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The theory of the open shop trade union reconsidered
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T,ABOUR ECONOMICS ELSEVIER
Labour Economics4 (1997) 71-84
The theory of the open shop trade union reconsidered Giacomo G. Cornet Department of Economics, University of Bonn, Adenauerallee 24- 42, D-53113 Bonn, Germany
Received 29 June 1994;revised 27 June 1996
Abstract
This paper provides a game-theoretic foundation of the social custom approach to trade union membership. The reputation effect of belonging to the union is endogenized as the outcome of a signalling game among the workers. The signalling value of being a union member depends in equilibrium on the union density, but the form of this relationship might differ from what the previous literature assumed. The extent to which comparative statics and critical-mass effects change is also investigated. JEL classification." J50; J51 Keywords: Trade union membership; Social custom; Signalling
I. Introduction
The rapid decline in the 1980s of the closed shop as an institutional device to organize workers into trade unions urged economists to explain unionism as a social arrangement occurring essentially on a voluntary basis. The basic difficulty of this enterprise was to escape the free-rider paradox implied by the public good characteristics of the union bargain with employers, i.e. that the benefits of collective negotiations accrue to union members and nonmembers alike while members alone have to bear the bargaining costs. The social custom approach to union membership, as developed by Booth (1985), Booth and Chatterji (1993), Naylor (1989, 1990), Naylor and Cripps (1993) offers an interesting solution of 0927-5371/97/$17.00 Copyright © 1997 Elsevier Science B.V. All rights reserved. PH S0927-5371 (96)00023- 1
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G.G. Corneo / Labour Economics 4 (1997) 71-84
this problem. Following an idea formulated by Akerlof (1980), these authors postulate that union members enjoy a better reputation than nonmembers, which directly enters the workers' utility function. This reputation effect derives from complying with a social custom that invokes workers to express mutual solidarity by joining collective actions. The worker's reputation acts as an incentive private good delivered by membership in the union. While in addition to social custom effects there might be pecuniary private incentive benefits to joining a union, the former were perceived by these authors as a compelling explanatory factor of unionization. A major finding of this approach is the presence of multiple union equilibria, and the possibility of a minimum union size below which a union is not viable. This implies that if the closed shop is made illegal in a situation of wide union presence, this will not have ravaging consequences for union membership, while the converse applies in a situation of already weak union presence. The explanation of the finding runs as follows, Suppose that the impact of reputation on worker utility is an increasing function of the union density, because when the number of people complying with the social custom grows, deviants are more severely punished with loss of reputation. Suppose also that the reputation effect is absent when union density is zero. In this case, given that nobody else joins the union, nobody has an incentive to join, and zero density is an equilibrium. For very small levels of density, the reputation effect may still be insignificant, which implies that the no-union equilibrium is stable. However, if the initial density is sufficiently large, the reputation effect may offset membership costs. Therefore, open shop unions have to guarantee themselves a threshold level of membership in order to be sustainable. 1 In the aggregate, this equilibrium property might possibly explain the intriguing stylized fact of diverging union densities across countries. 2 The social custom theory of the open shop trade union has proved to be supported by empirical evidence and rich in policy implications. On the other hand, its theoretical underpinnings are not completely satisfactory since the reputation effect, which is necessary to overcome the free-rider problem, lacks proper microfoundations. Indeed existing social custom models are models of complete information, which is at odds with the fact that the phenomenon of reputation can only be accounted for in contexts of incomplete information. The problem is that the term 'reputation' in these models covers two distinct notions.
An antecedent formalization of this type of effects is due to Schelling (1978). 2 An instructive comparison can be made between countries like Sweden and Denmark on the one hand, and France and the United States on the other. In 1970 union density for nonagricultural workers was about 70% in the former countries and about 30% in the latter. In 1987 the percentages were, respectively, 95% and 17%. See Blanchflower and Freeman (1992) for an empirical analysis and Corneo (1995) for a theoretical approach.
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First, it reflects the opinions held by workers about union members. Secondly, it represents the quality of social interactions for a worker, depending on his union status. The existing literature formalizes the latter notion - the additional term in the utility function - but does not explicitly deal with the first one. Rather, it adopts a kind of reduced form by positing that the effect of membership on the worker's utility ultimately increases with the union density. The main goal of the present paper is to disentangle these different notions by looking at unionization as a game played by the workers under incomplete information. In this sense, the paper develops a possible microfoundation of the social custom model of union membership. The basic idea can be formulated with reference to a generic problem of collective action. Suppose that individual participation in a collective action is socially visible. When an individual's predispositions are unobservable, his decision whether to join the collective action may affect the beliefs that others hold about his type. In fact, individuals may differ with respect to the utility loss inflicted upon them by participation in the collective action, so that a possibility to separate different types emerges. In turn, the beliefs held by others may determine the gains obtained by the individual in further social interactions. For instance, individuals may care about social esteem, which itself may depend on public perceptions about an individual's true predispositions. These gains correspond in my model to the reputation effect. If beliefs are formed rationally, this reputation effect will depend, in equilibrium, on aggregate behaviour, which gives a relationship between a worker's reputation and union density. 3 I model voluntary unionization as a signalling game following an approach developed by Corneo and Jeanne (1994) in a different context. The better reputation of union members is derived by the signalling properties of the equilibrium. It is shown that, in general, the reputation effect may be an increasing or a decreasing function of union density, so that the restrictions imposed in previous models cannot be justified on pure theoretical grounds. The reputation effect turns out to be increasing with density in conformist worker communities, which ostracize workers perceived as egoists. The reputation effect is a decreasing function of density in elitist communities, in which an extraordinary prestige is enjoyed by those who are perceived as the most solidaristic individuals. This has some interesting implications for the characterization of equilibria. First, multiplicity of union equilibria is only possible in conformist communities; if the community is of the elitist type, the critical-mass effect fails to exist. Secondly, certain union equilibria may exhibit bizarre comparative statics: increasing the costs of membership, e.g. by requiring harder class struggle from union members, raises the signalling value of joining the union and thereby increases union density.
3 Naylor (1989) mentions the possibility of a signalling interpretation of the social custom model.
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Finally, it is shown that for the ranking of equilibria, from the workforce's viewpoint, the form of the reputation effect is of no importance, which considerably simplifies the welfare analysis of unionism.
