We consider efficiency wage effects in a union-firm bargaining model with private information. We show that efficiency wage effects do not necessarily increase the wage level at equilibrium. However, if it is commonly known that the union is stronger than the firm and the productivity enhancing effects of paying higher wages are sufficiently large, then efficiency wage effects still increase the wage of equilibrium. More surprisingly, we show that efficiency wage effects increase the strike activity.Wages; Bargaining; Strikes; Efficiency wages

MAULEON, Ana

VANNETLEBOSCH, Vincent J.

English

Research Papers in Economics

E±ciency Wages, Union-Firm Bargaining, and
Strikes¤
Ana Mauleon
Department of Economics - IRES,
Universit¶ e catholique de Louvain.
Vincent J. Vannetelboschy
FNRS and IRES,
Universit¶ e catholique de Louvain.
May 2001
Abstract
We consider e±ciency wage e®ects in a union-¯rm bargaining model with private
information. We show that e±ciency wage e®ects do not necessarily increase the wage
level at equilibrium. However, if it is commonly known that the union is stronger than
the ¯rm and the productivity enhancing e®ects of paying higher wages are su±ciently
large, then e±ciency wage e®ects still increase the wage at equilibrium. More surpris-
ingly, we show that e±ciency wage e®ects increase the strike activity.
Keywords: Wages, Bargaining, Strikes, E±ciency wages.
JEL Classi¯cation: J41, J50, J52.
¤Vincent Vannetelbosch is Charg¶ e de Recherches at the Fonds National de la Recherche Scienti¯que.
The research of Ana Mauleon has been made possible by a fellowship of the Spanish government. Financial
support from the Belgian French Community's program Action de Recherches Concert¶ ee 99/04-235 (IRES,
Universit¶ e catholique de Louvain) and from the Basque Country government's research project PI-1998-48
is gratefully acknowledged.
yCorresponding author address : IRES, Universit¶ e catholique de Louvain, 3 Place Montesquieu, B-1348
Louvain-la-Neuve, Belgium. E-mail: vannetelbosch@ires.ucl.ac.be, Tel: 0032-10-474142, Fax: 0032-10-
473945.E±ciency Wages, Union-Firm Bargaining,
and Strikes
Abstract
We consider e±ciency wage e®ects in a union-¯rm bargaining model with private in-
formation. We show that e±ciency wage e®ects do not necessarily increase the wage level
at equilibrium. However, if it is commonly known that the union is stronger than the ¯rm
and the productivity enhancing e®ects of paying higher wages are su±ciently large, then
e±ciency wage e®ects still increase the wage at equilibrium. More surprisingly, we show
that e±ciency wage e®ects increase the strike activity.
Keywords: Wages, Bargaining, Strikes, E±ciency wages.
JEL Classi¯cation: J41, J50, J52.
11 Introduction
Clearly, it is likely that when¯rms bargain with workers over wages they are also in°uenced
by e±ciency wage considerations (see e.g. Campbell, 1993). Models of union bargaining
with e±ciency wages have been used to inquire into several considerations. Layard et
al. (1991) have shown in a general equilibrium framework that unionization aggravates
the unemployment due to e±ciency wages. Recently, Garino and Martin (2000) have
con¯rmed an original insight of Summers (1988) that e±ciency wage e®ects lead to higher
wages and result in lower employment. But all the previous studies have considered a
complete information framework so that strikes cannot occur in equilibrium.1
The aim of this note is to study the relationship among wages, strikes and e±ciency
wage e®ects in a union-¯rm bargaining model with private information. To describe the
wage bargaining process, we adopt Rubinstein's (1982) alternating-o®er bargaining model
with two-sided incomplete information, which allows the occurrence of strikes at equilib-
rium. We show that e±ciency wage e®ects do not necessarily increase the wage level at
equilibrium. However, if it is commonly known that the union is stronger than the ¯rm
and the productivity enhancing e®ects of paying higher wages are su±ciently large, then
e±ciency wage e®ects still increase the equilibrium wage.
With respect to the strike activity, one might expect at ¯rst that e±ciency wage
e®ects would reduce the strike activity. Indeed, e±ciency wages o®set the cost of higher
wages through higher productivity or lower turnover, and so, make pro¯ts less sensitive
to the wage, which might induce more concessions and less con°icts in wage bargains. In
the words of Summers (1998, p.386) : "... in any plausible bargaining environment ...
[e±ciency wage e®ects] ... make it easier to extract concessions". But, contrary to this
conjecture, we ¯nd that e±ciency wage e®ects increase the strike activity. The intuition
