THENONNEUTRALITYOF MONETARY POLICY WITHLARGE PRICE ORWAGESETTERS*

DAVID SOSKICE AND TORBEN IVERSEN

Monetaryrules matter for the equilibrium rate of employment when the numberof price-wage setters is small, even when assuming rational expectations, completeinformation, central bank precommitment, and absence of nominal rigidities.If the central bank is nonaccommodating, sufficiently large unions, bargainingindependently ,havean incentive to moderate sectoral money wages, andthereby expected real wages. The result is an increase in the real money supply,andhence higher demand and employment. This does not hold with accommodatingmonetary policy since unions’ wage decisions cannot then affect thereal money supply .Asimilarargument holds for large monopolistically competitiveprice setters.

I. INTRODUCTION Undera wide rangeof assumptions, the choice by acentral bank ofa monetaryrule does not affect theequilibrium rate of employment.We show in this article,however ,that with aŽnite numberof wageor price setters this is nolonger necessarily the case.In particular, weshow that aswitch by thecentral bank from an accommodatingto a nonaccommodatingmonetary rule leads to an increasein theequilibrium rate of output oremployment,and that this increaseis greaterthe smaller the number of price or wagesetters. The result does not challenge the weak neutrality of moneytheory; given the choice of monetary rule, a changein the moneysupply has noeffect on real variables. 1 Rather,it shows that the strategicinteraction ofprice-wage setters and monetary authoritiescan have important effects on theequilibrium rate of output and employment.In otherwords, with aŽnitenumber of wageor price setters, the character of the monetary rule is nonneutral.While it mayappear at Žrstsight counterintuitive that an increase in nonaccommodationshould increase equilib- riumemployment, we show that this is consistentwith data for seventeenOECD economiesover the period 1973– 1993.

*Wewould like to thank Christopher Allsopp, Thomas Cusack, Robert Franzese,Jeffry Frieden, Peter A. Hall,William Novshek, and in particular AlbertoAlesina, Olivier Blanchard, and two anonymousreferees for their many usefulcomments and suggestions. The Ž rst authorbeneŽ ted from the environ- mentof the RSSS intheAustralian National University in revisingthis article. 1.Bleaney {1996} shows this to be the case under a similarset ofassumptions usedhere. This result is simplya restatementof themoney neutrality thesis— a thesiswe obviously do not challenge. r 2000by thePresident and Fellowsof Harvard Collegeand theMassachusetts Institute of Technology. The Quarterly Journal ofEconomics, February2000

265 266 QUARTERLY JOURNALOF ECONOMICS

Asufficient setof assumptions under which choice of mone- tary rulehas noeffect on equilibriumemployment are (i) rational expectations,(ii) perfectcompetition, (iii) completeinformation, (iv) capacity forthe central bank tocredibly precommit, and (v) absenceof nominalrigidities. A largeliterature on central banks has subsequentlyshown that thecore conclusion is robustto changesin assumptions(iii), (iv), and (v). 2 Wedeliberately retain all theseassumptions (in addition to(i)), and showinstead what happens whenassumption (ii) isdropped. In its place,we present twogeneral equilibrium models, both based onBlanchard and Kiyotaki{1987} and Blanchard and Fischer{1989}, whichassume that eitherprices are set by monopolisticallycompetitive produc- ersor wages are set by monopolyunions. The Ž rst,a ‘‘yeoman farmer’’ modelof monopolistic competition in whicheach of N farmersproduces unaided oneproduct and consumesall N products,is simple,but givesthe intuition of ourargument. This is setout in SectionII. Thesecond model assumes a fully unionizedmultisector economy in whichmonopoly unions in each sectorset wages independently and simultaneously.Thisis setout inSectionIII. In bothcases, the economic agents care only about realvariables, so there is nomoneyillusion. 3 Thekey to our argument is that priceor wage setters with somemonopoly power can affect thereal money supply depending onthemonetary rule used by thecentral bank. If thecentral bank Žxesthe nominal money supply ,theeffect of increased sectoral pricesor wages on aggregate prices will translateinto reduced realdemand and hencelower output or employment. There is thereforean incentivefor producers or unions to lower their nominalprices or wages relative to those expected in other

