BaBargaining Theory, Trade Unions, And Industrial Strike Activityrgaining Theory, Trade Unions, And...

8/11/2019 BaBargaining Theory, Trade Unions, And Industrial Strike Activityrgaining Theory, Trade Unions, And Industrial Strike Activity

1/16

American Economic Association

Bargaining Theory, Trade Unions, and Industrial Strike ActivityAuthor(s): Orley Ashenfelter and George E. JohnsonSource: The American Economic Review, Vol. 59, No. 1 (1969), pp. 35-49Published by: American Economic AssociationStable URL: http://www.jstor.org/stable/1811091 .Accessed: 10/10/2013 04:34

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2/16

argaining T h e o r y T r a d e U n i o n s n d

ndustr ial t r i k e A c t i v i t y

By ORLEY ASHENFELTER AND GEORGE E. JOHNSON*

The purpose of this paper is to examinecertain received theories of the firm, tradeunion behavior, and bargaining n order toderive testable implications concerning heconditions under which labor disputes aremore likely to occur. There are at leastthree reasons why an investigation of in-

dustrial strike activity seems fruitful.First, it might be argued that, because oftheir relatively frequent disruption of keysectors of the economy, work stoppagesare the most important public policy issueraised by the existence of trade unions. Itwould therefore be useful to know whether,as Hicks thought, . . . the majority ofactual strikes are doubtless the result offaulty negotiation [18, p. 146] or whetherthey are an inevitable part of the function-ing of an institutionalized market econ-omy. Although it has long been knownthat the level of strike activity follows thebusiness cycle [23] [20] [29], this leavesopen the questions of the behavioral rela-tions involved and their stability overtime. Second, data on industrial disputesprovide a potentially rich source of mate-rial for testing the implications of bargain-ing theories which purport to explain theoutcome of labor-management negotia-tions.' Yet little work seems to have been

done to date on the application of bargain-ing theoretic models to nonexperimeiltaldata. A third reason for undertaking astudy of this problem stems from the con-tinuing interest in the effect of unions uponboth the relative wage structure and therate of change of aggregate money wages.

Most union power is derived from thethreat of the strike, and, accordingly, weagree with Charles Holt's recent suggestionthat . . . the theory and analysis of indus-trial disputes may belp to clarify the rolethat unions play in the determination ofwages [19, p. 50].

I. A Theoretical Formulation

Most bargaining models are addressedto a general two-party situation, e.g., bi-

lateral monopoly, in which conventionaleconomic theory fails to lead to a predict-able outcome of the terms on which agree-ments will be reached. If one views labor-management negotiations from this pointof departure it is usually difficult to deriveany testable implications concerning theconditions under which the parties will failto agree on a new contract prior to thepoint at which the previous contract ex-pires. It is generally assumed that theunion attempts to maximize some utilityor objective quantity, for example the dis-counted value of its members' wage incomeover the length of the contract.2 Likewisethe firm would attempt to maximize someobjective, say the discounted value of the

* The authors, lecturer and assistant professor ofeconomics at Princeton University and the Universityof Michigan, respectively, are indebted to J. Cross,H. Levinson, J. Pencavel, A. Rees, and D. Saks forcomments and guggestions. At the time this paper wascompleted Johnson was a visiting research associate atPrinceton participating in the Princeton Systems Analy-sis of the Labor Market Project, financed throughOMPER of the U. S. Department of Labor. Only theauthors are responsible for the views expressed in thispaper.

1 The two best-known theories of this sort are those

of J. R. Hicks [18] and F. Zeuthen [32]. A very readablesummary and critique of several more modern bargain-ing models is contained in Bishop [5].

2 For some other possibilities see Dunlop [9].

35

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3/16

36 THE AMERICAN ECONOMIC REVIEW

future profit stream. The desire of a par-ticular party to concede or hold out wouldthen depend upon: (1) a set of objectivefactors such as the state of product de-mand, the elasticities of labor demand andcapital-labor substitution, etc., as well as(2) a set of subjective factors such as theassessment of the bargaining strategy ofthe other party and attitudes toward risk-taking.3 Since the failure to agree on asettlement prior to the point of contractexpiration is costly to both parties (loss ofthe wage bill for the union and currentprofits for the firm), there should be a

tendency for the parties to adjust theirpositions in such a way that they come toan agreem nt in time to avert a strike. It isthe determination or solution of the termsof this agreement prior to a strike to whichmost bargaining theories appear to be ad-dressed.

