UNI\'ERSITETETI OSLO
CONTENTS
OKONOMISKE
DOKTORAVHAI\DLINGER
1.
fntroduc ti on
and
z.
N on-cooperati v e
?
Local
4.
Wage dri ft
R
A barg ai ni ng
6.
w age
and
s umnary
w age bargai ni ng
w age bargai ni ng
c entral
2 - 1990
\\AGE BARGAINING:
and bargai ni ng
theory
of
i nfl -ati on
THEORYAi\D SOME
NORWEGIAI\I
EVIDENICE
tests
BY
STEINARHOLDEN
UTGI:IT AV
SOSir\LOKO\ON'IISKINSTITU'IT
PO STI J O I { S1095BI , I N D E R N
0317O SLO 3
bargai ni ng
of
trade
and
uni on
effi c i enc y
rnodel s
w ages :
S ome i mpti c ati ons
for
A BARGAINTNG THEORY OF INFIATION
by
H ol den
S tei nar
p aper
Thi s
of
unemploymentil
at
of
U ni v ers i ty
E con orni c s ,
from
H oel ,
co mments
from
A ndrew
A s bj orn
parti ci pa nts
at
for
of
K arI
Ov e
Moene,
and
in
Fehr,
R ol f
(E E A ,
and
the
Department
hav e
benefi ted
Gol ombek ,
R agnar
Oddbj orn
B ol ogna
at
drafts
E arl i er
E rns t
R ods eth
pres entati ons
Research
Applied
os l o.
I' W age forrnati on
proj ec t
res earc h
H uw D i x on,
Os w al d,
S outhampton.
the
SAF Center
R ubi nstei n,
and
_l
part
is
Mi c hael
N y moen,
R aaum,
1988),
and
E s s ex ,
A ri el
from
Os l o
1.
TN T R OD U C TION
I nfl ati on,
al most
aIl
w ages
ov er
of
v ary i ng
c api tal i s t
ti me
degrees ,
ec onomi es .
s trongl y
is
a pers i s tent
is
Moreov er,
domi nated
v ari ati on
by
in
feature
in
in
c hanges
money
pri c e
the
ABSTRACT
are
co n sid e r e d
wo r ke r s
are
wage negotiations
model
where
there
is
a
in
a co n flict
nominal
counteract
tion.
th e
wage
th e
Hence
a
with in
to
a ssu m e d
th e
wh ile
in cr e a se ,
wo r ke r sr
str o n g
co n flict
model
fi rm
p o sitio n
of
in
i ncrease
the
is
in fl ati on
w age
Ii ttl e
to
s ay
to
vi ew
determi naa
has
are
a n a lyze d
with in
thi s
of
w age
s i tuati on
is,
that
i nfl ati on
is
there
of
rel ati v e
c ours e,
purel y
rec ent
w hy
in
of
w age model s ,
al l
c ons i s tent
phenomen,
foc us
s houl d
the
w hi c h
A n underl y i ng
w i th
ari s e
w i th
a v i ew
i nfl ati onr.
an ec onomy
i nfJ .ati on
more
w ages .
a monetary
be that
the
theori es ,
enti rel y
ex pl anati ons
to
i .s no reas on
or
real -
of
effi c i enc y
and c ompeti ti v e
v ery
hav e
v ers i ons
like
formati on,
of
T hi s
s eems
l .J age deterrni nati on
S tandard
model s
determi nati on
domi nated
of
i nfl ati on.
bargai ni ng
assumpti on
p o tiy
theori es
about
theori es
on the
obtai n
in
c urrent
uni on-firm
if
pri ces
generated,
m o d e l w h e r e a t l ag e n tsa r e r a tio n a l.T h e e ffe ctso fe xp ansi onary
economic
they
Y et
popul ar
bargarnrng
cooperati on
w i thdraw
A s a resul t,
b a r g a in in g .
th e
a mul ti -year
l eveI.
rati onal
w i thi n
agents ,
pri v ate
the
framew ork'
sector.
Thi s
paper
T hi s
basi c
set
in
a
pri ce
of
perfect
E ac h
N as h
there
i ts
is
c hal l enge
a dy nami c
and
betw een
i mperfec t
produc t.
egui l i bri um,
real
to
y ear,
bargai n
i nformati on.
dernand,
ai ms
dev el ops
el ements .
market
state
paper
w ages
thi s
w here,
and
eac h
uni on
agents
for
are
ec onomy ,
any
enpl oy ment
bel i ef.
mac ro rnodel w i th
c ompeti ti on,
A l -1
In
in
thi s
gi v en
are
fi rm,
and
fn
eac h
l ev el
c ons tant
and
is
s ets
there
a uni que
of
real
from
are
produc t
the
fi rrn
rati onal -,
there
fol l ow i ng
w ages
nomi nal
fi rrn.
so
the
the
is
s teady
aggregate
one y ear
to
I
One explanation is based on the view that inflation is the result of a game betu'een
government and the private sector, where the government tries to "fool" the private sector in
ordcr to achicvc a highcr activity lcvcl of the cconomy, cf eg Barro and Gordon (1983) and
Backus and Driffill (1985). Another explanation focus on inflation as a means of taxation, cf
eg P hcl p s and W i nrer (1973).
t-F;@Esi
5
I
and pric e
rate.
a
is
there
If
si mpl e.
is
r e su lt
th is
b e h in d
i n t u i tio n
The
that
an
d e l a y i n r e a c h i n g an a g r e e m e n tin th e wa g e b a r g a in in g ,t}reuni on
the
to
a cco r d in g
wo r k
or
c o op e r a tio n
withdraws
not
allowed
ty
the
w o r k e r s'
pay.
th e
Thus,
a
workers
will
n o m in a l
wa g e
s h ar e
the
w hen
in d e fin ite ly.
r a ise
ll
staggering
the
will
fi rm
on
not
the
l et
i ncrease
fi rms
stock,
and
p r i c e s , c a u s i n g i n fla tio n ,th e wo r ke r std isa g r e e m e n tp oi nti s
is
th e
by
ca u se d
as
pri ces
in cr easi ng
fir r n s
a conse-
with
th e
of
The
i m plica tio n s
the
c o n fli- ct/str u ctu r a list
popular
ten
to
ye a r s
twe n ty
to
a p p r o ach
a g o .2
w hi ch
i nfl ati on,
o n e probl em
w i th
the
w as
the
trcoretr
w a s p r o vid e d .
To
explicit-J-y
on m o d e r n
Rrrbinstein,
1982 ) ,
b a r g a in in g
and
the
T n co n tr a st,
a ll
th e o r y
a g e n ts
are
rate
rnodel
present
(B i nmore
et
assurned to
al ,
be
is
based
1996,
rati ona]
and
'
the
of
bas i c
the
v ery
be
c entre
of
ai r' .r at
z ero
pol i c i es
s unmers ,
i nfl ati on
co n o r r i - arl
and
are
s et
is
there
the
no
l i terature
(L982)
H art
produc t
the
w hi c h
1989).
c aus ed
and
mark et
if
the
features
as pos s i bl e.
are
mac ro model .
the
w age
the
money
Many gov ernments
w i th
abov e,
the
thes e
and pos s i bl y
c os ts
there
w age
of
is
i nfl ati on
a pos i ti v e
determi nati on,
the
be di s as trous .
r
hav e
H ow ev er,
di s c us s ed,
in
tri ed
in
to
the
order
B y i nc orporati ng
bargai ni ng,
in
pol i c y ,
H ow ev er,
by
ri s e
rnenti oned
the
pri v ate
the
A s s oc i ated
reduc e
c entraL
s ome ex tens i ons
a
rnonetary
the
as s i rnpl y
w i thi n
pol i c y .
i nf rati on
hi ghl i ght
in
to
eg
i nfl ati on.
c oul d
a more s ati s fac tory
i c
forl ow
by
ec onomi c
pol i c i es
paper
a w age
pri c es
So
s ee
c aus ed
thes e
i deas
al ternatel y ,
of
how ev er,
c an ari s e
of
consi derati ons
I S.:c e,.q.I-Iincs (1969), Qviqstacj(1975) and Scitovskry
(1978). A critique is given in Purdy and
(
7
e
7
4
\
.
Zis
of
s et
ex i s tenc e
c onc erni ng
i nfl ati on
a s tri c t
and
are
s ame.
s houl d
Fi s c her
is
moders ,
nec es s ari -l y
any
di fferenc e
mac ro
governm ents
from
The nai n
c an be rel ated
as s unpti ons
w hether
bank s
the
w age
model
of
a p p r o a c h , h o w e v e r ,wa sth a tn o r e a llysa tisfa cto r ym ic ro
foundation
of
at
consequenc es
confl i ct
the
for
on the
dec j .s i ons .
ex pranati ons
(cf
has many si mi l ari ti es
model
p r e se n t
as the
pri c es
l i terature
deterrni nati on,
I'moneta ry rr
abstaj -n
q u e n c e o f t h e w o r ke r slstr o n g p o sitio n in th e wa g e d e te rmi nati on.
w age
c ompeti ti on
not
r e d u c e d i n r e a l t e r n s,a sth e m o n e ywa g e isfixe d ' In sh o rt
inflation
the
and
modeL,
pres ent
and
central -
pres ent
the
i s s ue
is
c ruc i al
the
the
(1986).
w ages
w age and pri c e
ess enti -aI1y
sector,
res embl es
the
(1985),
The
is
after
of
w ei tzma n
are
(1986)
In
i mperfec t
rul e'
w i II
they
and
p r ice s,
se t
fir m s
th e
s pi ral .
aLs o
eg B ranc hard
w hi c h
F i naJ -l y ,
goi ng
gi vi ng
to
w ork
of
a p e r i od
the
the
as
had'
the
is
w i th
up
end
they
th a n
assumpti on
consequent-
bargai ni ng
the
in
a lwa ys
a vo id
to
in cr e a se
However,
workerrs
b a r g a in in g
h i gh e r
a wage
accept
p o in t
d isa g r e e m e n t
yet
i ts,
w orkers'
the
to
r e m u n e r a tio n
r e d u ce
to
is
prof
in
a drop
in vo lve s
T h is
b e l o w) .
ied
f i rr'r
cf
B l anc hard
i mmedi ateJ -y
a n i n f l e x i b l e w a y ( wo r kto r u le ) ( th isa ssu m p tio n wi} } b e
justif
s pi ral ,
in
pri ce
in
rul es
w orki ng
paper
The pres ent
constant
a
at
i ncrease
va r ia b le s
n o m i- n a f
a Il
w hile
next,
the
a phi rJ -i ps
s et
l as t
to
effi c i enc y
c urv e
out
part
dev erop
w age
effec t
-1
6
p a pe r
The
main
in
is
section
fo l1 o ws.
th e
2 presents
S ecti on
state
ste a d y
4 e xte n d s
Se ctio n
th e
summar-izes
th e
wh ile
a s s u m p t i o n s,
3.
as
o r g a n ise d
1
is
equi l i bri um
basi c
S taqe
anal ysed
and
rnodel ,
the
1:
spendi ng
secti on
5
over
under
T h e eco n o m y
a f i xe d
in
fir;r,
each
to
sold
C, and
a g ig a n tic
the
A,/
co n sid e r a tio n
number
la r g e
p r o d u ce s
firrn
Each
of
a
consi sts
n id e n ti cal
number of
a n d th e
of
n uni ons,
g o ve r n ment,
Y ,,
w hi ch
is
bei nq
2:
rn
the
stage
one
quanti ti es
the
of
government.