2. Endogenizing the reputation effect 2.1. T h e m o d e l
There is a continuum of workers indexed by i ~ [0, 1], each of them facing the decision of taking part in a collective action. For concreteness, the collective action is the formation of a trade union for wage bargaining purposes. Each worker acts independently and without coercion, and the gains from the collective action accrue in the same amount to every worker, irrespective of his behaviour. Each single decision has a negligible impact on the gains produced by the collective action. Participation in it affects individual well-being through three distinct channels. First, there is a net pecuniary cost, e.g. in the form of a membership fee. Secondly, there is a utility loss stemming from the direct involvement with the collective action: union members are required to take part in the decision process accompanying collective negotiations and are supposed to actively participate in protest actions and strikes decided by the trade union. This is the cost in terms of personal time and energy spent together with others in order to achieve collective goals. Thirdly, there is a reputation effect that is induced by the social visibility of participation in the collective action. Individuals have separable preferences, summarized by the following utility function: Ui = Yi -
Oiai q- e r i
(1)
where Yi = w - ~i c is a worker's income, equal to the wage (w) minus the membership fee (c) if the worker is a union member (~i = 0 if the individual does not join the union and ~i = 1 if he does); a i = ~i a is the amount of personal involvement required by participation (a > 0), measured e.g. in time units; r i = r(~ i) is the worker's reputation, depending on his membership in the union; 0 and e are strictly positive parameters that represent the worker's willingness to pay for less personal involvement and better reputation. The purpose of the union consists of raising the wage above its competitive level. The union wage is determined in a negotiation between the union and the firm. Instead of modelling it explicitly, I simply posit that the negotiated wage can be expressed as an increasing function of union membership: w = w(IX), where tx = f d ~ i d i is the union density. Examples of wage bargaining models in which the wage increases with union density are Cornet (1993) and Naylor and Raaum (1993). This relationship is motivated by the potential harm that the union can
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inflict upon the firm in the case of a disagreement. The larger the union, the more important its threat, which in turn improves the bargaining position of the union. Empirical studies generally confirm the notion that union membership has a positive impact on the union wage mark-up. 4 At this stage the model is equivalent to the basic social custom model of union membership: in the absence of a reputation effect, the dominant strategy for each worker is to free-ride on union members, since the impact of the individual membership decision on the bargained wage is nil whereas membership costs are strictly positive. Workers are assumed to differ with respect to their disutility from personal involvement with the collective action. Parameter 0 is distributed in the workforce according to a cumulative distribution function F(0). This parameter captures the individual's distaste for personal sacrifice in order to achieve collective aims. Thus, it can be seen as inversely related to an individual's degree of solidarity toward his workmates. Individuals are ordered according to their degree of solidarity in the following way: i < i ' , ~ 0 i < 0i,. Hence i is the rank of the individual with respect to his sentiments of solidarity: i = 0 is the most solidaristic individual and i = 1 is the least solidaristic individual in the community. While the degree of solidarity is private information of the worker, his decision to join the collective action is observed by the entire workforce. The collective action thus gives workers an opportunity to transmit credible information about the own degree of solidarity. The beliefs of fellow workers may matter for several reasons. First, solidarity may be correlated with the sense of duty and the cooperativeness of the individual, which may induce higher pecuniary payoffs in situations of the repeated prisoners' dilemma type (Frank, 1987). Secondly, others' beliefs may determine the social status of the individual. This is the interpretation to which I will stick hereafter. 5 In this case, the reputation utility does not take a pecuniary form. It consists of the esteem and sympathy awarded to the worker as a prize for his sentiments; it is a socially provided private good. Following sociologists, an individual's status is defined as the deference shown by others according to the individual's rank in the social hierarchy. 6 Formally, r(t~i) = E ( s ( i ) It~i)
(2)
where E(.I~) is the expectation conditional on the observation of ~, and s(i) is a continuous function defined on the unit interval, referred to as the status utility.
4 The logic of the model is unaltered if the wage also increases with a, the activity of union members. s Frank (1985) gives a detailed argument for the status orientation of individuals. 6 See e.g. Coleman (1990). Implicit in this definition is the idea that society is characterized by a unitary value system. This viewpoint goes back to Parsons (1951). While one might spell out various subcultures that are present in the workforce, it is convenient for modelling purposes to start with the hypothesis of a unitary value system.
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This utility represents the social esteem obtained under complete information by a worker according to his rank. Thus, it may be thought of as a decreasing function, i.e. more solidaristic workers enjoy a better treatment by their workmates. The assumption that social esteem depends on public perceptions about an individual's preferences rather than on his actions was put forward in a recent article by Bernheim (1994). The justification is that social esteem seems to depend on the motivations that are supposed to trigger an individual's behaviour. The natural explanation is that motivations are the best predictors of the individual's future actions. 7 The situation described so far can be analyzed as a game with incomplete information played by a continuum of players. Informally, a Bayes-Nash equilibrium of this game is defined as a membership decision for each worker that maximizes his utility function, given both the decisions of others and their beliefs about a worker's type. In turn, beliefs are deduced from membership decisions using Bayes's law. 2.2. The decision to join To begin with the equilibrium analysis I consider beliefs, and hence the reputation utilities, as given. Workers decide to adhere to the trade union if the reputation effect, which is the signalling value of belonging to the union R - r(1) r(O), is large enough. As the maximization of Eq. 1 readily shows, the condition for individual i to become a member is -
C+ Oia R> - -
(3)
E
Suppose that the reputation effect is positive. From the above condition it is not difficult to see that individual i participates in the collective action if and only if his degree of solidarity is larger than a threshold level 0 determined by eR - c =
-
-
a
(4)
Thus, the portion of individuals who join the union may simply be written as /x = F ( O ) .
(5)
For given beliefs, union density is a decreasing function of both the pecuniary cost of membership and the required amount of collective action, and an increasing function of the reputation effect.
7 The idea of a prize for solidarity is reminiscent of the social exchange approach to voluntary cooperation, as developed in a formal model by Holl~inder(1990). In his model, cooperativebehaviour is motivated by the expectation of sympathy prompted by the stimulus-response mechanism of the emotional system. Conversely, in the present model, reactions of deference are rationally determined.
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2.3. Beliefs formation Now, I examine how the reputation utilities are determined. As shown by Eq. (3), the workers who adhere to the union are at the same time sending a simple message, which is that they belong to the more solidaristic part of the workforce. The signalling value of this behaviour, which is the difference between the average status utility of union members and that of those who choose to free-ride, may thus be written as
f~s(i)di R(~)
fls(i)di
/x
1- ~
1
=
/x(1 - / x )
fo'~[ s( i) - ~]di
(6)
where ~ is the average status utility over the whole workforce. Notice that if s(i) is decreasing, the reputation effect is positive, as previously supposed. As a consequence, union members endogenously obtain a better reputation than nonmembers. Since the size of the reputation effect is a function of the total number of workers who join the union, Eq. (6) may be seen as the analogue of the exogenously specified relationship that appears in the social custom literature. However, in that literature the postulated relationship is positive, whereas this need not be the case in the present model. Whether the reputation effect becomes stronger or weaker when the union density grows, depends in general on the structure of the preferences for ranks that prevails in the workers' community. For the sake of illustration, consider the following example in which the status utility is given by
s( i) = a - f l i - y i 2
(7)
which implies the following reputation effect: =
+
~'(1 + ~ )
(8)
It follows that the reputation effect increases with union density if and only if Y is positive, that is if the status utility is concave. The special case of a reputation effect independent of union density obtains only when the status utility is linear. This result may be interpreted as follows. If the status utility is concave, it is more costly to lose one position in the hierarchy when one is classed low than when one is classed high. When the proportion of those who adhere to the collective action increases, the status awarded to both members and nonmembers diminishes, but the status awarded to nonmembers decreases more rapidly. Hence the reputation effect increases with membership. In essence, unionization is induced by the fear of being identified with the most egoistic fringe of the workforce. It may be said that social interactions create a pressure to conform with others, and unionization is motivated by conformism. If the status utility is convex, the converse applies.