2.In Barro andGordon, for example, inability of the central bank to credibly precommitto a monetaryrule raises in ation, but has no effects on equilibrium unemployment(see also Kydland and Prescott {1977}). Other work hasfocused on theconsequences of assumingincomplete information. For example, when voters donotknow howcompetent governments are in producing public goods for a given Žscalrevenue, governments may try tosignal their competency by engaging in expansionarypreelection Ž scaland monetary policies (see Rogoff and Sibert {1988},Cukierman and Meltzer {1986}, and Rogoff {1990}). Other modelsassume nominalrigidities in the presence of economic business cycles that create a trade-offbetween in ation conservatism (which reduces in ation) and  exibilityto respondto exogenous shocks (which reduces employment variability). This has consequencesof the optimal design of centralbank contracts, but does not affect equilibriumemployment. For examples of this approach, see Rogoff {1985}, Lohmann{1992}, Persson and Tabellini {1993}, and Svensson {1996}. 3.This contrasts with a recentpaper by Cukierman and Lippi {1999} which assumesthat the rate of in ation matters to unions. Absent this, the paper shows a nonneutralityresult (in a differentdirection to ours) only when relative wages as wellas real wages are added to the employment demand function. THENONNEUTRALITY OFMONETARY POLICY 267 sectors;and henceto increase production or employment. The smallerthe number of independentmonopoly price-wage setters, thegreater the individual effecton the aggregate price level, and thegreater the incentive for real price-wage restraint. In thecase ofunions, the standard trade-off betweenthe real wage and the employmentlevel along the sectoral employment demand curveis thus altered:greater real wage restraint lowers the relative price ofthe sector, and this raisesthe real money supply (given wage-pricesetting elsewhere). By contrast,if thecentral bank Žxesthe real money supply ,theincentive to exercise restraint is absentsince unions in this situationcannot affect realdemand and henceemployment. Because all unionsreason similarly ,real wagerestraint and equilibriumemployment are higher ,thefewer thenumber of unions, and themore nonaccommodating the monetaryregime. Sincewage-setting tends tobe more monopolized than price- setting,the argument applies toall economieswith asmall numberof independent unions. It does not apply toeconomies wherethere are a verylarge number of unions (or where individuals bargain wages),because here the aggregate price effectsof individual unionsare too small. Nor does it apply to economieswhere a singleunion sets wages, or where a small numberof unions can coordinate their wage policies effectively enoughto act as asingleunion, since the union(s) can thenchoose full employmentindependently ofthemonetary regime. 4 Rather, theargument is intended tosolve, and is motivatedby ,a persistentempirical puzzle in comparativepolitical economy:the capacity forgood unemployment performance by some,but not other,economies with intermediatelycentralized systems of wage- setting.Such systems are often portrayed as institutional dilem- maswhere large unions are capable ofinicting greatharm on the economy,yetincapable ofsolvingtheir collective action problems {Olson 1982; Calmforsand Driffill 1988}. But whileit istruethat someof these systems have performed poorly ,it is frequently notedthat othersare among the most successful, and institution- ally stable,economies in theworld (seeSoskice {1990}, Hall {1994}, and Iversen{1999}). Thepurpose of this articleis analytic ratherthan empirical, but thedata in TableI help toillustrate the puzzle (thetable is

4.The case of multilevel bargaining is more complicated; see Iversen {1998,1999}. 268 QUARTERLY JOURNALOF ECONOMICS

TABLE I LONG-RUN AVERAGE UNEMPLOYMENT RATES FOR 17 OECD COUNTRIES DEPENDING ON THE MONETARY RULE AND THE CENTRALIZATION OF WAGE BARGAINING, 1973–1993 (N, IN PARENTHESES)

Centralization

Very highIntermediate V ery low Mean:

Monetaryrule Accommodating 3.9 (3) 7.6 (3) 7.1(3) 6.2 (9) Nonaccommodating 5.6 (2) 3.6 (4) 7.4(2) 5.0 (8) Difference 2 1.7 4.0* 2 0.3 5.6 (17)

*Difference is signiŽcant ata.001level (one-sided test). Monetary rule refers tothe independence of the central bankexcept in the caseof Japanwhere a dependent bankhas followed anonaccommodating rule. Centralization refers tothe prevalent level and concentration of wage setting. Very high centralization meansthat a small number of national unions or confederations bargain wages and routinely coordinate their wage demands. Very low centralization means thatwages are predominantly bargained atthe plant or Žrm levels bylocal unions or individuals. Intermediate casesare characterized bya limited number of bargaining areas,but without any effective coordination of union wage demands. Beginning with the toprow, the countries in the tableare from left to right (with bracketsdemarcating cells): {Finland, Norway, Sweden}; {Australia, Belgium, Italy}; United Kingdom, France, New Zealand}; {Austria, Denmark}; {Germany, Japan,Netherlands, Switzerland}; {Canada, United States}. Sources: OECD{1996,1997}; Cukierman, Webb, and Neyapti {1992};and Hutchison, Ito, and Cargil {1997}. literallyonly illustrative). The table showsthe equilibrium rate of unemploymentin seventeenOECD countriescharacterized by different types ofunionsand monetaryrules. 5 Withone exception, weuse Cukierman, Webb, and Neyapti’s {1992} index oflegal centralbank independenceas aproxyfor the monetary rule, dividing thesample into an accommodatingand anonaccommodat- ing category. 6 Withregard to the number of unions, we use centralizationof wage bargaining as aproxy.Althoughthere is no consensuson the classiŽ cation of every bargaining system,most industrial relationsspecialists agreeon the ones that areeither highly decentralized(Canada, France,New Zealand, theUnited Kingdom,and theUnited States), or highly centralized(Austria, Denmark,Finland, Norway,and Sweden).We treat the remainder