and the
quanti ty
in
types
four
fi rms,
h o u sehol ds
good,
d iffe r e n t
h o u se h o ld s
3:
firn
negligible
the
sets
is
produc*the
p r i ce
Each
stages,
the
beginning
product
simplicity
a ssu m e d
m a r ke t
mation.
i-on
o n th e
ye a r
th e
is
th e
sta g e s
are
output
to
have
di vi ded
ta kin g
pl ace
at
th e
sa l- e s ,
ta ke s
p la ce
clisco u n tin g
th ird
stage,
throughout
w i thi n
the
the
perfect
are
onl y
a
IeveL.
so
a ctio n s
wh ile
any
and
have
competi ti on,
a ssu med
ye a r ,
n e g le ct
w i II
fi .rm
pri ce
im p e r fe ct
a g e n ts'
two
a sin gl e
a g g r e g a te
P,. A1 1 a q e n ts
and
I
sm a l- l,
th e r e
fir st
cf
total
money s toc k
on
fn
fi rm
i nfor-
i .nto
three
the
i mn.edi ate
pri ce
setti ng,
the
year.
year "
For
rel ati v e
uni on
w age
nomi nal
gov ernment
M. The gov ernment
pri c es ,
E ac h
fi rm
s ets
produc ti on
T here
is
cf
ti me
betw een
s ome
reas onabl e
gi ven
and
that
fi xed
the
tradeoff
bel ow .
l e ngth
of
ti ons
ov er
costs
in
th i s
i mmedi ate l y
throughout
thi s
is
w ages ,
the
be set
bel ow ,
the
for
i nv ol v es
the
there
are
the
gi v en
pri c e
l dages
y ear.
thei r
di s tri buted
equal s
wilr
tak en
tak e
is
and
demand
ov er
s al _es ),
not
the
thus
di s ti ngui s h
are
fi rms
c aptured
are
peri od
l -ev er
c os ts
s et,
is
the
to
rare.
to
are
bei ng
hol d
The
fac t,
as
negoti a_
any
bec ome
be
as
A ri k ery
w i th
l _ev ers
rev ers
then
fi rs t.
i nc orporate
as w i l l
it
as s umpti on
a s ty ri _z ed
v ery
it
uni ons ,
determi ned
is
but
behav i our
as s oc i ated
and,
for
and
by
and ernpl oy ment
w ages ,
ex ogenous ,
gov ernrnent
v ari abres
w age
as
many
and enproy ment
are
y ear.
1ev e1s ,
to
r s ha1l
r mak e no attempt
The pri c e
opti marl y
ev enl y
bargai n
c urrent
empl 0y ment
s i mpl i c i ty
w age c ontrac t
but
the
(produc ti on
Thi s
there
management)
ac c ordi ng
are
is
they
that
moder.
after
As
of
in
and
rnoder
dec i s i on
adj us tment
for
the
the
and demand
opti marl y .
gov ernment
conti nuou s
reason
of
that
adj us t
s ares
s uppl y
c omment.
seems
pri c e
and for
s truc ture
prev ai l
equi l i bri um
i nv entori es ,
(i e
buy produc ts
and
mark et
and fi rrn
r-ev er- to
functi on s .
year'
to
fi rm,
and gov ernment
The
in flu e n ce
eac h
notati onal l y
= C,*Ai'
each
depends
househol ds
deserves
As
nomi nal
nomi nal
r negl ec t
r e s p e ctive ly.
(1)
goods
determi nes
r e su lts.
THE MODEL
agents:
A and the
betw een
staqe
2.
gov ernment
The
s uc h
as s urned
apparent
deterrni _ned
c ons tant
9
I
W e ma ke
th e
ye a r ,
A1:
fn
the
e x p r e s sio n .
(2)
e a ch
H(
fo llo win g
e a ch
h o u se h o ld s
M n /Pi
{ C i,i) ,
gov ernmentrs
A 2:
Th e
the
sa me as
(i
r , ch
maxi mi zes
uti l i ty
accordi ng
( E- l) ' trl E l {E -1))
'(M,,/p,r)t-' ,
to
tl < r,
0<
(5)
G(
subj ect
=
)
{ A ,)
, gi v en
hous ehol ds r
the
([X ,
goods
betw een
tradeoff
assumptions .
by
is
c onv eni enc e
for
a max i mi z ati on
of
tr,t[' tl ' t]l E (u-l )) ,
to
F\1
X ; P ,A i = A .
(6)
to
th e
budget
w age
A11
A 3:
subject
current
X i Pjch i + M t, :
gov ernment
The
hol -ds.
(3)
the
h,
C n i is
th e
q u a n tu r n
m o n e y b a r a n ce s
P.n is
the
utility
the
n
g o od s
of
and
c o n su m p t j- o n .
f uture
p r ice
wh e r e
4
h o u se h o ld
h o u se h o r d
a g g r e g a te
f u n ctio n ,
(r,
E is
h
h,
Bn is
le ve I.
th e
r e fle cts
purchases
the
budget
th e
of
t radeoff
T h e a g g r e g a te
pri ce
of
i,
to
is
use
th e
for
the
to
hous e-
t
a frac ti on
tax es ,
and
fi nanc es
hol d
more
money ,
i ts
of
hous ehol d' s
eac h
defi c i ts
by
i nduc i ng
to
in
substi tuti on
betw een
l -evel
Mh i s
the
among
current
and
def i ned
by
po i s
(7)
IP .\Y A = M -
A -
ie
M-t,
househord
parameters
E and n are
e la sti ci ty
good
of
w here
Yo is
aggregate
real
brought
househol ds
hav e
the
c urrent
en d
of
T he uni on
ov er
y earrs
S now er,
M_, i s
to
money
nomi nal
s toc k
and M = Zn Mn i s
y ear,
money s toc k .
c are
L986) ,
the
prev i ous
from
nomi nal
as s umed
is
and
output,
onl y
defi ned
about
as
w ere
w ho
thos e
(c f
i ns i ders
the
eg
empl oy ed
p lt/n ) ttr r ) ,
in
which
c ol l -ec ts
as
i nc ome
Lj -ndbec k
p,r =
(.1)
di s tri buted
are
B5 ,
househol ds
where
profi ts
and
i nc ome
co n str a in t
goods
a p p r o p r ia te
th ^
n n cr r r ' ) r f o r r
p r ice
u til
ity
i ndex
f uncti on
from
duati ty
(2) ,
cf
theory,
Wei tzman
the
fi rm
y ear
l as t
focus
on
s teady
from
one
y ear
to
qui ts
will
vol untary
and
s tate
hav e
equi l i bri a
the
nex t.
s hel ter
fn
the
qui t
not
w here
empl oy ment
thi s
c as e
i ns i ders
I
v ol untari l y .
j -s
the
c ons tant
ex i s tenc e
the
from
s ha]l
ri s k
of
of
l os i ng
(1985).
T h e u tlr i- ty
of
future
soivc
of
money
co n sr .r m p tio n ,
a c on p le te
is
th u s
in te r te m p o r a l
a ssu m e d
r
d o n ot
to
be a proxy
assume
m a ximi zati on
that
for
the
probl en.
tLi e va]ue
househol -ds
thei r
j ob,
S o,
w ages
(thi s
as s urnpti on
A ssumi n g
real -
l i neari ty ,
wac l e ]ev el .
on
the
rnargi n,
is
the
not
uni on
the
c ruc i al
uti l i ty
uni on
for
w i Ll
the
c an
c are
res ul ts ,
be
s et
onl y
cf
equal
about
bel ow ).
to
the
11
t0
P\
n e xt
I th e
year,
ye a r,
cu r r e n t
in d ica tin g
subscript
e tc)
Ye a r ,
current
to
F u r th e r m ore,
one.
to
equal
se t
is
a n d th e
o m itte d
is
fir m
indicating
w hi l e
subscri P t
fol J.ow i ng
the
in
aggregate
save
.,
current
in
U , measured
uti l i ty
and
(here
by
g ive n
i=
pri-ces,
u n io n
a n d fu tu r e
cu r r e n t
Total
A4:
l evel
P ri ce
T
notati on
i -ndi cates
B
level
in
ye a r
P revi ous
yearrs
(11)
u tility
wJ :
and
fa cto r
u n io n
w age
Th e
Po :
W,/P .t; i s
w age
reaL
the
(I2)
by
so
that
profit
Y :
L.
T h e p a i' o ff
in
m e a su r e d
cu r r e n t
of
l { = arg
is
w ri tten
of
as a functi on
as
w i II
to
returns
th e
th e
onl y
fi rm
R( L )
-
wL ,
pay off
of
i nv ers e
to
fi rm,
the
by
( p i /Po ) tPi ( r - ) )r J - w j q l
r
wL +
and
fi rm.
[R -
is
deterrni ned
outc ome
The
N as h bargai ni ng
as y mmetri c
max
fi rm
eac h
WL -
+ p
r
-
{ V r(W )
through
of
thi s
),
a
w age
bargai ni ng
s ol uti on'
V r(W r)}
]'
be expl ored
i w - q + F {u r ( w ) - u r ( w r ) i
in
i nput'
the
scal e
The
current
producti -on
scal e
year
l t'"
beIow .
r
to
is
set
a del ay
is
the
bargai ni ng
I
Pr ice s
in
will
the
the
fi rmrs
of
happen
the
w age
the
di s c ounted
l ev el
in
the
is
uni onts
from
effec t
demand s c heduLe,
pay offs
res pec ti v e
B i nmore
w age
et
l ev el
reac hed.
equi l i bri um)
w ork ers
l -abour
al ,
l -986),
w here
duri ng
and c
is
the
fi rm.
that
agreement
the
(c f
the
as s ume
on the
and the
bargai ni ng
pow er
s hal l -
not
bei ng
empl oy ment
and q are
bargaj -n i ng,
( r o)
in
Last
a new w age
(e)
and future
gi v en
the
is
w
r e l- a tionshi p
L,
is
uni on
the
f') '
co n sta n t
J- a b o u r ,
with
technology
a
has
fir m
Each
pri c es ,
P (L) L -
{
l ev el -
betw een
subj ect
A5:
= max
V (w -r)
gi ven
is
a n d th is
c urrent
P (L)
co
bargai n
-1
w as
wa g e s,
real
Tota}
and
"j
( so W :
fu tu r e
T o ta l
fi rm,
i ='l
tl
j
c urrent
in
measured
A 6:
d isco u n t
th e
is
where
demand func ti on.
the
the
of
func ti on
rev enue
'
U ( wr ) :!' l+ tBj
-) - L
the
omi t
@
(8 )
is
will
no
s tart
y ear.
l as t
on
Thi s
future
B
y ears '
y earrs
{ V r (W ) profi t
c ons tant
j -f
that
i mpl i es
agreement
nex t
Thus
remai ns
is
reac hed
unti l
(w hi c h
in
bargai nj -ng
V r (W .r) }
of
the
w i th
ref l ec ts
reac hi ng
an
R:R( L) :P( L) L,
3 A s i s rrc l l -k norv n,the s ame rc s u l t s c a n
b e o b t a i n e d i n a n o n -c o o p e ra t i v c b a rg a i n i n q n t o d e l .
