a pure theory of job security and labour income risk
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8/11/2019 A Pure Theory of Job Security and Labour Income Risk
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The Review of Economic Studies, Ltd.
A Pure Theory of Job Security and Labour Income RiskAuthor(s): Giuseppe BertolaSource: The Review of Economic Studies, Vol. 71, No. 1 (Jan., 2004), pp. 43-61Published by: Oxford University Press
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8/11/2019 A Pure Theory of Job Security and Labour Income Risk
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Review fEconomic
tudies
2004)
71,
43-61
0034-6527/04/00030043$02.00
?
2004 The Review
fEconomic tudies
imited
A PureTheoryfJob ecuritynd
Labour
ncomeRisk
GIUSEPPE
BERTOLA
Universitt
i Torino nd
EUI
First
ersion eceived
anuary
000;
final
ersion
ccepted uly
002
(Eds.)
Models
of
abour
market
quilibrium
here
orward-looking
ecisions
maximize oth
rofits
nd
labour
ncome n a
risk-neutralasis
offer
aluable
nsights
nto he
ffectsf
employment
rotection
legislation.ince risk-neutralehaviourn the abourmarketresumes erfectnsurance, owever,ob
security
rovisions
lays
no useful
ole n suchmodels.
his
paper
tudies
stylized
model f
dynamic
labourmarket
nteractions here
abourreallocation
osts
are
partly
inanced
y
uninsured orkers'
consumption
lows.n the
esulting
econd-best
quilibrium,rovisions
hat hiftabour eallocationosts
to risk-neutral
mployers
an
ncrease
roductivefficiency
f
their
dministrative
ead-weight
osts re
nottoo
arge,
nd
increaseworkers'
welfare
s
long
as
employers'
iring
osts
t least
partly
inance
workers'
mobility.
1.
INTRODUCTION
Relationships
etween
he
nstitutionaltructurend
dynamic
onfiguration
f
abour
markets
are
well
understoodn
theory
nd
extensively
ocumented
mpirically
see
Bertola,
999,
for
a surveyndOECD, 1999,for ecentvidence). heimplicationsf ob securityrovisionr
employment-protection
egislation
EPL)
are
easily
characterized
f workers' nd
employers'
behaviourims t
maximizing
he
xpected
resent
iscounted
alue
f
profit
nd
abour-income
streams.
n
that
tandard
ramework,
abour
hedding
s
reduced
y
EPL
for
iven
abour
emand
and
wage dynamics.
f at
hiring
imes
mployers
nticipate
hat
uture
iring
illbe difficultr
costly,
owever,
ore
tringent
PL
alsotends o reduce ew
hires.
Hence,
PL should mooth
adjustment
ynamics,
ut
ggregate
mployment
nd
unemployment
hould
epend
n
average
wages
and
average
abour
demand
Bentolila
nd
Bertola,
990).
From his
perspective
t is
easy
to
interpret
heweak
empirical elationship
etween he
stringency
f EPL and
average
employment
erformance,
nd
similarlyimplensights xplain
much
harper
ssociations
f
stringent
PL with
ong
enures
mong
he
mployed,ong
unemploymentpells,
nd
ggregate
employmenttability.
While
tandard odels
rove
sefuln
nterpreting
he ffects
f
EPL,
they
annot
xplain
why
t should
e introduced.rom
general-equilibriumerspective,
isk-neutral
ehaviourn
the
abourmarket
elies n
the
xistence f
perfect
nd
omplete
inancial
arkets,
nd
ob
secu-
rity
an
hardly
e
valuedwhen
erfect
nsurance
s
already
vailable.
urther,
f
ntertemporal
state-contingent
ontracts
ere
complete
hen
mandatory
edundancyayments
o dismissed
workersould nd
should e offset
y
properlydjusting
ages
nd
other
ontractual
ayments
(Lazear,
1990).
