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Cost-of-Living Adjustment Clauses in Union
Contracts: A Summary of Results
Ronald G. Ehrenberg
Cornell University, [email protected]
Leif Danziger
Tel Aviv University
Gee San
Cornell University
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Cost-of-Living Adjustment Clauses in Union Contracts: A Summary of
Results
Abstract
Our paper provides an explanation why cost-of-living adjustment (COLA) provisions and their
characteristics vary widely across U.S. industries. We develop models of optimal risk sharing between a firm
and union to investigate the determinants of a number of contract characteristics. These include the presence
and degree of wage indexing, the magnitude of deferred noncontingent wage increases, contract duration, and
the trade-off between temporary layoffs and wage indexing. Preliminary empirical tests of some of the
implications of the model are described. One key finding is that the level of unemployment insurance benefits
appears to influence the level of layoffs and the extent of COLA coverage simultaneously.
Keywords
cost-of-living adjustment, COLA, union contracts, risk sharing, unemployment insurance
Disciplines
Human Resources Management | Labor Economics | Labor Relations | Unions
Comments
Suggested Citation
Ehrenberg, R. G., Danziger, L., & San, G. (1983). Cost-of-living adjustment clauses in union contracts: A
summary of results [Electronic version]. Journal of Labor Economics 1(3), 215-245.
Required Publisher Statement
© University of Chicago Press. Reprinted with permission. All rights reserved.
This article is available at DigitalCommons@ILR: http://digitalcommons.ilr.cornell.edu/articles/637
Cost-of-LivingAdjustmentClauses
in Union Contracts: A Summary
of Results
Ronald G. Ehrenberg,Cornell Universityand National
Bureau of EconomicResearch
Leif Danziger, Tel Aviv University
Gee San, Cornell University
Our paper providesan explanationwhy cost-of-living
adjustment
(COLA) provisionsand theircharacteristics
varywidelyacrossU.S.
industries.We develop models of optimalrisk sharingbetweena
firmand union to investigatethe determinants
of a numberof contractcharacteristics.
These includethe presenceand degreeof wage
indexing,the magnitudeof deferrednoncontingent
wage increases,
contractduration,and the trade-off
betweentemporarylayoffsand
wage indexing.Preliminaryempiricaltestsof some of the implications of the model are described.One key findingis thatthe level
of unemployment
insurancebenefitsappears to influencethe level
of layoffsand the extentof COLA coveragesimultaneously.
I. Introduction
escalatorclausesin unioncontractstie,or index,workCost-of-living
ers'wagesto some indicatorofprices,such as theConsumerPriceIndex.
The firstmajorU.S. laborcontractto containsuch a clausewas the 1948
contractbetweenGeneralMotors and the United AutomobileWorkers
Our researchhas been supportedby a grantto Ehrenbergfromthe National
ScienceFoundation.Withoutimplicatingthemforwhatremains,we are grateful
to David Card, Daniel Hamermesh,Wallace Hendricks,Dan Saks, a referee,and
theeditorsfortheircommentson earlierdrafts.
[Journal of Labor Economics, 1983, vol. 1, no. 3]
C) 1983 by The Universityof Chicago. All rightsreserved.
.50
0734-306X/83/0103-0001$01
215
216
Ehrenberg
et al.
(UAW).I Such provisionsbecameprevalentduringthe inflationthatacin themwanedas pricesstabilized
companiedtheKoreanWar, butinterest
byJanuary
duringtheearly1950s.As a result,
1955,only23% ofworkers
agreements-agreements
thatincoveredby majorcollectivebargaining
cluded 1,000or moreworkers-were also coveredby contractsthatcontainedcost-of-living
provisions.
Pricesrose duringthe late 1950s, and coverageexpandedas largenationalcontractsin steel,aluminumand can,railroads,and electricalequipmentincorporatedsuchprovisions.The relativepricestabilityoftheearly
provision
1960sled to a reductionin coverage;indeed,thecost-of-living
was droppedfromthe steelcontractin 1962. Since 1966, however,high
ratesof inflationhave been associatedwithsteadyincreasesin coverage:
duringthe 1976-81 period roughly60% of workerscovered by major
provisions.
union contractswere also coveredby cost-of-living
adjustment(COLA)
The growthin the prevalenceof cost-of-living
provisionshas rekindledboth academicand public interestin the topic,
and thisinteresthas takena numberof forms.2First,attentionhas been
process. During
directedtowardstherole of COLAs in theinflationary
the 1970s the wages of employeesin heavilyunionizedindustrieswho
relativeto thewages of other
werecoveredby COLAs grewsignificantly
employeesin the economy (see, e.g., Kosters 1977; Mitchell1980). In
addition, the growingprevalenceof multiyearcontractswith COLA
provisionshas been shown to have reduced the responsivenessof the
aggregaterate of wage inflationto the aggregateunemploymentrate;
now "buy" less reductionin wage
increasesin therateof unemployment
inflationthantheydid in the 1960s.3Because of thesefacts,COLAs are
thoughtby some to be one cause of thepersistenthighratesof inflation
we haveexperiencedin theUnitedStates-even thoughCOLAs typically
provideworkerswithmuchless than100% protectionagainstinflation.4
Second, attentionhas been directedto the role COLAs may play in
reducingthe level of strikeactivityin the economy. One reason thata
collectivebargainingnegotiationmaynot be settledbeforea strikeis that
the employer'sand the union's forecastsand perceptionsabout future
I See Douty (1975) for a more completediscussionof the historyof cost-oflivingclauses in union contractsin the United States.
2
We say rekindled,sinceacademicinterestin theeffectof indexationschemes,
such as COLAs, on the economy goes back at least as faras AlfredMarshall
(1886).
of the aggregaterate of wage inflationto un3 On the growinginsensitivity
of deferredwage increases,
employment,see Tobin (1980). On the insensitivity
see Mitchell(1978).
includingCOLAs, in union contractsto unemployment,
4For evidenceon the "yield" fromCOLAs, see Shefer(1979). We will return
to thispointbelow. Farber(1981), Kahn (1981), Vroman(1982), and Hendricks
and Kahn (1983), have presentedevidenceon the role of COLAs in the inflationaryprocess.
COLAs: A Summary
217
ratesofinflation
A COLA provision,
maydiffer
substantially.
whichties
thewage over the course of a contractto futureprices,reducestheneed
forthe employer'sand the union's price forecaststo coincide and thus
may reduce the likelihood of a strikeoccurring.-Since strikeactivity
involveslostoutput,COLAs maywell havea positiveeffecton aggregate
output.
Third, numerous economists have focused on the implicationsof
COLAs formacroeconomicstabilizationpolicy.6Among the questions
theyask are, "Can indexingschemesprotecttheaggregateeconomyfrom
real or monetaryshocks?" "How does the degreeof indexinginfluence
governmentstabilizationpolicy?" and, "What is the optimaldegreeof
indexing,fromthe perspectiveof macrostabilization
or aggregateefficiencypolicy?" Their objectiveis to show thatin a world of uncertain
futureoutcomes,whereit is impossibleto establishcontingentcontracts
thatcover everypossible stateof the world, COLAs do lead to welfare
gains.
Finally,anotherstreamof researchhas focusedon theimplicationsof
in particularthe sharingof risks
COLAs formacroeconomicefficiency,
of uncertainoutcomes by firmsand workers.These papers are in the
traditionof the "implicitcontract"literature,
and theyfocuson optimal
indexationfromtheperspectiveof a microleveldecisionmakingunit.7In
particular,theyexaminethe effectsof such variablesas the expectedrate
of inflation,uncertainty,
employeerisk aversion,the cost of indexing,
and nonlaborincomeon the optimaldegreeof indexing.
It is somewhatsurprisingthat,althoughthe lattertwo streamsof literaturehave focusedon the determination
of the optimaldegreeof indexingat the aggregateand micro levels, therehave been only a few
attemptsto see ifthesetheoriescan be used to explaineitherthevarying
prevalenceof COLAs in the aggregateU.S. economyover timeor why
theprevalenceof COLAs and theircharacteristics
varyacrossindustries
at a pointin time.8Bureau of Labor Statisticsdata indicatequite clearly
I For details of this argumentand aggregateevidence that the presence of
COLAs reducesstrikeactivity,see Kaufman(1981). See also Mauro (1982) for
a similarargumentand empiricalevidenceusing individualcontractnegotiation
data.
6 Important
hereincludeGray(1976, 1978),Barro(1977), Fisher
contributions
(1977a, 1977b), and Blanchard(1979).
7 The relevant
papers here are Shavell(1976), Azariadis (1978), and Danziger
(1980, 1983).
8 See Estenson (1981), Kahn (1981), and Hendricksand Kahn (1983); these
studiesare primarilyempiricalin nature;theydo not providerigorousanalytical
modelsthatpermitthemto identifyall of theforcesthatinfluenceCOLAs. Our
paper is more in the traditionof Card's (1981, 1982) work, althoughin some
respects(noted below) our model is more generaland his empiricalanalysesuse
Canadiancontractdata.
218
Ehrenberget al.
thattheprevalenceof COLAs in majorcollectivebargainingagreements
varieswidely across industries(see, e.g., LeRoy 1981). Moreover,one
cannotattributethesedifferences
solelyto differences
in union strength;
for example,a strongnationalunion existsin bituminouscoal mining
and stronglocal unions existin construction,
but in neitherindustryare
theremanycontractswithCOLAs.
Our paper seeks to provide an explanationwhy the prevalenceand
characteristics
of COLA provisionsvarywidelyacross U.S. industries.
We do thisin the contextof models of optimalrisksharingbetweena
firmand a unionthatallow us to investigate
thedeterminants
of a number
of characteristics
of union contracts.In additionto the degreeof wage
indexing,we focuson thedeterminants
of deferrednominalor realwage
increasesin multiperiodcontractsthatare not contingenton therealized
price level, on the determinants
of the durationof labor contracts,and
on theinterrelationship
betweencontractdurationand wage indexation.
