Institute for International Economic Studies Seminar paper No. 760 PATTERN BARGAINING AND WAGE LEADERSHIP IN A SMALL OPEN ECONOMY by Lars Calmfors

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1 Insttute for Internatonal Economc Studes Semnar paper No. 760 PATTERN BARGAINING AND WAGE LEADERSHIP IN A SMALL OPEN ECONOMY by Lars Calmfors and Anna Larsson

2 Semnar Paper No. 760 Pattern Barganng and Wage Leadershp n a Small Open Economy by Lars Calmfors and Anna Larsson Papers n the semnar seres are publshed on the nternet n Adobe Acrobat (PDF) format. Download from ISSN: X Semnar Papers are prelmnary materal crculated to stmulate dscusson and crtcal comment. August 2009 Insttute for Internatonal Economc Studes Stockholm Unversty S Stockholm Sweden

3 Pattern Barganng and Wage Leadershp n a Small Open Economy Lars Calmfors Anna Larsson August 7, 2009 Abstract Pattern barganng where the tradables (manufacturng) sector acts as wage leader s a common form of wage barganng n Europe. Our results queston the conventonal wsdom that such a barganng set-up produces wage restrant. We fnd that all forms of pattern barganng gve the same macroeconomc outcomes as uncoordnated barganng under nflaton targetng and a flexble exchange rate. Under monetary unon (a fxed exchange rate) wage leadershp for the non-tradables sector s conducve to wage restrant and hgh employment, whereas wage leadershp for the tradables sector s not. Loss averson and comparson thnkng n wage settng, where unons evaluate the utlty of the wages of ther members relatve to a wage norm, may lead the follower to set the same wage as the leader. Such equlbra can arse when the leader sector s the smaller sector and promote hgh employment. Keywords: Pattern Barganng, Wage Settng, Inflaton Targetng, Monetary Regmes JEL-classfcaton: E24, J50 We are grateful for comments and suggestons from semnar partcpants at HECER n Helsnk, the Department of Economcs at Stockholm Unversty, the Research Insttute of Industral Economcs n Stockholm and from partcpants n the 2009 workshop on "Wage Rgdty under Low Inflaton Regmes" at the Swedsh Insttute for Socal Research. Astrd Wåke provded excellent edtoral assstance. Fnancal support from Jan Wallander s and Tom Hedelus Research Foundaton s gratefully acknowledged. Insttute for Internatonal Economc Studes, Stockholm Unversty, SE Stockholm, Phone , Fax: , Emal: Lars.Calmfors@es.su.se Department of Economcs, Stockholm Unversty, SE Stockholm, Phone: , Fax , Emal: Anna.Larsson@ne.su.se

4 1 Introducton The wage-settng arrangements of many Western European countres are charactersed by barganng between employers and unons at the ndustry level. Pattern barganng s usually a key feature of these systems. Ths means that a key sector, usually the engneerng sector, concludes the frst agreement n a wage barganng round and that ths agreement sets a norm that gudes subsequent wage contracts n other sectors. Pattern barganng thus works as a coordnaton devce. Typcal examples are Austra, Denmark, Germany, Norway and Sweden (EEAG 2004). Ths form of pattern barganng has often been explaned by a perceved need to organse collectve barganng n such a way that t can ensure a degree of wage moderaton consstent wth hgh employment. It s usually beleved that ths can be acheved by choosng a tradables sector, heavly exposed to nternatonal competton, as wage leader. The gradual declne n the relatve mportance of the manufacturng (tradables) sector and the assocated rse of the servces (nontradables) sector has, however, put the earler system under stran n many countres. Clearly, t s easer for a sector to secure the poston of wage leader the larger the sector. The wage barganng system n Sweden provdes a good example of both earler thnkng and the current problems for pattern barganng. Snce the concluson n 1997 of a framework agreement determnng how wage barganng should be conducted (the so-called Industry Agreement), t has been generally accepted that the manufacturng sector should act as a wage leader, settng the norm for wage ncreases n all ndustry-level wage contracts. 1 Ths prncple has also been wrtten nto the nstructon of the Natonal Medaton Offce. The thnkng behnd ths goes back to the early 1970s and the normatve "Scandnavan model of wage formaton", accordng to whch wage ncreases should follow the room gven by prce and productvty ncreases n the tradables sector. 2 The dea was that n the fxed exchange-rate system of the tme, ths norm would dscplne wage settng, as frms n the tradables sector would have to adjust ther prces to those of foregn compettors f they were to mantan ther market shares. Hence, wage setters would realse that hgher wage 1 See, for example, Lönebldnng för full sysselsättnng (1999), God sed vd lönebldnng (2006) or Medlngsnsttutet (2007). 2 The Scandnavan model of wage formaton was orgnally formulated as a bass for wage barganng n Norway; see, for example, Aukrust (1972). The Swedsh verson was termed the EFO model, after the ntals of the chef economsts n the leadng labour market organsatons, who adapted the model to Sweden; see Edgren, Faxén and Odhner (1973). An early analyss of the model was provded by Calmfors (1975). 1

5 ncreases than accordng to the norm would reduce the proft share n the tradables sector and cause unemployment. The belef was that the ncentves for wage moderaton would be much weaker under uncoordnated barganng or f the non-tradables sector nstead would set the norm for wage ncreases, as the possbltes to shft wage ncreases on to prces are much greater there. Recently, the wage leadershp role of the manufacturng sector has begun to be questoned n Sweden. There s an ongong dscusson wthn the labour market organsatons on whether or not there s a need to revse barganng procedures. Thsdscussonwastrggeredbyconflcts, especally on the employer sde, regardng barganng outcomes n the 2007 wage negotatons on new threeyear wage contracts. There was wdespread dscontent on the part of servce sector employers assocatons wth the wage leadershp role of the manufacturng sector: t was wdely argued by servce sector employers that they had to adjust to an napproprate wage norm determned by the manufacturng sector. Smlar dscussons have taken place n other European countres, too, for example Germany. As far as we know, there s no prevous academc research on the consequences of dfferent choces of wage leader. Our am s to fll ths gap. A key ssue s how the effects of dfferent choces of wage leader are nfluenced by the monetary regme: a flexble exchange rate wth nflaton targetng or membershp n a monetary unon (an rrevocably fxed exchange rate). Another am s to explan why negotated wage ncreases n subsequent wage barganng tend to follow the key sector wage agreement very closely. We also examne the asserton sometmes made that the key sector agreement provdes a "floor" for subsequent agreements. A fnal ssue s how the effects of choosng a sector as wage leader are affected by ts sze. Our analyss s a follow-up to Calmfors (2008), who dscussed the development of pattern barganngnswedennannformalway. We present a two-sector model of a small open economy. Pattern barganng s modelled as a Stackelberg game where ether the tradables or the non-tradables sector can act as wage leader. Uncoordnated barganng s modelled as a Nash equlbrum. We consder frst a case wth standard trade unon utlty functons. Ths analyss gves a few unexpected results. It turns out that the monetary regme s crucal for the effects of wage leadershp. Under nflaton targetng, the two Stackelberg equlbra concde wth the Nash equlbrum. Pattern barganng thus provdes dentcal outcomes to uncoordnated barganng and t does not matter whch sector s wage leader. 2

