203 DOES THE COMPOSITION OF WAGE AND PAYROLL TAXES MATTER UNDER NASH BARGAINING?

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1 VATT-KESKUSTELUALOITTEITA VATT-DISCUSSION PAPERS 203 DOES THE COMPOSITION OF WAGE AND PAYROLL TAXES MATTER UNDER NASH BARGAINING? Erkki Koskel* Ronnie Schöb** Vlion loudellinen ukimuskeskus Governmen Insiue for Economic Reserch Helsinki 1999

2 * Erkki Koskel, Dermen of Economics Universiy of Helsinki, P.O. Box 54 Unioninku 37, FIN Universiy of Helsinki, Finlnd. el. 358/9/ , fx 358/9/ , ** Ronnie Schöb, CES - Cener for Economic Sudies Universiy of Munich, Schcksrsse 4, D Munich, Germny. el. 49/89/ , fx 49/89/397303, ronnie.schoeb@ces.vl.uni-muenchen.de ISBN ISSN Vlion loudellinen ukimuskeskus Governmen Insiue for Economic Reserch Hämeenie 3, Helsinki, Finlnd Emil: firs nme.surnme@v.fi Ylioisoino Oy

3 ERKKI KOSKELA - RONNIE SCHÖB: DOES THE COMPOSITION OF WAGE AND PAYROLL TAXES MATTER UNDER NASH BARGAINING? Helsinki, VATT, Vlion loudellinen ukimuskeskus, Governmen Insiue for Economic Reserch, 1999, C, ISSN , No 203. ISBN Absrc: Using he Nsh brgining roch o ge negoiions his er shos h convenionl isdom, ccording o hich he ol x edge is he sum of ge nd yroll xes, is vlid for equl x bses, e.g., hen he x exemion kes he form of x credi. Hoever, he equivlence resul ceses o hold hen he x bses re unequl due o x llonces. In his cse revenue-neurl resrucuring of lbour xes ords nrroer x bse decreses he gross ge nd is hus good for emloymen. Keyords: x edge, yroll x, ge x, ge brgining, nonequivlence JEL clssificion: H20, J51 Tiiviselmä: Hyödynäen ns. Nsh neuvoelumllilähesymis kirjoiuksess osoien, eä sovinninen viisus, jonk mukn verokiil, s. lkk- j yönnjverojen summ, kuv yhjenäväsi yön verouksen käyäyymisvikuuksi, äee yhäsuurien veroohjien uksess. Tämä ekvivlenssihyoeesi ei kuienkn idä ikkns siinä yleisesi hvivss uksess, joss veroohj ov verovähennyksisä johuen erisuuri. Tällöin yöverojen verokerymän suheen neurli muuminen kohi kem veroohj vähenää kokonisyövoimkusnnuksi j rn yöllisyyä. Asisn: verokiil, yönnjmksu, lkkvero, lkkneuvoelu, eiekvivlenssi JEL:n luokielunumero: H20, J51

4 Acknoledgemens The firs uhor is indebed o he Reserch Uni on Economic Srucures nd Groh RUESG for finncil suor nd he CES in Munich for is gre hosiliy. We re greful o n nonymous referee for helful commens.

5 Conens 1. Inroducion 1 2. The Nsh brgining model of ge negoiion 2 3. Vriions in he srucure of lbour xes 5 4. Inerreion of he resuls 7 References 10

