European
Economic
Review
35 (1991)
1543-l 557. North-Holland
Exchange rate policy and wage formation
in an economy with many trade unions*
Steinar
University
Received
Holden
of Oslo, N-031 7 Oslo 3, Norway
December
1989, final version
received
November
1990
Exchange rate policy may confront governments
with an important
credibility problem. While
there is usually a long run gain from abstaining
from devaluations,
there may also be a short
run benefit from a devaluation.
This short run benefit may cause expectations
of future
devaluations,
resulting in wage and price rises that make the expectations
self-fulfilling. This
issue is analysed within a model with many trade unions. If the government
pursues a nondevaluation
policy, the trade unions gain from voluntary
wage restraint, However, if the nondevaluation
policy isn’t credible, the cooperation
on wage restraint may break down.
1. Introduction
Since the collapse of the Bretton Woods system, exchange rate policy has
been an active part of the economic policy of many governments.
Devaluations have been used in order to improve a country’s competitiveness,
so as
to reduce any current account deficits and increase employment.
However,
frequent devaluations
also involve considerable
costs, as wage and price
setters will learn to expect future devaluations.
Thus some countries,
like
Denmark,
have explicitly
announced
a non-devaluation
policy, so as to
influence expectations
and break the vicious circle.
A problem with a non-devaluation
policy is its credibility. Wages are often
determined
in annual negotiations,
while the exchange rate can be changed
at any point in time. Thus, a government
may feel tempted to exploit the
short run rigidity of wages, and devalue in order to obtain a short run gain
in terms of improved competitiveness.
Problems of this kind have been discussed in the literature on credibility of
*This paper is part of the research project ‘Wage formation
and unemployment’
at SAF
Center for Applied Research at the Department
of Economics,
University
of Oslo I wish to
thank
Michael
Hoel, Karl Ove Moene, Oddbjorn
Raaum,
Jon Strand,
two referees and
participants
at presentations
in Barcelona and Bode for helpful comments on earlier drafts.
C@14-2921/91/$03.50
0
1991-Elsevier
Science
Publishers
B.V. All rights
reserved
1544
S. Holden, Exchange rate policy and wage formation
government
policy, see Blackburn
and Christensen
(1989) for a survey.’
Compared
to more traditional
analysis
of government
policy, the game
theoretic approach of this literature has the advantage
that both government
policy and the behaviour
of the private sector are endogenised,
allowing for
explicit focus on the interaction
between them. However, a problem with this
literature is that the private sector is treated as a single player. This makes
the existence of a conflict of interest between the government
and the private
sector, a crucial assumption
in this literature,
less obvious. After all, the
individuals
in the private sector and the political electorate consist of largely
the same people, and will therefore have largely the same preferences. In the
literature
one therefore
usually
assumes
that there is a labour
market
distortion
which is the cause of this conflict of interest. But this assumption
begs the question of why the government
does not pursue a first-best policy
and remove the distortion directly.
Once one allows for several agents in the private sector, the situation
is
entirely different. Each agent will be concerned
with the effects on its own
welfare only, and disregard any externalities
on the aggregate economy. The
government,
on the other hand, will mainly be interested
in the aggregate
outcome. If the wage setting takes place at a decentralised
level, externalities
will arise, and the government
will not be able to remove these.
This paper analyses the interaction
between wage formation
and exchange
rate policy in an economy
with many trade unions.
Compared
to the
literature
referred to above, the assumption
of many trade unions has two
main virtues. First, as discussed above, the existence of many agents in the
private sector allows for an explicit modelling of the externalities
in the wage
setting. Because of this, and because the preferred outcome of the government coincides with the preferred outcome of the private agents, it is also
possible to draw conclusions
on welfare implications.
This contrasts
with
most of the literature referred to above, where, as argued by Blackburn
and
Christensen
(1989), conclusions
on welfare implications
seem doubtful
as
long as the preferences of the agents in the private sector remain unmodelled.
Secondly, for unionised
economies, the assumption
of many trade unions
seems much more realistic than the assumption
of a single central trade
union. Even in countries
like Norway and Sweden, which are often considered the most centralised,
the largest unions’ confederation
LO represents
only 36 (1985) and 52 (1987) per cent of all wage earners, respectively. Other
confederations
cover 23 per cent in Norway and 37 per cent in Sweden [cf.
the country papers in Calmfors (1990)].
