Does the composition of wage and payroll taxes matter under Nash bargaining?

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1 Economics Leers 64 (1999) Does he comosiion of age and ayroll axes maer under Nash bargaining? Erkki Koskela *, Ronnie Schob a, b a Dearmen of Economics, Uniersiy of Helsinki, P.O. Box 54, Unioninkau 37, IN Helsinki, inland b Cener for Economic Sudies, Uniersiy of Munich, Schacksrasse 4, D Munich, ermany Receied 10 Augus 1998; acceed 9 Aril 1999 Absrac Using he Nash bargaining aroach o age negoiaions his aer shos ha conenional isdom, according o hich he oal ax edge is he sum of age and ayroll axes, is alid for equal ax bases, e.g. hen he ax exemion akes he form of a ax credi. Hoeer, he equialence resul ceases o hold hen he ax bases are unequal due o ax alloances. In his case a reenue-neural resrucuring of labour axes oards a narroer ax base decreases he gross age and is hus good for emloymen Elseier Science S.A. All righs resered. Keyords: Tax edge; Payroll ax; Wage ax; Wage bargaining; Non-equialence JEL classificaion: H20; J51 1. Inroducion According o conenional isdom i does no maer ho de jure ays he ax on labour. ross nominal ages are he same regardless of heher he emloyer ays a ayroll ax or he emloyee ays a age ax. Layard e al. (1991, ) use his conjecure in heir emirical sudy of non-comeiie labour markes. They argue ha he oal ax edge, hich is he sum of he age and ayroll axes, is sufficien o secify he disorion of age formaion caused by labour axaion. In heoreical sudies on ax incidence and age formaion no disincion is usually made beeen age and ayroll axes, hough here is some emirical eidence hich suggess ha he o yes of labour axes migh hae differen effecs on age formaion (see, e.g., Lockood and Manning, 1993; Holm e al., 1994). *Corresonding auhor. Tel.: ; fax: address: erkki.koskela@helsinki.fi (E. Koskela) / 99/ $ see fron maer 1999 Elseier Science S.A. All righs resered. PII: S (99)

2 344 E. Koskela, R. Schob / Economics Leers 64 (1999) This aer shos ihin a righ-o-manage age bargaining model ha if he goernmen grans a ersonal ax alloance o orkers, hich is deducible from axable income, ayroll axes and age axes differ in heir imac on he gross age rae and hereby on emloymen. In he resence of a ersonal ax alloance, he age ax urns ou o hae a smaller ax base han he ayroll ax. Hence any reenue-neural increase in he age ax mus be higher han he associaed fall in he ayroll ax. This increases he marginal ax rae hile leaing he aerage ax rae consan. As he recen lieraure on ax rogression has oined ou, an increase in he ax rogression leads o a fall in gross ages and booss emloymen because he rade union s benefi from age increases becomes less. By conras, if he goernmen grans a ersonal ax credi, hich is deducible from he ax aymens, boh labour axes urn ou o be equialen as he ax bases and, herefore, ax rogression, remain he same. Secion 2 deelos he Nash bargaining aroach o describe age negoiaion ih he relean comaraie saics, hile Secion 3 sudies he imac of a reenue-neural resrucuring of labour axaion and resens he main resuls. Secion 4 roides he economic inerreaion for hese resuls. 2. The Nash bargaining model of age negoiaion We consider a single firm hich roduces good Y ih caial K and labour L as inus. The echnology is linear-homogenous, he elasiciy of subsiuion s is assumed o be consan. We assume imerfec comeiion in he goods marke, i.e. each single firm faces a donard sloing 2 demand cure hich is assumed o be iso-elasic, Y 5 D( ) 5, ih denoing he ouu rice and ; 2 ( D/ )? ( /D) he ouu demand elasiciy. To guaranee a rofi maximum he ouu demand elasiciy mus exceed uniy. Profis are gien by 5 Y 2 L 2 rk, hereby he firm considers he ineres rae r and he age rae as gien. The age aid by firms may consis of he nominal age, acually aid o he emloyee, and a ayroll ax, i.e. 5 (1 1 ). The rade union oeraes a he firm leel and is objecie is o maximize he income of is N members. Each orker sulies one uni of labour if emloyed, or zero labour if unemloyed. In he former case he orker receies a age income (ne of he ayroll ax). Each orker has o ay a age ax on he age income minus a ersonal ax alloance a. In addiion, he orker migh be eligible o a ax credi c hich she can deduc from her oal ax aymen. Unemloyed orkers are eniled o unemloymen benefis b. The objecie funcion of he rade union can hen be rien as V * 5 ((1 2 ) 1 a1 c)l 1 b(n 2 L). We use he righ-o-manage aroach so ha is deermined in a bargaining rocess beeen he rade union and he firm and he firm unilaerally deermines emloymen. The fall-back osiion of 0 he rade union is gien by V 5 bn, i.e. all members receie heir reseraion age hich is equal o 0 he unemloymen benefi. The fall-back osiion for he firm is gien by zero rofis, i.e The Nash bargaining maximand can hen be rien as