For thi s parti c ul armodel , thi s i s d o n e i n H o l d c n (1 9 8 8 b ).
13
L2
agreement
lf
on
c o r r e s p on d in g
co m p a r e d
to
not
in te r p r e ta tio n
any
reachi ng
p
be gi ven
ca n
agreement,
{U r(W)
-
and
U r(w ,)
a
party
on the
).
ac ti on,
i ndustri ar
partyrs
A'/:
I f
ning,
th e r e
th e
without
is
wo r ke r s
a ctu a lly
assume
th a t
th e
w o rke r sr
the
a d e la y
direct
with d r a w
co o p e rati on,
thus
b r e a kin g
th e
rul ,es
e m p lo ye r
or
d u r in g
an agreement
r e a ch ing
is
The
w orkers
fr on
in
th e
the
(w ork
to
are
w ork
in
to
bargai ni ng
rul e).
l egal _l y
assumed
ruLe,
to
so
the
bargai -
to
the
f
threat
no
uni onrs
w ork
to
is
while
th e
payoff
cf
the
fir m
dur i ng
a
c onfl i c t
is
for
the
pi c ture
cent
other
the
is
(14)
n :OR- W_ tL
or
0 < o < 1,
where
g
is
th e
fr a ctio n
of
n o r m al
revenue
w hi ch
obtai ns
duri ncr
in
a c o n f l i c t.
the
the
A s th e
a ssu m p tio n
b a rg a in in g
is
l i t e ra tu r e
c o m m e n t.
F ir st,
of
cr u cia t
(one
wo r k
to
fo r
the
e xce p tio n
a p r o b le m
with
is
rul e
w hol e
Moene,
the
in
case
mcdel
19gB ),
assumpti on
of
but
it
of
a confl i ct
very
rare
deserves
other
types
in
in
sone
of
c hoos e
poi nt
in
manual
the
mai n
di s agreement
and
re al
i ts
res ul .t
bargai ni ng.
w ages .
equi l i bri um
z ero
Thus I
in
rul -e
the
agreed
of
ty pes
of
go
and
and
to
s l ow ,
w ork ers
60-70
uni ons r
not
that
number
non-nanual
s tri k es
c ountri es
that
to
rul e
rf
the
poi nt
z ero
there
w oul d
i nfl ati on,
thi s
totar
other
For
c ent
fac t
empi ri c al ry .
per
and the
us e
s tri _k es
w age bargai ni ng.s
w ork
rul "e
as
in
i nfl -ati on
w i th
per
30-40
s ome N ordi c
l oc aL
betw een
c ent.
in
s al ary
i ndi c ates
the
to
c as e
here.
(r987)
w ork
w hi c h
thei r
i mportant
of
thi s
di s c us s ed
k eep
appl y
in
be
in
is
w ork ers .
ban,
55 per
hav e
z ero
c ent
ov erti me
|
be
not
threat,
not
a c os t
i mpos e
need
w ork ers
s al amon
by
equi l i bri um
state
r ' f h c , c a s e *' h cr e th e r .,,o r kcr s' p a v r e clu ce d
is
cl uri nga ccl ntl i ct(a case I shal l refcr to as qo
skr'.r'.cf \'Ioenc, 1988).ftrr examplc hccauseof bonus schcmcs.is analvsedin Appcndix D. In
t h t s c a s c th e r c will still b c a u n ir lu estca d y sta te equi l i bri um,w i th a c(rnstantrate ol 'chanqe i n
l h e n o n t i n a l va r ia b lcs.If th e p e r ccn ta Ecr e d u c ti on i n the w orkers'pay i s l ess thrrn hal f the
r c d u t : t i o nin p r o lit, u ' h ich sce m s to b c a r ca sonabl eassumpti on,the rate of i nfl al i on u'i l l bc
positivc.
the
in
al s o
probrem
to
tak en
In
the
s eems
it
the
probJ _en w i l l
renai ni ng
w i th
coul d
A s the
ev en c rearer
T hi rdl y ,
equi l i br i um
1989).
per
as s oc i ati ons
l oc k -outs
(thi s
45
ac ti ons .
empl oy ers t
out
for
like
they
Thus
c arry
ruLe
ac c ount
that
ac ti on.
reported
ac ti on,
account
W.I ,
Q:
B ri tai n
is
c redi bre
thi s
to
ac ti ons
i .ndustri al
(13)
rul -e,
w ork
onl y
i ndustri ar
be
and H ol den,
for
stri kes
the
ac tual l y
not
s ec ondry ,
E vi denc e
s tri k es ,
tak es
to
will
1988,
duri -ng
reduce
have
w hi c h
i nteres ts
H al rer,
productj ,on
reduci ng
a posi ti on
in
d isu tility
a co n flict
w orki ng
not
r e m u n e r a tio n l.
u tility
payoff
in
like
or
i nfrati on
c as e
as
v r' as i n
uni on
order
no
s teady
be c hanged
s tri k e
ec onomy
the
in
not
is
to
c annot
i ts
obtai n
prev ai l
the
uni on
di s agreement
a
c ourd
if
s tate
s teady
s tate
c hoos e
w ork
hi gher
nomi nal
in
a s teady
to
ei ther.
5 Thcrc arc ho*cvcr
ccntral rvagc ncgotiations wherc lhcsc measuresmav bc uscd. This is
neqlected in the prcsent analysis. Thc intcrclependencebetween local and central wa[e
bar_qai n i nq
i s ex pl orc d i n H ol dc n (19ti 8a).
15
L4
be
of
Io ck- o u ts
o fte n
workers
as
a s y m r n e tr y
u se
by the
of
menti oned
above,
are
p a r ty
can
but
p o sition
a s th e
lo ck- o u ts,
a
cal l
al so
N ote
the
in
ment
pri c e
aJ s o
and
constant.
wilt
the
wilt
w i II
be
the
rate
(7),
c ondi ti on
c ons equentl y
of
p r o ce e d in g ,
by
meant
th a t
a ssu m p tio n
th e
be
sh a ll
I
more
preci se
fi rms
are
al l
be much
th a t
I
notation
but
firms,
in
th e
a lso
p a r a m e te r s
th e Y
e q u i - l,ib r iu m
€ and p are
is
w hat
about
of
si x
PA
=
A s teady
A =
v ec tors
s tate
equi l i bri um
(A ,.,A r,A z ,
do
set
are
the
(P46rP411P42,
\
),
al l
same i n
the
same pri ce
(but
!
(D3)
Pj/PN : kr,
\]j tJ W i
\
al I
model,
and
wh e r e
c r u tp u t
steady
sta te
b a r g a i n i ng
nominal
a ll
p r ice s
nominal
wa g e s
r e la tive
are
and
co n sta n t
wa g e s
e q u ilib r iu m
state
a steady
and
pri ces,
fr o m
ch a n g e
kr s
= P i + t/P 1 :
agents
other
d e fin e
The gov ern(thi s
the
so
and
nomi nal
real
money
aggregate
output,
will
be
in
l! -
thi s
ec onomy
s uc h
c ons i s ts
),
(Mo,MrrMz ,
),
lY =
the
aeti ons
(W 6rW 17W 2r
that
L^,
W i /P e1 = k 4,
so ) .
(D 5)
to
w age
the
i nfl ati on
that
(P 6rP 1 1P "7
)
mMj l / P A j
at
one
real
year
to
u n io n s
a ch ie ve
the
wa g e s,
ke e p in g
r e la tive
w ages
next,
rate
constant.
of
w hi l e
In the
i ncrease
E ach
fi rm
w here
9 rR ,k r,
total
l-abour
(D 1)
a
Loosel y,
rate.
as fol l ow s.
same
a ll
the
agents
as
pay offs ,
tak i ng
of
the
gi v en,
thi s
eni pl oyment
w ages,
a constant
ca n b e descri bed
in
equi l i bri um
P ..,+ t/P .A r = s ,
max i mi z e
T H E ST EADY ST AT E EOUIL IBRIUM
W e n o w p r o ce e d
of
the
= kz'
(D2)
rf nR
3.
:
(k r,Lr,l z ,
gA/Pa.+
To si npl i fy
P
),
L -
and
....)
Thi s
i denti cal .
i denti cal .
w ages
fi rms
al l
a ssu m e th a t
will
yearrs
l- a st
a ssu m e th a t
do not
I
E,
ov er
c ons tant.
ernpl oy rnent
al -s o
and
w e hav e
Formal Iy ,
D efi ni ti on:
/ nl
implies
mark up
in
l ev el
w age
c ons tant,
i nfl ati on),
greater.
B e fo r e
be
c ons tant
at
rate
prev ai l i ng
the
w ages
budget
at
a
be
s pendi ng
the
ri s es
ov er
pri c es
s o real
nomi nal
through
demand,
is
l -ev el
fi rm,
eac h
ri s es
stock
rel ati v e
Thus ,
in
mark up
i mproves
will
revenue
as a c ons tant
fi rm.
ensures,
be
it
that
bargai ni ng
in
r educti on
can
because
confl i ct,
the
Ievel
i ncurs
seems to
pri c e
the
aggrega te
that
because
(there
donrt'r).
fir m s
fir m ' s
producti vi ty,
unfai r
may
l ock-outs
that
is
al so
fi rm
as the
and
lo ck- o u ts
wh ich
th e
th a t
o b v io u s
is
o n co o p e r ati on
fe e lin g s
h a ve
'rworkers
and there
reason
An o th e r
th a t
to
occurs,
b e c redi bl e,
rnay not
a
as
never
One
th is.
fo r
e ffe ct
fe e l
a lm ost
l ock-out
uses
fi rm
the
that
T h is
lo ck- o u t.
a
d u r in g
a n a d ,ve r se
have
not
r u le .
r e a so n s
loss
an
to
s e v er a L
threats
a
wo r k
to
repJ-y
p o ssib ility
th e
n e g le ct
I
w age
in
sets
='!n:F
there
is
w hi l e
the
k t,
kl,
enough
and
(as s umed
s uppl y
i mpl i es
k r,
that
f
i nterpretati on
to
res tri c t
av ai l abl e
l -abour
of
pos i ti v e
s are
be
c ons tants ,
c ons tant
attenti on
in
(D 2)-(D 6)
and
to
s houl d
be
LA i s
ex ogenous ).
s i tuati ons
(c f
aggregate
and
(16)
obv i ous .
w here
bel ow ),
I7
16
of
state,
and
main
(1985),
to
A.
a p p e n d ix
so l- ve
one year
of
la st
stage.
part
In
taken
is
and
the
of
rest
P (L)
takes
a v ery
Yi :
( Pi/P.r)
fi rst
'''"
w hi c h
s etti ng)
constant
( 1s )
+ pv (w )
wL
),
profi t
v rel 1-k now n,
is
does
l ev el
at
determi ned
probl em
Thi s
pay off
future
bec aus e
al ready
are
As
.
is
pri c e
y earts
thi s
s i nc e
(15) .
of
i nv ers e
the
not
on
depends
ti me
the
of
the
l ui th
max l mi z ati on
eguati ons
tw o
fo l- l- o win g
is
(thi s
pay off
w ages ,
current
the
form,
s i mpl e
future
pri ce
th e
of
fo r m
in
model
-
P (L)L
t
P -r(nLl Y .r)-1/' [L
w here
affect
refati onshi p
the
max
the
government
and
=
L
Wei tzman
from
V(w -r)
steady
shorten
to
househoLd
gi ves
in
model
l argel y
government
th e
the
(L7)
pro-
state
steady
order
d e ri vati on
T h is
and
h o u se h o ld s
th e
between
the
d e r iva tion
th e
r e le g a te
behavj-our
expl ore
th is
a n d b e ca u se
I
sh a ll
th e
witn
sta r t
t e xt,
I
e co n o m y.
