modl o a framwor wh ass accumulao ad ovav acv, o xam h o drmao of dsrso, growh, ad umlom. 6

28 APPDIX Proof of Prooso : Usg.5-.7, h xcd rofs of h wo s of vacacs ar: π ad π. Solvg hs smulaousl lds.8 ad.9. I s asl show ha, > ff > ad / > /. Proof of Prooso : A ror maxmum of h socal lag roblm sasfs ad whch s h sam as h dcralsd coom. I follows from h roof of Prooso ha ad / ml. /, Proof of Prooso 3: I a saoar qulbrum h valus of {,,, Π, Π, Π, V, ar gv b A. V, A. Π max{ } A.3 Π max{,} A.4 Π max{,} A,5 Π A.6 Π A.7 Π A.8 βv A.9 A. βρv β ρ β ρv ρ β ρ } W hav dd quaos for h roosd saoar varabls. Th aramrs { β,,,,, ρ } of hs quaos ar cosa. Morovr, all of hs quaos ar dd of h oall o-saoar sa varabls,, M c.. Thrfor, {,,, Π, Π, Π, V, }ar saoar qulbrum. 7

29 Proof of Prooso 4: I a saoar qulbrum, quaos.,.3 ad.4 ml H H H ρ {, } o: a mls H H ρ {, } H / b dfo: {, } c d: W ca rwr ad as follows. ρ ρ ρ ρ ρ ρ o ha lus mls v ρ ρ or ρ ρ Ths gvs: ρ v ρ W ca subsu v o o g v [ ρ] ρ ρ Fall, b h d v Proof of Prooso 5: quaos A. ad A.9 ml ha h dffrc bw ad follows: s as A. β ρ quao A.4 ad > ml 8

30 A. quaos A. ad A. ld quao 3.4. I s as o s from quao 3.4 ha s alwas osv f > β ρ. Proof of Prooso 6: O-h-ob sarch mls ha. Thrfor, quaos A. ad A.3 ml A.3, > A.4 quaos A.9, A.3 ad A.4 ca b usd o lma, - ad - from quao A.. Th arora subsuos ld [ β ρ ] A.5 V. β quaos A.9 ad A.8 ml ha h dffrc - s gv b A.6 β β ρ V β ρ I a qulbrum wh good obs amd a umlod worrs mus b h cas ha A.7 Subsu A.5 ad A.6. Th subsu hs xrsso ad A. o A.7. Ths lds quao 3.5. Proof of Prooso 7: quaos A. ad A.8 ml ha h dffrc bw ad follows: s as A.8 β ρ β ρ β ρ β ρ βv β ρ 9

31 If w assum ha, >, w ca subsu A.5 o A.8 o g a xrsso for - rms of,,. Ths xrsso ca b subsud o quao A.4 o ld 3.6. Thrfor, a qulbrum wh,, > s characrsd b quaos 3.4, 3.5 ad 3.6. Accordg o Proosos ad, w ow ha, > ar drmd b quaos 3.4 ad 3.5 ad ha boh valus ar osv f > β ρ. W ca h subsu hs valus o quao 3.6 o chc whhr >. Proof of Prooso 8: Follows drcl from h quaos drvd Proosos 4 hrough 7. Proof of Prooso 9: Th valus of ar obad a fasho smlar o Prooso 4. v v H H ρ H / H H H {,, } {,, } o ha v also mls H ρ {,, }. Rcallg h roof of Prooso 4, w ca rwr, ad as follows. ρ ρ ρ ρ ρ ρ ρ ρ whch gvs: [ ρ / ρ] [ ρ / ρ]. ρ / ρ Proof of Prooso Thr ar wo s of hgh roducv vacacs - M ad M. Thrfor, s acuall cov o dsgush h worrs ha movd o good obs from umlom ad h worrs ha movd o good obs from bad obs. Df B. {, } 3

