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Massachusetts Institute of Technology
Department of Economics
Working Paper Series
The Joint Design of Unemployment
Insurance and Employment Protection.
A First Pass.
Olivier Blanchard
Jean Tirole
Working Paper 04-15
April 1,2004
Revised:
November
11,
2005
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The
unemployment insurance and employment
joint design of
A
protection.
first
pass.*
Jean Tirole
Olivier Blanchard^
November
11,
*
2005
Abstract
Unemployment insurance and employment protection
studied in isolation. In this paper,
on
we argue
are typically discussed
that they are tightly linked, and
we
and
focus
their joint optimal design.
We
start our analysis with a simple
neutral firms, and
random shocks
benchmark, with
to productivity.
risk averse workers, risk
unemployment insurance comes with employment protection
taxes; indeed, optimality requires that layoff taxes be equal to
We
we show
In this benchmark,
—
in the
form of
unemployment
that
layoff
benefits.
then explore the implications of four broad categories of deviations: limits on
insurance, limits on layoff taxes, ex-post
of firms or workers.
scope for insurance
We
wage bargaining, and ex-ante heterogeneity
show how the design must be modified
may be more
in each case.
limited than in the benchmark; so
employment protection. The general
principle remains however,
may
The
the scope for
namely the need
to
look at unemployment insurance and employment protection together, rather than in
isolation.
*We
are grateful to
Daron Acemoglu, Suman Basu, Larry Katz,
Tsyvinski for helpful comments.
T
MIT
and NBER.
'IDEI and
GREMAQ (UMR 5604
CNRS), Toulouse, and MIT.
Javier Ortega, John Hassler, and Aleh
Introduction
Unemployment insurance and employment
In this paper,
in isolation.
protection are typically discussed and studied
we argue that they
are tightly linked,
and we focus on
their
optimal joint design.
We
start our analysis in Section 1 with a simple
The productivity
entrepreneurs run firms and are risk neutral.
is
random.
If
productivity
is
benchmark. Workers are
risk averse;
of any worker-firm
low enough, the worker and the firm may separate,
in
match
which
case the worker becomes unemployed.
In this benchmark, a simple
employment
to achieve the
benefits so as to insure workers,
to internalize the cost of
benchmark shows the
ployment protection
unemployment
The same
allocation
their workers;
for the state to
pay un-
layoff taxes so as to lead firms
efficient layoff decision.
Thus, the
as layoff taxes.
This
common
The
level delivers
second, which follows from the
is
is
between unemployment insurance and em-
further characteristics:
benefits:
The
and to levy
tight conceptual relation
—defined
efficiency.
optimum
unemployment and take an
The optimum has two
to
way
first, is
first is
both
that layoff taxes are equal
full
insurance and production
that state intervention
is
not needed.
achieved by having firms voluntarily pay severance payments to
in effect, severance
payments act both
as
unemployment insurance and
layoff taxes.
This leads us to examine, in Sections 2 to
5,
how
these conclusions are affected by the
introduction of four empirically-relevant deviations from the benchmark, from limits on
unemployment insurance,
wage bargaining, and
we ask two
questions:
to limits on the ability of firms to pay layoff taxes, to ex-post
to ex-ante heterogeneity of either workers or firms.
The
first is
unemployment insurance and
how
In each case,
the distortion affects the optimal combination of
layoff taxes.
The second
is
whether state intervention
is
required.
We
find that, in general, efficiency
and unemployment
and insurance require
different levels of layoff taxes
benefits, with the difference being financed
through payroll taxes
—
positive or negative.
The
fact that layoff taxes are in general not equal to
that individual firms can no longer implement the
erance payments).
A pooling
firms which lay workers off
or insurance agency
unemployment
optimum on
is
and from firms that do
their
benefits also implies
own
(i.e.
through sev-
needed to receive payments both from
not,
and to
distribute
unemployment
benefits to laid off workers.
We show that,
in
some
cases, this role
can be
by a private
filled
agency, with voluntary participation by firms, but that in others, participation must be
compulsory, implying a clear role for the state.
We
also show, in Section 6, that, while, in
can be provided through a combination of severance payments by
some
cases, insurance
firms
and unemployment benefits by the agency,
exclusivity in the provision of insurance, lest the
in other cases, the
agency must require
outcome be suboptimal.
Our framework
Before we start, we want to emphasize the limits of our analysis.
As
a static, one-period, model.
is
such,
it
represents a substantial step back from recent
dynamic models of either unemployment insurance or employment protection.
two reasons.
employment
First,
we want
to focus
protection, which
on the
joint design of
makes things more
We do so for
unemployment insurance and
difficult.
Second, we want to explore
a large number of labor market imperfections, starting from as simple a benchmark as
feasible.
of
We
believe that the conclusions
we draw from our model, about the
unemployment insurance and employment
and payroll taxes
in response to various
state, are quite general
Section
A
1
7,
what we
articulation
protection, about the relative use of layoff
market imperfections, and about the
role of the
and can help design better systems. In that context, we draw,
see as our
main conclusions and our intended
in
extensions.
benchmark
Assumptions
1.1
Tastes and technology are as follows:
•
The economy
is
composed of a continuum
least) 1 of entrepreneurs,
•
and the
of
mass
of workers, a
continuum of mass
If
a firm
is
Productivity
created, a worker
is
which
is
is
hired,
the same for
all
and the productivity of the match
Realizations are iid across firms; there
firm, but not the
worker (or
is
off,
a
[0, 1].
is
The
then revealed.
firm can either
who then becomes unemployed.
no aggregate
for that
is
entrepreneurs.
given by y from cdf G(y), with density g(y) on
keep the worker and produce, or lay the worker
The
(at
state.
Entrepreneurs are risk neutral. Each entrepreneur can start and run a firm. There
fixed cost of creating a firm, /,
•
1
risk.
matter third parties such as an insurance
company
or the state) observes y.
•
Workers are
if
unemployed
risk averse,
utility function £/(.).
given by U(b) (so
is
The optimal
1.2
with
1
b is
Absent unemployment
the wage equivalent of being unemployed).
allocation
Let y be the threshold level of productivity below which workers are laid
payment
are laid
benefits, utility
to the workers
who remain employed, and
\i
off.
Let
w
be the
be the payment to the workers who
off.
The optimal
allocation maximizes expected worker utility subject to the economy's
2
resource constraint:
max Vw =
+ M + (l -
G(y)U(b
G(y))U{w)
)
subject to:
V=
-G(y)fi
+ I
y dG(y)
-
(1
- G(y))w =
I
ly
Prom
the first-order conditions,
it
follows that:
y*
Given
y*, the levels of
Condition
(1)
(2)
is
efficient for firms to
unemployed (we
1
[i*
laid-off
b
are determined
an insurance condition:
is
whether employed or
Condition
w* and
=
(2)
by the resource
constraint.
Workers achieve the same
level of utility,
and unemployed.
an efficiency condition: From the point of view of
total output,
it is
produce so long as productivity exceeds the wage equivalent of being
shall call b the production-efficient threshold level).
This assumption
is
maintained throughout the paper, except
in Section 4
which introduces ex-post
bargaining, and in which both the worker and the firm observe the realization of y.
2
We
derive the optimal allocation ignoring the assumption that y
show below that
this optimal allocation
can indeed be implemented.
is
observed only by the firm.
We
shall
Implementation
1.3
Any
provision of insurance by the firm (a severance payment) can be duplicated by the
unemployment
state through
benefits in this economy.
