Downward nominal wage rigidity – contracts or
fairness considerations?
by
Steinar Holden
Department of Economics
University of Oslo
Box 1095 Blindern, 0317 Oslo, Norway
email: steinar.holden@econ.uio.no
homepage: http://folk.uio.no/sholden/
First version: 31 May 2002
This version: 18 June 2002
Preliminary and incomplete
Comments are welcome.
Abstract
The literature on downward nominal wage rigidity is mainly empirical, often with a
reference to casual or survey evidence that workers and employers find nominal wage
cuts unfair. There is rarely a link to the mainly theoretical literature explaining nominal
wage rigidity as the result of efficient nominal wage contracts. This paper explores the
empirical implications of standard models of nominal wage rigidity, based on both
fairness considerations and contracts, and compares them with existing empirical
evidence. None of the models is fully consistent with the existing empirical evidence.
However, an extended theory where fairness considerations are added to a contract
model, seems more consistent with empirical evidence.
JEL Classification: C78, J3, J5, K31.
Keywords: Nominal wage rigidity, wage contracts, bargaining, fairness considerations.
1
1
Introduction
In recent years there has been a growing interest in the extent of downward nominal wage
rigidity in industrialised economies, motivated by the concern that the combination of
downward nominal wage rigidity and low inflation may lead to higher unemployment, as
suggested by Tobin (1972). The literature on downward nominal wage rigidity is mainly
empirical, often with a reference to casual or survey evidence that workers and employers
find nominal wage cuts unfair. However, there is also a mainly theoretical literature
explaining nominal wage rigidity as the result of nominal wage contracts that only can be
changed by mutual consent (MacLeod and Malcomson, 1993, Holden, 1994, 1999). Such
contracts exist in many countries, and they are efficient under a large variety of
circumstances. This paper explores the empirical implications of standard models of
nominal wage rigidity, based on both fairness considerations and contracts. These
empirical implications are compared with existing empirical evidence. It is argued that
neither theory is fully consistent with the existing empirical evidence. However, an
extended theory where fairness considerations are added to a contract model, seems to be
more consistent with empirical evidence.
Specifically, Altonji and Devereux (1999) (A&D) and Fehr and Goette (2000)
(F&G) base their empirical evidence on two features of downward nominal rigidity. They
define the notional or flexible wage as the wage that would prevail with no nominal
rigidity. A&D and F&G then define a threshold value α for the notional wage change,
with the interpretation that if the notional wage change is a nominal wage cut of less than
–α, then the actual wage change will be zero. (So for perfectly flexible wages, α = 0).
Furthermore, A&D and F&G define the possible difference in the actual and notional
wage change if a nominal wage cut takes place, λ. λ > 0 would imply that the downward
nominal rigidity affects the wage positively even when a wage cut takes place. The
evidence of A&D and F&G suggest that both α > 0 and λ > 0.
I show that simple models of downward nominal wage rigidity based on fairness
considerations suggest that there is a positive threshold value α. However, if a wage cut
takes place, then there should be no effect on the nominal wage, i.e. λ = 0, in contrast to
the empirical evidence. The contracting models can explain that both α and λ are positive,
however they also suggest that α = λ, on which there is conflicting evidence. I propose a
new model which combines the two explanations, and this model explains the finding of
F&G that α > λ > 0.
The remaining of the paper is organised as follows. In section 2, I describe the
empirical framework and evidence of A&D and F&G. Section 3 sets out the theoretical
framework used in the analysis of wage setting without a contract (section 4) and in the
discussion of empirical implications of wage setting with a contract (section 5). In section
6, I consider the empirical implications of a simple model of fairness considerations.
Section 7 presents a model that combines the contracting and fairness elements. Section 8
concludes.
2
Empirical evidence
In their empirical studies of downward nominal wage rigidity based on individual data
from the US, Altonji and Devereux (1999), and Switzerland, Fehr and Goette (2000) use
the following framework. They define a notional or flexible wage,
2
(1)
ln wF = xβ + ε
which should be interpreted as the wage that would apply with no nominal wage rigidity
(x is a standard vector of explanatory variables, β is the parameter vector and ε is the
error term). The notional wage change (the wage that would apply with no nominal
rigidity) is ln wF – ln w0, where w0 is the lagged wage. However, the actual wage change
may be affected by downward nominal rigidity, and is given by (neglecting measurement
error)1
∆ ln w =
ln wF – ln w0
0
ln wF – ln w0 + λ
if ln w0 < ln wF
if ln wF ≤ ln w0 ≤ ln wF + α
if ln w0 > lnwF + α
Thus, if there is no nominal rigidity, α = λ = 0. α is a possible threshold value for a wage
cut, in the sense that no wage cut will take place if the notional wage cut is smaller than
α. λ is the possible reduction in the actual wage cut relative to the notional wage cut,
given that a wage cut takes place. The relationship is illustrated in Figure 1. This
framework can be directly compared to the results of the various wage setting
frameworks that are presented here.
