A Pure Theory of Job Security and Labour Income Risk

8/11/2019 A Pure Theory of Job Security and Labour Income Risk

1/20

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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2/20

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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3/20

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.



4/20

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.



5/20

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



6/20


7/20

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.



10/20

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



12/20

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

--


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)

>



19/20

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



20/20

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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A Pure Theory of Job Security and Labour Income Risk

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