At
best, severance
redundant; in some circumstances (those envisioned in Section
must actually be ruled out
in order to
now
•
Stage
benefits
•
The
1.
until
we discuss
we assume away severance payments.
the following implementation of the optimal
benchmark
state chooses a payroll tax rate r, a layoff tax rate /,
offer contracts to workers.
and, implicitly (since y
the worker
allocation:
and unemployment
Contracts are characterized, explicitly, by a wage w,
not contractable), a threshold productivity level y below which
is
off.
firms face the
all
3.
laid
is
workers are
Stage
6,
they
Entrepreneurs decide whether to start firms and pay the fixed cost.
2.
They
•
shall see that
fi.
Stage
As
we
implement the optimal allocation. So,
alternative implementation schemes in Section
Consider
2),
payments are
same
cost
and distribution of productivity,
in equilibrium, all
initially hired.
The
productivity of each job
is
realized.
Firms decide whether to keep or dismiss
workers.
To show how the optimal
allocation can be implemented,
At Stage
such that the firm
and paying
3,
the cutoff y
w+r
in
is
is
we work backwards
in time.
between keeping the worker
indifferent
wage and payroll tax and dismissing the worker and paying
layoff
tax
/:
y
If
y
state.
>
If
the firm keeps the worker, produces
y,
y
= w + r-f.
<
y,
the firm lays the worker
off,
y,
(3)
pays
w
to the worker,
and r to the
pays / to the state; the state pays
/i
to the
worker.
At Stage
2,
firms'
Vf
wage
offer
w
satisfies
= -G(y)f +
J
ly
the free entry condition:
y dG{y)
-
(1
- G(y))(w
+ t)=I.
(4)
Consider now the problem faced by the government in choosing taxes and unemploy-
ment
benefits at Stage
Condition
1.
=
efficient layoff decision y*
b,
implies that to induce firms to take the production-
(3)
the following condition must hold:
w + r-f =
Because optimal insurance further requires that
f-r =
The
net
fiscal cost to
between
(5)
w = b+
fj,,
the state's policy must satisfy:
(6)
ti.
the firm of laying off a worker must be equal to the
benefits paid to the worker
the layoff
b.
by the
state.
and the payroll tax
Note that
rates:
unemployment
this condition implies a positive relation
For given unemployment benefits, the higher
the payroll tax, the higher the layoff tax needed to induce the firm to take the productionefficient decision.
The government budget
constraint implies a second relation between taxes and benefits:
VG =
-G(y)( f,-f)
+ (l-G(y))T =
(7)
This constraint implies a negative relation between the layoff and the payroll tax
rates:
For given unemployment benefits, the higher the payroll tax, the lower the layoff tax
required to balance the budget. Combining the two conditions gives:
f
The
layoff tax
to zero.
must be equal
The payment
to
=
unemployment
of layoff taxes equal to
internalize the cost of insurance provided
We
summarize our
Proposition
insured
(b
+
=
w*),
being unemployed (y*
=
(8)
benefits,
and the payroll tax rate
unemployment
and the threshold productivity
b).
makes firms
equal
fully
1.
benchmark, the optimal allocation
=
benefits
is
by the state to the unemployed.
results in Proposition
1. In the
n*
t
fi,
is
is
such that workers are fuJly
equal to the wage equivalent of
Implementation
taxes f
=
n*
.
achieved through unemployment benefits equal to n*
is
Payroll taxes are equal to zero.
defined as the ratio of layoff taxes to
,
and
layoff
Put another way, the contribution
unemployment
rate,
benefits, is equal to one.
Limits on Insurance
2
In our benchmark, workers could be and were fully insured. In practice, there are various
reasons
why
this
may
not be feasible. Workers
may
employed, or to search when unemployed. Or there
with becoming unemployed.
require incentives not to shirk
may be
when
a non-pecuniary loss associated
We explore the implications of this last assumption,
and return
to a discussion of other potential reasons later.
Assume
if
that the utility of workers
unemployed, so
B>
is
is
now given by U(c)
if
employed, and by U(c)
—B
the utility cost of being unemployed. All other assumptions are
the same as in the benchmark.
2.1
The optimal
The optimal
allocation
allocation
is
the solution to: 3
max Vw =
G(y)(U{b
+ /x) - B) +
(1
-
G(y))U(w),
subject to the resource constraint:
V=
-G(y)n
+ I[y
dG(y)
-
(1
- G(y))w =
I.
Jy
Prom
the first-order conditions,
it
follows that:
w*
Given
y*, the levels of
w* and
/i*
= b + /i*.
are determined
(9)
by condition that the resource constraint
holds with equality.
In deriving the optimal allocation, we again ignore the constraint that y
Again, we show below that this allocation can be implemented.
is
only observed by the firm.
Condition
(9)
shows that marginal
ployment. Because
B>
utility is equalized across
however, this implies that utility
Condition (10) shows that the threshold
production-efficient level
b.
employment and unem-
lower
is
when unemployed.
level of productivity, y*, is
lower than the
A
Implementation
2.2
Assume, as before, that the state
a wage to workers, and,
offer
allocation
is
At Stage
first
finally,
chooses taxes and benefits, the firms then enter and
productivity
is
To describe how the optimal
realized.
implemented, we again work backwards in time. 5
3,
the threshold productivity below which the firm lays a worker
off is still
given by:
y
At Stage
2,
=w+T-
(3)
f.
the wage must satisfy the free entry condition:
VF =
-G(y)f
+ f
Jy
y dG(y)
-
(1
- G(y))(w +r)=I.
Consider thus the problem faced by the government
ment
benefits at Stage
1.
Prom equations
(3)
take the socially-optimal layoff decision y*
=
and
b
hold:
f- T =n+
The
net
fiscal cost to
(10),
choosing taxes and unemploy-
in
it
follows that, to induce firms to
— B/U'(w),
the following condition must
B
U'{w)
the firm of laying off a worker must exceed the
unemployment
benefits
paid to the worker by an amount which depends on the cost of becoming unemployed.
The
other condition on taxes and benefits comes from the government budget con-
straint:
-G(y)(fi-f)
4
+ (l-G(y))r =
This overemployment result should be familiar from the "implicit contract literature"
Baily (1974), Azariadis (1975), Akerlof and Miyazaki (1980)):
substitute for
5
0.
The
(in particular
lower layoff rate serves as a partial
unemployment insurance.
We
continue to assume that severance payments are equal to zero. In this case, the assumption is not
innocuous: Allowing for both unemployment benefits and severance payments would lead to a co-insurance
problem and a suboptimal
allocation.
We
discuss the issue in Section
6.
Combining these two conditions
f
The
gives:
(11)
U'{wj
must exceed unemployment
layoff tax
T<0
= (*+-£-
benefits, implying, for
budget balance, a negative
payroll tax.
We
summarize our
Proposition
2.
results in Proposition 2.
In the presence of limits to insurance, the threshold productivity in the
(i)
socially efficient allocation
is
lower than the wage equivalent of being unemployed (y*
<
b):
The lower incidence of unemployment partly compensates for the limits on insurance when
unemployed.
Unemployment
(ii)
benefits,
u.,
must be financed by a combination of
> ji) and of negative payroll
now be greater than one.
exceed these benefits (f
contribution rate must
<
0).
Put another way, the
Implications and discussion
2.3
•
taxes, (V
layoff taxes which
The main
result in Proposition 2 is that, in the presence of limits to insurance, layoff
taxes must exceed unemployment benefits
one.
The
— the contribution rate must be greater than
higher the utility cost of unemployment, the lower the layoff rate, the larger the
layoff taxes.