Both A&D and F&G find a very strong rejection of the perfect flexibility case, as
α is found to be positive and highly significant. The value of λ is also generally found to
be significantly positive, but the value differs more across specifications and data. In their
leading results, A&D, Tables II and III, find method 1: α ≈ 0.65, λ ≈ 0.04 (huge standard
error), method 2: α ≈ 0.06, λ ≈ 0.06. F&G, Table 3, find (data from Swiss Labour Force
Survey): α ≈ 0.31, λ ≈ 0.08; (data from Swiss Social Insurance Files). α ≈ 0.27, λ ≈ 0.11.
A&D compares their results to the outside option result of MacLeod and
Malcomson (1993) (Result 3 below), otherwise there is no explicit comparison to
relevant theoretical models.
3
Theoretical framework
Consider an employment relationship between an employer and an employee. The
employer makes flow revenues v > 0 from hiring the employee, while r > 0 is the flow
cost of the employee from supplying labour. I assume that v > r, ensuring that trade is
efficient. Players’ payoffs in case there is no trade is normalised to zero.
To capture the explanations offered in the literature, I shall consider four different
institutional set-ups, distinguished along two dimensions;
i) whether the wage is set unilaterally by the employer, or in a bargain between employer
and employee;
ii) whether or not there is an existing nominal contract which only can changed by mutual
consent.
1
Altonji and Devereux also present a method 1 where they do not impose the assumption
that the initial contract is equal to the lagged flexible wage, wF-1 = w0.
3
In the case where there is an initial contract which can only be changed by mutual
consent, trade is voluntary, so either party may refuse to trade. However, if trade takes
place, the payment will be equal to the prevailing contract price. This situation has been
given two different interpretations in the literature. One interpretation is that there is an
explicit renegotiation of the existing contract, but where the terms of the initial contract
prevail until a new agreement is reached. As emphasised by Holden (1994a), a setting
where the initial contract only can be renegotiated by mutual consent is relevant for
renewals of collective agreements in Europe, where the terms of the old collective
agreements generally prevail until a new agreement is reached.2
Another interpretation, following Hart and Moore (1988) and MacLeod and
Malcomson (1993), is that there is a binding contract, and courts can enforce payment of
the contract price if trade takes place. However, in case no trade takes place, a court
cannot verify which party chose not to trade, and thus cannot enforce trade or breach
payments contingent on which party has caused the disrupting of trade. As discussed by
Malcomson (1997), this situation may fit well to the legal setting of individual
employment contracts in most of Europe.
In contrast, in most of the US labour market, the legal setting is different (see
Malcomson, 1997), as the requirement of mutual agreement does not apply in practice,
and the situation can better be described as unilateral wage setting by the firm (obviously
subject to possible restrictions concerning outside opportunities etc, to which we return).
To allow for a proper modelling of the bargaining situation, I consider an infinite
horizon of time periods of very short length, and focus on the case where the period
length converges to zero. Throughout the analysis, players are assumed to have complete
information.
4
Wage setting without a contract
In this section I derive two versions of the flexible wage, based on bargaining and
unilateral wage setting by the employer. The probably most common approach to
bargaining is the Nash bargaining solution, often justified as subgame perfect equilibrium
of a Rubinstein (1982) complete information, infinite-horizon, alternating-offer
bargaining game (see Binmore, Rubinstein and Wolinsky, 1986). The Nash bargaining
solution is the wage level that maximises the product of players’ gain of reaching an
agreement, where the alternative is endless disagreement (strike or lockout), giving both
parties zero payoff. Formally3
(2)
w = arg max (v – w)(w – r)
2
Sometimes, the remuneration may consist of several components, where some are part
of a contract and can only be changed by mutual consent, whereas others can be changed
unilaterally by the employer. This is neglected in the following.
3
For notational simplicity, I assume symmetric bargaining. Including asymmetric
bargaining power, e.g. motivated by different discount factors, would only add more
notation, but not affect the qualitative results.
4
which solves for
(3)
wN =
1
(v + r )
2
Thus, the outcome implies that the players share the gain of reaching an agreement, as the
1
equilibrium payoffs are v − w N = w N − r = ( v − r ) .
2
Alternatively, if the employer sets the wage unilaterally, the employer would clearly set a
wage equal to the employee’s cost of supplying labour, r. Formally,
(4)
wE = r
(If one introduced additional features, e.g. a shirking problem à là Shapiro and Stiglitz,
1984, the wage would typically be a markup over the cost of supplying labour.)