Moreover,to integrateour researchmorefullyinto theimplicitcontract
we investigate
theinfluenceofparameters
literature,
oftheunemployment
insurance(UI) systemon theextentofindexingand theleveloftemporary
layoffs.Afterdevelopinga seriesof theoreticalmodels, we proceed to
describeour attemptsto testsome of the hypothesesthesemodels generate,usingindividualcontractdata and pooled cross-sectiontime-series
data at the two-digitmanufacturing
industrylevel.
In themain,thispaperrepresents
a summaryand extensionof research
reportedin a longerpaper (Ehrenberg,Danziger, and San 1982). Space
does not permitus to describeall of the detailsof our researchor to
provide proofs of propositionshere. Interestedreadersshould see the
longerpaper fordetailsand derivations.
II. A 1-PeriodModel with Fixed Employment
Consider firstthe followingsimple 1-periodmodel. A union and an
employermustdecide on theprovisionsof a collectivebargainingagreementbeforethe aggregatepricelevelis known. At thetimenegotiations
takeplace, the aggregateprice level,p, is equal to unity,but duringthe
periodthatthecontractwillcoverthepricelevelis uncertain;theexpected
valueofp duringtheperiodis denotedbyfpand itscoefficient
ofvariation
itsdemandcurve,
by 4p > 0. We also treatthefirm'sproductionfunction,
and the pricesof its nonlaborinputsas beinguncertain,in a mannerto
be specifiedbelow.
In principle,an optimal risk-sharing
would make both
arrangement
thewage and the employmentlevelcontingenton therealizedoutcomes
of theaggregatepricelevel,thefirm'sproductivity,
its demandcurve(as
proxiedperhapsby its outputpricelevel), and the price of its nonlabor
inputs.For now, however,we assumethatthe employmentlevelis predeterminedand equal to the numberof union members,N. Thus there
COLAs: A Summary
219
in thismodel (we will relaxthis
is no temporarylayoffunemployment
assumptionin Sec. VI below).
In addition,we assumethatwhentheemployerand theunionnegotiate
a wage schedulew, thiswage is contingenton, or indexedonly to the
aggregatepricelevel
w = w(p).
(1)
Virtuallyall contractswith COLAs in the United Statesare structured
in this mannerand only rarelyare wages explicitlytied to futureproductivity,industryprice levels, or input price levels.9Our failureto
observemorecontractsthatalso tiewages to thesevariablesundoubtedly
reflectsfactorssuch as moralhazard (firmsmay have some controlover
and enforcing
theiroutputprices)and thecostsof obtaininginformation
involvedin measuringproductivityand
such contracts(the difficulties
demandshifts,etc.).10
Suppose thatworkersare riskaverseand havecardinalutilityfunctions
of the formU[(w/p) + M], with U' > 0 and U" < 0. Utilitydepends
on the worker'sreal incomein a period,withM beingthe level of real
nonwage labor income. For now we treatM as being identicallyequal
to zero; laterwe will indicatehow theextentthatit varieswiththeprice
level effectsthe optimaldegreeof indexingof wages.
The firmuses labor (L) and a compositevariableinput(X) to produce
output(Q) via the productionfunctionrelationship:
Q = f(L, X, e1) .
(2)
Here e1 is a randomproductivityshock whose realizedvalue becomes
is uncertain
knownonlyafterthecontractis signed.That is, productivity
at the time of the negotiations.For simplicity,we assume that e1 is
price
and realizationoftheaggregate
independent
of boththedistribution
level.
Demand forthefirm'soutputis assumedto dependboth on theprice
chargedby the firmand on the amountof unanticipatedinflation,with
the latterdefinedby
fi = p/.
(3)
9There are, of course,exceptionsto thisstatement.The "ton tax" methodof
financingfringebenefitsthatprevailedfor many years in the bituminouscoal
industryis an example of a contractwhere compensationis contingentupon
as is well known, thisschemewas designedto reduceemployers'
productivity;
to substitutecapitalforlabor. Similarly,therecentUAW contractwith
incentives
Chryslerand the airlinecontractswith EasternAirlines,thattie compensation
to profits,implicitlyare contingenton all uncertainevents.
10For moreon thispoint,see the discussionbetweenBarro (1977) and Fisher
(1977a).
Ehrenberget al.
220
inflationin theaggregatepricelevelmay
The notionis thatunanticipated
lead to increasesin the demandforsome firms'productsand decreases
in thedemandforothers."I
we assumethattheinversedemandfunctioncan be written
Specifically,
q = pg(Q,
fie2)
(4)
1
whereq is thepriceof thefirm'sproduct,e2 is a randomdemandshock
whose realizationbecomesknownonlyafternegotiationsare concluded,
demand
andtheinclusionof Q allowsthefirmto facea downward-sloping
ofthedistribution
curve.The demandshockis assumedto be independent
of the aggregateprice level and, accordingly,we assume that the real
price (q/p) the firmcan chargefor its productat any specifiedoutput
levelis independentof the expectedinflationrate.
The price of the variableinputX is also assumed to depend on the
amountof anticipatedinflationand is givenby
z = ph(fi,e3) ,
(5)
wherez is thepriceof theinputand e3 is a randomcost shock. As with
the othershocks,the realizedvalue of e3 becomesknown only afterthe
negotiationsare completedand e3 is assumedto be independentof the
distributionof the aggregateprice level (althoughit need not be independentof e, and e2). The firmis assumed,in (5), to be a pricetakerin
themarketforthe otherinputforexpositionalconvenienceonly.
Because employment(L) is always equal initiallyto the numberof
union members,the firm'sprofit(IT) is givenby
T
= pg[f(N, X, e,), fi,e27If(N,X, el) -
ph(fi,e3)X
-
wN
(6)
The variableinputX is chosenaftertherealizedvaluesofall oftherandom
variablesare known and, conditionalon them,X is always chosen by
thefirmto maximizeprofits.Assumingan interiorsolutionalwaysexists,
thisrequiresthat
= 0 Vp ande,
air/dX
(7)
wheree = (el, e2,e3).
The firm'sutilityfromreal profitsis givenby V(IT/p),where V is a
cardinalutilityfunction,V' > 0, and V' < 0( = 0) ifthefirmis riskaverse
(riskneutral).Given a wage schedulew(p), the firm'sexpectedutility
11The key role of unanticipatedinflationin the indexingdecision has been
previouslynotedby Card (1981).
221
COLAs: A Summary
in
of all oftherandomvariables
obviously
dependson thedistributions
themodel.
worker'sexThe goalof theunionis to maximizetherepresentative
pectedutility,
whilethe goal of thefirmis to maximizeits expected
process
utility.
Itisbeyondthescopeofthispapertomodelthebargaining
The onlyasand showhow it maylead to an agreeduponcontract.12
that
sumption
thatwe makehereis thatthepartieswillreacha contract
fromunanticipated
sharingof all risksstemming
providesforefficient
can be obtainedby choosinga wageindexing
inflation.
Suchcontracts
schedulethatmaximizes
?
=
E[U(w/p)] + X E [V(-r/p)]
p
p,e
(8)
thatindicatesthe "shareof thepie" thatthe
whereX is a parameter
valuesofXreflect
greater
employer
receives.Otherthingsequal,higher
employer
bargaining
power.
It is usefulto definethefollowing
functions:
of the wage rate,w, withrespectto the
the elasticity
pricelevel,p;
aggregate
ofthefirm's
demandcurve,g, withrespect
theelasticity
to unanticipated
inflation,
fi;
of
other
the
fi
ab
elasticity
inputprices,h, withrespectto
b
h
unanticipated
inflation,
8p
fi;
ofdemandwithredQ g the(absolutevalue)oftheelasticity
ag Q spectto the firm'sreal price,q/p;
of totalrevenuewithrespectto thefirm's
; -1 - -1 theelasticity
output,Q;
of outputwithrespectto theotherinput,
afX theelasticity
aX f
X;
of thefirm'srealvalueaddedwithrespect
A a - b~]4theelasticity
1 - rR to theaggregate
pricelevel,p; and
dw p
dp w
g p^
afig
W
S
riskaversion.
theworkers'relative
In
andnota parameter.
In generaleachofthesevariables
is a function
whatfollowswhenwe talkabouta changein anyone ofthemwe mean
a shiftin thewholefunction.
to theaggregate
Theelasticity
ofthewageratewithrespect
pricelevel,
of theextentto whichthewagerateis indexedto the
E, is a measure
12
See Svejnar(1982) foran attemptto accomplishthisobjective.
222
Ehrenberget al.
pricelevel. It is straightforward
to show (see Ehrenberg,Danziger, and
San 1982, app. A) thatmaximizationof (8) subjectto (1)-(7) yieldsthat
theoptimaldegreeof indexingis givenby
EV'A
E = 1-
e
SEV
e
(IT
+ wN/p)
- (wN/p) EV
9
e
That is, the optimaldegreeof wage indexingdepends both on factors
exogenousto thebargainingprocess(such as theextentof employerand
employeerisk aversion)and on the outcome of the bargainingprocess
itself(such as thelevelof wages) and hencetheparties'relativebargaining
power.
Note that if the firmis risk neutral(V" = 0), indexingis complete
(E = 1). In thiscase, the real wage is independent
of the aggregateprice
level and the firmfullyinsulatesworkersagainstinflationrisks. Since
collective bargainingagreementsseldom call for complete indexing,
throughoutthe restof thepaper we assumethatthe firmis riskaverse.
