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Massachusetts Institute of Technology
Department of Economics
Working Paper Series
THE OPTIMAL DESIGN OF
UNEMPLOYMENT INSURANCE
AND EMPLOYMENT PROTECTION.
A FIRST PASS.
Olivier Blanchard
Working Paper 04-15
April 1,2004
RoomE52-251
50 Memorial Drive
Cambridge,
MA 02142
This paper can be downloaded without charge from the
Social Science Research Network Paper Collection at
http://ssrn.com/abstract=527882
i
MASSACHUSETTS INSTITUTE
OP TECHNOLOGY
The optimal design
of
unemployment
insurance and employment protection.
A
first pass.*
Olivier Blanchardt
April
1,
and
Jean Tirole
*
2004
We
*
are grateful to Daron Acemoglu, Suman Basu, Javier Ortega, John Hassler, and to the
participants to the third Toulouse Macroeconomics workshop for helpful comments.
t
MIT and NBER.
IDEI and
MIT.
t
Visiting Scholar, Russell Sage Foundation
GREMAQ (UMR
5604 CNRS), Toulouse,
CERAS (URA
2036 CNRS), Paris, and
Abstract
Much
of the policy discussion of labor market institutions has
been at the margin,
with proposals to tighten unemployment benefits, reduce employment protection,
and so on. There has been
architecture should be.
little
discussion however of
The paper
what the ultimate goal and
focuses on characterizing this ultimate goal, the
optimal architecture of labor market institutions.
We
start
our analysis with a simple benchmark, with risk averse workers, risk
neutral firms and
random shocks
to productivity. In this benchmark,
we show that
optimality requires both unemployment insurance and employment protection
the form of layoff taxes;
it
also requires that layoff taxes
—
in
be equal to unemployment
benefits.
We
then explore the implications of four broad categories of deviations: limits on
insurance, limits on layoff taxes, ex-post
firms or workers.
The scope
We
wage bargaining, and heterogeneity
show how the architecture must be modified
for insurance
may be more
of
in each case.
limited than in the benchmark; so
may
the
scope for employment protection. The general principle remains however, namely
the need to look at unemployment insurance and employment protection together,
rather than in isolation.
Introduction
Much
of the policy discussion of labor market institutions has been at the margin,
with proposals to tighten unemployment benefits, reduce employment protection,
and so
There has been
on.
architecture should be.
provided,
how should
little
What
should be the level of insurance,
Our
What
focus in this paper
is
make payments
political
economy
on characterizing
this ultimate goal, the
We make
match
be
optimal archi-
no attempt to look
at transition
These are obviously highly relevant to policy makers,
issues.
start our analysis in Section 1 with a simple
averse; entrepreneurs
it
to the state, or directly to the
but they should come second, once the ultimate goal
We
should
should be the size of these payments?
tecture of labor market institutions.
and
how
be financed? Should there be some form of employment
it
protection? If so, should firms
workers they lay off?
what the ultimate goal and
discussion however of
run firms and are
is
clear.
benchmark. Workers are
risk neutral. Productivity of
risk
any worker-
random. In
this
benchmark, the proper institutions can achieve both
production efficiency and
full
insurance. This can be achieved in a
firm
is
number of ways.
For example, insurance can be provided through the payment of unemployment
benefits
by an unemployment agency. And
efficiency
layoff taxes, leading firms to internalize the cost of
can be achieved by using
unemployment.
In this benchmark, efficiency requires that layoff taxes be equal to unemployment
benefits.
This implies that layoff taxes
to use payroll taxes.
to
unemployment
The
is
—defined as
We
The presence
equal to one.
layoff taxes
of the
first
Unemployment
so,
and there
is
benefits
and employ-
—are essential components of the optimal
requires the presence of the other.
then consider deviations from the benchmark. There
ways of doing
no need
contribution rate, defined as the ratio of layoff taxes
benefits,
ment protection
architecture:
fully finance benefits, so there is
is
potentially a thousand
no agreement among labor economists as to which
imperfections are most relevant. Thus, our strategy
is
to explore the implications
of four broad categories of deviations:
Limits on insurance. Such
either to the
limits
unemployed to search
may come from
for
the need to give incentives
another job, or to the employed workers
not to shirk on the job.
We
show
in Section 2 that, in this case,
it is
optimal to
partly compensate for the limits on insurance by decreasing the incidence of un-
employment, so by decreasing
layoffs
below the
This
efficient level.
is
achieved by
choosing layoff taxes higher than unemployment benefits, thus by choosing a contribution rate higher than one.
As
layoff tax revenues
benefits, the state then balances its
Under
this deviation, optimality calls for higher
tighter the limits
now exceed unemployment
budget through a negative payroll tax.
employment protection: The
on unemployment benefits, the higher the optimal employment
protection, but at an increasing cost in terms of efficiency. Reforms of the un-
employment insurance system which allow
search effort
for higher insurance while
thus have both direct insurance
effects,
maintaining
but also indirect ones, as they
allow to decrease employment protection and improve efficiency.
Limits on layoff taxes. Shallow pockets may make
firms to pay layoff taxes.
feasible
on
and optimal to
layoff taxes
We show,
fully insure
in Section 3, that, even in this case,
now be
remains
financed partly
in
turn implies that
and
this leads to too
also consider, in this section, the case of multi-activity firms,
and the question
firms only partially internalize the cost of unemployment,
many
layoffs relative to the efficient level.
of whether taxing layoffs
We
it
workers against unemployment. But the limits
imply that unemployment benefits must
through layoff taxes and partly through payroll taxes. This
We
or impossible for
it difficult
show
that,
may
more
under shallow pockets, this
optimal layoff tax schedule
tax on the
lead to
first layoff
for
layoffs
may
—creating
"snowball effects"
indeed be the case, and derive the
a firm composed of two jobs. Intuitively, the layoff
should not be so high relative to the layoff tax on the second
job as to lead the firm to want to close the second job.
Ex-post wage bargaining. Our benchmark assumes that wages
are set ex-ante.
Thus, better insurance reduces the wage that risk averse workers are willing to
accept and reduces expected labor costs. In fact, wages are often partly renegotiated ex-post. In that case, rather than leading to lower wages,
social protection,
be
it
more generous
through unemployment benefits or layoff taxes, strengthens
the bargaining position of workers, and thus
is
likely to lead to
an increase rather
than to a decrease
wage
is
now
workers.
We
Ex-post wage determination also implies that the
depend on productivity, introducing wage
risk for
take up the case of ex-post wage bargaining in Section
that, in this case,
should be
in wages.
likely to
less
4,
employed
and show
workers have any bargaining power, the contribution rate
if
than one. The higher the bargaining power of workers, the lower
the feasible level of insurance, and the lower the contribution rate.
Heterogeneity. Our benchmark treats
tical.
This
first
consider heterogeneity of firms.
is
erogeneity
stochastically
is
and
workers as ex-ante iden-
all
consider various dimensions of het-
5.
in the distribution of productivity.
function
firms
We
clearly not the case in fact.
is
erogeneity in Section
We
all
We
Weak
assume two types of
firms are
more
dominated by that of strong
policy, the solution
benefits partly
is still
from
Their distribution
risky:
firms.
not observable by the state, and the state
firms, differing
We
relies
show that
if
het-
on a uniform tax
to provide full insurance to workers, but to finance
layoff taxes
and partly from
payroll taxes
—to have a contri-
bution rate below one. This leads to a transfer of resources from strong to weak
firms, and, because
a transfer
self select,
is
weak
firms are the relevant firms at the creation margin, such
indeed desirable.
If
the state can instead offer tax menus and
firms
only the contribution rate for weak firms needs to be lower than one;
the destruction margin of strong firms
servable
let
and the
is left
state can condition taxes
undistorted. If heterogeneity
on observable
characteristics,
is
ob-
then even
better can be done. Job subsidies can be used to transfer resources from strong
to
weak
firms, while leaving destruction
margins
for
both strong and weak firms
unaffected. This reasoning suggests the desirability of treating different types of
firms, for
example new versus mature
firms, differently.
We then consider heterogeneity of workers. In parallel to the treatment of firms, we
assume two types of workers, "low-ability" and
the distribution of their productivity.
"high-ability" workers, differing in
We show that
if
heterogeneity
is
not observ-
able by the state and the state relies on a uniform tax policy, then, to the extent
that the state cares about inequality,
full
insurance and a contribution rate below
one are again optimal. Lower layoff tax rates lead to a transfer from high-ability to
low-ability workers, a desirable
outcome as
it
reduces income inequality. Again,
if
feasible, offering
menus
or conditioning taxes on observable characteristics lead to
a better outcome, allowing for transfers from high-ability to low-ability workers at
a reduced efficiency cost. This reasoning again suggests the desirability of treating
different workers, for
example new entrants versus workers with higher
seniority,
differently.
we
Before
is
start,
we want
to emphasize the limits of our analysis.
a static, one-period, model.
enough already; but
its
Our only excuse
is
Our framework
that the framework gets complex
limitations prevent us from taking
up a
series of questions,
such as the design of experience rating systems as a way of implementing layoff
taxes, or the potential role of individual
we
mandatory unemployment accounts. Also,
are aware that our broad categories of deviations from the
not
fit
benchmark may
each specific imperfection. Nevertheless, we believe that the conclusions
we draw from our model, about
the articulation of unemployment insurance and
employment protection, about the
relation of the optimal contribution rate
and
the relative use of layoff and payroll taxes to various imperfections, are quite
we draw,
in Section
of workers, a
continuum
general and can help design better systems. In that context,
6,
what we
see as our
1
A
1.1
Assumptions
main
conclusions.
benchmark
Tastes and technology are as follows:
•
The economy
of
•
mass
is
composed
of a
continuum of mass
(at least) 1 of entrepreneurs,
and the
1
state.