There are two explanations expressed inthe bargaining literature regarding thereason why strikes take place at all. First,there is some possibility that one party

will misjudge the other's intentions andthat a strike will result. This view of strikeactivity, attributable to Hicks, may besummed up by the statement that

.... adequate knowledge will alwaysmake a settlement possible [18, p. 147],4although some strike activity is inevitableif trade unions are to keep managementconvinced of the effectiveness of their bar-gaining weapon. Second, there appears tobe the presumption in some of the litera-ture that a breakdown of negotiations can-not occur if the two parties are rational,so that one might argue that any break-down of negotiations is due to the fact thatthe two parties are irrational. 5

It is not apparent how the propensity ofeither or both of the parties to (a) mis-calculate the intentions of the other or (b)act irrationally would be systematicallyrelated to any of the conceptually observ-able variables in the system. Hence, theconventional bargaining theory approachis not very helpful in deriving implicationsabout the frequency or duration of strikes.6

A. An Alternative Bargainintg Model

A more fruitful-and more realistic -approach to the problem is to recognize atthe outset that there are not two but three

parties involved in labor-management ne-gotiations: the management, the unionleadership, and the union rank and file.This approach ncorporates a set of institu-tional assumptions derived from thewidely-accepted model of trade union be-havior which is based on a separate analy-sis of the motivation of the union leader-ship and rank and file. By this view7 theobjectives of the leadership are: (1) thesurvival and growth of the union as an

institution, and (2) the personal politicalsurvival of the leaders. These objectivesare accomplished, n most part, by satisfy-ing the expectations of the rank and file aswell as possible. Even if the union is notdemocratic in a political sense, the leader-ship will in most cases respond to the de-sires of the membership for reasons of con-viction. On the other hand, the leadershipis aware of the possibilities of each bar-gaining situation, and it does more thanmerely represent the wishes of the rankand file. If the membership's expectedwage increase is much greater than themanagement will agree to, the union leaders

3 Explicit discussion of both of these issues is con-tained in Harsanvi [161 and Hicks [18].

4 This is also the view expressed by Walton andMcKersie [28, p. 56]. For a model which explicitlytreats imperfect knowledge and a two-party learningprocess, see Cross [8].

6This position can be inferred from Harsanyi [171.See also Bishop's comment on Harsanyi's paper in [5].

6 Bishop states this explicitly: It should be appre-ciated that neither Zeuthen's theory nor this one[Bishop's] involves a prediction of the frequency orduration of conflicts; each is really concerned onlv withthe terms on which conflicts may be 'rationally'avoided [4, p. 4151.

7 The following view of the nature of unionism is

heavily dependent upon the position ofArthur M. Ross

[24, esp. Chs. 1-31.



4/16

ASHENFELTER AND JOHNSON: BARGAINING AND STRIKES 37

will attempt to convince the membershipto be satisfied with a smaller increase. Ifthey are unable to get the expected wageincrease down to a sufficiently low level bythe point of contract expiration, they facetwo alternatives: (1) signing an agreementwhich is less than the rank and file expectsor (2) incurring a strike. If the leadershiptakes the first alternative, it faces the pos-sibility that the contract will not be rati-fied by the membership and/or chargesthat they have sold out to management.The result will be internal union dissensionand a decline in the political appeal and

power of the leadership, both of which areantithetical to the basic objectives of theunion leadership. The second alternative,although actually contrary to the member-ship's best interests, is preferred to the

-first by the leadership. Under strike condi-tions the leadership may at least appear asadversaries against management in a cru-sade which may even raise their political

stock and will unify the workers. Theoutbreak of a strike, however, has the effect

of lowering the rank and file's expectationsdue to the shock effect of the firm's resis-tance and the resultant loss of normal in-

L come. After some passage of time theleadership feels that the minimum accept-able wage increase has fallen to a level atwhich it, can safely sign with management,and the strike ends.8

It is now possible to employ this essen-tially political model of the function of astrike to examine the firm's choice betweengiving in to the last union demand, whichis the wage increase the rank and file findsacceptable as of the date of contract ex-piration, and taking a strike in order to

obtain a lower settlement. The negotiatedwage increase9 which is acceptable to theunion rank and file is

(1) YA AW/I,where iV is the previous contract wagerate and AW is the absolute wage increase.By the reasoning of the preceding discus-sion YA depends on the length of the strike,S, say

(2) YA = V(S).

The precise shape of v is a matter of con-jecture and surely differs between collec-

tive bargaining situations, but one wouldsuppose that in the typical case it appearsas in Figure 1.10 Here yo=v(O) is the ac-ceptable wage increase at the point of con-tract expiration and y*=v(oo) is the wageincrease which the union would not acceptwith even an indefinitely long strike. Thisdecay function may be represented as

(3) YA = Y* + (YO - Y*)e-7S 11

For expository purposes et us suppose that

8 Notable practitioners in the area of collective bar-gaining have long recognized this aspect of the functionof a strike. William Simkin, Director of the FederalMediation and Conciliation Service, has stated that:

If it is a fact, as it appears to be in many situations,that the union membership is unwilling-to accept thereasonably attainable results of negotiations and is

more militant than responsible leadership, a strike maybe necessary to drive home the 'facts of life' [26].

9 Two comments are called for at this point. First,the analysis in the the text has been constructed on theassumption that bargaining takes place over theamount of a wage increase, not over the level of wages.This accords with the institutional literature with re-spect to collective bargaining, although this assumptioncould easily be changed. Second, nothing has been saidin the text about bargaining over nonwage items, e.g.,fringe benefits, and items relating to union functionssuch as company payment of shop stewards and duescheck-off schemes. It is assumed implicitly throughoutthe text that these items have monetary equivalentsand are imputed to the contracted wage.