6 1. Inroducion According o convenionl isdom i does no mer ho de jure ys he x on lbour. Gross nominl ges re he sme regrdless of heher he emloyer ys yroll x or he emloyee ys ge x. Lyrd, Nickell nd Jckmn 1991, use his conjecure in heir emiricl sudy of noncomeiive lbour mrkes. They rgue h he ol x edge, hich is he sum of he ge nd yroll xes, is sufficien o secify he disorion of ge formion cused by lbour xion. In heoreicl sudies on x incidence nd ge formion no disincion is usully mde beeen ge nd yroll xes, hough here is some emiricl evidence hich suggess h he o yes of lbour xes migh hve differen effecs on ge formion see e.g. Lockood nd Mnning 1993 or Holm, Honkohj nd Koskel This er shos ihin "righ-o-mnge" ge brgining model h if he governmen grns ersonl x llonce o orkers, hich is deducible from xble income, yroll xes nd ge xes differ in heir imc on he gross ge re nd hereby on emloymen. In he resence of ersonl x llonce, he ge x urns ou o hve smller x bse hn he yroll x. Hence ny revenue-neurl increse in he ge x mus be higher hn he ssocied fll in he yroll x. This increses he mrginl x re hile leving he verge x re consn. As he recen lierure on x rogression hs oined ou, n increse in he x rogression leds o fll in gross ges nd booss emloymen becuse he rde union's benefi from ge increses becomes less. By conrs, if he governmen grns ersonl x credi, hich is deducible from he x ymens, boh lbour xes urn ou o be equivlen s he x bses nd, herefore, x rogression, remin he sme. Secion 2 develos he Nsh brgining roch o describe ge negoiion ih he relevn comrive sics, hile secion 3 sudies he imc of revenue-neurl resrucuring of lbour xion nd resens he min resuls. Secion 4 rovides he economic inerreion for hese resuls.

7 2 2. The Nsh brgining model of ge negoiion We consider single firm hich roduces good Y ih cil K nd lbour L s inus. The echnology is liner-homogenous, he elsiciy of subsiuion σ is ssumed o be consn. We ssume imerfec comeiion in he goods mrke, i.e. ech single firm fces donrd sloing demnd curve hich is ssumed o be iso-elsic, Y = D = ε, ih denoing he ouu rice nd ε D D he ouu demnd elsiciy, resecively. To gurnee rofi mximum he ouu demnd elsiciy mus exceed uniy. Profis re given by π = Y L! rk, hereby he firm considers he ineres re r nd he ge re! s given. The ge! id by firms my consiss of he nominl ge, cully id o he emloyee nd yroll x, i.e.! = 1. The rde union oeres he firm level nd is objecive is o mximize he income of is N members. Ech orker sulies one uni of lbour if emloyed, or zero lbour if unemloyed. In he former cse he orker receives ge income ne of he yroll x. Ech orker hs o y ge x on he ge income minus ersonl x llonce. In ddiion he orker migh be eligible o x credi c hich he cn deduc from her ol x ymen. Unemloyed orkers re eniled o unemloymen benefis b. The objecive funcion of he rde union cn hen be rien s * V = 1 c L b NL. We use he righ-o-mnge roch so h is deermined in brgining rocess beeen he rde union nd he firm nd he firm unilerlly deermines emloymen. The fll-bck osiion of he rde union is given by V 0 = bn, i.e. ll members receive heir reservion ge hich is equl o he unemloymen benefi. The fll-bck osiion for he firm is given by zero rofis, i.e. π 0 = 0. The Nsh brgining mximnd cn hen be rien s * Ω= V V 0 β π 1 β, ih β reresening he brgining oer of he rde union. Using V V V he firs-order condiion ih resec o nominl ge is * 0,

