Open-shop unions and product market competition

Open-shop unions and product marketcompetition

Paulo Bastos Research Department, Inter-AmericanDevelopment Bank

Udo Kreickemeier University of TubingenPeter W. Wright GEP, University of Nottingham

Abstract. Evidence on the effect of product market competition on unionized wages ismixed. In this paper we show theoretically that the result may reflect genuine hetero-geneity in the response of union wages to product market conditions. For low levels ofunionization, union bargaining power may actually be enhanced by market competition,as firms have more to lose when there is a strike. Using recent data from the UK, weexplore interactions between the level of industry competition and unionization, and findsupporting evidence for this hypothesis. JEL classification: J51, J52, L13

Atelier ouvert, syndicats et concurrence sur le marche du produit. Les resultats de laconcurrence sur le marche du produit sur les salaires des syndiques ne sont pas concluants.Dans ce memoire, on montre theoriquement que cet etat de fait peut refleter une veritableheterogeneite dans la reponse des salaires des syndiques aux conditions dans le marchedu produit. Pour de faibles niveaux de syndicalisation, le pouvoir de marchandage dusyndicat peut etre exhausse par la concurrence sur le marche du produit puisque les firmesont davantage a perdre s’il y a greve. A l’aide de donnees recentes pour le RoyaumeUni, on explore les interactions entre le niveau de concurrence et de syndicalisation dansl’industrie, et les resultats supportent cette hypothese.

1. Introduction

In this paper we examine, from both a theoretical and an empirical point of view,the impact of product market competition on unionized wages. The standard

The authors would like to thank an anonymous referee, Kjell Erik Lommerud, and Rod Falveyfor helpful comments. Financial support from the Leverhulme Trust (Programme GrantF114/BF) is gratefully acknowledged. Paulo Bastos thanks Fundacao para a Ciencia e aTecnologia (SFRH/BD/17274/2004) for financial support. Email: [email protected]

Canadian Journal of Economics / Revue canadienne d’Economique, Vol. 43, No. 2May / mai 2010. Printed in Canada / Imprime au Canada

0008-4085 / 10 / 640–662 / C© Canadian Economics Association

Open-shop unions and product market competition 641

theoretical model of union bargaining in a Cournot oligopoly gives a clear andintuitively plausible prediction for the effect of product market competition onwages. In a widely cited paper, Dowrick (1989) finds that, under decentralizedbargaining, an increase in the number of firms competing in an industry hasthe unambiguous effect of reducing the bargained wage.1 In two recent papers,Naylor (2002a,b) explores the implications of this result for profits, at both theindustry and the firm level. Naylor (2002a) shows that because of the wagemoderation effect that results from product market competition, firm entry mayactually lead to an increase in industry profits. Naylor (2002b) demonstrates that,for similar reasons, it is actually possible for every firm’s profit to increase withfirm entry.

In contrast to the clear theoretical predictions, the empirical evidence on theeffect of product market competition on bargained wages is mixed. Indeed, anumber of studies for the US have found that decreased product market com-petition is associated with lower union wages (e.g., Block and Kushin 1978;Freeman and Medoff 1981). Abowd and Tracy (1989) find that although theimpact of increased sales concentration is positive at first, it becomes negativeat high levels of concentration. Bratsberg and Ragan (2002), analysing the effectof deregulation on the union wage premium over the period 1972–99, also showthat the results vary considerably across industries.

For the UK the results are similarly mixed. Stewart (1983) finds that the levelof concentration in the industry has no significant effect on the earnings of unionmembers, while Macpherson and Stewart (1990) and Van Reenen (1996) find anegative and (weakly) significant effect of concentration on wages.

In explaining these findings, the results of Hendricks (1975) may be instructive.He finds that an increase in the sales concentration raises wages only in highlyunionized industries. In industries characterized by low and medium unioniza-tion, increases in industry concentration cause statistically significant decreasesin wages. Thus, the preceding diversity of results might be caused by uncontrolledvariations in union density.

In this paper we develop a theoretical model that shows that the mixed em-pirical results may reflect genuine heterogeneity in the response of union wagesto product market conditions. We demonstrate that the established theoreticalprediction of a positive relationship between bargained wages and industry con-centration depends crucially on the assumption that the union is a closed shopwith 100% level of membership, implying that unionized firms stop producingin the event of a strike.2 However, this assumption is seldom realistic. In mostdeveloped countries, open-shop arrangements, where the union is recognized forbargaining purposes but membership is not compulsory, are the dominant form

1 Under the standard assumption of zero disagreement payoffs, this result holds whetherbargaining is restricted to wages or covers both employment and wages.

2 Under a pre-entry closed shop, the employer must recruit directly from people who are alreadyunion members. Under a post-entry system, workers are required to join the union as acondition of employment.

642 P. Bastos, U. Kreickemeier, and P.W. Wright

of union organization (see, e.g., Boeri, Brugiavini, and Calmfors 2001; Visser2003; Booth and Bryan 2004). In addition, empirical evidence indicates thatfirms normally do not stop operating during a strike.3 In the present paper, weanalyse the impact of product market competition on the outcome of union-firmbargaining when workers are organized in open-shop unions that represent onlypart of the workforce of a firm, implying that unionized firms can produce withtheir non-unionized workers in the event of a strike.4

As our main result, we show that, for sufficiently low (but strictly positive)levels of union density, increased product market competition leads to higherwages, thereby reversing the prediction of the standard model, while the standardresult prevails for sufficiently high levels of union density. The intuition as towhy the standard result can be overturned in the case of open-shop unions isstraightforward. Product market competition affects not only unionized firms’profits but also their payoff in the event of a dispute. If a union strikes at onefirm, competitors will optimally expand their production. As a consequence,the firm’s disagreement payoff falls, helping the union into the bargain. Hence,the union captures a larger share of a smaller pie, and the net effect on the wagerate is indeterminate. Owing to the robustness of this mechanism, our main resultholds for a broad class of specifications used in the literature with respect to theunion objective function and to the scope of bargaining.