behind this result is the following one. E±ciency wage considerations make the wage
objective of the ¯rm less obvious. Now, a wage rise not only increases the marginal cost
of labor, but also increases the marginal product of labor. As a consequence, the ¯rm has
plenty of scope to hide her type, which is private information, in order to reach a more
favorable agreement. Therefore, longer strikes may be needed for the union to screen the
private information.
1Strikes data seem to have a signi¯cant impact on the wage-employment relationship for collective
negotiations [see e.g. Kennan and Wilson (1989), Vannetelbosch (1996)].
22 The Union-Firm Bargaining Model
We consider a wage determination model with incomplete information between a ¯rm and
a union. The ¯rm is risk neutral and pro¯t-maximizer. Firm's technology is characterized
by a production function Q = (EL)® with 0 < ® < 1, where L is the level of employment
and E is the e®ort per worker. The ¯rm faces a demand function Q = P¡" with constant
elasticity of demand ", where P is output price. Firm's pro¯ts are given by ¦ = P¢(EL)®¡
WL, where W is the wage level. There is a continuum of identical risk-neutral workers
who supply each one unit of labor with no disutility. We denote by W the expected income
of a worker who loses his job. It may be interpreted as the unemployment bene¯t or the
wage elsewhere. Workers are represented in the wage bargaining process by a utilitarian
union. The continuum of workers who supply labor is normalized to unity. Hence, the
union's utility is given by U = L ¢ W + (1 ¡ L)¢ W.
We adopt Summers (1988) and Layard et al. (1991) functional form of e±ciency wage
e®ects,
E =
Ã
W ¡W
W
!¸
, with ¸ < 1 (1)
where E measures the e®ort put forth by workers which depends of the wage paid by the
¯rm relative to the wage workers expect to earn elsewhere, and ¸ measures the productivity
enhancing e®ects of paying higher wages. If ¸ = 0, e±ciency wage considerations are
absent. As ¸ increases, they become more important. Interactions between the output
and price decision, and the wage level are analyzed according to the following structure.
First, wages are determined by negotiations between the ¯rm and the union. Second, the
¯rm chooses employment, output and price. The model is solved backwards.
Taking as given the wage level, the output and the employment levels that maximize
the pro¯ts of the ¯rm are
Q¤ =
·µ
"
" ¡1
¶
W
®E
¸ ¡"®
®+"(1¡®)
and L¤ =
1
E
·µ
"
" ¡1
¶
W
®E
¸ ¡"
®+"(1¡®)
, (2)
respectively. The ¯rm and the union negotiate the wage level foreseeing perfectly the e®ect
of wages on output and employment levels. The negotiation proceeds as in Rubinstein's
(1982) alternating-o®er bargaining model. The ¯rm and the union make alternatively wage
o®ers, with the ¯rm making o®ers in odd-numbered periods and the union making o®ers
in even-numbered periods. The negotiation ends when one of the negotiators accepts an
o®er. No limit is placed on the time that may be expended in bargaining and perpetual
disagreement is a possible outcome. The union is on strike in every period until an
agreement is reached. Both negotiators are assumed to be impatient: the ¯rm and the
union have time preferences with constant discount rates rf > 0 and ru > 0, respectively.
3As the interval between o®ers and countero®ers is short and shrinks to zero, the
alternating-o®er model has a unique limiting subgame perfect equilibrium, which approx-
imates the Nash bargaining solution to the bargaining problem (see Binmore et al., 1986).
Thus the predicted wage is given by
W¤ = argmax[U ¡U0]
° ¢ [¦¡ ¦0]
1¡° (3)
where U0 = W and ¦0 = 0 are, respectively, the disagreement payo®s of the union and
the ¯rm, and ° 2 (0;1) is the union bargaining power which is equal to
rf
ru+rf. Simple
computation gives us
W¤ = W ¢
·
®(" ¡ 1)(1 ¡°) +"°
®(" ¡1)(1 ¡¸)
¸
. (4)
This is the wage expression Garino and Martin (2000) obtained and it tells us that, in
complete information, the wage is increasing with the union bargaining power (°), the
elasticity of demand ("), and the e±ciency wage e®ects (¸). Then, one can easily obtain
the equilibrium employment level as well as the equilibrium payo®s, which are denoted
by U¤(°) and ¦¤(°). However, both the asymmetric Nash bargaining solution and the
Rubinstein's model predict e±cient outcomes of the bargaining process (in particular
agreement is settled immediately). This is not the case once we introduce incomplete
information into the wage bargaining, in which the ¯rst rounds of negotiation are used for
information transmission between the two negotiators.
3 Private Information