5.Equilibrium unemployment rates are proxied by OECD’s {1996}estimates forthe nonaccelerating wage rates of unemploymentin the period 1973– 1993 (i.e., post-BrettonWoods), except in thecases of Switzerland and New Zealand where theseare not available (we use national deŽ nitions instead). 6.The exception is Japanwhere the monetary authorities began to adhere to anunambiguously nonaccommodating rule after 1973, even though the central bankremained legally dependent (see Cargil {1993}, Hutchison and Judd {1989}, andHutchison, Ito, and Cargil {1997}). This is recognized by Cukierman,Webb, andNeyapti {1992} who attribute nonaccommodating monetary policies in Japan tothe in uence of an exceptionally ‘ ‘conservative’’ Ministryof Finance {1993, p. 372}. THENONNEUTRALITY OFMONETARY POLICY 269

(Australia, Belgium,Germany ,Italy,Japan, Netherlands,and Switzerland) asintermediatecases. 7 Notethat monetaryrule appears tobe largely unrelated to unemploymentwhen the number of unionsis eithervery large or verysmall, but that nonaccommodatingrules are associated with signiŽcantly lower unemploymentthan accommodatingrules whenthe number of unionsis intermediate. 8 Althoughdata ofthis naturecan only be suggestive, a numberof moredetailed empiri- cal studies support thenotion that monetaryrules matter for unemploymentwhen their interactive effects with thecentraliza- tionof wage-setting are taken into account (see Iversen {1998, 1999}, Hall {1994}, Hall and Franzese{1998}, and Garrettand Way{1995}). SpeciŽcally ,if ourargument is correct,it would help us tounderstand why countrieswith intermediatelycentralized wage-settingsystems are characterized by suchwidely divergent long-termunemployment performance.

II. THE YEOMAN FARMER ECONOMY Toconveythe basic logicof the argument, we begin by consideringa simple‘ ‘yeomanfarmer ’’economywith monopolisti- cally competitiveproducers who provide their own labor input. As in Blanchard and Fischer{1989, pp. 376–380} weassume, with onemodiŽ cation, that thereare N identical monopolisticcompeti- torseach producing asinglegood indexed by i with price Pi and output Qi (i 5 1, . . . , N).(ThemodiŽ cation is that in eachsector , whileprice and totaloutput aredecided by asingle‘ ‘marketing agent,’’ weassumethat thereare many identical producerswhose productionquota is setby theagent but whotake individual consumptiondecisions; the agent maximizes their utility indi- rectly.Thisenables us tofocus on strategicprice-setting behavior whenthere are a smallnumber of sectors, while avoiding the complicationsof strategic consumption behavior .It requiresmi- norchanges— set out in theAppendix— to the Blanchard-Fischer argument).Blanchard and Fischerconclude that themacroeconom-

7.The centralization of wage bargaining in differentcountries is reviewed in arecentOECD study {1997}.Our classiŽcation is consistent with the most frequentlyused classiŽ cations of centralization. See also Flanagan, Soskice, and Ulman{1983}, and Iversen {1998}. 8.Any attemptto capture these relationships in a simplyadditive model wouldfail, and it isnotsurprising that past studies employing a simpleadditive methodologyhave not found any strong employment effects of eithercentral bank independence{Alesina and Summers 1993; Bleaney 1996}, or bargainingstructure {OECD 1997}. 270 QUARTERLY JOURNALOF ECONOMICS icsis unalteredas wemovefrom perfect competition to monopolis- ticcompetition, and that ‘‘...moneyis neutralunder monopolistic competitionjust as it isunderperfect competition’ ’ {p. 381}. However,if themonopolistic competitor’ s price Pi has a Žnite effecton the general price level, changes in themonetary rule may benonneutral.We assume that thecentral bank canprecommit to amonetaryrule, which we deŽne by aparameter a :9

(1) M 5 P a 0 # a # 1.

SpeciŽcally ,twolimiting cases can be distinguished. When a 5 0, M 5 1,the monetary rule consists in Žxing thenominal money supply equalto unity ,and thus doesnot accommodate any price increases.When a 5 1, M/P 5 1,and themonetary rule consists in Žxing thereal money supply equal tounity ,and thus accommo- dates all priceincreases. 10 It is convenientto assumethat central banks areendowed with aŽxedvalue of a whichmight be thought ofas theresult of past reputation-building. In what follows,we assumea sequenceof three moves: (1) thecentral bank precom- mitsto setting M contingenton P.(2) Thefarmers’ agents each set Pi simultaneously,in theknowledge of themonetary rule. (3) The centralbank thensets M given P(P1, . . . , PN).Sincestage 3 is automatic,the game is in effectconcentrated on stage 2. If Ui is theobjective function of the ith agent,we show that the ith agent should choose P*i such that Ui(P*i, P*2 i) $ Ui(Pi, P *2 i) for all i, where P*i is theequilibrium price of the ith agent and P *2 i is the vectorof equilibriumprices of the N 2 1 agents. Usingthe Blanchard and Fischermodel {1989, p. 433} with minornotational changes, the demand forgood i is given by