10 This is similar, but by no means identical, toHicks's union resistance curve [28, p. 143].

11A more formal justification of the precise form ofthis equation may be obtained by assuming that understrike conditions the typical union member reduces hisacceptable wage increase by some fraction of the dif-ference between the currently acceptable wage increaseand the lowest increase acceptable under any condi-tions, that is YA= --r(yA-y*). This may be interpretedas a learning function, where the purpose of a strike isto set it in motion. Integration of this learning functiongives equation (3) in the text. It is interesting to notethat y* may have any sign so that strikes to preventwage decreases are by no means ruled out. The case

y*>O may be taken, however, as the more typicalsituation of downward wage rigidity.



5/16


0y

FIGURE 1

the typical firm is aware of the parametersof this relation and that it expects to pro-duce a fixed output with the same tech-nology to sell at the same price into theindefinite future. The profit level in eachtime period is

(4) ar= aP-/3W-H,

where P is product price, H is the level offixed production costs, and W is the ne-gotiated wage rate. The latter may be re-

written from (1) as(S) W = IV_(1 + YA)-

The present value of the future profitstream is

(6) V= f7re-r d,

which may be written, after substitution of(3) into (5) and the result into (4), as

(7) V= [aP-8Wi(1+ Y*

+ (yo - y*)e-TS) ]e-rdt - fHe-rtdt.

Upon integration (7) becomes

(8) V=[caP-lWi(1 +y*

e-rS H+ (Yo - y*)e-7S)] -

r r

which depends only on S, the length of the

strike. 2 he firm that maximizes V has thechoice of agreeing to yo and avoiding astrike or of rejecting yo and incurring a

strike which will result in a lower wage in-crease. In effect, the firm must weigh theeffect on profits of strike costs against thepossibly lower wage costs which can be ex-pected to accompany a strike. The firmmaximizes V by not agreeing to yo andincurring a strike only if (i) d V/dS= 0 and(ii) d2 V/dS2 y*, which is true by assump-tion.'3 It follows from (9) that for a strike

12 Thus far we have assumed that, even though theunion-management relationship will continue indef-initely, contract negotiations take place only once.Without this assumption contract duration becomes abargaining issue and expectations must be introducedexplicitly into the analysis. Unfortunately, this involvescomplications all out of proportion to the authors' pur-pose in this paper. For an explicit justification of theassumption in the test, however, see Bishop [4, pp.416-17].

13Needless to say, it is not necessary that firms ac-tually make calculations such as those outlined in thetext, only that they act as if such calculations had beenmade. On the other hand, there is some casual evidenceto suggest that some firms explicitly engage in a maxi-mization process similar to that noted above. The fol-lowing quotations refer to the United Auto Workers-Ford Motor Company strike and may serve as an ex-ample of this casual evidence. They are taken from theFord Motor Company Report to Stockholders, November1967. We are convinced that, in this situation, theUAW leadership concluded that no realistic settlementcould be reached and ratified without a strike....Given these difficult conditions, we believe the settle-ment we reached is a realistic one, even though it ishigher than desirable.... A longer strike would haveraised strike costs out of proportion to any resulting im-provement in the outcome. In short, we believe thesettlement represents the lowest possible combinationof strike costs and settlement costs to the Company

and the country.



6/16


to occur, S >0, it must be true that

aP - W 1 --y*

(10) Yo >

This inequality is more likely to be satis-fied, ceteris paribus, the greater are yo and rand less likely the greater are P, a/: (aver-age product per worker, which is inverselyrelated to the ratio of the wage bill to totalcost), r, and y*. By using (4) it is possibleto rewrite (10) as

A7r +H + -Wy*r

(11) Yo >

,i (1?1)J

which implies that a strike is less likely tooccur over time in a given firm or industrythe greater is the previous profit level rela-tive to the previous wage bill.

Although the above model is a very over-simplified view of the collective bargainingrelationship, it does provide predictionsconcerning the probability of a strike'soccurrence and the expected duration ofsuch a strike. Without going into greatdetail, the following remarks seem appro-priate.

1. It is possible to increase the realismof this model substantially without dras-tically altering its implications. Introduc-tion of the possibility of

employmenteffects from wage increases, the fact thatcontracts are not negotiated once but atdiscrete intervals into the future, and theinventory position of the firm would alltend to increase the realism of the process.These extensions are unnecessary at thispoint, however, because the simple formof the present model is quite adequate forthe purposes of estimation considered inthe next section.

2. The present approach has the ad-

vantage of providing a determinate solu-tion to the bargaining problem in the single(but important) case of union-manage-

ment negotiations. Such a solution is pos-sible only because widely held views aboutthe institutional behavior of the partiesinvolved is explicitly considered. In thiscase it is assumed that only one party,management, can realistically vary itswage offer. The union leadership, whichmaximizes its utility by acting in accordwith the expectations of the rank and file,must act to represent the union member-ship's wage demands. On the assumptionthat firms maximize the appropriately dis-counted present value of the future profitstream, it is seen that the basic function ofthe strike is as an equilibrating mechanismto square up the union membership's wageexpectations with what the firm may beprepared to pay. For completeness theanalysis should probably include a fourthparty, stockholders, in so far as manage-ment has a separate, self-serving motiva-tion similar to that exposited by William-son [30]. We feel, however, that for thepresent partial analysis we may safelyassume that in the typical case manage-ment actions coincide with stockholder in-terests.