We then test the key predictions of our model using a panel data set of UKmanufacturing workers for the 1996–99 period, supplemented with informationon industry union density and concentration ratios. As our theory predicts, wefind that wages are negatively correlated with industry concentration in indus-tries with low union density, while they are positively associated with industryconcentration in industries with high unionization rates.

The remainder of the paper is organized as follows. In section 2, we introducethe basic model and derive the outcome of collective bargaining. We start by

3 Gramm (1991) and Gramm and Schnell (1994) examine firms’ operating capacity at struckfacilities during a strike. They use a sample of 35 large strikes (involving 1,000 or more workers)in single firm bargaining units in the US during 1984–88, and 21 small strikes (involving 6 ormore workers in 1984–85 and 20 or more workers in 1986–88) in New York. In the US sample,they find an average operating capacity of 57% when no replacements are hired, 77% whentemporary replacements are hired, and 90% when permanent replacements are used. In the NewYork sample the average operating capacity was 60% regardless of the use of replacements.Cramton and Tracy (1998) analyse strikes involving bargaining units of at least 1,000 workers inthe period 1980–89. They find that firms’ average operating capacity during the strike is 43%when no replacements are hired, 67% with temporary replacements, and 56% with permanentreplacements. In addition, they find that the fraction of strikes involving replacements isrelatively small (14.1%), which is in accordance with previous evidence provided by Olson (1991)and Gramm (1991).

4 In the theoretical literature on open shop unions, it is typically assumed that during a strike thefirm continues production with those of its workers who are not members of the union (seeNaylor and Cripps 1993; Naylor and Raaum 1993; Corneo 1993, 1995). In these models, byaffecting the payoff of the firm in event of a dispute, the level of union density impacts theoutcome of collective bargaining. However, this literature does not explicitly model the productmarket or the firms’ oligopolistic behaviour, and so it is unable to explain the interactionsbetween product markets structure and union-firm bargaining.


analysing the case in which a monopolist bargains over wages with an open shopunion. We then examine how the outcome of collective bargaining changes whenthe same firm competes with a second firm, which may or may not be unionized.In section 3 we show that, under fairly mild assumptions, our main results arereinforced if union membership is endogenously determined. In section 4, webriefly discuss the robustness of our main results with regard to the scope ofcollective bargaining. In section 5, we empirically test the key prediction of ourtheory. Section 6 concludes.

2. The theoretical model

Consider the market for a homogeneous commodity with inverse linear demand

p = a − by, (1)

where p denotes product price and y total output. Changes in the degree of prod-uct market competition are captured in the simplest way possible by comparinga monopoly firm 1 (in which case y = y1) and a Cournot duopoly with firms 1and 2 (in which case y = y1 + y2). Assume that this market is small relative tothe rest of the economy, so that we can abstract from income effects. Firm 1 isassumed to be unionized, while firm 2 may or may not be unionized.

Each firm is assumed to produce under constant returns to scale, with labourli(i = 1, 2) as the only input. The marginal product of labour is normalizedto unity. Therefore, one can denote output and employment interchangeably(yi = li) and firm i’s profit equals

πi = (p − wi)yi = (a − by − wi)yi. (2)

The objective of the union in firm 1 is represented by the Stone-Geary utilityfunction

�1 = (w1 − wc)θ l1−θ1 , (3)

where wc denotes the reservation wage and parameter θ ∈ (0, 1] the relativestrength of the union’s preference for wages over employment. This functionalform encompasses the common assumptions of rent maximization (θ = 1/2) andwage premium (θ = 1) as special cases. The reservation wage is assumed to beexogenous and, without further loss of generality, is set equal to zero (wc = 0 ).If a second unionized firm is present in the market, the utility of the union in thisfirm is represented by a function analogous to (3).

We assume that the union is an open shop, and the fraction of workers who areunion members is denoted by μ ∈ (0, 1]. The firm pays all its workers, whether


they are union members or not, the same bargained wage, w1.5 In this section, ourmain results are derived under the assumption that union density is exogenouslygiven when collective bargaining takes place, and hence that the individual de-cision to become a union member is independent of wage formation. In section3, we show that, under fairly mild assumptions, the introduction of endogenousunion membership would reinforce our main results.

Following Naylor and Cripps (1993) and Naylor and Raaum (1993), we con-sider a sequence of contract periods. In each contract period, the model can bedescribed as a two-stage game. In stage one, firm(s) and union(s) bargain overwages, for a given level of union density. In stage 2, firms decide on their level ofproduction, and hence employment, taking as given the wage of the other firm (inthe case of a duopoly) and taking into account their labour demand schedule.6

In order to solve the model analytically, we proceed by backwards induction.

2.1. Solving for productionUnder the right-to-manage assumption, firms will choose the level of output(employment) in order to maximize profits given the bargained wage. Considerfirst that firm 1 is a monopolist. Solving the first-order condition for profitmaximization yields

y∗1 = a − w1

2b. (4)

When we use (2) and (4), the monopolist’s profit follows as

π1 = (a − w1)2

4b, (5)

while the utility of the union implied by (3) and (4) is equal to

�1 = w1θ

(a − w1

2b

)1−θ

. (6)

Alternatively, with a duopoly in the product market, best-reply functions aregiven by the standard expressions

yi = a − wi

2b− 1

2yj i, j = 1, 2, i �= j, (7)

5 This amounts to assuming that the union wage effect is a pure public good. For empiricalevidence supporting this assumption see Barth, Raaum, and Naylor (2000) and Booth andBryan (2004). Using matched employer-employee data for Norway and the UK, respectively,these papers provide evidence that, when the level of union density in the establishment iscontrolled for, the individual membership status ceases to have a significant effect on the wage.