32 3 L ws H H H, } {,. I whch cas, h socal lag roblm ca b sad as follows: B.,,,,,,,, } { max M M M H H H M M M H H H S β subc o B.3 H B.4 H B.5 H B.6 H ρ B.7 H ρ B.8 H ρ whr M, M ad M. o ha B.3 ad B.6 mls B.9 / ρ or, alravl, B. l l M ρ Lws B.5 ad B.6 ml B. l l M ρ ρ ad B.4 ad B.8 ml B. l l M ρ W ca h rwr h socal lag roblm. B.3,,, { max V ρ ρ

33 3 l l ρ l l ρ l l V β ρ ρ Th frs ordr codos wh a slgh abus of oao ar as follows < > ' V < > ' V < > V ' < > ' V ρ β < > ' V ρ β < > ' V ρ β Ths ssm of quaos ca b solvd for h sad sa valus of,,.th rsuls ar as follows B.4 β ρ β ρ B.5 ρ β B.6 β ρ quao B.5 s h sam as quao 3.4. Maulao of quaos B.4 ad B.6 lds quaos 3.5 ad 3.6.

34 RFRCS Acmoglu, D., Good Jobs vrsus Bad Jobs, Joural of Labor coomcs, 9, -. Acmoglu, D. ad R. Shmr, "Wag ad Tcholog Dsrso", Rvw of coomc Suds, 67, Blachard, O., ad P. Damod, 989 Th Bvrdg Curv, Broogs Pars o coomc Acv,,-75. Burd, K. ad K. Judd, 983 "qulbrum Prc Dsrso", coomrca, 5, Burd, K.. ad D. Mors 998 "qulbrum Wag Dffrals ad mlor Sz", Iraoal coomc Rvw, 39, Burd, K. S. Sh ad R. Wrgh, "Prcg ad Machg wh Frcos" Joural of Polcal coom,forhcomg. Cols, M., qulbrum Wag Dsrso, Frm Sz, ad Growh, Rvw of coomc Damcs, 4, Davs, S., Th Qual Dsrbuo of Jobs ad h Srucur of Wags Sarch qulbrum Uvrs of Chcago mauscr. Dlacrox, A., Hrogous Machg, Trasfrabl Ul ad Labor Mar Oucoms, Purdu Uvrs mauscr. Damod, P., 97 A Modl of Prc Adusm, Joural of coomc Thor, 3, Jas, M., 999 "Job Aucos, Holdus ad ffcc", uroa Uvrs Isu mauscr. Jul, B., J. Ks ad I. Kg "Bddg for Labor", Rvw of coomc Damcs, 3, Jul, B., J. Ks ad I. Kg "Aucos ad Posd Prcs Drcd Sarch qulbrum", Tocs Macrocoomcs, Vol., Issu, -4. Kaz, L., ad D. Auor 999 Chags h Wag Srucur ad args Iqual, Hadboo of Labor coomcs, vol 3, O. Ashflr ad D. Card ds., lsvr Scc B.V., char 6. Kuh, P., ad A. Swma 998 Umlom Isurac ad Qus Caada, Caada Joural of coomcs, 3,

35 McAf, R.P., ad J. McMlla 987 Aucos ad Bddg, Joural of coomc Lraur, 5, Mo. 997 "Comv Sarch qulbrum", Joural of Polcal coom, 3, Arl, Mogomr, J., 99 qulbrum Wag Dsrso ad Irdusr Wag Dffrals, Quarrl Joural of coomcs, 5, Prs, M., 984 qulbrum wh Caac Cosras ad Rsrcd Mobl, coomrca, 5, 7-9. Pssards, C., 994 "Sarch Umlom wh O-h-Job Sarch", Rvw of coomc Suds. 6, Pssards, C., "qulbrum Umlom Thor" d do, Oxford Uvrs Prss. Sarg, T., ad L. Lugqus Rcursv Macrocoomc Thor, MIT Prss. Sh, S., a Produc Mar ad h Sz-Wag Dffral, Iraoal coomc Rvw, forhcomg. Sh, S., b Frcoal Assgm I: ffcc, Joural of coomc Thor, 98,