American Economic Association Bargaining Theory, Trade Unions, and Industrial Strike Activity Author(s): Orley Ashenfelter and George E. Johnson Source: The American Economic Review, Vol. 59, No. 1 (1969), pp. 35-49 Published by: American Economic Association Stable URL: http://www.jstor.org/stable/1811091 . Accessed: 10/10/2013 04:34 Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at . http://www.jstor.org/page/info/about/policies/terms.jsp . JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org. . American Economic Association is collaborating with JSTOR to digitize, preserve and extend access to The American Economic Review. http://www.jstor.org This content downloaded from 149.132.120.104 on Thu, 10 Oct 2013 04:34:55 AM All use subject to JSTOR Terms and Conditions Bargaining Theory, Trade Unions, and Industrial Strike Activity By ORLEY ASHENFELTER AND GEORGE E. JOHNSON* The purposeof this paper is to examine certainreceivedtheories of the firm,trade union behavior,and bargainingin orderto derivetestable implicationsconcerningthe conditionsunderwhich labor disputes are more likely to occur. There are at least three reasons why an investigation of industrial strike activity seems fruitful. First, it might be argued that, because of their relatively frequent disruptionof key sectors of the economy, work stoppages are the most importantpublic policy issue raisedby the existence of trade unions. It wouldthereforebe usefulto knowwhether, as Hicks thought, " . . . the majority of actual strikes are doubtless the result of faulty negotiation" [18,p. 146] orwhether they arean inevitablepart of the functioning of an institutionalized market economy. Although it has long been known that the level of strike activity follows the business cycle [23] [20] [29], this leaves open the questions of the behavioralrelations involved and their stability over time. Second, data on industrial disputes provide a potentially rich source of materialfor testing the implicationsof bargaining theories which purport to explain the outcome of labor-management negotiations.' Yet little work seems to have been done to date on the application of bargaining theoretic models to nonexperimeiltal data. A third reason for undertaking a study of this problem stems from the continuing interest in the effect of unions upon both the relative wage structure and the rate of change of aggregate money wages. Most union "power" is derived from the threat of the strike, and, accordingly, we agree with Charles Holt's recent suggestion that ". . . the theory and analysis of industrial disputes may belp to clarify the role that unions play in the determination of wages" [19, p. 50]. I. A Theoretical Formulation Most bargaining models are addressed to a general two-party situation, e.g., bilateral monopoly, in which conventional economic theory fails to lead to a predictable outcome of the terms on which agreements will be reached. If one views labormanagement negotiations from this point of departure it is usually difficult to derive any testable implications concerning the conditions under which the parties will fail to agree on a new contract prior to the point at which the previous contract expires. It is generally assumed that the union attempts to maximize some utility or objective quantity, for example the discounted value of its members' wage income over the length of the contract.2 Likewise the firm would attempt to maximize some objective, say the discounted value of the * The authors, lecturer and assistant professor of economics at Princeton University and the University of Michigan, respectively, are indebted to J. Cross, H. Levinson, J. Pencavel, A. Rees, and D. Saks for comments and guggestions. At the time this paper was completed Johnson was a visiting research associate at Princeton participating in the Princeton Systems Analysis of the Labor Market Project, financed through OMPER of the U. S. Department of Labor. Only the authors are responsible for the views expressed in this paper. 1 The two best-known theories of this sort are those of J. R. Hicks [18]and F. Zeuthen [32]. A very readable summary and critique of several more modern bargaining models is contained in Bishop [5]. 2 For some other possibilities see Dunlop [9]. 35 This content downloaded from 149.132.120.104 on Thu, 10 Oct 2013 04:34:55 AM All use subject to JSTOR Terms and Conditions 36 THE AMERICAN ECONOMIC REVIEW future profit stream. The desire of a particularparty to concedeor hold out would then depend upon: (1) a set of objective factors such as the state of product demand, the elasticities of labordemandand capital-laborsubstitution, etc., as well as (2) a set of subjective factors such as the assessment of the bargaining strategy of the other party and attitudes toward risktaking.3 Since the failure to agree on a settlement prior to the point of contract expirationis costly to both parties (loss of the wage bill for the union and current profits for the firm), there should be a tendency for the parties to adjust their positions in such a way that they come to an agreem nt in time to avert a strike.It is the determinationor solution of the terms of this agreementpriorto a striketo which most bargainingtheories appear to be ad- dressed. There are two explanationsexpressedin the bargaining literature regarding the reasonwhy strikes take place at all. First, there is some possibility that one party will misjudge the other's intentions and that a strikewill result.This view of strike activity, attributable to Hicks, may be summed up by the statement that ".... adequate knowledge will always make a settlement possible" [18, p. 147],4 although some strike activity is inevitable if trade unions are to keep management convincedof the effectivenessof their bargaining weapon. Second, there appears to be the presumptionin some of the literature that a breakdownof