2 h (2) Qi 5 m/N · pi , where pi Pi/P is therelative price, and m M/P is the real moneysupply .(It is shownin theAppendix how(2) is derivedfrom individual maximizationbehavior by farmers.This relies on the assumptionthat theagent can Ž xthesupply ofthe farmer ’s output toequilibrium demand.) Theaggregate price level P is deŽned as aconstantelasticity of substitution(CES) index: 1 1/(12 h ) (3) P 5 · P12 h . N i

9.We are indebted to Chris Allsopp for suggesting this form. 10. When a 5 1, M/P couldbe setequal to any constant other than 1 without affectingthe results (as we discuss below). Using 1 isfor convenience. THENONNEUTRALITY OFMONETARY POLICY 271

Assuming that thereare a Žxednumber of n farmersin each sector,with constantreturns to scaleproduction, it is shown(also in theAppendix) that maximizationof thedirect utility functionof thefarmer with CES preferencesover the N goods,disutility of labor,and utility ofreal money balances, and whomakes optimal consumptionand realcash balance choices,is securedby maximi- zation by thefarmer ’sagentof the following indirect utility function:

b (4) max Ui 5 pi · Qi 2 (d/b ) · Qi 1 m/N, pi

b where d8/b · (Qi/n) is theindividual farmer’sutility costin terms ofown-labor of production Q (b . 1),11 with d d8/nb 2 1, and 2 1 12 n · ( pi · Qi 1 m/N )is thefarmer ’swealth. Substituting (2) into(4) and differentiating with respectto pi givesthe Ž rst- ordercondition for utility maximization(see footnote 13). We focuson a symmetricequilibrium, implying that pi 5 1 and hence Qi 5 m/N, for all i.Togetherwith theŽ rst-ordercondition this yields13

1/(b 2 1) h 2 1 2 2­ ln m/­ ln pi (5) Qi 5 Q* 5 . dh 2 d · ­ ln m/­ ln pi where Q*istheequilibrium level of totaloutput persector (so the output perfarmer is Q*/n).The crucial term in (5) is ­ ln m/­ ln pi,

11.This is identical to equation (3) in Blanchard and Fischer {1989, p. 378}. 12.We assume that a changein M (whenthe central bank’ s monetaryrule is appliedafter prices have been set) is distributed across the farmers in proportion totheir original holdings of M. 13.T oseethis, Ž rst substitute(2) into (4) to derive the Ž rst-order condition:

m m b (1 2 h ) ? p2 h ? 1 dh p2 h b 2 1 ? i N i N 1 ­ m d m b 2 1 ­ m 12 h 2 h b 1 (1 1 pi ) ? ? 2 pi ? ? 5 0. N ­ pi N N ­ pi

Thendivide through by ( m/N)andimpose the equilibrium conditions ( pi 1 and Qi 5 m/N) to obtain

­ ln m ­ ln m b 2 1 b 2 1 (1 2 h ) 1 dh Qi 1 2 5 · dQi , ­ ln pi ­ ln pi whichcan be reformulatedas in (5).The second-order condition that d2U/dp2 , 0 is satisŽed; the proof is available from the authors upon request. 272 QUARTERLY JOURNALOF ECONOMICS and weneed to evaluate this. Since M 5 Pa , m 5 P(a 2 1), and ln m 5 2 (1 2 a ) · ln P. Hence,

E E ­ ln m ­ ln P(i) ­ ln P(i) ­ ln Pi (6) 5 2 (1 2 a ) · 5 2 (1 2 a ) · · , ­ ln pi ­ ln pi ­ ln Pi ­ ln pi

E E where P(i) is the ith agent’s expectationof P.Notethat, if Pj,(i) is the E value of Pj expectedby the ith agent, Pj,(i) is independentof Pi since agentsset prices simultaneously and independently.Sofrom (3)

E h 2 1 ­ ln P(i) 1 P 1 (7) 5 · 5 ­ ln Pi N Pi N given that P 5 Pi in equilibrium.Consequently ,

E 2 1 E 2 1 ­ ln Pi ­ (ln Pi 2 ln P(i)) ­ ln P(i) N (8) 5 5 1 2 5 . ­ ln pi ­ ln Pi ­ ln Pi N2 1

Substituting (7) and (8) into(6) yields

­ ln m 1 N 12 a (9) 5 2 (1 2 a ) · · 5 2 , ­ ln pi N N2 1 N2 1 and, substituting (9) into(5), thefarmers’ agent thus sets Qi in equilibriumto satisfy

h 2 1 1 2 (1 2 a )/(N 2 1) 1/(b 2 1) (10) Q* 5 . dh 1 d · (1 2 a )/(N 2 1)

Notethat if themonetary rule is completelyaccommodating, a 5 1, or if N 5 ` ,weget the Blanchard-Fischer result{1989 p. 380, equation7}:

h 2 1 1/(b 2 1) (11) Q* 5 . dh Comparing (10) and (11), wecan seethat theright-hand side of (10) is greaterthan that of(11) as longas ((1 2 a )/(N 2 1)) . 0.14 Thus,we reach the following conclusion: in theyeoman farmer monopolisticcompetition model, if a , 1, sothat monetary policy is