3. The above model has implications forvariables other than the frequency andduration of strikes and the rate of changeof money wages. Suppose, for example,that over a period of time wage changes

remain below what the rank and file unionmembership desires, perhaps because ofmoral suasion via the Presidential wageguideposts. The analysis of this paper pre-dicts that in such a case there will be anincrease in the number of contracts whichfail membership ratification and that therewill be an increase in internal union dissen-sion. George Perry has recently argued[22] that wage changes have been smallersince 1962 than would have been expected

on the basis of the experience of the 1950s.



7/16


Interestingly enough, there has been a sub-stantial increase in contract ratificationdefeats since the point at which Perry

dates the initial overprediction. Further,this period corresponds to a widely knownrash of rank and file rebellion against unionleadership.15

B. An Operational Formulation of the Bar-gaining Model

From the analysis of a typical firm'schoice between incurring and not incurringa strike it was concluded that the partieswere less likely to agree prior to conflictthe greater the acceptable wage increase(yo) and the speed at which the member-ship's expectations are reduced during astrike (r); the parties are the more likelyto agree the greater is the ratio of the pre-agreement profit level to the wage bill (7r*),the firm's discount rate (r), and the mini-mum acceptable wage increase (y*). Onlyone of these variables, 7r*, has an obviousempirical counterpart, so further hypothe-ses must be provided to relate the othervariables to observable phenomena.

It seems plausible to argue that althoughr, r, and y* may vary between industriesand regions because of different institu-tional arrangements, they will change onlyslowly through time. For example, r shoulddepend upon the size of benefits generallypaid out of strike funds, how much unem-ployment compensation may be paid

strikers, etc.; all of which are institution-ally determined.'6

Aggregating across firms and assuming a

linear relationship in the relevant rangesof the variables, the preceding discussionsuggests the following preliminary speci-fication:

(12) St = fio + #1T + f2yOt + f37t-1,

where St is the probability of a strike inperiod t, and T indexes the passage of time.We expect f2>O, 3O, since somestrikes take place for institutional reasons,and f3,


8/16


A second determinant of yo should be amoving average of previous changes inreal wages,

M

(13) yot al + a2 E piARt-i.i=o

Intuitively we would expect a, >0, a2


9/16


--so this assumption is tested in the nextsection.

II. Empirical Results

A. Specification and Estimation Problems

If time-series observations were avail-able on the number of strikes which beginin any quarter, St, and the number of con-tract expirations in any quarter, N,, thenS', could be set equal to St/N, and (19)could be estimated directly. Althoughthere are quarterly data for St, there areonly limited surveys for N.18 In essence,the difficulty faced is that even though

equation (19) is derived from a modelwhere the dependent variable is the prob-ability of occurrence of a strike, it will benecessary to estimate it with data on onlythe frequency of occurrence of strikes.

Lacking the necessary observations onNi, we are forced to make some plausible

assumption about how it varies. 9 One pos-sible hypothesis is that N,=n, where n isa constant. Given the near-plateau inunion membership reached in 1952 [27],and the increased tendency toward mul-tiple-employer bargaining, this assumptiondoes not seem implausible with respect tothe annual number of contract expira-tions.20 In order to deal with quarterlv

data, however, we must at least recognizethat there is a strong seasonal influence incontract expirations. There are, of course,

important economic reasons why thisshould be so. First, trade unions in theareas of the economy where inclementweather affects production and employ-ment will always try to gear contract ex-pirations to periods when the effects of astrike are least likely to be nullified by thefact that production would not have takenplace anyway. Second, most trade unionswill try to avoid contract expirations inperiods when the demand for current in-

come is high (the winter holidays, for ex-ample) and to obtain contract expirationsin periods with the fewest paid holidays.Both of the above considerations suggestthat the fall and winter quarters will con-tain fewer contract expirations and, ceterisparibus, fewer strikes. As a working as-sumption, therefore, we set

4

NF = E~ciNv1,j-l1

where (JP is the (constant) number of con-tract expirations in the jth quarter of allyears and Nit is a dummy variable setequal to one in the jth quarter of the yearand zero otherwise. Substituting St/Nt forSt in (19) and multiplying both sides by

4

E cfAAjtjl1

gives

(20) St = A ? bjNjt + E FAjNjtXtB+ E 4jYpet,

where for notational convenience the fourindependent variables in (19) have beenreplaced by the row vector X, and B is the

18 The data on St, for example, cover strikes involv-ing more than six workers, while the limited data on Ntcover negotiations involving 1,000 or more workers.There is, of course, the further problem that some insti-tutional strikes do not take place at a time of contractexpiration.