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The reputation effect is a decreasing function of membership because individuals are more sensitive to changes in their ranking when they belong to the top of the social hierarchy than when they belong to the bottom. When union density decreases, the status of both members and nonmembers increases, but the status awarded to members raises more rapidly. Hence the reputation effect grows when membership falls. In this case social interactions create a pressure for distinction. One might say that unionization is motivated by elitism, i.e. the desire to show that one belongs to the avantgarde of the working class. Are rank preferences of this type a mere theoretical curiosity? In the history of the labour movement situations did occur in which the working class attributed an extraordinary prestige to the individual who personified its leader, which might be taken as an indication of a convex status utility. 8 Thus the reputation effect may grow or decline when union membership increases, depending on how social esteem is awarded in the workers' community. The argument put forward in the social custom literature is not completely appropriate because it neglects the fact that when union density grows, the social esteem awarded to union members diminishes, since their average quality is lowered. Decisive for the impact on the reputation effect is whether social esteem diminishes more rapidly for members or for nonmembers. If the social esteem of nonmembers decreases more rapidly, the relationship between reputation effect and union size is as postulated in the social custom literature. Otherwise, the relationship is exactly the opposite.
3. Union membership 3.1. Determination o f equilibrium
Equilibrium of the union membership game may take one of two possible forms. First, both the decision to join and the alternative decision may be chosen by nonempty sets of players. In this case, only the most solidaristic portion of the workforce participates in the collective action. This outcome is called a semi-separating equilibrium. Second, one of the two possible decisions may be selected by the empty set. In this case no separation across types occurs and a pooling equilibrium obtains. In a semi-separating equilibrium, individual decisions are optimal given others' behaviour and beliefs; in turn, beliefs are consistent with actual behaviour. The
8 Examplesof union leaders who became labour heros are Jimmy Hoffa (InternationalBrotherhood of Teamsters,US) and Arthur Scargill (National Union of Miners, UK).
G.G. Corneo/ LabourEconomics4 (1997) 71-84
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~t
1
!q. (11) ~
Eq. (10)
0
)R
Fig. 1. Non-existenceof a semi-separatingequilibrium. equilibrium conditions are given respectively by Eqs. (5) and (6). Hence, the following fact can be established: Proposition 1. In a semi-separating equilibrium of the union membership game, the union density and the reputation effect are a pair (/x*, R * ) ~ ] O , I [ X R + determined by the following conditions: ER* - c )
/x* = F
,
a
1
(9)
fo~*[s(i)
~]di.
(10)
Clearly, the existence and uniqueness of the semi-separating equilibrium are not guaranteed in general. Figs. 1-3 plot Eqs. (9) and (10), and illustrate three types of outcomes that can occur according to the values of parameters. In Fig. 1 no semi-separating equilibrium exists because the reputation effect cannot offset the participation costs induced by the collective action. In Fig. 2, a semi-separating equilibrium exists and is unique. It may be noticed that if the status utility is of the
~t
1
0
- - - ' ~ , /~
Eq. (10)
~-R
Fig. 2. Uniquenessof the semi-separatingequilibriumunderelitism.
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G.G. Corneo / Labour Economics 4 (1997) 71-84
ta Eq. (11)
Eq. (10)
)R Fig. 3. Multiplicity of equilibria under conformism.
elitist type (R'(Ix) < 0) and a semi-separating equilibrium obtains, uniqueness is implied. The outcome depicted in Fig. 3 presents a multiplicity of semi-separating equilibria. It is readily seen that conformism (R'(Ix) > 0) is a necessary condition for multiple equilibria to appear. I turn now to the pooling equilibria, in which Bayes's law cannot be applied. The following result is proved in the appendix:
Proposition 2. ( A) A pooling equilibrium of the union membership game with Ix* = 0 exists if and only if c + Ooa
E(s(i)ll) < ~ + -
E
(11)
(B) A pooling equilibrium with Ix* = 1 exists if and only if ( c + 01a ) E(s(i)lO) _< ~ -
E
(12)
The existence of a pooling equilibrium depends on how one chooses to specify beliefs held out of equilibrium. If beliefs are unchanged when out-of-equilibrium behaviour is observed, they are called passive conjectures. As shown by Eqs. (11) and (12), under passive conjectures only the pooling equilibrium IX* = 0 exists. This is simple to understand. Under passive conjectures no reputation effect of union membership arises, so that the free-rider problems remains unsolved. Thus, one can always find beliefs when Bayes' rule cannot be applied, such that no-union is an equilibrium.
3.2. Some implications A standard result of the social custom literature on union membership is the existence of a critical mass, i.e. a minimum union density under which a trade
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union is not viable. Studying this property requires introducing some out-of-equilibrium dynamics or a stability criterion. For instance, one might conceive that at each point in time deference is shown only on the basis of an estimation of the current union density, which is gradually adjusted toward its true value. 9 The stability analysis easily follows by inspection of figures like Figs. 2 and 3. It implies that the semi-separating equilibrium under elitism (Fig. 2) is stable. In the conformist case depicted in Fig. 3 only the upper semi-separating equilibrium is stable. The other equilibrium is unstable: starting from any density level below the equilibrium value, an erosion of union membership ensues and the union disappears in the long run. Conversely, a small increase of union density above that equilibrium value leads to a growth of membership until the upper equilibrium value is reached. The unstable equilibrium identifies a critical mass for the trade union. The model's message is that if the status utility is of the elitist type ( R'( It) < 0), the critical-mass effect of unionization fails to exist. The presence of conformism ( R ' ( l ~ ) > O) is a necessary but not a sufficient condition f o r a critical-mass effect to arise. The form of the status utility is also important for the results of comparative statics. The parameters of the model (c, a, e) affect equilibrium only through the determination of the threshold level 0. In fact, as Proposition 1 shows, parameter changes merely affect Eq. (9). Hence, comparative statics can easily be performed by shifting the corresponding curve depicted in figures like Figs. 2 and 3. Standard results apply to the stable semi-separating equilibria under both elitism and conformism. Union density is increased by lowering membership costs in the form of c or a and by increasing the weight of social factors in the form of E, since all these changes shift the curve representing Eq. (9) upwards. The opposite is true for unstable equilibria, which are possible only under conformism. In these equilibria, increasing the self-sacrifice demanded of union members turns out to increase union density. The reason is that an increase in a amplifies the reputation effect of union membership and this effect more than offsets the utility loss due to the increased personal involvement with union activities. It is worthwhile examining how the equilibria of the union membership game can be ranked according to a welfare criterion. Supposing this criterion to be the sum of worker utilities, one can show that the ranking of possible equilibria is independent of the size of the reputation effect. To see this formally, write the aggregate worker welfare in an equilibrium as W=
(w-
c-
Oia + e r ( 1 ) ) d i +
(w + er(0))di.