6 The alternative of efficient bargaining, where firms and unions bargain over wages andemployment, is considered in section 4.


and equilibrium outputs follow as

y∗i = a − 2wi + wj

3bi, j = 1, 2, i �= j. (8)

The profit for unionized firm 1 is then given by

π1 = (a − 2w1 + w2)2

9b, (9)

while union utility follows from (3) and (8) as

�1 = wθ1

(a − 2w1 + w2

3b

)1−θ

. (10)

2.2. Solving the wage bargainThe wage wr

1 paid by firm 1 in each contract period is the outcome of a Nashbargain with the union:

wr1 = arg max

w1

{�

β

1 (π1 − π s1)1−β

}, (11)

where superscript r denotes the respective production regime, and it equals eitherum (unionized monopoly), ud (unionized duopoly) or md (mixed duopoly, i.e.,the case where firm 2 is not unionized). The disagreement payoff by the firm isgiven by π s

1, while β ∈ (0, 1) represents the relative bargaining power of the unionand reflects possible asymmetries in the underlying bargaining procedure.7 Weassume that, in the event of a disagreement, union workers strike and receive theirreservation wage wc, which we have normalized to zero.8 If a second unionizedfirm is in the market, bargaining within this firm is represented by a functionanalogous to (11). Clearly, π1, π

s1, and �1 depend on the market structure, and

hence so does the union wage wr1. We now proceed to derive wr

1 for the unionizedmonopoly, unionized duopoly, and mixed duopoly cases, respectively.

7 This formalization is consistent with the non-cooperative interpretation of the Nash solutionoffered by Binmore, Rubinstein, and Wolinsky (1986). In this context, the union’s relative powershould not depend on union density, provided that the influence of this variable is captured onthe firm’s disagreement payoff. Nevertheless, all qualitative results of the model would gothrough if β was assumed to be an increasing function of μ.

8 Income of union members during a strike may consist of strike pay financed by union resourcesand/or income from temporary jobs that union members obtain during the dispute (see Layard,Nickell, and Jackman 1991). If workers were to receive strike pay of less than the reservationwage wc, there would be a minimum level of union density that the union had to achieve inorder to raise the wage above wc (see Naylor and Cripps 1993; Naylor and Raaum 1993).


2.2.1. Unionized monopolyThe standard assumptions that the firm and the union behave rationally andpossess complete information exclude the possibility of a strike in equilibrium.However, by affecting the disagreement payoff of the firm, the threat of a strikeis crucial in the bargaining process.9 As in Naylor and Cripps (1993) and Naylorand Raaum (1993), we assume that, in the event of a strike, the firm continuesproduction with its non-union workers under the terms of the contract negotiatedin the previous period and, furthermore, that the firm is myopic in the sensethat it neglects the impact of its current employment decisions on future wagenegotiations.

Hence, the monopolist’s total sales in a strike are equal to the output itcan produce with its non-union workers, given the wage rate negotiated in theprevious contract period (w1). Therefore, the output of firm 1 in a strike is givenby ys

1 = (1 − μ)y∗1, where y∗

1 = (a − w1)/(2b) is the output (and employment)of the domestic firm in the previous contract period (that is, the firm’s profitmaximizing level of output at the wage rate w1). Output losses inflicted upon thefirm in the event of a strike are therefore an increasing function of union density.The conflict payoff of the monopolist then follows as

π s1 = (1 − μ2)

(a − w1)2

4b. (12)

We are now in a position to solve for the steady-state Nash bargained wage. Thisinvolves two steps. First, using (5), (6), and (12), we maximize the Nash productin (11), taking as given the wage of the previous contract period (w1). This leadsto the first-order condition for the current period Nash bargaining problem. Thesteady-state bargained wage follows by imposing the condition w1 = w1. Thisgives

wum1 = βθμ2

2 − β(2 − μ2)a. (13)

It is straightforward to check that the steady-state bargained wage is increasingin μ, β, and θ . The bargained wage also tends to zero whenever any of theseparameters tends to zero.

2.2.2. Mixed duopolyConsider now the entry of a second firm, which, in this section, is assumedto be non-unionized. In the absence of a union, this firm pays its workers thereservation wage w2 = wc = 0. Hence, π1 and �1 are obtained by setting w2 = 0

9 As noted by Binmore, Rubinstein, and Wolinsky (1986), the Nash bargaining solution can beinterpreted by looking at an underlying dynamic game of the type proposed by Rubinstein(1982). Therefore, the disagreement payoffs should correspond to the streams of income thataccrue to the parties when they are in a state of disagreement.


in eqs (9) and (10), respectively. By analogy with the previous section, the outputof the unionized firm in the event of a strike equals ys

1 = (1 − μ)y∗1, where now

y∗1 = (a − 2w1)/(3b).

In order to find the disagreement payoff for the unionized firm, one needs toknow the supply response of the non-unionized competitor in case of a strike.This is found by substituting ys

1 into the best-reply function of the non-unionizedfirm, yielding

ys2 = (2 + μ)a + 2(1 − μ)w1

6b. (14)

It is easily checked by comparing (14) with (8) that firm 2 would expand itsoutput in the event of a strike, as would be expected. Given this response, thedisagreement payoff (profit) for firm 1 follows as

π s1 =

[1 − μ (1 − μ)

2

](a − 2w1)2

9b. (15)

Solving for the steady-state wage yields

wmd1 = βθμ(1 + μ)

8 − β(8 − 2μ(1 + μ))a. (16)

As in the monopoly case, the steady-state bargained wage is increasing in theparameters μ, β, and θ .