negotiationscannot occurif the two partiesare "rational," so that one might argue that any breakdownof negotiationsis due to the fact that the two parties are "irrational."5 It is not apparenthow the propensity of either or both of the parties to (a) miscalculate the intentions of the other or (b) act irrationally would be systematically related to any of the conceptually observable variables in the system. Hence, the conventional bargaining theory approach is not very helpfulin derivingimplications about the frequencyordurationof strikes.6 A. An Alternative Bargainintg Model A morefruitful-and more "realistic"approachto the problemis to recognizeat the outset that there arenot two but three parties involved in labor-managementnegotiations: the management, the union leadership, and the union rank and file. This approachincorporatesa set of institutional assumptions derived from the widely-accepted model of trade union behaviorwhich is based on a separateanalysis of the motivation of the union leadership and rank and file. By this view7 the objectives of the leadership are: (1) the survival and growth of the union as an institution, and (2) the personal political survival of the leaders. These objectives are accomplished,in most part, by satisfying the expectations of the rankand file as well as possible. Even if the union is not democraticin a political sense, the leadership will in most cases respond to the desiresof the membershipfor reasonsof conviction. On the other hand, the leadership is aware of the possibilities of each bargaining situation, and it does more than merely represent the wishes of the rank and file. If the membership's expected wage increase is much greater than the managementwillagreeto, the unionleaders 3 Explicit discussion of both of these issues is contained in Harsanvi [161and Hicks [18]. 4 This is also the view expressed by Walton and McKersie [28, p. 56]. For a model which explicitly treats imperfect knowledge and a two-party learning process, see Cross [8]. 6 This 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 appreciated that neither Zeuthen's theory nor this one [Bishop's] involves a prediction of the frequency or duration of conflicts; each is really concerned onlv with the 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 of Arthur M. Ross [24, esp. Chs. 1-31. This content downloaded from 149.132.120.104 on Thu, 10 Oct 2013 04:34:55 AM All use subject to JSTOR Terms and Conditions ASHENFELTER AND JOHNSON: BARGAINING AND STRIKES 37 will attempt to convince the membership to be satisfied with a smaller increase. If they are unable to get the expected wage increasedownto a sufficientlylow level by the point of contract expiration,they face two alternatives: (1) signingan agreement whichis less than the rankand file expects or (2) incurringa strike. If the leadership takes the first alternative, it faces the possibility that the contract will not be ratified by the membership and/or charges that they have "sold out" to management. The resultwill be internalunion dissension and a decline in the political appeal and powerof the leadership,both of which are antithetical to the basic objectives of the union leadership.The second alternative, althoughactually contraryto the membership's best interests, is preferred to the -firstby the leadership.Understrike conditions the leadershipmay at least appearas adversariesagainst management in a crusade which may even raise their political "stock" and will unify the workers. The outbreakofa strike,however,hasthe effect of loweringthe rankand file'sexpectations due to the shock effect of the firm'sresistance and the resultant loss of normal inL come. After some passage of time the leadershipfeels that the minimum acceptable wage increasehas fallen to a level at whichit,can safely sign with management, and the strike ends.8 It is now possible to employ this essentially political model of the function of a striketo examinethe firm'schoicebetween giving in to the last union demand, which is the wage increasethe rankand file finds acceptable as of the date of contract expiration, and "taking a strike" in orderto obtain a lower settlement. The negotiated wage increase9which is acceptable to the union rank and file is (1) YA AW/I, where iV is the previous contract wage rate andAWis the absolutewage increase. By the reasoningof the preceding discussion YAdependson the length of the strike, S, say (2) YA= V(S). The precise shape of v is a matter of conjecture and surely differs between collective bargainingsituations, but one would suppose that in the typical case it appears as in Figure 1.10 Here yo=v(O) is the acceptablewage increaseat the point of contract expiration and y*=v(oo) is the wage increasewhich the union would not accept with even an indefinitely long strike. This decay function may be representedas (3) YA = Y* + (YO- Y*)e-7S 11 Forexpositorypurposeslet us supposethat 8 Notable practitioners in the area of collective bargaining have long recognized this aspect of the function of a strike. William Simkin, Director of the Federal Mediation 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 the reasonably attainable results of negotiations and is more militant than responsible leadership, a strike may be necessary to drive home the 'facts of life' " [26]. 9Two comments are called for at this point. First, the analysis in the the text has been constructed on the assumption that bargaining takes place over the amount of a wage increase, not over the level of wages. This accords with the institutional literature with respect to collective bargaining, although this assumption could easily be changed. Second, nothing has been said in the text about bargaining over nonwage items, e.g., fringe benefits, and items relating to union functions such as company payment of shop stewards and dues check-off schemes. It is assumed implicitly throughout the text that these items have monetary equivalents and are imputed to the contracted wage. 10This is similar, but by no means identical, to Hicks's "union resistance curve" [28, p. 143]. 