(13)
9 If /2 is the estimation of union density, dfx/dt = ~( izt - fxt) gives the adjustmentprocess, with /3>0.
G.G. Corneo / Labour Economics 4 (1997) 71-84
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Define ~9(/x) as the cumulated willingness to pay for less personal involvement with the collective action:
O ( I z ) =- foUOidi.
(14)
Using Eqs. (2), (6) and (14), worker welfare can be rewritten as
W = w( Ix) - g c -
~9( ~ ) a + e~.
(15)
When comparing different equilibria, the last term of this expression can safely be neglected as it does not depend on the union density. Hence, the ranking of equilibria can be calculated without reference to the social factors of unionization, i.e. without knowledge of E and s(i) or even 5. The reason is that social esteem is a relative phenomenon: when some workers obtain more, others have to obtain less, and the aggregate amount of esteem does not vary. For a welfare analysis of unionism, only its effects on wage formation and on the costs of the collective action need to be evaluated. For instance, comparing the pooling equilibria one obtains that full unionization of the workforce dominates the absence of a union if and only if w(1) - w(0) > c + aO(1).
4. Conclusion I have provided an incomplete information model of trade union membership in which workers care about social esteem as well as the costs of joining collective actions associated with trade union membership. Esteem shown by fellow workers depends on their beliefs about a worker's predispositions toward self-sacrifice in order to achieve collective goals. Since predispositions are unobservable, taking part in union activity signals predispositions and therefore affects the social esteem enjoyed by the worker, This theoretical framework suggests how one can rationalize a basic assumption of the social custom literature: that the reputation effect of union membership increases with the union density. Furthermore it makes clear that, depending on societal values, various shapes of the reputation effect may arise, and these may differ from those previously assumed in the literature. If conformism prevails in the workers' community, the reputation effect of belonging to the union increases with the union density. However, if elitism prevails the opposite applies. The shape of the reputation effect is crucial for the properties of the signalling equilibrium. Under conformism, the results put forward by the social custom literature continue to hold in this model. In particular, multiple union equilibria are possible and a critical-mass effect may arise. Under elitism, there is uniqueness of the equilibrium with an intermediate level of density and the critical-mass effect is absent. On the other hand, the shape of the reputation effect is of no importance for the ranking of equilibria: the optimal union size does not depend on the particular mechanism by which social esteem is allocated to the workers.
G.G. Corneo / Labour Economics 4 (1997) 7 1 - 8 4
83
The theory of union membership detailed in this paper makes a number of predictions that are amenable to empirical testing. Some of them, such as those related to the multiplicity of equilibria, are common to previous social custom models and may be used to explain the differences in unionization patterns across countries. Some predictions, instead, are original. One concerns the role of conformism versus elitism in establishing multiple equilibria. Conformist communities alone are characterized by multiple equilibria; only in these societies is there a potential role for union and anti-union propaganda in order to make one equilibrium more focal than the others. Another implication concerns the impact on unionization induced by manipulating the personal effort required from union members (e.g. the strike activity or the intensity of class struggle). In a situation of stable union presence, increasing the effort simply raises the cost of membership and therefore lowers the union density. On the other hand, in a situation of declining unionism, in which membership happens to be below the critical mass, increasing the intensity of the class struggle may be a way to temporarily increase unionization, by enhancing the esteem of union members in the eyes of their workmates. Finally, the present theoretical framework may be applied, with slight modifications, to a wide range of collective actions, including strike participation, consumer boycotts, and political activism. Participation in these collective actions may be understood as a signalling device utilized by the individual in order to gain the esteem of his social contacts.
Acknowledgements I thank two anonymous referees, Monique Ebell, Laszlo Goerke, Robin Naylor and participants at a seminar in Universith Cattolica of Milan for helpful comments. Financial support from the Deutsche Forschungsgemeinschaft, SFB 303 at the University of Bonn is gratefully acknowledged.
Appendix A. Proof of Proposition 2 (A). If ~ = 0, worker utility is given by = w +
(A.I)
if he does not join, and by Ui = w -
c -
Oia +
eE(s(i)ll)
(A.2)
if he joins the union. In order for/~ = 0 to be an equilibrium, the utility from not joining must be larger than the utility from joining, for all individuals. Since the former is independent of the individual's rank whereas the latter is decreasing with
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G.G. Corneo / Labour Economics 4 (1997) 71-84
the rank, the equilibrium condition is met if and only if the inequality is satisfied for the individual i = 0, which gives Eq. (11). (B). If ~ = 1, union members have utility Ui = w-
c-
Oia + e ~
(A.3)
and nonmembers have utility U, = w + , E ( s ( i ) 1 0 ) .
(m.4)
In order f o r / x = 1 to be an equilibrium, the latter expression must be smaller than the former for all individuals. Since all nonmembers would have the same utility whereas the utility of members is decreasing with the individual's rank, the equilibrium condition is met if and only if the inequality is satisfied for i = 1, which yields Eq. (12). Q.E.D.
References AkefloL G., 1980, A theory of social custom, of which unemployment may be one consequence, Quarterly Journal of Economics 95. Bernheim, D., 1994, A theory of conformity, Journal of Political Economy 102, 841-877. Blanchflower, D. and R. Freeman, 1992, Unionism in the United States and other advanced OECD countries, Industrial Relations 31, 56-79. Booth, A., 1985, The free rider problem and a social custom model of trade union membership, Quarterly Journal of Economics 100, 253-261. Booth, A. and M. Chatterji, 1993, Reputation, membership and wages in an open shop trade union, Oxford Economic Papers 45, 23-41. Coleman, J., 1990, Foundations of social theory (Harvard University Press, Cambridge, MA). Cornet, G., 1993, Semi-unionized bargaining with endogenous membership and management opposition, Journal of Economics 57, 169-188. Cornet, G., 1995, Social custom, management opposition and trade union membership, European Economic Review 39, 275-292. Cornet, G. and O. Jeanne, 1994, Conspicuous consumption and the existence of upward sloping demand curves, Discussion paper A-461 (University of Bonn, Bonn). Frank, R., 1985, Choosing the right pond (Oxford University Press, New York). Frank, R., 1987, If homo economicus could choose his utility function, would he choose one with a conscience?, American Economic Review 77, 593-604. Hollander, H., 1990, A social exchange approach to voluntary cooperation, American Economic Review 80, 1157-1167. Naylor, R., 1989, Strikes, free riders, and social customs, Quarterly Journal of Economics 104, 771-785. Naylor, R., 1990, A social custom model of collective action, European Journal of Political Economy 6, 201-216. Naylor, R. and M. Cripps, 1993, An economic theory of the open shop trade union, European Economic Review 37, 1599-1620. Naylor, R. and O. Raaum, 1993, The open shop union, wages and management opposition, Oxford Economic Papers 45, 589-604. Parsons, T., 1951, The social system (The Free Press, Glencoe, IL). Schelling, T., 1978, The micromotives of macrobehaviour (W.W. Norton, New York).