Since
hird-party
ayments
annot
e offset
y
contractsetween
mployers
nd
employees,
PL can
have
real
effects
nder isk
neutrality
hen t entails otificationnd cer-
tification
rocedures
atherhan
edundancyayments
o dismissed
mployees.
uch
red
ape
costs,
however,
an
only
reduce
he abourmarket's conomic
fficiency;ead-weight
osses
also arise f EPL is modelled s severance axespaidto a central evenue oolredistributedo
43
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44
REVIEW
OF
ECONOMIC STUDIES
all
individuals
Lucas
and Prescott
1974),
Hopenhayn
nd
Rogerson
1993)).
Since distortions
alter hedistributionfeconomic
urplus
t
the ame ime s
they
educe ts
ggregate
ize,
t s
possible
o
specify
macroeconomic odelswhereworkers
avour asteful
PL
(Bertola, 994).
In
perfect
nd
complete
inancial
arkets,owever,
ny
uch
redistribution
hould n
principle
be
achieved
y ump-sum
ather
han
istortionary
nstruments,
nd
contractshould ircumvent
legal
restrictionshenever
hey
ntail
ead-weight
osses.
In
summary,
or
models asedon risk-neutral
abourmarket ehaviour
t s hard o
explain
why
PL should avereal
ffects
n
equilibria
here
wages
re llowed
o
adjust.
And ince
he
efficiency
mpact
f
EPL,
if
any,
s
negative,
t s evenharder
or uchmodels o
explainwhy
EPL should ver e
introduced
n
the irst
lace.
Of
course,
ontractual
mperfectionsay
make
it
mpossible
or ide
greements
oundo he
mplications
fEPL
which,
ike therabourmarket
policies,
an
mprove
hewelfare f at east subset
f the
conomy's gents
n a second-best
environment.
This
paper
focuses n the
mplications
fEPL when
diosyncratic
abour
ncome hocks
arenot
nsurable. s
in
Flemming
1978),
Dixit ndRob
1994),
Alvarez
ndVeracierto
1998),
Acemoglu
nd Shimer
1999)
and other ecent nd
ess recent
ontributions,
class of
agents
( workers )
may
notaccess financialmarkets o as to smooth
onsumption
ver time nd
across tates f theworld.
mperfect
inancial-market
ccess,
while
obviously
ealistic,
s not
easily
modelled,
incemarketsan be
imperfect
nd/or
ncomplete
n
many
ifferent
ays.
A
discussion f ome elatediteraturean be found
n
what
ollows,
ut he
model onsidered ere
is
kept ery imple
nd ims t
offering
nambiguousnalytic
esults
f some
generality.
In
the
special
case whereworkers'
marginal
tility
s
constant,
he
model llustrateshe
simple nsights
utlinedbove:EPL is neutraln
steady
tate
f tmandates
edundancyayments
directly
rom
mployers
o
workers,
nd s
welfare-decreasing
f t ntails
ead-weight
osses.But
when abour-income
ncertainty
s
not
rivately
iversifiable,
hen
ollectively
dministered
PL
canaddress hat
mperfection,
nd
mprove
oth
roductive
fficiency
nd workers'
elfare.f
state-contingentidepaymentsere ontractible,f ourse here ould e no role or olicyand
any
policy
f the
ype
onsidered
ere ould
be circumvented
erfectly
y
market
nteractions).
And f
governments
ould
costlesslymprove
market
llocations,
f course
hey
hould. ess
obviously,
venwhen
art
f
redundancyayments
re
wasted
rom he
erspective
f
mployer-
employee elationships
heeffects f
EPL
and other
abour
market
olicies
an
be beneficial
if
their
ostly
dministrationffersn
mprovement
vermarketutcomes.
he
analysis
elow
offers
formalharacterizationfhow he elevance
f his
nsight
epends
nstructural
eatures
of themarket's
echnology
nd
ability
o
insure abour-income
isk,
ocusing
n
particular
n
distributional
ssues;
and a less formal iscussion f
whether,
n
reality, overnment
olicies
may
more r less
imperfectly
ddress
bviously
ealistic
market
ailuresn the
ntertemporal
dimensionf abourmarkets.
