IS TAX PROGRESSION GOOD FOR EMPLOYMENT? EFFICIENCY WAGES AND THE ROLE OF THE PRE-REFORM TAX STRUCTURE *** Erkki Koskela* and Ronnie Schöb**

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1 Forhcomig i: FizArchiv IS TAX PRORESSION OOD FOR EMPOYMENT? EFFICIENCY WAES AND THE ROE OF THE PRE-REFORM TAX STRUCTURE *** Erkki Kokl* d Roi Schöb** Fir ubmiio Augu, Rvid vrio: Fbrury 7, 2009 Abrc Wihi fficicy g frmork, udy h ffc of o rvu-url x rform h chg h progriviy of h lbour x ym. A rvu-url icr i boh h g x d x xmpio d rvu-url chg i h compoiio of lbour xio ord h x ih h mllr x b ill ld o h m rul: hy modr g, orkr ffor, ffciv lbour ipu d ggrg oupu. Whhr mploym ri or fll, hovr, dpd i boh rform o h mgiud of h pr-rform ol x dg. W ho h hi mbiguiy m from h ffc x progrio h o h mrgil rvu chg of x d x xmpio chg. Thi budgry ffc drmi h rul i h m y i boh x rform d ur ou o b h crucil forc i drmiig h impc h dgr of x progriviy h o mploym. Kyord: fficicy g, x progrio, rucur of lbour xio. JE clificio: H22, J4, J48. * Dprm of Ecoomic, P.O. Box Arkdiku 7, FIN-0004 Uivriy of Hliki, Fild. Emil: rkki.kokl@hliki.fi. ** School of Bui & Ecoomic, Fri Uivri Brli, Bolzmr. 20, D- 495 Brli, rmy. Emil: roi.chob@fu-brli.d. *** Comm by Sv Whk d o oymou rfr r grfully ckoldgd. Th uhor hk h Rrch Ui of Ecoomic Srucur d roh RUES, ficd by Acdmy of Fild, Yrjö Jho Foudio, Bk of Fild d Noki roup, for ficil uppor. Kokl lo hk Acdmy of Fild gr No for furhr ficil uppor d Fri Uivriä Brli for gr hopiliy.

2 . Iroducio Thi ppr ly i fficicy g frmork h impc of x progio o idividul ffor d ggrg mploym. I prfcly fucioig lbour mrk, lbour xio oly dior h lbour mrk d lor mploym bu do o cr ivolury umploym. Wh lbour mrk imprfcio ld o g r bov mrk clrig lvl, ivolury umploym occur d lbour x ormlly ggrv umploym by idig h gp b h lbour co d h opporuiy co of lbour. Bu i i o oly h mgiud of h x dg h mr. Th pcific rucur of lbour xio, i priculr h dgr of lbour x progrio, i lo of gr imporc. Th y i hich x progrio ffc umploym, hovr, crucilly dpd o h priculr udrlyig lbour mrk imprfcio. Th impc of x progrio i ll udrood ihi h g brgiig d h rch d mchig frmork. A icr i x progrio ld o g modrio d i good for mploym,.g., Kokl d Vilmu 996, Holm d Kokl 996, Pirid 998, Kokl d Schöb 999 d Hijdr d ighr 2009, bcu highr mrgil x kpig h vrg x co ork lik ply o g icr. By cor, h rul for fficicy g modl hr h hr of big lid off courg idividul orkig r ill mixd. Wg modrio h poiiv ffc o lbour dmd bu giv ffc o idividul lbour ffor d hu orkr produciviy. Hol 990 h fir o lyz h ovrll ffc of x progrio i uch frmork. H ho h highr mrgil icom x r, hich lv h vrg x lvl uchgd h iiil quilibrium g r, ill dcr h gro g d umploym lo ork 999. Fu d Hubr 998 ho h, for ri i x progrio uch h h x burd pr orkr i h m i h old d quilibrium, h rul migh b rvrd. Uig h Shpiro d Sigliz 984 hirkig modl, Pirid 998, i ur, do o fid y ffc of h x rucur o h g r. Thi i bcu h idividul ffor dciio i hi modl r dicr o h orkr ihr hirk or do o hirk. Wh ffor i coiuou vribl, hovr, Sor 999 idic h highr x progrio