5
Wage setting with a contract
In practice, contracts may be quite complicated, involving a number of different issues,
and if new events occur, it will often be possible with Pareto improving renegotiation.
However, in our one-dimensional setting, where a contract only specifies a wage,
renegotiation of the contract will always be to one party’s disadvantage. As a
renegotiation requires mutual agreement, this implies that a renegotiation will only take
place if the player that benefits from the renegotiation can put sufficient pressure on the
opponent that he/she accepts the change.
Two main types of threats can be distinguished: either to inflict a cost at the
opponent within the relationship, for example by disrupting trade (e.g. a strike), or to
leave the opponent permanently for an outside option (e.g. replace the worker with
another one, or quit the firm for a new job). In either case, such threats will only be
successful if they are credible. For example, a demand for a wage rise based on a threat
of leaving for an inferior job will be rejected by the employer, as the employee will not
realise his threat if the demand is rejected. The key issue is then to explore under which
circumstances threats of disrupting trade or taking an outside option are credible, and thus
will lead to a renegotiation of the initial contract. To analyse this issue, the strategic
bargaining framework originating from Rubinstein (1982) is a useful theoretical
framework.
Within a wage bargaining set-up, a threat of disrupting trade is most naturally
associated with a collective bargaining framework, where workers may strike, or the
employer may use a lock-out. The survey evidence of Bewley (1999, pp 407) indicates
that “only high-ranking executives and specialised professionals have enough bargaining
power .. to hold up firms”. So the analysis of threats of disrupting trade is probably most
relevant when the employee is associated with a group of workers or a union.
First, I consider threats of disrupting trade, then I turn to the effect of outside
options.
5
5.1
Threats of disrupting trade
The first papers to endogenise the trade decision in the Rubinstein (1982) model were
Haller and Holden (1990) and Fernandez and Glazer (1991). They considered a one-sided
version, where one player (the union) in each period could choose whether to disrupt
trade (strike) in that period; otherwise production took place under the initial agreement.
It was shown that there was a multiplicity of equilibria in the model (any wage in the
interval [w0, wN] could be sustained as a subgame perfect equilibrium (SPE) outcome)
and that strikes with a length in real time can occur in equilibrium. For applications,
however, the multiplicity was an important problem, by making comparative statics
problematic.
The presentation here will thus focus on two subsequent approaches, MacLeod
and Malcomson (1993) and Holden (1994a, 1999). In a key paper, MacLeod and
Malcomson’s (1993) analysed to what extent incomplete contracts induce efficient
investments, and they derived a number of important results in this regard. Here, the
focus will be on the properties of their model concerning the circumstances under which
a contract price (wage) will be renegotiated. MacLeod and Malcomson use on a
symmetric model, where both players could disrupt trade (MacLeod and Malcomson also
consider outside options, cf. below). A key assumption is that there is a finite number of
periods in the bargaining. This ensures that the game can be solved by backward
induction, thus avoiding the multiplicity of equilibria encountered by Haller and Holden,
and Fernandez and Glazer.4
As shown by MacLeod and Malcomson (1995), the outcome of this strategic
bargaining model coincides with the standard Nash bargaining solution, supplemented by
simple conditions for the circumstances under which the initial contract is renegotiated.
Specifically,
Result 1 (MacLeod and Malcomson, 1993):
The subgame perfect equilibrium outcome satisfies
w* = w0
w* = w N =
1
(v + r )
2
if v – w0 > 0 and w0 – r > 0
otherwise5
Thus, MacLeod and Malcomson find that as long as the players benefit from trade under
the initial contract, on a period-by-period basis (v – w0 > 0 and w0 – r > 0), the initial
4
MacLeod and Malcomson (1995) show that under the additional requirement that the
equilibrium is strongly renegotiation-proof, the equilibrium of the infinite-horizon
version of the model essentially coincides with the finite horizon version presented in the
main text. However, strong renegotiation-proofness entails Pareto efficiency, which is a
problematic assumption in an analysis of whether a strike threat (which clearly is Pareto
inefficient, if carried out) is credible.
5
In the specific cases where v – w0 = 0 or w0 – r = 0, there is a continuum of subgame
perfect equilibrium outcomes, from w0 to wN.
6
contract will not be renegotiated. However, if one party does not benefit from the initial
contract, i.e. v – w0 > 0 or w0 – r < 0, the player that does not benefit may credibly
threaten to stop trade. In this case the contract will be renegotiated to the Nash bargaining
solution wN. In Figure 2, we observe that the wage is renegotiated down to the wN if v <
w0, and renegotiated up to wN if r > w0, while the wage is constant for intermediate
values.