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T,ABOUR ECONOMICS ELSEVIER
Labour Economics4 (1997) 71-84
The theory of the open shop trade union reconsidered Giacomo G. Cornet Department of Economics, University of Bonn, Adenauerallee 24- 42, D-53113 Bonn, Germany
Received 29 June 1994;revised 27 June 1996
Abstract
This paper provides a game-theoretic foundation of the social custom approach to trade union membership. The reputation effect of belonging to the union is endogenized as the outcome of a signalling game among the workers. The signalling value of being a union member depends in equilibrium on the union density, but the form of this relationship might differ from what the previous literature assumed. The extent to which comparative statics and critical-mass effects change is also investigated. JEL classification." J50; J51 Keywords: Trade union membership; Social custom; Signalling
I. Introduction
The rapid decline in the 1980s of the closed shop as an institutional device to organize workers into trade unions urged economists to explain unionism as a social arrangement occurring essentially on a voluntary basis. The basic difficulty of this enterprise was to escape the free-rider paradox implied by the public good characteristics of the union bargain with employers, i.e. that the benefits of collective negotiations accrue to union members and nonmembers alike while members alone have to bear the bargaining costs. The social custom approach to union membership, as developed by Booth (1985), Booth and Chatterji (1993), Naylor (1989, 1990), Naylor and Cripps (1993) offers an interesting solution of 0927-5371/97/$17.00 Copyright © 1997 Elsevier Science B.V. All rights reserved. PH S0927-5371 (96)00023- 1
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G.G. Corneo / Labour Economics 4 (1997) 71-84
this problem. Following an idea formulated by Akerlof (1980), these authors postulate that union members enjoy a better reputation than nonmembers, which directly enters the workers' utility function. This reputation effect derives from complying with a social custom that invokes workers to express mutual solidarity by joining collective actions. The worker's reputation acts as an incentive private good delivered by membership in the union. While in addition to social custom effects there might be pecuniary private incentive benefits to joining a union, the former were perceived by these authors as a compelling explanatory factor of unionization. A major finding of this approach is the presence of multiple union equilibria, and the possibility of a minimum union size below which a union is not viable. This implies that if the closed shop is made illegal in a situation of wide union presence, this will not have ravaging consequences for union membership, while the converse applies in a situation of already weak union presence. The explanation of the finding runs as follows, Suppose that the impact of reputation on worker utility is an increasing function of the union density, because when the number of people complying with the social custom grows, deviants are more severely punished with loss of reputation. Suppose also that the reputation effect is absent when union density is zero. In this case, given that nobody else joins the union, nobody has an incentive to join, and zero density is an equilibrium. For very small levels of density, the reputation effect may still be insignificant, which implies that the no-union equilibrium is stable. However, if the initial density is sufficiently large, the reputation effect may offset membership costs. Therefore, open shop unions have to guarantee themselves a threshold level of membership in order to be sustainable. 1 In the aggregate, this equilibrium property might possibly explain the intriguing stylized fact of diverging union densities across countries. 2 The social custom theory of the open shop trade union has proved to be supported by empirical evidence and rich in policy implications. On the other hand, its theoretical underpinnings are not completely satisfactory since the reputation effect, which is necessary to overcome the free-rider problem, lacks proper microfoundations. Indeed existing social custom models are models of complete information, which is at odds with the fact that the phenomenon of reputation can only be accounted for in contexts of incomplete information. The problem is that the term 'reputation' in these models covers two distinct notions.
An antecedent formalization of this type of effects is due to Schelling (1978). 2 An instructive comparison can be made between countries like Sweden and Denmark on the one hand, and France and the United States on the other. In 1970 union density for nonagricultural workers was about 70% in the former countries and about 30% in the latter. In 1987 the percentages were, respectively, 95% and 17%. See Blanchflower and Freeman (1992) for an empirical analysis and Corneo (1995) for a theoretical approach.
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First, it reflects the opinions held by workers about union members. Secondly, it represents the quality of social interactions for a worker, depending on his union status. The existing literature formalizes the latter notion - the additional term in the utility function - but does not explicitly deal with the first one. Rather, it adopts a kind of reduced form by positing that the effect of membership on the worker's utility ultimately increases with the union density. The main goal of the present paper is to disentangle these different notions by looking at unionization as a game played by the workers under incomplete information. In this sense, the paper develops a possible microfoundation of the social custom model of union membership. The basic idea can be formulated with reference to a generic problem of collective action. Suppose that individual participation in a collective action is socially visible. When an individual's predispositions are unobservable, his decision whether to join the collective action may affect the beliefs that others hold about his type. In fact, individuals may differ with respect to the utility loss inflicted upon them by participation in the collective action, so that a possibility to separate different types emerges. In turn, the beliefs held by others may determine the gains obtained by the individual in further social interactions. For instance, individuals may care about social esteem, which itself may depend on public perceptions about an individual's true predispositions. These gains correspond in my model to the reputation effect. If beliefs are formed rationally, this reputation effect will depend, in equilibrium, on aggregate behaviour, which gives a relationship between a worker's reputation and union density. 3 I model voluntary unionization as a signalling game following an approach developed by Corneo and Jeanne (1994) in a different context. The better reputation of union members is derived by the signalling properties of the equilibrium. It is shown that, in general, the reputation effect may be an increasing or a decreasing function of union density, so that the restrictions imposed in previous models cannot be justified on pure theoretical grounds. The reputation effect turns out to be increasing with density in conformist worker communities, which ostracize workers perceived as egoists. The reputation effect is a decreasing function of density in elitist communities, in which an extraordinary prestige is enjoyed by those who are perceived as the most solidaristic individuals. This has some interesting implications for the characterization of equilibria. First, multiplicity of union equilibria is only possible in conformist communities; if the community is of the elitist type, the critical-mass effect fails to exist. Secondly, certain union equilibria may exhibit bizarre comparative statics: increasing the costs of membership, e.g. by requiring harder class struggle from union members, raises the signalling value of joining the union and thereby increases union density.
3 Naylor (1989) mentions the possibility of a signalling interpretation of the social custom model.
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Finally, it is shown that for the ranking of equilibria, from the workforce's viewpoint, the form of the reputation effect is of no importance, which considerably simplifies the welfare analysis of unionism.