Entrepreneurs are risk neutral. Each entrepreneur can start and run a firm.
There
is
a fixed cost of creating a firm: I, which
is
the
same
for all en-
trepreneurs.
If
a firm
is
created, a worker
then revealed. Productivity
is
is
hired,
and the productivity of the match
is
given by y from cd G(y), with density g(y) on
[0, 1].
The
lay the worker
who then becomes unemployed.
off,
Realizations are
•
and produce, or
firm can either keep the worker
Workers are
ii
across firms; there
with
risk averse,
benefits, utility
if
unemployed
no aggregate
is
risk.
utility function U(.).
Absent unemployment
given by U(b) (b
the wage equivalent of
is
is
being unemployed).
•
The state observes only the employment
employed or
is
status (whether the worker remains
laid off).
Accordingly, the state has three tools at
its
disposal, a payroll tax rate
a layoff tax /, and unemployment benefits,
t,
/i.
(Note the absence of job
creation subsidies or taxes; these are straightforward combinations of layoff
and payroll
The
taxes,
and are redundant
here).
state runs a balanced budget.
Decisions are taken in three stages:
•
•
1.
The
Stage
2.
Entrepreneurs decide whether to start firms and pay the fixed cost.
They
hire workers,
Stage
state chooses t,
and
offer
/ and
them
/x,
subject to budget balance.
contracts, characterized
threshold productivity level below which the worker
is
by
w
and
y*,
a
laid off (the threshold
be assumed to be interior in what follows.)
will
The assumption
of a constant
wage
w
rather than a schedule w(y) follows
straightforwardly from workers' risk aversion.
Note the absence of severance payments,
to the worker.
As
•
all
all
Stage
3.
y
>
and r
If
y
<
will
firms face the
rium,
If
As
y*
workers are
The
,
be
clear,
same
cost
i.e.
direct
payments from the firm
they would be redundant here.
and distribution of productivity,
in equilib-
initially hired.
productivity of each job
is
revealed.
then the firm keeps the worker, produces
y,
pays
w
to the worker,
to the state.
y*
,
state pays
the firm lays the worker
fx
to the
off;
the firm pays / to the state, and the
unemployed worker.
Given these assumptions, expected
utility is given by:
Vw =G{y*)U{h+u) + {l-G{y*))U{w)
The
(1)
free entry condition (or participation constraint) for entrepreneurs
is
given
by:
VF =
-G(y*)f
+ f
y dG(y)
-
(1
- G(y*))(w + r)>I
(2)
Jy"
The government budget
constraint
VG =
1.2
is
-G(j/*)(/z
given by:
-
/)
+
(1
- G(y*))r >
(3)
The optimization problem
The problem of the firm
Before turning to the problem of the state,
we need
to look at the
problem of the
firm.
At the time
of hiring, a firm chooses the labor contract that maximizes the value
of the firm, for a given level of expected utility for the worker:
maxVjp
Prom the
first-order conditions, y*
subject to
is
Vw = Vw
then given by:
,.(, +T - fl -( gabffi±i!i
and
w
is
determined
in
)
(
4)
turn by the condition that expected utility be equal to
Vw
The
first
term
in the expression for the threshold productivity
producing.
Were
output was
less
term which says
level will
this the only term, the firm
than the net cost of producing. But there
that, unless the worker
is
is
the net cost of
would simply lay the worker
is in
off
when
general a second
fully insured, the threshold productivity
be lower than the net cost of producing. This insurance-like term
may
be familiar from the old
later on;
we
line of research
shall discuss
it
more length
at
The threshold defined by equation
Ex
post,
layoff
i.e.
on implicit contracts, and
(4) is
will
reappear
then.
not however in general time-consistent.
once the firm has hired a worker, given the wage w, the payroll and
tax rates r and /, the threshold productivity below which the firm will want
to lay a worker off
given by:
is
= (w+-T-f)
y*
The expression no longer
In the benchmark,
it
(5)
includes the insurance term.
will
be the case that workers are
the two
fully insured so
expressions for the threshold will coincide. Later on, this will no longer necessarily
be the case, and so the question
will arise of
what assumption
to make, the choice
of the ex-ante or the ex-post threshold.
If
y
is
observable and contractible, then the threshold will be given by the ex-ante
value. If y
is
may
not contractible however, the firm
ex-ante value.
What
it
needs to do
is
still
be able to commit to the
to put aside funds in
amount {U(w) — U(b +
n))/U'(w), to be paid to a third party (not the worker) in case of
layoff.
This will
clearly lead the firm again to choose the ex-ante value for the threshold.
Our maintained assumption
will
be that y*
is
not contractible, that firms do not
put such funds aside, so firms choose the ex-post value of the threshold
value given
by equation
assumption when
it
The problem of the
The
(5).
matters in Section
2.
state.
state chooses tax rates
expected value of workers'
in this
We
—the
shall discuss the implications of the alternative
and unemployment benefits so
utility,
equation
(1),
as to
maximize the
(expected profits are equal to zero
economy, so we can ignore entrepreneurs'
utility),
subject to the free entry
condition, equation (2), the government budget constraint, equation (3),
threshold chosen by firms, equation
Note that we can consolidate the
and the
(5).
free entry condition
and the government budget
constraint to get:
VGF =
-G(y*)n + [ y dG(y) -
(1
- G(y*))w >
I
(6)
Jy*
Neither the payroll tax rate nor the layoff tax rate appear in the equation.
the point of view of expected profit, given the balanced budget constraint,
it
From
does
not matter whether unemployment benefits are financed by one or the other tax.
Thus, the consolidated
on / and
free entry condition
depends on
[i,
and w, not
y*
directly
t.
This suggests the following formalization strategy: To set up the maximization
problem as a mechanism design problem, finding the optimal allocation
subject to condition
(6).
by the appropriate choice of / and
so
much
in the
(io, fi,
y*)
Then, to find out how the solution can be implemented
t.
This approach turns out to be useful, not
benchmark but when we introduce deviations
later.
The optimization problem
In the
first step,
we
characterize the solution to the following problem.
max Vw
Vfg >
subject to
I
w,n,y"
or, equivalently
max {G(y*)U{b + /i) +
(1
-
G(y*))U(w)}
w,ii,y'
subject to:
-G{y*)pi
+
f y dG(y) -
(1
- G(y*))w >
I
Jy"
Note that
/j.,
ditions,
follows that:
it
w, y*
fully characterize the real allocation.
w =
b
=
b
V*
and the
levels of
w
and
/i
are determined
From
+n
by condition
the first-order con-
(7)
(8)
(6)
holding with equality.
10
The
of
condition
first
utility,
a
is
full
insurance condition: Workers achieve the same level
whether employed or
laid-off
The second
condition
output,
efficient for firms to
it is
is
an
and unemployed.
efficiency condition:
From the
point of view of total
produce so long as productivity exceeds the wage
equivalent of being unemployed.
Thus, in the optimal allocation, insurance does not stand in the way of
We now
efficiency.
turn to the characterization of taxes which support the optimum.
Implementation through payroll and layoff taxes
Payroll
dition
and
layoff taxes are
determined by the combination of the threshold con-
and the government budget
constraint.
Return to the threshold condition, equation
(5).
Replace both y* and
w
by
their
expressions from above, to get:
f-r =
The
(9)
ii
net tax associated with laying off rather than keeping a worker, which
to the layoff tax minus the payroll tax,
is
equal
must be made equal to the unemployment
benefits paid by the state to the worker. This implies a positive relation between
the two tax rates:
The higher the
induce the firm to take the
The second
equation
relation
payroll tax, the higher the layoff tax needed to
efficient decision.
between the two tax rates follows from the budget constraint,
(3):
G(y*)f
Unemployment
benefits
+
(1
- G{y*))r =
must be financed
either
G(y>
by
layoff or
implies a negative relation between the two tax rates:
(10)
by payroll
The higher
taxes. This
the payroll tax,
the lower the required layoff tax. Combining equations (9) and (10 implies:
/
The
layoff
/*,
t
=
tax should be equal to unemployment benefits. The payroll tax should
be equal to
ployment
=
zero. Define the contribution rate as the ratio of layoff taxes to
benefits: r
=
(f/n)-
An
equivalent
way
unem-
of stating the previous result
is
that the contribution rate should be equal to one.
11
We
summarize these
Proposition
1.
results in Proposition
In the benchmark, workers are fully insured (b
threshold productivity
The
b).
allocation is
benefits (f
=
u.),
is
=
/z
w).
The
implemented through
unemployment
layoff taxes equal to
or equivalently, through a unit contribution rate (r
=
=
=
1).
Payroll
0).
Implications and discussion
Our benchmark
yields a
Unemployment
•
+
equal to the wage equivalent of being unemployed (y*
taxes are equal to zero (r
1.3
1.
number
benefits
of conclusions:
and employment protection
ments by firms to the state at the time of
layoff
—defined
— are
as the pay-
both central compo-
nents of the optimal set of labor market institutions.
They
are
complements
higher need for
in that higher
unemployment
unemployment insurance
from firms to the
benefits,
(a lower b), require higher
benefits.
The reason
is
simple: This
makes firms
We have
The outcome
is
both
described the equilibrium as one where the state provides unemployment
and firms pay
layoff taxes to the state.