While this result has a clear intuitive interpretation, it also involves implications
that may seem implausible. In a wage bargaining context, it would presumably imply that
strike threats almost never are credible: as the employee voluntarily chose to work under
the initial contract, one would expect that w0 > r hold. Furthermore, it also implies that
the size of the revenues to the firm, v, does not affect whether strike threats are credible,
irrespective of how high v are. (However, if strike threats are credible, because w0 < r, v
does affect the renegotiated wage.)
Compared to the empirical results of A&D and F&G, the MM model is consistent
with the finding of a significant positive threshold value α for whether a wage cut takes
place. However, the MM model would predict that nominal rigidity has no effect given
that a wage cut takes place, λ = 0, which is not consistent with the results of A&D and
F&G.
Holden (1994a, 1999)
Holden (1994a, 1999) also considered a Rubinstein model where both parties could
choose whether to disrupt trade. To avoid the multiplicity of equilibria in the infinitehorizon model, it was assumed that once a strike or lock-out was initiated, trade could not
be resumed unless a new agreement was reached.6
Secondly, it was assumed that if trade is disrupted (a work stoppage takes place), it
always involves non-negligible costs to the parties (fixed costs). These costs may be
given several different interpretations. Most simply, they can be thought of as the costs
associated with a minimum time before work can be resumed after a work stoppage. In
Holden (1999), the model is extended to allow for uncertainty as to the wage outcome,
and if players are risk averse, the fixed costs may be interpreted as the amount that the
parties are willing to give up so as to avoid risk. A non-negligible probability of a lengthy
conflict (within an asymmetric information set-up) would have the same effect.7
Formally, it was assumed that when trade was resumed after a disruption, the payoffs
of the players were γ(v-w) and γ(w-r), where 0 < γ < 1 measured the costs of a disruption
(the specific form of the cost, including whether the cost is a permanent reduction in flow
payoff or a temporary cost, is inessential).
Figure 3 presents the strategic game, following Holden (1999). At step 3, there is an
ordinary Rubinstein alternating offers game, with exogenous payoffs, of two types (zero
6
In Holden (1994b) it is shown that a weaker assumption is sufficient, namely that both
players may commit to stop production for two periods (for arbitrary short period length),
unless an agreement is made before that.
7
If players’ costs during a disruption of trade depend on who initiates the disruption,
being less favourable for the disrupting player (eg lock-out being relatively more
favourable for the union than a strike, where unions e.g. incur the cost associated with
picket lines), the length of the interval in Prop 2 below would be increased.
7
if no trade, v – w0 and w0 if trade). Steps 1 and 2 determine which types of payoffs
prevail in step 3. (In equilibrium, an agreement is reached at step 1 or 2, and step 3 is
never reached.)
To explain the results, consider first a subgame (at step 3) where a strike or lock-out
has been initiated. The situation is then just like in the Rubinstein (1982) model, and the
unique SPE outcome is the Nash bargaining solution wN. However, as initiating a work
stoppage involves costs, a player contemplating to initiate a work stoppage will not do so
if the opponent offers a less favourable contract, which nevertheless gives the player the
same payoff as he would have got from initiating a work stoppage. Specifically, the firm
will not reject and initiate a lock-out at step 2 if the worker at step 2a offers a wage wL
that gives the firms the same payoff as it will get if a lock-out is initiated. wL is given by
(5)
v – wL = γ(v –wN)
which solves for
(6)
 γ γ
wL = v 1 −  + r > w N
 2 2
Likewise, the employee will not reject and initiate a strike at step 1 if the firm offers a
wage wS, given by
(7)
wS – r = γ(wN – r)
which solves for
(8)
wS =
γ
 γ
v + 1 −  r < wN
2
 2
Thus, if the initial contract is in the interval between wS and wL, both parties will obtain
lower total future payoff by disrupting trade than if they continue trade under the old
contract. In this case threats of disrupting trade will not be credible, and the unique
outcome to the wage setting is a prolongation of the existing contract w0. However, if w0
> wL, the firm would get higher total future payoff from initiating a lock-out than from
prolonging the initial contract. In this case lock-out threats are credible. The employee
will offer a new wage wL. This will accepted by the firm, and no lock-out will be called.
Likewise, if w0 < wS, threats of striking will be credible (as a strike would give higher
total payoff to the employee than a prolongation of the initial contract. The firm will offer
a wage rise up till wS, which will be accepted by the employee. No strike will take place.
The result is summarised in:
8
Result 2 (Holden, 1994a, 1999):
The SPE outcome satisfies
wS = w N −
w*
=
w0
wL = wN +
1− γ
(v − r )
2
1− γ
(v − r )
2
if w0 < wS
if wS ≤ w0 ≤ wL
if w0 > wL
The outcome of the wage setting is illustrated in Figure 4. If players’ payoffs v and r are
low relative to w0, implying that the Nash outcome wN is low relative to the w0, the wage
is renegotiated down to wL.