It is apparentfrom(9) thatthe elasticityof thefirm'sreal value added
withrespectto theaggregate
pricelevel,A, is a keyvariablein determining
theextentof indexation.IfA is greater(less) thanzero, so thatincreases
in theaggregatepricelevelincrease(decrease)thefirm'srealvalue added,
thenthefirmsharestherewards(costs) of inflationby providingworkers
witha more than(less than)completeindexing.That is, indexingis not
necessarilyless than full; optimalrisk-sharing
agreementsmay call for
workersto be "overcompensated"forinflation.Of course, if inflation
is neutralin the sense thatthe firm'sdemandand theprice of nonlabor
inputsare unaffectedby unanticipatedinflation(a = b = 0 for all e),
thenE = 1. In thisspecialcase inflationriskaffects
thefirmonlythrough
its effecton real wages, and fullindexingeliminatesall inflationriskfor
both workersand firm.The firmis stillexposed to otherrisks(e), but
sincethesearenotrelatedto inflation
theycannotbe alleviatedbyindexing
to the aggregatepricelevel.
The firstcolumn in table 1 summarizesthe main comparativestatic
resultsthat follow fromequation (9); how changesin various factors
influencethe optimaldegreeof indexing.An increasein the elasticityof
thedemandcurvewithrespectto unanticipated
inflation(a) increasesthe
degreeof indexingsince the largerthe increasein real value added that
resultsfroman unanticipated
increasein prices,thelargerthepie available
to sharewithworkers.Conversely,thelargertheelasticityof otherinput
priceswith respectto unanticipatedinflation(b), the more disadvantainflationto thefirm,and therefore
thesmaller
geous is theunanticipated
thedegreeof wage indexingthatoccurs.
The effectof the elasticityof the firm'sdemandcurvewithrespectto
COLAs:
223
A Summary
its real price,Aq,dependsupon the relationshipof a and b. To see this,
are equal (a = b).
considerfirstthespecialcase wherethesetwo elasticities
In thiscase, unanticipatedinflationcauses identicalpercentagechanges
in the real marginalrevenueproductof nonlaborinputs(MRP) and in
the inputs'real price. Since the inputlevel,X, is always chosen so that
its realmarginalrevenueproductequals its realprice(eq. [7]), therewill
be no adjustmentin the amountof the inputused and hencein output.
In termsof figurela the firmwill move fromM to N. Consequently,
thevalue of Xqdoes not affectthe changein real value added in thiscase
and E will be independentof Aq.
inflation
implies
In contrast,ifa is greaterthanb, a higherunanticipated
in
In
to
maintain
the
in
than
z.
order
a higherpercentageincrease MRP
its
revenue
and
the
variable
product
input's marginal
equalitybetween
price, the amountof the input and hence outputmust be higher.The
magnitudeof this effectwill be largerthe higherthe elasticityof the
marginalrevenueproductcurvewith respectto the input.This is illustratedin figurelb wherewe assume thata is greaterthan b. The firm
will move fromM to 0 witha less elasticdemandcurveand fromM to
P with a more elasticone. The lattercase is associatedwith a greater
increasein realvalue added and thuswe should observea higherdegree
of indexingassociatedwithit. Since,otherthingsequal, highervalues of
theelasticityof thefirm'sdemandcurvewithrespectto its realpriceare
Table 1
Summaryof Main Results:
1-PeriodFixed EmploymentModel
Increasein Parameter
Elasticityof demandcurvewithrespectto
unanticipatedinflation(a)
Elasticityof otherinputpriceswith
respectto unanticipatedinflation(b)
Elasticityof firmdemandwith respectto
real
realprice~~~~~~~q)
~0(-q)
price
Elasticityof outputwithrespectto other
input
input
(,3)
+
+
>
+
- as a <-b
+
>
O as a-b
<
>
+
-0 as a <-b
~
<
O as A-0
Employeeriskaversion(S)
Expectedinflation(p)
Coefficient
of variationin
expectedinflation(4+p)
Costs of indexation(ci)
Pure randomvariationin demand,
and otherinputprices
productivity,
(4v)t
(E)
Probabilityof
Inde~xing
(B)
Degree
of Indexing
~~~~~
+
0
0
0
+
_
0 as A(S -R)
+
+
>
O as a-b
<
-
>
0
+
The effectwill depend on thedistribution
of thecost betweenworkersand firmas well as on many
of the model.
parameters
t See thetextforthe specificassumptionsnecessaryto obtaintheseresults.
224
Ehrenberget al.
associatedwith more elastic marginalrevenueproduct curves for the
variableinput,higherelasticitiesof the demandcurvewill lead to higher
valuesofwage indexingin thiscase. In contrast,ifa is less thanb, similar
reasoningshows thatincreasingtheelasticityof thefirm'sdemandcurve
withrespectto its own pricewill reducethe extentof indexing.
The key point here,then,is thatthe firm'selasticityof demandwith
respectto its own real price (X) does affectthe optimaldegreeof wage
indexing,butthatthedirectionoftheeffect
dependsupon therelationship
of a and b, theelasticitiesof thefirm'sdemandcurve,and itsotherinput
priceswithrespectto unanticipated
inflation.If a is greater(less) thanb,
highervalues of Xq lead to more (less) wage indexing.Since a higher
elasticityof outputwithrespectto thevariableinput(X) is also associated
with a higherelasticityof the variableinput's MRP curve, analogous
resultsfollow with respectto this variable.That is, increasesin 3 are
associatedwith increases(decreases)in the extentof indexationif a is
greater(less) thanb.
Severalotherresultsare easierto explain. First,the more riskaverse
workersare, the greateris the value to themof smoothingvariationsin
therealwage. Consequently,increasedriskaversion(S) is associatedwith
values of E closerto unity.13
Second, the optimal degree of indexingis independentof both the
of inflation(4p). These
expectedlevelof inflation(p) and theuncertainty
resultsfollow directlyfromthe assumptionthat all real variablesare
unaffected
ofp, as opposed to its realizedvalue.14
by the distribution
MRP, z
MRP, z
MRP~
~ ~ ~ ~~~~~~~~~~R
M~~x
M
X
a
~~~X
rX
b
FIGURE 1
13 Hendricksand Kahn (1983) erroneously
concludedthatincreasedemployee
riskaversionalwayswould lead to increasedwage indexing.This is trueonly if
theinitialdegreeof indexingis less thanunity.
14 In a more generalmodel in which the aggregate
price shock has some joint
with the firm'sdemandshock and the inputprice shock, the result
distribution
of variationwould failto hold. In such a model,
withrespectto the coefficient
oftheconditionalinferences
a and b would measurethederivatives
ourparameters
of demandand inputpriceswithrespectto the aggregatepricelevel. The change
COLAs: A Summary
225
Finally,the optimaldegreeof indexingdepends also on the residual
uncertainty
in realvalueadded-the uncertainty
in realvalueaddedcaused
by shocks to productivity,demand, and other input prices. Unfortunately,its effecton the optimal degreeof indexingdepends on many
in themodel and on how theychange.If one further
parameters
assumes,
however,thata, b, rq,13,A, and R (whereR = -[ V'V'][Tr/p]) is the
firm'srelativeriskaversion)are constant,it can be shown that
klaIv>
0
as
A(S
-
R) -,
(10)
where 4), the coefficient
of variationof real value added, is used as a
measure of the residual uncertaintyin real value added. If employee
relativeriskaversion(S) is greaterthanemployerrelativeriskaversion,
thisimpliesthatincreasedresidualuncertainty
makesindexinglessperfect
(furtherfrom unity).15
Beforeconcludingthissection,two extensionsof themodel warranta
briefdiscussion. First, suppose that we relax the assumptionthat the
employee'snonlaborincome,M, is alwayszero. Assumingthatthelevel
of nonlaborincomeis positive,its effecton the optimaldegreeof wage
indexingdepends on how its varieswith the price level. If the level of
nonlaborincomeis fixedin nominalterms,thento stabilizethe sum of
realwages and realnonlaborincomewill requirea greaterdegreeof wage
indexingthanin the absence of the nonlaborincome,assumingthatindexingis positive. In contrast,if the nonlabor income is fixedin real
terms(perfectlyindexed),thenany desireddegreeof real incomestabilization(not equal to perfectstabilization)can be achievedwithnow less
fromunity).
perfectwage indexing(E further
Second, suppose we now allow wages to be indexednot only to the
aggregateprice level, but also to the shocks to the firm'sproductivity,
demandcurve,and inputprices. In thiscase, one can show thatif employersare riskneutralthenwages should be tied only to the aggregate
price level (with E = 1) and not to the otherforces. If firmsare risk
averse,in theorywagesshouldbe tiedto all of theotherforces.However,
smallvalues of the elasticityof the firm'stotalrevenueswithrespectto
in theseconditionalinferencesfora givenchangein pricesdependson the "information
content"of aggregateprices. Other thingsequal, the higherthe coefficientofvariationof aggregatepriceshocks,theloweris thisinformation
content
and thusthe closerwould be the elasticityof indexingto unity.We are grateful
to therefereeforcallingthispoint to our attention.
15See Ehrenberget al. (1982, app. A). Note further
thatifA is also less than
zero, so thatindexingis less thancomplete,thisimpliesthatincreasedresidual
uncertainty
reducesthe extentof indexing.This apparentlyis a hypothesisthat
Estenson(1981) and Hendricksand Kahn (1983) soughtto test.
Ehrenberget al.
226
its output(4I); of the elasticityof its outputwithrespectto otherinputs
ofoutput,demand,andinputpriceswithrespect
(13);and oftheelasticities
to the randomshockswill reducethe extentto whichwages are tied to
the otherforces(see Ehrenberget al. 1982, sec. 2). These factors,in
additionto the ones we have describedabove, may explainwhy wages
aretypicallynot indexedto anythingotherthantheaggregatepricelevel.
III. The Decision to Index
60% of all unionized
As noted above, in recentyears approximately
workerscovered by major collectivebargainingagreementswere also
covered by COLA provisions.It would be only a coincidenceif the
optimaldegreeof wage indexationimpliedby (9) was zero for40% of
unionizedemployees.What factorsare responsiblethenforsuch a large
numberof workerswho have contractsthatare not indexedat all?