Section introducesstylizedmodel f abour emand luctuationsnd ts wo ubsections
characterize
ynamic
abour emand nd
supply olicies,
n terms f
the urnovernd
mobility
costs
paid by employers
nd workers nd of the
wage
rates
pplicable
o
high-
nd low-
productivitymploymentelationships.
ection 3 constructs
n
equilibrium
here
firms'
andworkers'
wage-taking
hoices
nteract,
nd
proceeds
o
study
he
ong-run
quilibrium
implications
fEPL in the
esulting
odel
f
competitive
ut
dynamically
ncomplete
arkets.
Section discusses hemodel's
ssumptions
nd
results,
utlining
ow he imilar
nsights
ould
be
applicable
o other
olicy
nterventions
nthe ame
simple
rameworkf
analysis
ndhow
it
could be extended. he
concluding
ection5 summarizes
nd comments
n how
nsights
gained
from he
proposed pure
heoretical
erspective
ayhelp
evaluate
ess
pure
real-life
implementations
f EPL. An
Appendix
ontains
ormal
roofs
f the
nalytic
esults tated
n
themain ext.
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8/11/2019 A Pure Theory of Job Security and Labour Income Risk
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BERTOLA JOBSECURITY AND LABOUR
INCOME RISK
45
2. MODEL SETUP
Consider
labourmarket here n
ndefinitely
ivisibleabour
orces
employed
t
production
sites r
firms ,
ndexed
y
,
which orm
continuum
f
given
ize.1
The
marginalroductivity
J
1l,
o
V
of
labour at
firm
is
a
differentiable,
trictly
ecreasing
unction f its
current
employmentil, and also depends n an index fproductivitynddemand onditions,enoted
a.
For
the nterior
ptimality
onditions
erived
n what ollows
o be satisfied
n
equilibrium,
it willbe
conveniento assume hat
r(l, a)
>
0,
lim
or
r(l,
)
=
oo,
Va.
Exogenous,diosyncratic
abour emand
hocks
re
representedy simple rocess
whereby
i
fluctuates
etween wo
values,
g
and
b,
with
ymmetric
ransition
robability
x
(l,
ab),
VI
>
0.
In what
follows,
irm is dubbed
good
at time
if
a
=
ag
(marginal roductivity
f
ts
employment
s
high),
bad when
;
=
ab.
Theequilibriumf nterests symmetricall firmsnthe ameproductivitytate aythe
same
wage
andhave the same
employment);
table vertime
the
fraction
f firms
n
each
state s the
rgodic
ne);
based on
wage-taking
ehaviour
y
both
mployers
nd
employees;
and
assumed,
n the
basis
of
parametric
estrictions,
o feature
ositive
urnover
nd
positive
employment
t
bad
firms.
Accordingly,
et w
g
denote he
wage paid by
a
firm
hose
abour
demand s indexed
y
ag,
and et
wb
similarly
enote
he
wage
associated
with
b.
The
two
wage
rates re treated
s
parametricallyiven
nd onstantver imewhen
haracterizing
ptimal
ecentralized
ecisions,
in this
ection. he next ection
xplicitly
haracterizeshe
market
onfiguration
upportedy
wage-taking
ehaviour,
nd verifies
hat
n
the
ong-run onfiguration
f the
equilibrium
f
interest
ages
re ndeed onstantver ime.
2.1.
Firing
osts nd
dynamic
abour emand
To
represent
ob security
rovisions,
et cost
kf
be
mposed
n
employers
or ach
unit f abour
dismissed
pon
transition
rom
g
to
ab.
This
mayrepresentayments
o
dismissed
orkers
or to a
third
arty,
rthe hadow
rice
f
quantity
onstraints.
hese alternative
nterpretations
have
different
mplications
or he
quilibriumnalysis
f the
next
ection,
ut re
equivalent
from he
employers' oint
f view.To
simplify
otation,
et
no turnover
ostsbe
paid
when
employment
ncreases. he
mplications
f
hiring
osts re
qualitatively
imilaro those f
the
firing
osts
representedy
kf,
and
dentical nder
he
ssumption
made
below)
that iscount
rates renegligiblymall.