3 0 b 12b V 5 (V * 2V ), E. Koskela, R. Schob / Economics Leers 64 (1999) ih b reresening he bargaining oer of he rade union. Using V;V * 2V, he firs-order condiion ih resec o nominal age is V V 5 0 b] 1 (1 2 b )] 5 0, V here ariables ih subscris refer o arial deriaies (e.g., V 5 V/ ). or he comaraie saics of he age ax and he ayroll ax, e make use of he exlici form of he firs-order condiion, hich can be rien as V 5 ((1 2 ) 1 a1 c 2 b)[bh 1 (1 2 b )s(1 2 )] 1 (1 2 )b 5 0. (1) L, In Eq. (1), s denoes he share of labour cos in oal cos, s ; L/cY, ih c 5 c(,r) denoing he (consan) marginal cos, and hl, he age elasiciy of labour demand, hich can be deried analogously o he case of erfec comeiion (cf. Allen, 1938): L h L, ;]] 52s 1 s(s 2 ). L The second-order condiion is gien by V 5 y 1 xz, 0, ih y 5 (1 2 )[b(1 1h L, ) 1 (1 2 b )s(1 2 )], z 5 [b(s 2 ) 1 (1 2 b )(1 2 )]s (1 1 ) and x 5 (1 2 ) 1 a1 c 2 b, here e hae aken ino accoun he effec changes in he negoiaed age rae hae on he cos share of labour s. The comaraie saics of he ne-of-ax age ih resec o he age ax rae and he ayroll ax rae follos sraighforardly from imlici differeniaion of Eq. (1). Exressing he comaraie saics resuls in elasiciy forms, e obain (1 2 ) 21 a ;]]]] 5 ( y 1 xz) y 2 ]( y 2 b ), (2) (1 1 ) 21 ;]]]] 52( y 1 xz) xz. (3) The ersonal ax alloance a moderaes a age increase due o an increase in he age ax rae, bu does no hae a direc effec on he change of he negoiaed age if he ayroll ax rae changes. By conras, he ax credi c has no direc effec in eiher Eq. (2) or Eq. (3). Noe ha he sign of z deends on he comlemenariy relaionshi of facors and on he elasiciy of subsiuion. If facors 1 are rice comlemens, i.e. s 2, 0, e hae sign(z) 5 sign(1 2 s). 1 This can be seen from differeniaing he cos share of labour: s 5 s (1 1 ) 5 (s/)(1 2 s)(1 2 s).

4 346 E. Koskela, R. Schob / Economics Leers 64 (1999) Variaions in he srucure of labour axes In order o analyze he imac a reenue-neural change in he srucure of labour axaion has on he gross age and hereby on emloymen, e hae o formulae he goernmen budge consrain 5 [( 1 ) 2 a2 c]l 2 b(n 2 L). (4) The condiion for a reenue-neural change in ax rogression is gien by 21 d d 1 d d 52 d. or he Laffer cure being uard-sloing, i.e.,. 0, e can no deelo he formula for he gross age effec of a reenue-neural ax reform. The oal differenial of he gross age 5 (1 1 ) ih resec o and can be rien as d 5 d1 (1 1 )( d 1 d ). Uilizing he definiions for elasiciies from Eqs. (2) and (3) e end u ih (1 1 ) d 5 (1 1 )d 1]]] d. (5) (1 2 ) inally, by subsiuing he reenue-neuraliy condiion for d in Eq. (4) e can derie he imac a reenue-neural resrucuring of labour axaion has on he gross age: U d (1 1 ) 21 ] d (1 1 ) 1 ]]]. (6) d (1 2 ) In order o ealuae Eq. (6) e need o deelo exlici formulas for he marginal ax reenues hich accoun for he direc and indirec effecs of axes ia he negoiaed age rae and emloymen. I is shon in Aendix A ha a c 5 L 1 2] 1]]] (1 2 ) (7) and c c 2 ( 1 ) 5 L 1 1]]] 1 ]]]], (8) (1 1 ) (11 ) here c ; 1 1 ( 1 1 (b 2 a2 c)/)h L.. The exression in arenheses in Eq. (6), hich deermines he sign of he change of he gross age rae, can no be calculaed by using Eqs. (2), (3), (7) and (8): S (1 1 ) a 2 (1 1 ) 1 ]]] 52(1 1 ) 12] 1. (9) (1 2 ) D As Eqs. (2) and (3) imly ha 5 (1 1 ) 2 ( y 1 xz) a( y 2 b ), subsiuing his alue for in Eq. (9) yields afer some furher maniulaions