Compared to the framework for the empirical evidence, Result 2 predicts that
there is a positive threshold value for nominal wage cut, α > 0, and that the wage is
higher relative to the flexible wage even when the wage is cut, λ > 0. Both these
predictions are consistent with the evidence. However, the model also implies the
restriction that α = λ. This restriction is consistent with the evidence of A&D, method 2,
but not with F&G, who find α > λ > 0.
5.2
Work-to-rule/holdout
In the models of MacLeod and Malcomson and Holden above, it is assumed that if trade
takes place while the parties are bargaining, no costs are incurred. However, as argued by
Moene (1988), Holden (1989, 1997), and Cramton and Tracy (1992), even if the players
are bound to observe the details of the old contract, it is rarely so specific that it
completely determines the parties’ payoffs. Workers may reduce profits by use of a
variety of different industrial actions (see eg Blanpain, 1994), for example by strictly
adhering to the working rules (work-to-rule). The remuneration of the workers may also
consist of some elements that are at the discretion of management, which may be reduced
even under the existing contract. In this subsection I consider the consequences of this
assumption, following Holden (2002). Formally, this can be captured by assuming that
the payoffs during work-to-rule are (1-τ)(v – w0) and (1-ε)w0, where τ and ε are
parameters satisfying 0 < τ,ε < 1, reflecting that work-to-rule is costly. It is then
straightforward to show that the SPE outcome in case threats of disrupting trade are not
credible, is
(9)
wκ = (1+κ)w0
where κ = (τ-ε)/2.
The wage of the old contract affects the bargaining outcome because it determines
players' payoffs during a conflict in the bargaining. (8) allows for a simple interpretation:
Work-to-rule leads to higher nominal wages (κ > 0) if and only if a work-to-rule is more
costly to the firm than to the union, ie. τ > ε (this is the common assumption in the
literature, cf Moene, 1988, Holden, 1989, 1997, and Cramton and Tracy, 1992). wκ
should then be substituted for w0 in Result 2 above.
The empirical framework of A&D and F&G does not allow for the effect of workto-rule, as this would predict an increase in nominal wages also in the case where
downward nominal wage rigidity is binding. The implication of work-to-rule would be to
change the wage outcome under rigidity to w* = (1+κ)w0 if wF ≤ (1+κ)w0 ≤ wF + α.
9
A similar theoretical framework is the basis for an empirical investigation of the
aggregate wage setting in the manufacturing sectors in the Nordic countries (Holden,
1998), where it is found empirical support for the existence of a minimum annual
nominal wage growth varying from 1.5 to 3.9 percent, consistent with κ > 0.
5.3
Individual wage setting and outside options
Under individual wage setting, one would often expect the firm to have the upper hand,
although the employee may use a job offers from other firms to persuade the firm to raise
the wage. However, if there is an initial contract that can only be changed by mutual
consent, this put important restrictions on the firm’s possibilities. To analyse this
situation, we continue to consider a Rubinstein-type framework where players alternate in
making offers. We neglect the possibility of disrupting trade, so as long as the players are
bargaining, both receive the payoff of the existing contract. However, whenever a player
has rejected an offer, the player has the option of terminating the relationship
permanently. I assume that the outside opportunity is a relationship with another, yet
identical, partner, where the wage is given by the solution without contract, i.e. the Nash
Bargaining Solution wN. However, parties incur a switching cost zF > 0 (firm) and zW > 0
(worker).
The game thus constitutes a straightforward application of a standard Rubinstein
game with outside options, and it follows directly using standard arguments that the
outside option principle of Binmore, Shaked and Sutton (1989) applies (as also argued by
MacLeod and Malcomson, 1993): the outside options only affect the bargaining outcome
if they are better than the “inside” alternative (in this case the payoff of the existing
contract).
Result 3: Outside options, Binmore, Shaked and Sutton (1989), MacLeod and
Malcomson (1993)
The SPE outcome is
1
w N − zW = ( v + r ) − zW
if w0 < wN – zW
2
w*
=
w0
if wN – zW ≤ w0 ≤ wN + zF
1
wN + z F = ( v + r ) + z F
if w0 > wN + zF
2
Comparing Figures 4 and 5 shows that the characteristics of nominal wage rigidity under
outside options are very similar to the characteristics under the Holden (1994,1999)
version of disrupting trade. However, the key empirical interpretation is very different.
Under threats of disrupting trade, the source of downward nominal rigidity lies in the
costs that are incurred by threatening to disrupt trade. In contrast, the source of downward
nominal rigidity when outside options are the relevant threat is the switching costs. As
argued in Holden (2002), the employment protection legislation is a key institutional
variable for downward nominal wage rigidity, as strict employment protection makes it
difficult for the employer to replace a worker, which should be associated with a high
value of the switching costs zF.