Subtracting (16) from (13) yields the wage differential D between the unionizedmonopoly and mixed duopoly regimes:

D = wum1 − wmd

1 = Aβθμ

2a, (17)

where

A ≡ 2μ

2 − β(2 − μ2

) − 1 + μ

4 − β(4 − μ(1 + μ)).

Market entry of a non-unionized firm increases the wage paid by the unionizedfirm if and only if A < 0. In the case of symmetric Nash bargaining (β = 1/2),this is true for μ ∈ (0, 0.312).10

In order to gain some intuition for this result note that, in the polar caseof zero union membership (μ = 0), a strike would not have any effect, and thefirm pays the competitive wage in both situations (wum

1 = wmd1 = 0). With strictly

positive union membership on the other hand, the profit differential π1 − π s1

10 A critical level of union density below which increasing product market competition raises thebargained wage can be shown to exist for all relative bargaining strengths.


wr1

µ1µ∗

wum1

wmd1

FIGURE 1 Bargained wages and union density

and hence the bargained wage rate become regime specific. Under monopoly,a marginal increase of μ starting from 0 has only a second-order effect onthe disagreement payoff. This is different under mixed duopoly: there is a now anegative first-order effect on the disagreement payoff because of the increase in thecompetitor’s output that occurs during a strike. Therefore, for sufficiently smallunion densities, the profit differential π1 − π s

1 (and therefore the wage) is smallerunder unionized monopoly than under mixed duopoly. At the opposite extreme,when μ = 1, π1 − π s

1 is higher under monopoly than under mixed duopoly. Thisfollows from the fact that, when union membership is 100%, the disagreementpayoff is zero in either case, while the profit is higher in the monopoly casein the absence of a strike. By continuity this implies that, at some intermediatelevel of density, wage rates are equal in both situations. This result is illustrated infigure 1, where μ∗ denotes the critical level of union density below which increasedproduct market competition increases the wage rate.

As shown in appendix A, increasing product market competition raises notonly wages but also union utility for sufficiently low levels of union membership.However, the range of membership levels for which this is true is smaller than thatfor wages. This is due to the fact that product market competition causes a con-traction in the employment of the unionized firm which, ceteris paribus, lowersunion utility. Therefore, union utility will increase only if this fall is compensatedfor by a sufficiently large increase in the negotiated wage.

2.2.3. Unionized duopolyConsider now the case where the second firm is unionized as well. Workers areorganized in firm-specific unions and bargaining is decentralized in the sense thateach firm bargains independently with the corresponding union. In addition, it


is assumed that the negotiations take place simultaneously, and that firm 1 andits union correctly anticipate the outcome of the bargain between firm 2 and itsunion when negotiating their own wage.

To keep the model analytically tractable, we consider the perfectly symmetriccase. In particular, we assume that union density is the same in both firms(μ1 = μ2 = μ), and that unions have identical objective functions (�1 = �2) andbargaining power (β1 = β2 = β). As before, the output of firm 1 in the event of astrike is ys

1 = (1 − μ)y∗1, where this time y∗

1 = (a − 2w1 + w2)/(3b). Substitutinginto the best-reply function of firm 2 gives

ys2 = a(2 + μ) + (2w1 − w2)(1 − μ) − 3w2

6b, (18)

which is the level of production of firm 2 in the event of a strike in firm 1. Thedisagreement payoff of firm 1 then follows as

π s1 = (a − w1)(1 − μ) [(a − 2w1)(2 + μ) − w2(1 − μ) + 3w2]

18b. (19)

As in the previous section, the solution for the steady-state Nash bargainedwage is obtained in two steps. First, we maximize the Nash maximand in (11),taking as given the wages negotiated in the previous contract period (w1,w2) andthe contemporaneous wage of the other firm (w2). This leads to the first-ordercondition for the current period Nash bargaining problem. Second, using thefirst-order condition, we solve for the steady-state bargained wage by imposingthat w1 = w1 and w2 = w2. This gives

wud1 = wud

2 = βθμ(1 + μ)8 − β(8 − (2 − θ )μ(1 + μ))

a. (20)

Comparing (16) and (20), one can see immediately that wud1 > wmd

1 as long asβ, θ and μ are strictly positive. Hence, firm 1 pays a higher wage in steady-stateequilibrium if the competing firm 2 is unionized, compared with a situationwhere firm 2 is non-unionized. There is therefore now an even larger interval ofunion density for which increasing product market competition increases wages.In appendix A it is shown that, for the special case of a rent-maximizing union(θ = 1/2), the same is true for union utility.

3. Endogenous union membership

In the analysis so far, we have adopted a deliberately parsimonious set-up inorder to highlight the key mechanism at work in our model. In this section, weshow under what conditions our results continue to hold if union membership isendogenously determined.


It is now well established in the literature on open-shop unions that, since thebargained wage is a pure public good and union membership involves a privatecost (the membership fee), any theory of voluntary union membership has todeal with the free-rider problem associated with the individual decision to joina union. In order to explain voluntary union membership in the context of anopen-shop union, the existing literature typically assumes that the union providesa private good to its members. Examples of this excludable good, available onlythrough membership, are privileged access to grievance procedures or reputationgains from complying with a social custom. The valuation of these benefits areassumed to vary across individuals, and a worker will become a union memberif the utility gain associated with the private good provided by the union morethan compensates for the utility loss caused by the membership fee. In order toformally explore how firm entry impacts on the individual membership decision,we draw on the work of Booth and Chatterji (1995), who develop a simple modelof union membership determination in the context of an open-shop union.