3 2 iduc g modrio d lor boh umploym d ork ffor lo Picrd d Toulmod 2003, ho driv imilr rul i gric modl h llo h lyi of diffr yp of lbour mrk imprfcio. All h rul do o crry ovr o modl hr orkr diffr i hir produciviy. A x rform h ri mrgil x r ll icom lvl d icr dcr vrg x high lo icom lvl my ld o highr gro g d umploym Adr d Rmu 999. Rmu 2002 ho h i h log ru ih fr ry d xi of firm h ggrg mploym i drmid by h zro-profi codiio, chg i profi my imply h highr g x progriviy ill givly ffc mploym if h mrgil x r i high ough. Th rul c doub hhr x progrio i ly good for mploym i fficicy g frmork. I hi ppr, focu o rvu-url chg i h dgr of x progrio i fficicy g modl hr homogou orkr choo hir opiml ork ffor lvl coiuouly. I doig o, ould lik o coribu o h lirur i h folloig o y. Fir, o highligh h rol of h govrml budg i drmiig h impc x progrio h o mploym. Th dgr of x progrio o oly ffc gro g d orkr rrvio g, bu i lo ffc h y i hich h govrm c ubiu g x for pyroll x or icr x lloc i rvu-url y. To hi, coidr rvu-url x rform h ri boh h mrgil g x d h x xmpio by iiilly kpig h vrg g r co. Thi ld o g modrio. Th highr h ol mrgil x dg, h mor hi g modrio rduc x rvu d h l h govrm c ri h orkr x xmpio. For y giv icr of h mrgil x r, h ffor hcig ffc hu dcr ih h ol x dg. A lor ffor lvl dcr h orkr lbour produciviy d dmd bcom mllr y giv g r. If h rvu-url ri i h x xmpio bcom vry mll, h iiil poiiv mploym ffc my b rvrd.

4 3 Th cod impor poi o r i hi ppr i o ho h diffr y of lrig h dgr of x progrio yild h m rul. Thi i impor h compoiio of g d pyroll x of chg du o lbor x rform d h dgr of x progrio. Th impc of h compoiio of g d pyroll x o progriviy hv o y b lyzd i fficicy g frmork, hil rul from uio brgiig modl lrdy xi. Kokl d Schöb 999 ho h h x b for g d pyroll x r qul, i do o mr ho d jur py h x o lbour. I hi c h ol x dg, i.. h um of g d pyroll x, i uffici o pcify h diorio du o lbour xio. Bu hi quivlc rul c o hold h h x b r o qul bcu of x xmpio lo Kokl d Schöb A rvuurl rrucurig of lbour x ord h rror x b h dcr h gro g d boo mploym. I hi ppr, ill k hhr h fidig cocrig h impc of diffrc i h rucur of lbour xio hold i fficicy g frmork ih o-dicr ork ffor choic. I priculr, r ird i hhr x progrio pr or h pcific y i hich i i chivd mr for h drmiio of i mploym ffc. W procd follo. I cio 2, dvlop modl frmork h mirror h mi ylizd fc of lbour xio d provid compriv ic of x prmr o g ig, ork ffor, lbour dmd d ggrg oupu. I cio 3 h lyz x-rvu-url chg i x progrio by vryig h mrgil g x d h x xmpio d ho h imilrii o chg i x progrio vi chg i h compoiio of g d pyroll x. Scio 4 dicu h hpp h h x rform lo chg h rrvio g of orkr. Filly pr cocludig comm. Kokl d Schöb 999, Picrd d Toulmod 200, 2003, d Hijdr d ighr 2009 lyz mrgil x rform i hich g x ubiu for pyroll x i diffr lbor mrk modl bu oly Picrd d Toulmod 2003 coidr x progriviy i fficicy g frmork. Thy ho h, i grl, rvu-url hif of x o firm o x o orkr h icidc o mploym hir Propoiio 2; bu i hir modl x progriviy, hovr, i oly lyzd i h cox of vryig g x progrio hir Propoiio 3.

5 2. Modl frmork d compriv ic 4 To r ih, pcify h im quc of dciio, d h lyz h dciio of orkr o hir ork ffor, h opiml g ig d lbour dmd of firm. Filly, bd o h priv dciio, lyz h ffc of o diic rvu-url x rform h llo h govrm o lr h dgr of x progrio. 2. Tim quc of dciio Wh firm dcid o h g r hy py hir orkr d o h mploym lvl, hy k h x policy giv d um h hy co ifluc h x prmr. Th govrm hrfor bhv Scklbrg ldr by ig hr x irum. To ri rvu, h govrm c mploy ihr pyroll x or g x. Boh x r r co i rlio o h rpciv x b. I ddiio, h govrm c ffc h dgr of x progrio by grig x xmpio h rduc h x b for h g r o. I h prc of poiiv x xmpio, h mrgil x r xcd h vrg x r o h h x ym i lirly progriv. 2 Th of-x g i giv by. Whil h g x r progriv i ll OECD couri, h pyroll x cio 3, i.. h ocil curiy coribuio pid by mployr, r pproximly proporiol. W hrfor brc from ddiiol x xmpio for h pyroll x o h h x b for h pyroll x i. Th gro g r, i.. h lbour co, i h giv by g. W c udy o y i hich h govrm c lr x progrio ihou chgig x rvu. I c dircly ffc h g x progrio by icrig h g x r d icrig h x xmpio ccordigly. Alrivly, i c icr h g x d lor h pyroll x. Such chg i h rucur of lbour xio lo ffc h ovrll x progrio i chg h hr of h progriv g x d h proporiol pyroll x. 2 For mil ppr bou x progrio, Mugrv d Thi 948, d for ohr lborio,.g. mbr 200, chpr 7-8.