10
Within the empirical framework of A&D and F&G, Result 2 and Result 3 have
the same predictions, and the discussion applying to Result 2 above applies here too. The
model can explain α > 0 and λ > 0, but it also imposes the restriction α = λ.
6
Adverse productivity effects of a cut in nominal wages
In empirical literature on downward nominal wage rigidity, like Akerlof, Dickens and
Perry (1996), the source for the rigidity that is focussed is usually fairness considerations.
The survey evidence reported by e.g. Shafir, Diamond and Tversky (1997) and Bewley
(1999) suggest that a nominal wage cut may have an adverse effect on productivity. Thus,
the firm may abstain from cutting the wage, even if the situation otherwise would suggest
a cut. To capture the adverse effect on morale, I assume that total revenues are reduced
by c > 0 if a wage nominal wage cut takes place. Trade is nevertheless still efficient, as I
assume v – c – r > 0.
The set-up and analysis is simple. Firm sets wage unilaterally. The firm will profit
from cutting wage if v – c – r > v – w0, i.e. if the gain in lower wage costs outweigh the
costs associated with lower productivity. If w0 < r, the firm must raise the wage so as to
retain the worker. Otherwise, the wage is kept constant.
Result 4: Firm sets wage under adverse productivity effect of nominal wage cut
w*
=
w0
if
r + c ≥ w0 ≥ r
r
otherwise
The result is displayed in Figure 6 below. Compared to the empirical evidence, this
model can explain the threshold value α > 0. However, it cannot explain why downward
nominal wage rigidity may affect the wage given that a cut occurs, i.e. that λ > 0.
7
Contract renegotiation with adverse effects on productivity of a
cut in nominal wages
Although the contract and fairness explanations are alternatives, they can easily be
combined. Given the additional evidence supporting both explanations (contracts do
exist, and may be efficient; survey evidence does support the existence of fairness
considerations relative to a nominal wage cut), combining the two explanations seems an
obvious thing to do. Thus, in this subsection I extend the Holden (1999) model displayed
in Figure 3 to incorporate fairness considerations. Specifically, to capture the adverse
effect on morale, I assume that total revenues are reduced by c > 0 if a wage nominal
wage cut takes place. Trade is nevertheless still efficient, as I assume v – c – r > 0.
To analyse the effects of this extension, consider first the subgame taking place at
step 3, given that the firm has initiated a lock-out, with the aim of cutting nominal wages.
As before, the outcome is given by the Nash bargaining solution (but now taking into
consideration that the gain for the firm from reaching an agreement is reduced):
(10)
w = arg max (v – c – w)(w – r)
11
which solves for
1
(v − c + r )
2
The critical value for the initial contract, denoted wLQ, for which the firm at step 2 is
indifferent between initiating a lock-out, inducing a renegotiation to wC, or prolonging
the initial contract, is given by
(11)
wC =
(12)
v – wLQ = γ(v – c - wC)
which solves for
 γ γ
wLQ = v 1 −  + ( r + c )
 2 2
LQ
Thus, if w0 > w , a threat from the firm of initiating a lock-out to enforce a nominal
wage cut is credible, as the firm obtains higher total payoff from doing so than from
prolonging the existing contract.
However, in contrast to the case with no adverse effect on productivity of a nominal
wage cut, the actual wage that will be implemented is not equal to this critical value.
Rather, the wage implemented, denoted wLC, is the wage offered by the employee at step
2a that gives the firm the same payoff as it would get by initiating a lock-out, given by
(13)
(14)
v – wLC - c = γ(v – c - wC)
which solves for
 γ γ
wLC = ( v − c ) 1 −  + r
 2 2
LQ
LC
Note that w – w = c > 0. Intuitively, the results may be explained as follows.
Initiating a lock-out to enforce a nominal wage cut involves two types of costs for the
firm, the fixed costs of a work stoppage, and the adverse morale effects of a nominal
wage cut. Thus, the firm will only do this if the initial wage is a lot above the wage that
would result after lock-out, ie wLQ is “high”. However, given that initiating a lock-out is
in fact credibly (w0 > wLQ), the adverse productivity effects lose their strategic effect,
because they will be incurred irrespective of lock-out takes place, as long as the nominal
wage is cut. In fact, these costs weaken the worker position, as they make the firm less
eager to reach an agreement.
(15)
Result 5: Contract renegotiation with adverse productivity effects of a nominal wage
cut
The SPE outcome satisfies
1− γ
wS = w N −
if w0 < wS
(v − r )
2
w*
=
w0
if wS ≤ w0 ≤ wLQ
1− γ
wLC = w N +
( v − r − c ) if w0 > wLQ
2
12
The result is displayed in Figure 7 below. If the initial wage is in the interval [wS, wLQ],
the firm does not benefit from forcing a cut in nominal wages. However, if the revenues
and costs v and r are low relative to the initial wage, implying that wN also is so low that
w0 > wLQ, the firm benefits from enforcing a cut is nominal wages. The firm can then
enforce a cut down to wLC.