11A more formal justification of the precise form of this equation may be obtained by assuming that under strike conditions the typical union member reduces his acceptable wage increase by some fraction of the difference between the currently acceptable wage increase and the lowest increase acceptable under any conditions, that is YA= --r(yA-y*). This may be interpreted as a learning function, where the purpose of a strike is to set it in motion. Integration of this learning function gives equation (3) in the text. It is interesting to note that y* may have any sign so that strikes to prevent wage decreases are by no means ruled out. The case y*>O may be taken, however, as the more typical situation of downward wage rigidity. This content downloaded from 149.132.120.104 on Thu, 10 Oct 2013 04:34:55 AM All use subject to JSTOR Terms and Conditions 38 THE AMERICAN ECONOMIC REVIEW 0y FIGURE 1 the typical firm is aware of the parameters of this relation and that it expects to produce a fixed output with the same technology to sell at the same price into the indefinite future. The profit level in each time period is (4) ar= aP-/3W-H, where P is product price, H is the level of fixed production costs, and W is the negotiated wage rate. The latter may be rewritten from (1) as (S) W = IV_(1 + YA)The present value of the future profit stream 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."2The firmthat maximizesV has the choice of agreeing to yo and avoiding a strike or of rejecting yo and incurring a strike which will result in a lowerwage increase. In effect, the firm must weigh the effect on profits of strike costs against the possibly lowerwage costs which can be expected to accompany a strike. The firm maximizes V by not agreeing to yo and incurringa strike only if (i) dV/dS= 0 and (ii) d2V/dS2<0 for some positive S; otherwise S=O and YA=Yo. Differentiating (8) and solving for S one obtains 1 (9) S= - -X r a P-fW(1 + -*) and the second ordercondition is satisfied when yo>y*, which is true by assumption.'3It follows from (9) that for a strike 12 Thus far we have assumed that, even though the union-management relationship will continue indefinitely, contract negotiations take place only once. Without this assumption contract duration becomes a bargaining issue and expectations must be introduced explicitly into the analysis. Unfortunately, this involves complications all out of proportion to the authors' purpose in this paper. For an explicit justification of the assumption in the test, however, see Bishop [4, pp. 416-17]. 13Needless to say, it is not necessary that firms actually make calculations such as those outlined in the text, only that they act as if such calculations had been made. On the other hand, there is some casual evidence to suggest that some firms explicitly engage in a maximization process similar to that noted above. The following quotations refer to the United Auto WorkersFord Motor Company strike and may serve as an example of this casual evidence. They are taken from the Ford Motor CompanyReport to Stockholders,November 1967. "We are convinced that, in this situation, the UAW leadership concluded that no realistic settlement could be reached and ratified without a strike.... Given these difficult conditions, we believe the settlement we reached is a realistic one, even though it is higher than desirable.... A longer strike would have raised strike costs out of proportion to any resulting improvement in the outcome. In short, we believe the settlement represents the lowest possible combination of strike costs and settlement costs to the Company and the country." This content downloaded from 149.132.120.104 on Thu, 10 Oct 2013 04:34:55 AM All use subject to JSTOR Terms and Conditions ASHENFELTER AND JOHNSON: BARGAINING AND STRIKES 39 to occur, S >0, it must be true that aP - W 1 --y* (10) Yo > This inequality is more likely to be satisfied, ceterisparibus, the greater are yo and r and less likely the greater are P, a/: (average product per worker, which is inversely related to the ratio of the wage bill to total cost), r, and y*. By using (4) it is possible to rewrite (10) as A 7r+H + -Wy* r (11) Yo >> ,i (1?1)J which implies that a strike is less likely to occur over time in a given firm or industry the greater is the previous profit level relative to the previous wage bill. Although the above model is a very oversimplified view of the collective bargaining relationship, it does provide predictions concerning the probability of a strike's occurrence and the expected duration of such a strike. Without going into great detail, the following remarks seem appro- priate. 1. It is possible to increase the realism of this model substantially without drastically altering its implications. Introduction of the possibility of employment effects from wage increases, the fact that contracts are not negotiated once but at discrete intervals into the future, and the inventory position of the firm would all tend to increase the realism of the process. These extensions are unnecessary at this point, however, because the simple form of the present model is quite adequate for the purposes of estimation considered in the next section. 