6 In monetary unon, the real wage n the follower sector s the same under pattern barganng as under uncoordnated barganng. If the tradables sector s leader n a Stackelberg game, t sets a hgher wage than n the Nash equlbrum. In contrast, the non-tradables sector sets a lower wage when t s wage leader n a Stackelberg game than n the Nash game. As a consequence, wth pattern barganng aggregate employment s hgher wth the non-tradables sector than wth the tradables sector as wage leader. Ths result goes aganst the conventonal wsdom, accordng to whch wage leadershp for the tradables sector s regarded as conducve to wage restrant and hgh employment. We also analyse a case where trade unon utlty n the follower sector depends on a reference wage ("the wage norm"), whch s taken to be the wage set by the wage leader. The dea s to capture the tendency to use the barganed wage n the key sector as the comparson norm n subsequent barganng n other sectors. Ths analyss provdes an explanaton of the strong tendency for pattern barganng to result n more or less dentcal wage outcomes n dfferent sectors. Usng the Kahneman-Tversky (1979) concept of loss averson, we show the possblty of corner solutons where t s optmal for the follower to set the same wage as the leader. Such corner-soluton equlbra can arse under both monetary regmes when the smaller sector s wage leader. The leader may then have an ncentve to act strategcally to nduce the follower to choose such an equlbrum. We show that "comparson thnkng" n combnaton wth loss averson n wage settng may gve more wage restrant and hgher employment compared to a stuaton where such comparsons do not matter for trade unon utlty, because the possblty of favourable corner-soluton equlbra s opened up. The paper s organsed as follows. Secton 2 brefly revews the related lterature. The model assumptons regardng output, employment, prces and monetary polcy are presented n Secton 3. Secton 4 analyses wage settng assumng standard trade unon utlty functons and compares dfferent equlbra. Secton 5 consders the case where the leader determnes a wage norm that nfluences unon utlty n the follower sector. Secton 6 provdes numercal results. Secton 7 concludes. 3

7 2 Related lterature There exsts a lterature on the mpact of the monetary regme on wages and employment when wage setters are large. Ths lterature challenges the conventonal wsdom of the neutralty of money,.e. that money does not affect real wages, output and employment. Cukerman and Lpp (1999), Soskce and Iversen (2000), Corcell et al. (2006) and Larsson (2007) are contrbutons to ths research. The man dea s that when trade unons are large enough to nternalse the mpact of ther wage decsons on aggregate varables, the potental response of the central bank wll affect the labour market outcome n terms of real wages and employment. One mechansm s that trade unons may be nflaton averse (n addton to carng about unemployment and real wages). Large unons then have an ncentve to set low wages, promotng low unemployment, to avod that a tme-nconsstent lberal central bank (puttng a hgh weght on low unemployment) wll nflate as n Cukerman and Lpp (1999) and Corcell et al. (2006). Another, perhaps more plausble, mechansm s that conservatve central banks (emphassng prce stablty) may exert a postve effect on employment by provdng a deterrent to hgh wages: large wage setters wll perceve a hgher cost of wage ncreases n terms of employment, the more nclned s the central bank to pursue contractonary monetary polcy n response to wage hkes (Soskce and Iversen, 2000, Corrcell et al., 2006). 3 Although most of the lterature consders closed economes, exceptons nclude Vartanen (2002, 2008), Holden (2003) and Larsson (2007). Vartanen (2002) and Holden (2003) compare nflaton targetng under a flexble exchange rate wth a credbly fxedexchangerateregmenatwo-sector model of a small open economy. The concluson s that n the tradables sector, the real wage s hgher under nflaton targetng than under a fxed exchange rate, whle the reverse apples n the non-tradables sector. Under rather general assumptons, aggregate employment levels as well as welfare are hgher under nflaton targetng than under a fxed exchange rate. Larsson (2007) shows that when perfect labour moblty s ntroduced n a smlar settng, worker mgraton offsets the effects of the monetary regme and the neutralty of money s restored. However, n realty, labour moblty s lmted and the predcton that the monetary regme matters s lkely to be emprcally relevant. 3 See also Calmfors (2004) for a revew of ths lterature. 4

8 All the models dscussed above assume that wages n dfferent parts of the economy are set smultaneously and thus ndependently of each other (Nash equlbrum). Our contrbuton s to analyse also Stackelberg games where one sector acts as wage leader and the other as wage follower. The Stackelberg equlbra are compared wth the Nash equlbrum, whch s thus used as a benchmark. The closest counterpart to our paper s Vartanen (2008) who analyses how Stackelberg leadershp n general may be benefcal for employment but not the consequences of dfferent choces of wage leader. 3 The model Consder a small open economy consstng of a tradables (T ) and a non-tradables (N) sector, where subscrpt = N,T ndcates sector. Each sector conssts of a contnuum of dentcal perfectly compettve frms. The frms n each sector are ndexed on the nterval [0,1]. The economy s nhabted by a large number of households wth dentcal utlty functons and whch consume the two goods. Households consst of two groups: one group provdes labour to frms, the other group s made up of "captalsts" ownng the frms. The nomnal wage n each sector s set through barganng between one large unon and one employers federaton. In the labour market the ndvdual takes wages as gven. The monetary target s gven and credble to all players. The tmng of events s as follows: In stage one, wages are set. In stage two, the central bank determnes monetary polcy gven the wages set n stage one. In stage three, producton, employment, consumpton and prces are determned. Ths s done gven the wages and monetary polcy decded n the prevous stages. The model s solved by backward nducton and the equlbrum s subgame perfect. 3.1 Producton, consumpton and employment In the last stage of the game, proft-maxmsng frms decde how much to produce and utltymaxmsng households how much to consume. Both frms and households take prces and wages as gven. 5