‘The bulk of this literature
focusses on monetary
policy
atomistic private sector, following Kydland and Prescott (1977)
A smaller part of the literature
[cf. Calmfors and Horn (1985)
analyses fiscal policy or exchange rate policy in a game between
trade union.
in a closed economy
with an
and Barro and Gordon (1983).
and Horn and Persson (1988)],
government
and a single central
S. Holden, Exchange rate
policy and wage formation
1545
An important
premise of this paper is based on a conclusion
drawn by
among others Calmfors and Driflill (1988) that centralised wage setting leads
to lower real wages than does wage setting at industry
level. The basic
intuition
is the following. If wages are set at industry level for each union
independently,
then each union will obtain a high real wage level, leading to
a high unemployment
rate in the economy. This involves negative external
effects on the welfare of other unions. However, if the unions act cooperatively, then they will internalise
the negative external effects and thus set a
lower real wage.
If the unions have the opportunity
to enter into a binding agreement
on
wage restraint,
or to negotiate
wages jointly,
then the unions could be
expected to achieve the ‘low’ wage level they prefer. But either of these
alternatives
would make the case with many unions similar to the case with
a single central union. As argued above, this does not seem like a realistic
description
of the world. Thus, I explicitly exclude both alternatives.
Without
any of these options, it may be difficult for the unions to coordinate
their
wage setting, as each union will be tempted to deviate from an agreement on
wage restraint
and set as high wage. That this is a real problem, can be
illustrated
by the statement
by the leader of the Norwegian
unions’
confederation
LO that the total wage increases in 1986 had been too high
[Halvorsen
(1986)].
I analyse the question of whether union cooperation
on wage restraint can
be sustained as a non-cooperative
equilibrium
in a repeated game. In each
time period, each union has the possibility of defecting from the agreement
on wage moderation
and setting a high wage level, thus obtaining
a short
run gain. Such defection will lead to a breakdown
of the agreement.
As is
standard
in repeated games, cooperation
will be sustainable
as long as the
short run gain from a defection is less than the subsequent
loss from a
breakdown
of the cooperation.
The loss, i.e. the outcome of independent
wage setting compared
to the
outcome of cooperation,
arises through a higher real wage and a higher
unemployment
rate. However, the adverse effects on unemployment
will be
mitigated if the government
pursues a devaluation
policy, as the real wage
will be reduced towards its full employment
level. Government
policy will
therefore affect whether or not unions are able to cooperate, as a devaluation
policy may make the costs of independent
wage setting so small that
cooperation
is not sustainable.
The idea that industry unions may cooperate to achieve wage restraint is
neither surprising nor new [cf. Danthine
and Lambelet (1987)]. Yet the issue
of how this cooperation
may come about has received little attention.
Because of this, there is no framework for evaluating
how such cooperation
may be affected by government
policy. The present
paper shows that
credibility
of government
policy can be crucial for the existence of union
1546
S. Holden, Exchange rate policy and wage formation
cooperation
on wage restraint, and that the policy will be credible only if the
government
is sufficiently patient.
The basic setup is similar to that in Holden and Raaum (1989). However,
Holden and Raaum (1989) contains a more general discussion of union wage
moderation,
and no analysis of the effects of varous exchange rate policies.
Furthermore,
this paper extends the basic setup considerably,
by including
government
policy as an endogenous
part of the model.
The paper is organised as follows. Section 2 sets out the macroeconomic
model, which is kept as simple as possible in order to focus on the game
theoretic aspects. The government’s
and the unions’ policy alternatives
are
presented
in section 3. In section 4 I discuss union cooperation
within a
repeated game setting, while in section 5 I extend the model by endogenising
government
policy. Finally, there are some concluding
remarks in section 6.
2. The model
We consider a small open economy,
with K 22 symmetrical
industries,
each consisting of many identical firms. In each industry there is production
of a different traded good with a given world market price. There is also a
single union in each industry,
covering
all workers in the industry.
The
economy’s exchange rate is determined
by the Government.
The Government
cares about
its popularity,
which depends
on the
employment
level and the rate of inflation. These variables are influenced by
the nominal wage in each industry, which is set in a wage bargain between
the union and an employers’ federation
in each industry. The leadership
in
each union also cares about its popularity,
which depends on the after-tax
real wage level and the employment
level in its industry.