The answerhingeson thepossibilitythattheremaybe fixedrealcosts
indexingclauses thatmust
per workerof negotiatingor administrating
be borneeitherby theunionor theemployer.These costsmayarisefrom
a numberof factors.For example,if a contractis indexed,unionleaders
may not receive"credit" fromtheirmembersforthe periodicnominal
wage increasesthatautomaticallyarise due to inflation.As a result,to
maintaintheirpoliticalpositionsin the union, union leadersmay push
foradditionalperiodicnoncontingent
money
duringcontractnegotiations
to reach a contractsetwage increases;thismay make it more difficult
tlement.
To take anotherexample, in a world of heterogeneousworkersof
to alter
skilllevels,employerswould like to have theflexibility
differing
relativewages in responseto externalshortagesor surplusesof workers
in particularskill classes. Cost-of-livingprovisions,however,typically
are specifiedas a givenpercentageincreasein wages foreach percentage
increasein prices,or as a givenabsoluteincreasein wages foreach percentage-pointincreasein prices. The formerscheme rigidlypreserves
to be comrelativewage rates,while the lattercauses skill differentials
pressed. In eithercase, the employerloses the abilityto alter relative
wages duringthe period covered by the contract,and this reduceshis
willingnessto agreeto COLA provisions.
Suppose that we can representthese fixedreal costs per workerof
havingan indexedcontractby ci.Indexing,of course,yieldsrisk-sharing
benefitsto both employerand employees.The monetaryvalue of these
benefits
is thetotalamountin realtermsthatbothpartieswould be willing
to pay to have wages indexed. One can show thatthis real benefitper
workerless the real cost per workerof havingan indexed contractis
approximately
equal to
B
=lz
2
,E2(S
-
- ci,
WE
NEV'/EV')
e e
(11)
COLAs: A Summary
227
wherezD = w(f)/f, r = rr(ft)/,E is evaluatedatP, S is evaluatedat WE,
and V' and V' are evaluatedat -r (Ehrenberget al. 1982, app. B).
While in generalone cannot observethe continuousvariableB, one
can observewhethera contractcontainsa COLA, and it is reasonable
to postulatein empiricalimplementations
that
h =1
if B + v>0
= 0
otherwise.
(12)
Here B equals 1 if a contracthas a COLA, zero otherwise;and v is a
randomvariablethatsummarizesall otherunobservableforcesthatmay
influenceCOLA coverage.
From (11) and (12) it is straightforward
to see how various forces
influencetheprobabilityof a COLA's existing;theseare summarizedin
table 1. First,note thata, b, q, and 13influenceB only throughe; thus
theireffecton theprobabilityof observinga COLA is the same as their
on thedegreeofindexing,giventhatindexingoccursand is positive.
effect
Second, one can show thatthe more riskaverseworkersare the greater
thegainfromindexingto themand thusthemorelikelyone will observe
an indexedcontract.Third, while the expectedrateof inflationhas no
effecton theprobabilityof indexing,giventhatworkersare riskaverse,
themoreuncertaininflationis thegreateris thegainto themof indexing
and thusthe greateris thelikelihoodof indexing.Fourth,an increasein
thecostsof havingan indexedcontractobviouslyreducestheprobability
of havingsuch a contract.16
Finally,if one additionallyassumesthata,
b, a, 1, A, R, and S are constantsand thatthe extentof employerrisk
aversionjust equals that of employee risk aversion(R = S), then an
increasein residualuncertaintyincreasesthe probabilityof observing
indexedcontracts.
In themain,then,thesamevariablesthataffectthedegreeof indexing,
ifit occurs,also influencetheprobabilityof indexing.However, as table
1 indicates,in severalcases the effectof a variableon theformermay be
different
fromits effecton the latter,and one variable,thecoefficient
of
variationof expectedinflation,influencesonly the latter.
IV. A 2-PeriodModel,DeferredPayments,
and theRelationship
betweenContractLengthand COLA Generosity
The models discussedin the previoustwo sectionsare not structured
in a way thatenables us to addressa numberof issues. These include,
Whatdetermines
thelengthof collectivebargainingagreements?
How do
16
The effectof thesecostson thedegreeof indexing,ifit occurs,is ambiguous
and dependson the distribution
of the costs betweenthe workersand the firm,
amongotherthings.
Ehrenberget al.
228
COLA provisionsvarywithcontractduration?Whatdetermines
thesize
of deferredwage increasesthatare not contingenton the price level in
multiperiod
contracts?Is therea trade-off
betweendeferredincreasesand
COLA provisions?To answerthesequestionsone mustmove to a multiperiodmodel. We do so in thisand the followingsection.
We consider,forsimplicity,a 2-periodmodel in whichneitherfirms
nor workerscan borrow or lend. Let a subscript1 (2) denoteperiod 1
(2). Suppose first,thattheworkers'and thefirm'sutilityfunctionsboth
exhibitequal constantrelativerisk aversion(S) and can be writtenrespectivelyas
U = U(w1/p1) + pU(w2/p2),
V = V(iTl/pl)+
(13)
PV(T2/P2),
wherep(>O) is a discountfactorcommonto both workersand firms.
Suppose, also, thatthe firm'sproductionfunctioncan be writtenas a
Cobb-Douglas function
LXellX
1
Q
e
= L2X te
2
111
2
(14)
1 12'
wheret1 - 0 in period2. Values of t1greaterthanunityindicatepositive
expectedratesof productivity
growthin thisformulation.
Suppose next thatthe inversedemand functionsand the inputprice
functionsare of constant-elasticity
typeand are given,respectively,
by
q=
p
,e
q2
t21
(15)
=
and
Z=
,e3l
Z2
=
p2filbp2t3e32
e
(16)
Note thatthisspecificationallows both the demandfunctionand input
ofunanticipated
priceschedulesto changebetweenperiodsand theeffects
inflationto persistover time,so thatunanticipatedinflationin period 1
may affectthe demandcurveand otherinputpricesin period2.
herey(8) is thedegreeof serialcorrelationin theeffectof
Specifically,
unanticipatedinflationon the demand function(input prices). If y(8)
equals zero, unanticipatedinflationin period 1 has no effecton the demand curve (inputprices) in period 2. In contrast,if y(8) equals unity
thenunanticipatedinflationin period 1 has the same effecton demand
(inputprices)in period2 as does unanticipated
inflationin period2. The
expectedgrowthbetweenperiodsin real demandis given,in theabsence
of any unanticipatedinflation,by t2 and the expectedgrowthin input
termse1 =
prices is similarlygiven by t3. While the vector-of-error
COLAs: A Summary
229
(e1l,e21,e31)and e2 = (e12,e22,e32)are assumedto be independentof the
realizedvalues of Pi and p2, theyare not requiredto be independentof
each other.
Finally,suppose thatthe wage thatwill prevailin the second period
of thecontractcan be writtenas
(17)
W2 = w1y(p),
wherew1is thewage thatprevailsex post in period 1, p equal to P2/p1is
the actual relativeincreasein the price level in the second period, and
y(fi)is the multiplierthattranslatesthe wage in period 1 into the wage
in period 2. We assume thatthe realizationof P is independentof the
realizationof pi and thatits expectedvalue (the expectedinflationrate
inperiod2) isf, thesameexpectedrateas in period1. It is straightforward
to see thatthe deferredwage change,as a percentageof the wage that
prevailsin period 1, is givenby D - 1 where
D = y(i)
(18)
.
WhenD is greaterthan(less than)unitya deferredincrease(decrease)is
17
called forin the contract.
As before,thefirmwillalwayschoose thevariableinputsin eachperiod
to maximizethe profitsin thatperiod and, giventhatthis is done, all
contractsthatoptimallyshareinflationriskscan be obtainedby choosing
indexingschemesw1(p1)and y(p) to maximize
? = E U(
Pl Pi
+
) +
EPU (
P 1,
AFLE
V(IT) + P
-P
1,el
Pi
plopp
P2
)
(19)
P
ed
1(P)l
P2
It is tediousbut straightforward
to show thatgiventhe assumptionswe
havemade, the magnitudeof the deferredpaymentand theformulasfor
theoptimaldegreeof wage indexingin the 2 periodsare givenby (Ehrenberget al. 1982, sec. 4, app. C)18
D = tP
(20)
17 Note thatthedefinitions
followingeq. (18) requirethatthedeferredincrease
be specifiedas a percentageof the wage thatactuallyprevailsin period 1. This
assumptionis made foranalyticconvenience;one could also specifythe deferred
increaseas an absoluteamount.
is more complexforp
18 The formula
- in (21a).
Ehrenberget al.
230
E, =
1 + [(A + kA-)/(l + k)]
E2=
1 + A,
for
Pi
=
f
(21a)
(21b)
where
= ay - b6,4
1 - +13
A
is the now constantelasticityof the real value added in period 2 with
respectto theincreasein theaggregatepricelevelin thepreviousperiod,
t =
(tt2t3
is the expectedgrowthin real value added when unanticipatedinflation
is zero in both periods,and
k
=
pDl-SfA('-s)
p
is thecommon,forworkersand thefirm,ratioof theexpectedmarginal
utilityin period 1 froman increasein thewage in period 1 to theexpected
marginalutilityin period2 of an increasein thewage in period 1, when
the rateof inflationin period 1 equals its expectedvalue.
Equations (20) and (21a, b) immediately
a numberof points.
highlight
First,withthe additionalassumptionswe have made in thissection,the
formulafortheoptimaldegreeofindexingin the1-periodmodelbecomes
identicalto theformulafortheoptimaldegreeof indexingin thesecond
period.19Second, thedeferredincreaseD is proportionalto theexpected
growthin real value added which the firmfaces(t) when unanticipated
inflationis zero in bothperiods.While theexpectedrateof productivity
growth(t1) influencesthisvariable,so does the expectedgrowthin demand(t2)and theexpectedgrowthin otherinputprices(t3). Third,unless
theelasticityof real value added withrespectto the increasein theprice
levelin thesame period(A) is zero, theexpectedinflationrateinfluences
the size of the deferredincrease,with higherexpectedinflationrates
leadingto lower(higher)deferredincreasesifA is greater(less) thanzero.
