Strategic U n
ionDel
egationand Strike Ac tivity
¤
An
a M aul
eon
LAB O R E S,
U niversit¶e c atholique d e Lille,
and
IR E S,
U niversit¶
e c atholique d e Louvain.
Vin
c en
t Van
n
etel
b osch
yF NR S and IR E S,
U niversit¶e c atholique d e Louvain.
M arc h 2 0 0 2
A bstract
W edevelop amodelofwagedeterminationwithprivateinformation,inwhichthe unionhastheoptiontodelegatethewagebargainingtoeithersurplus-maximizingdel-egatesortowage-maximizingdelegates(suchasseniorunionmembers).W eshowthat the strike activity is greaterwheneverthe union chooses wage-maximizingdelegates insteadofsurplus-maximizingdelegates.W ealsoprovidethenecessaryandsu±cient conditionsuchthatitis always optimalfortheuniontochoosewage-maximizingdel-egates and we ¯nd thatthe e±ciency loss due tostrategic delegation may be quite important.
Keywords:U nion delegation,W agebargaining,P rivateinformation,Strikeactiv-ity.
JEL Classi¯cation:J41 ,J50 ,J52.
¤Vincent Vannetelb osch isCharg¶e d e R ec herc hesat the FondsNationald e la R ec herc he Sc ienti¯que.
T he researc h ofAna M auleonhasb eenm ad e possib le b y a fellow ship ofthe Spanish governm ent.F inancial support from the B elgianFrench Com munity'sprogram Ac tiond e R ec herc hesConcert¶ee 9 9 /0 4 -2 35(IR E S, U niversit¶e c atholique d e Louvain).
yCorrespondingauthor ad d ress: IR E S,U niversit¶e c atholique d e Louvain,3P lac e M ontesquieu,B -134 8
Louvain-la-Neuve, B elgium . E -m ail: vannetelb osch@ires.uc l.ac .b e, T el: 0 0 32 10 4 74 14 2 , Fax: 0 0 32 10 -4 739 -4 5.
1
In
trod uc tion
T hepurposeofthis paperis toprovideatheoreticalstudyofhowtheoptionforunions to delegatethewagebargainingwilla®ectthewageoutcomeandtheincentivesforstrikes.U p tonowtheliteraturehas mainlyfocusedonstrategicdelegationonbehalfofshareholders. FershtmanandJudd(1 987)haveaddressedtheissueofstrategicmanagerialdelegationin the contextofoligopolisticindustries with Cournotcompetition (see alsoSklivas, 1 987). R egardingstrategicunion delegation,Jones (1 989)has shown thatadivergencebetween the objectives ofunion leaders and union members willnaturally arise in a democratic union as partofa rationalbargaining strategy. Essentially, the reason is thatin many bargainingsituations,commitmentcan bevaluable,and theunion members can credibly commit to a bargaining stance, which they could not otherwise sustain, by delegating authoritytoanegotiatorwhoseobjectives makethisstanceanoptimalone.M orerecently, Conlin and Furusawa(20 0 0 )haveprovided an explanation ofwhy seniorunion members may represent the union in contract negotiations with a monopolist. B y strategically delegatingcontractnegotiations towage-maximizingindividuals,thesurplus-maximizing union may bebettero®than ifsurplus-maximizingindividuals negotiatethecontract.
B utthese previous studies haveconsidered complete information frameworks sothat strikes,which wasteindustry resources,cannotoccuratequilibrium.1 So,we gobeyond the analysis o®ered in Jones (1 989)and Conlin and Furusawa (20 0 0 )by developing a modelthatenableus toinvestigatein presenceofstrategicunion delegation howprivate information a®ects thewageleveland thee±ciencyloss duetothestrikeactivity.2
P recisely,wedevelop amodelofwagedetermination in which both theunion andthe ¯rm haveprivateinformation.First,theunionchooses whethertousesurplus-maximizing delegates ortouse wage-maximizingdelegates (such as seniorunion members)whowill negotiate the wage with theemployer.Second,the wage bargainingoccurs.T odescribe the wage bargaining process, we adopt R ubinstein's (1 982)alternating-o®erbargaining modelwith two-sided incomplete information, which allows the occurrence ofstrikes at equilibrium.Finally,the¯rm chooses its outputleveltobeproduced.