3.1. Union membership determination under a monopolyConsider union membership determination at monopoly firm 1 described insection 2.2.1. At the beginning of the contract period, each worker k employedat firm 1 in the previous period decides whether or not to join the trade union atthe establishment. Once the level of union density is defined, the current periodcollective wage w1 is determined by a decentralized Nash bargaining process.Subsequently, the firm unilaterally chooses employment according to the labourdemand curve.

An individual’s total utility uk is given by

uk ={

u(w1) if not a union member

u(w1 − α) + δk if a union member,

where u(·) is a continuous, twice differentiable indirect utility function, which isstrictly increasing and concave in the individual’s income, α is the monetary costassociated with being a union member, and δk denotes individual k’s valuation ofthe private good provided by the union. We assume that α is smaller than w1 andidentical for all individuals and that δ varies across individuals (and specificallythat it is uniformly distributed between 0 and 1). Workers not employed in theunionized firm 1 receive their reservation wage, and hence their utility is u(0).

The marginal union member is indifferent between joining the union or not,and hence δ∗ = u(w1) − u(w1 − α), where δ∗ denotes the critical level of δ abovewhich a worker will decide to join the union.11 Owing to the assumption that δ is

11 As in Booth and Chatterji (1995), we assume that the probability of being employed in thecurrent period is independent of the worker’s union membership status and that membershipfees are refunded to the unionized worker if they are eventually not employed by the firm.


uniformly distributed, we have μ = 1 − δ∗. The membership demand curve cantherefore be expressed as

μ(w1, α) = 1 − [u(w1) − u(w1 − α)] , (21)

where [u(w1) − u(w1 − α)] is normalized to lie in the interval [0,1]. Thus, byconcavity of the individual’s utility function, the membership demand functionis positively sloped in (w1, μ)-space. Intuitively, with a higher wage rate the utilityloss incurred from paying the membership fee is reduced, making it worthwhilefor workers with a lower valuation of membership to join the union.

A steady-state equilibrium in wages and membership is determined simultane-ously from the union membership demand function (21) and the bargained wagefunction (13). Given that both these curves are positively sloped in (w1, μ)-space,multiple equilibria may exist. For the comparative statics to be meaningful, wefollow Booth and Chatterji (1995) in assuming that the equilibrium satisfies thecondition φη < 1, where φ and η denote, respectively, the elasticity of the unionmembership demand function with respect to the wage rate and the elasticity ofbargained wage function with respect to union density. Intuitively, this assump-tion implies that the membership demand function is steeper in (w1, μ)-spacethan the bargained wage function at the equilibrium point. Equilibrium densityclearly depends on the position of each of the two curves. It can be easily checkedthat the equilibrium level of union density is increasing in β and θ and decreasingin the size of the membership fee α.

3.2. The impact of firm entry on wages and membershipWithin this setting, it is now straightforward to analyse the effects of market entryby a second firm. Figure 2 plots two alternative membership demand curves μA

and μB (where μB represents a situation with a lower union membership fee) andfurthermore replicates the bargained wage curves wum

1 and wmd1 from figure 1.

Under unionized monopoly, the equilibrium union densities are given by μI andμII , respectively. Entry of a second firm, as explained previously, changes thebargained wage curve; figure 2 represents this situation for the case where firm2 is non-unionized. With endogenous membership, the new equilibrium wageis given by the intersection point of the respective membership demand curve(μA or μB) with wmd

1 (not drawn, in order to avoid clutter). It is easily checkedthat the induced change in union density in both cases contributes to reinforcethe wage effect described in the previous sections. If the equilibrium level ofdensity under a monopoly is below μ∗, the shift of the bargained wage curveinduced by higher product market competition leads to higher union density andtherefore to an even more pronounced rise in the equilibrium wage. Conversely,if the equilibrium level of density under a monopoly is above μ∗, the shift of thebargained wage curve induced by increased product market competition causesa fall in union membership and hence leads to an even lower wage.


wr1

µ1µ∗µI µII

wum1

wmd1

µA

µB

FIGURE 2 The bargained wage with endogenous union membership

4. Efficient bargaining

As a further robustness check, we consider whether changing the scope of bar-gaining qualitatively alters the results. Specifically, we look at the case of ef-ficient bargaining, in which firms and unions negotiate over both wages andemployment. This section contains a description of the outcomes for the caseof a rent-maximizing union, with the detailed calculations being relegated toappendix B.

When we compare the wage outcome in a unionized monopoly and a mixedduopoly, the logic from the right-to-manage model carries through: the presenceof a competitor serves to improve the position of the union in the bargain, asthe firm faces a reduction in its fallback level of profits in the event of a strike asits competitor expands output. There is, therefore, a range of union density forwhich increased product market competition leads to higher wage levels. Underefficient bargaining this range turns out to be even higher than under the right-to-manage model. Specifically, we find that product market competition from anon-unionized firm leads to a higher bargained wage for μ ∈ (0, 1/2].

The same is not true, however, if the competitor is unionized. This is be-cause the hands of a non-striking firm are tied under efficient bargaining, andshort-term employment re-contracting is ruled out in the event of a strike at itscompetitor.12 Hence, the non-striking firm cannot expand production. Indeed,

12 The assumption that union contracts over wages and employment are binding is common in theunionized oligopoly literature (see, e.g., Zhao 1995).


we find that for levels of union density strictly between zero and one, the wagelevel is lower under unionized duopoly than it is under both monopoly and mixedduopoly.