A (a, b, a, 1) will haveopposite
Moreover,anyparameterthatinfluences
effectson the size of the deferredincreaseand on the degreeof wage
betweenCOLA
indexingin thesecondperiod.Thereis, then,a trade-off
provisionsand deferredwage increases.
What about the extentof wage indexingin the firstperiod of the
2-periodcontract?Is it largeror smallerthantheextentof indexingthat
19
That is, eq. (9) would reduceto (21b).
COLAs: A Summary
231
would prevailin a 1-periodcontract,(1 + A)? Equation (21) makesclear
thatthe degreeof indexingis largerin the firstperiod of the 2-period
contractthan it is in the 1-periodcontract(recall the latterequals the
degreeof indexingin the second period of the2-periodcontract)only if
A is less thanA:-. The latterrequiresthatay - beef3> a - buff.
can be
Is thislikelyto occur? While no generaltheoreticalstatements
made, we can considertwo special cases. First,suppose that b equals
zero, so thatunanticipatedinflationdoes not influenceinputprices. If
thedegreeof indexationin period2 is less thancomplete(E2 < 1), which
is typicallythe case, thenA and hence a will be less thanzero. In this
case, theinequalitywill be satisfiedas long as y < 1. That is, the extent
of indexingwill be greaterduringthe firstperiod of the2-periodmodel
inflationon thefirm'sdemandcurve
as long as theeffectof unanticipated
depreciatesover time(-y< 1).20
Second, suppose that b is not equal to zero but that the effectof
unanticipated
inflationon thedemandand inputpricecurvesdepreciates
at the same rate(,y= 8). In thiscase, again as long as indexationis less
thancomplete,so thatA and a - be 3 are bothless thanzero, it follows
thatif Byis less thanunitythe extentof indexationwill again be greater
duringthe firstperiod of the 2-periodcontract.
These special cases suggestthata reasonablehypothesisto testempiricallyis thatas long as the observedextentof indexingis less thanunity
in the second period of a 2-periodcontract,the extentof indexingwill
be higherin thefirstperiod.Sincetheformerequals theextentofindexing
in the 1-periodcontract,on averagetheextentof indexingwill be higher
in the2-periodcontract.Put moregenerally,one mightexpectto observe
contractsof longerdurationshavingmore generousCOLA provisions.
Since the same factorsthat influencethe generosityof a COLA also
influencethe probabilityof COLA coverage(see Sec. III), one should
expecttheincidenceof COLAs to increasewithcontractlength.In fact,
thisoccurs.21
V. The Optimum Duration of Labor Contracts
In determining
the optimaldurationof a collectivebargainingagreement,the partiesto the agreementmustconsiderthe benefitsand costs
20 If a equals 0, and E2 <
1, one similarlycan show that8 < 1 is requiredto
getthe same result.
21 For example,Douty (1981) reports
thatin 1975, 3.2% of all contractswith
a durationof 1 year, 14.8% of all contractswitha durationof 2 years,and 50%
of all contractswitha durationof 3 yearscontaineda COLA (thesefiguresrefer
to major collectivebargainingagreementsonly). Note thatit may also be reasonable to assume that the effectof within-periodunanticipatedinflationon
demandand inputpricesis closer to zero in the second period thanin the first.
If thisis thecase, it providesanotherreasonwhy thedegreeof indexingis closer
to completein long-termcontracts.
232
Ehrenberget al.
of contractsof different
lengths.22
For expositorypurposeswe shallcontinueto contrast1- and 2-periodcontractsin the contextof our simple
model.
Given the formof equation (17), whichwe believeto be a reasonable
approximationto manyactual contracts,thereis inefficient
risksharing
in the2-periodcontract.Specifically,because inflationin thefirstperiod
(Pi) can affectwages in the second period (w2) only throughits effecton
wages in the firstperiod (w1), inflationrisks are generallynot shared
efficiently
in the2-periodcontract.A sequenceof two 1-periodcontracts
withequal degreesof wage indexingwithineach periodcan be shownto
be preferableto the 2-periodcontractfroma risk-sharing
perspective.
The sequence of two 1-periodcontractshas costs as well as benefits,
however.These costs are of two types.First,thereare costs to the employer and the union of conductingcollectivebargainingnegotiations.
These are the explicitand implicitresourcecosts of the negotiations
processincluding,but not limitedto, thetimedivertedfromproduction,
contractadministration,
and planningactivities.Althoughlost output
due to strikesis an exampleof such costs, we emphasizethattheymay
be substantialeven in the absence of a strikeor threatof strike.Multiperiod contractsobviouslyreducethe frequencywithwhichthesecosts
are incurred.Second, since the two. 1-periodcontractsare negotiated
sequentially,thereis invariablysome uncertainty,
as ofperiodone, about
what the termsof the second contractwill be, and thisuncertainty
will
generatecostsforthepartiesiftheyare riskaverse.Multiperiodcontracts
reducethisformof uncertainty
also.
The choice of contractdurationobviouslyinvolvesa weightingof the
loss frominefficient
sharingof inflationrisks,if a multiperiodcontract
is chosen, againstthe loss fromadditionalbargainingcosts and the unabout thesecond-periodcontract,iftwo 1-periodcontractsare
certainty
chosen. It is again straightforward
to show thatan increaseeitherin the
cost of collectivebargainingor in the uncertainty
in the firstof two 1period contracts,caused by not knowingwhat thewage bargainwill be
in thesecond period,will increasetheprobabilityof a 2-periodcontract.
On the otherhand, since the expectedinflationrate(f) does not affect
the expectedutilityfromcontractsof eitherlength,it will not affectthe
choice of length.The serial correlationin the effectsof unanticipated
inflationon demand(-y)and otherinputprices(8) can also be shown to
influencecontractdurationin a predictablemannerthatdependson the
magnitudesof severalotherparametersin the model. Finally,while the
remainingparametersin the model all influencethe optimumduration
22 See Ehrenberg
et al. (1982), sec. 7, for a more extendeddiscussionof the
questionof contractdurationincludingthepresentationof formalmodels.
COLAs: A Summary
233
of labor contracts,withoutfurtherrestrictive
assumptionsone cannot
obtainunambiguousimplicationsabout theireffects.23
VI. TemporaryLayoffsand COLA Coverage
In the finaltheoreticalsection of our longerpaper, we returnto a
1-periodmodel withindexingof wages, but we allow employmentto be
variableacross statesof the world. This sectionstressesthattemporary
layoffsand the extentof indexingare simultaneouslydeterminedand
highlightsthe role played by severalparametersof the unemployment
insurance(UI) system.24
To capturewhatwe considerto be theessential
featuresof theUI system,nominalUI benefitsthatlaid-offunemployed
workersreceiveare specifiednot to be contingenton the realizedprice
levelduringtheperiod,and employers'nominalunemployment
insurance
tax paymentsare specifiedto be imperfectly
experiencerated.As in the
previousmodels,employersseek to maximizetheirexpectedutilityfrom
profitsand the union seeks to maximizethe expectedutilityof its representativemember.The latter,in each state of the world, is now a
weightedaverageof the worker'sutilitywhen he is employedand his
utilitywhen he is laid off,where the weightsreflectthe probabilityof
beingon layoffin the stateof the world.
In such a framework,contractsthatprovide for efficient
sharingof
inflationriskwill requirethatboth the wage rate and the employment
leveldependon theaggregatepricelevel.25Giventhemodel of our longer
to deriveemployment(L[p]) and wage (w[p])
paper,it is straightforward
schedulesand to see how theydepend on parametersof the UI system
(see Ehrenberget al. [1982] fordetails).
Our key resultsare, first,an increasein UI benefitsor a decreasein
theextentof experienceratingwill lead to increasedlayoffsin each state
23 An alternative
approach to the determination
of optimalcontractduration
is foundin Gray (1978). There,contractlengthis determinedby thefactthatthe
conditionalinferencesof the observedreal variables,givenaggregateprices,becomes less and less preciseas timegoes on. At some point, in thisframework,
thecost of renegotiation
is just equal to the expectedbenefitfrombeingable to
adjustwages back to their"full-information"
levels. Because of our specification
ofthejointdistribution
of aggregateand relativepriceshocks(see n. 14), we have
ignoredthisaspectof the contractlengthtrade-off.
24 Feldstein
on temporary
(1976) has stressedtheeffectofUI systemparameters
layoffs,but he does so in thecontextof a modelin whichbothworkersand firms
are riskneutral,so thatthe degreeof indexationis indeterminate.
See also Baily
(1977).
25 As the referee
has pointedout, it is hardto thinkof empiricalanaloguesto
the employmentfunctionour model produces thatare explicitlycontingenton
theaggregateprice level. Why we observewage escalatorsbut not employment
escalatorsin actual labor contracts,is an open question.
234
Ehrenberget al.
oftheworld.Second,ifindexingis lessthancomplete(e < 1), an increase
in experienceratingwilllead to an increasein theextentofwage indexing.
Third,if indexingis less than completeand experienceratingis "sufficientlyimperfect,"an increasein UI benefitswill decreasethe extentof
wage indexing.Althoughwe have not formallymodeledthe forcesthat
influencethe decision to have an indexedcontractin thisvariableemploymentmodel, our discussionin SectionIII suggeststhatthe effects
of theUI parameterson theprobabilityof observingan indexedcontract
are likelyto be of thesame signas theireffects
on theextentof indexing,
that
exists.
given
indexing
VII. EmpiricalAnalyses: Two-Digit ManufacturingIndustryData
This sectionand the followingone provideinitialempiricaltestsof a
fewof thehypothesesgeneratedby our models. Here, we use data at the
two-digitmanufacturing
industrylevel and focus on the determinants
bothof theindustrylayoffrateand of thepercentageof workerscovered
by major collectivebargainingagreementswho are also covered by a
COLA provision.In the next,we use individualcollectivebargaining
agreementdata and analyze the determinants
of COLA coverage,characteristicsof COLAs (when theyexist), and the durationof collective
bargainingagreements.