A sabenchmarkwe¯rstconsiderthecompleteinformationsituationandweshowthat, the weakerthe union is, the more likely the union willchoose tosend wage-maximizing delegates.T hechoiceofwage-maximizingdelegates always increasethewagelevelandde-creases theproductionoutput(andtheemploymentlevel)as wellas theconsumersurplus.
1Strikes d ata seem to have a signi¯c ant im pac t onthe w age-em ploym ent relationship for c ollec tive
negotiations(see e.g.K ennanand W ilson,19 89 ).
2
See K ennanand W ilson(19 89 , 19 9 3) for surveysofb argaining m od elsw ith private inform ationand their relationto strike d ata.See K ennan(19 86) for a survey ofthe em piric alresultsonstrike ac tivity.
O ncethenegotiators haveprivateinformation,thecompleteinformationresults arenotal-ways valid.Forexample,itmightbethatthewageoutcomeincaseofsurplus-maximizing delegates is greaterthan the wage outcome in case ofwage-maximizingdelegates.H ow-ever,ifitis commonlyknown thatunion is strongerthan the¯rm and thelabordemand is quite elastic, then we recoverthe complete information result, namely thatthe wage outcomein caseofsurplus-maximizingdelegates is always strictly smallerthan thewage outcomein caseofwage-maximizingdelegates.
Finally,weshowthatthestrike activity is greaterwheneverthe union chooses wage-maximizingdelegates instead ofsurplus-wage-maximizingdelegates.W eprovidethenecessary and su±cientcondition such that, even in presence ofprivate information, itis always optimalforthe union to choose wage-maximizing delegates. W e ¯nd thatthe strategic delegation can increasequitesubstantially thee±ciency loss duetothestrikeactivity.
T he paperis organized as follows. In Section 2 the modelis presented. Section 3 describes the wagebargaininggameand choiceofdelegates undercompleteinformation. Section4 is devotedtothewagebargainingwithprivateinformation.Section5 o®ers some predictionsregardingtheactualstrikedurationandthee±ciencylossincurredduringwage negotiations.Finally,Section 6 concludes.
2
T he B asic M od el
Consideramarketforasingle homogenous product,where the demand is given by P = a¡b¢Qc, P is the marketprice, Q is the quantity produced, and c> 0 .T here is one
¯rm producingthegood.L et¦ denotethepro¯tlevel.T heonly variableinputis labor. T echnologyexhibits constantreturns toscaleandis normalizedinsuchawaythatQ = L , where L is laborinput,and the unitproduction costofeach ¯rm is the wageW .T hus, thepro¯tofeach ¯rm is given by
¦ = (a¡bQc)Q ¡W Q . (1 )
T he¯rm belongs toandis controlledbyonerisk-neutralownerwhoseobjectiveis tomax-imizepro¯ts.In addition,the¯rm is unionized,and enters intoaclosed-shop agreement with its risk-neutralunion.T heunion objectiveis tomaximizetheunion surplus:
U = L (W ¡W ), (2)
where W is the reservation wage.T he wage rate is determined by negotiations between the¯rm andtheuniondelegates.P recedingthenegotiations,theunionmaya®ectthene-gotiationoutcomebyselectingdelegates whoseobjectiveis eithertomaximizetheunion's surplus ortomaximizethewagerate.
W e develop a three-stage game.In stage one, the surplus-maximizingunion chooses whethertouse surplus-maximizingdelegates orto use wage-maximizing delegates (such as seniorunion members)whowillnegotiatethewage with theemployer.T heobjective ofawage-maximizingdelegateis simplyV = W ¡W .In stagetwo,thewagebargaining occurs.Finally,instagethreetheemployerchooses theoutputlevel.T hemodelis solved backwards.
In the last stage of the game, knowing that the wage level (W )has already been determined,theemployerchooses Q (W )= ·a¡W (1 + c)b ¸1 c (3) tomaximize its pro¯ts.In stage two, the negotiation takes place.W e ¯rstconsiderthe completeinformation bargainingas abenchmark.