Unemployed
workers
receive an unemployment
benefit which is financed
by a proportional
tax on all labour income in the economy. Thus, higher wages in
one industry will raise aggregate unemployment
and the tax rate. (To keep
the analysis tractable, this is the only external effect that is incorporated
in
the model.)
In each time period, the nominal
wage is determined
simultaneously
in
each industry; afterwards the Government
sets the exchange rate. This time
structure
captures
the fact that wage settlements
are made at discrete
intervals while the exchange rate can be changed at very short notice. As in
Horn and Persson (1988) I rule out any indexing in the wage settlements
by
assumption
(this conforms with the empirical observation
that wage indexation is rare [cf. Oswald and Turnbull
(1985) and the country
papers in
Calmfors (1990)]). Throughout
the paper I assume that all players have
complete information.
An important
assumption
in this paper, as well as in much of the literature
referred to in the introduction,
is the existence of short run nominal
wage
S. Ho/den, Exchange rate policy and wage formation
1547
rigidity. Clearly, without nominal rigidities, a devaluation
would be entirely
useless, and credibility
of exchange
rate policy would not be an issue.
However, Poterba et al (1986) present evidence for the existence of nominal
rigidities in the U.S. and the U.K. Furthermore,
the introduction
of Calmfors
(1990) summarises
evidence from the Nordic countries
showing
that all
major devaluations
but one during the last two decades have resulted in at
least a temporary improvement
of the competitive position.
World market prices are assumed constant over time and normalised
to be
equal to unity in all industries.
This implies that the domestic price is the
same for all goods, P,, and that it is set directly by the Government
via its
exchange rate policy. In each industry, labour demand is given by
Li,=L(wyPt),
L’<O,
(1)
where I+$ is the nominal wage in industry i. At the aggregate level, we define
total employment
L,= Ci Lit, and the average wage w=Ei ~*Li,/L. If the
wage and price levels are equal in all industries,
then total employment
is
given by
L, = N( kt/P,) = Ci L( i+/P,),
N’ < 0.
(2)
The total labour force in the economy is normalised
and set equal to one.
Hence, there will be full employment
if P,=ZW,,
where I have defined
Z= l/N-‘(l).
The Government’s
per period popularity
G, is a strictly quasiconcave
function of the employment
level and the rate of inflation,
G,= G(L,,fl,),
defined
neglect
assume
(3)
over L,E [0, l] and IIt= P,/P,_ 1 - 1 E [0, co). (This implies that
the possibility
of revaluations).
Concerning
the partial derivatives
that they are continuous
and that
G,(L,,ZI,)=O
for L,= 1,
G,(L,,17,)>0
I
I
for L,< 1,
(4)
G2(L,, Ii’,) = 0 for ITI,= 0,
G,(L,, H,) > 0 for II, > 0.
Thus, Government
popularity
is maximised
when there is full employment
and zero inflation. Furthermore,
if full employment
and zero inflation are not
attainable
simultaneously,
then the assumptions
on the partial derivatives
ensure that the Government
will set the exchange rate so that there are both
a strictly positive rate of inflation and a strictly positive unemployment
rate.
1548
S. Holden, Exchange rate policy and wage~ormation
The Government’s
popularity:
f
overall
objective
is to maximize
the present
value
of its
6pGj,
(5)
j=t
where 6, is a discount
factor. 6, is assumed
to include
an exogenous
probability
1 - pc that the Government
is replaced
by a new identical
Government
(so the game finishes for this Government).
(A better approach
would clearly be to endogenise
this probability,
but this would complicate
matters considerably.)
Thus 6, = pc/( 1 -i), where i is the pure interest rate.
The per period popularity
of the leadership
of the union in industry
i
(hereafter referred to as union utility) is an increasing function of the aftertax real wage level and the employment
level in the industry, or
where r, is the tax rate. The overall
objective
of each union
is to maximise
(7)
where the discount factor of the unions is 6u=p,/(l
-i), and 1 -p.
is an
exogenous probability
that the leaderships of all unions are replaced by new
leaderships. A replacement
of the Government
is assumed to be uncorrelated
with a replacement
of the leaderships of the unions.