2. The present approach has the advantage of providing a determinate solution to the bargaining problem in the single (but important) case of union-management negotiations. Such a solution is possible only because widely held views about the institutional behavior of the parties involved is explicitly considered. In this case it is assumed that only one party, management, can realistically vary its wage offer. The union leadership, which maximizes its utility by acting in accord with the expectations of the rank and file, must act to represent the union membership's wage demands. On the assumption that firms maximize the appropriately discounted present value of the future profit stream, it is seen that the basic function of the strike is as an equilibrating mechanism to square up the union membership's wage expectations with what the firm may be prepared to pay. For completeness the analysis should probably include a fourth party, stockholders, in so far as management has a separate, self-serving motivation similar to that exposited by Williamson [30]. We feel, however, that for the present partial analysis we may safely assume that in the typical case management actions coincide with stockholder in- terests. 3. The above model has implications for variables other than the frequency and duration of strikes and the rate of change of money wages. Suppose, for example, that over a period of time wage changes remain below what the rank and file union membership desires, perhaps because of moral suasion via the Presidential wage guideposts. The analysis of this paper predicts that in such a case there will be an increase in the number of contracts which fail membership ratification and that there will be an increase in internal union dissension. George Perry has recently argued [22] that wage changes have been smaller since 1962 than would have been expected on the basis of the experience of the 1950s. This content downloaded from 149.132.120.104 on Thu, 10 Oct 2013 04:34:55 AM All use subject to JSTOR Terms and Conditions 40 THE AMERICAN ECONOMIC REVIEW Interestingly enough, there has been a substantial increase in contract ratification defeats since the point at which Perry dates the initial overprediction. Further, this period corresponds to a widely known rash of rank and file rebellion against union leadership.15 B. An Operational Formulation of the Bargaining Model From the analysis of a typical firm's choice between incurring and not incurring a strike it was concluded that the parties were less likely to agree prior to conflict the greater the acceptable wage increase (yo) and the speed at which the membership's expectations are reduced during a strike (r); the parties are the more likely to agree the greater is the ratio of the preagreement profit level to the wage bill (7r*), the firm's discount rate (r), and the minimum acceptable wage increase (y*). Only one of these variables, 7r*, has an obvious empirical counterpart, so further hypotheses must be provided to relate the other variables to observable phenomena. It seems plausible to argue that although r, r, and y* may vary between industries and regions because of different institutional arrangements, they will change only slowly through time. For example, r should depend upon the size of benefits generally paid out of strike funds, how much unemployment compensation may be paid strikers, etc.; all of which are institutionally determined.'6 Aggregating across firms and assuming a linear relationship in the relevant ranges of the variables, the preceding discussion suggests the following preliminary speci- fication: (12) St = fio + #1T + f2yOt + f37t-1, where St is the probability of a strike in period t, and T indexes the passage of time. We expect f2>O, 3<0, f0>O, since some strikes take place for institutional reasons, and f3,0, a2 <0, and the ui to have an inverted U-shape. That is, we would expect that when real wages have been increasing rapidly yo would be low. A more formal justification for these expectations is as follows: Suppose that yodependspositively on the difference between the expected long-runincrease in real wages, ARL, and the currently anticipated increase in real wages, ARA, i. e., (14) Yot=- y[JAR -AR]t Supposefurtherthat ARRLis composedof a very long-runconstant increase ("workers alwayswant more")and a moving average of previous real wage changes: N (15) AR, = (13-a)V+caZiEA?Rt-i, i=O whereO0, Byig<0, B2<0, and B4<0. Since B3=-2a4+ 33, and 32a4 > 0, f3 < 0, the signof the coefficienton profitsin equation (19) is indeterminant. Although management is morelikely to give in when previous profitsare high, the unionis also likely to increase its demands. Hence, it is not clearwhether the net effect of an increase in profits will be to increase, decrease, or have no appreciableeffect on the probability of occurrenceof a strike. The specification of (19) concerningthe effect of previous changes in real wages is based on the implicit assumption that workers view money wage changesand price changes as the reverse of each other. It is, of course, possibile that this is not so-complete money illusionbeing an extremeexception This content downloaded from 149.132.120.104 on Thu, 10 Oct 2013 04:34:55 AM All use subject to JSTOR Terms and Conditions 42 THE AMERICAN ECONOMIC REVIEW --so this assumption is tested in the next section. II. Empirical Results A. Specification and Estimation Problems If time-series observations were available on the number of strikes which begin in any quarter, St, and the number of contract expirations in any quarter, N,, then S', could be set equal to St/N, and (19) could be estimated directly. Although there are quarterly data for St, there are only limited surveys for N.18 In essence, the difficulty faced is that even though equation (19) is derived from a model where the dependent variable is the probability of occurrence of a strike, it will be necessary to estimate it with data on only the frequency of occurrence of strikes. Lacking the necessary observations on Ni, we are forced to make some plausible assumption about how it varies."9One possible hypothesis is that N,=n, where n is a constant. Given the near-plateau in union membership reached in 1952 [27], and the increased tendency toward multiple-employer bargaining, this assumption does not seem implausible with respect