19 Needless to say, if we were willing to proceed by

simply regressing the frequency of strike activity onany number of intuitively relevant independent vari-ables, none of the above assumptions would be ex-plicitly introduced. The use of such an ad hoc approach,however, would imperil any attempt to understand themechanism which underlies the determination of strikeactivity.

20 Some casual evidence for this assumption in theperiod 1963-67 is contained in Simkin [26]. The im-plication of the argument in the text is that the unionalways has its way on the seasonal aspect of disputesover contract expiration, which is not fully consistentwith the caveat in footnote 16. In fact, the seasonalpattern implicitly suggested for strike activity has been

observed over a long period of time. See, for example,

Dale Yoder [31]. Our argument is simply that the pre-cise period of the year in which a strike takes place ismost generally under the control of the union, even if the

point of contract expiration is not.



10/16


column vector of coefficients on these vari-ables.

Since the (Diare unknown, the simplest

procedure for obtaining an unbiased es-timator for (20) would be to use a separaterelationship for each quarter of the year.Unfortunately, the number of variableswhich will be needed on the right-hand sideof (20) is too large to make this solutionfeasible with the length of the time seriesavailable. Therefore, as an admittedlyrough approximation to (19) and (20), wehave specified the following equation:

(21) St = AI,INit + A4l2N2t + A4T3N3tM

+ A14N44t + B, E AiARt-.i=O

, *+ B2ut + B3,rj_ + B4T' + Et

where the Nj, are a set of seasonal dummiesand e' is an error term.2' It is not difficultto show, under the usual assumptionsabout the way in which the independentvariables in (21) are generated [14, pp.268-69], that the least squares estimatorsof BAi, B2, B3 and B' are consistent andasymptotically unbiased estimators of12kDj(Bj/ij) 12AB2, 12M51B3, nd 12fxB4.That is, our estimates of the coefficients nequation (21) may be interpreted as themean response, averaged across quarters,of a stimulus from the independent vari-able. Since each of the (D must be positive,all of the previous predictions about thesigns of the coefficients in equation (19)

hold for equation (21).Before turning to estimation and testingof equation (21). one final difficulty must

be resolved. The lag coefficients on AR_pose two estimation problems. First, wehave a priori reason to suppose that these

coefficients will not have the familiar ex-ponential-decay form. Second, we expect alag distribution on AR,j but not on theother variables in the equation.22 As an al-ternative to the standard technique, there-fore, we have used the straightforward pro-cedure suggested by Shirley Almon [1 ] forestimating equation (21). On the assump-tion that the lag distribution can be ap-proximated by a polynomial, Lagrangianinterpolation polynomials are used to cre-ate moving averages of the independentvariable. These moving averages are thenintroduced into an ordinary regressionequation and their coefficients (and hencethe implied coefficients of the lag distribu-tion) estimated. In the results that followwe have used a third degree polynomialapproximation and constrained the lag dis-tribution to assume zero values at the be-ginning and at a finite lag.23

B. The ResultsOur discussion of empirical results is

divided into three sections. First, we dis-cuss the general implications of the esti-mated version of equation (21). Second, wemodify the estimating equation to allowfor the possibility of money illusion on thepart of workers. Finally, we test the sta-bility of the preferred equation and con-sider the effect of some important institu-

tional changes on the volume of aggregatestrike activity.1. The initial results of fitting equation

(21) are reported in Tables 1 and 2 underthe rubric of equations (21a) and (21b),

1 If the disturbance term in (19) is homoscedastic,then the disturbance term in (21) is heteroscedastic be-cause its variance moves systematically with the quar-ter of the year being considered. Namely, if var (et) = C,a constant, then var (et') = var (1)= 4,j2C. If oneviews St' in (19) as a sample proportion, however, theprocedure used to obtain (21) suggests that et' will be(nearly) homoscedastic. Since this becomes an em-pirical issue, we have tested the estimated version of(21) for unequal residual variances to see if this dif-

ficulty is damaging to our results. See footnote 24 below.

22For a discussion of the estimation problems raisedby these difficulties see Griliches [15].

23 This means that two Almon variables were en-tered into the regression to estimate the lag distributionon real wage changes. It should be noted, however, thatthe results were generally insensitive to either the de-gree of the polynomial or the constraints placed on the

lag coefficients.



11/16

44 TIHETE AMERICAN ECONOMIC REVIEW

TABLE

1-ESTIMATED

REGRESSION

COEFFICIENTS

AND

RELATED

STATISTICS b

FOR

THE

VARIABLESIN

EQUATIONS

21a,

21b,

21c,

AND

21d

Equa-

Ut

MARI,

ZAW(_

ZAPI,

ri

N1

N2

Ns

T

C

LG

R2

R2

DW

SEE

tion21a)

-123.0

-62.2

-

-

1.6

213.6

594.8

457.9

-2.2

1519.8

-

.938

.820

1.44

75.9

(13.1)

(12.9)

(136.7)

(30.8)

(28.4)

(27.9)

(0.7)

(170.0)

(21b)