9 3.1.1 Frms Frms n each sector produce a homogeneous good wth labour as the only nput. A representatve frm n sector maxmses real profts Π by choosng employment N so as to: max N Π =(P Y W N ) /P, (1) where P s the product prce n the sector, W s the nomnal wage n the sector, Y s the output of the frm and P s the aggregate prce ndex, subject to the producton functon: Y = 1 θ N θ, where θ (0, 1). The frst-order condton for proft maxmsaton gves employment n a representatve frm n sector : N = µ W P η, (2) where η =(1 θ ) 1 > 1 s the labour demand elastcty wth respect to the real product wage W /P. The correspondng supply functon s gven by: Y = 1 µ σ W, (3) θ P where σ = θ / (1 θ ) s the output elastcty wth respect to the real product wage. Substtutng the proft-maxmsng levels of output and employment nto the proft functon, t can be wrtten; Π = 1 W η 1 P µ W P η. (4) Households Households do not save but nstead spend all ther current ncomes. We assume that households have Cobb-Douglas preferences over the two types of goods. A household solves the followng optmsaton problem: max C γ C N,C N C1 γ T, T where C s consumpton of good, subject to I/P =(P N C N + P T C T ) /P, 6

10 where I s the nomnal ncome of the household. Real ncome s gven by w for a worker employed n sector I/P = π for a captalst n sector 0 f unemployed, where w = W /P s the real consumpton wage and π s the real ncome from profts of a captalst n sector. Solvng the problem yelds the household demand functons C N = γi/p N and C T = (1 γ)i/p T. Denotng aggregate ncome Ĩ, aggregate demand for non-tradables C N and aggregate demand for tradables C T,weobtan The consumer prce level (CPI) s gven by C N = γ Ĩ (5) P N C T = (1 γ) Ĩ. P T P = P γ N P 1 γ T. (6) The budget share, γ, of non-traded goods s a measure of the economy s openness, so that when γ =0the economy s completely open wth producton of only tradables and when γ =1the economy s completely closed wth producton of only non-tradables. Tradables produced n dfferent countres are perfect substtutes. So, there exsts a common world market for tradables. Ths market clears and determnes a foregn-currency prce of tradables, whch by way of the small-country assumpton s taken as exogenously gven by domestc producers. Aggregate output of non-tradables s R 1 0 Y Nd = Y N. Aggregate output of tradables s R 1 0 Y T d = Y T. Clearng of the domestc market for non-tradables mples Y N = C N. It then follows that Y T = C T. To see ths, use the fact that the zero-savngs assumpton mples that nomnal aggregate expendture must equal nomnal aggregate ncome (the nomnal value of output),.e. P N Y N + P T Y T = P N CN + P T CT. We assume that the producton technology s the same n the two sectors,.e. θ N = θ T θ. Usng the equalty between domestc supply and demand n both sectors, the demand functons (5) and the supply functons (3), we obtan the followng condton for "relatve market clearng": µ P N γ 1 θ µ θ WN =. (7) P T 1 γ 7 W T

11 The equaton states that the relatve prce between non-tradables and tradables P N /P T s unquely determned by the relatve wage between the sectors W N /W T. Snce the elastcty between the relatve prce and the relatve wage s θ<1, an ncrease n the relatve wage causes a less than proportonal ncrease n the relatve prce. (7) wll play a crucal role n the subsequent analyss Employment It wll be convenent for the subsequent analyss to rewrte the labour demand equatons n terms of real consumpton wages. By usng the defnton of the aggregate prce level (6) and the equaton for the equlbrum relatve prce(7)we obtan: N N = w η N N T = w η T µ wn w T µ wt w N (1 γ)σ µ γ (1 γ) (8) 1 γ γσ µ γ γ. (9) 1 γ Equatons (8) and (9) mply that employment n a sector depends negatvely on the real consumpton wages n both sectors. 4 two sectors: N = µ wn w T 3.2 Monetary polcy Aggregate employment s obtaned by summng employment n the (1 γ)σ µ γ (1 γ) µ γσ µ w η N 1 γ + wt γ γ w η T (10) w N 1 γ Let E denote the nomnal exchange rate n domestc currency per unt of foregn currency and PT the exogenously gven foregn-currency prce of tradables. Snce the law of one prce apples for tradables, we have P T = EPT = E f we normalse the foregn-currency prce to unty. Takng logs and dfferentatng, (6) mples d ln P = γdln P N +(1 γ)d ln P T. (11) Under nflaton targetng, the central bank pursues monetary polcy n such a way that d ln P =0 always. Ths means that polcy must nduce such exchange rate changes that prce changes for tradables exactly offset the effects on the CPI of prce changes for non-tradables. More precsely, 4 Note that (1 γ) σ η =[(1 γ)θ 1] / [1 θ] < 0 and γσ η =[γθ 1] / [1 θ] < 0. 8

12 Table 1: Producer and consumer prce effects under the two regmes (1) (2) Regme I M d ln P N d ln W N d ln P T d ln W N d ln P d ln W T d ln P N d ln W T h (1 γ) θ 1 d ln W T h d ln W N γθ 1 d ln W T d ln W N h θ 1 d ln W T d ln W N 0 h d ln W N 0 γθ 1 d ln W T h d ln W N d ln P T γθ 1 d ln W N d ln W T 0 h h (1 γ) θ 1 d ln W N d ln W T θ 1 d ln W N d ln W T d ln P d ln W T 0 γθ h 1 d ln W N d ln W T (11) mples that d ln P T = γ/(1 γ)d ln P N. In monetary unon (wth a fxed exchange rate) t smply holds that d ln P T =0. Takng logs of the relatve goods market equlbrum condton (7) and dfferentatng gves: d ln P N d ln P T = θ (d ln W N d ln W T ). (12) Together wth (11), (12) determnes the perceved elastctes of prces wth respect to wages on the part of wage setters under the two monetary regmes and dfferent wage barganng arrangements. In Table 1, column (1) shows the prce elastctes under nflaton targetng (I) andcolumn(2) the correspondng elastctes under monetary unon (M). The elastctes are total elastctes, takng nto account the possblty that a wage change n one sector may affectthewagentheother sector. 4 Wage settng In the frst stage of the game, wages are set through barganng between one large unon and one employers federaton n each sector. The unon organses all workers n the sector and the employers federaton organses all frms n the sector. The employers federaton seeks to maxmse 9