Compared to the empirical framework, this model is consistent with both the
existence of a threshold value α and a higher wage relative to the notional wage given a
cut takes place, λ. Furthermore, α > λ > 0, consistent with the evidence of F&G.
7.1
Outside options with adverse productivity shocks of a nominal wage cut
Similar results hold if the outside option case described above is extended to allow for
adverse productivity effects of a nominal wage cut in the same way. As before, the payoff
of the firm from keeping the worker at the initial contract is v – w0, while the payoff from
replacing the worker is v – wN – zF. Thus, the firm can credibly threaten to replace the
worker if v – w0 > v – wN – zF, which is equivalent to w0 > wN + zF. The issue is then
whether the worker can and will make a counteroffer that the firm prefers compared to
replacing the worker. The firm will accept a counteroffer from the worker of w’, given by
v – w’ – c = v – wN – zF, as this gives the firm the same payoff as it obtains by replacing
the worker. w’ can be solved for w’ = wF + zF – c. The worker will benefit from making
this counteroffer if this gives higher payoff than finding another job, i.e. if w’ > wN – zW.
Thus, comparing the requirements for w’, there is a counteroffer which the worker
benefits from and the firm will accept if and only if zF + zW > c, i.e. if the total costs
associated with a separation are greater than the costs associated with a nominal wage
cut. The result can be summarised in
Result 6: Outside options under adverse productivity effect of a nominal wage cut
The SPE outcome is
1
w N − zW = ( v + r ) − zW
if w0 < wN – zW
2
w*
=
w0
if wN – zW ≤ w0 ≤ wN + zF
1
wN + z F − c = ( v + r ) + z F − c
if w0 > wN + zF and zF+zW ≥ c
2
separation if
if w0 > wN + zF and zF+zW < c
The outcome will be similar to the one described in Figure 7, associated with α > λ > 0.
7
Concluding remarks
Empirical studies of downward nominal wage rigidity conducted by Altonji and
Devereux (1999) and Fehr and Goette (2000) document the existence of substantial
downward nominal wage rigidity in both the US and Switzerland. There is evidence for
the existence of a threshold value (α) for a wage cut, so that a “notional” wage cut
smaller than this threshold value will not be realised. The estimates of the threshold value
α are in the order of magnitude 20 to 30 percent. Altonji and Devereux and Fehr and
13
Goette also find evidence that the downward nominal wage rigidity affects the actual
wage even when the wage is cut, so that the wage cut is smaller, and the actual wage
greater (the difference is denoted λ), than what would have been the case without
downward nominal wage rigidity.
In this paper, I show that simple models of downward nominal wage rigidity
based on fairness considerations explain the existence of a positive threshold value α.
However, if a wage cut takes place, then there should be no effect on the nominal wage,
i.e. λ = 0, in contrast to the empirical evidence. I then show that common contracting
models can explain that both α and λ are positive, however they also suggest that α = λ,
on which there is conflicting evidence. I propose a new model where adverse productivity
effects are incorporated in a standard contracting model, and shows that this model
explains the finding of Fehr and Goette that α > λ > 0.
14
References:
Akerlof, G.A., W.T. Dickens and W.L. Perry. (1996). The macroeconomics of low
inflation. Brookings Papers on Economic Activity 1, 1-75.
Altonji, J.G. and P.J. Devereux (1999). The extent and consequences of downward
nominal wage rigidity. NBER Working Paper 7236.
Bewley, T.F. (1999). Why Wages Do Not Fall During a Recession? Harvard University
Press.
Blanpain, R. (ed) (1994). International Encyclopaedia for Labour Law and Industrial
Relations. Deventer: Kluwer Law and Taxation Publishers.
Binmore, K., A. Rubinstein, and A. Wolinsky (1986).The Nash bargaining solution in
economic modelling. RAND Journal of Economics 17, 176-188.
Binmore, K., A.Shaked, and J. Sutton (1989). An outside option experiment. Quarterly
Journal of Economics 104, 753-770.
Cramton, P. and J. Tracy. (1992). Strikes and holdout in wage bargaining. Theory and
data. American Economic Review 82, 100-121.
Fehr, E. and L. Goette (2000). Robustness and real consequences of nominal wage
rigidity. Institute for Empirical Research in Economics, University of Zurich, WP 44.
Fernandez, R. and J. Glazer (1991). Striking for a bargain between two completely
informed agents. American Economic Review 81, 240-252.