-123.2

-62.2

-

-

-

213.7

594.8

457.9

-2.2

1521.7

-

.938

.820

1.44

75.2

(9.4)

(12.3)

(28.7)

(27.4)

(27.5)

(0.7)

(70.4)

(21c)

-132.6

-

-80.6

64.4

-

227.3

602.4

459.4

-2.8

1663.8

-

.941

.828

1.52

75.0

(11.8)

(24.7)

(14.2)

(30.2)

(27.8)

(27.4)

(1.1)

(168.4)

(21d)

-135.3

-62.9

-

225.7

598.7

460.5

-2.3

1570.4

87.8

.946

.843

1.61

70.7,

(9.8)

(11.5)

(27.3)

(25.8)

(25.8)

(0.6)

(68.4)

(30.9)

a

R2

iS

the

coefficientof

determination

about

the

overall

mean,R2is

the

coefficientof

determination

about

the

quarterly

means,

DWis

the

Durbin-Watson

statistic,and

SEEis

the

Standard

Errorof

Estimate

for

the

regression

equation.

b

Estimated

standard

errorsof

the

estimated

regression

coefficients

arein

parentheses

under

the

relevant

coefficients.

Sources:

The

civilian

unemployment

rate,

ut,isa

quarterly

averageof

the

monthly

rates

publishedin

Table

A-6of

the

Monthly

Labor

Review,U.S.

Bureauof

Labor

Statistics.

The

Consumer

Price

Index

is

obtained

from

D-1of

the

MLR.

Our

wage

rateisan

average,

weighted

by

relative

1957

production

worker

employ-

ment,

of

average

hourly

earningsin

mining,

construction,

and

manufacturing,

andthe

data

are

obtained

from

Employment

and

Earnings

volumes,U.S.

Bureau

of

Labor

Statistics.

Noneof

these

variables

is

seasonally

adjusted.

Our

profits

variableis

the

ratioof

Corporate

Profits

after

tax,

excluding

Inventory

Valuation

Adjustment,to

Total

Compensation.

The

sourceof

these

datais

various

issuesof

the

Suirveyof

Current

Business,

Table3,U.S.

Dept.of

Commerce.

Finally,the

numberof

strikes

beginningin

each

quarter

are

obtainedin

Table

E-1of

various

issuesof

the

MLR.



12/16


TABLE 2-ESTIMATED LAG COEFFICIENTS AND THEIRSTANDARD ERRORS FOR EQUATIONS 21b AND 21c

Lag (21b) (21c)ZaRt_, z2AWt_i 2;AP'ti

0 -4.0 (1.6) - 7.0 (2.6) 4.5 (2.0)1 -6.9 (2.3) -11.4 (4.0) 7.5 (2.9)2 -8.6 (2.4) -13.4 (4.3) 9.3 (3.0)3 -9.5 (2.1) -13.5 (4.1) 10.0 (2.6)4 -9.4 (1.9) -12.2 (3.7) 9.8 (2.2)5 -8.6 (1.9) -10.0 (3.6) 8.7 (2.0)6 -7.1 (2.1) - 7.2 (3.5) 7.1 (2.1)7 -5.2 (2.1) - 4.3 (3.2) 4.9 (2.1)8 -2.7 (1.5) - 1.8 (2.2) 2.5 (1.5)

and the lag distribution coefficients forequation (21b) are charted in Figure 2.The following symbols are used in thesetables:

u,= the civilian unemployment rate,ARt= AWt-APt,

AWIt= he annual percentage rate ofchange of money wages,

P,= the annual percentage rate ofchange of consumer prices,

Irt* = the ratio of corporate profits aftertaxes to total compensation,

Njt=seasonal dummies for first, sec-ond, and third quarters,

T= time in quarters,C= constant term.

The period of fit is 1952I-1967II, which is

consistent with our assumption that theannual number of contract expirations hasbeen relatively constant since 1952.

As can be seen from Tables 1 and 2, theresults provide strong support for the hy-potheses advanced in Section I. In equa-tion (21a) the coefficients of each of the in-dependent variables, except that for prof-its, are highly significant.24 Although sev-eral different measures of profits and mov-ing averages of profits were tried, noneproduced results substantially differentfrom those reported in Table 1. Our tenta-tive conclusion s that the net effect of prof-

its on strike activity is small. In equation(21b) r*,_1 has been deleted. The indepen-dent variables in this preferred equationexplain about 94 per cent of the varianceof the dependent variable about its overallmean, and about 82 per cent of the vari-ance of the dependent variable about itsquarterly means. The standard error for

24Since there is some question about the appro-priateness of the usual statistical tests in the case wherethe disturbance variances are unequal (see footnote 21),

we have applied Bartlett's well-known test for unequalvariances to these data. See Bennett and Franklin [3]concerning the computational procedures of this test.For the number of degrees of freedom in each of thequarterly groupings, B, the test statistic, is satisfac-torily approximated by the x2 distribution with 3 de-grees of freedom. In this case, B=2.01, and we cannotreject the hypothesis of equal quarterly residual vari-ances at even the .25 level.