13 the proft of a representatve frm n the sector. The unon tres to maxmse the rents from unonsaton. Snce the unon s utltaran and there s no labour moblty between the sectors, the rents from unonsaton equal the excess of the utlty of unon members over the stuaton that would preval n the absence of a unon. Jobs are randomly assgned among the workers n each sector. L s the number of unon members per frm n sector. Workers are rsk neutral so that the utlty of an employed worker n sector s equal to the real consumpton wage w. The utlty of an unemployed worker s b, whch s taken as exogenous. b can be thought of as the value of home producton. Unon utlty n sector s thus gven by: V = N w +(L N )b L b = N (w b). (13) The nomnal wage W n sector s set so as to maxmse a weghted (geometrc) average of the utltes of the two partes: Ω =[N (w b)] λ Π 1 λ, where λ s the "relatve barganng power" of the unon n sector. Equvalently, the maxmsaton problem can be wrtten: µ " µ # W max ln Ω = λ ln N ln W P b +(1 λ )ln (η 1) 1 W η W. P The maxmsaton s done under a set of constrants that dffer dependng on the monetary regme and the barganng set-up. In all cases, wage setters realse that the sector they bargan n s so large that the wage has a potental effect on both the own product prce and the aggregate prce level. The constrants can be wrtten on the followng general form: N = µ η W P P = P (W,W j ) P = P (W,W j ) W j = f (W ), where ndex j denotes the other sector. Let ϕ =1 d ln P /d ln W and =1 d ln P/dln W. The frst-order condton for maxmsaton s w Ω W = λ (w b) ηϕ +(1 λ )[ ηϕ ]=0, (14) 10 P

14 where Ω W = ln Ω / ln W throughout the paper. The frst-order condton states that the margnal gan for the unon from a wage ncrease must balance the margnal loss for the employers federaton. The margnal gan for the unon s the (postve) dfference between the utlty gan from a hgher real consumpton wage and the utlty loss from lower employment. Solvng for the real consumpton wage we obtan w = W P =[1+λ M ] b, (15) where M = /(ηϕ ). The real consumpton wage n a sector s thus a postve mark-up on the value of unemployment. The parameters ϕ and depend on the monetary regme and the wage-settng arrangement and wll therefore determne how the equlbra dffer. Below we analyse both a Nash equlbrum (uncoordnated barganng) and the two possble Stackelberg equlbra (pattern barganng) wth one of the sectors as wage leader and the other as wage follower. 4.1 The wage follower It s nstructve to frst analyse wage behavour of the follower n a Stackelberg game. The follower takes the nomnal wage set by the leader as gven. It thus acts n the same way as n a Nash game, when each sector takes the nomnal wage of the other sector as gven. The assumpton of a gven money wage n the other sector means that f 0 =0. Hence, we have ϕ =1 d ln P /d ln W =1 ln P / ln W (16) and =1 dln P/dln W =1 ln P/ ln W (17) n (15) when t apples to the follower sector n a Stackelberg game and to each sector n a Nash game. 4.2 The wage leader Barganng n the leader sector n a Stackelberg game also has to take nto account the reacton functon of the follower,.e. the leader nternalses the mpact of ts wage decson on the wage of 11

15 the follower. Lettng ndex denote the leader and ndex j the follower, applyng (15) to the leader gves ϕ = 1 d ln P =1 ln P ln P d ln W j d ln W ln W ln W j d ln W = 1 d ln P =1 ln P ln P d ln W j. d ln W ln W ln W j d ln W When evaluatng the prce effects of an own wage ncrease, the leader thus takes nto account that prces are not only nfluenced by the drect effect of the own wage ncrease but also by an ndrect effect from the nduced change n the wage of the follower. It follows mmedately from (15) appled to the follower sector that d ln W j = d ln P, (18) d ln W d ln W.e. the elastcty of the nomnal wage n the follower sector wth respect to the nomnal wage n the leader sector equals the elastcty of the CPI wth respect to the nomnal wage n the leader sector. Ths s the consequence of the fact that for a gven value of unemployment b, (15) determnes a unque real consumpton wage W /P for the follower n each regme. 4.3 Perceved prce elastctes under dfferent monetary regmes and barganng arrangements To compare dfferent equlbra we need to develop the expressons n Table 1 for the perceved total prce elastctes under dfferent monetary regmes and barganng arrangements. We do so by nsertng the proper values of d ln W N /d ln W T and d ln W T /d ln W N. In a Nash equlbrum we set both dervatves to zero. If sector s wage leader, t nternalses the mpact t has on the follower sector j accordng to (18) and we thus mpose d ln W j /d ln W = d ln P/dln W. The follower sector j, on the other hand, takes W as gven and we therefore mpose the restrcton d ln W /d ln W j =0 for t. In Table 2, columns (1)-(3) show the perceved prce elastctes under nflaton targetng for dfferent wage-settng assumptons. Column 1 apples to the Nash equlbrum, column 2 to the 12