5 E. Koskela, R. Schob / Economics Leers 64 (1999) (1 1 ) 21 ab 2 (1 1 ) 1 ]]] 5 ( y 1 xz) ]H, J0 ahj (10) (1 2 ) Condiion (10) in combinaion ih Eq. (6) shos ha if he ersonal ax alloance a graned o orkers is osiie, a shif of labour axes oards age axes reduces he gross age rae and booss emloymen. As he age ax is leied on he ax base ( 2 a) hile he ayroll ax is leied on he age rae, his can be summarized as follos. Non-equialence resul. Under Nash bargaining a reenue-neural ax reform hich reduces he ayroll ax rae and increases he age ax rae ill decrease he gross age rae and booss emloymen if he emloyee s ax base is narroer han he emloyer s ax base. If he ax alloance a is zero, a reenue-neural resrucuring ill hae no effec on gross ages so ha he srucure of labour axaion becomes irrelean. This resul holds irresecie of he alue he ax credi c akes. In he absence of a ersonal ax exemion, ax bases are equal. Hence, his resul can be summarized as follos. Equialence resul. Under Nash bargaining a reenue-neural ax reform affecs neiher he gross age rae nor emloymen hen he ax bases are equal, as is he case hen he ax exemion akes 2 he form of a ax credi. 4. Inerreaion of he resuls Wheher ayroll axes and age axes are equialen or no urns ou o deend on heher a change in he srucure of labour axaion affecs ax rogression. Resrucuring labour axaion may change ax rogression for o reasons. irs, if he income changes as a resul of he ax reform, he acual ax rogression ill change for any gien ax schedule. Second, as he ax rae changes, he ax schedule may change for any gien income. The recen lieraure on ax rogression (cf., e.g., Koskela and Vilmunen, 1996) has oined ou ha if he ax rogression increases a a gien leel of income, gross ages ill fall and emloymen ill boos because he rade union s benefi from age increases become less. Hence, by looking a he quesion of heher he incenies for he rade union hae changed due o a change in he srucure of labour axaion, e hae o see heher he reform has changed he ax schedule. An aroriae and inuiie ay o define ax rogression is o look a he aerage ax rae m rogression, hich is gien by he difference beeen he marginal ax rae and he aerage ax rae a m ARP 5 2. a The ax sysem is rogressie if ARP is osiie, and ax rogression is increased if he difference 2 Holm and Koskela (1996) roed he non-equialence and he equialence resul under he more resricie assumion of a monooly rade union and for he secial case of a consan age elasiciy of labor demand. They do no, hoeer, make he imoran disincion beeen ax alloance and ax credi.

6 348 E. Koskela, R. Schob / Economics Leers 64 (1999) increases (a a gien income leel; cf. Lamber, 1989,. 159). Defining he ax edge for a orker m ih resec o he gross age rae, he marginal ax edge is gien by ; ( 1 )/(11 ) and he a m aerage ax edge by ; 2 ( a1 c)/. Hence, e hae m a a1 c ARP ]]]. If here is no ersonal ax alloance, a 5 0, Eq. (6) shos ha he gross age does no change and he aerage ax rae rogression is indeenden of he ax raes and. If, hoeer, he goernmen grans some ersonal ax alloances, i.e. a. 0, he ax rogression increases as a resul of a reenue-neural shif oards higher age axes: U darp a d ]] d50 5] 1 2]] ud50 g. 0. d d As he age ax has a smaller ax base han he ayroll ax, he increase in he age ax mus be higher han he fall in he ayroll ax hich increases he marginal ax rae for a gien aerage ax rae. I is herefore he effec a change in he srucure of labour axaion has on he rogressiiy of he ax schedule hich dries our resul. As ax rogression is good for emloymen in unionized labour markes a shif aay from ayroll axes oards age axes moderaes gross ages and alleiaes unemloymen. Acknoledgemens The firs auhor is indebed o he Research Uni on Economic Srucures and roh (RUES) for financial suor and he CES in Munich for is grea hosialiy. We are graeful o an anonymous referee for helful commens. Aendix A. Deriaion of Eqs. (7) and (8) Differeniaing he goernmen budge consrain (4) ih resec o yields 5 ( 2 a)l 1 ( 1 )L 1 ( ( 2 a) 2 c 1 b 1 )L (1 1 ) a 1 b 2 a2 c 5 L1 2] 1]]S1 1S 1 1]]]]DhL, D, (A.1) 1 2 hich gies Eq. (7). Analogously, he differeniaion ih resec o gies 5 L 1 ( 1 )L 1 ( ( 2 a) 2 c 1 b 1 )L 1 ( ( 2 a) 1 )L (1 1 ) 1 b 2 a2 c ]]S S ]]]]D D 1 1 L, 5 L h (1 1 ), (A.2) hich is Eq. (8) of he ex.

7 E. Koskela, R. Schob / Economics Leers 64 (1999) References Allen, R..D., Mahemaical Analysis for Economiss, Macmillan, London. Holm, P., Honkaohja, S., Koskela, E., A monooly union model of age deerminaion ih caial and axes: an emirical alicaion o he innish manufacuring. Euroean Economic Reie 38, Holm, P., Koskela, E., Tax rogression, srucure of labour axaion and emloymen. inanzarchi 53, Koskela, E., Vilmunen, V., Tax rogression is good for emloymen in oular models of rade union behaiour. Labour Economics 3, Lamber, P.J., The Disribuion and Redisribuion of Income. A Mahemaical Analysis, Basil Blackell, Cambridge, MA. Layard, R., Nickell, S., Jackman, R., Unemloymen: Macroeconomic Performance and he Labour Marke, Oxford Uniersiy Press, Oxford. Lockood, B., Manning, A., Wage seing and he ax sysem. Journal of Public Economics 52, 1 29.