The main feature of the negotiation is that both negotiators have private information.
Each negotiator does not know the impatience (or discount rate) of the other party. It
is common knowledge that the ¯rm's discount rate is included in the set [rP
f ;rI
f], where
0 < rP
f · rI
f, and that the union's discount rate is included in the set [rP
u;rI
u], where
0 < rP
u · rI
u. The superscripts "I" and "P" identify the most impatient and most patient
types, respectively. The types are independently drawn from the set [rP
i ;rI
i] according to
the probability distribution pi, for i =u,f. We allow for general distributions over discount
rates. This uncertainty implies bounds on the union bargaining power which are denoted
by ° = rP
f ¢
h
rI
u + rP
f
i
and ° = rI
f ¢
h
rP
u +rI
f
i
.
Lemma 1 Consider the wage bargaining with incomplete information in which the dis-
tributions pf and pu are common knowledge, and in which the period length shrinks to
zero. For any perfect Bayesian equilibria (PBE), the payo® of the union belongs to
h
U¤(°);U¤(°)
i
and the payo® of the ¯rm belongs to
h
¦¤(°);¦¤(°)
i
.
4This lemma follows from Watson's (1998) analysis of Rubinstein's alternating-o®er bar-
gaining model with two-sided incomplete information.2 As Watson (1998) stated, Lemma
1 establishes that "each player will be no worse than he would be in equilibrium if it were
common knowledge that he were his least patient type and the opponent were his most
patient type. Furthermore, each player will be no better than he would be in equilibrium
with the roles reversed".3 From Lemma 1 we have that wage outcome, W ¤(°;°), satis¯es
the following inequalities:
W ¢
"
®(" ¡ 1)(1 ¡°) + "°
®(" ¡1)(1 ¡¸)
#
· W¤(°;°) · W ¢
·
®(" ¡1)(1¡ °) +"°
®(" ¡ 1)(1 ¡¸)
¸
. (5)
Notice that each wage satisfying these bounds can be the outcome by choosing ap-
propriately the distribution over types. The lower (upper) bound is the wage outcome of
the complete information game, when it is common knowledge that the union's type is rI
u
(rP
u) and the ¯rm's type is rP
f (rI
f) (and the union bargaining power is ° (°)). Expression
(5) implies bounds on the ¯rm's employment level, as well as on the ¯rm's output, at
equilibrium.
In complete information, the e±ciency wage e®ects increase the equilibrium wage level.
But once the union and the ¯rm have private information, this complete information result
does not necessarily hold. The necessary and su±cient condition to recover the complete
information result is
¸ ¸ 1 ¡
®(" ¡ 1)(1 ¡°) +"°
®(" ¡ 1)(1 ¡°) +"°
(6)
That is, the larger the amount of private information
¯ ¯ ¯° ¡°
¯ ¯ ¯ the larger ¸ should be in
order to get for sure that e±ciency wage e®ects increase the wage at equilibrium in case
of union-¯rm bargaining with private information. However, if it is commonly known that
the union is stronger than the ¯rm (i.e. ° ¸ 1
2) and the productivity enhancing e®ects
of paying higher wages are su±ciently large (i.e. ¸ ¸ 1
2), then e±ciency wage e®ects still
increase the wage at equilibrium.
2Watson (1998) characterized the set of PBE payo®s which may arise in Rubinstein's alternating-o®er
bargaining game and constructed bounds (which are met) on the agreements that may be made. The
bounds and the PBE payo®s set are determined by the range of incomplete information and are easy to
compute because they correspond to the SPE payo®s of two bargaining games of complete information.
These two games are de¯ned by matching one player's most impatient type with the opponent's most
patient type.
3Lemma 1 is not a direct corollary to Watson (1998) Theorem 1 because Watson's work focuses on
linear preferences, but the analysis can be modi¯ed to handle the present case. Translating Watson
(1998) Theorem 2 to our framework completes the characterization of the PBE payo®s. For any e U 2
[U
¤(°);U
¤(°)], e ¦ 2 [¦
¤(°);¦
¤(°)], there exists distributions pu and pf, and a PBE such that the PBE
payo®s are e U and e ¦. In other words, whether or not all payo®s within the intervals given in Lemma 1 are
possible depends on the distributions over types.
5Lemma 1 and Expression (5) also tell us that ine±cient outcomes are possible, even as
the period length shrinks to zero. The wage bargaining game may involve delay (strikes
or lockouts), but not perpetual disagreement, at equilibrium. Indeed, Watson (1998) has
constructed a bound on delay in equilibrium which shows that an agreement is reached in
¯nite time and that delay time equals zero as incomplete information vanishes.
In the literature onstrikes (see e.g. Kennan and Wilson, 1989), three di®erent measures
of strike activity are usually proposed: the strike incidence, the strike duration, and the