If
abour urnovers
costly
or
mployers,ynamic
abour
emand
mustook forward
o
the
dynamic
volution fthe
marginal roduct
nd
wageprocesses.
ince
diosyncraticapital-
incomerisk
may
be diversified
n
financial
markets
y
holding portfolio
f
many
firms'
shares,
et
employers
im
at
maximizing
he
risk-neutral
xpectation
f the
discounted ash
flows.n an
environmenthere
wages,
ndividual
irms'
mployment
evelsand
productivity
all
fluctuate
etween wo
values,
o
does the
xpected
resent
alue
of thedifference
etween
labour's
marginal roduct
nd
wage.
Let
V,
denote the
marginal
alue
of
employment
for
a
good
firm,
b
thatfor
a
bad one. These
marginal
sset
values
satisfy
he recursive
1. For
simplicity,ntry
r exit f firmss ruled ut.Bertola
1994)
and Alvarez nd
Veracierto
1998)
study
he
implicationsfconstrainedabourmobilityor irmreationndcapital ccumulationndynamiceneral quilibrium.
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46
REVIEW OF ECONOMIC STUDIES
relationships
1
Vg
=
2(lg, ag)
-
Wg
+
1(1
-
p)Vg
+
pVb,
1
Vb
=
Jr(lb, Ob)
-
wb
+
[pV,
+
(1 - p)Vb],
(1)
1+p
where
_
0
is the
discount ate
pplied
o thenext
eriod's
ashflow.
Turnovers
optimal
f
the
value
of the
marginal
ismissedworkerffsetshe
firing
ost
kf
exactly,
nd that f the
marginal
orker ired
quals
zero in the bsence f
hiring
osts).
Thesefirst-orderonditions
re sufficient
f,
s
assumed,
he
marginal
evenue
roduct
f abour
is
decreasing
n
employment.
nserting
b
=
-kf
and
Vg
=
0
in
1)
yields
P
r(lg,ag)=
wg
+
kf,
1+p
P+P
Ir(lb, Oab)
=
Wb
-
kf.
(2)
1+p
A
bad
firm
ays
ts
employees
more han heir
marginalroduct,
ecause
he
xpense
f
firing
them s wasted f abour
emand ncreases ndnewworkers
rehired. he
wagespaidby good
firms,
onversely,
re ower
han
marginal roductivity:
ince
dismissalsccur n thenext
eriod
with
robability,
a fraction
ofthe
iring
ost
kf
s discounted
o the
resent
ndadded
o
the
marginal
orker's
age.
The conditions
n
(2)
jointly
etermine
g
and
lb
if,
as
assumed,
he function
n(.)
is
continuousnd
strictly
ecreasing.
hose
conditions,
owever,
dentify
n
interesting
nterior
equilibrium
nly
f
heirolution
s such hat
,
>
lb
> 0. This
s
ensured
y
simple
estrictions
on
the
parameters
f the
economy's
echnology:
t
might
ail
to
be the
case if the
frequency
and
intensity
f labour
demand
luctuations
re smallrelative
o
kf,
to
imply
hat
omplete
inactionat a history-dependentmploymentevel g = lb) is optimal; r ifnegativeabour
demand
hocksmake t
optimal
or bad
firms o shut
down
temporarily.
uch
parameter
configurations
re not
nteresting
or he
purposes
f
this
paper,
ecause
the
precise
value of
kf
s
irrelevanthen
(non-unique)
quilibrium
s
supported
y strict-inequality
corner)
ather
than ndifferenceonditionsn
decentralized
ecisions.
ence,
he erivationshat ollow ssume
that
arameters
re such
hat
,
>
lb
>
0
when
2)
is satisfied.