This implies that, with respect to variations
in
B, unemployment insurance' and em-
ployment protection are therefore substitutes: The lower the
feasible level of insurance, the
higher the implied level of employment protection. Higher employment protection however
is
a poor substitute
for insurance, as it leads to distortions in the layoff decision.
unemployment insurance reforms which reduce
interpreting
B
as a result of the
and
(better insurance)
•
The second result
is
need
for
B
Thus,
(we shall give an example below, when
search incentives) have both favorable direct
indirect (lower layoff taxes
and lower distortions)
effects.
that payments by firms in case of layoffs must be larger than payments
to the laid-off workers. This obviously could not be achieved
by severance payments, which
imply equal payments by firms and payments to workers, and requires the presence of a
third party. 6
This
is
We
have taken this third party to be the state, collecting layoff taxes and
an example of the genera] proposition
(for
example Holmstrom (1982))
that,
when both
incen-
and paying unemployment
(negative) payroll taxes,
is
needed
what
Formally,
benefits to workers.
a pooling or insurance agency, collecting payments from firms that
is
layoff,
paying unemployment benefits to workers, and distributing the difference to the remaining
firms. In this case, firms
who
join are better
The agency may
off.
therefore be private
and
participation voluntary.
•
We
formalized limits to insurance as coming from a non-financial cost of being unem-
The
ployed.
limits
may come
instead from incentives.
Consider for example a modification of the benchmark based on shirking. Once hired,
but before productivity
is
B
brings private benefits
revealed, the worker decides whether to shirk or not. Shirking
but results in zero productivity and thus a
Shirking
layoff.
is
unobservable. Thus, to prevent shirking, the following condition must hold:
{l-G{y)){U{w)-U{b + y))>B.
The expected
utility gain
some value B.
The
from being employed
relative to being
identical to those above, except for the replacement of
An
tive constraints are likely to lead
search
effort,
(1
are then
— G(y))B/U'(w)
in
comes from the need to motivate the unemployed to
While we cannot formally analyze
difference in utility
B/U'(w) by
7
alternative rationalization
search.
unemployed must exceed
optimum and the implementation
characterization of the
the relevant equations.
(12)
this case in our one-period
however to
results similar to those
model, search incen-
we have
between unemployment and employment has to be
yielding a constraint of the
form (U(w) — U(b + fi) >
would however require a dynamic model, and we cannot provide
it
derived.
sufficient to
B).
A
full
The
induce
treatment
here.
Shallow pockets
3
In our benchmark, firms were risk neutral and had deep pockets. These assumptions are
again too strong. Even in the absence of aggregate
risk,
the owners of many firms, especially
small ones, are not fully diversified, and thus are likely to act as
tives
and insurance considerations are present, there
company or the state.
Under the more general assumption that
is
if
they were risk averse.
typically a need for a "budget breaker"
,
such as an
insurance
shirking does not yield zero productivity but instead shifts
the distribution of y from G(-) to H(-), with G(-) stochastically dominating H(-), results are
In the absence of further restrictions, it is not necessarily the case that / is greater than jj,.
10
less clear cut.
And, even
if
entrepreneurs are risk neutral, information problems in financial markets are
on the funds available to
likely to lead to restrictions
firms.
In this section,
we
focus
on
the implications of limited funds.
We
assume that each entrepreneur
with assets I
starts
+
f,
the free cash flow available to the firm after investment. While
point, the exogeneity of /
obviously too stark, and
is
we
where /
it is
discuss a
>
is
therefore
a convenient starting
number
of extensions
below.
3.1
The optimal
allocation
The government budget
payments by the firm
constraint (7), the threshold condition (3), and the condition that
in case of layoff
to give the following constraint
on
cannot exceed free cash flow
y, w
(/</), can be combined
8 9
and
/j:
G(y)fi-(l-G(y))(y-w)<fTherefore, the optimal allocation
max VW =
is
the solution
G(y)U(b
to:
+ n) + {l-
G(y))U(w),
subject to the resource constraint:
V=
and the additional
-G(y)/i
+ f
y dG(y)
-
(1
- G(y))w =
/,
constraint:
G(y)n-(1-G(y))(y - w) <
f.
One may wonder whether allowing for job creation subsidies/taxes in addition to payroll and layoff taxes
might alleviate the shallow pocket constraint, and improve the allocation. This is not the case. Subsidies,
even if allowed in the government budget constraint, would not appear in the equation below.
9
This constraint is derived as follows. First rewrite the threshold condition as t = y-w + f and replace
r in the government budget constraint to get -G(y){fi - f) + (1 - G{y))(y - w 4- /) = 0: For a given y-w,
the lower /, the lower
is /i.
Reorganize and use /
< /
11
to get the equation in the text.
,
Prom
the first-order conditions,
it
follows that the worker
still
10
receives full insurance
:
w * = b + n*.
Furthermore,
the second constraint
if
binding (that
is
benefits in the optimal allocation derived in Section 1)
By
limiting
payments by firms
is,
if
/
is less
than unemployment
:
in case of layoff, the shallow pocket constraint prevents
the state from achieving the production-efficient threshold, and the layoff rate
than the production-efficient
/, the larger
w*, and
fi*
(fi*
—
level.
The
/), the higher y*,
is
tighter the shallow pocket constraint
and
so,
the larger the layoff rate.
are determined by (13), the full insurance condition,
The
now
higher
— the lower
levels of y*
and the condition that
the resource constraint holds with equality.
The optimal
allocation
offers full insurance to workers.
still
But limited funds lead to
a higher threshold productivity, and thus a higher layoff rate than in the benchmark.
Implementation
3.2
If
the shallow-pocket constraint
unemployment
benefits
ji"
,
is
binding, the state chooses the layoff tax /
-
;w-/»o.
cm
benefits exceed layoff taxes, payroll taxes
The threshold productivity chosen by
w >
To
b
see
+
p..
Given
Gte
i
10
/•
the government budget constraint then implies:
As unemployment
=
firms
is
must be
positive.
therefore given by:
why the presence of shallow pockets does not prevent full insurance, consider an allocation where
and an equal increase in payments by firms
Now, consider a decrease in the wage of Aui <
to the state. This change affects neither the threshold condition nor the firm's profit. Use these increased
payments to increase unemployment benefits by —[(1 — G(y))/G(y)] Aw. Together, these changes imply a
change in utility of [-(1 - G(y))U'(w) + (1 - G(y))U'(b + fj.)](-Aw) > 0. Thus, welfare can be improved
until workers are fully insured.
12
This
is
the same expression as in (13), and
The
the optimal allocation.
so, layoff
and payroll taxes indeed implement
shows that we can think
derivation
of the shallow pocket
constraint as affecting the threshold productivity level directly (through the limit on the
layoff tax)
and
indirectly (through the
need
tax and the higher payroll tax reduce the
We
of layoff for firms,
layoff
and thus lead
to a
level.
fi*.
summarize the
Proposition
results in Proposition
3.
presence of shallow pockets, workers remain fully insured (w*
3. In the
=
The threshold productivity is higher than the wage equivalent of being unemployed
b-\-u*).
>
both the lower
the same argument as before, the resource constraint implies that workers receive
the optimal w* and
(y
fiscal cost
than the production-efficient
layoff rate higher
By
for positive payroll taxes);
b),
leading to a higher layoff rate than in the benchmark.
This allocation can be implemented by the government choosing unemployment benefits
u*
t
and financing them partly through
,
>
0.
layoff taxes f,
and partly through payroll
taxes,
Put another way, the implementation implies now a contribution rate smaller than
one.