2. Endogenizing the reputation effect 2.1. T h e m o d e l
There is a continuum of workers indexed by i ~ [0, 1], each of them facing the decision of taking part in a collective action. For concreteness, the collective action is the formation of a trade union for wage bargaining purposes. Each worker acts independently and without coercion, and the gains from the collective action accrue in the same amount to every worker, irrespective of his behaviour. Each single decision has a negligible impact on the gains produced by the collective action. Participation in it affects individual well-being through three distinct channels. First, there is a net pecuniary cost, e.g. in the form of a membership fee. Secondly, there is a utility loss stemming from the direct involvement with the collective action: union members are required to take part in the decision process accompanying collective negotiations and are supposed to actively participate in protest actions and strikes decided by the trade union. This is the cost in terms of personal time and energy spent together with others in order to achieve collective goals. Thirdly, there is a reputation effect that is induced by the social visibility of participation in the collective action. Individuals have separable preferences, summarized by the following utility function: Ui = Yi -
Oiai q- e r i
(1)
where Yi = w - ~i c is a worker's income, equal to the wage (w) minus the membership fee (c) if the worker is a union member (~i = 0 if the individual does not join the union and ~i = 1 if he does); a i = ~i a is the amount of personal involvement required by participation (a > 0), measured e.g. in time units; r i = r(~ i) is the worker's reputation, depending on his membership in the union; 0 and e are strictly positive parameters that represent the worker's willingness to pay for less personal involvement and better reputation. The purpose of the union consists of raising the wage above its competitive level. The union wage is determined in a negotiation between the union and the firm. Instead of modelling it explicitly, I simply posit that the negotiated wage can be expressed as an increasing function of union membership: w = w(IX), where tx = f d ~ i d i is the union density. Examples of wage bargaining models in which the wage increases with union density are Cornet (1993) and Naylor and Raaum (1993). This relationship is motivated by the potential harm that the union can
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inflict upon the firm in the case of a disagreement. The larger the union, the more important its threat, which in turn improves the bargaining position of the union. Empirical studies generally confirm the notion that union membership has a positive impact on the union wage mark-up. 4 At this stage the model is equivalent to the basic social custom model of union membership: in the absence of a reputation effect, the dominant strategy for each worker is to free-ride on union members, since the impact of the individual membership decision on the bargained wage is nil whereas membership costs are strictly positive. Workers are assumed to differ with respect to their disutility from personal involvement with the collective action. Parameter 0 is distributed in the workforce according to a cumulative distribution function F(0). This parameter captures the individual's distaste for personal sacrifice in order to achieve collective aims. Thus, it can be seen as inversely related to an individual's degree of solidarity toward his workmates. Individuals are ordered according to their degree of solidarity in the following way: i < i ' , ~ 0 i < 0i,. Hence i is the rank of the individual with respect to his sentiments of solidarity: i = 0 is the most solidaristic individual and i = 1 is the least solidaristic individual in the community. While the degree of solidarity is private information of the worker, his decision to join the collective action is observed by the entire workforce. The collective action thus gives workers an opportunity to transmit credible information about the own degree of solidarity. The beliefs of fellow workers may matter for several reasons. First, solidarity may be correlated with the sense of duty and the cooperativeness of the individual, which may induce higher pecuniary payoffs in situations of the repeated prisoners' dilemma type (Frank, 1987). Secondly, others' beliefs may determine the social status of the individual. This is the interpretation to which I will stick hereafter. 5 In this case, the reputation utility does not take a pecuniary form. It consists of the esteem and sympathy awarded to the worker as a prize for his sentiments; it is a socially provided private good. Following sociologists, an individual's status is defined as the deference shown by others according to the individual's rank in the social hierarchy. 6 Formally, r(t~i) = E ( s ( i ) It~i)
(2)
where E(.I~) is the expectation conditional on the observation of ~, and s(i) is a continuous function defined on the unit interval, referred to as the status utility.
4 The logic of the model is unaltered if the wage also increases with a, the activity of union members. s Frank (1985) gives a detailed argument for the status orientation of individuals. 6 See e.g. Coleman (1990). Implicit in this definition is the idea that society is characterized by a unitary value system. This viewpoint goes back to Parsons (1951). While one might spell out various subcultures that are present in the workforce, it is convenient for modelling purposes to start with the hypothesis of a unitary value system.
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This utility represents the social esteem obtained under complete information by a worker according to his rank. Thus, it may be thought of as a decreasing function, i.e. more solidaristic workers enjoy a better treatment by their workmates. The assumption that social esteem depends on public perceptions about an individual's preferences rather than on his actions was put forward in a recent article by Bernheim (1994). The justification is that social esteem seems to depend on the motivations that are supposed to trigger an individual's behaviour. The natural explanation is that motivations are the best predictors of the individual's future actions. 7 The situation described so far can be analyzed as a game with incomplete information played by a continuum of players. Informally, a Bayes-Nash equilibrium of this game is defined as a membership decision for each worker that maximizes his utility function, given both the decisions of others and their beliefs about a worker's type. In turn, beliefs are deduced from membership decisions using Bayes's law. 2.2. The decision to join To begin with the equilibrium analysis I consider beliefs, and hence the reputation utilities, as given. Workers decide to adhere to the trade union if the reputation effect, which is the signalling value of belonging to the union R - r(1) r(O), is large enough. As the maximization of Eq. 1 readily shows, the condition for individual i to become a member is -
C+ Oia R> - -
(3)
E
Suppose that the reputation effect is positive. From the above condition it is not difficult to see that individual i participates in the collective action if and only if his degree of solidarity is larger than a threshold level 0 determined by eR - c =
-
-
a
(4)
Thus, the portion of individuals who join the union may simply be written as /x = F ( O ) .
(5)
For given beliefs, union density is a decreasing function of both the pecuniary cost of membership and the required amount of collective action, and an increasing function of the reputation effect.
7 The idea of a prize for solidarity is reminiscent of the social exchange approach to voluntary cooperation, as developed in a formal model by Holl~inder(1990). In his model, cooperativebehaviour is motivated by the expectation of sympathy prompted by the stimulus-response mechanism of the emotional system. Conversely, in the present model, reactions of deference are rationally determined.
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2.3. Beliefs formation Now, I examine how the reputation utilities are determined. As shown by Eq. (3), the workers who adhere to the union are at the same time sending a simple message, which is that they belong to the more solidaristic part of the workforce. The signalling value of this behaviour, which is the difference between the average status utility of union members and that of those who choose to free-ride, may thus be written as
f~s(i)di R(~)
fls(i)di
/x
1- ~
1
=
/x(1 - / x )
fo'~[ s( i) - ~]di
(6)
where ~ is the average status utility over the whole workforce. Notice that if s(i) is decreasing, the reputation effect is positive, as previously supposed. As a consequence, union members endogenously obtain a better reputation than nonmembers. Since the size of the reputation effect is a function of the total number of workers who join the union, Eq. (6) may be seen as the analogue of the exogenously specified relationship that appears in the social custom literature. However, in that literature the postulated relationship is positive, whereas this need not be the case in the present model. Whether the reputation effect becomes stronger or weaker when the union density grows, depends in general on the structure of the preferences for ranks that prevails in the workers' community. For the sake of illustration, consider the following example in which the status utility is given by
s( i) = a - f l i - y i 2
(7)
which implies the following reputation effect: =
+
~'(1 + ~ )
(8)
It follows that the reputation effect increases with union density if and only if Y is positive, that is if the status utility is concave. The special case of a reputation effect independent of union density obtains only when the status utility is linear. This result may be interpreted as follows. If the status utility is concave, it is more costly to lose one position in the hierarchy when one is classed low than when one is classed high. When the proportion of those who adhere to the collective action increases, the status awarded to both members and nonmembers diminishes, but the status awarded to nonmembers decreases more rapidly. Hence the reputation effect increases with membership. In essence, unionization is induced by the fear of being identified with the most egoistic fringe of the workforce. It may be said that social interactions create a pressure to conform with others, and unionization is motivated by conformism. If the status utility is convex, the converse applies.