Our approachin thissectionis to estimateequationsof the form
13
4
BlVit +
Fit=
E4klakit
3
+ FUIi
+
E D.1dit + Ulit
(22)
and
lVjit
13
4
+
E 4k2akit
k=i
3
+ F2UI +
E Dm2dit
m=1
+
U2it
(23)
Here Fitrepresents
thefractionoftheworkerscoveredby majorcollective
bargainingagreementsin industryi in year t who are also coveredby
COLA provisions,and lit representsthe 3-year averagelayoffrate in
industryi in year t. The v's are variablesthatreflectpersonalcharacteristicsof unionizedworkersin the industryand the industrybargaining
thea's are estimatesof severaldemand-related
structure,
variables(elasticityofindustrydemandwithrespectto unanticipated
inflation[a1 = a],
serialcorrelationin the effectof unanticipatedinflationon industrydemand [a2 = y], the expectedgrowthof demand[a3 = t], and pure random variationsin demandand productivity
the
UI represents
[a4 = 4<J),
averagenet unemployment
insurancereplacementratein theindustrythe averageweeklyUI benefitsdividedby the averageweeklynet (after
COLAs: A Summary
235
tax) loss of incomeincurredby laid-offunemployedworkersin the industry,the d's are industryand year dummyvariables,the u's random
variables,and 0, X, F, andD parameters
to be estimated.A morecomplete
descriptionof the data, includingits sources,is foundin Ehrenberget
al. (1982, app. D), and a completelist of the explanatoryvariablesis
foundherein table2.
Severalcommentsshould be made about thisspecification.First,we
use datapooled across3 years.Sincemanylaborcontractsare long-term,
we do not use data foradjacentyears,whichwould make it possiblefor
thesame contractto influencetheindustry"outcome" variablesin more
thanone year. Rather,we use data for 1975, 1978, and 1981.
Second, it is difficult
to make unambiguouspredictionsabout the expected signs of many of the v variables,because they do not always
correspondneatlyin a one-to-onefashionwithvariablesfromthe theoreticalmodels. For example,a bargainingstructure
variable,such as the
numberof unionsin the industry,may serveas a proxyforthe costs of
havingan indexedcontract,thecostsofconcludinga collectivebargaining
agreement,
and theshareof thepie thattheemployerwins (A). Similarly,
whilepersonalcharacteristics
of unionizedworkersmayreflectemployee
relativeriskaversion(S), some mayalso influencethecostsof conducting
negotiations,the costs of indexedcontracts,and, indeed,employerand
employeedemandsforlong-termemployment
As such,we
relationships.
will not discussthesevariables'coefficients
below.
Third,theestimatedparametersof thedemandfunctionwereobtained
as follows.Using quarterlydata on the ConsumerPrice Index (P,) from
1970 to 1978, an expectedCPI series (E[P(t)]) was generatedusing a
fourth-order
model. For each two-digitmanufacturing
inautoregressive
dustry,equationsof the form
= h1l+ h12log[P,/E(P,)]
+ h13T+ u1l
log(S.t/P,)
(24)
and
log(Sit/Pt) h2l + h22log[Pt/E(Pt)]
+
h23log(Sit
1/Pt-)
+
(25)
h24T +
U2t
werethenestimatedusingquarterlydata from1971 to 1978, whereSit is
termthat
thevalue of shipmentsin industryi in yeart, T is a time-trend
is incrementedquarterly,and the u's are random errorterms.When
equation(24) is used, whichallows forno serialcorrelationin theeffects
of unanticipatedinflationon demand,al, a3, and a4 are estimated,respectively,by h12,h13,and &2{1 Similarly,when equation (25) is used,
236
Ehrenberget al.
whichallows forserialcorrelation,one can show thatal, a2, a3, and a4
are given,respectively,
by h22,h23,h24/(1- h23),and (Tr2.
Fourth,a key explanatoryvariableis the averageunemployment
insurancenet replacementrate (UI)-the averageweeklyUI benefitsdivided by the averageweekly net (aftertax) loss of income by laid-off
unemployedworkersin the industry.These data are obtainedfroma
modeloftheunemployment
largescale microsimulation
insurancesystem
builtby the Urban Institute,and are based on data fromthe Surveyof
Income and Education.27
Finally,dummyvariablesthatindicatetheyearof thedataand whether
theindustryis in durablemanufacturing
are also includedin themodel.
The formerare meantto controlforvariationsin expectedinflationand
in the coefficient
of variationof expectedinflationover time.The latter
is anotherproxyfornegotiationscosts,theelasticityofthefirm'sdemand
curvewithrespectto its own price,and the costs of indexedcontracts.
Estimatesof variantsof equations (24) and (25) are foundin tables2
and 3; where the dependentvariablesare, respectively,the fractionof
the workersundermajor collectivebargainingagreementswho are covered by a COLA and the 3-yearaverageof the industrylayoffrate.28
Quite strikingly,
a numberof key implicationsof the models are confirmed.
First,as suggestedin Section VI, higherUI replacementratesin an
industryare associatedwitha lowerprobabilityof observingan indexed
contractand a higherlevel of industrylayoffs.These resultssupportthe
notionthatcost of livingindexingand thelevel of temporarylayoffsare
simultaneously
determined.29
A
26
A
A
A
Suppose that
(SiIP,)
= a, JJ[(Pt-i/E(Pt)lala2ea3teuit
wherea, representsthe effectof unanticipatedinflationon demand,a2 the serial
correlationin the effectsof unanticipatedinflationand a3 theexpectedgrowthin
the
demand.Taking logs of the equation,laggingit one period and multiplying
thisfromtheunlaggedequation,the
laggedequationby a2, and thensubtracting
follows.We should cautionherethattheseparamresultin thetextimmediately
etersmay actuallyrepresentparametersof the real value-addedfunction,not
parametersof the demandcurve.However, sincetheimplicationsare essentially
the same, forexpositoryconveniencewe continuein the textto referto themas
parametersof the demandfunction.
27 See Vroman(1980) fora description
of the model and data. We are grateful
to himforgenerouslyprovidingus withthesedata.
28 Virtually
identicalresultsto thosein table2 wereobtainedwhenthefraction
of agreementscontainingCOLAs was used as a dependentvariable.
29 A referee
suggestedthe possibilitythatUI replacementratesare negatively
may simply
correlatedwith industrywage levels and hence the UI coefficient
indicatethatCOLAs are more frequentin higherwage industries.Inclusionof
the industrywage as an additionalexplanatoryvariable,however,did not alter
thesignor significance
of the UI variablesin tables2 and 3.
Table 2
Determinantsof Fraction of WorkersCovered by a COLA,
by Two-Digit Manufacturing:1975, 1978, 1981
V1
v2
v3
v4
v5
v6
v7
V8
V9
V10
(1)
(2)
(3)
(4)
- .117
- .054
- .056
- .039
(2.9)
-.008
(1.5)
.087
(1.7)
-.001
(.1)
.559
(1.5)
4.315
(2.9)
.048
(1.8)
- 6.357
(3.5)
- 1.983
(1.1)
- .933
(1.8)
-.002
(.4)
.040
(.9)
-.008
(1.1)
.769
(2.9)
5.123
(4.3)
.114
(4.5)
- 4.325
(3.1)
- 6.597
(3.1)
- .146
(1.5)
-.017
(3.3)
.268
(4.7)
-.007
(.8)
.440
(1.4)
.422
(.3)
.031
(1.3)
- 6.127
(4.2)
1.255
(.7)
.152
(1.2)
-.007
(1.4)
.141
(2.7)
-.011
(1.5)
.696
(2.6)
2.795
(2.0)
.098
(3.9)
-5.010
(3.7)
-4.914
(2.3)
.524
(1.7)
( 4)
v12
.185
(.1)
.329
v13
1.187
1.091
(1.2)
(1.2)
V11
a,
a2
a3
a4
UI
D1
(1.0)
.078
(2.6)
. ..
27.120
(1.5)
-59.172
(2.2)
. . .
. . .
.688
(.7)
.360
(1.2)
.044
(1.6)
-.995
(3.0)
1.006
(.7)
-5.914
(.2)
. . .
(.3)
-4.176
(3.2)
.759
(2.6)
-2.061
(2.0)
33.506
(2.2)
-75.091
(3.3)
1.891
(1.3)
-25.556
(1.0)
. . .
(.1)
-.012
(2.2)
.222
(3.6)
-.011
(1.2)
.220
(.7)
- .192
(.1)
.054
(2.0)
- 3.789
(1.8)
1.522
(1.0)
.653
(1.1)
-3.053
(2.1)
.390
(1.0)
- 1.481
(1.3)
(.3)
-.007
(1.6)
.133
(2.5)
-.011
(1.5)
.540
(1.8)
1.980
(1.2)
.100
(4.0)
- 3.524
(1.9)
- 3.432
(1.4)
.685
(1.5)
- 1.634
(1.1)
.442
(1.1)
-.685
(.6)
.031
(1.0)
. . .
.003
(1.0)
-.664
10.794
(.5)
-43.323
(1.4)
1.752
(1.2)
- 7.547
(.2)
- 1.754
(1.9)
- 1.226
(1.6)
(1.2)
.431
.142
(1.6)
-.009
(1.1)
.144
(1.8)
-.012
(1.3)
.263
(.6)
.290
(.1)
.089
(2.4)
- 1.255
(.5)
- 2.162
(.7)
1.072
(1.9)
- 1.365
(.7)
.193
(.4)
-.607
(.4)
.000
(.0)
-.834
(2.0)
1.111
(.6)
1.144
(.0)
- 2.637
(1.8)
.435
(2.8)
.091
(4.9)
.099
(3.0)
.112
(2.5)
-.063
.085
.138
.127
...