As
before, implementation can be achieved
fG(y*) from firms that
layoff
by a pooling agency, receiving contributions
and contributions r(l — G(y*) from those that do not, and
paying unemployment benefits G(y*)j±* to laid-off workers.
join,
and the agency may therefore be
Firms have an incentive to
private.
Discussion
3.3
Two
extensions of this analysis of shallow pockets are explored more formally in a com-
panion paper (Blanchard-Tirole 2005). Here
a short
is
summary
of the conclusions of that
paper:
(a)
Endogenization of limited pocket-depth. There are at least two reasons
shallow pockets.
The
first
reason
they can. This arises when,
government policy
the state cannot
is
is
may
in contrast to the
set after rather
commit and
that they
maintained assumption of
than before firms
sets (t, /,
(j.)
why
firms have
not want to have deep pockets even
after firms
invest.
if
this paper, the
Suppose, for example, that
have invested and hired workers, but
before they learn the productivity of the match. In this case, firms will obviously choose to
be "judgment proof,
i.e.
to have
no assets
left in
13
case of layoff, so /
=
0.
The threshold
is
= b + fJ.*/[l —
then given by: y*
layoff rate, reflects
two
G{y*).
The high
threshold,
one coming from zero
distortions,
and by implication, the high
layoff taxes
and the other from
positive payroll taxes.
Second, firms
income.
When
may
have limited access to external finance due to a dearth of pledgeable
the entrepreneurs enjoy a rent
cannot appropriate the
in the
benchmark.
We
R >
in case of continuation, investors
more
surplus from continuation, which leads to
full
find
however that,
should
in this case, the state
than
layoffs
still
make the
"investor-entrepreneur coalition" fully accountable for the cost of layoffs, so the optimal
contribution rate remains equal to one.
(b) Multi-activity firms.
A
concern often expressed by policy makers
firm can pay the layoff taxes,
companion paper,
may have
it
to collect the fully collectable
If it
did collect the
amount
full
shows that the state
amount, the marginal
excessive incentives for the firm to shut
4
one
the
The
and implication
in general does not
want
(/ in the notation of this section) in case of partial
layoff tax
be equal to zero (as the state cannot collect more than
in
if
to close otherwise healthy activities.
in a two-activity context, investigates the possibility
of such "spillovers" or "snowball" effects. It
layoffs.
that, even
is
down
entirely
/.)
on further
layoffs
would
This would in turn provide
when having low
productivity only
activity.
Ex-post wage bargaining
Our benchmark embodied the assumption that wages were
hiring.
set ex-ante,
i.e.
at the time of
This had the implication that, by offering unemployment insurance to
workers, a firm could not only offer a lower wage, but actually lower
its
risk averse
expected labor
costs.
To some extent however,
there
is
always some room
the case, a firm which has to pay a layoff tax
position vis-a-vis that worker; a worker
off is in
of
a stronger position.
unemployment
benefits
The
if it
who
for ex-post bargaining.
lays a worker off
will receive
is
in a
unemployment
layoff tax, the severance
When this is
weaker bargaining
benefits
if
laid
payments, and the provision
both lead to higher, not lower, wages, and thus increase labor
costs.
In this section,
we
therefore modify our earlier assumption about
wage
setting,
ex-post wage bargaining instead, and characterize the optimal allocation and
14
its
assume
imple-
In order to avoid the complexities attached
mentation under ex-post wage bargaining.
we assume,
to bargaining under incomplete information,
the firm and the worker observe productivity ex post.
in this section only, that
both
Thus "ex-post wage bargaining"
includes the assumption of symmetric information between worker and firm ex post.
A
4.1
The
formalization of wage bargaining
following formalization captures the effects of benefits
and taxes on ex-post wage
determination in a simple way:
Assume wage
setting
now
takes place after productivity
of a two-stage game. In stage
either accept the offer or turn
by the worker with probability
realized,
down.
turns
down, the wage
it
by the firm with probability
or
/?,
If it
Under the assumption that the firm chooses the threshold
to
maximize
profit ex-post, in stage 2, the highest
the wage offered by the worker,
and therefore the wage
accept,
wage
in stage 2
is
given by (3{y
worker will make the highest
and
is
equal to y
offered
—
r
offer
by the
—
+ f.
firm,
is
The
firm can
is
set in stage 2, either
—
/3.
will accept,
lowest
equal to
+ /) + (1 — (3){b + /i).
The
level of productivity so as
wage the firm
r
1
the outcome
is
the worker makes a wage offer to the firm.
1,
it
is
b
+
and therefore
wage the worker
fi.
will
Thus, the expected
This implies that,
acceptable by the (risk neutral) firm,
i.e.
in stage 1, the
an
offer of
w(y)-=P(y-r+f) + {l-0)(b + n).
The
higher the layoff tax, or the lower the payroll tax, or the higher the unemployment
benefits, the higher
The threshold
is
the wage.
value for productivity,
y, is
given by the condition that w(y)
+T—y =
f.
Using the expression for the wage and rearranging:
y
Note that the threshold
of /
see,
=
fi,
t
=
would
is
=
b+l_l
+ T-f.
(14)
privately efficient. Just as in the benchmark, the combination
deliver the production-efficient threshold, y
other considerations are
now
=
b.
But, as we shall
relevant.
Expression (14) allows us to rewrite the wage schedule
w(y)
=
(b
+ fj,)+P(y-y).
15
as:
(15)
The wage paid
to the marginal worker, the worker in a job with productivity equal to
the threshold level,
unemployment
equal to
is
benefits
+
(b
wage equivalent
the
fj,),
unemployed plus
of being
and severance payments. The wage then increases with
/?
times
the difference between productivity and threshold productivity.
4.2
The optimal
The optimal
allocation
same problem
allocation solves the
ditional constraint that the
wage
as in the
benchmark, subject to the ad-
no longer a decision variable, but
is
is
instead given by
equation (15):
max
G(y) U(b
+ n) + [
U(w(y)) dG(y),
subject to the resource constraint:
-G{y)n+ J (y-w(y))dG(y)=I,
and the wage
relation
w(y)
=b+
+ P(y
n
Under pure ex-post wage bargaining, the scope
surance to workers
is
extremely limited:
An
-y).
unemployment
for
increase in
change the slope of the income schedule, increasing
employment
y
benefits.
in the worker's
The
Put
differently, the only
all
b+
is
utility if
=
y]
1
(J- .
employed, and
expected value of marginal
So long as
marginal
so y*
is
/3
utility
is
the location of the kink
is
if
P(l-G(?))
G(y*)U'(b
E[U'\y
b.
The
*n
> y*}
(16)
EU'
-
G{y*))
+ n) +
J-\
is
the expected value of marginal
U'{w{y)) dG{y)
is
the unconditional
utility.
strictly positive,
and workers
strictly risk averse,
then the expected
utility,
and
layoff rate exceeds the production-efficient level. Setting y*
=b
employed
greater than
follows:
implicitly defined by:
U'(w(y))dG(y))/{\
E U' =
benefits does not
wages by an amount equal to un-
degree of freedom
g(F)
>
unemployment
income schedule. The solution can be characterized as
threshold level of productivity
where E[U'\y
benefits to provide in-
is less
than the unconditional expected marginal
16
=
Our formalization shows that
it is
optimal
to choose a threshold higher than the production-efficient level so as to decrease
income
(and /
fi)
would achieve production
risk averse the workers, or the stronger the workers in bargaining,
The more
uncertainty.
the higher the threshold
Given
y,
efficiency.
and
level,
11
so the higher the layoff rate.
and by implication the wage schedule w(y) are determined by the resource
fj,
constraint above.