3 T he W age B argainingw ith Com pl
ete In
f
orm ation
First,weconsiderthecasein which theunion sends surplus-maximizingdelegates whose interestis thesameas theunion's objective.T henegotiation proceeds as in R ubinstein's (1 982)alternating-o®erbargainingmodel.T he ¯rm and the union delegates makealter-nativelywageo®ers,with the¯rm makingo®ers in odd-numbered periods and theunion delegate making o®ers in even-numbered periods.T he length ofeach period is ¢ .T he negotiation starts in period 0 and ends when oneofthenegotiators accepts an o®er.N o limitis placed on the time thatmay be expended in bargainingand perpetualdisagree-mentis a possible outcome.T he union is assumed tobe on strike in every period until an agreementis reached.B oth the¯rm and theunion areassumed tobeimpatient.T he ¯rm andtheuniondelegatehavetimepreferences withconstantdiscountrates rf> 0 and
ru> 0 ,respectively.3
T o capture the notion that the time it takes to come to terms is smallrelative to the length ofthe contract,weassume thatthetime between periods is very small.T his allows astudy ofthe limitingsituations in which the bargainingprocedure is essentially symmetricand the potentialcosts ofdelayingagreementby one period can be regarded
3T w o versionsofR ub insteinalternating-o®er b argaining m od elc apture d i®erent m otivesthat ind uc e
partiesto reac h anagreem ent rather thanto insist ind e¯nitely onincom patib le d em and s.Ina ¯rst version the parties' incentive to agree liesinthe fac t that they are im patient : player iisind i®erent b etw een rec eiving x¢exp(¡ri¢¢ ) tod ay and x tomorrow , w here ri> 0 isplayer i'sd isc ount rate. Ina sec ond
versionthe partiesare not im patient b ut they fac e a riskthat ifagreem ent isd elayed thenthe opportunity they hope to exploit jointly m ay b e lost : player ib elievesthat at the end ofeac h b argainingperiod there isa positive prob ab ility 1¡ exp(¡ri¢ ) that the proc essw illb reakd ow n,ri> 0 .So,ric anb e interpreted
as negligible. A s the interval between o®ers and countero®ers is short and shrinks to zero,thealternating-o®ermodelhas auniquelimitingsubgameperfectequilibrium,which approximates theN ashbargainingsolutiontothebargainingproblem (seeB inmoreetal., 1 986).T hus thepredicted wageis given by
W sSP E = argmax
h
U ¡U0i® ¢h¦¡¦0i1¡® (4) where the lowerscript"s" means thatwage bargaining is between the ¯rm and surplus-maximizinguniondelegates,andwhereU0 = 0 and¦0 = 0 are,respectively,thedisagree-mentpayo®s ofthe union delegate and the ¯rm.T he parameter® 2 (0 ;1 )is theunion bargainingpowerwhich is equalto rf ru+ rf.Simplecomputation gives us W sSP E = W + ® c 1 + c(a¡W )= W + rf (ru+ rf) c (1 + c)(a¡W ). (5) O bviously, the wage is increasingwith the reservation wage W , with the union bargain-ing power ®, and with the parameter c. T hen, one can easily obtain the equilibrium employmentlevel L ¤s= ·1 + c ¡® c (1 + c)2b ³ a¡W ´¸ 1 c , (6)
as wellas the union's payo®and the ¯rm's pro¯t, which are denoted Us¤(®)and ¦¤s(®),
and aregiven by Us¤(®) = ·® c 1 + c ¸·1 + (1 ¡®)c (1 + c)2b ¸1 ch a¡W i 1+ c c , (7) ¦¤s(®) = ·1 + (1 ¡®)c (1 + c)2 ³ a¡W ´¸ 1+ c c c b1c . (8)
Second, we considerthe case in which the union sends wage-maximizing delegates. T hen,thepredicted wageis given by
W wSP E = argmaxhV ¡V0i® ¢h¦¡¦0i1¡® (9) where the lowerscript "w" means that wage bargaining is between the ¯rm and wage-maximizinguniondelegates,andwhereV0 = 0 and¦0 = 0 are,respectively,thedisagree-mentpayo®s ofthe union delegate and the ¯rm. T he parameter® 2 (0 ;1 )is stillthe union bargainingpowerwhich is equalto rf
ru+ rf. 4 Simplecomputation gives us W wSP E = W + ® c 1 ¡® + c(a¡W )= W + crf (1 + c)ru+ crf(a¡W ). (1 0 )
4It isassum ed that allunionm emb ershave the sam e d iscount rate.T he w orkersonlyd i®er w ith respec t
to their seniority w ithinthe ¯rm (senior w orkersw ho are alm ost insulated from the threat ofjob loss) or ifthey are uniond elegatesw ho are protec ted b y law from b eing d ism issed .So,the c hoic e ofthe unionis either to send a negotiator w ho w illrepresent the entire w orkforc e or to send a senior w orker (or a union d elegate).Involuntary lay-o®sare typic ally d one b y inverse seniority w ithinthe plant or ¯rm ,the so c alled last in, ¯ rst out (see Carruth and O sw ald,19 89 ).