But an equivalent
allocation can clearly be achieved without the state: All which
case,
is
insurance of laid off workers, and production efficiency.
benefits to workers,
firms to
unemployment
fully internalize the cost of
insurance provided by the state to the unemployed.
full
payments
state.
Indeed, in this benchmark, layoff taxes must be equal to
•
coming from a
make severance payments
in
amount
\i
is
needed
is
for
to the workers directly. In this
payments to workers and payments by firms are automatically equal; there
no need
for third party intervention; and, indeed, firms are eager to provide
such insurance to the risk averse workers as this allows them to reduce expected
labor costs.
In fact, going beyond the confines of this benchmark, there are
good reasons to
conclude that unemployment insurance should be provided by a separate agency,
financed by taxes paid by firms:
12
•
As
of the time of the layoff, the loss from
The outcome
able:
how
long he
is
of search
is
unemployment
a
is
random
going to be unemployed.
severance payment to offset that
If
the firm were to
make a one-time
one-time payment would do a
loss, this
poor job of insuring the laid-off worker.
the firm decided instead to pay
If
the laid-off worker over time, contingent on his unemployment status,
other issues would arise:
The
difficulty for
worker, and determine whether he
is still
many
the firm to actually track the
unemployed or has found another
job; the difficulty in monitoring his search effort
is
vari-
know
uncertain, and the worker does not
and making sure that he
indeed looking for another job. Rather obviously, individual firms cannot
monitor laid
ance.
The
off
workers well enough to provide them with adequate insur-
role of monitoring
unemployment status and search
be therefore delegated to an agency, private or public. The
existing administrative structure,
is
likely to
intensity
must
state, given its
be in the best position to do
the monitoring, and to administer the payment of unemployment benefits,
either alone or in conjunction with the private sector.
There are good reasons to dissociate benefits (which provide insurance to
•
workers) from layoff taxes (which provide the right incentives for firms).
The
benchmark,
this
two serve
will
different purposes.
While the two are equal
in the
no longer be the case when we relax some of the benchmark assumptions.
This dissociation could not be achieved
if
one limited oneself to the use of
severance payments.
The benchmark model
about the
issues.
the labor market.
But
is
it
useful in setting
up the
clearly ignores a
We now
introduce those
stage,
number
we
and as a way of thinking
of important imperfections in
see as
most important, and derive
their implications.
2
Limits on insurance
In our benchmark, workers were fully insured. In practice, incentive reasons com-
mand
that workers not be perfectly insured. This
may be because
workers must
have incentives to search while unemployed, and because they must have incentives
not to shirk
when employed.
13
2.1
A
With
this in
generic constraint
mind, we introduce the following additional constraint in our opti-
mization problem:
{l-G(y*))(U(w)-U(b + fJ.))>B
The expected
utility gain
(11)
from being employed relative to being unemployed must
exceed some value B. Call this constraint the incentive compatibility condition
for the worker, or
A
ICW
condition.
simple shirking interpretation
is
Modify the benchmark to allow the
as follows.
worker to shirk or not shirk. Once hired, but before productivity
is
revealed, the
worker has to decide whether to shirk or not shirk. Shirking brings private benefits
B but results in zero productivity and thus a layoff. Shirking is unobservable. Thus,
to prevent shirking, the condition above
Under the search
effort interpretation, the constraint that the
from being employed must be
constraint in a
must hold.
sufficient to justify search effort
dynamic model. Even
in
expected
utility
gain
would be the natural
our static model, a simple modification of
the benchmark leads to a constraint close to equation (11). Suppose that,
if
laid off,
the unemployed can, by exercising search effort, get another job in an alternative
sector
same
(home production, job abroad)
as equation (11),
with
w
at
wage w. Then, the
instead of w.
The
ICW constraint
is
the
basic implications, in particular
with respect to the contribution rate, are the same as those derived below.
The optimization problem
2.2
The
state solves the
ICW
same problem
as in the
benchmark, subject to the additional
constraint. So:
max {G(y*)U(b +
fi)
+
(1
- G(y*))U(w)}
subject to:
-G{y*)n
+ f V
Jy"
dG(y) -
(1
-
G(y*)) w
>
I
14
and (l-G(y*))(U(w)-U{b
The
+ (i)) > B
solution to this problem can be characterized as follows.
Unemployment
straint,
benefits,
/z,
can be no higher than allowed by the incentive con-
thus providing incomplete insurance:
U{b
_*
+ „) = U{w)1
The threshold
level of productivity, y*
.
9
Or
=
,
^
(
(12)
)
satisfies:
^_Mp>
reorganizing:
»
For any concave
i
utility,
r
,1.
U(w)-U(b + n),
n
the term in brackets
is
negative; the stronger the curva-
ture (the stronger the degree of absolute risk aversion), the
if
workers are risk averse, the optimal threshold
is
unemployed. The lower
more
negative. Thus,
lower than the efficient
Firms keep some workers although their productivity
alent of being
.„,,.
is
level.
lower than the wage equiv-
layoff rate serves as a partial substitute for
unemployment insurance.
The
level of
w
itself is
given by condition
(6),
holding with equality.
Implementation through payroll and layoff taxes
Replacing y* from (13) in the expression for the threshold decision of firms,
gives us the first relation
between / and
f- T = »+
(5)
r:
U(w)-U(b + ri
JTv)
or, equivalently:
/-t
=p+
(l-G(y*))U'(w)
15
Together with the budget constraint, this condition
yields:
If
B
is
the layoff tax rate, the more negative the payroll tax rate. In other words,
positive, the equilibrium has
is
the contribution rate, that
unemployment
/ >
fi
and r <
0.
The
higher B, the higher
the ratio of the layoff tax paid by the firm to the
is
benefit received
by the worker, must now exceed one. The reason
is
the need to decrease layoffs, a need coming from the limits on the unemployment
insurance that can be provided to the workers.
Proposition
We
summarize these
results in
2.
Proposition
2. In the presence
ity is lower than the
of limits on insurance, the threshold productiv-
wage equivalent of being unemployed
(y*
<
b):
The lower
incidence of unemployment partly compensates for the limits on insurance
unemployed. The allocation
employment
benefits (f
In other words,
it is
>
is
u.),
when
implemented through layoff taxes that exceed un-
and negative payroll taxes
to balance the budget.
implemented through a contribution rate greater than one.
2.3
Implications and discussion
•
Despite our appeal to either shirking or search effort as motivations for equation (11), there
is
a sense in which the results carry
more
generality under
the search interpretation. In the shirking interpretation, equation (11) was
derived under the implicit assumption that,
tivity
was equal to
zero.
shifts the distribution
nates H(.),
less
Our
is
the worker shirked, produc-
Under the more general assumption that shirking
from G(.) to H(.), where G(.) stochastically domi-
built
examples
than one. Under a search
the firm
•
we have
if
in
which the optimal contribution rate
effort interpretation
is
however, productivity in
unaffected by search effort, and thus the problem does not arise.
results in this extension
bear a close relation to the results obtained
in the "implicit contract literature" (in particular Baily (1974), Azariadis
(1975), Akerlof
and Miyazaki
(1980)).
16
That literature looked
risk averse workers.
at the optimal contract
between
risk neutral firms
and
Under the assumption that there were neither severance
payments nor unemployment
benefits,
one of the conclusions was that there
would be overdevelopment, that firms would
to the efficient outcome.
One
lay too few workers off relative
of the criticisms addressed to those papers
was
the question of why firms did not offer unemployment insurance or severance
payments. In the discussion here, the limits come from monitoring problems,
and the solution takes the form of a
But the
logic is very
much
Indeed, the connection
is
layoff tax rate
imposed by the
state.
the same.
even closer than
The
the choice of the threshold by firms.
looks. Recall our discussion of
it
results
above were derived under
the assumption that firms choose the threshold according to equation (5),
that they choose
it
ex post and do not
to workers at the time of hiring.
are
bound by that commitment,
In this case,
=
and t
0.
it is
We
feel
bound by any
earlier
can ask what happens
so that y*
is
if,
commitment
in fact, firms
given instead by equation
easy to check that the layoff tax rate
is
given by: /
(4).
=
pi
In other words, because firms voluntarily distort the destruction
margin, the state does not need to introduce any other distortion, and thus
can
•
still
With
set the contribution rate equal to one.
respect to variations in B,
unemployment
protection (defined as layoff taxes) are
sis is
now
purely normative, the same trade-off
model
of labor
market
institutions.
is
benefits
substitutes.
likely to
and employment
While our analy-
emerge
in a positive
To the extent that the unemployment
insurance system provides limited insurance (for any reason), there will be
a demand for high employment protection.
Continental Europe
is
An
interesting characteristic of
indeed the presence of such an inverse relation be-
tween the generosity of the unemployment insurance system and the degree
of
•
employment protection
Governments
in
many
(see for
example Boeri
[2002]).
countries are exploring ways of providing generous
insurance while making sure that the unemployed exert search effort and
accept employment (for example by requiring them to accept "reasonable
job offers"). In the context of our model, such reforms can be thought of as
17
decreasing B.
welfare.
The
As
one
direct
need to reduce
and an
such, they have both favorable direct
layoffs
better insurance.
is
below the
The
and
indirect effects
indirect one
is
on
the decreased
leading to better allocation
efficient level,
efficiency gain.
Shallow pockets
3
Our benchmark model embodied the assumption that
firms were risk neutral and
had deep pockets. These assumptions are surely too strong. Even
of aggregate risk, the owners of
diversified,
and thus are
many
in the absence
firms, especially small ones, are not fully
likely to act as
if
they were risk averse. And, even
if
entrepreneurs are risk neutral, information problems in financial markets are likely
to lead to restrictions
on the funds
and focus on the implications
3.1
The
I
+
A
available to firms.