Implementation through payroll and
4.3
Replacing y from (16)
first
relation
in the expression for the threshold decision of firms, (14), gives
between / and
/-r
relation
is
=
A*
-P
(1-G(y«))
E[U'\y
7=^
given, as before,
efficient level.
namely
By
unity.
shortfall of the
11
clear
is
This
is
is
now
in
left
fi
and
so,
/—r <
must be
(i.
(7).
As the
Together with
a contribution rate below
higher than the production-
is
its
benchmark
value,
positive, in order to finance the
unemployment insurance system.
of getting more intuition
and reorganize to read:
+
n)
+ f
Jy
((b
for the
The
optimal threshold
+ /j) + P(y -
y))
dG{y)
is
to
combine the
< G(y)b + /
first
and the second
y dG{y)
Jy
side gives the value of total workers'
the economy.
<
negative,
from above: The optimal threshold
implication, payroll taxes
G{y){b
The
(17)
achieved by lowering the contribution rate from
One way
constraints,
y*
by the budget constraint, equation
the government budget constraint, this implies /
The reason
>
EU'
)
second term on the right side of equation (17)
one.
the
r:
g{y
The other
layoff taxes
income (the sum of wages, reservation wages, and benefits)
income in the economy. The two are the same, as
right side gives the value of total
free entry implies zero profit income.
Suppose, counterfactually, that changes in y do not affect total income, and so do not affect total workers'
Then, changes in y change the shape of the income profile without affecting the total workers'
income.
income.
An
increase in y implies that
the same, but the income schedule
=
more workers
receive
(fi
+ b). The
overall workers'
income remains
Indeed, the best value of y from the point of insurance
workers receive the same income.
is
flatter.
is
where all
The assumption that changes in y do not affect total income is, however, clearly incorrect. Starting from
y = b, small changes in y do not affect total income; this implies that, as it decreases risk, at least a small
increase in y is desirable; this explains why the optimal y exceeds b. But, as y increases, the output loss
increases, and total income decreases. For y = 1 for example, total income is just b and so fi must be equal
to zero. This implies that the optimal value of y is greater than 6, but less than one.
y
1,
17
Note that
for
/3
=
0, i.e.
if
workers have no bargaining power, then we obtain the same
characterization as in the benchmark: /
the wage schedule
now
is
=
fi
and
=w—
/j,
increasing in productivity,
it
b.
As
becomes
(3
positive,
and
can be shown that the equations
above imply:
df
i
That
is,
<
du
Tp
<0
both the unemployment benefit and the
more bargaining power, and the
-
layoff tax decrease as the workers acquire
layoff tax falls faster, leading to a decreasing contribution
rate.
We
summarize our
When wages
Proposition
4.
worker
same
is
the
results as follows:
as for the
unemployed workers, and workers with higher productivity
These outcomes are independent of the
receive a higher wage.
is
are set through ex-post bargaining, utility for the marginal
state's policy choices.
optimal to induce a threshold higher than the production-efficient
choice decreases the uncertainty faced by workers at
some
level: (y*
>
b)
.
It
This
cost in efficiency.
This optimal allocation can in turn be implemented through a combination of layoff
taxes, payroll taxes,
ployment
benefits,
and unemployment
Layoff taxes must be
benefits.
with payroll taxes used to
make up
less
than unem-
the difference; equivalently, the
contribution rate must be less than one.
Heterogeneity
5
We
have assumed so far that
clearly are not.
Firms
all
workers and
assets.
firms were ex-ante identical. In reality, they
differ in the distribution of
the distribution of productivity and relative
Workers
all
productivity shocks
demand
(or,
more
generally,
shocks) they face, and in their initial
also differ in the distribution of productivity.
We
study
in this section
the implications of heterogeneity in productivity, both on the firm and on the worker side,
both observed and unobserved.
5.1
A
Heterogeneity of firms
worry often expressed by policy makers
than others, a layoff tax
will penalize
is
that,
if
them more, and
18
some
this
firms have higher layoff rates
may be
undesirable.
To explore
this idea,
suppose there are two types of firms, "strong" and "weak", which
The productivity
differ in their productivity distributions.
of "strong firms"
is
drawn from
12
cumulative distribution Gh(-) and that of "weak firms" from distribution Gl(-)-
distribution function of strong firms stochastically dominates that of
Gh(v) < Gl{v)- The
in (0, 1),
fraction of strong firms
is
equal to
Let us start with the assumption that this heterogeneity
unable to
is
weak
The
firms: for all
y
p.
unobserved, so the state
is
the two types of firms apart. Let us also start with the assumption that the
tell
state sets a uniform policy (t, /,
We
/i).
return to these two assumptions below.
Note that given the distribution assumptions and uniform taxation, strong firms have
We
higher expected profits than weak firms.
fixed.
By
Thus, at the creation margin, the
both types may
contrast,
assume that the number of strong firms
free entry condition
lay workers
off,
is
relevant for
so the destruction
margin
is
weak
is
firms only.
relevant for both
types of firms.
The
fact that the free entry condition
difficult to follow
now.
We
is
relevant only for
weak
firms
we have
the optimal allocation/implementation approach
makes
it
more
followed until
take instead the more "pedestrian" route of solving the optimization problem of
the state given firms' behavior.
We
assume that the state maximizes the welfare of workers. Allowing the state to also
put some weight on the positive rents earned by the owners of strong firms would not alter
the results.
The
problem
state's optimization
max
[
P G H (y)
+
(1
is
given by:
- p)G L (y)\ U(b +
p.)
{T,f,p.,w,y}
+
[p(l
- G H (y)) +
(1
- P )(l -
GL {y))\
U(w),
subject to the free-entry condition for weak firms
-G L (y)f+ I
(y-w-T)dG L (y)=I,
the government budget constraint
-[pG H (y) + (l-p)G L (y)}(p-f)
+ [p(l-G H
"We assume
fb ydGi(y) > I
m + (l-p)(l-G
L (y))}r
that the weak firms are not too unproductive.
:
Weak
firms have positive
NPV
=
0,
Namely we assume that 6Gl(&) +
for the production-efficient threshold.
19
and the threshold productivity condition, which
y
The
the same for weak and strong firms:
is
=w+r-
f.
solution can then be characterized as follows:
•
The
•
The threshold
state fully insures workers:
w = b+
fi.
level of productivity is given by:
{P9H(y)
By
+
G H {y))
-
P (G L (y)
= b+
y
(l-p)9L(y))'
the definition of weak and strong firms, Gi(y)
threshold level
This solution
benefits, so
is
is
higher than the efficient
in turn
>
Gh(jj)-
So, unless p
=
0,
the
level.
implemented by choosing
layoff taxes lower
than unemployment
through a contribution rate lower than unity. The difference
is
financed through
payroll taxes.
The
firms
intuition for
why
the contribution rate
may lay workers off and so the
is
destruction margin applies to
creation margin corresponds to the
welfare by allowing for
than one
is less
weak firms
only.
The
some cross-subsidy from strong
the rents of strong firms to wages. Because the state
is
to
as follows:
all firms.
Both types of
By contrast,
the
state can then improve workers'
weak
firms
—transferring some of
unable to assess the firms' strength,
the cross-subsidy operates through the contribution rate:
Weak
firms lay workers off
more
than strong firms and so benefit more from a contribution rate smaller than unity.