th is
perties
I
fo llo win g ,
th e
In
o rder
demand
of
el -as ti c i ty
pri c i ng,
mark -up
i mpl i es
and
the
is
c ondi ti on
n ,
^/
P = bW ,
(18)
and
Y.r :
(1 6 )
w here
b = I/(I
order
c ondi ti on
m are
and
p o sitive
from
deri ved
co n stants
the
A.
appendi x
a b o ve ,
fa cin g
e a ch
fir m ,
Eq u a tio n
(16)
d e fines
E quati on
(15)
same
the
w i th
al l
E.
d e r n an d
agqregate
real
of
g o ve r n m e n t
real
l et
(18)
by
h o u se h o ld s
each
tu r n
In
f ir m .
variabLes
are
to
th e
sta te
co n sta n t,
so I
p r o g r a m m in g
price
is
year
It
can
and
empl oyrnent
V(w -r)
ca n omi t
p r o b le m
faci ng
=
vr (W)
subscri pt
the
fi rs t
be
ens ure
for
be opti mal
a uni que
the
fi rm
after
the
to
max i mum.
s et
the
pri c e
to
(18)
i mmedi ateJ -y
w age
bargai ni ng,
the
pri c e
l ev el
c ons tant
remai n
the
throughout
y ear.
defi nes
the
uni gue
profi t
max i mi z i ng
pri c e
l -ev el
of
the
pri c es
s et
by
other
fi rms ,
the
fol l -ow i ng
tri v i al -Iy .
as
i nterpreted
rel ati on-
m acroeconomi c
p r :ice
ste a d y
T h e d y n a m ic
l e ve l
p r e vio u s
Ke yn e sia n - typ e
a r e c l u c e d - fo r m
We now
fr o m
the
brouqht
Iemma f ol l ow s
over
so
L,
a
as
demand
money stock
and the
sp e n di ng
in
el asti ci ty
i rrespect i v e
functi-on
to
w i tl
it
ac c ordi ng
As
of
s uffi c i ent
c onc av e
is
the
is
and then
fu n ctio n
demand
(r7)
uti J-i ty
l evel
cf
r a te
a n d ta x
functions
> 1."
L/E )
is
that
N o te
g
where
-
m > 0,
g > 1,
9 A/P^ + n I"I/PA,
fi rm
in
determi nati on
because
i ndi cati rrg
w hen
real
aII
it
\rear.
sets
the
{' As a sinqlc firm has onlv a negligible impact on thc agqregatepri c e and output l ev el s ,I
assumethat the firms rcgarcl the aqgregatevariablesas cxogenous.
19
18
and,
1
Lel[na
A s su m e A.1 - A7 .
for
each
fir m .
In
sta g e
th e
a ffe ct
:
Y' /P,' t
( 19 )
constant
\d a g e
th e
-L
:
d vld ( w- t) .
r a te
s- 1 ,
V'
in
pri ces,
w in
each
gi ven
by eguati on
a
b a r g ai ni ng,
p a r tie sr
of
future
(17)
w rt
Wi
cruc j -al
payoff.
and
part
is
how
so
w here
of
the
d w/d w 1 + B v I dw l dw .r
'
ste a d y
state
al ,I
vari abl -es
change
at
w orker
d W/d W1 :
to
res pec t
W .t and
Ut
= dU /d (w -r) .
a
and
and
a re
\/(1-B ),
future
on the
w age l ev el
form
refl ec ts
ful l
i mpac t
on the
W e c an
us e
Tayl or
s how qui te
(23)
Thi s
of
that
the
onc e
i ntui ti v el y
are
approx i mati on
(23)
and
w hi l e
a
a w age
per
i nc reas e,
an i nfi ni te
annui ty .
will
i nc reas e
as
rei ai n
y ears .
l ater
to
obtai n
is
of
w age
in
(25)
by
v al ue
obtai ned,
w age l ev el
(21)
affec ted
pres ent
profi t
how future
(
(24)
is
a fi rs t
order
ex ac t)
W:sW- 1 , a nd
(24)
(20)
u'
(2:.)
w i th
they
In
U w i th
(18)
S tarti nq
appl i cati on
of
y i el ds
reorgan i s i ng
there
fi rrn,
we g e t
th e o r e m ,
envelope
where
2,
d e r iva tio n
by
f i r rn ,
the
l evel
w age
deri v ati on
fi rm,
the
for
(23)
wa g e s
current
a g ive n
Na sh e q u ilib r iu n
a u n iq u e
exist
For
as
i V ,(tf)
-
V r(w .r)
U i (W )
U r(i \rr)
)/L
!
V r (w -
I{ r) /L
:
-(w
-
w t)/(\-P ),
1 ,/Pn r = s.
and
( 2 O)
fnserting
in
(19)
a n cl r e a r r a ngi ng
w e get
the
per
deri vati ve
(25)
worker
= - L / ( I- B)
(2L)
Y' /L
fn
sta te ,
to ta l
U( w.r )
= W *
steady
written
(22)
:
U ' (W
-
i ,i l )
=
(W -
W r)/(I-B ).
We now hav eT
.
cu r r e n t
-
and
future
uni on
uti l i ty
can
be
as
BU( w) ,
7 Thi s requi res
s onte ueak and reas onabl eas s umpti onson the parametersrv hi c h c ns uresthri t
(1-c)(1-o)(1-B )R ,L < w .
2L
20
the
Lemma 2
A ssu m e
a given
level
A1 - A7
wa g e le ve l
is
and
in
steady
current
state.
For
yearrs
w age
pr,i ce
w -
(26)
so
(Proof,
se e
At
perfect
th e
tim e
of
fo r e ca st
s u b s t i t u te
out
of
fo r
th e
th e
R/L
wa g e
negoti ati -ons,
su b se quent
fr o m
( 1 8),
pri ce
usi ng
R /L
parti es
the
So
setti ng,
= P,
to
w -
( 1- c ) ( 1- o) ( 1- P)
for
money s toc k
k ept
is
s pendi ng
that
al s o
N ote
as
)
s
i nfl ati on,
of
rate
the
c ons tant,
ec onomy
thi s
in
gov ernment
nomi nal
the
ec onomy
c an
there
1,
and
w age
the
by
be
i nfl -ati on.
w i thout
make
we
can
4.
E CON OMIC P OLIC Y
obtai n
ec onomi c
gov ernment
real
c hangi ng
of
consequenc es
bw + w_l,
of
effec ts
the
to
turn
W e now
(27 )
adj us ts
B ).
appendi x
s ee
'
and the
(18),
by
determi ned
is
gov ernment
equi l i bri um
s tate
no stea dy
the
s tate.
s teady
in
ff
aggregate
real -
be
i nfl ati on
(P roof
(29).
by
of
nomi nal
the
and
that
will-
B)
a p p e n d ix
rate
deterni nati on.
spendi ng
R/L + wr.
( 1- c ) ( 1- o) ( r - P)
the
T hus ,
gi v en
is
s -l
i nfl ,ati on
of
rate
by
d e te r m in e d
u n iq u e ly
is
year,
f i rrn l ast
e a ch
W- , in
economy
th e
th a t
gi v en
is
w age } ev el
real
the
w here
ec onomy ,
and
the
W e hav e
the
P oIi c Y ,
s pendi ng.
foI l ow i ng
which
yie ld s
2:
P roposi ti on
The em pl oy ment
W/Wr = = ,
(28)
in
i ncreas i ng
where
rate
s = 1/ lL
( 2e)
-
( 1- c ) ( 1- o) ( 1 - p ) b l
W e c an now pr ov e t he
of
Thus,
f oJ .lo w i n g
as
money s toc k
P r o p o s i tio n
A ssu m e
fulfils
demand ,
_1 :
( Dl) ,
A1 - A7 .
th e r e
Then,
e xist
f or
an y p a i r
U nder
o f vectorsA andH w hi ch
a uni g u e s t e a d y state
equi l i bri ui n
for
*4tFF
(P roof,
rnoneta ry
the
the
abov e
in
s ee
ec onomy w i l l
prev ai l i ng
pol i c y
will-
denand,
of
i nfl ati on
ex hi bi t
the
as s umpti ons ,
rai s e
output
w hi l e
real -
of
a } ev el
real
real
are
s tri c tl y
w ages
and
aggregate
the
in
demand
B ).
gov ernment
of
rate
w i th
equi l i bri um
s tate
appendi x
nomi nal
the
as s oc i ated
i ndependent
are
a ri s e
s teady
aggregate
real
i nfl ati on
s tate.
steady
> 1.
a
in
demand
aggrega te
l ev el s
and output
s pendi ng
will
s tandard
and
rai s e
K ey nes i an
ex pans i onary
w i thout
real
affec ti ng
the
nomi nal
aggregate
features .
fi s c al
ei ther
and
the
23
22
price
le ve l
g o v e r n me n t
policy,
or
th e
tr ie s
th is
to
wilr
real
go ve r n m e n t
wi-1I
no t
be
of
r a te
i nfl ati on.
in fla tio n
cu r b
by fol l ow i ng
o u tp u t
r e d u ce
sp e n d in g
Furthermore,
in
a n d th e
l i ne
real
if
a ti ght
w i th
the
the
economi c
reducti on
money stock,
but
in
(LA -nL)/LA
@:
a cost
The
qui t
the
bec ome
rate
l ow er
now
u nio n
is
c o n s t a nt,
1
and
wiLl
h o ld
because
is
as
th e
lo n g
inflation
of
the
it
u n io n ' s
Ho we ve r ,
th e
is
r
th e
ta ke s
l- a st
sh a ll-
wh e r e
e fficie n cy
quitting
model
in
function
of
given
sa lo p
f ir r ir .
2
egui l i bri um
u n io n
has
e ffect
on
)
O,
the
of
of
i nc ur
(c f
appendi x
ie
a
hi gher
on
w age
rel ati v e
v aLue
abs ol ute
to
be
01 w i l l
is
of
o u tp ut
is
r l- lu str ate
robust
thi s
by
(rg7g)
are
e a ch
fi rm
the
that
to
resul _t
i ncorporated
goi ng
the
experi ence
those
in
in
appendi x
fol l ow i ng
A 1-A 4,
for
A 5' -A 7).