. . .
. . .
.093
..
.872
60
(1.1)
(1.9)
(1.4)
(1.6)
...
.870
60
. ..
.904
60
.724
(7)
.413
D3
.771
. . .
.014
.731
. . .
60
(1.7)
(6)
.008
. . .
. . .
R2
N
(1.0)
.056
(2.2)
-.606
D2
. ..
(2.3)
-1.084
.065
(2.6)
. . .
(4.8)
.066
LD
(1.2)
-2.172
(1.6)
.732
(5)
(1.6)
(2.0)
..
.869
60
(2.2)
(2.0)
...
.908
60
(1.0)
.121
(.7)
.945
40
NOTE.-See app. D of Ehrenberget al. (1982) fora descriptionof data sources. Absolutevalue of tstatisticsin parentheses.Variablesas follows:
vI = 3-yearaveragequit rate;
v2 = numberof unions in industry;
v3 = percentageof unionizedworkersin industry;
v4 = 3-yearaverageprofitrate;
v5 = percentageof workerscoveredby multiemployer
agreementsin industry;
v6 = percentageof incomedue to wage earningsof union member;
v7 = mean age of union members;
v8 = percentageof union membersmarried;
v9 = percentageof union memberswhite;
viO = percentageof union membersmale;
vII = percentageof union membersresidingin SMSAs;
v12 = mean schoolinglevel of union members;
v13 = mean numberof childrenin marriedunion members'families;
1 ifdurablegoods industry,0 otherwise;
DI
D2 = 1 if 1981, 0 otherwise;
D3 = 1 if 1978, 0 otherwise;
weeklynet (aftertax)
UI = averageUL net replacementrate = averageweeklyUL benefits/average
loss of incomeby laid-offunemployedworkersin the industry;
LD = lagged(3 years)dependentvariable;
al = estimateof elasticityof industrydemandwithrespectto unanticipatedinflation;
a2 = estimateof serialcorrelationin effectof unanticipatedinflationon industrydemand;
a3 = estimateof expectedgrowthin demand;
and otherinputprices.
a4 = estimateof pure randomvariationin demand,productivity,
238
Ehrenberget al.
Second, an increasein the elasticityof the demandcurvewithrespect
to unanticipatedinflation(al) appears to be associatedwith an increase
in the probabilityof an indexed contract,as suggestedin Section III.
the effectof an increasein the serialcorrelationof unanFurthermore,
ticipatedinflationon theprobabilityofan indexedcontractcan be shown,
fromequation (21), to be the same sign as the elasticityof the demand
curve with respectto unanticipatedinflation.If indexingis less than
will tend
complete(E < 1), whichis typical,ceterisparibus,thiselasticity
Table 3
Determinantsof the IndustryLayoffRate (3-Year Average),
by Two-Digit ManufacturingIndustry: 1975, 1978, 1981
(1)
V1
v2
v3
v4
v5
v6
v7
V8
V9
V10
V11
v12
v13
al
a2
(2)
.006
(6.3)
.000
(.6)
.004
(3.1)
-.001
(.4)
-.024
(2.8)
-.028
(.8)
-.000
(.5)
-.002
( 0)
.215
(5.2)
-.021
(1.7)
.042
(1.5)
-.025
(3.2)
.064
(2.7)
-.001
(1.9)
.
.
.
-.076
(1.8)
1.106
(1.7)
a3
a4
UI
. . .
D 1
D2
. . .
. . .
.006
(7.5)
- .000
(.9)
.005
(4.2)
.000
(.1)
-.021
(2.8)
-.025
(.7)
-.001
(1.4)
.022
(.5)
.268
(4.7)
-.038
(3.4)
.057
(2.0)
-.031
(3.6)
.083
(3.3)
-.002
(2.4)
-.029
(3.0)
-.107
(2.4)
.539
(.6)
. . .
. ..
. ..
D3
. . .
. . .
. . .
R2
N
.749
60
.788
60
LD
NOTE.-See
. ..
(3)
.004
(4.9)
.000
(1.5)
.003
(2.6)
-.000
(1.6)
-.015
(2.1)
-.030
(.9)
-.000
(.3)
-.016
(.5)
.189
(5.0)
-.014
(1.2)
.023
(.8)
-.020
(3.0)
.046
(1.9)
-.001
(2.1)
. . .
-.686
(2.0)
.967
(1.8)
. . .
.003
(.9)
-.001
(.5)
-.006
. . .
.857
60
(4)
.004
(5.7)
.000
(.9)
.002
(1.8)
-.000
(1.2)
-.007
(1.0)
.026
(.7)
-.000
(.1)
-.014
(.4)
.171
(3.1)
-.037
(3.3)
.074
(2.0)
-.026
(3.1)
.091
(3.0)
-.001
(1.8)
-.024
(2.6)
-.085
(2.2)
.566
(.8)
. . .
-.004
(1.0)
-.000
(.3)
-.006
. . .
.866
60
(5)
.003
(2.2)
.000
(.6)
.004
(3.0)
-.000
(1.2)
-.011
(1.3)
-.017
(.5)
-.001
(1. 0)
-.066
(1.4)
.184
(4.9)
-.025
(1.8)
- .000
(.0)
- .012
(1.4)
.033
(1.3)
-.000
(.6)
(6)
(7)
-.202
(.4)
.291
(.4)
.001
(.8)
.000
(1.4)
.003
(2.5)
-.000
(1.3)
.004
(.6)
.086
(2.4)
-.000
(.4)
-.122
(2-9)
.065
(1. 1)
-.049
(4.8)
.035
(1.0)
-.005
(.6)
.062
(2.3)
.001
(.9)
-.020
(2.5)
-.075
(2.2)
- .739
(1.0)
.001
(.0)
.000
(1.6)
.003
(1.9)
-.000
(1.2)
.011
(1.1)
.127
(2.4)
.000
(.4)
-.197
(3.0)
.043
(.5)
-.063
(4.0)
.031
(.7)
-.002
(.1)
.074
(2.1)
.001
(1.2)
-.018
(1.8)
-.085
(1.9)
- .805
(.7)
(1.4)
(3.7)
(2.9)
. . .
.037
.003
(9)
-.001
(.)
-.007
. . .
.860
60
.089
-.005
.124
-.008
(1.5)
(1.8)
(1-7)
(2.1)
. . .
- .284
(1.5)
.921
40
-.002
-.009
.903
60
.005
. . .
table 2 fordefinitionof variables.Absolutevalue of t-statistics
in parentheses.
COLAs: A Summary
239
to be lessthanzero and thisimpliesthatan increasein theserialcorrelation
parametershould decreasethe probabilityof observingan indexedcontract.In fact,we observethisresult.
Third,an increasein residualuncertainty
appearsto reducetheprobabilityof indexedcontracts.This resultis consistentwiththetheoretical
resultthatdegreeofindexingdeclineswithincreasedresidualuncertainty,
when the optimal degree of indexingis less than unityand employee
relativeriskaversionis greaterthanemployerrelativeriskaversion.Where
statistically
significant,
increasedresidualuncertainty
also increasesthe
industrylayoffrate,a resultconsistentwitha prioriexpectations.
Fourth, an increasein the expectedgrowthof demand reduces the
industrylayoffrateas mightbe expectedand, wheresignificant,
appears
to increasethe probabilityof indexed contracts.One can show, from
(21), thatthe effectof an increasein the expectedgrowthof demandon
wage indexingis of the same signas (A* - A)(1 - S). Since it is likely
thatA*: > A (see Sec. IV), thisresultis consistentwithemployees'relative
riskaversion's(S) beingless thanunity.30
Finally,wherestatistically
sigto the
nificant,the greaterthe percentageof familyincome attributable
wage earningsof theunionmember,thegreatertheprobabilityof COLA
coverage.In termsof thediscussionin SectionII, thissuggeststhatother
formsoffamilyincometendto be fixedin realratherthannominalterms.
Numerousassociationsbetweentheotherexplanatory
variables,COLA
to our
coverage,and thelayoffrateare also found.The readeris referred
longerpaperfora discussionof thesefindings.Whiletheresultspresented
thereand in this section cannot be describedas totallyunambiguous,
theydo generatesome supportforthe relevanceof the models thatwe
developedin earliersections.
VIII. EmpiricalAnalyses: Individual Contract Data
Cost-of-livingprovisionsvary widely across union contracts,on a
numberofdimensions.For example,theyvaryin thefrequency
ofreview.
Some contractscall forquarterlyreviewsand adjustments
ofwages,some
forsemiannualreviews,and stillothersforannualones. Some allow for
a COLA increasein theinitialyearof thecontract,whileothersdo not.
Otherthingsequal, theearlierthefirstadjustmentand themorefrequent
the reviews,the greaterthe "yield" of the COLA. That is, the more
completeindexingwill be.
Cost-of-living
adjustmentprovisionsalso varyin theirgenerosityper
review.Some specifyminimumpriceincreasesbeforeany cost-of-living
wage increaseis granted.Others specifymaximumCOLAs, or "caps."
Stillothersspecifybands of priceincreases(e.g., 5%-6%) forwhichno
30 Some studies,however,findthatrelativerisk aversionexceeds unity.See,
e.g., Friendand Blume 1975; Farber1978.
240
Ehrenberget al.
COLA wage increaseswill be granted.Clearly, such provisionsaffect
theyieldof a COLA.
Increasesare typicallyspecifiedas a 1-centincreasein wages foreach
fractional
pointincreasein theconsumerpriceindex. Among 102 major
union contractsin 1979, this fractionvaried between .3 and .6 (see
AFL-CIO 1979). Larger fractionsobviously representless generous
COLAs. The generosityof a COLA provisionalso dependson thelevel
ofearningsofthecoveredemployees.SinceCOLAs typicallyarespecified
in absoluteterms(so many centsper hour), the higherthe earningsof
employees,otherthingsequal, the less generousa COLA will be.