We leave risk aversion
aside,
of limited funds.
generic constraint
simplest assumption to
f where /
>
is
make here
is
that each entrepreneur starts with assets
therefore the free cash flow available to the firm after
investment.
In this context,
we need
to extend the set of tools available to the state. Until
now, job subsidies or taxes were redundant.
the case. So
we
taxes /, and job creation taxes
The new
It is
no longer obvious that
give the state four instruments, benefits
t
(job subsidies
if t is
constraint on the optimization problem
is
(i,
this
is
payroll taxes r, layoff
negative).
therefore:
f<f-t
(16)
Layoff taxes must be less than or equal to free cash flow minus job taxes (equivalently: plus
job subsidies).
We
call it
the "shallow pockets" constraint.
This specification raises the issue of the potential role of outside, "deep pockets"
investors in alleviating the constraint.
We
shall return to this point below.
18
3.2
The optimization problem
With the introduction
of job creation taxes, the government budget constraint
becomes:
GW(/-/i) + [l-G(w?)]T + t>0.
Combining
this equation
with the shallow pocket constraint
changed) threshold condition
/,
and
(5) gives
(16),
and the (un-
an equation which no longer depends on
t,
t:
G(y*)n-[1-G(y*)](y*- W )<f
The optimization problem
of the state
is
max {G (y*) U(b + »)
w,/j.,y~
(17)
given therefore by:
+ [l-G (y*)} U (w)}
subject to:
G(y*)n-[l-G(y*)]{y*-w)<f
-G (if)/i+
and
/ ydG(y)-[l-G(y*)]w>I
Jy"
where the second constraint
the introduction of
Prom
t,
is
the consolidated budget constraint, which, despite
turns out to be the same as before,
equation
(6).
the first-order conditions, the solution can be characterized as follows:
Workers are
still fully
insured:
w = b+n
and the threshold
=
lrj
=
(18)
level is given by:
y*
where
i.e.
g(y*)y*/(l
—
I
7
U
\
+ 9J
TV
(19)
\T)
G(y*)) denotes the elasticity of employment with respect
to the threshold (or, equivalently, with respect to the payroll tax, or with respect
19
to (minus) the layoff tax),
ated with the
constraint
the efficient
and the second constraints
first
>
binding, v
is
and v and 6 are the non-negative shadow prices
then y*
0,
b:
respectively. Provided that the first
The optimal
threshold
is
higher than
level.
Implementation through taxes
straint
>
associ-
is
and the threshold equation imply that /
we
The government budget
straightforward:
is
smaller than
=
equal to zero, f
\x.
The job
con-
creation
The contribution
rate
tax
t is irrelevant,
less
than one, and the difference between unemployment benefits and layoff taxes
is
made up by a
To understand
so
if
set
it
f-
is
positive payroll tax rate.
these results, note
first
that the shallow pocket constraint does
not affect the ability of the state to fully insure workers. To see why, suppose
for
example that
w >
b
+
Consider a decrease in
fi.
w
and an increase
in
r by
the same unit amount. This affects neither the threshold condition nor the firm's
profit.
Then, from the government budget constraint, the unemployment benefit
can be increased by [(1— G(y*))/G(y*)] At. Together, these changes imply a change
in utility of [-(1
will decrease
Note
w
- G{y*))U'(w) +
and increase
fi
(1
until
-
G{y*))U'(b
+ /i)]Ar >
still
plays no useful role here.
why, consider the introduction of job subsidies in amount At
(16), this allows the state to increase layoff taxes
compensate
Thus, the state
workers are fully insured.
also that the job creation tax or subsidy
layoff taxes does not
0.
<
0.
To
From equation
by —At. But the increase
for the increase in
see
in
job subsidies, and to satisfy
the government budget constraint, the state must increase payroll taxes by —At.
The
effect of similar increases in layoff
and payroll taxes
leaves the threshold
chosen by firms unchanged, and thus has no effect on the allocation. In other
words, the state has no
way
to
move cash around
so as to soften the shallow
pocket constraint.
Given
full
insurance, and the limit on layoff taxes, the state must therefore finance
benefits partly
from
layoff taxes,
shallow pocket constraint
We
summarize our
is
and partly from payroll
taxes. This
binding, the contribution rate
is less
is
why,
if
the
than one.
results in the following proposition:
Proposition 3 In the presence of shallow pockets, workers are
still
fully insured
20
— b+
(w
Layoff taxes are however
fj,).
less
than unemployment benefits, leading to
a contribution rate less than one, and a threshold productivity level higher than
the wage equivalent of being unemployed (y*
3.3
A
>
b).
Multi-activity firms
concern often expressed about layoff taxes (more generally, about payments
imposed on firms
in
bad times)
is
that, even
if
the firm can pay the taxes,
it
can
only do so at the expense of other activities in the firm. For example, in order to
pay the
layoff tax associated with the closing
to close otherwise healthy activity
In the
extend
i
model we have
it
= 1, 2.
as follows.
The
down
of activity
may have
a firm
2,
1.
just presented, firms are one-activity (one-job) firms.
We assume
firms to be
composed of two
joint distribution of productivity in the
•
With
probability a, yi
•
With
probability 1
-
is
two jobs
drawn from distribution
a, y\
is
drawn from
though, of course, their productivity
may be
G(.),
as follows:
is
and
distribution G(.),
For convenience, we shall refer to firms for which y^
low),
=
We
activities (two jobs),
j/2
=
and
2/i
j/2
=
0.
y\ as "strong firms" (al-
and to firms
for
which
2/2
=
as "frail firms."
All firms have initial assets 2(1
On
+ /),
sink investment 27, and hire two workers.
the government side, the state levies payroll tax t per job, layoff taxes /i in
case of a single layoff, 2/2 in case of two layoffs, and pays
The assumption
is
benefits are the
of the firm that laid
that there
is
not restrictive.
in a position to fully insure workers,
unemployment
is
them
no gain
same argument
benefits
\x.
that unemployment benefits and payroll taxes are not conditional
on the number of jobs preserved
the state
unemployment
off,
same
for all
and given by
By the same argument
and
so
it
does. This implies that
unemployed, irrespective of the state
\i
= w — b.
Similarly,
it
can be shown
in allowing for different payroll taxes. Finally,
as before,
it
as before,
and by the
can be shown that the job creation tax or subsidy
plays no useful role here, and so, without loss of generality,
we
set it equal to zero.
21
The problem of the firms
Ex-post strong firms face the choice of laying
the workers, their profit
both workers
is
off,
is
4 2/2
by — 2/2
given by yi
their profit is given
.
If
—w — t).
2(y\
they keep
If
they lay
Thus, their threshold productivity
given by:
y
Ex-post
worker
frail
off,
their profit
=
*
(«,
+ r) - h
(20)
firms face the choice of laying off one or two workers. If they lay one
their profit
is
is
given by y\
— (w + t) —
f\. If
= w + T)-(2f2 -f1
(
This expression embodies the concern described
tax /1 encourages layoffs by
on the otherwise healthy
priori, there
strong or
frail
frail firms. It creates
appears to be
now two
—that lay two workers
frail
is
given by:
(21)
)
earlier:
off,
An
increase in the layoff
a "spillage" or "snowball effect"
activity.
constraints on layoff taxes. First, firms
have to be able to pay layoff taxes:
off,
2/2
Second, those
they lay both workers
given by —2/2. Thus, their threshold productivity
y**
A
two workers.
off zero or
— 2(io + r) =
<
2/.
(22)
firms that lay only one worker off
must
also
be able to pay
— (w + r)]. As the
[j/i
state does not observe j/i, it cannot levy more than 2/4- [y** — (w + t)], so
/1 < 2/4 [y** - (w + t)}. Using condition (21), this condition reduces to 2/2 < 2/,
the layoff tax. Their profit on the remaining activity
so
we only need
is
to impose condition (22).
Tie optimization problem
Using the result (which
still
holds here) that workers will be fully insured, the
optimization problem can then be written
max
as:
U(b
4
m)
22
subject to two conditions:
The
first is
obtained by combining the government budget constraint, the
insurance condition (w
= b + (i),
conditions (20) and (21) for the two thresholds,
and the shallow pocket condition
2M
The second
-
-
2a(l
(22):
-
G(y*))(y*
b)
-
(1
-
a)(l
-
G(y**))(y**
-b)<
surance condition and the two threshold conditions, can be written
2a
+ (1 - a) f (y - b)dG(y) >
Jy"
{y- b)dG{y)
Jy"
Prom
2/
(23)
the consolidated budget constraint which, using again the
is
full
27
full in-
as:
+ 2M
(24)
the first-order conditions, the two thresholds are given by:
v
=y
v
where, as
and v and
earlier,
77
is
the elasticity of
6 are the two non-negative
+ ej
\r]
employment with respect to the threshold
shadow
prices associated with the first
and
the second constraints respectively.
Implementation through taxes
olds, together
is
straightforward.
The
equality of the two thresh-
with the two threshold conditions, implies that /1
firm has shallow pockets so v
unemployment
benefits
the contribution rate
is
>
0, /1
= ji = /
and
layoff taxes
less
than one.
Proposition 4 Limited
is
We
.