6 5 Wh h govrm ouc i x policy i h fir g, firm dcid o h g r d h mploym lvl i h 2 d g. I hi proc, hy co prfcly moior h idividul ork ffor of hir orkr. A ffor icr h diuiliy of orkig, orkr hv iciv o hirk, bu hi iciv c b off by pyig highr g ic hi ri h ply for hirkig orkr ho r cugh d fird. O-h-job orkr c dcid upo hir ork ffor i h 3 rd g. Th im quc of dciio i ho i Figur. I h follo, procd by uig bckrd iducio d r our lyi ih h 3 rd g of h gm, i hich h g r, mploym d x prmr r lrdy drmid. Figur : Squc of dciio g d 2 g rd 3 g Tx policy,, Wg ig d lbour dmd Effor drmiio 2.2 Effor drmiio Ech orkr provid o ui of lbour d dcid bou ffor i h 3 rd g by kig h x policy, g ig d lbour dmd giv. Sic ffor co b fully corolld by firm, hy c drd ffor h ormliz o o. If orkr m hi drd, hir job r cur, bu if hy hirk by providig l ffor, firm c fir hm. Hovr, ffor co b moiord prfcly. Th mploym probbiliy c hu b dcribd by miimum fucio. For ffor lor h h drd, um, for lyicl covic, io-lic probbiliy fucio of mploym d hr d 0 do h co mploym probbiliy liciy of ffor. 3 Th mploym 3 W xclud h c hr d = 0 bcu i hi c, h job ould b cur v ihou providig ffor d ol oupu ould fll o zro. Thi ould ld firm o g r qul o zro. Boh mploym upply d dmd ould h b idrmid. Furhrmor, o h if h dcio probbiliy hould b cocv i ffor, ould hv o um d.

7 6 probbiliy ri ih ffor for d i for highr ffor lvl, o h hv h d mploym probbiliy fucio mi, d h probbiliy of big lid off i mi, d. Th prmr d i icrig i boh moiorig iiy d moiorig fficicy. o vlu of d mk i l riky for orkr o hirk, hil d impli prfc moiorig d h firig of ll orkr ho do o m h orkig ffor drd. W coidr rpriv rik-url orkr ih pcific uiliy fucio h i ddiivly prbl d qui-lir, V mi, d [ g ] d d d mi, b g b V, hr b do h orkr rrvio g, hich, of cour, i from h vipoi of h orkr of x, d, for h im big, umd o b xogou for furhr / lborio cio 4, d g, 0, do h covx diuiliy of ffor. Workig im pr orkr i fixd d ormlizd o uiy. I h follo oly focu o h irig c. V d Th opiml idividul ffor lvl c b drivd from h fir-ordr codiio d d b 0. Th orkr choo ffor lvl hich h xpcd uiliy lo of orkig hrdr, hich occur ih probbiliy d, qul h xpcd uiliy gi from icrd probbiliy of yig i mploym d d d rcivig h urplu / b ih. Thi yild h folloig ffor fucio A b, 2 hr A d d i co. W um cocv ffor fucio ih rpc o h diffrc b h -of-x g r d h orkr rrvio g o h hv 0. Effor i icrig i h -of-x g r, 0, 4 d dcrig i h rrvio g, 0. Furhrmor, hv 0, bcu hi rduc h ply h b 4 I h follo, pril driviv ill b dod by ubcrip.

8 7 cugh hirkig, 0, d 0, boh highr g r d highr x xmpio icr h r from big mployd Wg ig d lbour dmd I h 2 d g, ch firm k h x prmr giv d dcid o h g r d lbour dmd. I doig o, i k io ccou ho h rpriv orkr ill dju ork ffor h h g r chg. Producio dpd o ffciv lbour ipu. For lyicl covic, prmriz h producio fucio for h rpriv firm f ih 0 doig h rvu hr of lbour d h profi hr. Hc hv cocv producio fucio i rm of ffciv lbour ipu, i.. f ' 0 d f '' 0. Th oupu pric i ormlizd o uiy d profi r dfid by f. Th fir-ordr codiio i rm of d r f ' / d f ' /, o h obi h Solo codiio, 3 Solo 979, ccordig o hich h g liciy of ffor i qul o o, i.. h opiml g i uch h o prc icr i h g r d hu h producio co ld o o prc icr i oupu giv mploym lvl. From h Solocodiio 3 c driv xplici oluio for h opiml fficicy g r for b 0 : b. 4 Th compriv ic of h g fucio ho h ig ig b d 0. Th Solo codiio h i i opiml for h firm o h g uch h h rliv chg i h g r i qul o h rliv chg i ffor. If b, h lvl of h o 5 W could llo for mor grl uiliy fucio h i cocv i rm of r d covx i rm of diuiliy of ffor o h could iclud rik vrio. Quliiv rul by uig h drd HARA-yp uiliy fucio uggd origilly by Mro 97 r imilr d r vilbl upo rqu.