8 3 V Ω = 0 β 1 β π = 0, V π here vribles ih subscris refer o ril derivives e.g. V = V /. For he comrive sics of he ge x nd he yroll x, e mke use of he exlici form of he firs-order condiion, hich cn be rien s = 1 c b βη 1β s 1 ε 1 β = 0. 1 Ω L,! In eq. 1 s denoes he shre of lbour cos in ol cos, s L! cy, ih c= c!, r denoing he consn mrginl cos, nd η L,! he ge elsiciy of lbour demnd, hich cn be derived nlogously o he cse of erfec comeiion cf. Allen 1938: The second-order condiion is given by L! η σ s σ ε L,!! =. L Ω = y xz<0, ih y = 1 β 1 η 1β s 1ε, z = β σ ε 1β 1 ε s 1 L,! nd x = 1 cb here e hve ken ino ccoun he effec chnges in he negoied ge re hve on he cos shre of lbour s. The comrive sics of he ne-of-x-ge ih resec o he ge x re nd he yroll x re P follos srighforrdly from imlici differeniion of eq. 1. Exressing he comrive sics resuls in elsiciy forms, e obin! ω 1 1 ω = y xz y y β, = y xz xz. 3 The ersonl x llonce moderes ge increse due o n increse in he ge x re, bu does no hve direc effec on he chnge of he negoied ge if he yroll x re chnges. By conrs, he x credi c hs no direc effec in eiher eq. 2 or 3. Noe h he sign of z deends on he

9 4 comlemenriy relionshi of fcors nd on he elsiciy of subsiuion. If fcors re rice comlemens, i.e. σ ε <0, e hve sign z = sign 1σ. 1 1 This cn be seen from differeniing he cos shre of lbour: s = s 1 = s/ 1 s 1 σ.!

10 5 3. Vriions in he srucure of lbour xes In order o nlyze he imc of revenue-neurl chnge in he srucure of lbour xion hs on he gross ge nd hereby on emloymen, e hve o formule he governmen budge consrin G = c Lb NL. 4 The condiion for revenue-neurl chnge in x rogression is given by dg = = G d G d d = G 1 0 G d. For he Lffer curve being urdsloing, i.e. G, G > 0 e cn no develo he formul for he gross ge effec of revenue-neurl x reform. The ol differenil of he gross ge! = 1 ih resec o nd P cn be rien s d! = d 1 d d. Uilizing he definiions for elsiciies from eq. 2 nd 3 e end u ih d 1 1 ω d ω d 1 ~. 5 = Finlly, by subsiuing he revenue-neurliy condiion for d in eq. 4 e cn derive he imc revenue-neurl resrucuring of lbour xion hs on he gross ge: d~ d dg= 0 = 1 G G 1 ω G 1 1 ω. 6 In order o evlue eq. 6 e need o develo exlici formuls for he mrginl x revenues hich ccoun for he direc nd indirec effecs of xes vi he negoied ge re nd emloymen. I is shon in endix h nd G G L ψ 1 = ω ψ = L 1 1 1, 7 ω ψ 1, 8

11 6 ψ b c η ~. The exression in here L. renheses in equion 6, hich deermines he sign of he chnge of he gross ge re, cn no be clculed by using he equions 2, 3, 7 nd 8: 1 G 1 = 1 ω G ω 1 ω 1. 9 ω 1 As eq. 2 nd 3 imly h ω = 1 ω y xz yβ 1, subsiuing his vlue for ω in eq. 9 yields fer some furher mniulions G 1 1 ω β < > 0 0 = = 1 ω G = y xz Condiion 10 in combinion ih eq. 6 shos h if he ersonl x llonce grned o orkers is osiive, shif of lbour xes ords ge xes reduces he gross ge re nd booss emloymen. As he ge x is levied on he x bse hile he yroll x is levied on he ge re, his cn be summrized s NON-EQUIVALENCE RESULT: Under Nsh brgining revenue-neurl x reform hich reduces he yroll x re nd increses he ge x re ill decrese he gross ge re nd booss emloymen if he emloyee's x bse is nrroer hn he emloyer s x bse. If he x llonce is zero, revenue-neurl resrucuring ill hve no effec on gross ges so h he srucure of lbour xion becomes irrelevn. This resul holds, irresecively of he vlue he x credi c kes. In he bsence of ersonl x exemion, x bses re equl. Hence, his resul cn be summrized in n EQUIVALENCE RESULT: Under Nsh brgining revenue-neurl x reform ffecs neiher he gross ge re nor emloymen hen he x bses re equl, s is he cse hen he x exemion kes he form of x credi. 2 2 Holm nd Koskel 1996 roved he non-equivlence nd he equivlence resul under he more resricive ssumion of monooly rde union nd for he secil cse of consn ge elsiciy of lbor demnd. They do no, hoever, mke he imorn disincion beeen x llonce nd x credi.