Coefficient

+2

+1 1 2 3 4 5 6 7 8 9? Lag

-1-2

-3

-4

-5

-6

-7

-8

-9

-10

FIGuRE 2-LAG DISTRIBUTION COEFFICIENTS ON REALWAGE CHANGES



13/16


this equation is a remarkably low 75strikes, as against a mean of about 980strikes per quarter. A glance at Figure 2suggests that the lag distribution on realwages is of the shape predicted. A steady-state decline of one percentage point in therate of change of real wages is associatedwith an increase of about 62 strikes perquarter. The seasonal dummies confirmthe hypothesis that strike activity is muchheavier in the spring and summer quartersthan in the fall and winter quarters.25Finally, a decline of one percentage pointin the civilian unemployment rate is asso-

ciated with an increase of about 123 strikesper quarter.2. The results for equation (21c) re-

ported in Tables 1 and 2 incorporate thehypothesis that the rates of change ofmoney wages and prices are not mirrorimages in their effects on aggregate strikeactivity, i.e., we allow for the possibilitythat the rate of change of money wages hasa more (or less) important effect on strikeactivity than the rate of change of prices.

It is clear from these results that the effectof money wage changes on strike activity issomewhat greater than the effect of price

changes. The differences in the effects ofthese variables, however, is not very sub-stantial. More formally, we may test thenull hypothesis that

9 9

i=O i3O

by forming the ratio

t w EPvar (,, P)?Zwhere the pu' are the estimated lag distri-bution coefficients on money wage changes

and the -P are the estimated lag distribu-tion coefficients on price changes. In thiscase t=-1.07 which clearly is not signifi-cant at conventional test levels. We mayalso test the null hypothesis /Z =-pi (i=0, *, 9) with an F-ratio. In this caseF(2, 49) = 1.09, which also is not significantat conventional test levels.26 We tenta-tively conclude that wage and pricechanges act essentially as mirror-imageswith respect to aggregate strike activity.

3. Since the volume of strike activityhas heretofore been associated with anynumber of unstable causal factors, theremay be some question about the generalstability of an equation like (21b) overtime. In order to test for the possible in-stability of this equation we have arbi-trarily divided the sample period in halfand performed the standard test of thenull hypothesis that the parameters ofequation (21b) are identical for the twotime periods. In this case F(8, 46) = 1.40,which clearly is not significant at conven-tional test levels. We conclude that thereis little evidence to suggest that this re-lationship is unstable.

25The coefficients on the seasonal dummies and theconstant term in equation (21b) allow us to estimateA24j and A4j(i= 1, , 4). Hence, they provide es-timates of

AZ(i- = (j= 1 4),

i.e., the percentage of total annual contract expirationswhich take place in each quarter. These estimates are,

from the first to fourth quarters: 23.6 per cent, 28.9per cent, 26.9 per cent, 20.4 per cent. Simkin [26] pro-vides the number of active Federal Mediation andConciliation Service cases closed each month in 1966,which, assuming a short lag from beginning to closureof a case, should be a good proxy for the typicalnumber of contract expirations per month. Assuming amean lag of one month for closures, these independentdata provide the following estimates of the percentageof total contract expirations which take place in eachquarter: 22.8 per cent, 32.3 per cent, 25.6 per cent, 19.2per cent. These latter estimates are strikingly close tothose obtained from equation (21b), and lend additionalcredence to our argument that the seasonality in strikeactivity is due to a seasonality in contract expirations.

26 The first test described in the above paragraph re-quires computation of the estimated variance of ZAT+?,2A, which can easily be worked out as a linear com-bination of the variances and covariances of the Almonvariables in the regression equation. The second test isa straightforward application of some of the results inChow [6].



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Finally, we have estimated equation(21d) to allow for the possibility that pas-sage of the Landrum-Griffin Act in 1959

has hada positive impact on the amount

of aggregate strike activity. It has beenargued that this law, which is designed toregulate the internal affairs of trade unionsin order to ensure union democracy, 27has had the effect of: (a) increasing themilitancy of union leaders as a response tothe implicit encouragement the law givesto the growth of dissident groups withinthe union, and (b) making the leadershipmore sensitive to the less responsible

wage demands of the union members.28Adding a dummy variable, LG, to theestimating equation to test for the effect ofthe Landrum-Griffin Act gives the resultsreported as equation (21d) in Table 1. Thestandard error, Durbin-Watson Statistic,and R2 are all improved by this modifica-tion. The coefficient of LG suggests a mod-est, but significant increase of about 88strikes per quarter over the pre-Landrum-Griffin period.29

III. Conclusions and Implications

Although we are not firmly wedded tothe precise estimates presented in this pa-per, it seems that the aggregate level ofstrike activity is behaviorally related tothe degree of tightness of the labor market

and previous rates of change of real wages.Among the implications of our analysis arethe following:

1. The incorporation of a widely ac-cepted set of assumptions about the be-havior of trade unions into the traditionaltheory of the firm produces a straight-forward solution to the outcome of union-management bargaining which lies withinthe corpus of conventional economic rea-soning. Although conventional bargainingmodels are based on assumptions which donot seem to represent the institutionalframework of union-management negoti-

ations, this could be excused if they pro-vided refutable predictions about observ-able behavior, but they do not. The simpleformulation of this paper, which specif-ically acknowledges the three-party natureof collective bargaining, does yield refut-able predictions, and they are found to beconsistent with the data.