to the annual number of contract expirations.20 In order to deal with quarterlv data, however, we must at least recognize that there is a strong seasonalinfluencein contract expirations.There are, of course, important economic reasons why this should be so. First, trade unions in the areas of the economy where inclement weather affects production and employment will always try to gear contract expirations to periods when the effects of a strike are least likely to be nullifiedby the fact that productionwouldnot have taken place anyway. Second, most trade unions will try to avoid contract expirations in periods when the demand for current income is high (the winter holidays, for example) and to obtain contract expirations in periods with the fewest paid holidays. Both of the above considerationssuggest that the fall and winter quarterswill contain fewercontract expirationsand, ceteris paribus,fewer strikes. As a working assumption, therefore,we set 4 NF = E~ciNv1, j-l1 where (JPis the (constant) number of contract expirations in the jth quarterof all years and Nit is a dummy variable set equal to one in the jth quarterof the year and zero otherwise.Substituting St/Nt for St in (19) and multiplying both sides by 4 E cfAAjt jl1 gives (20) St = A ? bjNjt + E FAjNjtXtB + E 4jYpet, wherefor notational convenience the four independent variables in (19) have been replacedby the rowvector X, and B is the 18 The data on St, for example, cover strikes involving more than six workers, while the limited data on Nt cover negotiations involving 1,000 or more workers. There is, of course, the further problem that some institutional strikes do not take place at a time of contract expiration. 19Needless to say, if we were willing to proceed by simply regressing the frequency of strike activity on any number of intuitively relevant independent variables, none of the above assumptions would be explicitly introduced. The use of such an ad hocapproach, however, would imperilany attempt to understand the mechanism which underlies the determination of strike activity. 20 Some casual evidence for this assumption in the period 1963-67 is contained in Simkin [26]. The implication of the argument in the text is that the union always has its way on the seasonal aspect of disputes over contract expiration, which is not fully consistent with the caveat in footnote 16. In fact, the seasonal pattern 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 precise period of the year in which a strike takes place is most generally under the control of the union, even if the point of contract expiration is not. This content downloaded from 149.132.120.104 on Thu, 10 Oct 2013 04:34:55 AM All use subject to JSTOR Terms and Conditions ASHENFELTER AND JOHNSON: BARGAINING AND STRIKES 43 columnvector of coefficientson these vari- ables. Since the (Diare unknown, the simplest procedure for obtaining an unbiased estimatorfor (20) wouldbe to use a separate relationshipfor each quarter of the year. Unfortunately, the number of variables whichwillbe neededon the right-handside of (20) is too large to make this solution feasible with the length of the time series available. Therefore, as an admittedly roughapproximationto (19) and (20), we have specifiedthe followingequation: (21) St = AI,INit + A4l2N2t+ A4T3N3t M + A14N44t+ B, E AiARt-. i=O , * + B2ut+ B3,rj_+ B4T' + Et wherethe Nj, area set of seasonaldummies and e' is an error term.2' It is not difficult to show, under the usual assumptions about the way in which the independent variables in (21) are generated [14, pp. 268-69], that the least squaresestimators of BAi, B2, B3 and B' are consistent and asymptotically unbiased estimators of 12kDj(Bj/ij) 12AB2, 12M51B3,and 12fxB4. That is, our estimates of the coefficientsin equation (21) may be interpreted as the mean response, averaged across quarters, of a stimulus from the independent variable. Sinceeach of the (Dmust be positive, all of the previous predictions about the signs of the coefficients in equation (19) hold for equation (21). Beforeturningto estimationand testing of equation (21). one final difficulty must be resolved. The lag coefficientson AR_ pose two estimation problems. First, we have a priorireasonto suppose that these coefficientswill not have the familiar exponential-decayform. Second,we expect a lag distribution on AR,j but not on the other variablesin the equation.22As an alternative to the standardtechnique,therefore,we have usedthe straightforwardproceduresuggestedby ShirleyAlmon [1] for estimating equation (21). On the assumption that the lag distribution can be approximated by a polynomial, Lagrangian interpolationpolynomials are used to create moving averages of the independent variable. These moving averages are then introduced into an ordinary regression equation and their coefficients(and hence the impliedcoefficientsof the lag distribution) estimated. In the results that follow we have used a third degree polynomial approximationand constrainedthe lag distribution to assume zero values at the beginning and at a finite lag.23 B. TheResults Our discussion of empirical results is divided into three sections. First, we discuss the general implications of the estimated versionof equation(21). Second,we modify the estimating equation to allow for the possibility of money illusionon the part of workers. Finally, we test the stability of the preferredequation and consider the effect of some important institutional changeson the volume of aggregate strike activity. 1. The initial results of fitting equation (21) are reportedin Tables 1 and 2 under the rubric of equations (21a) and (21b), 21 If the disturbance term in (19) is homoscedastic, then the disturbance term in (21) is heteroscedastic because its variance moves systematically with the quarter of the year being considered. Namely, if var (et) = C, a constant, then var (et')= var (1)= 4,j2C. If one views St' in (19) as a sample proportion, however, the procedure used to obtain (21) suggests that et' will be (nearly) homoscedastic. Since this becomes an empirical issue, we have tested the estimated version of (21) for unequal residual variances to see if this difficulty is damaging to our results. See footnote 24 below. 