5. Empirical analysis

5.1. Econometric specificationThe key prediction of our theory is that the effect of increased product marketcompetition on wages depends crucially on the level of union density in theindustry: more competition lowers wages in highly unionized industries, while itcauses wages to rise in industries with low union density. In this section we seekto test this hypothesis empirically. To that end, we estimate a Mincerian wageequation of the form

ln wijt = α.xijt + β.Concentrationjt + λi + νj + ηt + μijt, (22)

where, ln wijt is the log of the real hourly wage of worker i, employed in industryj in year t. The set of explanatory variables includes: xijt, a vector of individualattributes; λi, a pure individual unobserved effect; νj, an industry fixed-effect;and ηt a fixed time-effect. μijt is an exogenous disturbance term.

Our main interest, however, lies in the impact of Concentrationjt, which cap-tures the effect of the degree of product market competition in industry j, onwages. To this end we examine how β varies according to the extent of unioniza-tion.

5.2. DataThe empirical analysis is based on the United Kingdom, whose labour market isa suitable test bed for our purposes, since it is characterized by open-shop unionarrangements and firm-level bargaining (see, inter alia, Metcalf 2003). The dataare taken from the same sources as Guadalupe (2007), who recently examined theimpact of product market competition on the returns to skill in the UK, thoughnot the interaction between product market competition and unionization. Ourprimary source of information on wages comes from the New Earnings Survey(NES). The NES is a 1% random sample of employees and is selected on the basisof the last two digits of an individual’s National Insurance number. Since the sametwo digits are chosen each year, we are able to follow individuals over time andconstruct a panel. The NES includes detailed employer-reported informationon earnings, hours worked, age, occupation, and industry code. It also indicateswhether the worker held the same job in the preceding year.

We restrict our sample to full-time male workers, whose pay has not beenaffected by absence in the reference week. Our dependent variable is the log ofthe real hourly wage excluding overtime. The vector of worker characteristics


in the regression includes age and its square and a dummy variable indicatingwhether the worker is of low tenure.13 Although the NES does not contain dataon education levels, as in Guadalupe (2007), we use information on the workers’occupation to construct three skill measures, according to (i) the level of generaleducation required to perform a job and (ii) the job-related formal trainingneeded to perform a job.14

We have supplemented the individual-level data in the NES with informationon industry union density and concentration ratios, both computed at the 3-digitlevel of the SIC 1992 classification. The information on unionization is derivedfrom the UK Labour Force Survey, while our measure of product market com-petition is the five-firm industry concentration ratio derived from the AnnualRespondents’ Database (ARD).15 The shortcomings of using such a concentra-tion ratio as a measure of product market competition are well known: firstly,doubts about whether it is an exogenous measure of market structure; secondly,the problem of appropriately defining the economic market for an industry’sproduct16; finally, the fact that concentration indices ignore the effect of inter-national competition (Perloff, Karp, and Golan 2007). Its empirical applicationin this paper is therefore made bearing these caveats in mind. Since the concen-tration measures are available only for manufacturing, our analysis is restrictedto this subset of industries. Also, since the industrial classification in the NESchanged from 1996 onwards, we analyse the period 1996–99. The resulting panelcomprises 31,613 workers, yielding a total of 80,071 worker-year observations.

In order to account for worker-specific unobserved heterogeneity, we exploitthe longitudinal nature of the data and estimate an individual fixed-effects model.Furthermore, we introduce a full set of year and 3-digit industry-dummies tocontrol for time- and industry-specific effects. Thus, identification of the mainparameter of interest comes from the within-industry variation of concentrationratios over time.

5.3. Descriptive statistics and econometric resultsThe theoretical model presented above indicates that the level of union densitybelow which increased competition increases wages is approximately one-third inthe right-to-manage model and one-half in the efficient bargaining model. Whilethe stylized nature of the theory would suggest that caution is needed in under-taking a strict transposition of these cutoffs to real-world data, they nevertheless

13 The NES does not contain complete information on tenure, but records whether the individualholds the same job as in the previous year. We code the individual as having low tenure if theirjob has changed. We are able to compute alternative measures of tenure (notably years of tenureand its square), though the estimated impact of product market competition on wages is notsensitive to this choice.

14 See appendix C for further details on the definition of skill groups, which are based on Elias(1995).

15 Defined as the share of industry employment accounted for by the five largest firms. The authorswould like to thank Maria Guadalupe for access to the five-firm concentration ratio data.

16 Ideally, this should include all firms that (potentially) constrain the price of the product.


TABLE 1Summary statistics

Average union density ≤ 40% Average union density >40%

Concn ratio≤ 20%

Concn ratio> 20%

Concn ratio≤ 20%

Concn ratio> 20%

Mean St. Dev. Mean St. Dev. Mean St. Dev. Mean St. Dev.

ln(real hourlywage)

2.09 0.45 2.25 0.52 2.20 0.42 2.24 0.41

Age 39.80 11.73 39.13 11.18 41.08 11.07 40.87 10.87Low tenure 0.14 0.35 0.15 0.36 0.11 0.32 0.12 0.33Low skill 0.45 0.50 0.45 0.50 0.51 0.50 0.47 0.50Medium skill 0.37 0.48 0.27 0.44 0.31 0.46 0.34 0.47High skill 0.17 0.38 0.28 0.45 0.18 0.39 0.19 0.39Concentration

ratio0.09 0.05 0.32 0.09 0.12 0.03 0.44 0.19

Union density 0.24 0.09 0.24 0.12 0.44 0.04 0.54 0.11

Observations 39596 10231 11187 19057

constitute a natural starting point for the empirical work. We therefore take anintermediate point in this range of union density (40%) to define our ‘low’ and‘high’ unionization sub-samples. Table 1 presents some descriptive statistics forboth of the sub-samples that are used in the regression analysis. Note that, in theraw data, less concentrated industries have lower levels of wages whether unionpresence is high or low.