12 7 4. Inerreion of he resuls Wheher yroll xes nd ge xes re equivlen or no urns ou o deend on heher chnge in he srucure of lbour xion ffecs x rogression. Resrucuring lbour xion my chnge x rogression for o resons. Firs, if he income chnges s resul of he x reform, he cul x rogression ill chnge for ny given x schedule. Second, s he x re chnges, he x schedule my chnge for ny given income. The recen lierure on x rogression cf. e.g. Koskel nd Vilmunen 1996, hs oined ou h if he x rogression increses given level of income, gross ges ill fll nd emloymen ill boos becuse he rde union's benefi from ge increses become less. Hence, by looking he quesion heher he incenives for he rde union hve chnged due o chnge in he srucure of lbour xion, e hve o see heher he reform hs chnged he x schedule. An rorie nd inuiive y o define x rogression is o look he verge x re rogression, hich is given by he difference beeen he mrginl x re m nd he verge x re m ARP =. The x sysem is rogressive if ARP is osiive, nd x rogression is incresed if he difference increses given income level, cf. Lmber 1989, Defining he x edge for orker ih resec o he gross ge re, he m mrginl x edge is given by 1 nd he verge x edge by m c!. Hence, e hve m c ARP = =.! If here is no ersonl x llonces, = 0, eq. 6 shos h he gross ge! does no chnge nd he verge x re rogression is indeenden from he x res nd. If, hoever, he governmen grns some ersonl x llonces, i.e. > 0, he x rogression increses s resul of revenue-neurl shif ords higher ge xes: darp d ~ ~ 1 d ~ d = dg= 0 dg= 0 > 0.

13 8 As he ge x hs smller x bse hn he yroll x, he increse in he ge x mus be higher hn he fll in he yroll x hich increses he mrginl x re for given verge x re. I is herefore he effec chnge in he srucure of lbour xion hs on he rogressiviy of he x schedule hich drives our resul. As x rogression is good for emloymen in unionized lbour mrkes shif y from yroll xes ords ge xes moderes gross ges nd llevies unemloymen.

14 9 Aendix: Derivion of equions 7 nd 8 Differeniing he governmen budge consrin 4 ih resec o yields = = L c b L L b c L L G ω η ~, ~ A1 hich gives eq. 7. Anlogously, he differeniion ih resec o gives = = ~, ~ ~ L c b L L L b c L L G ω η A2 hich is eq. 8 of he ex.

15 10 References Allen, R.G. D. 1938: Mhemicl Anlysis for Economiss. Mcmilln: London. Holm, P., Honkohj S., Koskel, E. 1994: A Monooly Union Model of Wge Deerminion ih Cil nd Txes: An Emiricl Alicion o he Finnish Mnufcuring. Euroen Economic Revie 38, Holm, P., Koskel, E. 1996: Tx Progression, Srucure of Lbour Txion nd Emloymen. Finnzrchiv 53, Koskel, E. nd Vilmunen, V. 1996: Tx Progression is Good for Emloymen in Poulr Models of Trde Union Behviour. Lbour Economics 3, Lmber, P. J. 1989: The Disribuion nd Redisribuion of Income. A Mhemicl Anlysis. Bsil Blckell: Cmbridge, Mss. Lyrd, R., Nickell, S., Jckmn, R. 1991: Unemloymen: Mcroeconomic Performnce nd he Lbour Mrke. Oxford Universiy Press, Oxford. Lockood, B., Mnning, A. 1993: Wge Seing nd he Tx Sysem. Journl of Public Economics 52, 1-29.