There are a numberof strategiesone mightfollow to ascertainthe
generosityof a COLA provision.First,one mightestimatethe ex ante
degreeof indexingby the ex post degreeof indexing-the elasticityof
thatactuallyoccurred.This is theapproach
wageswithrespectto inflation
followedby Hendricksand Kahn (1983).
Its weaknessis that,giventhe complexway COLAs are formulated,
thisnumberwill typicallydependnonlinearlyon boththeactuallevelof
inflationand thevariousCOLA provisions.Since theelasticityof wages
withrespectto inflationtypicallyvarieswiththe level of inflation,it is
unclearwhetherone should attemptto summarizethe provisionsof a
COLA by thissinglenumber.Furthermore,
sucha numberat bestwould
be an averageex post elasticity;itwould tellus nothingaboutthemarginal
to thinkof circumeffectof inflationon wages. Indeed, it is not difficult
stancesin whichcontractA shows a greaterCOLA increasethancontract
B, giventhe actual inflationratethatoccurred,but wherethe marginal
of inflationwould be largerin B thanin
COLA increaseforincrements
A because of a cap on the COLA increasein A. It is unclearin such a
case whichcontracthas the more generousCOLA provision.
A second approachis to arguethatit is difficult
to disentangleCOLA
wage increasesthat
increasesfromtheportionof deferrednoncontingent
are implicitlybased on expectationsof inflation.Indeed, ifintracontract
real-wagechangesare generallysmall,one mighttreatthemas zero and
argue that the sum of the percentagedeferredwage increasesand the
COLA increasesthatoccurredex post, dividedby the ex post inflation
rate,is a good measureof the ex anteelasticityof wages withrespectto
prices.
The theoreticalmodelswe presentedin SectionsIV and V suggestthat
such an approach may be incorrect;it is possible to model both the
determinants
of COLA increasesand of deferredincreases.Moreover,a
inherentin
simplenumericalexampleillustratestheempiricaldifficulties
such an approach. Consider two contracts.Suppose thatthe firstcalls
fora 5% deferred
increaseand no COLA increase,whilethesecondcalls
forno deferredincrease,but a 1% COLA increaseforeach 1% increase
in prices.If the ex post increasein priceswas 5%, the two would yield
COLAs: A Summary
241
equal percentageincreasesin wages and, if the ex anteincreasein prices
was also 5%, the two would also yield equal expectedwage increases.
However, theformerwould provideworkerswithno protectionagainst
unanticipatedinflation,while the latterwould providethemwith complete protection.Since we and Card (1981) have argued that a major
motivationforCOLAs is theirrisk-sharing
provisions,in particularthe
sharingof risksdue to unanticipatedinflation,it seemsstrangeto argue
thatthe two contractsofferequal COLA protection.
A thirdapproach,followedby Card (1982), is to argue thatbecause
of theinterdependence
betweendeferredand COLA increases,it makes
littlesense to focuson theoverallex post changein wages. Rather,Card
measuresthe ex ante elasticityby the marginalelasticityof the wage
escalator;thecentsper pointincreasein theCPI thattheescalatoryields
(while active) divided by the real contractualwage at the startof the
contract.The weaknessof thisapproach,of course,is thatit ignoresthe
presenceof caps, nonlinearities,
and so on. For example,two contracts
may initiallyofferthe same COLA paymentper point increasein the
CPI, but if one has a cap on the maximumsize of the COLA payment
and the otherdoes not, one would not want to argue thatboth offer
equal COLA protection.The weaknessof Card's measurethenlies in
the restriction,
"while active."
The discussionabove suggeststhatit may be inappropriate-indeed,
about the gennearlyimpossible-to summarizeall of the information
erosityof a contract'sCOLA provisionsin a singlenumber.Hence, the
on a
strategywe followedin our longerpaper was to use information
whole vector of contractprovisionsthat we obtained fromindividual
manufacturing
collectivebargainingagreements
coveringmorethan1,000
workersthatwere on filewith the Bureau of Labor Statisticsin 1981.
These provisionsincludedwhethertherewas a COLA provision,how
frequentCOLA reviewswere, whethertherewas a reviewin the first
yearof the contract,the numberof centsor percentagewage increasea
workerwould receiveunder a COLA for a givenincreasein the CPI,
thepresenceof guaranteedminimumCOLA increasesand caps (or maximumCOLA increases),and the durationof the underlyingcontract.
Each of thesevariableswas relatedto a vectorof explanatoryvariables
suggestedby our models thatwere similarto thevectorused in Section
VII, and theresultingequationswere estimatedusingindividualcontract
data and appropriateestimationmethods (the dependentvariablesincludeddichotomousand truncatedones).
Each of these variablesprovides informationon the existenceof a
Our discussionofthesetwo approachesshouldmakeitclearwhywe consider
itequallyinappropriate
to use theexpectedCOLA increase,valuedattheexpected
levelof inflationover the contract,as a measureof the generosityof a COLA;
thismeasuretellsus littleabout theresponseof wages to unanticipated
inflation.
31
242
Ehrenberget al.
COLA, its generosity,or the durationof the underlyingcontract.A
testof our models,then,is to look at thecoefficients
of a given
stringent
explanatory
variableacrossequationsand to see ifa consistentpatternof
resultsis present:thatis, Does itappearthata givenvariableis influencing
each of the outcomes in a way thatis consistentwith the underlying
theoreticalmodels?
Details of the formof theseequationsand a table of resultsappearin
Ehrenberget al. (1982). The resultscan at bestbe describedas mixedand
do not providestrongsupportforthevalidityof our theoreticalmodels.
An explanationmaylie in our methodof testing.It may be unreasonable
to expectthatone can estimatethe effectof an explanatoryvariableon
10 different
dimensionsof a COLA provisionand hope to observe a
consistentpatternof coefficients
acrossequations.Afterall, thetheoretical modelsprovidehypothesesabout theelasticityof wageswithrespect
to prices,not about timingof reviews,minimumincrease,caps, and so
forth.While we believe our criticismsof the approaches of previous
investigators
arevalid,theapproachwe describein thissectionobviously
has its own problems.
IX. Concluding Remarks
This paper has presenteda seriesof theoreticalmodels thatsoughtto
of COLA provisionsin union contracts,the
ascertainthe determinants
of theseprovisionswhentheyexist,themagnitudeof deferred
generosity
wage increasesthatare not contingenton thepricelevel,thedurationof
laborcontracts,and theleveloftemporary
layoffs.The factorshighlighted
were variedand encompassedcharacteristics
of thefirm'sdemandcurve
(includinghow it responds to unanticipatedinflation),employee and
of thebargainingrelationship(inemployerriskaversion,characteristics
cludingthe costs of concludingnegotiations),macroeconomicvariables,
and parametersof the unemployment
insurancesystem.
Two initialempiricaltestsof the hypothesesgeneratedby the models
were provided. The firsttestused data at the two-digitmanufacturing
of the
industrylevel of aggregationand focused on the determinants
fractionof workerscoveredby COLA provisionsand on the industry
layoffrate.This analysis,whichmade use of pooled cross-sectiontimeseries data, appeared to confirma numberof key implicationsof the
models. The second testused data at theindividualcollectivebargaining
of COLA coverage,the
leveland focusedon thedeterminants
agreement
of COLA agreementswhen theyexist,and the duration
characteristics
theresultshereweremuchmoremixed
oflaborcontracts.Unfortunately,
and did not providestrongsupportforthe models.
In spiteof themixednatureof theseresults,we believeour paper has
of theseunion
demonstrated
theusefulnessof analyzingthedeterminants
COLAs: A Summary
243
contractprovisionsin the contextof risk-sharing
models. Numerous
extensionssuggestthemselves.At theempiricallevel,itis clearthatbetter
measuresof the ex antedegreeof indexingmustbe devised.Neitherthe
singleparametermeasuresused by Card (1981) and Hendricksand Kahn
(1983), based on ex antemarginalelasticitiesover an initialrangeand ex
post wage increases,respectively,
nor the multipleparametermeasures
used by us seem to be appropriate.At theveryleast,whatis requiredis
a two-parameter
measurethatcontainsinformation
on boththeexpected
COLA wage increaseand the marginalchangein thewage increasethat
would resultfromunanticipatedinflation.
We have also only begunto testthe implicationsof the models. One
productiveline of testingwould focuson the trade-off
betweenCOLA
increasesand deferrednoncontingent
wage increases.Much more work
also needs to be done on the determinants
of contractdurationand on
theeffects
ofUI parameters
ratesand experiencerating)
(bothreplacement
on the COLA-layoff trade-off.
At the theoreticallevel, an importantunresolvedissue is why COLA
provisionstypicallytake the formof "X centsper one pointincreasein
theCPI" ratherthan"X% increasein wages foreach percentageincrease
in theCPI." As is well known,thefirstformwill fendto compresswage
withina firm,while the second will keep them constant.
differentials
Whatis neededhereare modelsof union decision-making
processesthat
highlighthow heterogeneityof union membersand different
voting
schemeswill lead to different
typesof contractprovisions.Ultimately,
such theoreticalmodelingshould lead to empiricalresearchon the determinants
of the typeof COLA provisionadopted.
Similarly,theminimumpriceincreasesthatare requiredbeforeCOLA
coveragestartsin some contractsand the caps or maximumincreasesin
otherssuggestthatrisk-sharing
agreements
oftenexistonly overa subset
of possible statesof the world. It may be usefulto tryto model the
and thento testthe usefulness
conditionsthatlead to such restrictions
of such models empirically.
References
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Baily, Martin B. "On the Theory of Layoffsand Unemployment."
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Barro,RobertJ. "Long-TermContracting,StickyPricesand Monetary
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Blanchard,Olivier. "Wage IndexingRules and theBehaviorof theEconomy."Journalof PoliticalEconomy87 (August 1979): 798-815.
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