22For a discussion of the estimation problems raised by these difficulties see Griliches [15]. 23 This means that two "Almon variables" were entered into the regression to estimate the lag distribution on real wage changes. It should be noted, however, that the results were generally insensitive to either the degree of the polynomial or the constraints placed on the lag coefficients. This content downloaded from 149.132.120.104 on Thu, 10 Oct 2013 04:34:55 AM All use subject to JSTOR Terms and Conditions 44 TIHETEAMERICAN ECONOMIC REVIEW TABLE 1-ESTIMATED REGRESSION COEFFICIENTS AND RELATED STATISTICS"b FOR THE VARIABLES IN EQUATIONS 21a, 21b, 21c, AND 21d Equa- Ut MARI, ZAW(_ ZAPI, r i N1 N2 Ns T C LG R2 R2 DW SEE tion(21a) -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 coefficient of determination about the overall mean, R2 is the coefficient of determination about the quarterly means, DW is the Durbin-Watson statistic, and SEE is the Standard Error of Estimate for the regression equation. b Estimated standard errors of the estimated regression coefficients are in parentheses under the relevant coefficients. Sources: The civilian unemployment rate, ut, is a quarterly average of the monthly rates published in Table A-6 of the Monthly Labor Review, U. S. Bureau of Labor Statistics. The Consumer Price Index is obtained from D-1 of the MLR. Our wage rate is an average, weighted by relative 1957 production worker employ- ment, of average hourly earnings in mining, construction, and manufacturing, and the data are obtained from Employment and Earnings volumes, U. S. Bureau of Labor Statistics. None of these variables is seasonally adjusted. Our profits variable is the ratio of Corporate Profits after tax, excluding Inventory Valuation Adjustment, to Total Compensation. The source of these data is various issues of the Suirvey of Current Business, Table 3, U. S. Dept. of Commerce. Finally, the number of strikes beginning in each quarter are obtained in Table E-1 of various issues of the MLR. This content downloaded from 149.132.120.104 on Thu, 10 Oct 2013 04:34:55 AM All use subject to JSTOR Terms and Conditions ASHENFELTER AND JOHNSON: BARGAINING AND STRIKES 45 TABLE 2-ESTIMATED LAG COEFFICIENTSAND THEIR STANDARDERRORSFOR EQUATIONS21b 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 for equation (21b) are charted in Figure 2. The following symbols are used in these tables: u,= the civilian unemploymentrate, ARt=AWt-APt, AWIt=the annual percentage rate of change of money wages, P,= the annual percentage rate of change of consumerprices, Irt*= the ratio of corporateprofitsafter taxes to total compensation, Njt=seasonal dummies for first, second, and third quarters, T= time in quarters, C= constant term. The period of fit is 1952I-1967II, which is consistent with our assumption that the annualnumberof contract expirationshas been relatively constant since 1952. As can be seen fromTables 1 and 2, the results provide strong support for the hypotheses advanced in Section I. In equation (21a) the coefficientsof each of the independentvariables, except that for profits, are highly significant.24Although several differentmeasuresof profitsandmoving averages of profits were tried, none produced results substantially different fromthose reportedin Table 1. Ourtentative conclusionis that the neteffectofprofits on strike activity is small. In equation (21b) r*,_1 has been deleted. The independent variables in this preferredequation explain about 94 per cent of the variance of the dependentvariableabout its overall mean, and about 82 per cent of the variance of the dependent variable about its quarterly means. The standard error for 24Since there is some question about the appropriateness of the usual statistical tests in the case where the disturbance variances are unequal (see footnote 21), we have applied Bartlett's well-known test for unequal variances 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 the quarterly groupings, B, the test statistic, is satisfactorily approximated by the x2 distribution with 3 degrees of freedom. In this case, B=2.01, and we cannot reject the hypothesis of equal quarterly residual variances at even the .25 level. Coefficient +2 +1 1 2 3 4 5 6 7 8 9 ?0f Lag -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 FIGuRE 2-LAG DISTRIBUTIONCOEFFICIENTSONREAL WAGE CHANGES This content downloaded from 149.132.120.104 on Thu, 10 Oct 2013 04:34:55 AM All use subject to JSTOR Terms and Conditions 46 THE AMERICAN ECONOMIC REVIEW this equation is a remarkably low 75 strikes, as against a mean of about 980 strikes per quarter. A glance at Figure 2 suggests that the lag distribution on real wages is of the shape predicted. A steadystate declineof one percentagepoint in the rate of change of real wages is associated with an increase of about 62 strikes per quarter. The seasonal dummies confirm the hypothesis that strike activity is much heavierin the springand summerquarters than in the fall and winter quarters.25 Finally, a decline of one percentage point in the civilian unemploymentrate is associatedwith an increaseof about 123strikes per quarter. 