14.Writing ((1 2 a )/(N2 1)) as K,theright-hand-side bracket of(10) becomes (h 2 1 1 2K )/(h 1 K ) 5 ((h 2 1)/h ) · (((1 1 2K)/(h 2 1))/((1 1 K)/h ))andthis is greaterthan the right-hand-side bracket of(11)when 2 Kh . K · (h 2 1). Since by assumption h . 1,thisrequires K . 0. THENONNEUTRALITY OFMONETARY POLICY 273 notcompletelyaccommodating, and Nis Žnite (butgreater than 1 ), equilibrium outputwill be higherthan when monetary policy is completelyaccommodating; the difference will be larger thesmaller is N,and thesmaller (i.e.,the more nonaccommodating ) is a . Thereason for these effects is that monopolisticcompetitors will takeinto account their own effect on theaggregate price level, and hencethe real money supply ,whenthey set prices; and this effectis contingenton the monetary rule. Given a , 1, if the ith agentis toreduce the aggregate price level P,that implies Pi must fall relativeto prices in othersectors. Since all sectorsare identical,the output, and thusmarginal cost in termsof own- labor,of each farmer must be sufficiently largeto eliminate the incentiveto engage in furtherrelative price-cutting. This will thenbe the equilibrium output and pricelevel. Anotherway oflookingat this is in comparativestatic terms. Suppose that thecentral bank reduces a ,thus tighteningmone- tary policy.Withsmall enough N,eachagent will nowhave an increasedincentive to reduce his price(hence to undercut the others)to take advantage ofthe increased impact that this will haveon the real money supply .In effect,the real marginal revenuecurve has shifted outbecause the elasticity of the real moneysupply and hencedemand with respectto the sector ’s relativeprice, ­ ln m/­ ln pi,has increased;this elasticityplays an exactlyparallel roleto the direct elasticity of demand. Competi- tiveundercutting will thus continueuntil theequilibrium be- tweenmarginal revenue and marginalcosts has beenrestored at ahigherlevel of output, with ahigherreal money supply and a loweraggregate price level. Thisdoes not mean, however ,that outputis alsononneutral with respectto the nominal money supply .Toseethis, we can breakthe monetary rule into two parts: (a) thedegree of accommo- dation ofthecentral bank, and (b) thescale of thenominal money supply.Theaccommodation part oftherule is

­ ln m (1a) 5 2 (1 2 a ) . ­ ln P

Integrating(1a) givesus

(1b) m 5 K · P2 (12 a ) .

In themodels of this articlewe have taken K 5 1tosimplify the 274 QUARTERLY JOURNALOF ECONOMICS presentation.But in general K is thenominal scale part ofthe rule.DeŽ ning

(1c) K 5 µ12 a , we have that P 5 m*1/(12 a ) ·µsothat equilibriumoutput is neutral with respectto µ ,thenominal scale parameter . But when N is Žnite,equilibrium output is nonneutralwith respectto the degree of accommodationin themonetary rule ( a ), and themain objective of this sectionhas beento show that the analysis ofmacroeconomics changes fundamentally as wemove froma largenumber of monopolistic competitors to a small number;hence also from a perfectlycompetitive economy to a world ofimperfect competition with asmallnumber of price setters.It can beobjected, however ,that thepractical signiŽcance ofthis insight is limitedsince price setting rarely occurs at alevel that would makegeneral price considerations relevant for indi- vidual pricing agents.But this objectionneed not apply towage setting,which is frequentlyconducted at theindustry ,sector,or evennational level.Indeed, relatively centralized wage setting is therule rather than theexception in amajorityof OECD countries{OECD 1997}. Becausecentralized wage setters exert aneffecton the general price level, our argument has considerable practical importancefor understanding realwage behavior and henceemployment performance. In thefollowing section we show this by introducingsectoral labor markets where each sectoral wageis setby thesectoral monopoly union. T oensurethat our resultsdo notdepend onlarge price setters, we assume that there aretwo or more Bertrand competitorsin eachsectoral product market.

III. A MODEL WITH MONOPOLY UNIONS

Nominalwages Wi areset in eachof N identical sectorsby a sectoralmonopoly union; there are n workersin eachsector ,all of whomare union members, and thereis nomobility between sectors.As before,the demand forthe good in eachsector is a constantelasticity function of the relative price of the sector ’s goodmultiplied by thereal supply ofmoney de ated by the numberof sectors;this is equation(2). Hourlylabor productivity isconstantand equalto unity,and thereare two or moreBertrand competitorsin eachsector; thus, the price in sector i, Pi, is equal to theconstant marginal cost Wi.Producershave to hire at the THENONNEUTRALITY OFMONETARY POLICY 275 union-determinedwage, which determines total hours employed Ei,and eachworker is hiredfor the same number of hours, Ei/n. Wagesand pricesin eachsector are set independently ofwageand pricesetting in othersectors. Finally ,theaggregate price level is derivedfrom a constantelasticity of substitution index ofthe individual sectoralprices, as in equation(3) in thelast section. 15 Whenanalyzing this case,it is helpful tokeep in mind the implied gameof complete and quasi-perfect information.The gameconsists of four stages.