Unemployment
benefits are assumed to be taxable, set in nominal terms in
the beginning
of the year, and denoted
B,. In this case, the tax rate is
determined
by
T,ci ~,Li, = B,( 1 - Z,)( 1 - L,),
(8)
where the left hand side shows the tax proceeds from the employed workers,
and the right hand side shows total benefits net of taxes. Eq. (8) yields
(1 - T.,)= Ci wilLi,/Cci M/;~Li,+ B,( 1 -L,)].
We can substitute
(9) into (6), to obtain
To
exposition,
simplify
the
I assume
that,
(9)
if wages
are
identical
in all
S. Holden, Exchange rate policy and wage formation
industries,
level.
then (10) is maximised
3. Union and Government
1549
when wages are set at the full employment
policy alternatives
We first consider exchange rate setting in one time period in isolation, and
when all unions have set the same wage. Full employment
is achieved if the
Government
sets P,=ZII$
while zero inflation
will be realised
if the
Government
holds the exchange rate fixed, P, = P,_ t. If w = P,_ l/Z, then full
employment
and zero inflation can be achieved simultaneously.
I shall distinguish
between two types of exchange rate policy. Accomodating policy is to set the exchange rate at the level which is optimal when one
period in considered in isolation, taking as given the wage level already set in
the industry bargaining.
That is
P:’ = argmax G(L,, n,).
(11)
From the assumptions
on G it follows that P:’ is unique. As noted above, it
also follows that if W,> P,_,/Z,
then Z~>P~>Pt_l,
that is, the Government will set the exchange rate so that there is a strictly positive rate of
inflation and a strictly positive unemployment
rate.
Strong policy is to hold the exchange rate fixed, so that there is zero
inflation, i.e.
p;=p,_,.
(12)
We now turn to the industry wage setting. The outcome of the industry wage
bargaining
is assumed to be given by the Nash bargaining
solution, that is
(13)
subject to Li, =L( WJPJ,
where /I is the bargaining
power of the union,
n, = (P,F(L,)
- Wi,Lt,)/P,
is the real profits of the firm, and U,, and rctO are
the parties’ respective disagreement
points. Following
standard
practice [cf.
Jackman, Layard and Nickel1 (1990)], I assume that the disagreement
point
of the firm is zero, rr10=0, while the disagreement
point of the union is an
increasing
function
of the after-tax
real benefit level and a decreasing
function
of the unemployment
rate (aggregate
wages are omitted
for
simplicity,
but
this
is of no importance
for the
results),
U,,=
U,(B,(l -Q/P,,
u,), where u,= 1 -L, is the aggregate
unemployment
rate. The
solution to (13) is a real wage equation
1550
S. Holden, Exchange
rate policy and wageformation
where h, >O, h, ~0, while the sign of h, is indeterminate (subscripts denote
partial derivatives) (The proof is available from the author on request). As
the industries are symmetric, the outcome of the wage bargaining will be the
same in all industries, so we can omit subscript indicating industry.
Substituting out for the aggregate unemployment rate and the tax rate, and
straightforward calculation yields the reduced form wage equation
where, under reasonable assumptions H’ r 0 (derivation is available from the
author on request) [this is also the standard result, cf. Jackman, Layard and
Nickel1 (1990)]. The intuition here is that higher real benefits will raise the
payoff of the unions during a dispute, which strengthens the bargaining
position of the unions.
If unions and firms expect the Government to pursue an accommodating
policy, the outcome of the wage bargaining r/v: is given by W;‘/P;‘=
H(B,/Pf). A crucial assumption on Wf is that W: > P,_ ,/Z, so wage setting
by each union independently will lead to unemployment
even if the
Government
pursues an accommodating
policy. If the Government
is
expected to pursue a strong policy, the outcome of the wage bargaining Ws
is given by Ws/Pf= H(B,/Pf). As Pf> P;“, it follows that B,/P;‘<B,/Pf
and
thus that Wf/P;” < Wf/Pf, so the real wage level will be higher when the
Government is expected to follow a strong policy. The reason is that the
price level is lower under a strong policy, making the real benefit level higher
which strengthens the bargaining position of the unions.
If the Government pursues an accommodating policy, total employment is
L~=~(W~/~~)=L~
< 1. Let UA denote union utility in this case. If the
Government
pursues a strong policy, total employment will be L,=
N( Wf/P;) = Lf < L;4. Us denotes union utility in this case. As Lf < Lt, it
follows that Us< UA, i.e. if there is independent wage setting the unions are
better off when the Government follows an accommodating policy. The
intuition here is that all unions lose from the high wage level and high
unemployment rate under independent wage setting. However, if the Government follows an accommodating exchange rate policy, the real wage level
and the unemployment rate will be lower, and the loss will be reduced.