(D 1),
ful fi l
the
Then,
there
ec onomy ,
w here
ex i s t
the
pai r
any
for
of
s teady
a uni gue
A and
s tate
is
\A /age } ev el
real
v ec tors
egui l i -
gi v en
by
the
a qui t
P = brW ,
(3f)
pay.
rate
of
modi fi cati ons
to
I't w hi ch
bri um
account),
i nvesti gati ng
si nri rar
gi -v en
uti J.i ty
i nto
to
z,
not
wa g e effects
T h u s,
equal
the
of A 5-A 7 are
3:
A s s ume
to
i nfl ati on
margi nal
on emproyment
proposi ti on
of
zero
w e hav e
and
P roposi tion
robust
the
w i th
a posi ti ve
poi nt
part
fai rl y
c,
w here
br
=
f/t(r
I/E )
-
gi v en
i nfl ati on
is
(32)
W /W _, = s
( 1-A ' o $/W ^ , tr) ) )
)
1,
and
the
rate
of
by
one
in
the
I
profi t
rate
o,
w here
by
s'
(30)
as s umed
the
is
are
proposi ti on
effects.
are
as
etasti ci tj -es
More speci fi carl y,
sta te
th e
assumpti ons,
demand
w age
p r o p osi ti on
d j- sa g r e e m e n t
e x a m p l e,
th e
w ages,
n o e ffici ency
ste a d y
as
a b o ut
restri cti ve
a ssu m p tio ns.
in d e p e n d e n t
m o d e l.
se veral
of
th e se
no
( wh e n
are
part
of
t,h e r e
u se d
co n ce r n e d
fir st
that
wages
h a ve
th e r e
n o d i f i c a tio n s
of
r
o n ly
and
th e
(the
effec t
al terati ons
The c orres pondi ng
the
mak e the
is
c ons tant
that
is
and
smal l er).
LLIPS
un til
here
wA
rate
fi rm
The
a pos i ti v e
o' i s
w i l ,I
rate
unempl oy rnent
ec onomy .
as s urnpti on
c ruc i al
unempl oy ment
a ffe cte d .
the
the
qui t,
per
PiD'
is
in
rate
w age
average
c).
i nfl -ati on
=
p
w here
o =
o ( \t/W^ ,u )
ot,
02 < O,
on
= I/(I
-
[(1-c )
(1-o)(l -p)b' /(1+ 0ol br)]
)
> 1.
> O,
Furtherm ore,
equi l i bri a
sr
w i th
is
dec reas i ng
as s oc i ated
in
rates
p,
of
ie
for
any
i nfl ati on
tw o
s teady
s tl
and
s ' 1,
s tate
and
25
24
p' ) . ( Pr oof
LL1<
if
o nly
modern
bargai ni ng
theory ,
and
as s umed
are
agents
atl
and
rati onat.
c) '
s ee a p p e n d i x
'
srl
pt and F2, then
unem ploy m ent r at es
asso c iat ed
on
based
> sr2 if
Themodel has pol i c y i mpl i c ati ons w hi c hdi ffers harpl y from
mostothertheori es ofi nfl ati on.w i thi nthepres entmodel
th e
T h u s,
of
s:ze
a
accept
i - n c r e ase
care
the
h iq h
wa g e
will
be
p o licy
e c o n o m ic
d e p e n d ing
on
a posi ti ve
w age
qui ts.
(A
al so
uni ons
of
be
sti l l
how ever
will
a
speci fi cati on
exact
the
no
expansi onary
and
i nfl ati on,
h a ve
still
wiII
in
w here
a model
There
with out
e q u ilib r ia
sta te
stea,Jy
in
fu n ctio n ) .
u tility
un io n
o b ta in ed
be
of
costs
reducti on
to
w i l l i ng
more
net
the
the
to
be
will
because
o win g
sm a lle r
e m p lo ym e n t,
about
fi rms
in cr e a se ,
co u ld
r e su l- t
similar
T h us
on aggregate
effect
o u t r : u t.
6.
S UM M ARY AND CONCL USIONS
wh e r e
rnodel,
ning
paper
th is
In
th e
with d r a w
to
h a ve
I
ce n tr a l
a h ig h e r
n o m in a l
p r i c e sf
ca u sin g
in fla tio n .
with
in
th e
c o n tr a st
th is
body
are
fe a tu r e s
r'rage.
In
the
Thi s
thi s
of
theory,
will
al w ays
i nduce
respect
the
of
the
B y threate-
fol l ow i ng.
w i j -]
theory
bargai ni ng
mul ti -year
w orkers
the
co n f 1 i- ct/str u ctu r a list
to
a
p resented
co o p e r a tio n ,
o b t a - in
empl oy ment
possi bl e
to
w ages.
\d a g e .
r e la tive
th e
will
reduci -n g
on the
dependant
be more
q u j-ts
m a r ke t,
]a b o u r
a tig h t
with
steady
w age
be abl e
model
is
to
rai se
to
fi rms
i nfl -ati on'
perrnanentl y '
a si tuati on
in
that
3 is
Pr oposi ti on
b e h in d
in tu itio n
The
state.
as
monetar y pol i c y c annotbeus edtoc urbi nfl ati onw i thout
in
rel -ated
be negati vety
will
a n d u n e m p lo ym e n t
inflation
effect,
curve
a P hi l l i ps
e xhi bi t
witl
e co n o m y
in
l i ne
H ow ever,
deterni nati on
*t
is
s top
i nfl ati on
enti rel y
Furthermore'
as l ong
it
will
as uni ons
nev er
w ant
be
hi gher
27
26
A p p e n d ix
and
Ho u se h o ld
A.
g o vernrnent
(5)
rn
ye a r ,
e ach
rnaxi mi zes
h o u se h o ld
uti l i ty
accordi ng
H(
max G(
subj ec t
o <
( 1 :,cn ( E- t)nl E (E -l ))'7'tn/po)t-',
Yln /Pe ) :
{ Cr ,;) ,
(3)
to
ti
The
Mh =
output
The
y i el ds
(a13)
Ch i :
t ota l
(a3)
and
re a l
(a4)
In
Y,r =
(1),
amount
of
vr
--si
vhi
-
lll
a g g r r e g a te ,
Xi
i
co nsumed
in
the
economy
is
Yi =
(1) ,
we th e n
C = r 7 B/P1 .,
(a6)
M -
(a7)
M + Po C= B
w e obtai n
(P i ,/P e) -uy ,r/n.
c ol l ec ts
househol drs
c urrent
househol ds
is
(rec al I
di stri buted
to
the
a
as
s o the
tax es ,
that
is
aI1
total
h a ve
(a14 )
It
of
a1l
w age
i nc orne
and
profi ts
are
(7)
A -
( 1 - n ) B,
(1-t)P A Y A + M-1.
B-
foll ow s
from
tP ^Y .r :
(a7),
M -
gov ernment
so
the
to
hold
more
(ars)
(a13)
agai n
fi nanc es
money .
y i el ds
and
(16)
(a14)
that
M-,,
i ts
get
W e then
C = n(f-t)Y A +
( Pi/p n ) ' u "/n ,
w hi ch
defi c i ts
by
(us i ng
(a5)
i nduc i ng
and
(us i ng
(a13)
and
Y a= gA /P A + mM-r/P A ,
(a15) )
g> L,
B:X5 8 6
m> 0,
w here
M = Xp M 6 .
(al -6)
are
6 T h i s pa r t is vcn b r ie l a s it fo llo u ' sWe itzman (1985)
th e
g = I/ tr-n(1-t)
rel ev ant
fi s c al
I
and
and
m = t/ tt-ry (1-t)
monetary
mul ti pl i ers .
l
hous ehol ds
(a14) )
Otl t/P e,
and
(a10)
budget
hous ehol ds )
where
/ > o\
(0
L,
frac ti on
i nc ome
and
Ci =
(6) )
and
PiCi/PA.
(as)
(a8)
(a4)
(a11),
and
gov ernment
The
as
,
co n su m p tio n
a g g r e g a te
C :
good
defi ned
PiYi/PA,
(us i ng
(aB )
(15)
E4 Bn ln Po .
( P,/Pt)
Xi
is
Y a= C + A /P ^.
From
(a2)
X , A (E ' t)rl u' (ot)) ,
ue/n.
aggregate
( 1 - n ) Br ,
and
probl ern
max i mi z ati on
A,
G;/P a)
w hi ch
is
(t
Ai :
(a12)
p r o b le m
th is
to
:
)
gov ernment
the
is
R eaI
co n str a in t
Pr ch i + M 5 = 8 6 ,
so lu tio n
(a1)
budget
th e
{Ai)
X 1 P ,A ; :
(a11)
s u b j e ct
to
to
(6)
j- o n
e x p r e ss
(2)
e a ch
s ol uti on
The
behavi our8
29
28
A p r r e n dix
B.
f ir st
order
(bl)
co n d itio n
cF ",/ ( F - F o )
+
( L2)
of
( r - c)
can
Sw/ (S -S o)
be w ri tten
go to
as w ag es
as
L emma 2
where
Fw = -L
+
-
( F - F ,r )
BVt,
we ca n
(25) ,
and
su b stitu te
sin p lify,
out
to
fo r
- U(wr)).
(13),
(2r),
(L4),
will
- V ( w - r ) },
q + ptu(w)
S w : 1 + p U' a n d ( S- So ) - W
state
w L - T r + B {v ( w )
R -
In
(23),
steady
(24) and
al l
yi el ds
the
(D 4)
:0,
- c / | ( 1- o) ( 7- B) R/ L- ( w- w _ r ) I + ( r - c ) / ( w - w - r )
(b2)
s o lvin g
w -
(2 6)
( 1- c ) ( 1- o) ( 1- p)
R/L + wr.
unj -que nes s
of
in
at
will
as
(the
are
pri c e
QE D
P ropos i ti on
2
bec aus e
and
s ane
(w hi c h
pri c es
(D 2)
(s o
guaranteed
are
in
l emma I
of
(18),
reaL
by
(D 3),
aggregate
that
fu1fi l l ed).
and
ex i s tenc e
and the
we
s o real
ens ures
is
(26)
in
ful fi l
(15)
(D 1) ),
through
c ons tant
and
that
(18)
as w ages ,
rate
c ons tant
rel ati v e
s etti ng
l emrna 2.
the
bargai ni ng
l -emma l - w e hav e
fns erti ng
(29) ,
be
l atter
uni quenes s
the
(18).
w age
the
and from
to
i nc reas e
empl oy ment
and
(26),
i nfl ati on
pri c es
s tate
s teady
ac c ordi ng
w age
of
c ons tant
E xi stence
nati on
pri c es
pri c es
and
output
W we g e t
fo r
by
(D 5) ) . Moreov er,
a nd
demand are
and
gi v en
rel -ati v e
and
w ages
w ages
al l
know th at
o b ta in
z ero.
1
in
rate
i f,
happen
tow ards
s l ow er
c onv erge
the
that
W , as w oul d
al l
W for
profi ts
that
s et
fi r rns
in
pos s i bi l i ty
the
out
rul e
ens ures
in
re s ul t
to
i nfi ni ty ,
P ropos i ti on
of
P roof
= 0,
is
i nc reas i ng
is
N ash ex pres s i on
The
(b3)
behi nd
i ntui ti on
T h e wa g e bargai n
Lenma 2,
w age determi -
f assu m e
P roof
(b3 )
(1-o)
( 1 - B) b
of
Lemma 1 and
< L,
changes
th a t
implying
d e c r e a sin g
w.
th e
T h is
d e r i v a t i- ve
positive
values,
d e n o m in a to r
e n su r e s
of
fo r
So
d e n o m in a to r
w ( r e ca l1
in
(18) ) and
in
th e
th e
a 1 l-
th e
th a t
Na sh
lo we r
se co n d
th a t
the
in
:
R/ L
term
fi rst
bw through
the
of
pri ce
or
(b2)
in
(29).
th e
(26)
rast
gi ves
e xp r e ssi on
va r u e s
order
of
term
the
w i th
w and
condi ti on
in
(b2)
uni que
respect
negati ve
hol -ds.
is
to
for
The
w
al t
aggregate
H enc e
i nc reas ed
and w age Lev el s
demand,
real
i nfl -uen c e
w ages
or
pri c es ,
as
w hi c h
Y o does
aggregate
and c ons equentl y
setti ng
i ncreasj -ng
maxi mum,
real -
pri c e
are
not
i nv ari ate
enter
s pendi ng
in
to
(18)
does
not
output
and
is
empl oyrnent
in
2 gi v e
ds
the
then
is
hi gher
econoni c
through
(15).