Can
the state do better by offering
menus and
shows that while offering a menu improves
acteristics of the
uniform
with a contribution rate
If
heterogeneity
apart, the state can
It is still
is
policy,
for
weak
Appendix
1
the solution carries the main char-
namely cross-subsidization
observable,
do even
letting firms self select?
efficiency,
of
weak
firms by strong firms,
firms below one.
i.e.
if
the state
is
able to
tell
weak and strong
better. Characterizing the optimal policy
optimal to subsidize weak firms.
is
firms
straightforward:
This can now be done however by offering a
20
job creation subsidy to the weak firms, while setting the net contribution rate equal to
1 for
both types of
firms.
This achieves the desired redistribution from strong to weak
(Note that both layoff and
firms, while avoiding distortions at the destruction margin.
payroll taxes must be higher than in the benchmark, as the extra revenue
finance job creation subsidies to
weak
The
firms.
unemployment
payroll tax remains however equal to
between the
difference
benefits, so there
is
needed to
layoff tax
is
and the
no distortion at
the destruction margin.)
We
can summarize our results as follows:
Proposition
5.
Suppose that there are two types of
Strong
"strong" or "weak".
firms:
weak firms Gl(-), and Gl(u) > Gjj(y)
firms have productivity distribution Gh(-),
for all
y in (0,1).
if
optimal policy
is
to fully insure workers (w
=
the state relies on a uniform policy, then the
and
If this heterogeneity is unobserved,
the efficient level (y
>
b),
If the state offers a
and implement
menu
b
+ fi),
instead, then the optimal
the following properties: Workers are fully insured.
rate of unity, and choose the efficient threshold.
below one, and the threshold exceeds the
the same, cross-subsidization of
Whether the state
offers
to set
If heterogeneity is
separates the firms and has
Weak
firms face a net contribution rate
The underlying mechanism remains
weak firms through the use of a lower contribution
menus or
a unit contribution
menu
than one.
less
Strong firms face a net contribution
efficient level.
not,
small enough, to not have them operate at
and
choose a threshold level higher than
through a contribution rate
it
it is
all
optimal,
if
rate.
the proportion of weak firms
is
—at the cost of some ex-ante unemployment—
rate.
observed by the state, then the optimal policy
subsidy to weak firms, choose the
efficient
is
to offer a job creation
threshold for productivity, and implement
it
through a unit net contribution rate for both types of firms.
5.2
Heterogeneity of workers
Another frequently expressed worry
others,
and that a
layoff tax
these workers worse
To explore
is
that
may make
some workers
firms
are
more reluctant
more
likely to
be
than
laid-off
to hire them, and thus
make
off.
this idea,
we
set
up a case very similar to that of
are two types of workers, "high-ability"
and
21
firms.
"low-ability" workers.
We
assume there
High-ability workers
A
.
have a productivity distribution given by Gh(.), low-ability workers a distribution given by
> Gn(y)
Gl{-), with Gl{v)
is
equal to
We
for all
y in
(0, l).
13
The
fraction of workers with high ability
p.
assume that firms know the workers'
abilities.
Proceeding in parallel with the earlier
case of heterogeneity in firms,
we
workers' abilities, and that
chooses a uniform policy
We
it
start
by assuming both that the
state does not
know the
(r, /,//).
can simplify the set-up of the optimization problem, by noting that workers of each
type will be fully insured, and that, because high-ability workers are more valuable to
they will be paid more, both when employed and when unemployed.
firms,
Suppose therefore that low-ability workers receive
employed, and are
fully insured, so
when employed, and p +
A
w = b + p.
w when
employed, and p when un-
High-ability workers will then receive
when unemployed
(so
w+A=b+p+ A),
where
A
w+
is
the
additional expected profit brought about to the firm by a high-ability worker. Noting that
A
does not affect the layoff decision, so the threshold productivity
types of workers,
A=
Payment
who
is
when
paid
it
follows that
[G L (y)
- GH
A
{y)}
f
is
is
the same for both
given by:
+ J
Jy
[y
-
(b
+ p) - r)
[dG H
(y)
- dG L
(y)]
A can be achieved by wage-indexed unemployment benefits, so a worker
w + A receives p + A (and the firm pays correspondingly higher layoff taxes
of
laying a high-ability worker off).
With
this characterization of
wage
setting,
and assuming that the
utilitarian social welfare function, the optimal policy
max
{(1
is
the solution
- p)U{b + (j,)+pU{b +
ti
state maximizes a
to:
+ A)},
{t,/,M,5}
subject to the free entry condition
-G L (y)f+ I [y-(b + iJ.)-T}dG L (y)=I,
Jy
13
We
assume that the low productivity workers are not too unproductive. Namely we assume that
ydGL{y) > I- Under observed heterogeneity, the low-ability workers are sufficiently productive
justify investment by firms.
bGL^b)
to
+ J*
22
and the government budget constraint
-
[(1
where
A
The
G L (y) + pG H (y)}
p)
(/
-
p)
+
P)
[1
" Gl
(v)}
+P[l-G H (y)]] r = 0,
and y have been defined above.
solution has the following form:
• If the proportion of low-ability workers
is
-
[(1
is
high enough, then the threshold for productivity
given by:
p(l
+
V
[(1
-
-
p)g L (y)
Note that Gi{y) - Gh(V)
on the
right
is
positive,
This solution
rest of
is
is
positive,
and so
f/p >
1;
No
job
is
small enough, however, then
The
unity,
with the
not optimal to
created for them, and they receive
unemployment
=
is
given by:
b.
implemented by relying on a gross contribution rate greater than one:
and a net contribution rate equal
turn given by r
level.
it is
is
y
is
A). So the fraction
higher than the efficient
is
for sure. In this case, threshold productivity
This solution
+b+
benefits being financed by payroll taxes.
facilitate their employability.
p
U'(p
implemented by using a contribution rate below
• If the fraction of low-ability workers
benefits
+ b) -
U'(p
is
and the optimal threshold
in turn
unemployment
- G H {y)\ [U'(p + b) - U'(p + b + A)}
+ P9h(v)} 1(1 - pW(p + b) + P U'(p + b + A)Y
p){G L (y)
=
[(1
—
to one:
f — t
=
p.
The
payroll tax rate
is
in
p)j p\ p.
intuition for these results
is
as follows.
When
both types of workers are employed,
the use of a contribution rate below one reduces the cost to firms of hiring a low-ability
worker. This in turn leads to a higher relative wage for low-ability workers, and therefore
reduces inequality, but at some cost in efficiency.
is
very low,
it is
more
efficient to
If
the proportion of low-ability workers
have them not work, and then to choose tax rates so as
to have efficient separations for high-ability workers.
Because unemployment benefits
taxes, the solution requires having
for low-ability
workers exceed corresponding layoff
both a positive payroll tax and a correspondingly higher
23
layoff tax
on high-ability workers. This increases revenues while maintaining a net
bution rate equal to one.
Note that the
logic of the results
under firm and worker heterogeneity
workers (firms) are more likely to be laid
of the externality of the layoff on the
What
if
UI fund
The
aimed
aimed
at firms that
It is
at firms that
a net contribution rate below one.
similar:
Weak
Both types
straightforward to
announce they have
announce they have hired a low-ability
option has a net contribution rate equal to one.
first
is
and an incomplete internalization
benefits the creation margin.
state then offers two options, one
hired a high-ability worker, one
worker.
off (to lay off),
the state can offer menus and firms then self-select?
show that the
contri-
14
The second option has
of workers are fully insured.