Haller, H. and S. Holden (1990). A letter to the Editor on wage bargaining. Journal of
Economic Theory 52, 232-236.
Holden, S. (1989). Wage drift and bargaining. Evidence from Norway. Economica 56,
419-432.
Holden, S. (1994a). Wage bargaining and nominal rigidities, European Economic Review
38, 1994, 1021-1039.
Holden, S. (1994b). Bargaining and commitment in a permanent relationship. Games and
Economic Behaviour 7, 169-176.
Holden, S. (1997). Wage bargaining, holdout, and inflation. Oxford Economic Papers 49,
235-255.
Holden, S. (1998). Wage drift and the relevance of centralised wage setting.
Scandinavian Journal of Economics 100, 711-731.
15
Holden, S. (1999). Renegotiation and the efficiency of investment. Rand Journal of
Economics 30, 106-119.
Holden, S. (2002). The costs of price stability – downward nominal wage rigidity in
Europe. NBER working paper 8865.
Knoppik, C. and T. Beissinger (2001). How rigid are nominal wages? Evidence and
implications for Germany. IZA Discussion Paper 357, University of Regensburg.
MacLeod, W.B. and J.M. Malcomson (1993). Investment, holdup, and the form of market
contracts. American Economic Review 37, 343-354.
MacLeod, W.B. and J.M. Malcomson (1995). Contract bargaining with symmetric
information. Canadian Journal of Economics XXVIII, 336-367.
Malcomson, J.M. (1997). Contracts, hold-up, and labor markets. Journal of Economic
Literature 35 (4), 1916-1957.
Moene, K.O. (1988). Union threats and wage determination. Economic Journal 98, 471483.
Rubinstein, A. (1982). Perfect equilibrium in a bargaining model. Econometrica 50, 97109.
Shafir, E., P. Diamond and A. Tversky (1997). Money illusion. Quarterly Journal of
Economics CXII, 341-374.
Shapiro, C. and J. Stiglitz (1984). Equilibrium unemployment as a worker discipline
device. American Economic Review 74, 433-444.
Tobin, J. (1972). Inflation and unemployment. American Economic Review 62, 1-18.
16
Actual wage changes
ln w – ln w0
Cuts
-α
α-λ
ln wF (Flexible wage)
Freezes
450
Notional wage changes
ln wF – ln wF0
Figure 1: The relationship between actual and notional wage
changes in the empirical studies of Altonji and Devereux and Fehr
and Goette.
17
w
wN = (1/2)(v+r)
w0
wN
2w0/(k+1) 4w0/(k+1)
Figure 2: Outcome of wage bargaining in MacLeod and
Malcomson (1993). The wage is cut if v < w0 (which is equivalent
to wN < 2w0/(k+1)); the wage is increased if r > w0 (which is
equivalent to wN > 4w0/(k+1)).
In Figures 2, 4, 5, and 7 , the x-axis measures wN, based on a
proportional increase in r and v: it is assumed that v=kr, k > 1,
implying that wN = [(k+1)/2]r.
Figure 3. The wage bargaining game of Holden (1999)
Negligible time
1a
1b
1c
2a
2b
Firm:
Offer w1
Employee: Employee: Employee: Firm:
Reject/
Strike ?
Offer w2
Reject/
Accept
Accept
2c
3
Firm:
Lock-out?
Alt. off. barg.
Starting at step 3, there is an alternating offers game of the Rubinstein (1982), with two
alternative exogenous payoffs, zero if strike or lock-out, otherwise the payoffs of the initial
contract. Steps 1 and 2 determine which type of payoffs prevails. In equilibrium, an agreement is
reached at step 1 or 2, so that step 3 is not reached, and no strike or lock-out is realised.
18
wL=(1-γ/2)v +(γ/2)r
w
wN = (1/2)(v+r)
wS=(γ/2)v+(1-γ/2)r
w0
wN
Figure 4: Outcome of wage bargaining in Holden (1994, 1999).
See also explanation in Fig 2.
wN = (1/2)(v+r) + z
w
wN = (1/2)(v+r)
wN = (1/2)(v+r) - z
w0
z
-z
wN
Figure 5: Outcome of wage bargaining with outside options. See
also explanation in Fig 2.
19
w
w=r
w0
w0 - c
w0
r
Figure 6: Firm sets wage unilaterally, adverse productivity cost c
> 0 of a nominal wage cut.
wLQ = (1-γ/2)v +(γ/2)(r+c)
w
wLC = (1-γ/2)(v-c) +(γ/2)r
wN = (1/2)(v+r)
wS=(γ/2)v+(1-γ/2)r
w0
-(1-γ/2)c
wN
Figure 7: Outcome of wage bargaining under adverse
productivity effect c > 0 of a nominal wage cut. See Fig 2.
20