As the industry unions realise that independent wage setting leads to a bad
outcome for all, they will wish to come together and agree on a lower wage
level. Such an agreement can be implemented through the industry wage
bargaining. The employers will clearly not object to a wage level which is
lower than what each union can enforce through industry bargaining. The
unions will prefer an agreement on W: = P,_ ,/Z. The Government will then
set P,=P,_ ,, and the outcome will be full employment and zero inflation.
Let U’ denote union utility in case, where UC> UA.
S. Holden, Exchange rate policy and wage formation
1551
Even though the unions have agreed on a lower wage level, each one of
them will nevertheless
have the opportunity
to deviate from the agreement
and conduct a normal industry wage bargaining.
If union i alone deviates
from cooperation,
it will obtain the wage level W$ given by
W!JP, - I= h&/P,
_ 1) 1 - Ld, 1 - ?d),
(16)
where
L”=C L(w:/P,_,)+L(w~*/P,_,)
j#i
and
1-zd=
w:
[
c L(w:/P,_,)+
j#i
j#i
W: 1 L(W:/P,-,)+
[
W~*L(W~*/P,_,)
I/
w:L(w;t/P,_l)+B,(l-Ld)
1(
and where I have assumed
that each industry
is so small that the
Government
always set P, = P,_ 1 if only one union
deviates
from the
agreement on W: (this assumption
simplifies the exposition without affecting
the substance
of the paper). Define Vd as the utility of a deviating
union,
when all other unions stick to the agreement. As a deviating union benefits
both from the wage restraint in the other industries and from its own high
wage, we have Vd> V’.
4. Conflict or coordination?
We now look at one time period in isolation, where Government
policy is
exogenous,
but without any restrictions
about whether or not the unions
cooperate. Clearly, the unions would wish to cooperate, as this gives a higher
payoff. However, given the actions taken by the other unions and irrespective
of what the Government
will do, the best action for each union is to deviate
from any agreement
and obtain as high wage as possible. Thus the unique
Nash equilibrium
in a one-shot game is independent
wage setting in each
industry, resulting in W: or Wf, depending on the policy the Government
is
expected to pursue.
Consider now the complete game, with an infinite number of time periods,
and the following strategy for the unions.
(1) Cooperate
until some union
alone deviates
from cooperation.
S. Holden, Exchange rate policy and wage formation
1552
(2)
If some union alone has ever
cooperate in the future.
deviated
from
cooperation,
then
never
Thus, if one of the unions deviates from the agreement, all unions revert to
the one-shot
Nash equilibrium.
Let us first assume that the Government
follows an accommodating
policy. The strategy specified above will support
cooperation
as a subgame perfect equilibrium
if
Ud-uc~S”(UC-UA)/(l-S”),
(17)
where the left hand side indicates the immediate
gain from defecting while
the right hand side shows the subsequent
loss from lack of cooperation
in
the future. If the Government
follows a strong policy, the corresponding
condition is
Ud- UC5 S,( UC- V)/( l-6,).
Proposition I.
There
such that cooperation
(18)
exist two critical values c?~,S~E(O, l), where dA> 6’,
is sustainable as a subgame perfect equilibrium [f and
only if
(i)
c&,Z;~~ and the Government follows an accommodating
and the G overnment follows a strong policy.
policy, or
(ii) fi,zt?
Proof.
See appendix.
Thus, there may exist situations
(if S’<S,<
SA), where union cooperation
is
sustainable
only if the Government
is expected to follow a strong policy. In
these situations
a ‘strong’ Government
will be able to achieve both full
employment
and zero inflation,
while a ‘weak’ Government
will achieve
neither. The reason is that under an accommodating
policy the situation with
independent
wage setting is not bad enough
for the unions
to deter a
deviation, whereas it is bad enough under a strong policy.
5. Is strong policy credible?
We now depart from the assumption
that Government
policy is exogenous. From Proposition
1 we know that cooperation
is never sustainable
if
of government
policy.
6, < Ss, and always sustainable
if S,>SA, irrespective
We shall focus on the more interesting
intermediate
case, where S’<S, <SA.