Thus, just
as in the uniform case, heterogeneity leads to lower layoff taxes, but in this case only for
low-ability workers.
What happens
differences
if
between workers are observable?
apart high-ability from low-ability workers
tell
or disabled
—then
the optimal policy
—
is
solution combines job creation subsidies
summarize our
Proposition
ability".
G L (-),
6.
if
they hire a low-ability worker. The net
when
differences are only partly observable, the
and a net contribution rate below one.
results in the following proposition:
Suppose that there are two types of workers:
"high- ability"
and "low-
High-ability workers have productivity distribution £?#(•), low-ability workers
and
G L (y) > G H (y)
If this heterogeneity is
optimal policy
is
for all y in (0,
1).
unobserved and the state
to fully insure workers (w
the efficient level (y
The
workers are in bad health
if
set equal to one for both types, and the destruction margin
undistorted for both types. In general,
We
example
the state can
to offer a job creation subsidy (or, equivalently,
is
uniformly lower payroll and layoff taxes) to firms
contribution rate can then be
for
When
>
b),
and implement
relies
on a uniform policy, then the
=
b
it
through a contribution rate
+ fi),
choose a threshold level higher than
less
than one.
lower layoff tax leads in effect to a transfer from high-ability workers to low-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
L4
This result
is
Cahuc and
and payroll tax rates.
related to the result in
also leads to higher layoff
Jolivet (2003)
24
where the need to finance a public good
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
The underlying mechanism remains the same,
through the use of a lower contribution
Whether or not the
low-ability workers
is
state
is
efficient level.
cross-subsidization of low-ability workers
rate.
allowed to use menus,
it is
optimal, if the proportion of
small enough, to leave them unemployed, and use a unit contribution
rate for the remaining, high-ability workers.
If heterogeneity
is
observed by the state, then the optimal policy
creation subsidy to low-ability workers,
and implement
it
and choose an
efficient
is to offer
a job
threshold for productivity,
through a unit contribution rate.
Mixing unemployment benefits and severance pay
6
We
We
have assumed throughout that the state was the sole provider of insurance to workers.
saw how, even under
was able to implement the optimal
assumption however raises two issues relative to the scope
location. This
provision of insurance.
for the state.
this assumption, the state
The
As we have
first is
for private-sector
whether a private third-party insurer can substitute
seen, the answer
firms or across workers, are absent,
al-
i.e.
is
yes as long as redistributive concerns, across
except in section
5.
The second
issue
is
whether
the third party insurer, whether the state or a private insurance company, needs to de-
mand
exclusivity
and prohibit the firm from
offering
supplemental insurance in the form
of severance pay.
A
recurrent
theme of the insurance
literature
is
that the insurer must be wary of the
externality imposed by supplemental insurance contracts (Pauly (1974)). For this reason,
insurance companies often
demand
exclusivity
and managerial compensation contracts pre-
vent executives from undoing their incentives through insider trading or derivatives contracts with financial institutions.
In the context of this paper, the state's provision of
insurance to workers raises the question of welfare-reducing supplemental insurance.
Let us
it
first
note that allowing severance pay does not reduce (nor, of course, does
increase) welfare
suggests,
when
the state already provides
full
insurance to workers.
and analysis confirms, that the firm does not want to undo the
full
Intuition
insurance pro-
vided by the state by overinsuring the worker (severance pay) or underinsuring her (asking
the worker to return some of the unemployment benefits, assuming this were feasible).
Thus, the analysis of Sections
1
(benchmark), 3 (shallow pockets) and 5 (firm or worker
25
heterogeneity)
is
immune
to the introduction of severance pay.
The co-insurance problem may
insured, that
Section
4,
is
in Sections 2 (incomplete insurance)
though, the firm
is
when
therefore arise only
new wage
is
imperfectly
and 4 (ex post wage bargaining). In
unable to exchange a bit more insurance against a lower
wage. Indeed, severance pay increases the wage one-for-one;
pay, the
the worker
if /j,p
denotes the severance
function, w(y), can be written as:
w{y)
= P (y - r + f + nF + (1 - 0)
= w(y)+/j, F
+ n + ii F
(b
)
)
.
The threshold
f
+ fip',
that
is,
value for productivity,
independent of severance pay. Put
no externality on the state
(as
it
Thus, the analysis of Section 4
The only
is
is
fi
differently, the introduction of severance
.
immune
also
Vw =
And
to the introduction of severance pay.
utility of
workers
is
-G(y)(f
is
therefore optimal
and allow firms
see this, return to stage 2
is
w
and a severance
given by:
+ n)-B) + (l-
G(y)(U(b +fiF
the free entry condition
VF =
To
2).
benchmark, contracts which specify both a wage
The expected
pay exerts
doesn't change y) and only serves to increase labor costs.
that of incomplete insurance (Section
fip
+t — y =
= b + + r-f
case in which co-insurance reduces welfare and exclusivity
to offer, as in the
payment,
given by the condition that w(y)
the threshold
y
is
y, is
G(y))U(w),
given by:
+ »f) +
V dG(y)
I
-
(1
- G(y))(w +t) =
I.
Jy
Now,
starting from fip
w = b + fi,
=
0,
and assuming the economy
consider the effects of a small increase in fip.
is
at the optimal allocation, so
From
the two equations above,
it
follows that
dVw =
Firms therefore have an incentive to
allocation.
The reason why
is
9{ y
-
1
Bdixp >
-n
G(y)
offer
0.
more insurance than required
in the
optimal
that increasing fip has two effects on the expected utility of
26
workers. First,
it
wedge between marginal
creates a
starting from the optimal allocation, this effect
reduces the probability of a
is
equal to
When
U{w) — U(b
This
is
+B =
B, this
up however, they
firms increase
unemployment
+ /j)
because the
layoff;
is
utility
when employed and unemployed;
of second order.
loss in utility
effect is of first
The other
is
that
it
from becoming unemployed
order and dominates the
first.
decrease layoffs, and given that layoff taxes exceed
benefits paid by the state, they impose a negative externality on the state.
why, in the end, letting firms freely choose severance payments leads to a suboptimal
allocation.
Proposition
7.
In the incomplete insurance extension of Section
pay severance payments in addition
to the
unemployment
2,
allowing the firm to
benefits paid by the state leads to
oversinsurance, an unemployment insurance deficit and suboptimal welfare.
By
contrast,
severance pay has no impact on welfare in the benchmark and in the other extensions.
7
We
Extensions and Conclusions
are very
much aware however
of the limits of our analysis.
model, there are a number of issues
An important issue not
as triggered
taken up here
b,
The
first is
and
depend very much
y),
work
If
we think
of layoffs
and quits as triggered by reservation wage
—which we do not have
actions by firms to induce workers they
layoffs.
in each case
The
by workers
The second
off instead (shirking).
to mislabel quits
issues in
that of quits versus layoffs.
explicitly in our
of the layoff tax as applying only in case of layoffs, this raises
quit instead (harassment), and actions
them
is
or to the disutility of
we think
sets of issues.
to lay
to be explored. Let us mention two.
by productivity shocks (shocks to
shocks (shocks to
model), and
still
Even within our one-period
is
would
to induce firms they
two
like to lay off to
would
like to quit
actions by firms and workers together
incentives to harass, shirk, or cooperatively misreport,
on the contribution
rate.
We
have informally explored these
Blanchard and Tirole (2003b), but a formal treatment remains to be given.