9 8 ffc o h opiml g r. If b, hovr, x r icr ri h impc g r icr h o ffor: h highr i, h rogr h rliv icr of b du o g icr i. A highr x xmpio, by cor, mk orkig mor rciv d hrfor llo h firm o dcr h fficicy g r. No h h pyroll x do o ffc g drmiio. Th lbour dmd fucio i giv by, 5 hr d. Th compriv ic of lbour dmd ih rpc o ffor d h pyroll x r 0 d 0, rpcivly. Th g x d h x xmpio lvid o orkr oly ffc lbour dmd idircly vi h ffor drmiio, d h pyroll x oly ffc lbour dmd dircly vi h gro g r. Th ol ffc of chg i h g r, hovr, ifluc lbour dmd i o diffr y. Thr i giv dirc ffc, 0, d poiiv idirc 2 ffc of h g r vi ffor,. Th formr ffc domi, o h highr g r dcr lbour dmd. For h cocv producio fucio, h bolu vlu of h g liciy of lbour dmd i lor h i h c h g do o ffc ffor. Irig h Solo codiio, h ol g liciy of lbour dmd i h firm profi mximum bcom d. 6 d Effciv lbour ipu d h g bill rmi co du o mrgil g icr d hu profi. Thi i complmry codiio o h Solo codiio. Hvig lyzd orkr d firm bhviour ih rpc o chg i h x prmr, c o ur o h fir g. Rhr h lyzig opiml x ym, coidr mll x rform i h fir g d focu o h ffc of rvu-url chg i i g x progrio d ii h rucur of lbour xio o g formio, ffor drmiio, mploym d oupu.

10 Tbl : bour xio i h OECD couri Coury Avrg g x Socil curiy cori- Mrgil Socil curiy cori- pyroll x xmpio / m bfi vrg Tx Clculd Umploy- vrg g buio pid g x x r buio pid r i Euro by mploy progrio b i Euro by mployr progrio Sdrdizd umploym r 2004 Aurli , Auri , , Blgium , , Cd , , Czch Rpublic , , Dmrk , , Fild , , Frc , , rmy , , rc , Hugry , , Icld , ,98 3. Irld , , Ily , , Jp , , Kor , , uxmbourg , , Mxico , Nhrld , , N Zld , Nory , , Pold , , Porugl , , Slovk Rpublic , , Spi , , Sd , , Sizrld , , Turky , , Uid Kigdom , , Uid S , , Sourc: OECD 2004 gd: Tx r r for h yr 2004 for igl pro ih 00% of vrg g. Colum 4 ho h diffrc b mrgil d vrg r of icom x. Socil curiy coribuio pid by mploy r umd o o b ubjc o x xmpio. Socil curiy coribuio r mrgil coribuio. A pproximio i i umd h for ch coury h x chdul coi of x xmpio d co mrgil x r. W ook h xchg r b US Dollr d Euro of Dcmbr 3, 2004: US Dollr = Euro. Socil ic lvl do o iclud houig co. Numbr of ocil ic r from 2002 k from OECD 2004, Bfi d Wg, OECD Idicor.

11 0 3. Rvu-url chg i g x progrio Tx progrio c b ffcd by x xmpio d by h rucur of lbour xio h x b diffr. Tbl provid om iformio bou g x d pyroll x i h OECD couri, clculd for vrg produciv orkr ho i o mrrid. Th fir d cod colum rpor h vrg g x d h ocil curiy coribuio pid by h mploy. Th hird colum ho h mrgil icom x. Th vrg g x progrio mbr 200, chpr 7-8 i rpord i h fourh colum. Thi r h diffrc b h mrgil d h vrg icom x r du o h x xmpio for g x. Th highr hi diffrc, h mor progriv g xio i. Tbl ho h ll OECD couri hv progriv g x ym, hough hr r hug diffrc ih h high dgr of progrio big rpord for Ily, ih 6.3 prcg poi, d h lo o for Turky, ih oly 2.2 prcg poi. Pyroll x, rpord i h fifh colum, mily coi of ocil curiy coribuio pid by h mployr. Th vrg pyroll x progrio i h ixh colum i vry mll, d v giv for om couri bcu of om ork-rld ocilcuriy coribuio h r o dpd o g icom. Whil h mximum diffrc b coury vrg d mrgil g r i bov 6 prcg poi, h diffrc b vrg d mrgil pyroll x r ubilly lor i ll couri, ih mximum diffrc blo fiv prcg poi. Thu, hil obrv highly progriv g x ym, h pyroll x ym r pproximly proporiol. I h follo, focu o h lyi of x-rvu-url chg i h compoiio of lbour x, i.. h progriviy of h g x ym d h brifly dicu ho h rul crry ovr o chg i x progrio vi chgig h rucur of lbour xio. Th govrm budg i giv by. 7