16 Table 2: Producer and consumer prce effects across regmes and assumptons about wage leadershp (1) (2) (3) (4) (5) (6) Regme I I I M M M Leader Nash N T Nash N T Restrctons d ln W d ln W j =0, d ln W N d ln W T =0 d ln W T d ln W N =0 d ln W d ln W j =0, d ln W N d ln W T =0 d ln W T d ln W N =0 d ln P N θ d ln W N (1 γ) θ (1 γ) θ (1 γ) θ θ 1+γθ θ d ln P T d ln W N γθ γθ γθ d ln P γθ d ln W N γθ 1+γθ γθ d ln P T d ln W T γθ γθ γθ d ln P N d ln W T (1 γ) θ (1 γ) θ (1 γ) θ θ θ θ (1 γθ) d ln P d ln W T γθ γθ γθ (1 γθ) Stackelberg equlbrum wth the non-tradables sector as wage leader and column 3 to the Stackelberg equlbrum wth the tradables sector as wage leader. Columns (4)-(6) show the correspondng elastctes n monetary unon. It s useful to frst gve the ntuton n the Nash equlbrum. Consder frst nflaton targetng. Then by defnton there are no consumer prce effects, whch mples that both d ln P/dln W N and d ln P/dln W T are zero. The mechansms at work are as follows. If there s a wage ncrease n the tradables sector, there s a reducton n output n that sector, leadng to lower aggregate ncome and lower demand for non-tradables. The fall n demand puts downward pressure on the prce of non-tradables. To offset the effect on the CPI, the central bank must engneer an exchange rate deprecaton, rasng the prce of tradables. A one-percent wage ncrease n the tradables sector wll cause the prce of non-tradables to fall by (1 γ) θ percent and the prce of tradables to rse by γθ percent. A wage ncrease n the non-tradables sector generates upward pressure on the CPI. Hence, under nflaton targetng the central bank must engneer an exchange rate apprecaton to counter ths effect. A one-percent wage ncrease n the non-tradables sector wll rase the prce of non-tradables by (1 γ) θ percent, whereas the prce of tradables wll fall by γθ percent. In monetary unon, the nomnal exchange rate does not change n response to a wage change. 13

17 If the wage ncreases n the tradables sector, the prce of tradables s not affected, but output falls. Ths n turn leads to a fall n aggregate ncome, whch reduces the demand for non-tradables. A one-percent wage ncrease n the tradables sector s assocated wth a prce fall n the non-tradables sector of θ percent and a fall n the CPI of γθ percent. A wage ncrease n the non-tradables sector causes a negatve supply shft n the sector. The elastctes of the prce of non-tradables and the CPI wth respect to the wage n the non-tradables sector are θ and γθ respectvely. How does pattern barganng change the perceved elastctes? It s obvous that the consumer prce effects under nflaton targetng are stll zero. But the table also shows that the perceved producer prce elastctes under nflaton targetng are the same as n the Nash game. Ths s self-evdent for a wage change by the follower, who takes the money wage of the leader as gven. The reason why the perceved prce elastcty s the same for the leader as well s that the effect of the leader s wage on the follower s wage accordng to (18) goes va the CPI. Snce the wage leader nternalses the fact that the central bank wll prevent an own wage ncrease from rasng the CPI, t realses that the nomnal wage of the follower wll reman unchanged just as n the Nash game. Under a fxed exchange rate, the barganng arrangement does matter for the sze of the prce elastctes. Consder frst the case where the non-tradables sector s leader. An ncrease n the N-sector wage rases the prce of non-tradables. Wth a gven nomnal wage n the tradables sector, a one-percent rse n W N causes P N to rse by θ percent. As a consequence the CPI rses by γθ percent. But the wage setters n the non-tradables sector realse that ths consumer prce ncrease wll cause the wage n the tradables sector to ncrease by as much. As the tradables sector ncreases ts wage, output n the sector falls (as P T s fxed) and thus also aggregate ncome. The assocated fall n demand counteracts the rses n both the prce of non-tradables and the CPI. Hence, both the own producer prce and the consumer prce effects of a wage rse n the non-tradables sector are perceved to be smaller when the sector s wage leader than when wages are set smultaneously. If the tradables sector s wage leader the mechansms at work are as follows. A rse n W T causes a fall n the output of tradables and thus n aggregate ncome. Ths reduces the demand for non-tradables and causes ther prce to drop. The assocated fall n the CPI leads to a decrease n the nomnal wage n the non-tradables sector, holdng the real consumpton wage there, W N /P, 14

18 Table 3: Wage mark-up factors across regmes and barganng arrangements (1) (2) (3) Leader Nash N T M NI M TI M NM M TM 1 θ γθ 1 θ (1 γ)θ 1 γθ γθ (1+γθ)(1 θ) θ(1 γ+γθ) 1 θ γθ 1 θ (1 γ)θ 1 θ γθ (1+γθ)(1 θ) θ(1 γ+γθ) 1 θ γθ 1 θ (1 γ)θ 1 γθ γθ 1 θ (1 γ)θ unchanged. The nomnal wage reducton n the N-sector amplfes the decreases n the prce of nontradables and the CPI. Wage setters n the tradables sector wll thus perceve larger falls n the prce of non-tradables and the CPI when they are wage leaders than when wages are set smultaneously. 4.4 Comparson of equlbra We use (15) to compare the wage outcomes under dfferent barganng set-ups and monetary regmes. In ths part of the paper we focus exclusvely on wthn-sector comparsons of monetary regmes and barganng set-ups whch mples that dfferences n the mark-up λ M only depend on dfferences n M. 5 So a rankng of M (whch wll subsequently be referred to as the "markup factor") across regmes and barganng arrangements s also a rankng of the correspondng real wages. By usng the perceved total prce elastctes under dfferent barganng set-ups and monetary regmes n Table 2, we obtan the mark-up factors n Table 3. Below, let superndex k = N,T,Nash ndcate the Stackelberg equlbrum wth sector N as leader, the Stackelberg equlbrum wth sector T as leader and the Nash equlbrum, respectvely. Multple superndces ndcate that the mark-up factor assumes the same value for the ndcated nsttutonal settngs. As before subndex = N,T ndcates for whch sector the mark-up factor apples. Subndex m = I,M denotes the monetary regme. The followng propostons can be made. 5 The rankngs of real wages and employment across sectors nagvenregmehavebeenaddressedbyvartanen (2002) and Holden (2003). 15