2.2. Worker
mobility
In
reality,
workers
may
or
may
not be insured
gainst
heir
mployers'
abour demand
fluctuations.n themodel, eteach ndividual's hole abour upply e allocated o the ingle
occupation,
ector,
r
region
epresentedy
one of
the firms ntroduced
bove,
nd
ethis or
her
onsumptionqual
currentabour ncome.While
perfectonsumption
moothing
ould
be
achieved t n abstract
arket-clearingtage
f
omplete
inancial arkets
xisted,
ere
he ocus
is on
the
opposite
xtreme
nd
perhaps
o more nrealisticase
where t s
simply mpossible
forworkerso
transfer
esourcescross
eriods
nd states fnature.
As in the
nalysis
f
employers'
ptimal
abour
emand,
et
wage
rates e taken s
given
by
workers,
nd let them
epend
nly
on
the currenttate
f
each
firm's
abour
demand.
f
u(.)
is a worker's
ncreasing
nd at least
weakly
oncave
period-utility
unction,
nd
good
firms
ay wage
Wg,
heir
mployees'
tility
low s
U(Wg).
n
the bsenceof financial
ssets,
the
only ntertemporal
hoice
by
workersntails
ob-to-job
movements.et
Ug
and
Ub
denote
theexpected resent iscountedlow futilityorworkersmployed y currentlyoodand
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8/11/2019 A Pure Theory of Job Security and Labour Income Risk
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48
REVIEW
OF ECONOMIC STUDIES
Result . If
p
O,
hen
(a)
wg
-
kw
0
in
12)
(a)
has no
effectsf
X =
1,
(b) decreases roductivefficiencyfX< 1.
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8/11/2019 A Pure Theory of Job Security and Labour Income Risk
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BERTOLA
JOBSECURITY
AND LABOUR
INCOME RISK 51
If ll
firing
osts
epresentedundancyayments
orisk-neutral
perfectly
nsured)
orkers,
they
re
completely
rrelevant. s
wages endogenouslydjust
o offset he
mplications
f
redundancyayments
n
thebasis of
risk-neutral
xpectations,
nly
he
umtotal
f
mobility
costs,
not heirncidence
n workers r
employers,
as realeffects.
nd f
EPL
entails ead-
weight
osses from he
point
f view of
employers
nd
redundant
orkers
as
itoften oes in
reality),
hen
iring
ostsreduce
fficiency.
hilewastefulPL
may
ffecthedistributionf
output
cross
isk-neutralorkersnd
employers
see
Bertola, 994,
ndResult
below),
uch
effectsre mall ndof
mbiguousign.
rom risk-neutral
ong-run
erspective,
t s
quite
hard
to understand
hy ob
securityrovisions
xist.
If
insteadworkersre
imperfectly
nsured,
hen PL as
modelled oes
have
potentially
beneficial
mplications:
Result4.
If
u(.)
is
concave nd
p
0
in
12)
increases
roductivefficiency
f
X
=
1,
as
long
s
kf
0
in 12) certainlyecreases roductionhen
X
=
0;
(c)
for
< X
0
in
(12)
may
or
may
not ncrease
roduction,epending
n
the
degree
f
concavity
fthe
utility
unctionndon the
pecification
f abour emand.
Since
laissez-faire
abour llocations inefficient
henuninsured
orkers akeforward-
looking
ecisions,
olicy
nterventionsan ncrease hemarket's
roduction
low. ven when t
the evel f
microeconomic
mploymentelationships
PL entails
ead-weight
osts,
epresented
by
X
0,
regardless
f
whethert
mproves roductive
fficiency.