12 Rvu-urliy i irprd kpig h ol x rvu from lbour xio co h lvl. Tx progrio icr h h diffrc b h ol mrgil x dg d h ol vrg x r / icr. W cll rvu-url icr i boh h g x r d h x xmpio icr i g x progrio. Wh i h combiio of chg i h g x r d h x xmpio combid ih h icurrd chg i h g r h ill kp govrm x rvu co? Tol diffriio of 7 giv d d d d 0. Tkig io ccou h iducd chg i h g r Appdix for dil d d d, hi c b ri d d d 0. 8 If r o h uprd-lopig pr of h Dupui-ffr curv for boh h g x r d h x xmpio, hich m h h x rvu icr i d dcr i, h hv 0 d 0. Sic / 0 Appdix d 0 umig b, uffici codiio for hi o hold r 0 d Th ffc of x rvu-url chg i mrgil g x d x xmpio Wg d Effor No r prprd o xplor h bhviourl ffc of x rvu-url chg i g x progrio. Afr om clculio dlgd o Appdix, obi h ffc of icr i g x progrio o h g r : d d d0. 9 Du o our umpio of uprd-lopig Dupui-ffr curv, h domior of 9 i poiiv. A for h umror i 9, uig h pril driviv of 4 imply

13 2 b 2 2 o h obi umbiguou g modrio ffc of riig x progrio: d d d0 0. 0, If h firm lor h g r, i bfi from lor g co bu h m im uffr from lor ork ffor, hich rduc lbour produciviy. I h iiil quilibrium, h firm h g r uch h h o ffc blc ou h mrgi. A rvu-url icr i g x progrio impli h i bcom bficil for firm o lor h g r bcu h ffc o ffor bcom mllr h h mrgil x r icr. To drmi h impc o lbour dmd d ork ffor, hv o driv h chg i h gro d -of-x g r, rpcivly. A kp h pyroll x co, fll i h g r lo lor h gro g r. Th chg i h -of-x g r i giv by: d d d0 d d d0 d d d0. 0 If h x rform did o chg h g r, icrig x progrio ould lv h of-x g r uffcd. 6 Bu h h g r fll, hr r o giv ffc o h -of-x g r. Fir, hr i h immdi dirc ffc of g modrio. Scod, hr i idirc budgry ffc. A g modrio lor x rvu, h govrm h o rduc h x of h icr i h x xmpio rliv o h poil icr d/ d i umbiguouly giv:. Thi furhr rduc h -of-x g r, o h h ol ffc d d d d d0 d Thi c b from ubiuig A4 from Appdix i 0 d ig d / d 0. d 0

14 3 Effor dpd poiivly o h -of-x g, i.. 0, o h c immdily dduc h orkr ffor lo fll: Th fidig r ummrizd i d d d 0. d d0 d0 Propoiio : A icr i h rvu-url g x progrio ld o g modrio h rduc boh h gro g r d h -of-x g r. A fll i h -of-x g r rduc idividul ork ffor d hu givly ffc lbour produciviy. Employm d oupu bour dmd dpd boh o h gro g d ffor. Firm ill lor h gro g bu lo fc lor lbour produciviy. Thu hr r o courvilig ffc o lbour dmd. From h ol diffril of mploym d d d d d by uig h rvu-url chg i h x xmpio 7, obi d d d. 2 Th fir rm qul h mploym ffc of rvu-url x rform h h g r do o chg. Thi rm i zro Appdix 2 for h clculio bcu rvu-url chg i x prmr ihou chg i h g r ould o lr h -of-x g r. If h fficicy g r do o chg, boh ffor d mploym do o chg. Th mploym ffc hu oly dpd o h iducd g r chg, o h hv: d d d d d0 d0. 3 To irpr hi rul d o ig h ffc, rri 3 i h folloig y:

15 4 d ig d d0 ig d ig d d d ig. Th fir rio of h righ-hd id idic h rliv impc h g r d h x xmpio hv o mploym. u um h icr h g r by o prc d h x xmpio by h m bolu mou. Th ffc of h g r, coiig of dirc ffc vi h gro g d oppoig idirc ffc vi riig ffor o mploym, i h. Th chg i h x xmpio oly icr ffor. Hovr, h ffc of qul-iz icr i h x xmpio o h -of-x g r i oly / of h ffc of g r icr. Muliplyig by h ffor liciy of lbour hu yild h ol ffc of h bov icr i h x xmpio: d/ d / /. By ho much c cully chg h g r d h x xmpio h coidr h rvu-urliy dpd o h mrgil x rvu? Th highr h x rvu of x irum, h lor i i rvu-url djum. If i h c h rogr h ol x dg i, lo bolu vlu of i lrg, hich, hich i h c h i lo, rquir lrg rducio i h x xmpio o comp for h iducd ffc. Th rliv mgiud c b b by irig / i quio 3. Thi yild h folloig codiio: / d d d If h ol x dg bcom vry high, h g modrig ffc rquir highr dord djum of h x xmpio. If hi lrdy h rog impc o ffor hich dpd o h chology prmr, i bcom vry likly h mploym ill fll. Th dvr ffc of x progrio o h budg djum rquirm h ouigh h g modrig ffc o h gro g.