Another
issue
is
the role of judges, who, in
and are often ultimately
the logic of our argument
many European
in charge of deciding
is
that this
is
whether
countries, play a central role,
layoffs are justified or not. Clearly,
better accomplished through a 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
27
—
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
by leaving some discretion to judges.
of firms, or
when judges do
in fact
and more informed
have the information, the
It
remains to be shown however
ability,
and the
if
and
incentives, to take better
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 solve.
The only model we know which
derives optimal institutions
defined as the optimal combination of payroll taxes, layoff taxes, job creation subsidies or
and unemployment
taxes,
However,
it
benefits
—was developed by Mortensen
assumes risk neutrality and so cannot deal
interaction between insurance
and
efficiency.
in
and Pissarides (2003).
a convincing
way with the
(A model by Alvarez and Veracierto
[1998]
has risk averse workers, self-insurance as well as state-provided insurance, payroll and layoff
taxes,
and severance payments. While
of these instruments,
it
The
first is
is
effects of
changes
in
some
model as
We
essential:
the role and the implications of self insurance by workers (in terms of the
here, the role
question
shows (numerically) the
does not give a characterization of optimal taxes and benefits.)
see two extensions of our
model
it
the role,
and implications
if
any, of
of the endogeneity of b). In this context,
an important
mandatory individual unemployment accounts such
as are
being considered or introduced in a number of Latin American countries. (Three papers
All three allow for self-insurance,
provide a useful starting point here.
role of state-provided insurance in the presence of other imperfections.
Imrohoroglu (1992), moral hazard
in search limits the
scope
and look
In
at the
Hansen and
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
it
faces.
We
feel,
nevertheless, that as
it
stands, the paper can be helpful in thinking about
reform about employment protection
in
Europe
(the origin of the
paper was indeed a
request to define the contours of employment protection reform in France; our conclusions
are presented in Blanchard and Tirole [2003a,b]):
28
The
basic conclusion from the
nanced through
layoff taxes
odds with reality
in
is
benchmark that unemployment
straightforward conceptually.
It is
benefits should be
fi-
however very much at
Europe. All European unemployment insurance systems are financed
through payroll rather than layoff taxes; other things equal, both lead to too high a layoff
rate.
The
lack of layoff taxes
is
counterbalanced however, in
many countries, by heavy judicial
intervention. This suggests that a shift from judicial intervention to higher layoff taxes
firms
may be
desirable, reducing uncertainty
and channeling
layoff costs into
on
unemployment
benefits.
The
to insurance, higher layoff
also very relevant.
this
—that in the presence of limits
taxes and a contribution rate larger than one are
—
basic conclusion from considering limits to insurance
comes
justified
Employment protection
is
at the cost of production efficiency. This suggests the
unemployment insurance which allow
search. Recent reforms,
for better
insurance while
if
importance of reforms of
still
which make unemployment benefits more
search and acceptance of jobs
is
then a partial substitute for insurance, but
providing incentives to
explicitly conditional
available, go in that direction. If successful, they
on
can bring
not only better insurance, but also lower employment protection and lower production
inefficiencies.
The
final
broad insight
is
that layoff and payroll tax schedules should be tailored to
the economic environment in which firms operate. Lower layoff taxes and higher payroll
taxes are called for in industries, countries, or periods in which firms have shallow pockets.
Similarly,
and
less
unobserved firm or worker heterogeneity suggests relying more on payroll taxes,
on layoff taxes in the financing of unemployment benefits.
29
References
[1]
Acemoglu,
ical
[2]
D.,
Economy,
Acemoglu,
D.,
and R. Shimer, (1999),
"Efficient
Unemployment Insurance", Journal of Polit-
107-5, October, 893-928.
and R. Shimer, (2000), "Productivity Gains from Unemployment Insurance",
European Economic Review, 44-7, June, 1195-1224.
[3]
Akcrlof, G.,
the
[4]
Wage
and H. Miyazaki (1980) "The Implicit Contract Theory of Unemployment Meets
Bill
Argument," Review of Economic Studies,
Alvarez, F., and
M. Veracierto
48: 321-338.
(1998), "Search, Self-Insurance
and Job Security provisions,"
working paper WP98-2, Federal Reserve Bank of Chicago.
[5]
Azariadis, C. (1975) "Implicit Contracts and
ical
[6]
Economy,
Baily,
Underemployment
Equilibria," Journal of Polit-
83: 1183-1202.
M.(1974) "Wages and Employment under Uncertain Demand," Review of Economic
Studies, 41: 37-50.
[7]
Blanchard, O., and
J.
Tirole (2003a), "Redesigning the
Employment Protection System," De
Economist, 152: 1-20.
[8]
(2003b), "Licenciements et Institutions
dAnalyse Economique. La Documentation
[9]
(2005),
du Marche du
Travail,"
Rapport pour
le
Conseil
Frangaise, pp. 7-50.
"Layoff Taxes and Shallow Pocket Firms,"
mimeo,
MIT
and University of
Toulouse.
[10]
Cahuc,
P.
islation?",
[11]
and G.
Jolivet, (2003),
mimeo
Paris
"Do
We
Need More Stringent Employment Protection Leg-
I.
Hansen, G. and A. Imrohoroglu, (1992) "The Role of Unemployment Insurance
in
an Economy
with Liquidity Constraints and Moral Hazard", Journal of Political Economy, 100-1, February,
118-142.
[12]
Holmstrom, B. (1982) "Moral Hazard
in
Teams," Bell Journal of Economics, 13-2: 324-340.
30
[13]
Mortensen, D., and C. Pissarides (2003) "Taxes, Subsidies and Equilibrium Labor Market
Outcomes"
Enterprise,
[14]
Pauly,
M.
,
Designing Inclusion:
Edmund
(1974)
S.
Phelps
Tools to Raise
(ed),
Low-End Pay and Employment
in Private
Cambridge: Cambridge University Press.
"Overinsurance and Public Provision of Insurance:
The Roles
Hazard and Adverse Selection", Quarterly Journal of Economics, 88(1): 44-62.
31
of
Moral
—
Appendix
Policy
1:
Suppose the state
offers
menus under
an option
(tx,
firm heterogeneity
fL ) targeted
at strong firms, rather than the single option (r, /).
olds, payroll
is
and
now indexed by the type
layoff taxes are
identical to the
problem above, except that the
y
is
-
[w
weak
at
firms
and another (r#, /#)
With obvious notation change
of firm), the optimization
(thresh-
problem
last constraint,
+ t - f] = 0,
replaced by the constraints:
yL
-
[w
+
tl
-
fL
yn ~[w + th - fH =
=0,
]
\
0,
and the incentive compatibility constraint that the strong firms do not want to masquerade
as
weak ones
is
given by:
-G H (Vh) fu+
It is
(y-w-TH dG H (y) > -G H (vl) !l +
I
(y
-w-
tl )
dG H {y).
useful at this point to define the net contribution rate as the ratio of the layoff tax
minus the payroll tax
to
unemployment
as the net contribution rate
here
f
)
is
not the layoff tax
is
benefits, (fi
— Ti)/fii,
i
equal to one, the layoff decision
= H,L.
Note
is efficient:
that, so long
What
matters
but the difference between the layoff tax and the payroll
itself,
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:
/j,.
efficient
threshold:
yH
•
Weak
=
b
=
and fH - th
firms face a net contribution rate below one,
than the
/J-
and so choose a threshold higher
efficient level:
G l {Vl) -G H {y~L)
t^—
VL=b + p -— 1
PWLiVL)
,
.
r
32
and f,L
,
-TL <.
fi.
^28/4
02
7
IAB 2 4 2UG5
Date Due
3 9080 02618 0643