QE D
it
rai s es
I
31
30
A p p en d ix
C.
Pr o o f
of
Pr o p o sition
3
A 6r : T he w age Lev el
e
( A6 )
and
( A7 )
ca n
be
r e pl aced
fir m
Ea ch
e xp e r ie n ce
a qui t
rate
o,
gi ven
W :argmax
tP (L)L-(w + Oo)L-r+ p
o =
o ( W/W^ ,1 t")
oz I
oL,
O, 6tz )
average
a
c o st
p a y o ff
( L ' \- n L ) /t A
p
wa g e r a te
O of
th e
lr ) p e r
Po
th e
in
is
fir m
th e
e co n omy.
q u it,
if
unernpl oyment
th e r e
O'
is
The
is
a
fi rm
rate
no confl i ct
and
wA is
i -s assumed
posi ti ve
to
constant,
P( L ) L
-
cu r r e n t
p r i c e s,
is
a n d fu tu r e
g ive n
i ncur
so
the
A7 | :
there
If
bargai n i ng,
l'
q + p
(U i (w )
-
U r(w r))
]' ' ' ,
bei ng
on the
l abour
demand
s c hedul -e.
is
the
a
del ay
uni onrs
in
reac hi ng
pay off
an
agreement
in
the
is
is
9 = W -r,
( w + Oo(W/w ^,p))L,
p a yo ff
to
the
fi rm,
measured
in
pay off
the
(14')
v ( w- r ) = m ax t p( L) L- ( w+ oo ) "
;
-
of
the
fi rro
duri ng
a c onfl i c t
is
currenc
by
7r:
w here
(1 1')
-V r(w r)}
the
w hi l e
Total-
empl oy ment
to
(13)
(10')
{ V r(W )
o,
subj ect
where
N as h
as y mmetri c
by
[w -
(30)
by the
by
(72,)
A5r:
gi v en
is
s ol uti on
bargai ni ng
(A5) ,
fj .rm
eac h
in
( B t / p ; t I p r ( L , ) ! - ( w j +o j o j ) i 1 ] ) .
is
e
oP (L)L
the
-
(w r
of
frac ti on
+ A o(w /W ' t,p))L
normal
w hi c h
rev enue
obtai ns
duri ng
a confli c t.
H ous ehol d
+ -1
J_L
and
equati o ns
(15)
state
fi rmrs
the
(l .7')
and
v (w .r)
gov ernment
(16).
:
max
behav i our
Turni ng
max i mi z ati on
(
P (L)L
ll)
and
th e
fi rs t
order
c ondi ti on
the
to
probl em
L
" This scction is bricf as the arqument is vcrv similar to thc proof of proposition 1.
T o scc ultv lhis is.t r clsottable spccilieution. obs er y e that ( 10') c an be r er v r i r tc n l r s I) ( 1 - @ +o) L
- WL, so o* can be interpreted as thc avcrage reduction in productiviti, per quit.
O < e < L,
is
-
is
pri c e
as
gi v en
before
s etti ng,
in
is
(w + oo)L
+ pv (w )
l,
by
s teady
['
33
32
(31)
P:
where
L,
br
s o th e
(c5)
-c /t
and
so l v i ng
b r W,
r /L ( r
fir st
order
> 1.
( 1 - O' o ( w /w ^,p))l
r /E)
-
to
suffi ci ent
is
co n d itio n
(31)
is
concave
ensure
in
a uni que
r,,,r=
(c6)
of
the
sta g e
Na sh
(cl)
2,
th e
+
cEw/ ( F - F o )
Fw =
where
( 12 ')
e xp r e ssio n
+
B{U(w ) - U( wr ) ) .
In
fi rst
t (1-c )
I
-
(w +oo)L
-
7r +
w hi ch
ens ures
then
is
hi gher
(c2 )
dW /dW 1
:
and
by
the
of
d e r iva tio n
e n ve J- o p e
th e o r e m ,
( I7 ' )
with
and
respect
r e a r r angi ng,
W-t and appl i cati on
to
aII
V,/L
(c 6)
pos i ti v e
N as h
for
so
as s ume
al l
the
for
1L,
gi v es
the
ex pres s i on
row er
s ec ond
s i rnpl i c i ty
R /L
= - ( Qo r /W' \+ t) /
s o W = W A and p:
fi rms ,
:
brW ,
(c 6)
of
uni que
w i th
v arues
order
that
max i mum,
res pec t
of
w and
c ondi ti on
the
to
c an
brw A
negati v e
be rew ri tten
ie
for
W -
[(1-c )
(1-e)(1-B )/(Q' orb' + l )]
(l g' )).
l ev el
Thus ,
as 0:
as
b' w
*
w _1,
or
Thus,
(c4)
{ Vr ( W)
-
vr ( r ,r i)
} /L
=
-(oo,/w ',q+l )
(W -
W )/
(L-p)
W /W -t= s '
,
w here
and
by
su b stitu tin g
out
fo r
( 13) ,
(14')
,
(c3) ,
(23) ,
(c4)
and
(33)
(25)
in
( c1 ) ,
and
sir n p lifyin g ,
w e obtai n
s'
:
I/(L
(c 6),
al l
prev ai ts
( l-p).
(32)
the
hol ds .
s ame w age
(by
W,
as
w e obtai n
(c8)
(c3)
+ w -1.
R /L
Sr r
in
so
the
v al ues ,
I
:
L/Ptt
(1-p)b./(oo/w ^+ i ,l
that
of
(S -S o)=Wq+
s t at e
s t eady
(1-e)
deri vativ e
L + PUr a n d
(1-p) / (oor/w ^+ t\1
assume
(c7)
P (L)L
(1-o)
condi ti on
= 0,
(F,-Fo) =
F Y' ,
order
as
be w ri tten
c an
( 1 - c) Sr v/(S -so)
- ( Oo r /wA+ l) L
- V( W - r ) ) , Sw:
BtV(w)
the
b a r g a i ni ng,
wa g e
= 0,
w w e get
for
m a x i m um .
In
) + (1-c ) /(w -w .)
(L-p)/(aor/w ^+ 1)l R /L-(w -w r)
i (1-e)
t(1-c )(1-o)(r-B )b,/(1+ o' o1b' )l
) > 1.
pO'
t'
35
34
w here
O is
frac ti on
the
of
normal
rev enue
w hi c h
obtai ns
duri ng
a confl i c t.
(31)
(32)
an d
br
d e fin e s
and
sr
functi ons
as
of
F,
and
w e see
The model
that
as i n
the
fi rst
order
is
now gi v en
rnai n tex t.
by
Turni ng
c ondi ti on
of
to
the
A 7, , .
A 1-A 6 ,
s tage
2,
the
S tage
3 is
ex ac tl y
w age bargai ni ng,
(12)
N as h ex pres s i on
the
c an be w ri tten
d b t/d 1 .t < O,
(c9)
AS
o2 < 0),
(because
d s' /d p
(c10)
(because
of
( c9 )
and
(d1)
< 0,
w here
a n d o t < O, o r z > 0).
QE D
Sw =
1 +
state
q/e c an
and
(d2)
In
this
a p p e n d ix
go
slow
d u r in g
th u s
ning,
during
Fw = -L+
(25),
th e y
in
a d e la y
o n ly
r e ce ive
A7 is
a co n flict.
an
r e a chi ng
a
w here
the
agreement
in
case
the
we in ve stig a te
fracti on
d. of
thei r
w orkers
If
b a r g a i n in g ,
(13'
while
th e r e
th e
the
-c /
:
(S -S o)
R -
w -
out
to
(I-B )R /L-
(1-p)
n + B { V (W )
+ ptu(w )
(13,,),
for
s i mpl i fy ,
q
WL -
-
-
V (W -r)),
U (W _r)).
(14"),
(2I),
In
s teady
(23),
(24)
obtai n
i- s
a
d e la y
( 1- c) / l( r - P)
normal
u n io n ' s
p a yo ff
p a yo ff
of
th e
fir m
r :OR- a W_ ,L
(w -aw _1) -F(w -w -r)
I +
( w- cw_, ) - F( w- w-Ir )= o,
pay
and
reachi ng
in
t(1-e)
bargai -
sol -v i ng
an
agTreernent
is
in
for
W w e get
w -
f
a confl i ct
is
O<e<1,
(l -e)
Q-p)
R /L
+
l (L-p)o+ B l w _1.
assu me
(d4)
d uri ng
(1-c )
the
w hi ch
(1-o)
ens ures
deri vativ e
(14'')
-
(F-Fo)
o,
by
r e p la ced
q = a w- 1 r 0 < o < L ,
')
th e
and
:
(1-c )S w l (s -S ' )
s ubs ti tute
use
(d3)
A7 | | :
pv t,
and
BU'
+
Go slo w
D.
A p p e n dix
c Fw / (F-Fo)
of
(1-B )b
that
the
< L,
(d3)
N as h
gi v es
ex pres s i on
the
w i th
uni que
res pec t
max i mum,
to
w,
as
ie
the
(d2) ,
37
36
then
so
va lu e s,
higher
fr o r n
R/L :b W
I n se r tin q
o r d er
se co n d
th e
val ues
Io we r
a ll-
fo r
p o sitive
is
for
negati ve
al l
R EF ER EN CE S
hol ds.
condi ti on
pri ce
th e
W and
of
(18) , and
setti ng
rearran-
B ackus,
W :
(d5 )
st
tW - l
and
R .J .
B arro,
Gordon,
a lg e b r a
(d7 )
cr > 1
(d6),
on
we f ind
that
sr ' > 1 is eguivalent
E c onomj -c s
to
na 1
We know
th a t
( d 7)
for
to
b > L,
h o ld
and
if
we se t
c = I/2,
th e
if
Thus,
th a n
is
less
of
i n f l a tio n
b:2,
then
Fi scher,
is
p e r ce n ta g e
h a lf
th e
sr r
witl
sr r >
and
1 is
in
p e r ce n ta g e
be
reducti on
p o sitive
e q u iva le n t
for
to
pay during
w orkersl
al l
in
b.
profits,
If,
pol i c y .
J ournaf
of
The
N as h
101-L21.
and
ec onomi c
(1986).
A.
W ol i ns k y ,
R and J ournal
model l i ng.
(1986) . The w age-pri c e
E c onomi c s
S.
and
IO4,
w i .th
S ummers ,
for
go slow
H al l er,
H.
79,
(1988).
P a per |
the rate
chi nc
example,
L.
of
s pi ral .
Ouarterfy
J our-
543-566.
(f989).
A meri c an
i .nfl ati on?.
P roc eedi ngs
r e d u ctio n
in
monetary
condi ti ons
suffi ci ent
r/2 + o /2 .
ct
di s c reti on
R ul es ,
176-188.
of
live
(d 8 )
17,
of
A.
s ol uti on
O.J .
B l anchard,
( 1- c ) ( r - e) b.
12,
R ubi ns tei n,
bargai ni ng
By sinple
i nfl ati on.