16 5 Th ffc of h rvu-url chg i h g x progrio o ffciv lbour ipu d hrfor o oupu r priori uclr bcu icr i x progrio h giv ffc o ffor d mbiguou ffc o mploym. Th ol diffril for i d d d0 d d d0 d d d0 d d d0. 5 Solvig 5 by uig h rul drivd bfor Appdix 2, obi: d d d0 d0 d d 0. 6 Th ffor ffc of highr x progrio i umbiguouly giv, hil h mploym ffc i priori mbiguou bu, ccordig o quio 6, h fir ffc domi. Th dirc ffc of g r chg o lbour dmd ould xcly comp for lor ork ffor, bu h idirc ffc h forc h govrm o rduc h x of h x xmpio icr furhr lor ffor, mploym d, hrfor, ffciv lbour ipu. I ummig up h fidig of hi ubcio, c coclud ih Propoiio 2: A icr i h rvu-url g x progrio ri lor mploym h h rio of -of-x g d rvu hr of h g i highr lor h h ffor liciy of lbour dmd. Effciv lbour ipu d oupu fll umbiguouly. No h h ffc o ffciv lbour ipu d oupu hig o h fuciol form cho d my o hold i grl. 3.2 Rvu-url chg i h compoiio of g d pyroll x Alrivly x progrio c b ffcd by chg i h compoiio of g d pyroll lbour xio bcu uch rform chg h progriviy h h x b r diffr, i.. 0. Icrig h g x o h rro x b d rducig h pyroll x o h brordr x b ri h mrgil x giv vrg x r d hu icr h dgr of x progrio. Tkig h ol diffril of h govrm budg

17 6 cori 7 ih rpc o g x, pyroll x d gro fficicy g giv d d d d 0. Th chg i h fficicy g dpd oly o chg i h g x r, d d, o h hv d d d0. 7 If r o h uprd-lopig pr of h Dupui-ffr curv, hv 0 hich ly hold h 0 d b d 0, o h rvu-url icr i impli lor pyroll x. Th pyroll x bor by h mployr do o ffc h fficicy g r firm choo [cf. quio 4]. Th g r hrfor i oly ffcd by h g x r, i.. d d. Irrpcivly of h ig of 0, h -of-x g fll d hu lo ffor. d Th ol diffril of mploym ih rpc o g r, pyroll x r d g x r c b ri d d d d. By uig h rvuurl chg i lbour xio 7, obi d d d. 8 A chg i h compoiio of g d pyroll x ld o boh dirc d idirc ffc. Th o dirc ffc riforc ch ohr. Boh h icr i d o h hv d d ill hv giv ffc o lbour dmd. Th idirc ffc ork vi h govrm budg. Th rm i h igh of h poiiv dirc ffc i h fir brck rm d drmi ho much h ffc du o icr i i off. Sic h g r lo icr, h cod idirc ffc ork i xcly h m quliiv y h fir idirc ffc, hrby i h cod brck rm i h igh of h poiiv idirc ffc. I ur ou h codiio 4 i lo rlv h x progrio i ffcd by h chg i h compoiio of lbour x if 0. Furhrmor, irrpcivly of h y i hich x progrio i rid, ffciv lbour ipu d hu oupu ill fll. Oly if h x b r qul, i.. 0, ihr ffor or lbour i ffcd by h rvu-url chg

18 7 i h compoiio of g d pyroll x bcu x progrio i uffcd i hi pcil c Appdix 3 for h clculio. I ummig up h fidig of hi ubcio, c coclud ih Propoiio 3: A rvu-url chg i h compoiio of lbour xio h ri x progrio i.. 0 icr dcr mploym h h rio of h -of-x g d h rvu hr of h g i highr lor h h ffor liciy of lbour dmd. Effciv lbour ipu d oupu fll umbiguouly. Wh h x b r qul, ffor, mploym d oupu do o chg. Th iuiio for 0 i imilr o h iuiio for Propoiio 2 d ill o b rpd hr. Thi rul ho h i h c of qul x b, h rucur of lbour xio do o mr i rm of mploym i h fficicy g frmork. Th m rul hold i h uio brgiig frmork ihou fficicy coidrio Kokl d Schöb 999. Furhrmor, boh x rform icr x progrio d yild imilr ffc ih rpc o ffor, lbour dmd, ffciv lbour ipu d oupu. Thi idic ymic pr of ho h dgr of x progrio cully ffc h lbour mrk d producio. 4. Th rol of h rrvio g So fr hv umd co rrvio g b. Th rrvio g ormlly dpd o h lbour mrk codiio d i dogouly drmid i grl quilibrium. Hovr, vry lil i ko bou h xc rliohip. For ic, Bly 999 irvid mor h 300 bui xcuiv, lbour ldr, profiol rcruir d dvior o h umployd d cocludd h h orkr morl i impor for orkr prformc bu h orkr morl dpd o big rd firly ihi firm