19 Proposton 1 Under nflaton targetng, the Nash equlbrum concdes wth the two Stackelberg equlbra, snce MI Nash = MI N = M I T for = N,T. So, t does not matter what sector s wage leader under pattern barganng and ths form of barganng gves the same outcome as uncoordnated barganng. Ths s an mportant concluson as t mples - n contradcton to the presumpton n the general debate - that the barganng set-up s rrelevant under nflaton targetng. 6 The result s easy to understand. The dfference between a Nash and a Stackelberg game s that the leader n the latter game takes the effect of ts wage decson on the follower s wage nto account. But ths effect goes va a change n the CPI: the follower s nomnal wage rses equproportonally to the CPI ncrease so that the real consumpton wage s held constant. But under nflaton targetng ths channel s cut off, as the central bank prevents the CPI from changng. Hence, the central bank response mples that the leader can take the follower s nomnal wage as constant also n the Stackelberg game. Ths means that each sector faces exactly the same optmsaton problem when the game s Nash, when the sector s wage leader n a Stackelberg game and when the sector s follower n a Stackelberg game. The mplcaton s that the real consumpton wage n each sector s the same n all three cases. Ths mples that employment and profts are the same across alternatve barganng set-ups. Proposton 2 In monetary unon, the real consumpton wage n a sector s the same when the sector s wage follower n a Stackelberg game as n a Nash game, snce M j M = M M Nash N,T, 6= j. for, j = The ntuton s obvous, snce the follower n the Stackelberg game solves the same optmsaton problem as the sector would n the Nash game. Note, however, that the equalty of real consumpton wages between the two games does not mply equalty between nomnal wages, as these wll dffer to the extent that the CPI levels dffer. 7 Proposton 3 In monetary unon, the real consumpton wage n the non-tradables sector s lower n the Stackelberg game when the sector s wage leader than n the Nash game as M Nash NM >MN NM. 6 Ths result hnges on the assumpton of Cobb-Douglas preferences snce ths mples reacton functons accordng to whch the wage n one sector s ndependent of the wage n the other sector. Vartanen (2008) analyses the case of CES-preferences where the wage set n one sector s a functon of the wage set n the other sector, but he looks only at nflaton targetng and does not address the possblty of comparson norms. 7 Seefootnote9. 16

20 The Stackelberg game wth the non-tradables sector as wage leader results n hgher employment n both sectors, and thus also hgher aggregate employment, than n the Nash game. Proof. It s straghtforward to show that MNM Nash >MN NM (1 θ)/γθ, whch must hold as γ<1. s equvalent to (1 γθ)/γθ > When the non-tradables sector s wage leader, wage barganers n that sector know that f they rase the wage, the resultng ncrease n the prce of non-tradables pushes up the CPI. Ths trggers a wage ncrease n the tradables sector. As a consequence, output of tradables and aggregate ncome fall. Ths lowers the demand for non-tradables and counteracts the rse n the prce of non-tradables. Ths addtonal negatve producer prce effect has a moderatng nfluence on wage settng n the non-tradables sector whch s not present n the Nash equlbrum. The negatve producer prce effect also trggers a fall n consumer prces that benefts both employers and employees, but ths effect s smaller n magntude than the dscplnng producer prce effect. 8 The employment consequences follow drectly from equatons (8)-(9). As the real consumpton wage s lower n the (leader) non-tradables sector than n the Nash equlbrum (Proposton 3) and the same n the (follower) tradables sector (Proposton 2), employment n both sectors must be hgher n the Stackelberg equlbrum wth the non-tradables sector as wage leader than n the Nash equlbrum. Proposton 4 In monetary unon, the real consumpton wage n the tradables sector s hgher n the Stackelberg game when the sector s leader than n the Nash game as MTM T >MNash TM. The Stackelberg game wth the tradables sector as leader results n lower employment n both sectors than n the Nash game. Proof. It can be shown that M T TM >MNash TM f, and only f, (1 θ)/(1 γ)θ >(1 + γθ)(1 θ)/θ(1 γ + γθ). Ths s equvalent to γθ > γθ(1 γ), whch must hold snce γ<1. In monetary unon, there are no producer prce effects that affect the wage decson n the tradables sector, as the prce of tradables s fxed. But there s a negatve consumer prce effect 8 As W N /P slowernthscasethannthenashequlbrumandw T /P the same, t follows from the relatve market clearng equaton that P N/P T s lower. Wth a gven P T, P N and thus also P must be lower. It follows that the nomnal wage n the (follower) tradables sector W T s lower n the Stackelberg equlbrum wth the non-tradables sector as wage leader than n the Nash equlbrum. A smlar reasonng shows that the nomnal wage n the (follower) non-tradables sector W N s hgher n the Stackelberg equlbrum wth the tradables sector as wage leader than n the Nash equlbrum. 17

21 from a wage rse n the tradables sector that comes from the fall n output of tradables, and hence n aggregate ncome, whch causes a reducton n the demand for non-tradables and consequently a fall n the CPI. Ths negatve consumer prce effect strengthens the ncentves for a hgh wage n the tradables sector n both the Nash and the Stackelberg equlbrum, snce t rases the purchasng power of the wage. But the ncentve effect s stronger n the latter case. The reason s that the reducton n the CPI causes the barganers n the non-tradables sector to reduce the wage there. Ths reduces consumer prces even more than n the Nash game. Hence, snce the negatve consumer prce effect s amplfed by the fall n non-tradables wages, the ncentve for hgh wages n the tradables sector s even stronger when the sector s wage leader under pattern barganng than n the Nash equlbrum. Because the real consumpton wage s hgher n the (leader) tradables sector than n the Nash equlbrum and the same n the (follower) non-tradables sector, t follows drectly from equatons (8) and (9) that employment n both sectors s lower n the Stackelberg equlbrum wth the tradables sector as wage leader than n the Nash equlbrum. The above results go aganst the conventonal wsdom that under fxed exchange rate or monetary unon pattern barganng wth the tradables sector as wage leader promotes wage restrant and hgh employment as compared to uncoordnated barganng. 9 The outcome n our model s the reverse one: t s pattern barganng wth the non-tradables sector as wage leader that s conducve to wage restrant and hgh employment n a fxed exchange rate regme. Proposton 5 When there s sequental wage settng, the leader sector sets the same real consumpton wage across monetary regmes,.e. wi = w M for = N,T. The follower s wage s, however, regme-specfc. When the non-tradables sector s wage leader, the (follower) tradables sector sets a lower real wage n monetary unon than under nflaton targetng as MTM N <MN TI. When the tradables sector s leader, the (follower) non-tradables sector sets a lower real wage under nflaton targetng than under monetary unon as MNI T <MT NM. It follows that wth the non-tradables sector as leader, employment n both sectors, and thus also aggregate employment, s hgher under monetary unon than under nflaton targetng. Wth the tradables sector as leader, employment n both sectors, and thus also aggregate employment, s nstead hgher under nflaton targetng than under 9 See, e.g., Calmfors (2008). 18