A gain, the wage is increasing with the reservation wage W , with the union bargaining power®,and with theparameterc.T hen,onecan easilyobtain theequilibrium employ-mentlevel L ¤w = · 1 ¡® (1 ¡® + c)b ³ a¡W ´¸ 1 c , (1 1 )
as wellas the union's payo®and the ¯rm's pro¯t, which are denoted Uw¤(®)and ¦¤w(®),
and aregiven by Uw¤(®) = · ® c 1 ¡® + c ¸· (1 ¡®) (1 ¡® + c)b ¸1 ch a¡W i 1+ c c , (1 2) ¦¤w(®) = · (1 ¡®) (1 ¡® + c) ³ a¡W ´¸ 1+ c c c b1c . (1 3)
From (5),(8),(1 0 )and (1 3)weobviouslygetthatW wSP E > W sSP E and ¦¤s(®)> ¦¤w(®).
A naturalquestion toaskatthis pointis whetherunion delegation reduces consumer surplus orsocialwelfare.W edenotebyC S theconsumersurplus.Itis equalto
C Ss= c (1 + c)(b)1c ·1 + c¡®c (1 + c)2 (a¡W ) ¸1+ c c (1 4) forthecasein which theunion sends surplus-maximizingdelegates,and itis equalto
C Sw = c (1 + c)(b)1c · 1 ¡® 1 ¡® + c(a¡W ) ¸1+ c c (1 5) forthe case in which the union sends wage-maximizing delegates. Comparing both ex-pressions yields thatthe consumersurplus is always lowerwhen the union sends wage-maximizingdelegates ratherthan surplus-wage-maximizingdelegates.
Inthe¯rststageofthegame,theunionchooseswhethertousesurplus-maximizingdel-egates orwage-maximizingdelInthe¯rststageofthegame,theunionchooseswhethertousesurplus-maximizingdel-egates tonegotiatethewagewiththeemployer.Comparing (7)with (1 2)weobtain thefollowingproposition.
P roposition1 T he union willsend wage-maximizingdelegates ifand only if (1 + c)c+ 2 (1 ¡®)¸(1 ¡® + c)c+ 1(1 + c¡®c):
P roposition 1 tells us that: (i)forany given union bargainingpower® 2 (0 ;1 ), the moreinelastictheproductdemand is (i.e.cis big),themorelikelytheunion willchoose tosend wage-maximizingdelegates;(ii)forany given degreeofelasticity ofthedemand, the weakerthe union is (i.e. ® is small), the more likely the union willchoose to send wage-maximizing delegates. Indeed, as c increases the more inelastic the product and labordemandsbecome,andsoevenstrongunionsaremorelikelytosendwage-maximizing
delegates.Incasetheproductdemandis linear,c= 1 ,theunionwillchoosetosendwage-maximizingdelegates ifand onlyif8(1¡®)¸(2 ¡®)3.T hatis,theunion willchooseto send wage-maximizingdelegates ifand onlyiftheunion bargainingpoweris less orequal than ®¤' :76.So,iftheunion is relatively nottoostrong,then theunion willdelegate thenegotiationtasktowage-maximizingdelegates.T his resultadvocates thatcarewillbe needed in the interpretation ofeconometricestimates oftrade unions objectives done in thepastsincetheseestimates didnotdistinguishbetweentheobjectiveofthetradeunion andtheobjectiveoftheuniondelegatewhoactuallynegotiated.5Forexample,D ertouzos
and P encavel's (1 981 )originalanalysis ofthe InternationalT ypographicalU nion (IT U ) forthe years 1 946 to 1 965 was to discriminate between popularalternative hypotheses aboutunionobjectives.T heresults theyobtainedsupportconsiderablediversityinunion objectives among IT U locals. In regards with ouranalysis, theirconclusion should be taken cautiously.Indeed,itcould havebeen thatIT U locals had thesameobjectivebut decided tosend delegates whohad di®erentobjectives.