19 8 for ic by pyig fir g ccordig o om blihd irl py rucur. A xogou b my b hu good pproximio. 7 By cor, Agll d Bmrkr 2003, 2007 rpor from rdom urvy of Sdih hum rourc mgr h o-hird of hir rpod bliv h icr i xrl g i driml o orkr ffor: Mo Sdih mgr idic h boh irl d xrl g r impor coidrio i h locl g brgi. Agll d Bmrkr 2003, p. 25. Thu, h rrvio g b i our modl hould rflc h lbour mrk codiio, mly ggrg umploym d vrg g. Dpdig o h y i hich h lbour mrk codiio ffc h rrvio g, h ol ffc my icr or rduc h fir-roud or hor-ru ffc hv lyzd i cio 3. Sic o lil i ko bou h fuciol form, oly pr huriic rgum ho h grl quilibrium ffc r lrd h h fir-roud ffc yild zro mploym ffc. A chg i h rrvio g ri h g, i.. h pril driviv of 4 yild 0. Th ffc o ffor i poiiv bcu h poiiv g ffc ouigh h giv dirc ffc, o h b d b b 0. 9 db b Th mploym ffc c b lo igd. I i ricly giv hv d db b d d b A pcil c, frquly ud i h lirur, um h umployd orkr fc h probbiliy u of big mployd i ohr idury d h probbiliy u of rmiig umployd. Formlly, h -of-x rrvio g i h giv by b u ub, 2.g. yrd, Nickll d Jckm 99, pp. 00-0, hr do h vrg g r d h opiml ffor lvl h vrg g r. For imilr firm i vriou 7 I imilr li, Cmpbll d Kmli 997 rpor h orkr mily compr hir g ih hir o p g, h g of ohr orkr ihi h firm, d ih firm profi.

20 9 iduri, h vrg g r qul h g r ch igl firm, i.., d opiml ffor ill b h m for ll orkr. For impliciy b 0. Th ol ffc o b i Appdix 4 for h clculio: d d db g. 22 d d d Ho do rul chg h h iiil mploym ffc ccordig o 4 i qul o zro? I hi c, h fir rm i 22 vih d h rrvio g umbiguouly fll. Thi riforc h fir-roud ffc o h g icom d ffor. From 20 i follo h c. pr. mploym h ri i quilibrium fr h rrvio g djud. If h iiil mploym ffc i poiiv, hv o courvilig ffc. Bu log db 0, hich ill b h c for prmr vlu h ur ufficily mll vlu of d d, h fir-roud mploym ffc ill b riforcd. Bu h db 0 bcom d0 ufficily lrg, h grl quilibrium ffc my vully ovrcomp h firroud ffc. Wh h iiil mploym ffc i giv ccordig o 4, h grl quilibrium ffc o ffor d h g icom r rogr h h fir-roud ffc hil h mploym ffc my bcom poiiv clo o d d 0 or my b l giv. d0 5. Cocludig rmrk Th rucur of lbour x, i.. pyroll d g x, i OECD couri vri coidrbly du o diffr x r d diffr rgulio cocrig x lloc ih rpc o g d pyroll x. Wg xio i OECD couri i progriv, lhough h dgr of progriviy vri cro couri. I h c of pyroll x, h diffrc b mrgil d vrg pyroll x i vry mll, i.. obrv pproximly proporiol pyroll x ym i mo OECD couri. For h ylizd fc, udid h impc of o diffr x-rvu-url chg i g x progrio. Fir, lyzd h rvu-url x rform hr boh h g x r

21 20 d h x xmpio r icrd o h g x progrio icrd. Scod, comprd h fidig ih ri i x progrio du o chg i h compoiio of lbour xio ord h x ih h lor x b. Our lyi ho h h h g x ym bcom mor progriv, hi ld o g modrio d o fll i orkr ffor. Whhr mploym ri or fll dpd o h pr-xiig x ym rliv o h lbour dmd liciy i rm of ork ffor quio 4, 22, bcu h mgiud of h ol x dg ffc h y i hich h govrm c ifluc orkr ffor i rvu-url y. Th icr i h g x c. pr. ri h gro g d lor lbor dmd. Th lrgr h x dg, h grr h fll i x rvu du o h iducd g modrio d h mllr h rvu-url ri i h x xmpio or h cu i pyroll x, hich cri pribu boh icr lbor dmd. Thi budgry ffc ffc h rul i h m y i boh x rform dicud i hi ppr d i hu h crucil forc i drmiig h impc h dgr of x progriviy h o mploym. Appdix Th ol diffril for 6 giv d d d d 0. Uig 0, A c ri h ol diffril d 0 d d d 0. Irig h rpciv pril driviv of lbor d ffor, pplyig d umig h h x rvu r poiivly rld o h g x r d givly rld o h x xmpio ccordig o h uprd-lopig Dupui-ffr curv, c drmi h ig of d follo: 0, A2 0. A3 Uig h xprio A2 d A3, c o drmi h rvu-url chg i h x xmpio h h g x r i icrd mrgilly:

22 2 d d0 d d. A4 Subiuig h RHS of A4 for d i h ol diffril d d d yild 9. Appdix 2 Subiuig A4 for d i h ol diffril d d d d d d giv d d d0 d 0 Uig h pril driviv of h mploym d ffor fucio, obi 0. Uig A d A3, obi fr om furhr mipulio d d d d d0 d 0. A5, A6 hr / 0. From h ffor drmiio 2 hv / b b d d o h d0 0 b. A7 Subiuig h fficicy g quio 4 for i A7 giv codiio 4. Uig h quio d A5, c rri 5 follo uig d d d0 d d Uig pril driviv of h mploym d ffor fucio, h commo rm c b ri Irig h, obi codiio 6. d0 d 0. A8 d

23 22 Appdix 3 Tkig h ol diffril of govrm budg cori 6 ih rpc o g x, pyroll x d gro fficicy g giv d d d d 0, hrby A9 Uig, obi for h fir rm of h RHS of quio 2 / A0 Th cod RHS rm of quio 2 i /. A Uig quio 8 impli / / 0 0 d d d d d d A2 Filly, combiig A0 d A2 yild 0 ig ig d d ig d, 0. A3 Thi giv h m codiio i 4. Cocrig ffciv lbour ipu d oupu hv 0. 0 b d d d A4 d hu 0 / 0 0 d d d d d d. 0 A5

24 23 Appdix 4 Uig b from 4, d rriig h diuiliy of ffor 2 d d b A6 d d Uig A6, c pcify h ol ffc o h rrvio g: db b d d b d b d b d d d d d d d. d d d d d b d d d d d d d d d d d d d d d d d d d A7 7. Rfrc Agll, J. d Bmrkr, H Edogou g rigidiy, CESifo Workig Ppr No 08, Novmbr. Agll, J. d Bmrkr, H Wg iciv d g rigidiy: rpriv vi from ihi, bour Ecoomic 4, Adr, T. M., Rmu, B. S Effor, xio d umploym, Ecoomic r 62, Bly, T. F Why Wg Do Fll Durig A Rcio, Hrvrd Uivriy Pr, Cmbridg. Cmpbll, C. M. d Kmli, K. S Th ro for g rigidiy: vidc from urvy of firm, Qurrly Jourl of Ecoomic 2, Fu, C. d Hubr, B Efficicy g, mploym, d h mrgil icom-x r: o, Jourl of Ecoomic 68, ork,. 999: Efficicy g d x, Aurli Ecoomic Ppr 38, Hijdr, B.J. d ighr, J. E bor x rform, umploym, d rch, Iriol Tx d Public Fic 6, Hol, M Efficicy g d icom xio, Jourl of Ecoomic 5,

25 24 Holm, P. d Kokl, E Tx progrio, rucur of lbour xio d mploym, FizArchiv 53, Kokl, E. d Schöb, R Do h compoiio of g d pyroll x mr udr Nh brgiig?, Ecoomic r 64, Kokl, E. d Schöb, R Why govrm hould x mobil cpil i h prc of umploym?, Coribuio of Ecoomic Alyi & Policy, Aricl. Kokl, E. d Vilmu, J Tx progrio i good for mploym i populr modl of rd uio bhviour, bour Ecoomic 3, mbr, P. J Th diribuio d rdiribuio of icom, 3 rd diio, Mchr Uivriy Pr. yrd, R., Nickll, S. d R. Jckm, R. 99. Umploym: Mcrocoomic Prformc d h bour Mrk, Oxford Uivriy Pr. Mro, R. 97. Opimum coumpio d porfolio rul i coiuou-im modl, Jourl of Ecoomic Thory 3, Mugrv, R. A. d Thi, T Icom x progrio, , Jourl of Poliicl Ecoomy 56, OECD Txig Wg , OECD Pri. Picrd, P. M. d Toulmod, E. 200, O h quivlc of x pid by mployr d mploy, Scoih Jourl of Poliicl Ecoomy 48, Picrd, P. M. d Toulmod, E. 2003, Txio d lbour mrk, Jourl of Ecoomic 78, Pirid, C. A Th impc of mploym x cu o umploym d g: h rol of umploym bfi d x rucur, Europ Ecoomic Rvi 42, Rmu, B. S Efficicy g d h log-ru icidc of progriv xio, Jourl of Ecoomic 76, Shpiro, C. d J. E. Sigliz 984. Equilibrium umploym orkr dicipli dvic, Amric Ecoomic Rvi 74, Solo, R. M Aohr poibl ourc of g icki, Jourl of Mcrocoomic, Sor, P. B Opiml x progriviy i imprfc lbour mrk, bour Ecoomic 6,