22 monetary unon. The conclusons on wages follow drectly from Table 3. The dfference n wage outcomes for a sector between the two monetary regmes are the same when t s a follower n the Stackelberg game as n the Nash game, whch has earler been analysed by Vartanen (2002), Holden (2003) and Larsson (2007). 10 The reason why the Stackelberg leader sets the same real consumpton wage under both monetary regmes s that t s n effect solvng the same real optmsaton problem n both cases. Accordng to equaton (15) and the dscusson n Secton 4.3, the follower s choce f real consumpton wage s ndependent of the real consumpton wage chosen by the leader. Hence, when optmsng, the leader takes the follower s real consumpton wage as gven. The perceved effect of a one percent change n the leader s real consumpton wage on the relatve prce between non-tradables and tradables wll therefore - accordng to equaton (12) - be the same ndependent of the regme. Ths mples that the leader meets the same ncentves n both regmes and sets the same real consumpton wage. The conclusons regardng employment follow from the conclusons on wages and the employment equatons (8)-(10). Because only the follower s wage decson s regme specfc, the regme that promotes most wage restrant for the follower (nflaton targetng for the non-tradables sector, monetary unon for the tradables sector) s the one gvng the hghest aggregate employment. Under pattern barganng the choce of wage leader thus matters for whch monetary regme gves the hghest employment. Ths complements the results of Holden (2003) and Larsson (2007), who found that wth uncoordnated (Nash) barganng nflaton targetng results n hgher aggregate employment than monetary unon under realstc parameter assumptons. 10 The ntuton for a lower real consumpton wage n the tradables sector under monetary unon than under nflaton targetng n the Nash game s as follows. An ncrease n the real consumpton wage n the tradables sector reduces employment and output there and hence also aggregate demand. Ths reduces the prce of non-tradables. To compensate for that, the central bank engneers a rse n the prce of tradables under nflaton targetng, whch counteracts the fall n employment n the tradables sector. Ths effect reduces the cost of real consumpton wage rses n the tradables sector. Under monetary unon there s no such offsettng effect from a prce rse for tradables. There s a smlar ntuton for why the real consumpton wage n the non-tradables sector s lower under nflaton targetng than under monetary unon n the Nash game. If there s a rse n the real consumpton wage n the non-tradables sector, ths causes a rse n the prce of non-tradables. Under nflaton targetng the central bank engneers a fall n the prce of tradables, whch tends to lower output n the tradables sector. Ths n turn counteracts the rse n the prce of non-tradables and hence ncreases the employment losses n the non-tradables sector. Under monetary unon there s no such fall n the prce of tradables that rases the cost of wage ncreases n the non-tradables sector. 19

23 5 Wage settng wth wage norms A well-known feature of collectve barganng s the mportant role played by wage comparsons. As noted n the ntroducton, under pattern barganng the wage ncreases negotated n the key sector often become a reference norm for subsequent agreements. There s a strong tendency for wage ncreases n other sectors to follow ths norm closely. Ths secton extends our analyss to account for ths phenomenon. Ths s done by ncorporatng the Kahneman-Tversky (1979) concept of loss averson n the way proposed by Bhaskar (1990), accordng to whch a larger weght s attached to losses relatve to a reference norm than to gans. 5.1 Trade unon utlty We now assume that the utlty of an employed worker n sector, as perceved by the unon, depends on both the real wage receved and on a wage comparson norm, denoted w n. 11 Followng Holden and Wulfsberg (2007), the assumpton s that the perceved utlty of an employed worker n sector s ew = w 1+α k /w α k n,whereα k measures the mportance of wage comparsons. In accordance wth the Kahneman-Tversky hypothess of loss averson, α k takes on dfferent values dependng on whether or not the wage exceeds the norm. More specfcally, we assume that wage comparsons matter for unon-perceved utlty only when the wage s below the comparson norm,.e. α k = ½ α1 > 0 when w w n, 0 when w >w n. The mplcaton s that the unon-perceved margnal utlty of the real wage for an employed worker s a non-dfferentable functon at w = w n and takes on a larger value for a wage mmedately below than for a wage mmedately above the norm, as shown n Fgure 1, snce µ ew αk w =(1+α k ). w w n We contnue to assume that the unon-perceved utlty of an unemployed worker s the value of home producton b. For the unon, wage comparsons thus play no role wth regard to the unemployed. 11 Our assumpton s thus that comparson thnkng nfluences the unon utlty functon, whch matters for wage settng, but not the utlty functon of consumers, whch determnes the demand functons for goods. 20

24 w ~ w w n w Fgure 1: Unon-perceved margnal utlty of the real wage for an employed worker (N.B. The dagram s drawn under the assumpton that 0 <α 1 < 1). Hence, the utlty functon for the unon n sector s now; " # w 1+α k V = N ( ew b) =N w α b. (19) k n (19) s now substtuted for the earler (13) n the weghted utlty functon to be maxmsed when the wage s set. 5.2 The wage follower We frst examne the optmsaton problem of the follower. We assume that the real consumpton wage n the leader sector serves as the reference norm. As before we denote the leader by subndex and the follower by subndex j. Hence, the assumpton s that w n = w. It follows that the wage n the follower sector s now set so as to maxmse: " Ã w 1+α λj k j Ω j = N j w α b!# [Π k j ] 1 λ j. 21

25 The nomnal wage n the follower sector s thus gven by the soluton to " Ã!# " W 1+α k j max ln Ω j = λ j ln N j ln W j W α kp b +(1 λ j )ln (η 1) 1 W j P subject to N j = µ η Wj P j P = P (W j,w ) P j = P j (W j,w ), µ Wj P j η # and takng W as gven. Let ϕ j =(1 d ln P j /d ln W j ) and j =(1 d ln P/dln W j ) as before. Note that: ln W j ln à W 1+α k j W α k! P b = W 1+α k j W α k P ³ ³ 1+α k ln P ln W j µ = ew j (α k + j ), W 1+α k j W α b ( ew j b) k P where ew j W 1+α k j W α k P = w 1+α k µ αk j wj w α = w k j. w The dscontnuty of the unon utlty functon means there could be both an nteror and a corner soluton. The nteror soluton s gven by: ln Ω j W j = Ω Wj = λ j ηϕ j + ew j (α k + j ) ( ew j b) +(1 λ j ) j ηϕ j =0 (20) Solvng (20) for ew j, we obtan: ew j = h1+λ j f Mj b, (21) where f M j =(α k + j ) / ηϕ j j λ j α k. Equaton (21) states that the unon-perceved utlty of an employed worker s agan a mark-up over the value of unemployment. Equvalently, equaton (21) can be wrtten as an equaton for the real consumpton wage n sector j, whch s homogenous of degree one n the value of unemployment and the wage n the leader sector: w j = h1+λ j f Mj 1 1+α k b 1 α k 1+α 1+α k w k, (22) 22