2. As was shown with the case of theLandrum-Griffin Act, even a simple ver-sion of the model described in this paper

can be helpful in evaluation of the effectsof changes in the institutional frameworkwithin which collective bargaining mustfunction. Other institutional changes, e.g.,the payment of unemployment compen-sation to strikers, could be investigated.Further, the model described in this paperprovides a more explicit rationale for someof the work which has been done on ex-planations of the rate of change of aggre-gate money wages.30

3. Finally, the results have a number ofimplications for public policy with respectto wage determination in the unionizedsector of the economy. First, policies which'

27 See [12] for details on the provisions of this law.It was signed in September of 1959 and most of itsprovisions were in effect within ninety days. Hence, inthe following results we have assumed that the law

began having an effect in 1959 IV and reached its fulleffectiveness linearly by 1960 IV.28 For arguments similar to these see Estey [11, pp.

57-59). In terms of the formulation in Section I, thesearguments suggest that yo would generally be higherafter passage of the Landrum-Griffin Act than before.

29 To test for the possibility that we had confused theeffect of the Landrum-Griffin Act with the effect of theGuideposts, we added another dummy variable to theequation. The coefficient of LG remained similar withrespect to its standard error while the Guideposts co-efficient was negative and less than half its standarderror. In terms of the formulation in Section I, thisnegative effect is what would be predicted since theGuideposts supposedly lower Yo.

30 For example, the studies by 0. Eckstein and T. A.Wilson [10] and G. L. Perry [21] both include profits asdeterminants of money wage changes on the basis ofcasual bargaining model considerations, and J. D.Sargan [25] estimates a model which includes the levelof real wages. In [2] a variable specifically measuringthe volume of strike activity is found to have an effecton aggregate money wage changes.



15/16

48 ITHE AMERICAN ECONOMIC REVIEW

are geared to induce labor leaders to con-vince their constituencies to be satisfiedwith more reasonable wage settlementsare likely to result eventually in politicalturmoil within trade unions. It does not,therefore, seem likely that such a policycan continue for long without encouragingthe growth and power of more militantleadership and a subsequent decline in theeffectiveness of the original policy. Second,in addition to the well-known tradeoff be-tween wage changes and unemploymentthere seem also to be tradeoffs betweenunemployment, wage changes, and indus-

trial strike activity. To the extent that themaintenance of industrial peace is a goal ofpublic policy, this adds an additional di-mension to the problem of maintainingfull employment and stable prices.

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1. S. ALMON, The Distributed Lag Be-tween Capital Appropriations and Ex-penditures, Econometrica, Jan. 1965,

33, 178-96.2. 0. ASHENFELTER, G. E. JOHNSON, ANDJ. H. PENCAVEL, Trade Unions and theRate of Change of Money Wages in theUnited States: 1914-1960, IndustrialRelations Section, Princeton University,(mimeo), 1968.

3. C. A. BENNETT AND N. L. FRANKLIN,Statistical A nalysis in Chemistry and theChemical Industry. New York 1954.

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eds., Regulating Union Government. NewYork 1954.

13. M. GART, Labor's Rebellious Rank andFile, Fortune, Nov. 1966, 74, 150-53.

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Relation and Union Influence, Theoryand Evidence, Univ. of Wisconsin Firmand Workshop Paper 6705, Dec. 1967.

20. F. S. O'BRIEN, Industrial Conflict andBusiness Fluctuations: A Comment,Jour. Pol. Econ., Dec. 1965, 73, 650-54.

21. G. L. PERRY, The Determinants ofWVageRate Changes and the Inflation-Unemployment Tradeoff for the UnitedStates, Rev. Econ. Stud., Oct. 1964, 31,287-308.

22. , Wages and the Guideposts,Am. Econ. Rev., Sept. 1967, 57, 897-904.

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24. A. M. Ross, Trade Union Wage Policy.Berkeley and Los Angeles 1948.

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Mills,and

J.K.

Whitaker, eds., Econo-



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metric A nalysis for National EconomicPlanning, London 1964, pp. 25-54.

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tracts, Lab. Rel. Reporter, Nov. 16,1967, 66LRR 234.27. L. TROY, Trade Union Membership,

1897-1962, Rev. Econ. Stat., Feb. 1965,47, 93-113.

28. R. E. WALTON AND R. B. MCKERSIE, ABehavioral Theory of Labor Negotiations.New York 1965.

29. A. R. WEINTRAUB, Prosperity vs.Strikes: An Empirical Approach, Indus.

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tionary Behavior: Management Objectives

in a Theory of the Firm, EnglewoodCliffs, N. J. 1964.31. D. YODER, Seasonality in Strikes,

Jour. Am. Stat. Assoc., Dec. 1938, 33,687-93.

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