Whatever
=
/2,
and
difference exists
made up through
if
the
between
positive payroll taxes;
can summarize our results as
follows:
assets in a multi-activity firm raise the possibility of
"snowball effects". In that case, the state in general does not want to collect the
full collectable
amount
in case of partial layoffs. In the
where a two-job firm has assets 2/
layoff,
and 2/
for
two
layoffs (if
f
example we presented,
after investment, the state levies tax
is
/ for one
not too large).
23
The
however that the
result
and due
layoff tax schedule is linear is too strong,
to the stochastic structure of our example. In our example, /i affects only the
decision of "frail" firms to lay one or two workers
if
By
off.
contrast
we know
that,
the relevant choice were between zero and one layoff as in the previous section,
maximum
then
Unsurprisingly,
layoff taxes
if
we add
and y2
G(-),
j/i
whose relevant
with probability a and
trade-off
that for the complementary fraction 1
—
2/2
from distribution H(y). (All firms are ex-ante
= 1, h = h = /,
3.4
and
for
=
0,
h
drawn
(= 2/2 )
J/i
identical.)
=
> f2 To
see this,
-
as above (y\
with probability
of the firms,
fi).
between zero and one
is
structure: /i
=
<
2/ whenever 2/
of the firms have y\ and y 2
suppose that a fraction
from
firms
=
(/i
we obtain a concave tax
layoff to our example,
=
would be optimal
=
1
and y2
is
Then we know
2/. In general,
A
> f2
drawn
- a), and
1
drawn
that
if
.
Implications and discussion
Our benchmark looked
at the case in which firms
and concluded that /
layoff tax
=
/x.
By
had enough
assets to
pay the
we
contrast, the shallow pocket firm
looked at in this section had limited assets and could not pay more than /, leading
to a lower contribution rate. This raises the question of
We
The
how / is
itself
determined.
have explored this question in two ways.
first is
that policy
to assume, in contrast to the maintained assumption in this paper,
is
set after rather
than before firms
the state cannot commit and sets
(t, /,
invest.
Suppose, for example, that
n) after firms
have invested and hired
workers, but before they learn the productivity of the match. In this case, firms
will obviously
layoff, so
/=
choose to be "judgment proof",
0.
The optimal threshold
is
i.e.
to have no assets
then given by: y*
—
6/(1
—
left in
case of
(1/t?)).
(This
condition directly follows from equation (19): Under ex-post policy setting, the
entry condition becomes irrelevant to the decision problem of the state, so 8
and
=
0,
this equation obtains.)
The second
finance.
is
to
assume that the firm has limited assets but has access to outside
The answer, not
surprisingly,
firm and the investors. Suppose
investors,
first
depends then on the relation between the
that there are deep-pocket, risk-neutral,
but that these investors are uninformed: Like the state, they cannot
24
observe productivity directly, just whether workers axe employed or unemployed.
Then,
it is
clear that allowing for the presence of such investors
we
to the results
do by
itself.
just derived.
Whatever the investors
For example, in the one-activity case,
investors to the firm be equal to F,
be
D
if
is
this is exactly the
choice of
t,
/, t
could not use
(for
t
if it
x
to the investors
does not. Then, the investors' break
given by:
G{y*)D 1 +
But
D
difference
the funds advanced by the
and the payments of the firm
production takes place, and
even condition
let
makes no
do, the state could already
- G(y*))D >
(1
same condition
a given value of
fj.)
F
as the condition faced
earlier.
And,
for the
by the
state in its
same reason the
state
to relax the shallow pocket constraint, nor can the presence of
investors relax this constraint.
Things are clearly different
if
investors are informed,
of productivity y. In this case, they can ask
give
is
more
to the firm in
clear that the firm
bad
and
more
states. Indeed, in the
i.e.
can assess the realization
good
of the firm in
states,
and
absence of other constraints,
it
investors together are just like the deep-pocket firm of
the benchmark. In that case / can be set equal to
fi,
independent of the
free
cash
flow of the entrepreneur.
Things become more interesting
and
so can ask for
we assume
that investors are indeed informed
payments from the firm contingent on
trepreneur enjoys a rent
investors can get at
if
R >
y,
in case of continuation (so
but that the en-
if
y
is
total value,
most y — R). This assumption implies the standard corporate
finance feature that the entrepreneur
more eager than investors to continue
is
since he receives a private benefit even
when
the firm no longer makes profits.
Setting
up the model and characterizing the solution would take us too
and we
refer the reader to
Blanchard and Tirole (2004). In that extension, we find
that the threshold level of productivity
is
higher than the efficient level (y*
leading to more layoffs than in the benchmark. But
to set a unit contribution rate,
in this case,
far afield,
and workers are
it is still
fully insured
>
b),
optimal for the state
/
=
/x
= w — b.
Thus,
shallow pockets lead to inefficiently high layoffs, but do not justify
a lower contribution rate.
The reason
for these results is
that low entrepreneur's
25
solvency
is
the culprit and the state, constrained to balance the budget, can do
nothing to boost this solvency.
Ex—post wage
4
negotiation
Our benchmark embodied the assumption that wages were
set ex-ante,
i.e.
at the
time of hiring. This had the implication that, by offering unemployment insurance
to risk averse workers, a firm could not only offer a lower wage, but actually lower
its
unemployment
To some
firm offered the option of joining the layoff tax
benefits system,
extent however, there
this is the case, a firm
in
A
expected labor costs.
would have voluntarily joined.
is
always some room
which has to pay a
for
layoff tax
ex-post bargaining.
provision of
benefits
if
laid off
unemployment
is
in a stronger position.
When
lays a worker off
if it
a weaker bargaining position vis a vis that worker; a worker
unemployment
cum
The
who
is
will receive
layoff tax
and the
benefits both lead to higher, not lower, wages,
and
thus to increase labor costs.
In this section,
we
therefore modify our earlier assumption about
wage
setting,
assume ex-post wage bargaining instead, and characterize the shape of optimal
labor market institutions under ex-post wage bargaining.
A
4.1
The
formalization of
wage bargaining
on ex-post
following formalization captures the effects of benefits and taxes
wage determination
Assume wage
in a simple way:
setting
now
takes place after productivity
outcome of a two-stage game. In stage
firm.
The
wage
is
1,
probability
1
—
it
down.
maximize
If
by the worker with probability
is
the
it
/?,
turns
or
it
down, the
by the firm with
/3.
Under the assumption that the firm chooses the threshold
as to
and
realized,
the worker makes a wage offer to the
firm can either accept the offer or turn
set in stage 2, either
is
profit ex-post, in stage 2, the highest
and therefore the wage
offered
by the worker,
is
level of productivity so
wage the firm
equal to y
+f—
r.
will accept,
The
highest
26
wage the worker
b
+
fi.
and therefore the wage
will accept,
Thus, the expected wage in stage 2
This implies that, in stage
1,
the (risk neutral) firm,
an
i.e.
=
w(y)
The higher the
is
offered
given by 0(y
the worker will
make the
by the
firm,
is
equal to
+ f - t) + (1 - /?)(& + /x).
highest offer acceptable by
offer of
+ f-r) + (l-P)(b +
(3(y
layoff tax rate, or the higher
i)
(25)
f
unemployment
benefits, the higher
the wage.
The threshold value
for productivity, y*
=
y*
,
is
w(y*)
given by:
+t-f
and rearranging:
Equivalently, using equation (25)
y*
= b + fi + r-f
Just as in the benchmark, the combination of /
efficient threshold, y*
=
But, as
b.
we
(26)
=
//,
r
=
would deliver the
shall see, other considerations are
now
relevant.
Expression (26) allows us to rewrite the wage schedule
w(y)
The wage paid
{b
+ ti)+0{y-y*)
(27)
to the marginal worker, the worker in a job with productivity equal
to the threshold level,
plus
=
as:
unemployment
is
equal to
benefits.
(6
+ /z),
the wage equivalent of being unemployed
The wage then
increases with
(3
times the difference
between productivity and threshold productivity.
4.2
The
The optimization problem
state solves the
constraint that the
same problem
wage
is
as in the
benchmark, subject to the additional
no longer a decision variable, but
is
instead given
by
equation (27):
27
max
G(y*) U{b
+ fi) + f
U{w(y)) dG(y)
subject to:
-G(y*)fi+ f (y-w(y))dG(y)>I
Jy"
and
The
w(y)
= b + /i + (5{y - y*)
solution can be characterized as follows:
The threshold
level of
V
where E[U'\y >
marginal
y*}
utility if
=
productivity
=b+ 0(1
(J
1
,
is
implicitly defined by:
~
E[U'\y>y*}
-G(y*))
W)
EU r
[
U'{w{y))dG(y))/{\
employed, and
E
U'
=
marginal
ity,
and
level.
is
strictly positive,
utility if
so y*
is
The more
employed
greater than
,
the
One way
of getting
G(y*)(b
more
+ /J.
+ ri+
I
((b
+
U'{w(y)) dG(y)
then the expected
than the unconditional expected marginal
The
is
utility.
util-
layoff rate exceeds the production efficient
workers in bargaining,
the higher the layoff rate.
unemployment
benefits,
Vfg =
|i,
is
then determined by
I-
intuition for the optimal threshold
constraints,
Jy'
left
level,
feasible level of
and the second
fJ.)
strictly risk averse,
constraint above, the condition that
first
The
b.