That is, cooperation
is sustainable
only if the Government
is expected to
follow a strong policy. Clearly, as the Government
benefits from cooperation,
it will be tempted
to announce
that it will pursue a strong policy if
cooperation
breaks down. We shall look at whether such an announcement
is credible, that is, whether strong policy is time-consistent.
S. Holden, Exchange rate policy and wage formation
1553
This problem is somewhat more complicated
to analyse than a standard
repeated game problem. As long as the unions cooperate,
full employment
and zero inflation
are achieved simultaneously.
Thus, accommodating
and
strong policies coincide, so there is no policy choice for the Government.
Yet
whether
or not cooperation
is sustainable
depends
on the policy the
Government
will follow if cooperation
breaks down.
If there is no agreement on wage moderation
(because the agreement has
broken down), the per period payoff of the Government
is higher if it follows
an accommodating
policy. Furthermore,
the Government
has no hope that
the present
leaderships
in the unions
will restart cooperation.
Yet the
Government
will also be interested in what the new leaderships of the unions
It seems intuitive
that the Government
will do if there is a replacement2
can ‘encourage’ the new leaderships of the unions to reach an agreement on
wage restraint
by following a strong policy before there is a replacement.
Correspondingly,
if the Government
follows an accommodating
policy, then
it seems reasonable
that this might lead to independent
wage setting also for
new leaderships
of the unions. This intuition
is formalised in the following
strategies and Proposition:
Government
(1) Follow a strong policy if the Government
has followed a strong policy
until now.
(2) If the Government
has ever followed an accommodating
policy, then
follow an accommodating
policy.
Unions
(1) Cooperate
if the Government
has followed a strong policy until now,
and if no single union (with the present leadership)
has ever deviated
from cooperation.
(2) Do not cooperate if the Government
has ever followed an accommodating policy or if some union alone (with the present leadership) has ever
deviated from cooperation.
Proposition 2. Let ~3~~6~~6~. For all pUe(O, l), there exists a critical value
6* ~(0,l) such that cooperation is sustainable as a subgame perfect equilibrium
if and only if 6,26*.
Furthermore, 6* is increasing in po, so that the smaller
‘Assuming
that the leaderships
of all the unions are replaced at the same time is of course
unrealistic. A more realistic interpretation
of this feature is that an exogenous event takes place
which makes all unions reconsider any agreement on wage moderation.
Examples of such events
can be an adverse supply shock to the economy or that ‘many’ of the leaderships of the unions
are replaced.
1554
S. Holden, Exchange rate policy and wage formation
the probability that the leaderships of the unions are replaced,
‘patience’ is required of the Government.
Proof:
the more
See appendix.
The intuition
here is that a patient Government
will be willing to follow a
strong policy if the agreement breaks down, because a patient Government
puts sufficient weight on the expected future gain of inducing new leaderships
of the unions
to reach an agreement
on wage restraint.
The existing
leaderships of the unions will realise this, thus, a patient Government
will be
able to achieve both full employment
and zero inflation in situations where a
less patient Government
will achieve neither.
Trigger strategy equilibria
have been criticised on the grounds that they
are not ‘renegotiation
proof’, i.e. if a deviation
were to occur, the unions
would have an incentive to agree on not undertaking
the punishment.
This
argument
seems compelling
in an analysis
of a game between
perfectly
rational players. Yet renegotiation
proofness is not necessarily an appropriate
requirement
concerning
models of union behaviour.
It would be very hard
for the leadership of a union to suggest wage moderation
if another union
defected the previous year. Arguments like ‘Last year was a mistake, but they
promised
that this year...’
may have trouble
in convincing
the union
membership.
Thus, a deviator cannot be certain that a deviation
will be
‘forgotten’. I find it more realistic to assume that whether or not it is possible
to restart an agreement
is determined
by other aspects, rather than being
inferred directly from assumptions
concerning
union behaviour.
The best
would be to have an explicit model for these other aspects, but in the
absence of this, I let this be determined
by an exogenous random variable.
6. Concluding remarks
I have analysed the interaction
between wage formation and exchange rate
determination
in an economy with many trade unions. It is shown that such
an economy can exhibit some of the same features as Horn and Persson
(1988) argue hold in an economy
with a single central trade union, as
accommodating
exchange rate policy may lead to both high inflation
and
high unemployment.
The intuition
behind the results is different, however.