The
proof
n
the
Appendix
stablishes hatworkers
ntuitivelyain
from
etterabour
allocation
a
larger
),
and
agree
n
this
espect
with
hypothetical
ocial
planner
nterested
in
maximizingroductivefficiency.
he welfare f
workers,owever,
lso increaseswhen
larger
is obtained
y costly
PL
configurations
a
small
X),
and even
whenP
decreases
s
long
s thedirectnsurance
ffectfEPL-which
brings
he wo
onsumption
low ealizations
closer o each
other-is
not
more han ffset
y
ower
verage onsumption.
n
the
proof
f the
result,
he
onditionhat abour
emand as constant
lope
with
espect
o
employment
nsures
thatworkers' verage onsumptionannot ecrease s increasinglyostly urnover orsens
productive
fficiency.
n
the bsence f
discounting
ffects,
n
fact,
he otal
wage
billofa
given
labour orce
oes not
epend
n
employment
atterns
f abour emands
linear,
nd ess ntense
turnoveran
only
ncrease
onsumption
fworkers hobear ome
f ts osts. ormore
eneral
labour
emand
pecifications,
he
distributional
ffect f
firing
osts
s
not
eroevenunder
isk
neutrality,
ut ts
sign
s
ambiguous
nd
depends
n features
f
high-order
erivativesf
the
production
unction
hich,
nlike heir
tilityounterparts,
ave
no obvious
nterpretation
and
arediscussedn
somedetail
n
Bertola
1992),
andother eferences
nBertola
1999)).
4.
DISCUSSION
Themodelofthispaper ntroduces single mperfection-amissing inancialmarket-in n
otherwise
tandardmodelof
wage-taking
ompetitive
quilibrium
imilarothose tudied
y
Lucas and
Prescott
1974),
Topel
1986)
andothers.
hemodel elies n a
numberf
implifying
assumptions
oobtain
risp
nalytical
esults,
nd both
ssumptions
nd
results
eserve
o be
discussed ere.
In
the
model,
edundancyayments
ot
only
reduce
onsumption
luctuationsor hose
membersf
ociety
hat re
uninsuredut
may
lso
mprove
roductive
fficiency,
y
redirecting
aggregate
esources owardsndividuals hose
consumption
low s
unfairly
urdened
y
labour
eallocationost nd
encouragingorward-looking
obility
nvestments
y
workers
ho
valuecurrentesourcesmore
han
representative
ndividual
ould.This
paper
ocuses n
the
effectsnd
possible
rationales f EPL in an
incomplete-markets
etting,
ut he
nsight
s
of
course pplicable o other olicy nterventionsn similar econd-bestituations.tmayhelp
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BERTOLA
JOB
SECURITY AND
LABOUR INCOME RISK
53
intuition
ndease
discussion o
consider
riefly
ow axes
nd subsidies
mayplay
similar
ole
in
the ame
etting.
Unemployment
nsurance
UI)
schemes avebeen
extensively
tudied
n
both
partial
nd
general
quilibrium
mperfect-market
ettings,
nd active
abourmarket
olicies
ALMP)
which
ffer
raining
nd
ob-search
ssistance o
displaced
workersnd
ob
subsidies
o
low-
earners avealso receivedxtensive
crutiny
see Karni 1999),Heckman, alonde nd Smith
(1999)
for
ecent
urveys
f
theoreticalnd
empirical
ork).
he
stylized
model tudied
ere,
whereworker
obility
s
costly
ut
nstantaneous,
oes not
xplicitly
ccount or
nemployment
but
UI
andALMPschemes
meant
o nsure orkers
gainst
ncome
oss and/oro ase
ob finding
may
be
qualitatively
epresentedy simple olicy ackage:
Result . Consider
policy
hat
mposes payroll
ax
r
on all
employmentelationships
at
good
firms,
ays
a
subsidy
f
the ame absolute ize to
all workers
mployed y
bad
firms,
and uses
a
portion
of
remaining
evenues o
pay
a
subsidy
to
all workers ho are
changing
jobs,
while
eaving mployers
ree f ll turnoverosts. uch
a
policy:
(a)
if
X=
1,
achieves
roduction
fficiency
ndfull nsurance
ith
=
pk,
=
k;
(b)
can
improve
roductivityfficiency
nd afford
Pareto
mprovement
ver
aissez-faire,
even f
X
-u(w
-ks
>
0,
dwg u(wb) - U(wg - kw) (u(wb)
--
u
(w
g
-
kw))2
'
S
-
(u(wb) u(Wg
-k))20,
d u(wg)
-
u(wb)-
u(wg
-km))
- (u(wg) u(wb))u'(wb)
=~
0
and
u(-)
is concave. Hence
r(P, ag)
-
r(1
-
P,
ab)
-
2pkf
>
2pkw.