Stage 1: TheCB precommitsto the monetary rule implied by a ; Stage 2: unionssimultaneously and independently choose Wi (i 5 1, . . . ,N); Stage 3: producerssimultaneously and independently set Pi and Ei (i 5 1, . . . , N ); Stage 4: the CB sets M contingenton P aspredeterminedby a (for all a . 0 since a 5 0is anoncontingentstrategy). Thesolution is found by backward induction,but in Stage4 the centralbank acts as an automatonin setting M equal to P a (as a resultof the precommitment assumption); in Stage3 Bertrand competitorsin eachsector i set Pi 5 Wi;and in Stage1 theCB precommitsto a monetaryrule ( a )that it will subsequently adhereto. So we simply focuson union wage-setting behavior in Stage2. All weneedto retain from Stage 3 arethe two constraints onunionwage-setting. The Ž rstis

(12) pi 5 wi, whichis implied by Bertrand pricing,using wi Wi/P. The second providesthe union with atrade-off betweentotal hours employed and thereal wage, and is found bysubstituting (12) into(2), and using theassumption of constantunit laborproductivity , Qi 5 Ei:

2 h (13) Ei 5 m/N · wi . Equations (12) and (13) hold as equilibriumresults for any possiblevalue of W1, . . . ,WN ,i.e.,for each possible subgame starting at Stage3. Just as themarketing agent in theyeoman farmermodel sets production quotas for individual farmers,we assumehere that theunion sets the number of hoursworked by its members.This assumption ensures that theunion’ s supply of

15.Hence, if effective collusion occurs betweenseveral unions, this would alterthe number of sectors as deŽ ned here. 276 QUARTERLY JOURNALOF ECONOMICS laboralways satisŽes Ž rms’demand forlabor ,and hencethat 16 thereis an equilibriumfor any valueof W1, . . . ,WN . As in theyeoman farmer model we assume that eachunion memberhas autility functionin whichconsumption and real moneybalances affect utility positivelyand directlyand whichis negativein hoursworked. We show in theAppendix howthe demand forlabor schedules in eachsector can be derived from utility maximizationby individual workers.In addition, ifthe ith unionmaximizes the utility oftherepresentative union member , this impliesthat theunion should choose wi tomaximize the indirectutility function:

b (14) Ui 5 wi · Ei2 (d/b ) · Ei 1 m/N, where d (d8/nb 2 1) and (d8/b ) · (E/n)b is thedisutility ofworkand 2 1 n · (wi · Ei 1 m/N )thewealth of the individual unionmember (seethe Appendix). In Stage2 unionschoose their sectoral money wagesimultaneously such that Ui(W*i,W*2 i) $ Ui(Wi,W*2 i) for all i. Thisis equivalentto choosing wi tomaximize (14) subjectto (12) and (13). Wefocus on thesymmetric equilibrium pi 5 wi 5 1, for all i. Maximizing (14) subjectto (13) thenimplies that theequilibrium numberof hoursof employment per sector is givenby 17

1/(b 2 1) h 2 1 2 2­ ln m/­ ln wi (15) E* 5 . dh 2 d · ­ ln m/­ ln wi

Since Pi 5 Wi,sincethe aggregate price index is deŽned in the sameway asin SectionII above,and since pi 5 1in equilibrium, wecan usethe same reasoning as in that sectionto establish

­ ln m 1 N 12 a (16) 5 2 (1 2 a ) · · 5 2 ­ ln wi N N2 1 N2 1 sothat theequilibrium employment rate is givenby

h 2 1 1 2 · (1 2 a )/(N 2 1) 1/(b 2 1) (17) E* 5 dh 1 d · (1 2 a )/(N 2 1) with equilibriumhours per worker of E*/n. Thus,exactly as output