To examine further the relationship between product market competition andwages, we estimate equation (22) controlling for other determinants of wages,while allowing the impact of concentration to change above and below the 40%union density threshold.17 The results are reported in table 2, with the standarderrors clustered at the industry level.18

Focusing first on columns (1) and (2), we find, as would be expected, thatreal hourly wages are higher for older workers, though the impact diminisheswith age. Low-tenure workers also earn lower wages, as do those of lower skill.Further, consistent with the theory presented, wages are negatively correlatedwith industry concentration in industries with low union density, while they arepositively associated with industry concentration in industries with higher union-ization rates, an effect which is statistically significant once individual effects arecontrolled for. These findings are confirmed in column (3) where the data aresplit into two sub-samples, with the impact of concentration significantly lowerand negative in the low-unionization sub-sample.19

17 We use average union density by industry over the sample period.18 This is necessary as our key variable, the concentration ratio, varies at the industry level

(Moulton 1986).19 A test of equality of effects rejects with a p-value of 0.007


TABLE 2The determinants of wages [ln(real hourly wage)]

(3)

Average union Average unionCoefficient (1) (2) density ≤ 40% density > 40%

Age 0.0451∗∗∗ 0.0478∗∗∗ 0.0526∗∗∗ 0.0278∗∗∗

(0.0018) (0.0046) (0.0056) (0.0053)Age squared/100 −0.0499∗ −0.0513∗∗∗ −0.0518∗∗∗ −0.0460∗∗∗

(0.0021) (0.0053) (0.0073) (0.0045)Low tenure −0.0498∗∗∗ −0.00716∗∗ −0.0106∗∗ −0.00154

(0.0053) (0.0032) (0.0040) (0.0057)Medium skill 0.1633∗∗∗ 0.0370∗∗∗ 0.0317∗∗∗ 0.0340∗∗∗

(0.0106) (0.0050) (0.0070) (0.0073)High skill 0.6271∗∗∗ 0.1103∗∗∗ 0.1139∗∗∗ 0.0956∗∗∗

(0.0161) (0.0074) (0.0104) (0.0111)Concentration ratio −0.2914∗ −0.1267∗ −0.1466∗∗ 0.1480

(0.1513) (0.0651) (0.0610) (0.0896)Concentration ratio∗ 0.2300 0.3073∗∗∗

average union density >40% (0.2023) (0.1166)Constant 0.9197∗∗∗ 1.3321∗∗∗ 0.9491∗∗∗ 1.9535∗∗∗

(0.0420) (0.1584) (0.1597) (0.1830)Industry effects Yes Yes YesIndividual effects No Yes YesObservations 80071 80071 49827 30244

Standard errors clustered on industry in parentheses. ∗∗∗p < 0.01, ∗∗p < 0.05, ∗p < 0.1. Year dummiesare included.

To investigate whether our results are sensitive to the choice of the union den-sity threshold, we re-estimate the model, defining our sample based on a rollinginterval of union density, that is, 0–20%, 5–25%, and so on. To facilitate presen-tation of these results, figure 3 plots the estimated coefficient on concentrationand the corresponding 95% confidence intervals for each of these sub-samples.20

The change in the impact of industry concentration is apparent. At low levelsof union density the impact of increased concentration on wages is negative,while for higher levels of density the wage-effect of increased concentration issignificantly positive, as the model would predict.

6. Concluding comments

In this paper we have analysed the impact of changes in product market com-petition on wage outcomes when workers are represented by open shop unions.In such a situation, unionized establishments continue to operate in the event

20 In figure 3: union density is the midpoint of the interval; the standard errors are clustered byindustry.


FIGURE 3 The variation in the effect of industry concentration on wages by union density

of a strike with their non-unionized workers, and so the wage outcome is af-fected by the level of union density. Additionally, the bargain is now affectedby the extent to which the firm’s competitors expand their own production inthe event of a strike. This introduces a previously unnoticed mechanism wherebyproduct market competition impacts on the negotiated wage. The implicationsof this extension to the simple union-firm bargaining framework are profound.In contrast to the prediction of the standard model, increases in product marketcompetition may now increase wage levels. The model presented in this papercan therefore accommodate the diverse existing empirical evidence regarding theimpact of product market competition on bargained wages. Furthermore, it issupported by new evidence based on UK individual data for the 1996–99 periodthat is presented in the paper.

While the open-shop assumption is a natural way of uncovering this previouslyunnoticed mechanism, we conjecture that the main insights of the model arealso relevant for other applications of union-firm bargaining. In effect, for ourresults to hold, we need two ingredients: Firstly, that unionized firms continueto operate at reduced capacity during a dispute; secondly, that the shortfall inoutput imposed by the dispute induces competitors to expand their own sales.The latter of these ingredients arises directly from the standard Cournot model ofcompetition. The former, besides being supported by empirical evidence (see fn 3,above), is a prevalent feature of many other influential applications of union-firmbargaining in a bilateral monopoly set-up. In fact Moene (1988) and Cramtonand Tracy (1992) convincingly argue that a significant number of labour disputestake the form of ‘holdout,’ ‘work-to-rule,’ or ‘go-slow’ practices, where workerscontinue to operate at reduced productivity while bargaining over a new collective


agreement. In addition, casual observation suggests that in many disputes, aunion engages in ‘partial strikes’ involving work stoppages during nominateddays (or indeed during part of some working days). Lastly, as argued by Colesand Hildreth (2000), even when firms fully stop production during a strike, theycan continue to sell from their inventory of finished goods and hence have apositive disagreement payoff. In all of these situations, the disagreement payoffof the firm would be influenced by the extent to which the firm’s competitorsexpand production and, thus, the main mechanism highlighted in this paperwould be expected to apply.