ProofofResult
.
Differentiating
9)
with
kw
=
-Xdkf
yields
dP (1 -
2p)u'
+
ub
+
2u
(p
-X)
_
p
(A.2)
dk
(1
-
2p)ugrg
+
ub
+
2pumrg(A.2)
where
,
du(x) du(x)
,
du x)
u ->
,
ub
>
O, u,
> 0, (A.3)
dx
=Wg
x
=Wb
x=wg-kw
and
/
3r(x,ag)
,
ar(x,ab)
S0,
Jb
--
-
8/11/2019 A Pure Theory of Job Security and Labour Income Risk
18/20
BERTOLA
JOB
SECURITY
AND LABOUR
INCOME RISK
59
When
'(.)
is
constant,
A.2)
reads
dP
(1
-
2p)p
+
p + 2p(p
-
X)
2p
= (1 - 1)
ub
>
u under he onditions
iven.
Hence,
-[(1
-
2p)ug
+
ub + 2un(p
-
1)]
>
-[(1
-
2p)un
+
un +
2un(p
-
1)1
=
0.
Under
he ame
onditions,
ypart
d)
ofResult
r(P,atg)
-
r(1
-
P,
b)
-
(kw+ kf)2p
> 0.
Hence,
A
1
unambiguouslymplies
hat
Y/dkf
>
0
as
long
s
kf
?
k and
kw
>
0.
(b) If
A
= 0,
dY dP
- [r(P,
ag)
-
r(1
-
P,
cb)
-
(kw
+
kf)2p]
-
p(2P
-
1). (A.6)
dkf
dk
Under he onditions
iven,
r(P,
g)
-
7r(1
P,
ab)
-
(kw
+
kf)2p
>
0
bypart
d)
ofResult
.
The
sign
f
dP/dkf
is
again
he
pposite
f
that fthenumeratorf
expression
A.2),
which eads
(1
-
2p)ug
+
u,
+
2ump]
when
A =
0.
Usingum
ub
>
ug,
(1
-
2p)ut
+
u
+
2up
>
(1
-
2p)u,
+
ug
+
2ugp
=
2ug
> 0.
Thus,
oth
erms re
negative
n
A.6).
(c)
For
general
0
requires
hat
(1
-
2p)ug
+ ub
+
2urn(p
-
A)
=
2(1
-
)un
-
2(1
-
p)$i
-
(1
-
2p)2
be
negative,
here
1
-
um
-
ub
>
0
and
2
-
ub
- ug
> 0. A
necessary
ondition
s therefore
(1
-p)1
P2
> (1
-)u
i.e.
the
portion
f
firing
osts
onsisting
f
redundancy
ayments
ust e
large
elativeothe
marginal-utilityedges
associatedwith
ackof
nsurance. ewritten
n
terms f
marginal
tilities,
he ondition
> 2
ub+u+2p
(u-u)
>
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60
REVIEW OF
ECONOMIC STUDIES
is
necessary
or he
ffect
f
EPL
on
production
obe
possibly ositive.
ncreased
roduction
illobtain f he
llocation
effect
epresented
y
the
firsterm
n
(A.7)
is
larger
han he
dead-weight
ost n the ast term. n
turn,
his s
more
likely
obe the
ase when evere
nsurance
roblems
mply
hat is much maller hanwould e
mplied y
risk-neutral
reallocationecisions.
ProofofResult. Insertinghewageexpressionsrom8) in 15) yields
u
=
u(7r(P, g)
-
pkf)
+u(r(1
-
P,
ab)
+
pkf),
hence
di,
dP
dkf
=
(ugr
-U'b r)
dkf
+ p[ub
-
ug]
U(g
dP ,,dP)
u---
-
)
dP
(fI
.)