H owever, both the asymmetricN ash bargainingsolution and the R ubinstein's model predicte±cientoutcomes ofthe bargaining process (in particularagreementis reached immediately).T hisisnotthecaseonceweintroduceincompleteinformationintothewage bargaining,in which the¯rstrounds ofnegotiation areused forinformation transmission between thetwonegotiators.
4
T he W age B argainingw ith P rivate In
f
orm ation
T he main feature ofthe negotiation is that both negotiators have private information. Each negotiatordoes notknowthe impatience (ordiscountrate)ofthe otherparty.It is common knowledge thatthe ¯rm's discountrate is included in the set[rP
f;rIf], where
0 < rfP · rI
f, and that the union's discount rate is included in the set [ruP;rIu], where
0 < rPu·ruI.T hesuperscripts "I"and "P "identifythemostimpatientand mostpatient
types,respectively.T hetypes areindependentlydrawn from theset[rP
i;rIi]accordingto
theprobabilitydistributionpi,fori =u,f.W eallowforgeneraldistributions overdiscount
rates.T his uncertaintyimplies bounds on theunion bargainingpowerwhich aredenoted by® = rP f¢ h rI u+ rfP i¡1 and ® = rI f¢ h rP u+ rfI i¡1 . L emma1 Considerthewagebargainingwithincompleteinformationinwhichthedistrib-utions pfandpuarecommonknowledge,andinwhichtheperiodlengthshrinkstozero.For
any perfectB ayesian equilibria (P B E), the payo® ofthe union belongs to [U¢¤(® );U¢¤(®)] andthe payo®ofthe ¯rm belongs to [¦¤¢(®);¦¤¢(® )].
T his lemma follows from W atson's (1 998)analysis of R ubinstein's alternating-o®er bargainingmodelwithtwo-sidedincompleteinformation.6L emma1 is notadirectcorol-lary to W atson (1 998)T heorem 1 because W atson's work focuses on linearpreferences, butthe analysis can be modi¯ed tohandle the presentcase.T ranslatingW atson (1 998) T heorem 2 toourframeworkcompletes thecharacterization oftheP B E payo®s.
L emma2 Considerthe wage bargainingwithincompleteinformation in whichtheperiod length shrinks to zero. For anyUe 2 [U¤
¢(®);U¢¤(®)],¦e 2 [¦¤¢(®);¦¤¢(®)], there exists
distributions puandpf, and a P B E such thatthe P B E payo®s areU ande ¦.e
In otherwords, whetherornotallpayo®s within theintervals given in L emma1 are possibledepends onthedistributions overtypes.A s W atson (1 998)stated,L emma1 and L emma 2 establish that"each playerwillbe no worse than he would be in equilibrium ifitwere common knowledge thathe were his leastpatienttype and the opponentwere his mostpatienttype. Furthermore, each playerwillbe no betterthan he would be in equilibrium withtheroles reversed".From L emma1 wehavethattheP B E wageoutcome in caseoftheunion chooses tosendsurplus-maximizingdelegates,W s¤(®;®),satis¯es the followinginequalities: W + r P f (rI u+ rfP) c (1 + c)(a¡W )·W ¤ s(®;® )·W + rfI (rP u+ rIf) c (1 + c)(a¡W ). (1 6) N oticethateach wagesatisfyingthesebounds can betheoutcomebychoosingappropri-ately the distribution overtypes.T he lower(upper)bound is the wage outcome ofthe complete information game, when it is common knowledge that the union's type is rI
u
(rP
u)and the¯rm's typeis rfP (rfI)(and theunion bargainingpoweris ® (®)).Expression
(1 6)implies bounds on the ¯rm's employmentlevel, as wellas on the ¯rm's output, at equilibrium. In case ofthe union chooses to send wage-maximizing delegates, the P B E wageoutcome,W w¤(®;® ),satis¯es thefollowinginequalities:
W + cr P f (1 + c)rI u+ crPf (a¡W )·W w¤(®;®)·W + crIf (1 + c)rP u+ crIf (a¡W ). (1 7) W ith complete information, the choice ofwage-maximizingdelegates always increase the wage leveland decreases the production output(and the employmentlevel)as well
6W atson(19 9 8) c harac teriz ed the set ofP B E payo®sw hic h m ay arise inR ub instein'salternating-o®er
b argaining gam e and c onstruc ted b ound s(w hic h are m et) onthe agreem entsthat m ay b e m ad e. T he b oundsand the P B E payo®sset are d eterm ined b y the range ofincom plete inform ationand are easy to c om pute b ec ause they c orrespond to the SP E payo®softw o b argaining gam esofc omplete inform ation. T hese tw o gam esare d e¯ned b y m atc hing one player'sm ost im patient type w ith the opponent'sm ost patient type.