+
the expected value of
is
risk averse the workers, or the stronger the
the higher the threshold
Given y* the
and workers
is less
G{y*))
G(y*)U'(b
the unconditional expected value of marginal
So long as
-
()
]
is
to combine the first
and reorganize to read:
i)
f
+ P(y-y*))dG(y)<G(y*)b+ f
Jy'
side gives the value of total workers'
y dG(y)
-
I
income (the sum of wages, reservation
28
wages, and benefits) in the economy.
in the
The
economy. The two are the same, as
Suppose
do not
for the
moment
free entry implies zero profit
Then, changes
in y*
change the shape of
the income profile without affecting the total workers' income.
more workers
receive
the same, but the income schedule
point of insurance
The assumption
from y*
this implies that, as
why
and
increases,
and
just b
so
p,
is
greater than
6,
4.3
is flatter.
where
it
=
b,
increase in y*
income remains
Indeed, the best value of y* from the
workers receive the same income.
all
is
however clearly
decreases risk, at least a small increase in y*
=
1 for
example, then total income
increasing in the degree of concavity of
It is
increasing in
desirable;
This implies that the optimal value of y*
zero.
than one.
less
It is
is
But, as y* increases, the efficiency loss
b.
income decreases. For y*
but
An
overall workers'
small changes in y* do not affect total income;
must be equal to
the utility function.
/3,
(fj,
The
b).
the optimal y* exceeds
total
is
The higher
1,
+
that changes in y* do not affect total income
incorrect. Starting
this explains
=
y*
is
income.
that changes in y* do not affect total income, and so
affect total workers' income.
implies that
income
right side gives the value of total
the share of the surplus going to workers:
/3,
the steeper the wage schedule, the larger the
Implementation through payroll and
demand
for insurance.
layoff taxes
Replacing y* from (28) in the expression for the threshold decision of firms,
gives us the first relation
between / and
f-T-p-pa
The other
relation
is
r:
E[U'\y>y*\
(l-G(y*))
j^—]
[i
g{r)
given, as before,
is
now
negative,
/
<
fi
Together with the government budget constraint, this implies /
is
higher than the efficient
from
its
benchmark
The reason
level.
value,
This
namely
(29)
by the budget constraint, equation
the second term on the right side of equation (29)
contribution rate below one.
is
(26),
is
clear
(3).
—r <
As
/z.
and so a
from above: The optimal threshold
achieved by lowering the contribution rate
unity.
By
implication, payroll taxes
positive, in order to finance the shortfall of the
must be
unemployment insurance system.
29
Note that
=
for
0, i.e. if
workers have no bargaining power, then
same characterization as in the benchmark: /
As
it
(3
becomes
positive,
'
=
and the wage schedule
fi
is
and
now
=w—
pL
we
obtain the
b.
increasing in productivity,
can be shown that the equations above imply:
#
<
is,
0.
d/3
d/3
That
d
±
<
both the unemployment benefit and the layoff tax decrease as the work-
more bargaining power, and the
ers acquire
tax
layoff
falls faster,
leading to a
decreasing contribution rate.
We
summarize our
Proposition
5.
marginal worker
results as follows:
When wages
is
the
same
are set through ex-post bargaining, utility for the
as for the unemployed workers,
and workers with
higher productivity receive a higher wage. These outcomes are independent of the
state policy choices.
The remaining
choice for the state
is
that of y*
optimal to choose a threshold higher than the
efficient level: (y*
decreases the uncertainty faced by workers at
some
is in
4.4
>
It is
.
then
This choice
b).
cost in efficiency. This choice
turn implemented by a contribution rate lower than unity.
Implications and discussion
Under pure ex-post wage bargaining, the scope
provide insurance to workers
is
extremely limited:
benefits does not change the slope of the
an amount equal to unemployment
freedom
is
for
An
unemployment
increase in
unemployment
wage schedule, increasing
Put
benefits.
differently, the
benefits to
all
wages by
only degree of
the location of the kink y* in the worker's income schedule.
Indeed, in our framework, given the threshold level of productivity, the level of
unemployment
benefits
entry condition
—which implies that workers' income, the sum of wages, reserva-
tion wages,
is
entirely determined
and unemployment
benefits,
by the wage schedule and the
must be equal to
In that dimension however, our framework
is
too extreme.
free
total output.
The
static, one-period,
nature of the model implies a fixed unemployment duration. In dynamic models,
30
such as Mortensen and Pissarides (1994) for example, the state
free to
is
choose
the level of unemployment benefits; but the higher the level of unemployment
benefits, the longer the equilibrium
result with the
an increase
same
flavor obtains. In the Pissarides (2000)
unemployment
in
unemployment duration. And an
an increase
benefits leads to
exactly such that the "pain of unemployment"
i.e.
,
model
in
irrelevance
for
example,
expected duration
the difference in the expected
value of being employed or unemployed, remains constant.
Heterogeneity
5
We
have assumed so far that
reality,
more
(or,
they
all
they clearly are not. Firms
face,
workers and
differ in
firms are ex-ante identical. In
generally, the distribution of productivity
and
in their initial assets.
New
productivity:
Workers
and
relative
demand
shocks)
also differ in the distribution of
entrants have distributions characterized by higher uncertainty
than workers with more labor market
We
all
the distribution of productivity shocks
seniority,
and so on.
study in this section the implications of heterogeneity, both on the firm and
on the worker
distributions,
5.1
side,
both observed and unobserved.
focus on differences in
but discuss some other dimensions of heterogeneity
later.
Heterogeneity of firms
Suppose there are two types of
productivity distributions.
The
and "weak" which
firms, "strong"
,
productivity of "strong firms"
mulative distribution Gh{-) and
The
We
is
differ in their
drawn from cu-
that of "weak firms" from distribution Gl(-).
distribution function of strong firms stochastically dominates that of
firms: for all y in (0, 1),
Gn(y) < Gl{v)- The
fraction of strong firms
is
weak
equal to
P-
We
is
start with the
unable to
tell
assumption that
this heterogeneity is
the two types of firms apart.
that the state sets a uniform policy
strong and weak firms
may
(t, /, p);
We
we
unobserved, so the state
also start with the assumption
shall look later at
menus
in
which
self select.
31
Note that given the distribution assumptions and uniform taxation, strong firms
have higher expected profits than small firms. Thus, at the creation margin, the
free entry condition is relevant for
lay workers
off,
weak
firms only.
so the destruction margin
is
By
contrast,
both types
may
relevant for both types of firms.
This in turn implies that we can no longer merge the free-entry condition and the
government budget balance constraint: The former applies to a subset of firms
(the
weak
firms)
and the
latter to the
whole set of
firms.
We
take the more "pedestrian" route of optimizing with respect to
We
therefore have to
all
the variables.
assume that the state maximizes the welfare of workers. Allowing the state to
also put
some weight on the
would not
alter the results.
max
positive rents earned
The
[p(l
problem
is
given by:
+ {l-p)G L {y*)]U(b + n)
\pG H (v*)
+
by the owners of strong firms
state's optimization
- G H {y*)) +
subject to the free entry condition for
-G L {y*)f + /
(1
-
p){l
- G L {y*))\ U(w)
weak firms
(y
- w - T)dG L (y) >
I
the government budget constraint
+ (l-p)GL (y*)](n-f)
+[p(l-GH (y*)) + (l-p)(l-GL (y*))]T >
-[pGH (y*)
and the threshold productivity condition, which
is
the
same
for
weak and strong
firms:
y*
The
=w + t- f
solution can then be characterized as follows:
•
The
•
The threshold
state fully insures workers:
w = b + \x.
level of productivity is
given by:
32
y
*^
b
P(G L (y*)-G H (y*))
,
(P9H(y*)
By
p
the definition of
=
0,
ployment
is
weak and strong
the threshold level
This solution
is
in turn
benefits, so
+ (i-p)gL<y*))
firms, Gl(j/*)
higher than the efficient
is
implemented by choosing
> Gh(v*)-
So, unless
level.
layoff taxes lower
through a contribution rate lower than
unity.
than unem-
The
difference
financed through payroll taxes.
The
intuition for
types of firms
firms.
By
why
may
the contribution rate
lay workers off
contrast, the creation
than one
is less
as follows:
Both
and so the destruction margin applies to
margin corresponds to the weak firms
state can then improve workers' welfare
strong to weak firms. Because the state
by allowing
is
for
The
some cross-subsidy from
Weak
firms lay workers off
more from a contribution
so benefit
only.
all
unable to assess the firms' strength, the
cross-subsidy operates through the contribution rate:
more than strong firms and
is
rate smaller than
unity.
Can the
state do better
by
offering
the state offers an option (tl,
menus and
targeted at
/x,)
strong firms, rather than the single option
(thresholds, payroll
and
optimization problem
is
layoff taxes are
identical to the
letting firms self select?
weak
(r, /).
Suppose
firms and another (th,Jh) at
With obvious notation change
now indexed by
the type of firm), the
problem above, except that the
last con-
straint,
y*
is
-
[w
+ t - f] =
replaced by the constraints:
L - [w
+ rL - fL =
H -
+ th - fH =
y*
y*
[w
]
]
and the incentive compatibility constraint that the strong firms do not want to
masquerade
as
weak ones
is
given by:
33
-G H (vh)
fn+ [ (v-w-t„) dG H (y)
'Vh
,
> -G H
It is useful at this
(y*
L)
h+
(y-w-rL dG H (y)
)
[
point to define the net contribution rate as the ratio of the layoff
tax minus the payroll tax to unemployment benefits,
that, so long as the net contribution rate
efficient:
What
matters here
is
is
(fc
—
Ti)/fj,i,
i
=
H,L. Note
equal to one, the layoff decision
not the layoff tax
itself,
is
but the difference between
the layoff tax and the payroll tax.