16.One referee generously wrote out a formalproof of the existence of equilibriafor all possible vectors of Wi,andpointed out that this is not the case in a standardmodel with market-determined wages. We will pass the proof on to anyoneinterested. 17.Recall that the number of workers persector, n,isŽ xed,so the equilib- riumnumber of hoursworked perworker issimply E*/n. THENONNEUTRALITY OFMONETARY POLICY 277 in theyeoman farmer model, if Nis Žniteand greaterthan unity, theequilibrium rateof employmentis higherwhen a , 1 (less than fully accommodatingmonetary policy) thanwhen a 5 1 (fully accommodatingmonetary policy); given N, thedifference increases as a falls tozero(fully nonaccommodatingpolicy); and given a , the differenceis greaterthe smaller is N. Analogousto the yeoman farmermodel, the reason is that unionshave an incentiveto take intoaccount the effect of theirown wages on aggregateprices and henceon the real money supply .Thesmaller is a and N (for N . 1), thegreater is this incentive. If N is verylarge— so that (1 2 a )/(N 2 1) approximates 0—the equilibrium employment rate is independentof the central bank’s monetaryrule. If N 5 1—when there is eithera single encompassingunion, or when a smallnumber of unions are capable ofacting as one—(17) is undeŽned, and ourmodel does notcover this situation.However, we can sketch an Olson-type argumentfor expecting an encompassingunion to act soas producefull employmentfor 0 # a , 1,(although adifferent argumentis neededin thelimiting case of afully accommodating monetarypolicy). The encompassing union controls W hence P, and thereforecan choose m (which is feasibleif a , 1). Theunion will choose m tomaximize utility function(14) subjectto the equilibriumvalues w 5 1 and E 5 m;this impliesan equilibrium employmentrate of E* 5 (2/d)1/(b 2 1).It is canbe easily checked that this is greaterthan E*forany othervalue of N. This argumentdoes not apply in thespecial caseof a 5 1,since the CB canset real money supply at any level,as longas it is lessthan or equal to (2/d)1/(b 2 1).But apart fromthis limitingcase, when N 5 1, it is reasonableto expect full employmentin thesense that no workercould be made better off by workingmore. For all intermediatecases, however ,whenthere is asmallnumber of independently acting unions,the monetary rule of the central bank mattersfor equilibrium employment. Theresults are illustrated in FigureI whichplots the equilibriumrate of employment as afunctionof N fordifferent values of a .18 Notethat as thenumber of sectors decreases, employmentrises (except in thelimiting case of a 5 1). For a Žnitenumber of sectorsgreater than one,the more nonaccommo- dating thecentral bank, the higher the equilibrium rate of employment;and this effectincreases as N decreases.When N 5

18. N istreated as a continuousvariable by assuming a continuumof sectors. 278 QUARTERLY JOURNALOF ECONOMICS

FIGURE I TheEffects of N and a onEquilibriumEmployment

1,asingleencompassing union can, and will, choosefull employ- ment.The special caseof N 5 a 5 1is notcovered by themodel. Althoughthe central bank can choosefull employmentin this case,we have not deŽ ned a CBobjectivefunction that ensuresit will. Wecan also interpret our main result in Layard-Nickell terms,in whichequilibrium employment is determinedby the intersectionof thereal wage imposed by businesspricing behavior (the‘ ‘FeasibleReal Wage’’) and theunion-determined ‘ ‘Target Real Wage’’ (seeLayard, Nickell, and Jackman{1991}; and Blanchard and Fischer{1989}). Thisis donein FigureII, where theunion-determined real wage schedule is obtainedfrom equa- tions(13) and (17). Becauseunions have an effecton aggregate prices,they can in uence the real money supply and hence employment.The less accommodating the central bank (the smaller a ),and thesmaller the number of unions (the smaller N ), thegreater the effect of each union’ s wageon the real money supply,and thegreater the incentive to exercise restraint. This shifts theunion-determined real wage schedule downward and raisesthe equilibrium level of employment. THENONNEUTRALITY OFMONETARY POLICY 279

FIGURE II Layard-NickellInterpretation of theMain Result

IV. CONCLUSIONS Themain result of this articlecan be summarized as follows: underthe assumptions of rational expectations,complete informa- tion,credible precommitment,and aŽnitenumber of price orwage setters,the accommodating or nonaccommodating nature of mone- taryrules affects theequilibrium level ofemployment. The conven- tionalresult that themonetary rule is unrelatedto the equilib- riumrate of employmentemerges as aspecial casein ourmodel, when N ` .In that caseprivate agentsare not engaged in a strategicinteraction with theCB: verysmall unionsor marketing agentscannot affect thegeneral price level. We also sketched out a complementarymodel of the case of an encompassingunion (N 5 1) and showedhow monetary policy was alsoneutral in this case—apart froma setof measurezero. Here the lack of strategic interactionre ected the ability ofthe encompassing union to determinethe price level. But whenevera limitednumber of unionsor agentsset wages or prices independently ,themonetary ruleof theCB affects theequilibrium employment (or output) rate sinceit determinesthe extent to which unions (or marketing agents) can affect thereal money supply ,and hencethe level of demand and employment. Althoughour model is deliberatelybased onastringentset of 280 QUARTERLY JOURNALOF ECONOMICS assumptions—rational expectations, complete information, cred- ibleprecommitment, and absenceof nominal rigidities— these ordinarily militate against Žnding employmenteffects of mone- tary policies.Ipso facto,we expect that if theseassumptions are relaxedour basic resultwill remain.From a policyperspective onlythe union-determined wage assumption cannot be dropped, but this is apermissiveone that enablesus to theorize about a broad rangeof economiescharacterized by relativelycentralized wage-settingsystems. Thus, we expect our model to have some- thing tosay aboutthe interaction between monetary policies and wagesetting in abroad rangeof countries including Australia, Austria, Belgium,Denmark, Finland, Ireland,Italy ,Japan, Ger- many,theNetherlands, Norway ,Sweden,Switzerland, and sev- eralnewly industrializing countries.It canalso be used to understand theeffects on theequilibrium rate of employmentrate ofchanging the size of a currencyarea, as in thecase of the EuropeanMonetary Union (see Soskice and Iversen{1998}). Consideringthe simplicity ofthe model, one obviously has to becautious in drawing strongpolicy implications. However, the results,which are at Žrstblush paradoxical, stronglysuggest that incountrieswith asmallnumber of independently acting unions, anonaccommodatingcentral bank canhave substantial beneŽts forlong-term employment. In effect,such a bank alleviatesthe coordinationproblems between unions that arelarge enough to affect thewelfare of all, yettoo numerous to reach effective collusion.This is an importantlesson for both countries where unionfragmentation has underminedpeak-level coordination (such as Sweden),and fortransition economies where strong unionshave reemerged in asettingof ‘ ‘weak’’ centralbanks. While theremay be offsetting political oreconomicbeneŽ ts fromhaving accommodatingcentral banks (especially in theshort term), for thecategory of countrieswhere our argument is mostsalient, the beneŽts wehave described are likely to outweigh the costs.