as theconsumersurplus.B utwhen theplayers possess privateinformation,thecomplete informationresults arenotalways valid.T henecessaryandsu±cientconditiontorecover the complete information result that the wage outcome in case of surplus-maximizing delegates is always strictly smallerthan the wage outcome in case ofwage-maximizing delegates is c< r P frIf¡rIurIf+ ruPrfP rI urIf¡ruPrPf . (1 8)
T his condition is satis¯ed the smallerthe amountofprivateinformationj® ¡®jand the parameterc are. So, the more elastic the productdemand is the more likely the wage outcomeincaseofwage-maximizingdelegateswillbehigherthanthewageoutcomeincase ofsurplus-maximizingdelegateseveninpresenceofincompleteinformation.T hecondition (1 8)canberewrittenas ®(1 + c)> ®(1¡® + c).H ence,ifitiscommonlyknownthatunion is strongerthan the¯rm (® ¸:5)and thelabordemand is quiteelastic(c·1 ),then we getW w¤(® ;®)> W s¤(®;® ),C Sw(®;®)< C Ss(® ;®)andL ¤w(®;®)< L ¤s(®;® ).T heintuition
behindthis resultis thefollowingone.Firstly,incompleteinformation in themodeltakes into accounttwo main features. T he ¯rstone is the amount ofprivate information in possession oftheplayers.B y the amountofprivate information wemean thesizeofthe setin which player's discountrateis contained and which is common knowledgebetween theplayers.T hesecond oneis theuncertainty aboutwhois themorepatientplayer,i.e. who is the strongerplayer. W hen itis common knowledge that the union is stronger, this second feature disappears, and information tends to play a less crucialrole in the process ofthe negotiation between the ¯rm and the union delegates. Secondly, ifthe elasticity ofproductand labordemands is high, a wage increase willimply a signi¯cant drop in employmentleveland, hence, itwillrefrain surplus-maximizing delegates from demanding high wages. T herefore, we recover the above complete information results onceitis commonknowledgethattheunionis strongerthanthe¯rm andtheelasticityof productandlabordemands is highenough.T henextproposition summarizes this result. P roposition2 Ifitis commonlyknown thatthe union is strongerthan the ¯rm (® ¸12)
andthe labordemandis quite elastic(c·1 ),then W ¤
w(® ;®)> W s¤(®;®).
O bviously,from L emma1 and L emma2 ine±cientoutcomes arepossible,even as the periodlengthshrinkstozero.Ine±ciencycanoccurintwoways.First,playersmightagree tothrowawaysomeoftheresourceoverwhichtheyarebargaining,evenwhenagreement is reached withoutdelay.Second,thenegotiation mayinvolveconsiderabledelay,even if theeventualagreementis e±cienton its own.W hile the scope ofpossible ine±ciency is clearfrom L emma 1 and L emma2, whatis notsoobvious is the potentialfordelay.In fact,thewagebargaininggamemayinvolvedelay(strikes orlock-outs),butnotperpetual
disagreement,atequilibrium.Indeed,W atson(1 998)has constructedaboundondelayin equilibrium which shows thatan agreementis reached in ¯nitetimeand thatdelay time equals zeroas incompleteinformation vanishes.