(A 8)
Jbdkf
+
[u,
--
U]
~~1P~
C'~~
Pg
it
s positive
f
The
second erm ould anish
nder
isk
eutrality.
hen
ub
>
ug
it s
positive
f
,
dP
p >
nbb
dkf
Since
r'b
0,
the
econd erms
surely
ositive
f
dP/dkf
>
0
(i.e.
fEPL increases
roductionfficiency),
n
which
case the irst
erm
s
also
positive
and
EPL
increases orkers'
elfare)
s
long
s
7rg
_
.
he welfare f
workers,
owever,
ncreases
ven when small
X
leads EPL to reduce
productivefficiency.
Inserting
A.2)
in
A.8)
yields
dii
,
dP
(1
-
p)U-g
+u +
2um(P
-X)
dk
f
ug
(
-
b
-dk
+
[ub
-
U'g
p
1
(1
-
2p)u'g
u'gb
+2pum
If
=
Tr,
this
xpression
oes not
epend
n
dP/dkf
and
implifies
o
di2
(1 - 2p)U'g u + 2u~(P -
,)
=?
[ub
-
u'g]
1--
+ (
dkf
LUb
U
(1
-
2p)u'g+ub
+
2pum
2hum
[Ub- u
2g]up>0
S ]p (1
-
2p)ug
+
ub
+
2pum
where
he
nequality
ollows rom >
ug.
Proof
f
Result . In
steady
tate,
fraction
ofthemarket's
obs pay
he
ayroll
ax
r,
the
emainder
receive
a
subsidy
;
the
evenue,
et f
he
roportional
ost 1
-
X,
s usedto subsidize
he
p(2P
-
1)
workers ho re
moving
from
eclining
o
expanding
irms.
ence,
ach suchworker eceives
[Pr
-
(1
-
P)r].
T
p(2P
-
1)
p
and bears
mobility
ostk - a = k -
?P.
n the bsence f turnover
osts,
Wg
=
7T(P,
Ig),
wb
=
Tr(1
P,
ab),
and
accounting
or
he
mpact
f taxes
nd subsidies
n workers'
onsumption
evels,
he
mobility-indifference
ondition
reads
u(r(P,
fig)
r)(1
-
2p)
=
u(r(1
-
P,
cb)
+
r)
-
2p
[u
(r(P,
ig)
- t
+
-
k)1.
(A.9)
Writing
=
pkf,
condition
A.9)
is the
ame s
the
ersion f
9)
that
pplies
oEPL as modelledn
the
ext,
u(w(P,
ag)
-
pkf)(1
-
2p)
=
u(r(1
-
P,
ab)
+
pkf)
-
2p[u(r(P,
acg)
pkf
+
Xkf
-
k)].
Hence,
he
quilibrium
ffectsfthis
olicy
re he
ame s those fthe
quivalent
PL
policy
with
f
=
r/p.
Part
a)
of he
esult
ollows rom esult
,
part
b)
from esult
,
and
part
c)
restates
esult .
Acknowledgements.
revious
ersions f this
material ffered umericalatherhan
nalytical
esults,
irculated
under lightly ifferentitles, nd were read as the Review of EconomicStudiesLecture t a Royal Economic
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8/11/2019 A Pure Theory of Job Security and Labour Income Risk
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BERTOLA
JOB
SECURITY
AND
LABOUR
INCOME
RISK
61
Society
meeting,
s
an
ASSET
Lecture,
nd at several
eminars. his version enefits
rom
seful omments
eceived
on
those
ccasions,
t
a UCL
seminar
resentation,
rom
hree eferees
nd
Orazio
Attanasio,
nd
fromGiulio
Fella,
Winfried
oeniger
nd
Mirko
Wiederholt.he
hospitality
f the
MF Research
epartment,
he
upport
f
Consiglio
Nazionale
elle
Ricerche,
nd hat f he
.U.I.
Research ouncil re
lso
gratefullycknowledged.
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