2. The results for equation (21c) reported in Tables 1 and 2 incorporatethe hypothesis that the rates of change of money wages and prices are not mirror images in their effects on aggregate strike activity, i.e., we allow for the possibility that the rateof changeof moneywageshas a more (or less) important effect on strike activity than the rate of change of prices. It is clearfromthese resultsthat the effect of moneywagechangeson strikeactivity is somewhat greater than the effect of price changes. The differencesin the effects of these variables, however, is not very substantial. More formally, we may test the null hypothesis that 9 9 i=O i3O by formingthe ratio t w+EP var (,, P)?Z where the pu'are the estimated lag distribution coefficientson money wage changes and the -Pare the estimated lag distribution coefficientson price changes. In this case t=-1.07 which clearly is not significant at conventional test levels. We may also test the null hypothesis /Z =-pi (i= 0, *, 9) with an F-ratio. In this case F(2, 49)= 1.09,whichalsois not significant at conventional test levels.26We tentatively conclude that wage and price changes act essentially as mirror-images with respect to aggregate strike activity. 3. Since the volume of strike activity has heretofore been associated with any number of unstable causal factors, there may be some question about the general stability of an equation like (21b) over time. In order to test for the possible instability of this equation we have arbitrarily divided the sample period in half and performed the standard test of the null hypothesis that the parameters of equation (21b) are identical for the two time periods. In this case F(8, 46)= 1.40, which clearly is not significantat conventional test levels. We conclude that there is little evidence to suggest that this relationship is unstable. 25The coefficients on the seasonal dummies and the constant term in equation (21b) allow us to estimate A24j and A4j(i= 1, , 4). Hence, they provide estimates of AZ(i- = (j= 1 4), i.e., the percentage of total annual contract expirations which take place in each quarter. These estimates are, from the first to fourth quarters: 23.6 per cent, 28.9 per cent, 26.9 per cent, 20.4 per cent. Simkin [26] provides the number of "active" Federal Mediation and Conciliation Service cases closed each month in 1966, which, assuming a short lag from beginning to closure of a case, should be a good proxy for the "typical" number of contract expirations per month. Assuming a mean lag of one month for closures, these independent data provide the following estimates of the percentage of total contract expirations which take place in each quarter: 22.8 per cent, 32.3 per cent, 25.6 per cent, 19.2 per cent. These latter estimates are strikingly close to those obtained from equation (21b), and lend additional credence to our argument that the seasonality in strike activity is due to a seasonality in contract expirations. 26 The first test described in the above paragraph requires computation of the estimated variance of ZAT +?,2A, which can easily be worked out as a linear combination of the variances and covariances of the "Almon variables" in the regression equation. The second test is a straightforward application of some of the results in Chow [6]. This content downloaded from 149.132.120.104 on Thu, 10 Oct 2013 04:34:55 AM All use subject to JSTOR Terms and Conditions ASHENFELTER AND JOHNSON: BARGAINING AND STRIKES 47 Finally, we have estimated equation (21d) to allow for the possibility that passage of the Landrum-GriffinAct in 1959 has had a positive impact on the amount of aggregate strike activity. It has been arguedthat this law, which is designedto regulatethe internalaffairsof tradeunions in order to ensure "union democracy,"27 has had the effect of: (a) increasing the militancy of union leadersas a responseto the implicit encouragementthe law gives to the growth of dissident groups within the union, and (b) making the leadership more sensitive to the "less responsible" wage demands of the union members.28 Adding a dummy variable, LG, to the estimatingequationto test for the effect of the Landrum-GriffinAct gives the results reportedas equation (21d) in Table 1. The standard error, Durbin-Watson Statistic, and R2are all improved by this modification. The coefficientof LGsuggests a modest, but significant increase of about 88 strikesper quarterover the pre-Landrum- Griffinperiod.29 III. Conclusions and Implications Although we are not firmly wedded to the preciseestimates presentedin this paper, it seems that the aggregate level of strike activity is behaviorally related to the degreeof tightness of the labormarket andpreviousrates of changeof realwages. Amongthe implicationsof ouranalysisare the following: 1. The incorporation of a widely accepted set of assumptions about the behavior of trade unions into the traditional theory of the firm produces a straightforwardsolution to the outcome of unionmanagement bargainingwhich lies within the corpus of conventional economic reasoning. Although conventional bargaining modelsarebased on assumptionswhich do not seem to represent the institutional framework of union-management negotiations, this could be excused if they provided refutable predictions about observable behavior,but they do not. The simple formulation of this paper, which specifically acknowledgesthe three-partynature of collective bargaining, does yield refutable predictions,and they are found to be consistent with the data. 2. As was shown with the case of the Landrum-GriffinAct, even a simple version of the model describedin this paper can be helpful in evaluation of the effects of changes in the institutional framework within which collective bargaining must function. Otherinstitutional changes,e.g., the payment of unemployment compensation to strikers, could be investigated. Further,the model describedin this paper providesa moreexplicit rationalefor some of the work which has been done on explanations of the rate of change of aggregate money wages.30 3. Finally, the results have a numberof implicationsfor public policy with respect to wage determination in the unionized sectorof the economy. First,policieswhich' 27 See [12] for details on the provisions of this law. It was signed in September of 1959 and most of its provisions were in effect within ninety days. Hence, in the following results we have assumed that the law began having an effect in 1959 IV and reached its full effectiveness linearly by 1960 IV. 28 For arguments similar to these see Estey [11, pp. 57-59). In terms of the formulation in Section I, these arguments suggest that yo would generally be higher after passage of the Landrum-GriffinAct than before. 