number of work days lost due to work stoppages. Since we allow for general distributions
over types andwe may encounter a multiplicity of PBE, we are unable to compute measures
of strike activity as the ones just mentioned.4 However, we propose to identify the strike
activity with the maximal delay in reaching a wage agreement. Following Watson (1998)
Theorem 3, the larger is the di®erence between the upper bound and lower bound on
the bargaining outcome, the larger is the potential delay for obtaining an agreement.
Therefore, the strike activity is given by the di®erence between the upper bound and the
lower bound on the wage outcome.5 So, the strike activity, ª(¸), is given by the following
expression.
ª(¸) =
h
° ¡ °
i
¢ W ¢
·
® + (1 ¡ ®)"
®(" ¡ 1)(1 ¡¸)
¸
, (7)
where
° ¡° =
h
rI
f rI
u ¡rP
f rP
u
i
£
rP
f +rI
u
¤£
rI
f + rP
u
¤
From expression (7) it is immediate that the strike activity is always increasing with the
e±ciency wage e®ects: @ª
@¸ > 0. The intuition behind this result has to do with the time
needed to screen or to learn each other's type. The incorporation of e±ciency wage e®ects
makes the wage objective of the ¯rm less obvious. Indeed, the ¯rm may still be interested
in reaching low wages, but low wages reduce the e®ort produced by the workers (hence,
their productivity). As a consequence, the ¯rm has plenty of scope to hide her type,
which is private information, in order to reach a more favorable wage outcome. Therefore,
the union (who still claims higher wages) may need more time, during the negotiation,
to screen the ¯rm's type. Finally, notice that the strike activity is decreasing with the
elasticity of substitution between the demand and the price: @ª
@" < 0.
The next proposition summarizes our main results.
4In order to compute an expected strike duration one would need to ¯x some parameters of the model
such as the distribution over types but it would imply a substantial loss of generality.
5Our measure of strike activity gives the scope each player has for screening his opponent by making
wage proposals satisfying the expression (5), and hence, for delaying the wage agreement. Only in average
this measure is a good proxy of actual strike activity.
6Proposition 1 In case of union-¯rm bargaining with private information, e±ciency wage
e®ects increase the strike activity but do not necessarily increase the wage outcome. How-
ever, if it is commonly known that the union is stronger than the ¯rm (° ¸ 1
2) and the
productivity enhancing e®ects of paying higher wages are su±ciently large (¸ ¸ 1
2), then
e±ciency wage e®ects still increase the wage at equilibrium.
References
[1] Binmore, K.G., A. Rubinstein, and A. Wolinsky, 1986, "The Nash Bargaining Solution
in Economic Modelling," Rand Journal of Economics 17, 176-188.
[2] Campbell, C.M., 1993, "Do Firms Pay E±ciency Wages? Evidence with Data at the
Firm Level," Journal of Labor Economics 11, 442-470.
[3] Garino, G. and C. Martin, 2000, "E±ciency Wages and Union-Firm Bargaining,"
Economics Letters 69, 181-185.
[4] Kennan, J. and R. Wilson, 1989, "Strategic Bargaining Models and Interpretation of
Strike Data," Journal of Applied Econometrics 4, S87-S130.
[5] Layard, R., S. Nickell and R. Jackman, 1991, Unemployment: Macroeconomic Perfor-
mance and the Labour Market, Oxford University Press (Oxford).
[6] Rubinstein, A., 1982, "Perfect Equilibrium in a Bargaining Model," Econometrica 50,
97-109.
[7] Summers, L.H., 1988, "Relative Wages, E±ciency Wages and Keynesian Unemploy-
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[8] Vannetelbosch, V.J., 1996, "Testing Between Alternative Wage-Employment Bargain-
ing Models Using Belgian Aggregate Data," Labour Economics 3, 43-64.
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tion," Review of Economic Studies 65, 573-594.
7

Alternating-O®er Bargaining with Two-Sided Incomplete Information,&quot;

Do Firms Pay E±ciency Wages? Evidence with Data at the Firm Level,&quot;

E±ciency Wages and Union-Firm Bargaining,&quot;

Perfect Equilibrium in a Bargaining Model,&quot;

Relative Wages, E±ciency Wages and Keynesian Unemployment,&quot;

Strategic Bargaining Models and Interpretation of Strike Data,&quot;

Testing Between Alternative Wage-Employment Bargaining Models Using Belgian Aggregate Data,&quot;

The Nash Bargaining Solution in Economic Modelling,&quot;

Unemployment: Macroeconomic Performance and the Labour Market,

Efficiency Wages, Unio-Firm Bargaining, and Strikes

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Efficiency Wages, Unio-Firm Bargaining, and Strikes

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