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The reputation effect is a decreasing function of membership because individuals are more sensitive to changes in their ranking when they belong to the top of the social hierarchy than when they belong to the bottom. When union density decreases, the status of both members and nonmembers increases, but the status awarded to members raises more rapidly. Hence the reputation effect grows when membership falls. In this case social interactions create a pressure for distinction. One might say that unionization is motivated by elitism, i.e. the desire to show that one belongs to the avantgarde of the working class. Are rank preferences of this type a mere theoretical curiosity? In the history of the labour movement situations did occur in which the working class attributed an extraordinary prestige to the individual who personified its leader, which might be taken as an indication of a convex status utility. 8 Thus the reputation effect may grow or decline when union membership increases, depending on how social esteem is awarded in the workers' community. The argument put forward in the social custom literature is not completely appropriate because it neglects the fact that when union density grows, the social esteem awarded to union members diminishes, since their average quality is lowered. Decisive for the impact on the reputation effect is whether social esteem diminishes more rapidly for members or for nonmembers. If the social esteem of nonmembers decreases more rapidly, the relationship between reputation effect and union size is as postulated in the social custom literature. Otherwise, the relationship is exactly the opposite.
3. Union membership 3.1. Determination o f equilibrium
Equilibrium of the union membership game may take one of two possible forms. First, both the decision to join and the alternative decision may be chosen by nonempty sets of players. In this case, only the most solidaristic portion of the workforce participates in the collective action. This outcome is called a semi-separating equilibrium. Second, one of the two possible decisions may be selected by the empty set. In this case no separation across types occurs and a pooling equilibrium obtains. In a semi-separating equilibrium, individual decisions are optimal given others' behaviour and beliefs; in turn, beliefs are consistent with actual behaviour. The
8 Examplesof union leaders who became labour heros are Jimmy Hoffa (InternationalBrotherhood of Teamsters,US) and Arthur Scargill (National Union of Miners, UK).
G.G. Corneo/ LabourEconomics4 (1997) 71-84
79
~t
1
!q. (11) ~
Eq. (10)
0
)R
Fig. 1. Non-existenceof a semi-separatingequilibrium. equilibrium conditions are given respectively by Eqs. (5) and (6). Hence, the following fact can be established: Proposition 1. In a semi-separating equilibrium of the union membership game, the union density and the reputation effect are a pair (/x*, R * ) ~ ] O , I [ X R + determined by the following conditions: ER* - c )
/x* = F
,
a
1
(9)
fo~*[s(i)
~]di.
(10)
Clearly, the existence and uniqueness of the semi-separating equilibrium are not guaranteed in general. Figs. 1-3 plot Eqs. (9) and (10), and illustrate three types of outcomes that can occur according to the values of parameters. In Fig. 1 no semi-separating equilibrium exists because the reputation effect cannot offset the participation costs induced by the collective action. In Fig. 2, a semi-separating equilibrium exists and is unique. It may be noticed that if the status utility is of the
~t
1
0
- - - ' ~ , /~
Eq. (10)
~-R
Fig. 2. Uniquenessof the semi-separatingequilibriumunderelitism.
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G.G. Corneo / Labour Economics 4 (1997) 71-84
ta Eq. (11)
Eq. (10)
)R Fig. 3. Multiplicity of equilibria under conformism.
elitist type (R'(Ix) < 0) and a semi-separating equilibrium obtains, uniqueness is implied. The outcome depicted in Fig. 3 presents a multiplicity of semi-separating equilibria. It is readily seen that conformism (R'(Ix) > 0) is a necessary condition for multiple equilibria to appear. I turn now to the pooling equilibria, in which Bayes's law cannot be applied. The following result is proved in the appendix:
Proposition 2. ( A) A pooling equilibrium of the union membership game with Ix* = 0 exists if and only if c + Ooa
E(s(i)ll) < ~ + -
E
(11)
(B) A pooling equilibrium with Ix* = 1 exists if and only if ( c + 01a ) E(s(i)lO) _< ~ -
E
(12)
The existence of a pooling equilibrium depends on how one chooses to specify beliefs held out of equilibrium. If beliefs are unchanged when out-of-equilibrium behaviour is observed, they are called passive conjectures. As shown by Eqs. (11) and (12), under passive conjectures only the pooling equilibrium IX* = 0 exists. This is simple to understand. Under passive conjectures no reputation effect of union membership arises, so that the free-rider problems remains unsolved. Thus, one can always find beliefs when Bayes' rule cannot be applied, such that no-union is an equilibrium.
3.2. Some implications A standard result of the social custom literature on union membership is the existence of a critical mass, i.e. a minimum union density under which a trade
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81
union is not viable. Studying this property requires introducing some out-of-equilibrium dynamics or a stability criterion. For instance, one might conceive that at each point in time deference is shown only on the basis of an estimation of the current union density, which is gradually adjusted toward its true value. 9 The stability analysis easily follows by inspection of figures like Figs. 2 and 3. It implies that the semi-separating equilibrium under elitism (Fig. 2) is stable. In the conformist case depicted in Fig. 3 only the upper semi-separating equilibrium is stable. The other equilibrium is unstable: starting from any density level below the equilibrium value, an erosion of union membership ensues and the union disappears in the long run. Conversely, a small increase of union density above that equilibrium value leads to a growth of membership until the upper equilibrium value is reached. The unstable equilibrium identifies a critical mass for the trade union. The model's message is that if the status utility is of the elitist type ( R'( It) < 0), the critical-mass effect of unionization fails to exist. The presence of conformism ( R ' ( l ~ ) > O) is a necessary but not a sufficient condition f o r a critical-mass effect to arise. The form of the status utility is also important for the results of comparative statics. The parameters of the model (c, a, e) affect equilibrium only through the determination of the threshold level 0. In fact, as Proposition 1 shows, parameter changes merely affect Eq. (9). Hence, comparative statics can easily be performed by shifting the corresponding curve depicted in figures like Figs. 2 and 3. Standard results apply to the stable semi-separating equilibria under both elitism and conformism. Union density is increased by lowering membership costs in the form of c or a and by increasing the weight of social factors in the form of E, since all these changes shift the curve representing Eq. (9) upwards. The opposite is true for unstable equilibria, which are possible only under conformism. In these equilibria, increasing the self-sacrifice demanded of union members turns out to increase union density. The reason is that an increase in a amplifies the reputation effect of union membership and this effect more than offsets the utility loss due to the increased personal involvement with union activities. It is worthwhile examining how the equilibria of the union membership game can be ranked according to a welfare criterion. Supposing this criterion to be the sum of worker utilities, one can show that the ranking of possible equilibria is independent of the size of the reputation effect. To see this formally, write the aggregate worker welfare in an equilibrium as W=
(w-
c-
Oia + e r ( 1 ) ) d i +
(w + er(0))di.