5 T he Strike Ac tivity
In the literature on strikes [see e.g. Cheung and D avidson (1 991 ), Kennan and W ilson (1 989, 1 993)], three di®erentmeasures ofstrike activity are usually proposed:the strike incidence,the strikeduration,and thenumberofworkdays lostdue toworkstoppages. Since we allowforgeneraldistributions overtypes and we may encountera multiplicity ofP B E,weareunabletocomputemeasures ofstrikeactivityas theones justmentioned. In ordertocompute an expected strike duration one would need to¯x someparameters ofthe modelsuch as thedistribution overtypes butitwould imply asubstantialloss of generality.N evertheless, we propose to identify the strike activity (strikes orlock-outs) with the potentialine±ciency in reaching a wage agreement. Following W atson (1 998) T heorem 3,thelargeris thedi®erencebetween theupperbound and lowerbound on the bargaining outcome, the largeris the potentialine±ciency forobtaining an agreement and the largeris the possibility ofdelay in reachingan agreement.T herefore, the strike activity is given by the di®erence between theupperbound and the lowerbound on the wage outcome and it can be interpreted as an indicator ofboth the levelof potential ine±ciencyand thestrikeduration.7
W hen the union chooses surplus-maximizing delegates tobargain the wage with the ¯rm,thestrikeactivityis given bythefollowingexpression.
ªs = (® ¡®) µ c 1 + c ¶ ³ a¡W ´ (1 9) = h rI frIu¡rfP rPu i £ rP f + rIu ¤£ rI f+ ruP ¤ µ c 1 + c ¶ ³ a¡W ´. (20 ) T herefore,ªsis anincreasing(decreasing)functionofruI(rPu),is adecreasing(increasing)
function of rfP (rI
f), and is decreasing with the reservation wage W . W e observe also
thatthestrikeactivityis decreasingwith thedegreeofelasticityoftheproductdemand:
@ªs
@c> 0 .T hatis,themoreinelasticthedemand is themorestrikes willoccur.
W hentheunionchooses wage-maximizingdelegates tobargainthewagewiththe¯rm,
7O ur m easure ofstrike ac tivity givesthe scope eac h player hasfor screening hisopponent b y m aking
w age proposalssatisfying the expressions(16) or (17),and hence,for d elayingthe w age agreem ent.O nly inaverage thism easure isa good proxy ofac tualstrike d uration.
thestrikeactivityis given bythefollowingexpression. ªw = c · ® 1 ¡® + c¡ ® 1 ¡® + c ¸ (a¡W ) (21 ) = c(1 + c) h rI frIu¡rfP rPu i £ crP f + (1 + c)rIu ¤£ crI f+ (1 + c)ruP ¤³a¡W ´. (22) A gain, ªw is an increasing (decreasing)function ofrIu(rPu), is a decreasing (increasing)
function ofrfP (rIf), and is decreasingwith the reservation wage W .B utnowthe strike activity might be decreasing orincreasing with the degree of elasticity of the product demand. P recisely, the strike activity is decreasing with the degree ofelasticity ofthe productdemand,@ªw
@c > 0 , ifand only if(1 + c)2rPu ruI> c2rPf rIf.So, we can state the
following results: (i)ifitis common knowledge thatthe union is weakerthan the ¯rm then@ªw
@c > 0 ;(ii)ifitis common knowledge thatthe¯rm is
³ 1+ c c ´2 times weakerthan theunion then@ªw @c< 0 .
From both expressions of strike activity we observe that, for any given amount of private informationj® ¡®jthe strongerthe union mightbe (i.e. the bigger® is)the greater the strike activity willbe. T his result is con¯rmed by T racy (1 986)empirical study ofthe determinants ofU .S.labordisputes. H e found that the higherthe union coveragerate(whichis aproxyfortheunionbargainingpower)is,themorelikelystrikes willoccurand last.M oreover,comparingthe expressions (1 9)and (21 )we can statethe followingproposition.
P roposition3 T hestrikeactivityisgreaterwhenevertheunionchooseswage-maximizing delegates instead ofsurplus-maximizingdelegates.T hatis,ªw > ªs.