Appendix A: Impact of product market competition on union utility

We may straightforwardly show for a mixed duopoly model that, for sufficientlylow levels of union membership, increasing product market competition increasesunion utility. For simplicity, we confine attention to the case of symmetric Nashbargaining (β = 1/2) and a rent maximizing union (θ = 1/2). Substitution of(13) into (6) yields an expression for union utility in the monopoly case:

�um1 = a

2√

b

(4 + μ2

2 + μ2

) 12(

μ2

4 + μ2

) 12

. (A1)

Substituting (16) into (10) yields the equivalent expression for union utility in thepresence of a non-unionized competitor:

�md1 = a

2√

b

(μ(1 + μ)

4 + μ(1 + μ)

) 12(

8 + μ(μ + 1)4 + μ(μ + 1)

) 12

. (A2)

One can show by comparison of (A1) and (A2), that union utility is higher undera mixed duopoly when μ ∈ (0, 0.187).

In the case of unionized duopoly, we again confine our attention to the case ofsymmetric Nash bargaining (β = 1/2) and a rent-maximizing union (θ = 1/2).Substituting (20) into (10) yields an expression for union utility in the presenceof competition from an equally unionized firm:

�ud1 = a

2√

b

(μ(1 + μ)

48 + 9μ(1 + μ)

) 12(

8 + μ(μ + 1)16 + 3μ(μ + 1)

) 12

. (A3)


Comparison of (A3) and (A1) allows us to conclude that, if Nash bargainingis symmetric and the union maximizes rents, the presence of product marketcompetition from an equally unionized firm leads to higher union utility if μ ∈(0, 0.193).

Appendix B: Efficient bargaining

As a robustness check of our results, we repeat the analysis assuming efficientbargaining. As in the right-to-manage model, we consider a sequence of contractperiods. In each contract period, bargaining is over both wages and employment.For simplicity we assume that the union maximizes rents (θ = 1/2). This impliesthat output is independent of the bargained wage and equal to its competitivelevel

y∗1 = a

2b. (B1)

Equilibrium is given as the generalized Nash solution of the cooperative gameplayed by the firm and the union:

wr1 = arg max

w1

{�

β

1

(π1 − π s

1

)1−β}s.t. y1 = y∗

1, (B2)

where, as before, the union disagreement payoff is normalized to zero. Using (2),(3), and (B1) we get

π1 = 1b

(a2

)2− w1

( a2b

)(B3)

�1 = w121

( a2b

) 12. (B4)

Using the same reasoning as in the right-to-manage model, the disagreementpayoff of the firm is given by

π s1 = a(1 − μ)(a(1 + μ) − 2w1)

4b, (B5)

and the steady-state bargained wage under monopoly follows as

wum1 = βμ2

4 − 2β(μ − 2)a. (B6)


Introducing competition by a non-unionized firm 2, which pays all its workersthe reservation wage (w2 = wc = 0), yields equilibrium outputs of

y∗1 = y∗

2 = a3b

. (B7)

When evaluated at (B7), firm 1’s profit and union utility are given by

π1 = 1b

(a3

)2− w1

( a3b

)(B8)

�1 = w121

( a3b

) 12. (B9)

In the event of a strike, the unionized firm produces ys1 = (1 − μ)y∗

1, where y∗1 =

a/(3b) is the level of employment in the previous period. From (7), this inducesthe non-unionized firm to produce ys

2 = (1 + μ/2)y∗2. The conflict payoff of the

unionized firm can now be derived as

π s1 = a(1 − μ)(a(2 + μ) − 6w1)

18b. (B10)

Solving for the steady-state bargaining wage yields

wmd1 = βμ(1 + μ)

6(2 − β(μ − 2))a. (B11)

Comparing (B6) and (B11) shows that product market competition from a non-unionized firm leads to a higher bargained wage if μ ∈ (0, 1/2).

If firm 2 is unionized as well, and if union contracts over employment are bind-ing, the rival firm cannot expand production in case of a strike. The disagreementpayoff of firm 1 becomes

π s1 = a(1 − μ)(a(1 + μ) − 3w1)

9b. (B12)

This exceeds the disagreement payoff under mixed duopoly and under monopolyand, as a consequence, the steady-state bargained wage is lower than under mixedduopoly and under monopoly. Specifically, we obtain

wud = βμ2

6 + 3β(μ − 2)a. (B13)


Appendix C: Definition of skill groups

TABLE C1Construction of skill groups in the NES

Skill SOC codelevel Major groups (minor gr.)

High Managers and administrators 10, 11, 12, 15, 19(excluding office manag. /prop. in agric. and services)Professional occupations

Medium Office managers and manag. /prop. in agric. and services 13, 14, 16, 17Associate professional and technician occupations 30-39Craft and relations occupations 50-59Buyers, brokers, sales representatives

Low Clerical, secretarial occupations 40-46, 49Personal and protective services occupations 60-67, 69Sales occupations (except buyers, brokers, sales reps) 72, 73, 79Plant and machine operatives; other occ. in agric., forestry, fishing 80-89, 90Other elementary occupations 91-95, 99

SOURCE: Elias (1995).

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Open-shop unions and product market competition

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