The
solution can then be characterized as follows:
w = b+
•
The
•
Strong firms face a net contribution rate equal to one, and so choose the
state
still fully
insures workers:
fi.
efficient threshold:
H—
y*
Weak firms
•
and
b
face a net contribution rate
Jh-th = H
below one, and so choose a threshold
higher than the efficient level:
In short, while offering a
menu improves
characteristics of the uniform policy,
efficiency,
the solution carries the main
namely cross-subsidization of weak firms by
strong firms, with a contribution rate for weak firms below one.
If
heterogeneity
is
observable,
i.e. if
the state
is
able to
tell
weak and strong firms
apart, the state can do even better. Characterizing the optimal policy
forward:
by
It is still
optimal to subsidize weak firms. This can
offering a job creation subsidy to the
tion rate equal to
1 for
from strong to weak
weak
is
straight-
now be done however
firms, while setting the net contribu-
both types of firms. This achieves the desired redistribution
firms, while avoiding distortions at the destruction
margin
(Note that both layoff and payroll taxes must be higher than in the benchmark,
as the extra revenue
is
needed to finance job creation subsidies to weak
firms.
The
34
difference between the layoff tax
unemployment
We
and the payroll tax remains however equal to
no distortion
benefits, so there is
at the destruction margin).
have focused above on heterogeneity in productivity distributions. While we
shall not present results here,
we have
also explored heterogeneity in assets, in-
cluding the model of corporate finance described informally in Section 3 (with
informed investors, and some non pledgeable income.) There, the same type of
sults emerges, for the
assets,
have smaller
same
reason.
profits,
The weaker
firms,
i.e.
those firms with the least
and thus are the relevant firms
at the creation margin.
As, in order to satisfy investors, weaker firms also lay workers off
more from a decrease
firms, they benefit
Thus,
is
if
heterogeneity
is
in the layoff tax
unobservable and the state
re-
relies
more than other
than stronger firms.
on uniform taxation,
it
optimal for the state to decrease the contribution rate below one, transferring
profits
We
from stronger to weaker firms, and favoring job creation.
can summarize our results as follows:
Proposition
6.
Suppose that there are two types of firms: "strong" or "weak".
Strong firms have productivity distribution Gh(-), weak firms
G H {y)
G l(.)
,
andG/,(y)
>
for ally in (0,1).
If this heterogeneity
the optimal pohcy
higher than the
is
is
unobserved, and
if
the state relies on a uniform policy, then
to fully insure workers (w
efficient level (y*
>
b),
= b + fi),
and implement
it
choose a threshold level
through a contribution
rate less than one.
If the state offers
a
menu
and has the following
instead, then the optimal
menu
separates the firms
properties: Workers are fully insured. Strong firms face a
net contribution rate of unity, and choose the
efficient threshold.
Weak
firms face
a net contribution rate below one, and the threshold exceeds the efficient
The underlying mechanism remains
level.
the same, cross-subsidization of weak firms
through the use of a lower contribution rate.
If heterogeneity is
creation subsidy to
implement
it
observed by the state, then the optimal policy
weak
is
to offer a job
firms, choose the efficient threshold for productivity,
and
through a unit net contribution rate for both types of firms.
35
Heterogeneity of workers
5.2
A
similar set of issues arises on the workers' side.
particular,
some
more uncertain and thus more
are
To think about the
issue,
we
up a case very
set
Not
all
likely to
workers are
be
In
alike.
laid off.
similar to that of firms.
We
assume there are two types of workers, "high- ability" and "low-ability" workers.
High- ability workers have a productivity distribution given by Gh(-), low- ability
workers a distribution given by Gl(-), with Gl(v)
fraction of workers with high ability
We
is
assume that firms know the workers'
earlier case of heterogeneity in firms,
does not know the workers'
We
equal to
abilities,
we
and that
y € (0,1). The
for
p.
abilities.
start
> Gn(y)
Proceeding in parallel with the
by assuming both that the state
it
chooses a uniform policy
r, /,
fi.
can simplify the set-up of the optimization problem, by noting that work-
ers of each type will
more valuable to
be
fully insured,
firms, they will
and
that, because high-ability workers are
be paid more, both when employed and when
unemployed.
Suppose therefore that low-ability workers receive
unemployed, and are
receive to +
A
where
fully insured, so
A when employed,
and
fi
w =
b
w when
+ p.
\i
when
High-ability workers will then
+ A when unemployed (so w + A = b+p + A),
the additional expected profit brought about to the firm by a high-
is
A
ability worker.
Noting that
productivity
the same for both types of workers,
A=
employed, and
is
[G L (y*)
- GH
(y*)]
does not affect the layoff decision, so the threshold
/
+
/
[y
-
(b
it
+ p) -
follows that
r]
[dG H
(y)
A
is
- dG L
given by:
(y)]
Jy'
Payment
of
A can be achieved through higher wages when employed and severance
payments from the firm to the high-ability workers when
laid-off. Alternatively, it
can be achieved by wage-indexed unemployment benefits, so a worker
w+A
receives
p.
+A
is
paid
(and the firm pays correspondingly higher layoff taxes when
laying a high-ability worker
With
who
off.)
this characterization of wage setting,
and assuming that the state maximizes
36
a utilitarian social welfare function, the optimal policy
is
the solution
to:
max {(1- p)U(b + (j,)+pU{b + n+ A)}
tJ,h,v"
subject to the free entry condition
-G L (y')f+ [
Jy'
[y-(b + ri-T}dG L (y)>I
and the government budget constraint
[(1
-
p)
where
The
•
G L (y*) + P G H
A
(y*)] (J
- M)+[(l - p)
[1
- GL
(y*)]
+p[l-GH (y*)]] r >
and y* have been defined above.
solution has the following form:
If
the proportion of low-ability workers
for productivity
is
given by:
pO--
„-_,,
[(i
-
high enough, then the threshold
is
p)EW) - G H (y*)}
p)9l{v*)
+ pg H
{y*)) [(i
+ b)- u'{n + b + A)]
p)U'(h + b) + P U'(p + b + A)]
[U'jii
-
G L (y*) - G H (y*)
is
positive,
and so
So the fraction on the fight
is
positive,
and the optimal threshold
Note that
than the
U'(p,
+ b) -
U'(n +
is
b
+ A).
higher
efficient level.
This solution
unity,
is
is
in turn
implemented by using a contribution rate below
with the rest of unemployment benefits being financed by payroll
taxes.
•
If
however, the fraction of low-ability workers
optimal to not
facilitate their employability.
and they receive unemployment
productivity
is
benefit
is
No
small enough, then
job
is
created for
it
is
them
for sure. In this case, threshold
given by:
y*
This solution
\i
is
=
b
implemented by relying on a gross contribution rate greater
37
>
than one: (f/p)
The
The
1;
payroll tax rate
and a net contribution rate equal
is
by r
in turn given
intuition for these results
is
as follows.
=
[(1
When
—
to one:
/ — r
=
p.
p)/p] p-
both types of workers are em-
ployed, the use of a contribution rate below one leads to a transfer from high-ability
to low-ability workers,
and therefore reduces
ciency. If the proportion of low-ability workers
is
very low,
efits
cost in
effi-
more
efficient to
efficient
separations
it is
have them not work, and then to choose tax rates so as to have
for high-ability workers.
some
inequality, but at
Because low-ability workers receive unemployment ben-
but no corresponding layoff taxes are collected, the solution requires having
both a positive payroll tax and a correspondingly higher
on high-ability
layoff tax
workers. This increases revenues while maintaining a net contribution rate equal
to one (This result
is
related to the result in
Cahuc and
Jolivet (2003)
where the
need to finance a public good also leads to higher layoff and payroll tax
Note that the
Weak
logic of the results
workers (firms) are more
under firm and worker heterogeneity
likely to
be
laid off (to lay off),
internalization of the externality of the layoff on the
UI fund
rates.)
is
similar:
and an incomplete
benefits the creation
margin.
What
to
the state can offer menus and firms then self-select?
if
show that the
state then offers
two menus, one aimed
It is
straightforward
announce
at firms that
they have hired a high-ability workers, one aimed at firms that announce they
have hired a low-ability worker. The
to one.
The second menu has a
workers are
fully insured.
first
menu
has a net contribution rate equal
net contribution rate below one.
Both types of
Thus, just as the uniform case, heterogeneity leads to
lower layoff taxes, but in this case only for low-ability workers.
What
if
differences
between workers are observable?
high-ability from low-ability workers
disabled
—then the optimal policy
—for example
is
When
if
The
tell
apart
workers are in bad health or
to offer a job creation subsidy (or, equiva-
lent^, uniformly lower payroll and layoff taxes) to firms
worker.
the state can
if
they hire a low-ability
net contribution rate can then be set equal to one for both types, and
the destruction margin
is
undistorted for both types. In general,
when
differences
are only partly observable, the solution combines job creation subsidies
and a net
38
contribution rate below one.
We
summarize our
Proposition
7.
results in the following proposition:
Suppose that there are two types of workers: "high- ability"
or "low-ability". High-ability workers have productivity distribution Gh{-), lowability workers Gl(-),
and Gl(v) > Gh{v)
If this heterogeneity is unobserved
the optimal policy
is
and the state
to fully insure workers (w
higher than the efficient level (y*
rate less than one.
for all y in (0, 1).
The lower
>
b),
relies
on a uniform
= b + fi),
and implement
policy, then
choose a threshold level
it
through a contribution
layoff tax ieads in effect to a transfer
from high-
ability workers to low-ability workers. If the proportion of low-ability workers
is
small enough, then
it is
optimal to leave them unemployed, and use a unit
contribution rate for the remaimng, high-ability workers.