(13)
9 If /2 is the estimation of union density, dfx/dt = ~( izt - fxt) gives the adjustmentprocess, with /3>0.
G.G. Corneo / Labour Economics 4 (1997) 71-84
82
Define ~9(/x) as the cumulated willingness to pay for less personal involvement with the collective action:
O ( I z ) =- foUOidi.
(14)
Using Eqs. (2), (6) and (14), worker welfare can be rewritten as
W = w( Ix) - g c -
~9( ~ ) a + e~.
(15)
When comparing different equilibria, the last term of this expression can safely be neglected as it does not depend on the union density. Hence, the ranking of equilibria can be calculated without reference to the social factors of unionization, i.e. without knowledge of E and s(i) or even 5. The reason is that social esteem is a relative phenomenon: when some workers obtain more, others have to obtain less, and the aggregate amount of esteem does not vary. For a welfare analysis of unionism, only its effects on wage formation and on the costs of the collective action need to be evaluated. For instance, comparing the pooling equilibria one obtains that full unionization of the workforce dominates the absence of a union if and only if w(1) - w(0) > c + aO(1).
4. Conclusion I have provided an incomplete information model of trade union membership in which workers care about social esteem as well as the costs of joining collective actions associated with trade union membership. Esteem shown by fellow workers depends on their beliefs about a worker's predispositions toward self-sacrifice in order to achieve collective goals. Since predispositions are unobservable, taking part in union activity signals predispositions and therefore affects the social esteem enjoyed by the worker, This theoretical framework suggests how one can rationalize a basic assumption of the social custom literature: that the reputation effect of union membership increases with the union density. Furthermore it makes clear that, depending on societal values, various shapes of the reputation effect may arise, and these may differ from those previously assumed in the literature. If conformism prevails in the workers' community, the reputation effect of belonging to the union increases with the union density. However, if elitism prevails the opposite applies. The shape of the reputation effect is crucial for the properties of the signalling equilibrium. Under conformism, the results put forward by the social custom literature continue to hold in this model. In particular, multiple union equilibria are possible and a critical-mass effect may arise. Under elitism, there is uniqueness of the equilibrium with an intermediate level of density and the critical-mass effect is absent. On the other hand, the shape of the reputation effect is of no importance for the ranking of equilibria: the optimal union size does not depend on the particular mechanism by which social esteem is allocated to the workers.
G.G. Corneo / Labour Economics 4 (1997) 7 1 - 8 4
83
The theory of union membership detailed in this paper makes a number of predictions that are amenable to empirical testing. Some of them, such as those related to the multiplicity of equilibria, are common to previous social custom models and may be used to explain the differences in unionization patterns across countries. Some predictions, instead, are original. One concerns the role of conformism versus elitism in establishing multiple equilibria. Conformist communities alone are characterized by multiple equilibria; only in these societies is there a potential role for union and anti-union propaganda in order to make one equilibrium more focal than the others. Another implication concerns the impact on unionization induced by manipulating the personal effort required from union members (e.g. the strike activity or the intensity of class struggle). In a situation of stable union presence, increasing the effort simply raises the cost of membership and therefore lowers the union density. On the other hand, in a situation of declining unionism, in which membership happens to be below the critical mass, increasing the intensity of the class struggle may be a way to temporarily increase unionization, by enhancing the esteem of union members in the eyes of their workmates. Finally, the present theoretical framework may be applied, with slight modifications, to a wide range of collective actions, including strike participation, consumer boycotts, and political activism. Participation in these collective actions may be understood as a signalling device utilized by the individual in order to gain the esteem of his social contacts.
Acknowledgements I thank two anonymous referees, Monique Ebell, Laszlo Goerke, Robin Naylor and participants at a seminar in Universith Cattolica of Milan for helpful comments. Financial support from the Deutsche Forschungsgemeinschaft, SFB 303 at the University of Bonn is gratefully acknowledged.
Appendix A. Proof of Proposition 2 (A). If ~ = 0, worker utility is given by = w +
(A.I)
if he does not join, and by Ui = w -
c -
Oia +
eE(s(i)ll)
(A.2)
if he joins the union. In order for/~ = 0 to be an equilibrium, the utility from not joining must be larger than the utility from joining, for all individuals. Since the former is independent of the individual's rank whereas the latter is decreasing with
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G.G. Corneo / Labour Economics 4 (1997) 71-84
the rank, the equilibrium condition is met if and only if the inequality is satisfied for the individual i = 0, which gives Eq. (11). (B). If ~ = 1, union members have utility Ui = w-
c-
Oia + e ~
(A.3)
and nonmembers have utility U, = w + , E ( s ( i ) 1 0 ) .
(m.4)
In order f o r / x = 1 to be an equilibrium, the latter expression must be smaller than the former for all individuals. Since all nonmembers would have the same utility whereas the utility of members is decreasing with the individual's rank, the equilibrium condition is met if and only if the inequality is satisfied for i = 1, which yields Eq. (12). Q.E.D.
References AkefloL G., 1980, A theory of social custom, of which unemployment may be one consequence, Quarterly Journal of Economics 95. Bernheim, D., 1994, A theory of conformity, Journal of Political Economy 102, 841-877. Blanchflower, D. and R. Freeman, 1992, Unionism in the United States and other advanced OECD countries, Industrial Relations 31, 56-79. Booth, A., 1985, The free rider problem and a social custom model of trade union membership, Quarterly Journal of Economics 100, 253-261. Booth, A. and M. Chatterji, 1993, Reputation, membership and wages in an open shop trade union, Oxford Economic Papers 45, 23-41. Coleman, J., 1990, Foundations of social theory (Harvard University Press, Cambridge, MA). Cornet, G., 1993, Semi-unionized bargaining with endogenous membership and management opposition, Journal of Economics 57, 169-188. Cornet, G., 1995, Social custom, management opposition and trade union membership, European Economic Review 39, 275-292. Cornet, G. and O. Jeanne, 1994, Conspicuous consumption and the existence of upward sloping demand curves, Discussion paper A-461 (University of Bonn, Bonn). Frank, R., 1985, Choosing the right pond (Oxford University Press, New York). Frank, R., 1987, If homo economicus could choose his utility function, would he choose one with a conscience?, American Economic Review 77, 593-604. Hollander, H., 1990, A social exchange approach to voluntary cooperation, American Economic Review 80, 1157-1167. Naylor, R., 1989, Strikes, free riders, and social customs, Quarterly Journal of Economics 104, 771-785. Naylor, R., 1990, A social custom model of collective action, European Journal of Political Economy 6, 201-216. Naylor, R. and M. Cripps, 1993, An economic theory of the open shop trade union, European Economic Review 37, 1599-1620. Naylor, R. and O. Raaum, 1993, The open shop union, wages and management opposition, Oxford Economic Papers 45, 589-604. Parsons, T., 1951, The social system (The Free Press, Glencoe, IL). Schelling, T., 1978, The micromotives of macrobehaviour (W.W. Norton, New York).