Horn and Persson’s result arises as the central trade union sets a high
nominal wage in anticipation
of a devaluation,
thus obtaining
its target real
wage. In my model the trade unions have a comon interest in achieving full
employment,
yet this may not be possible to realise because each union will
have an incentive
to deviate from any agreement.
An accommodating
exchange rate policy will reduce the costs to the unions of a breakdown
of
S. Holden, Exchange rate policy and wage formation
1555
an agreement, and this may make cooperation
less likely, as the punishment
for a defection from the agreement wll be less severe.
In my model, as well as Horn and Persson’s, a short-sighted
government
will find it difficult to make a non-accommodating
policy credible, as the
government
is assumed
to make a short-term
gain from breaking
its
Thus both Horn and Persson
(1988) and this paper provide
promises.
arguments
for the use of external constraints
on government
policy. In fact,
in Britain and Norway advocates of joining the European
Monetary
System
often use the argument
that this would make a non-devaluation
policy
credible [see e.g. the Economist
(1989)]. Furthermore,
within these models
one can also argue, as do Fischer and Summers (1989) that governments
should not make any attempts to reduce the costs of inflation, as this may
reduce credibility.
But one should be aware that any of these conclusions
depend crucially on the assumption
that anti-inflationary
policy is indeed
enough to remove inflation
without large reductions
in output. Empirical
evidence on these matters is as yet scarce [cf. Blackburn
and Christensen
(1989)] so more research, both theoretical
and empirical,
seems necessary
before firm policy conclusions
can be drawn.
Appendix
Proof of Proposition 1. The existence of a critical value is a general property
of trigger strategies in repeated games, so no proof is provided
for this.
Observe that it is not possible for the unions to inflict a harsher punishment
on a deviator than what is the case with the strategy above, as a single union
can always achieve Wt or Wf (depending
on Government
policy) through
industry
bargaining,
and the other unions
cannot
get more. Thus, the
strategy above constitutes
an optimal penal code, implying
that if cooperation is not sustainable
with this punishment,
then no other punishment
will
do [cf. Abreu (1988)]. To see that 6*> as, note that VA> Us, so equality in
(17) and (18) gives 6* > 6’.
0
Proof of Proposition 2. It follows from Proposition
1 that the strategy of the
unions is a best reply in every possible subgame, and that it inflicts the
harshest possible punishment
on any deviator. As I have neglected revaluations, following a strong policy is also the harshest punishment
the Government can inflict on a deviating
union.
It remains
to show that the
Government
strategy is a best reply in every possible subgame. If cooperation breaks down and the Government
follows an accommodating
policy,
then a new agreement will never be formed with this Government,
resulting
in W: and accommodating
policy in all future periods. Let GoA denote the
per period payoff of the Government
in this case (total expected payoff is
GoA/( 1 - 6,)).
E.E.R.-
C
S. Holden, Exchange rate policy and wage formation
1556
If cooperation
breaks down and the Government
instead follows a strong
policy, the old leaderships of the unions will set Wf. However, in each period
there is a probability
1 -pv that the leaderships are replaced, and in this case
the new leaderships
will form an agreement.
Denote Go’ and GS the per
period payoff of the Government
with the old leaderships
(without cooperation) and the new leaderships
(with cooperation),
respectively.
The total
expected payoff of the Government
is
Go’ + pu~GGos + p:G;GoS +. . . + (1 - pu)G,GS
+(l -p;)G;GS+(l
=
Gas/(
1-
The Government
pu&J
-p;)S;G’+...
+ &A
will choose
GoA5 Go?1- 6,)/( 1-
1-
p,)@IC(
a strong
~“6,)
I-
6,)(
1 -p&)1.
policy if
+ a,(
1 -pu)Gs/(
1 -pa&J.
(A.1)
We have GoS< GoA < GS, and note that the right hand side on (A.l) is a
weighted average of Go’ and GS. For any given p”~(0, l), the weight on GS is
one when 6, approaches
one and
strictly increasing
in 6,, approaching
approaching
zero when 6, approaches
zero. Thus equality in (A.l) defines a
critical value 6* such that (A.l) will hold if and only if 6,26*.
To see that
in pa.
6* is increasing
in pa, observe that the weight on GS is decreasing
Thus, if pu increases, a higher value of 6, is required to preserve equality in
(A.1).
•I
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