29 To test for the possibility that we had confused the effect of the Landrum-GriffinAct with the effect of the Guideposts, we added another dummy variable to the equation. The coefficient of LG remained similar with respect to its standard error while the Guideposts coefficient was negative and less than half its standard error. In terms of the formulation in Section I, this negative effect is what would be predicted since the Guideposts supposedly lower Yo. 30For example, the studies by 0. Eckstein and T. A. Wilson [10] and G. L. Perry [21]both include profits as determinants of money wage changes on the basis of casual bargaining model considerations, and J. D. Sargan [25] estimates a model which includes the level of real wages. In [2] a variable specifically measuring the volume of strike activity is found to have an effect on aggregate money wage changes. This content downloaded from 149.132.120.104 on Thu, 10 Oct 2013 04:34:55 AM All use subject to JSTOR Terms and Conditions 48 ITHE AMERICAN ECONOMIC REVIEW are geared to induce labor leaders to convince their constituencies to be satisfied with "morereasonable"wage settlements are likely to result eventually in political turmoil within trade unions. It does not, therefore, seem likely that such a policy can continuefor long without encouraging the growth and power of more militant leadershipand a subsequentdeclinein the effectivenessof the originalpolicy. Second, in addition to the well-knowntradeoffbetween wage changes and unemployment there seem also to be tradeoffs between unemployment, wage changes, and industrial strikeactivity. To the extent that the maintenanceof industrialpeaceis a goal of public policy, this adds an additional dimension to the problem of maintaining full employment and stable prices. REFERENCES 1. S. ALMON, "The Distributed Lag Between Capital Appropriations and Expenditures," Econometrica, Jan. 1965, 33, 178-96. 2. 0. ASHENFELTER,G. E. JOHNSON,AND J. H. PENCAVEL,"Trade Unions and the Rate of Change of Money Wages in the United States: 1914-1960," Industrial Relations Section, Princeton University, (mimeo), 1968. 3. C. A. BENNETT AND N. L. FRANKLIN, Statistical Analysis in Chemistryand the ChemicalIndustry. New York 1954. 4. R. L. BISHOP,"A Zeuthen-Hicks Theory of Bargaining," Econometrica,July 1964, 32, 410-17. 5. , "Game-Theoretic Analyses of Bargaining," Quart. Jour. Econ., Nov. 1963, 77, 559-602. 6. G. C. CHOW,"Tests of Equality Between Sets of Coefficients in Two Linear Regressions," Econometrica,July 1960, 28, 591-605. 7. D. COLE, "Preface," in J. Dunlop and N. Chamberlain, eds., Frontiersof Collective Bargaining, New York 1967, pp. vii-ix. 8. J. G. CROSS, "A Theory of the Bargaining Process," Am. Econ. Rev., March 1965, 55, 67-94. 9. J. DUNLOP, Wage Determination Under Trade Unions. New York 1944. 10. 0. EcKSTEIN AND T. A. WILSON, "The Determinants of Money Wage Changes in American Industry," Quart. Jour. Econ., Aug. 1962, 76, 379-414. 11. M. ESTEY, The Unions. New York 1967. 12. M. S. ESTEY, P. TAFT, AND M. WAGNER, eds., Regulating Union Government.New York 1954. 13. M. GART, "Labor's Rebellious Rank and File," Fortune, Nov. 1966, 74, 150-53. 14. A. S. GOLDBERGER, EconometricTheory. New York 1964. 15. Z. Griliches, "Distributed Lags: A Survey," Econometrica, Jan. 1967, 35, 16- 49. 16. J. C. HARSANYI, "Approaches to the Bargaining Problem Before and After the Theory of Games," Econometrica, April 1956, 24, 144-57. 17. , "Notes on the Bargaining Problem," So. Econ. Jour., April 1958, 24, 471-76. 18. J. R. HICKS,The Theoryof Wages. New York 1963. 19. C. C. HOLT, "Job Search, Phillips' Wage Relation and Union Influence, Theory and Evidence," Univ. of Wisconsin Firm and Workshop Paper 6705, Dec. 1967. 20. F. S. O'BRIEN, "Industrial Conflict and Business Fluctuations: A Comment," Jour. Pol. Econ., Dec. 1965, 73, 650-54. 21. G. L. PERRY, "The Determinants of WVageRate Changes and the InflationUnemployment Tradeoff for the United States," Rev. Econ. Stud., Oct. 1964, 31, 287-308. 22. , "Wages and the Guideposts," Am. Econ. Rev., Sept. 1967, 57, 897-904. 23. A. REES, "Industrial Conflict and Business Fluctuations," Jour. Pol. Econ., Oct. 1952, 60, 371-82. 24. A. M. Ross, Trade Union Wage Policy. Berkeley and Los Angeles 1948. 25. J. D. SARGAN, "Wages and Prices in the United Kingdom," in P. E. Hart, G. Mills, and J. K. Whitaker, eds., EconoThis content downloaded from 149.132.120.104 on Thu, 10 Oct 2013 04:34:55 AM All use subject to JSTOR Terms and Conditions ASHENFELTER AND JOHNSON: BARGAINING AND STRIKES 49 metric Analysis for National Economic Planning, London 1964, pp. 25-54. 26. W. SIMKIN, "Refusals to Ratify Contracts," 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. WALTONANDR. B. MCKERSIE, A Behavioral Theoryof Labor Negotiations. New York 1965. 29. A. R. WEINTRAUB, "Prosperity vs. Strikes: An Empirical Approach,"Indus. Lab. Rel. Rev., Jan. 1966, 19, 231-38. 30. 0. E. WILLIAMSON, Economics of Discretionary Behavior: ManagementObjectives in a Theory of the Firm, Englewood Cliffs, N. J. 1964. 31. D. YODER, "Seasonality in Strikes," Jour. Am. Stat. Assoc., Dec. 1938, 33, 687-93. 32. F. ZEUTHEN, Problems of Monopoly and Economic Warfare. London 1930. 33. U. S. BUREAU OF THE CENSUS, Historical Statistics of the United States. Washington, D.C. 1960. This content downloaded from 149.132.120.104 on Thu, 10 Oct 2013 04:34:55 AM All use subject to JSTOR Terms and Conditions