If the state offers a
menu
instead, then the optimal
menu
separates workers and
has the following properties: Workers are fully insured. Firms hiring high-ability
workers face a net contribution rate of unity, and choose the
efficient threshold.
Firms hiring low-ability workers face a net contribution rate below one, and the
threshold exceeds the efficient
level.
The underlying mechanism remains the same,
cross-subsidization of low-ability workers through the use of a lower contribution
rate.
If heterogeneity
is
observed by the state, then the optimal policy
job creation subsidy to low-ability workers, and choose an
productivity,
it
to offer a
threshold for
through a unit contribution rate.
Conclusion
6
We
and implement
efficient
is
see our analysis as suggesting a few general principles:
The
use of layoff taxes
employment
transfers
same
benefits.
is
the natural counterpart to the state provision of un-
The second
requires the
from firms to workers, can be seen
principle. In that sense,
tion are basic
components
first.
Severance payments, direct
as a crude
way
of implementing the
unemployment insurance and employment protec-
of the optimal set of labor
market
institutions. In the
39
benchmark, they allow the state to achieve both
insurance and an efficient
full
allocation.
The
principle
is
important. But
it
must be adjusted to take
into account the
imperfections present in the labor market.
Some
imperfections lead to higher layoff taxes than in the benchmark. This
case for constraints on the
affecting search or
work
amount
effort.
The
amount
the higher the optimal
of insurance
the
lower the limit on the provision of insurance,
of employment protection, thus the higher the
optimal layoff tax. This however comes at some cost in
Most others
is
which can be provided without
efficiency.
lead to lower layoff taxes than in the benchmark:
Constraints on the assets available to firms in case of layoffs obviously put a
on
limit
layoff taxes. In this case,
insurance, but
some
it
it is still
feasible
must be financed through both
efficiency cost.
The
and optimal to provide
layoff
and payroll
full
taxes, again at
asset constraint also affects the layoff tax schedule, the
number
relation of the layoff tax to the
of layoffs.
Ex-post wage bargaining reduces the scope
for insurance.
And
it is
optimal in this
case to have a lower layoff tax rate than in the benchmark. This provides
income insurance, but at some
some
efficiency cost.
Finally, heterogeneity of firms or of workers also typically implies a lower layoff tax
rate than in the benchmark.
To the
extent that
weak
firms face higher layoff risk,
a reduced layoff tax rate, together with a corresponding increase in the payroll
tax, transfers resources
argument holds
from strong to weak
for workers.
A
firms,
improving
efficiency.
A parallel
reduced layoff tax rate transfers resources from
strong to weak workers, improving aggregate welfare. To the extent that the state
can
offer
rates for
menus and let firms
weak
on observable
a
firms, or
are very
our results suggest offering lower layoff tax
weak workers. To the extent that the
characteristics, job subsidies for
less distortionary solution
We
self-select,
than lower
much aware however
one-period model, there
is
weak
firms or
state can condition
weak workers provide
layoff tax rates.
of the limits of our analysis.
a number of issues
still
Even within our
to be explored. Let us mention
two.
40
An
important issue not taken up here
layoffs as triggered
reservation
is
that of quits versus layoffs.
by productivity shocks (shocks to
wage shocks (shocks to
b,
and quits
y),
or to the disutility of
work
If
we think
of
by
as triggered
—which we do not
have explicitly in our model) and we think of the layoff tax as applying only in
,
The
case of layoffs, this raises two sets of issues.
workers they would
The
actions by firms
is
actions by firms to induce
(harassment), and actions by
like to lay off to quit instead
workers to induce firms they would
The second
first is
like to quit to lay
them
off instead (shirking).
and workers together to mislabel quits and
incentives to harass, shirk, or cooperatively misreport,
each case on the contribution rate.
We
layoffs.
depend very much
in
have informally explored these issues in
Blanchard and Tirole (2003), but a formal treatment remains to be given.
Another
role,
issue
the role of judges, who, in
is
and are often ultimately
is
that this
countries, play a central
whether
in charge of deciding
argument
not. Clearly, the logic of our
many European
layoffs
were justified or
better accomplished through a
is
combination of layoff taxes and severance payments, with the decision then being
left
to the firm.
But our look
at the implications of imperfections,
from shallow
pockets to heterogeneity, also suggests the desirability of adapting layoff taxes
to particular situations. This can in principle be done through offering menus,
or allowing taxes to be conditional on observable characteristics of firms, or by
leaving
some
in fact
have the information, the
discretion to judges. It remains to
more informed
ability,
be shown however that judges do
and the
incentives, to take better
and
decisions.
Then, and obviously
so, there are
dynamic
issues
we could not
consider at
all in
our one—period model. Dynamic models of the labor market with risk aversion
and imperfections are notoriously hard to
derives optimal institutions
—
solve.
The only model we know which
defined as the optimal combination of payroll taxes,
layoff taxes, job creation subsidies or taxes,
and unemployment benefits
developed by Mortensen and Pissarides (2001). However,
it
assumes
— was
risk neutrality
and so cannot deal in a convincing way with the interaction between insurance
and
efficiency.
self- insurance
(A model by Alvarez and Veracierto
[1998] has risk averse workers,
as well as state-provided insurance, payroll
severance payments. While
it
shows (numerically) the
and
effects of
layoff taxes,
and
changes in some
41
of these instruments,
We
benefits.)
•
The
it
does not give a characterization of optimal taxes and
see two extensions of our
first is
model
as crucial.
the role and the implications of self insurance by workers (in
terms of the model here, the role and implications of the endogeneity of
In this context, an important question
vidual
unemployment accounts such
is
the role,
if
any, of
mandatory
b).
indi-
as are being considered or introduced
a number of Latin American countries (Three papers provide a useful
in
starting point here. All three allow for self-insurance,
and look
at the role of
state-provided insurance in the presence of other imperfections. In Hansen
and Imrohoroglu (1992), moral hazard
in search limits the scope for state-
provided insurance. In Acemoglu and Shimer (1999, 2000), state-provided
insurance affects search, which in turn affects match quality.)
•
The second
is
the role of experience rating systems, such as the
US
system,
as ways of implementing the collection of layoff taxes. This requires a careful
look not only at the dynamic problem of the firm, but at the exact nature
of the financial constraints that
There
is
a
final set of issues for
it
faces.
which our analysis
extended. These issues indeed provided the
initial
is
useful but
must
also
be
motivation for our project.
In most European countries, governments are considering reforms of their labor
market
institutions. In
what labor market
many emerging
countries, governments are considering
institutions to put in place.
The
challenge
practical implications of our conclusions for such purposes.
this in
We
is
to draw the
have tried to do
Blanchard and Tirole (2003), focusing on France, characterizing existing
institutions,
and sketching a tentative path
for reforms.
But, here again,
much
more can and should be done.
42
References
[1]
Acemoglu, D., and R. Shimer, (1999),
"Efficient
Unemployment Insurance", Journal
of Political Economy, 107-5, October, 893-928
[2]
Acemoglu, D., and R. Shimer, (2000), "Productivity Gains from Unemployment
Insurance", European Economic Review, 44-7, June, 1195-1224
[3]
Akerlof, G.,
and H. Miyazaki (1980) "The Implicit Contract Theory of Unemploy-
ment Meets the Wage
[4]
Bill
M. Veracierto
Alvarez, F., and
provisions," working paper
[5]
Argument," Review of Economic Studies, 48: 321-338.
(1998),
"Search, Self-Insurance and Job Security
WP98-2, Federal Reserve Bank
Azariadis, C. (1975) "Implicit Contracts and
of
Chicago
Underemployment
Equilibria," Jour-
nal of Political Economy, 83: 1183-1202.
[6]
Baily, M.(1974)
Economic
[7]
Blanchard, O., and
MIT
[8]
"Wages and Employment under Uncertain Demand," Review of
Studies, 41: 37—50.
Tirole (2003), "Contours of
J.
Employment Protection Reform"
working paper 03-35, November
Blanchard, O. and
J.
Tirole (2004), "Notes on Corporate Finance and Layoffs",
mimeo, January
[9]
[10]
[11]
Boeri, T. (2002)
"Making Social Europe Compete," mimeo, Universita Bocconi.
Cahuc,
P. (2003),
France,
May
Cahuc,
P.
and G.
"Pour une Meilleure Protection de l'Emploi", mimeo Paris
Jolivet, (2003),
"Do
mimeo
I.
tection Legislation?"
[12]
,
Paris
We
I,
Need More Stringent Employment Pro-
Hansen, G. and A. Imrohoroglu, (1992) "The Role of Unemployment Insurance in
an Economy with Liquidity Constraints and Moral Hazard", Journal of
Economy,
Political
100-1, February, 118-142
43
[13]
Ichino, A.,
fort,"
[14]
mimeo, EUI and University
of Basel.
Mortensen, D., and C. Pissarides (1994) "Job Creation and Job Destruction
Theory
[15]
and R. Riphahn (2003) "The Effect of Employment Protection on Ef-
of
Unemployment," Review of Economic
in
the
Studies, 61-3(208): 397-116.
Mortensen, D., and C. Pissarides (2001) "Taxes, Subsidies and Equilibrium Labor
Market Outcomes", mimeo, April
[16]
Pissarides, C.
(2000) Equilibrium
Unemployment Theory. Second
edition,
MIT
Press.
[17]
Pissarides, C. (2002)
cations for Optimal
3837
"Consumption and Savings with Unemployment Risk: Impli-
Employment Contracts," mimeo, March
:28
44
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