53O-538.
(l -983).
D.
model
E c onomi c s
K .,
B i nmore,
(1-c) (r-e) (1-F)br.
-
tl
t ( 1- B) a+ FJ
a
in
Monetary
where
s l, =
75,
R ev i ew
and
R eputati on
,
rep utati on
(d6)
(1985).
J.
D ri ffi l l ,
E c onomi c
A m erj -c an
yie ld s
ging,
and
D.
i ns ti tute
gov ernments
E c onomi c
R ev i ew
to
fearn
P apers
and
382-387 .
D epartment
and
s tate
game.
as a s trategi -c
W age bargai ni ng
88-O9-O2 |
S houl d
of
E c onomi c s ,
V i rgi ni a
W ork i ng
P ol y te-
uni v ers i ty .
o > g.
H art,
O.
(1-982).
fea tures .
A model
of
i mperfec t
The Ouarterl v
J ournal
c ompeti ti on
of
E c onomi c s ,
w i th
K ey nes i an
l -09-138.
39
38
( l- 969) . W agr einf lat ion
A.G.
Hin es,
L 96 22 A Dis aggr egat ed
in
St udy .
the United
Kingdom 1948-
S.
(1988a).
dinavian
L o ca l
Jo u r n a l
of
and
ce n tr al
Eco n o m ics
h'age bargai ni ng.
9O ,
H aav el mo
(1988b).
S.
d u m n o.
6,
A b a r g a in in g
R ubi nstei n,
93-99.
De p a r tm e n t
of
th e ory
of
Eco n o mi cs,
at
( f9 8 9 ) .
S.
Department
No n - co o p e r a tive
of
Eco n o m ics,
i nfl ati on.
of
r .vage bargai ni ng.
of
and
A.
and
K.O.
E c o n o r nic
Phelps,
a€
vr
Purdy ,
in
E.S.
n,rL,'r
sal amon,
Osl o.
sal op,
OsIo.
the
Pr o ce e d in g s
Jo u r n a l
9 8 , 4 7 I- 4 8 3 .
and
i^
and
Win te r ,
U. K. :
s.c.
and
M.
s.
(1987).
(1979).
c.
(7974).
A r e a p p r a isa l- .
a n d la b o u r
E conomi c
R evi ew
S ci tovsky,
T.
w age
w ei -tzman,
determi nati on.
M.L.
shari ng .
( Le73) .
Trade
E c onomi c s ,
bas ed
on Lec tures
U ni v ers i ty
of
by
Os Io.
perfec t
50,
equi ri bri um
in
a bargai ni ng
mo-
97-LO9.
rndus tri al
R el -ati ons :
Theory
and
prac ti c e.
London.
A rnodel
E c onomi c
of
R ev i ew
the
natural
G9,
rate
of
unempl oy menc .
LI7-I29.
(1978)
Mark et
P ow er
and fnfl ati on.
E c onomi c a
45,
22I-223.
InfLati on
Swedis h J our n a l
finance.
Z is,
th r e a ts
N o 3,
i nfl as j ons teori en.
unempl oyrnent
2 3 5 - 239.
Un io n
( e d s . ) , fn fla tio n
Press.
76 ,
A meri can
of
fra
manuscri pt,
Wage setti ng,
r e la tio n s.
(1988).
l/uvr lu
D.L.
(1986).
D.J.
i n sid e r - o u tsid e r
Papers
Moene,
a n d Sn o we r ,
s tudenter,
D ept.
E c onornetri -c a
A meri c an
Lindbeck,
emner
Memoran-
U ni versi ty
Un ive r si ty
for
(l -982).
A.
P renti c e/H aII,
Holden,
N oen
Sc an-
del .
Holden,
(1975).
A bonnements s eri en
Ec o n o m i c J o u r n a l , 6 6 - 8 9 .
T.
Holden,
J .F.
Qvi gstad,
of
uni ons
f n Lai dl er,
r n a r kets,
in
the
theory
E conomi cs
75,
67-82.
and
D.
w age i nf l -ati on
and
Manchester
P urdy,
U ni versi ty
D.
(l 9B 5).
A neri c an
The
s i mpl e
E c onomi c
mac roec onomi c s
R ev i ew
75 |
g37-g53.
of
profi t
AR BEID
NR.
( k ap.
6 )
W A GE B A R GA IN IN 6
for
S ome i mpl i c ati ons
A rb e i d e t
er
l1g_m-ofCl_dg-U,
tes ts
of
11 ,
S o s i a I d k o n o mi
U n i v e rs i t e t e t
trade
uni on
p u b l i s e rt
t i d l i g e re
nr .
W A GE S :
A N D E FFIC i E N C Y
sk
e3.
auqus
som
t
i ns t i tu t t
i
Oslo
1988
model s
n
W A GE B A R GA IN IN G A N D E FFIC IE N C Y
S ome i rnpl i c ati ons
of
tes ts
for
W A GE S :
trade
uni on
model s
by
Ste i n a r
Holden
ABSTRACT
rnodel
A w age barqai ni ng
w ork ers
depend
that
w i thi n
will
be
Thi s
paper
H oe1 ,
of
s uc h
w here
the
outs i de
a framew ork
av erage
w age
is
effi c i enc y
pres ented.
c omrnon tes ts
of
It
of
the
is
s how n
uni on
trade
model -s
i nv al i d.
unem pl ormentr
men t
on the
is
part
at
E c onomi c s ,
K arl
of
the
res earc h
S A F C enter
U ni v ers i ty
for
A ppl i ed
of
Ov e Moene and R agnar
rW age formati on
proj ec t
Os l o.
N y noen
the
R es earc h
at
C omments
from
are
apprec i ated.
and
D epart-
Mi c hael
3
S on e of
the
(19 86),
Mac urdy
and
penc av er
carruth,
os w ard
and
Fi ndl ay
mos t
w eII
k now n
s tudi es
TNTRODUCTION
Trade
last
ye a r s,
10-15
large
different
w he th e r
or
if
an
whil-e
or
th e
t h e ir
r e d u n d a n cY
c o r n p u lso r y
The
ke y
o th e r
to
indifferent
as the
' fla t
one
acce p ts
the
two
F IC,
by
O sw al d
se n io r ity
e r n p ir ica lly,
the
adj ustment
th e se
and
in
cause
is
r el ated
to
no
the
sLze
w i th
the
care
thei r
tery
modi fi ed
to
a bargai ni nq
how ev er,
if
the
w age
somew hat
unc rear
B el -ow i t
is
in
arLow
s tate
is
a bargai ni ng
thi s.
Thi s
or
the
obj ec t
by
n egoti ati ons .
that
thi s
if
framew ork ,
w i rr
of
i nv ari date
the
the
any
bargai ni ng,
the
by
other
s tate
di fferentLy
(1987
demand. rnodeL appropri ac ons i d.erti ons .
thi s
they
c oul d
They
be the
and
ac tuarry
w age
empi ri c ar
it
fi ndi ngs
hav e
w hen
the
w age
is
gi v en
in
mi nd.
prev ai l
rnay be
on unj -on
c as e
remai ns
c ons i derati ons
c onc l us i ons
ev en
of
and w adhw ani
negoti ati ons ,
effi c i enc y
res ul ts
ex pl ai ned
i nterpreted
w age
w hat
are
mos t
do not
(1986),
(1987)1.
ernpi ri c al
be
N i c k err
that
is
s tudi es
they
be
effi c i enc y
by
thes e
w hi l e
c oul d
a l abour
determi ned
Turnbul r
narrow l y .
c ourd
ex pl i c i tery
and
the
rnoders ),
by
for
w hether
s how n
v al ue,
framew ork .
fi ndi ngs
B ean
s v ej nar
due
to
preferenc es
is
determi ned
rul es
uni on
to
is
often
referred
to
C 1earl y,
if
l onger
ex prai n
res ul ts
(1986),
though
fi ndi ngs
nage
and A s henfel ter
about
voti ng
(FIC ).
thei r
a'b)
i nvol ves
the
be
i nteresti ng,
as
resul ts.
questi ons
test
uni on
maj ori ty
Thi s
i denti cal
order
the
assurnpti on
q u esti on
yie ld s
not
(1984),
nay
cu r v er
fir st
or
l evel .
e m p lo ym e n t
vie ws
ye a r s
w here
whether
th e
bargai ni ng
i ntensi ve
w ay:
fol l ow i ng
adj usti ng
conti nuousl y
- i- ssu e is
in d iffe r e n ce
o p p o sin g
Re ce n t
a d r e s se d
th e
ca ses
the
t .
in ve r se
by
fir in g
rare
in
1984)
effi c i enc y
that
ev en
s omew hat
thei r
B row n
c ard
and
unques ti onabl e
that
w i thi n
even
demand
N i ckel l ,
(l i k e
do not
that
i nterpreted
even
trade,
empl oyment.
of
(1986),
(1986)
argues
rec ogni s e
expli c i try
the
and
been
theo ri es
on the
l abour
e9.
studi es
w i th
from
and
(cf.
(1983)
any
wj.th o u t
As a r g u e d
u n e m plo ym e n t.
and
th e
tradi ti onal
a re
fir m s
fo r ce
in
e xce p t
unions
as the
a n d An drew s
th a t
la b o u r
both
m a n a g e rassumpti on
Nicke II
o b se r va tio n
'the
to
' r iq h tby
d efe n d e d
to
r e fe r r e d
vie w,
w ages
covers
the
paper
done
may hav e
i ssue
by
deci de
gai ns
unexpl oi ted
le a ve
b a r g a in '
' e fficie n t
l a tte r
model
will
it
]e ve I,
e m p l o yn e n t
capabl y
empl oyment,
and
associ ated
fi rms
if
that
a r g ue
fi rst
uni l atteral l y
often
vi ew ,
fo r m e r
th e
(1981),
So lo w
and
M c D o n a ld
of
of
Ad vo ca te s
of
The pres ent
A
yi el di ng
most
The
w ages
determi ned
is
le ve l
i ssues.
both
about
b a r g a in in g
e r n p lo ym e n t
th e
firm.
is
is
th e r e
key
tw o
around
(1944).
proposed,
Y et
the
over
D unl op
concl usi ons.
co n tr a d icto r y
ce n te r e d
has
d i s c u ssio n
The
o fte n
and
by
been
have
r n odel s
th e o r e tica l
outset
the
a fter
tir n e
i nterest
i ncreasi ng
an
r e ce ived
lo n g
of
number
is
h a ve
m o d e ls
u n io n
are
the
have
vari ous
al so
been
hypotheses.
1 A n i nteres ti ng
( 1e88 )
s urv ey
and
di s c us s i on
in
N y moen
I
5
TESTS ON TRADE UNION MODELS
cons i derati ons ,
ev en
if
the
is
i l l us trated
w age
is
determi ned
through
negoti a-
ti ons .
whether
both
b a se d
are
th e y
variables
( 1 ike
rate)
sig n ifica n t
are
problem
o ne
This
is
ned
of
is
in fe r
not
ca n
th e
in
p o in t,
a general
a lso
a ckn o wl- e d g e
general
p o in t.