26 Wth an nteror soluton, the real wage n the follower sector s thus a mark-up on a weghted geometrc average of the value of unemployment and the wage norm set by the leader sector. A corner soluton wth w j = w s obtaned when lm wj w lm wj w + Ω W j lm wj w Ω + W j lm wj w + ln Ω j ln W j ln Ω j ln W j h = λ j ηϕ j + w j(α 1 + j ) ( w j b) +(1 λ j ) j ηϕ j > 0 h = λ j ηϕ j + j w j ( w j b) +(1 λ j ) j ηϕ j < 0, where Ω W j Ω Wj for w j w and Ω + W j = Ω Wj for w j >w. Ths means that when the weghted gan to the barganng partes of a wage ncrease s postve mmedately below the wage w set by the leader, but negatve mmedately above ths wage, t s optmal for the follower to choose the same wage as the leader. Ths s a consequence of our loss averson assumpton. 5.3 The wage leader Snce the wage comparson norm s the wage of the leader, the utlty of an employed worker n the leader sector s the same as n Secton 4.1.e. ew = w 1+α k /w α k = w. It follows that the trade unon utlty functon wll be the same, as wll the weghted utlty functon to be maxmsed n the wage-settng process. The employment and prce equatons are also dentcal. However, the maxmsaton problem of the leader s now more complex than n Secton 4.1 because of the possblty of varous types of equlbra for the follower. It s not enough for the leader to maxmse subject to the response functon of the follower gven the type of equlbrum for the latter. The leader can also set ts wage strategcally to acheve the type of equlbrum (corner soluton or nteror solutons for the follower) that gves t the hghest utlty. We proceed n the followng way. In a frst step, we analyse potental equlbra wth nteror solutons for the follower. In a second step, we analyse potental equlbra wth corner solutons for the follower. In a thrd step, we derve the actual equlbra that are realsed. 23

27 Table 4: Wage mark-ups under dfferent assumptons about sector servng as wage norm Leader N T (1 θ)(1+α M 1 ) NI θ(α 1 +γ) (1+α fm 1 )(1 θ) TI (1 γθ) (1+λ T α 1 )(1 θ) (1 θ)(1+α M 1 ) TI θ(α 1 +1 γ) (1+α fm 1 )(1 θ) NI (1 (1 γ)θ) (1+λ N α 1 )(1 θ) (1 θ)(1+α M 1 ) NM θ(α 1 +γ) (1+α fm 1 +γθ)(1 θ) TM θ(1 γ+γθ) λ T α 1 (1 θ) (1 θ)(1+α M 1 ) TM θ(α 1 +1 γ) 1+α fm 1 γθ NM γθ λ N α Potental equlbra wth nteror solutons for the follower Wth an nteror soluton for the follower, the wage response functon of the latter can be derved from (22) as: d ln W j d ln W = α k + 1 d ln P, 1+α k 1+α k d ln W where α k = α 1 > 0 apples for w j <w and α k = α 2 =0for w j >w Potental nteror solutons wth a lower wage for the follower than for the leader We frst examne potental equlbra wth nteror solutons for the follower where w j <w. The real wage of the leader s stll gven by an equaton of the same form as (15). The real wage of the follower s gven by equaton (22). Dvdng the two equatons by each other gves w j w = Ã 1+λ j f Mj 1+λ M! 1 1+α 1. Assumng, for smplcty, that λ = λ j = λ, t s obvous that an equlbrum wth w j <w requres that f M j <M. The expressons for these mark-up factors under our varous leadershp 24

28 Table 5: Crtcal values for the mportance of wage comparsons, α 1, below whch there s a potental equlbrum wth a lower wage for the follower than the leader Leader N T Inflaton targetng Monetary unon 1 2(1 γ) 1+λ(1 θ)/θ 2[1+ λ (1 θ)] [2(1 γ)+ λ (1 θ)] θ 2[1+ λ (1 θ)] θ θ 1 2γ 1+λ(1 θ)/θ [2γ+ λ (1 θ)] θ ± µ λ 1/2 [2γ+ θ (1 θ)]2 + [1 2γ+γ(1 γ)θ] 4[1+ λ θ (1 θ)]2 [1+ λ (1 θ)] θ ± µ [2(1 γ)+ λ 1/2 θ (1 θ)]2 + [2γ 1 γ2 θ] 4[1+ λ θ (1 θ)]2 [1+ λ (1 θ)] θ and monetary regme assumptons are gven n Table 4. It can be shown that the condton for a potental equlbrum wth a lower wage for the follower than for the leader s that the α 1 -term, measurng the mportance of wage comparsons, s below a crtcal value α, the magntude of whch depends on the monetary regme and what sector s leader. These crtcal values are gven n Table 5. It can be seen that under nflaton targetng an equlbrum wth a lower wage for the follower than the leader can never come about f the leader sector s the larger one. If, for example, under nflaton targetng the N-sector s leader and γ> 1 2, so that ths sector s the larger one, the crtcal value s negatve (frst row, frst column n the table). But snce α s always postve by assumpton, t can never be below ths crtcal value Potental nteror solutons wth a hgher wage for the follower than for the leader In the case of an nteror soluton wth a hgher wage for the leader than for the follower, equaton (15) gves the wage outcomes for both the leader and the follower. The mark-up factors are the same as n Table 3, as α 2 =0when w j >w mples that we are back to the case wthout comparson norms. From Table 3, t s straghtforward to derve under what condtons nteror solutons wth a 12 Smlarly, f the tradables sector s wage leader and ths sector s the larger,.e. 1 γ> 1, then the crtcal 2 value s agan negatve (frst row, second column n Table 5). 25