APPENDIX: THE MICROECONOMIC BASES OF THE MODELS In this appendix weshow ,Žrst,how in theyeoman farmer modelthe demand functionin sector i against whichthe ith ‘‘marketingagent’ ’ maximizes,and theindirect utility function whichthe agent maximizes, are derived from the individual maximizationbehavior of producers. Second, we show how the analogouspropositions hold in themonopoly union model. THENONNEUTRALITY OFMONETARY POLICY 281

TheY eomanFarmer Model In eachsector i there are n farmersproducing good i under constantreturns to scale. The marketing agent sets the price Pi and hencetotal supply ofgood i, Qi,and eachfarmer is then requiredto produce Qi/n. Theutility oftheindividual farmer, s,producing good i is

g 12 g b Cis Mis/P d8 Qi (A1) Uis 5 · 2 , g 1 2 g b n where Cis is aggregateconsumption by s, given by

N h /(h 2 1) 1/(12 h ) (h 2 1)/h (A2) Cis 5 N · C jis j sotheindividual farmer’sutility depends positivelyon consump- tionand realmoney balances and negativelyon output.

s chooses the N consumptionlevels Cjis and demand for nominalmoney balances Mis tomaximize (A1) subjectto the budget constraint:

N Qi (A3) PjCjis 1 Mis 5 Pi 1 Mis Iis, j n where Mis is initial cash balances.This yields

2 h Pj g Iis (A4i) C 5 · · jis P N P and

Cis Mis/P Iis (A4ii) 5 5 . g 1 2 g P Wecan nowderive the demand functionfor the jth good:

g Iis 2 h (A5) Qj 5 pj · · , N i s P where Qj is demand forthe jth good and pj is its relativeprice. Weneed to show Ž nally that thedouble sum term in (A5) is proportionalto initial realcash balances.Since Cis/g 5 Iis/P,

Iis (A6) g · 5 Cis 5 pjCjis Y, i s P i s j i s 282 QUARTERLY JOURNALOF ECONOMICS where Y isaggregatedemand. In equilibrium,aggregate demand isequalto output whichis equalto S i pi · Qi.Hence,from (A3), Y 1 M/P 5 S i S s Iis, where M 5 S i Mi · n 5 S i S s Mis so from (A6) g M 2 h (A7) Qj 5 p · · . j N · (1 2 g) P Themarketingagent for the jth goodis constrainedby (A7); this is thesame as equation(2) in themain text with M/P m and g/(1 2 g)normalizedto unity . Finally,substituting theoptimal values of Cis and Mis from (A4ii) and (A3) into(A1), multiplying (A1) by n and deŽning d 5 d8/nb 2 1 yields theindirect utility function,equation (4) in thetext, whichthe marketing agent for the ith goodmaximizes.

TheMonopoly Union Model Theargument in themonopoly union model is similarto the yeomanfarmer model, with thefollowing differences. The utility oftheindividual member, s, of union i is

g 12 g b Cis Mis/P d8 Ei (A8) Uis 5 · 2 , g 1 2 g b n sotheindividual member’sutility depends positivelyon consump- tionand realmoney balances and negativelyon number of hours worked Ei/n (Ei is thetotal number of hoursworked in sector i and n is thenumber of union members; all workersare union members,and thereis nomobility between sectors). Utility is maximizedsubject to thebudget constraint:

N Ei (A9) PjCjis 1 Mis 5 Wi 1 Mis Iis. j n Thedemand functionin the jth sectoris derivedidentically ,noting that proŽts in themonopoly union model are zero (as aresultof N Bertrand pricing and constantmarginal costs) so that Y 5 S i Wi /P · Ei. Finally,substituting theoptimal values of Cis and Mis from (A4ii) and (A9) into(A8), multiplying (A8) by n and deŽning d 5 d8/nb 2 1,yields theindirect utility functionin thetext, equation (14), whichthe ith unionmaximizes.

WISSENSCHAFTSZENTRUM BERLIN FU¨ R SOZIALFORSCHUNG , GERMANY DEPARTMENTOF GOVERNMENT, HARVARD UNIVERSITY THENONNEUTRALITY OFMONETARY POLICY 283

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