If
a h yp o th e sis
certain
wh e th e r
it
is
j-s false.
is
Co n ce r n in g
F r o m t his
manage'
however,
to
reject
Svejnar,
F IC
th e
sig n ifica n ce
Ca r r u th
will
r ^ J a g r ec on sj- d e r a tio n s
wh e th e r
standard
in
se ts
e fficie n cy
bargaining
Hoel,
it
f9 8 8 ) .
a n em p lo ym e n t
et
a It
L986)
th e
e q u a tio n
the
It
and
fir m
sig n ifica n c e
or
the
(thi s
of
m a y b e a si gn
case
ment
of
the
not
in
is
determi ned
for
through
opti mal ty .
r
outs i de
v ari abLe,
onl y
barqai ni ng,
hav e
generari ty
the
s i mpl e
of
w hi l e
i -nc ruded
the
but
is
the
thi s
of
res ul ts .
R ( e ( W/WA)L ) - WL
al ternati ve
w age
w here
wA is
e (w /w A )
,
is
an
for
w age),
and
w and
the
is
i nc reas i ng
1984
rel ati v e
empl oy ment
fl nn
fi rm,
another)
L are
aLternati v e
the
av erage
func ti on
j us ti fi c ati on
w e as s ume
of
rri ght
the
ac c ordi ng
to
manage'
to
R ' ( e ( w /WA)L )
empl oy ment
a func ti on
fna
v/age
(3)
w age
and
the
s uc h
of
rerati v e
an
enrpl oy -
(defi ned
effi c i enc y
as s umptj -on,
w /e ( w /r ,A)
no
l-n
w age
effec t
in
the
w age
of
a
R r (eL)
(eg.
maki ng
of
the
> o.
Fol l ow i ng
enough
the
the
Y erl en,
eg.
e' (w7w A )
the
due
in
(see
E ffi ci ency
fj -rm,
l ev el -
of
w hi c h
fi rnts
manager
determi ned
effi ci ency
the
i mportanc e
w orkers ,
menti oned
the
( as
is
to
is
to
observati on
eg.
equati ons.
is
profi t
one w ay or
that
'ri ght
framew ork.
w age
the
is
not
of
is
a v ery
be
above,
vari abl es
profi t
no
as
r r ( W,L , WA) =
be the
orrri qht
of
w age
ernpl oy ment
w age
/1 \
sarne resul ts
is
cour s e
w hj -ch
studj -es
the
adj us ts
al -te rnati v e
hypothesi s
bargai ni ng
that
fi rn
the
in
menti o-
not
can
and
w here
bel ow
Let
one
wa g e uni l -atteral l y
m o d e ls)
above
the
empl oyment
the
outsi de
a b argai ni ng
th e
u n io n
He n ce
of
in flu e n ce
wa g e
b e twe e n
of
the
correct.
a rel ated
FIC
the
rej ect
wage model .
with in
e ve n
the
w age and
the
j.s r e cogni sed
a n e ffie n cy
(eg.
of
frarn ew ork ,
c onc l us i on
an hypotheis
to
In
The
how ever
referred
findi ng
e fficie ncy
it
equati on.
an auxci l l i ary
or
in
is
rej ected,
issues
general
fr o m
1986) ,
natter
ke y
general
In
th a t
th e
wh ile
h yp o th e se s,
de r ive
m a in
so m e stu d ie s
r e su lt,
s u p p o r t ed .
is
th e
d o m a tte r
va r ia b le s
outside
could
The
fo llo wj- n g .
the
There
th is .
of
Thi s
unempl oyment
al ternati ve
and rnost
is
some outsi de
the
w age
model s.
one may rej ect
a speci fi c
th a t
co u r se
s t u d ie s
or
e r npl oyment
w hi l e
the
studi es
form
on w hether
w age or
th a t
rnenti oned
reduced
based
' a lte r n a tive r
te sts
su ch
with
sis,
th e
a re
te sts
above
or
str u ctu ral
on
th e
h o we ve r ,
c ase s
the
b e twe e n
d iffe r e n ce s
r n a in
The
L ( W,WA)
of
the
form
the
fj -rm
c hoos es
f
6
where
This
the
d e r i ve s
opposite
fall
sig n s
fr o m
more
w i ll
and
If
le a d
th e
o th e r
to
be
is
w orki ng
producti vi ty
the
the
rj 'se
i mpl i ed
th e
effects
in
in
same l evel
uni t
Mos t
will
of
l abour
bargai ni nq
through
N ash
a n asymmetri c
betw een
the
bargai ni ng
solution
(4)
= arg
w
max
ro]"tu(w )
-
[n ( w,L ,wA)
-
uo]l -c
=
L
where
the
a c c o r d a n ce
L ( w,wA) ,
u n io n
with
p o in ts
threath
(4)
wh e r e
will
is
F IC
h a ve
an
the
h yp o th e sis.
i- s th e
c
l evel ,
of
the
the
respecti ve
fi nn.
form
frui tful
approac h
(5)
pres ent
may s av e
the
Frc
and
from
(3)
wi}l
h a ve
an
bargaining
(5)
ir n p a ct
namel y
o utsid e
a b o ve
we se e
e ve n
th is
va r ia b le s
th a t
th e
wh e n
r e su lt
a ]so .
general
in
w age and
rri ght
c an
to
easi l y
the
al ternati ve
empl oyment
manage'
be
Level
and
FIC
general i sed
w age
in
a
hol d.
to
the
bei ng
approx i matel y
there
is
the
need
di rec t
will
the
uni on
more
to
ev i denc e.
be more
of
c ons i d.erati ons
robus t
out
the
to
be
c ompurs ory
c onc erni ng
referred
be
than
c ons i s tent
red.undanc i es
i s s ues .
the
to
i ns i der/outs i der
new as s i gnrnents .
c ontrac ts
c as e
c ons i d.erati ons
al s o
on
in
a v ery
parti c ul ar
w oul d
in
s eemi ngl y
argument
bas ed
on thes e
uni on
thes e
w age
(1983)
rt
there
w age
hy pothes es .
hy pothes i s
ferent
y et
bargai ni ng
effi c i enc y
oppos i ng
i ns pec ti on
perhaps
rn
appeal .
Frc
i ndi f
for
ec onomi c s .
and A ndrew s
i ntui ti v e
of
turn
manage'
effi c i enc y
through
c ornbi ni ng
my opi ni on
to
' ri ght
that
many c as es .
effi c i enc y
paper,
N i c k el r
a s trong
a v ari ati on
effec ts ,
(1984)
o n b o th
fr a m e wo r k,
A s e m p h a size d
other
and
the
in
in
determi ned
a v /ay of
l abour
the
appro ac h.
Thus
in
in
has
are
is
and w i rl
ac k now l edge
i mportanc e
w ages
di scu s s ed
l atter,
of
framew ork
v i ew s ,
l -i ke
W = 9 ( WA,r 0 ,Ug r c) .
that
probabl y
rnc orporati ng
oppo s i nq
w i th
in
w i rr
are
i ndus trj -es .
abov e
functi on
and U g are
pow er
o n the
uti l i ty
empl oyrnent
rg
b a r g a i ni ng
so fu tio n
unj -on
the
is
to
in d iffe r e n t
th e
and
U( W)
be no doubt
a bargai ni ng
the
given
ec onomi s ts
c ons i derati ons
many
d e te r m in e d
as
w age
can
o u tp u t.
u n io n ,
tr a d e
tw o
CONCLUDING REMARKS
i ndeterrni nate.
produce
to
n e eded
hand
r e d u ce d
le ve l
are
t here
wA increases,
eg.
will
are
d eri vati ves
th a t
fa ct
wo r ke r s
T h e wa g e
firm
th e
o n th e
but
costs
p a r tia l
th e
d ir e ctio n s.
and
output,
of
w hi l _e
c l earJ _y
other
like
s tandard
in
methods
os w ar.d
ec onometri c
I
9
R E F E R E NCES
Bean,
and
C .R.
c o al
P.J.
A te st
in d u str y:
s i on
School
of
th e
Ce n tr e
Xa 2 7 4 ,
Pa p e r
rE rnpl oyment
( 1 9 87):
T u r n b u ll
the
demand model r,
l -abour
Labour
for
in
E conomi cs,
model s
z ed
rnark ets r,
P enc av el
w age and
J ournal
(1986):
empl oy rnent
of
betw een
' Tes ti ng
determi nati on
P ol i ti c al
E c onomy
c ompe-
in
uni oni -
L-39.
94,
B ri ti sh
D i scus-
McDonaId,
ment I
London
and R .
I.M.
A meri c an
rW age bargai ni nq
(198f):
S ol ow
E c onomi c
R ev i ew
21,
and
empl oy -
896-908.
Eco n o m ics.
of
and
J.N.
J .H .
of
ti ng
N i ck el l ,
Brown,
and
E .T.
MaC urdy ,
e r n p lo ym e n t
O.
( 1986):
Ash e n fe lte r
'Testi ng
of
Jo u r nal
co n tr a ctst,
the
effi ci ency
E conomy
P oIi ti -ca1
of
94,
40-
H endry ,
tThe model l i ng
(1984):
S .J .
D .F.
and K .F.
Ouanti tati v e
W al l i s
of
w ages
(eds .)
and
empl ol rmentr,
E c onornetri c s
E c ononi c s ,
Ox ford:
B as i l
M. A ndrew s
(1983):
rU ni ons ,
1n
and
B l ac k w el l .
87.
N i ckel l -,
Card,
(1986):
D.
Carruth,
' Efficie n t
Eco n o m ic
A r n e r ica n
A.J.
A.,
tr a d e
t r i es
in
Br ita in '
tics
a8 ,
and
u n io n
,
76,
L.
w i th
The
Bul l eti n
coal
of
and
empl oy ment
in
B ri tai n
rA test
and
steel
E conomi cs
of
a
N i ckel l ,
i ndus-
and
S tati s-
L-L7.
S .J .
and
empl oy ment:
P aper
S.
M.
b a rg a in in g ' ,
sity
of
Oslo .
Ox ford
w ages
and
E c onomj _c papers
35,
N o 291,
bas ed
C entre
for
rU ni ons ,
(1987a):
on U K fi rm-1ev el
Labour
w ages
datar,
E c onomi c s ,
and
D i s c us s i on
London
S c hool
of
E c onomi c s .
under
Trade
U ni ons.
N ew
M a cm ilL a n .
(1988):
W adhw ani
Tes ts
N i cke l l ,
S .J .
effi c i enc y
and
S.
' Efficie n cy
Memorandum
wa g es
7,
and
verstts
l ocal
D epartment
of
central
E conomi cs,
w age
E c onomi c s ,
W adhw ani
w ages
mi c ro-datar,
Hoe1,
1951-79' ,
real
L83-206.
(1986):
Fi ndl ay
b e h a vio ur:
Oxfo r d
adj ustmentr,
costl y
LO45-l -071-.
( 1 9 4 4 ) z Wa q e d e te r m inati on
J.T .
Y o rk:
r e vie w
o swa ld
m o d e l- o f
Dunlop,
co n tr acts
S .J .
and empl oy ment:
D i s c us s j -on
London
(1987a):
S c hool
P aper
of
'
Fi nanc i al
fac tors ,
Inv es ti gati ons
N o 295,
C entre
us i ng
for
UK
Labour
E c onomi c s .
U ni verN ymoen,
R.
(1988):
om forhandl i nger,
of
l l orw ay .
' N oen
k ommentarer
ti r
ny ere
l @nn og s y s s el s etti ngr,
empi ri s k
fors k ni ng
unpubl i s hed,
B ank