W hetherstrategicunion delegation willincreaseordecreasethe strike activity is not obvious at¯rstsight.T he wage objective ofsurplus-maximizingdelegates (whodocare aboutoutputlevels)is notclear-cutas itis forthe wage objective ofwage-maximizing delegates (who do notcare about¯rm's output). H ence, surplus-maximizing delegates havemorescopetohidetheirtype,which is privateinformation,in ordertotrytoreach amore favorable outcome.A s aconsequence, the¯rm whostillclaims lowerwages may needmoretime,duringthenegotiation,toscreentheunion's typewhenbargainingoccurs with surplus-maximizingdelegates ratherthan with wage-maximizingdelegates.B utthis e®ectis in factdominated by thecon° ictofinterestwhich is sostrongbetween the ¯rm and thewage-maximizingdelegates and which induces thewage-maximizingdelegates to concedemoreslowlythan surplus-maximizingdelegates do.
From P roposition 3 we knowthatifthe union chooses tosend wage-maximizingdel-egates then the strike activity is going to increase.N owwe turn to investigate whether
and when itis optimaltodelegate forthe union.T he necessary and su±cientcondition such thatitis always optimalfortheunion tochoosewage-maximizingdelegates is
· ® c 1 ¡® + c ¸c· (1 ¡®) (1 ¡® + c)b ¸ ¸ ·® c 1 + c ¸c·1 + (1 ¡®)c (1 + c)2b ¸ (23) T akethecaseofalineardemand (cis equalto1 ).T hen,theabovecondition becomes:
® (1 ¡®) (2¡®)2 ¸
® (2¡®)
8 (24)
From (24)wecanmakethefollowingtworemarks.First,ifitis commonlyknownthatthe unionis weakerthanthe¯rm (i.e.® ·12)andtheunionis nottooweak(i.e.® ¸25)then
itis optimalfortheunion tosend wage-maximizingdelegates.Second,ifitis commonly known thatthe union is strongerthan the ¯rm (i.e. ® ¸12)and the union is nottoo
strong(i.e.® ·13
2 0)then itis optimalforthe union tosend wage-maximizingdelegates.
Finally, notice thatthe increase in strike activity due tostrategicdelegation may be far from being negligible. Forexample, if® = 12 and ® = 25then allowing strategic union delegation willincrease atequilibrium the strike activity by 66%.Even more, if® =12 and® =132 0 thenstrategicuniondelegationwillincreasethestrikeactivityby1 0 0 %.A s a measureofthee±ciencyloss duetostrategicdelegationweproposetheratiobetweenthe strikeactivityincasetheunionchooses wage-maximizingdelegates andthestrikeactivity in casetheunion chooses surplus-maximizingdelegates,
ªw
ªs =
(1 + c)2
(1 ¡® + c)(1 ¡® + c) (25) T his ratio is bounded above by (1+ cc)2 and below by 1 (cfr. P roposition 3). So, by
givingtheoptiontotheuniontodelegate,thestrikeactivityandtheine±ciencyloss can increaseconsiderably.Indeed,thestrikeactivity with wage-maximizingdelegates can be up to(1+ cc("+ c)2) times thestrikeactivitywith surplus-maximizingdelegates with"small.For example, ifthe demand is linear(c = 1 )then this ratio willbe close to 4 which is not negligible.
6 Con
c l
usion
W e have developed a modelofwage determination with private information, in which the union has the option to delegate the wage bargaining to eithersurplus-maximizing delegatesortowage-maximizingdelegates(suchasseniorunionmembers).W ehaveshown thatthestrikeactivityis greaterwhenevertheunion chooses wage-maximizingdelegates instead of surplus-maximizing delegates. W e have also determined when it is always optimalforthe union tochoose wage-maximizingdelegates and we have found thatthe
e±ciencyloss duetostrategicdelegationcanbeimportant.From apolicyperspectiveour analysisquestionswhetheroneshouldallowforstrategicdelegation(forexample,bymeans oflaws protecting union delegates from being dismissed). From a research perspective ouranalysis questions theoreticalresults obtained undercompleteinformation as wellas empiricalstudies ofthe tradeunion objectives.A direction forfuture research is totest empirically therelevanceofstrategicunion delegation and toovercometheidenti¯cation problem with respecttothetradeunion objectiveand thenegotiatorobjective.
R ef
eren
c es
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