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Working Papers Series
Search, Self-Insurance and Job-Security
Provisions
By: Fernando Alvarez and Marcelo
Veracierto
Working Papers Series
Research Department
WP 98-2
Search, Self-Insurance and Job-Security
Provisions¤
Fernando Alvarez
University of Chicago and
Universidad Torcuato Di Tella
Marcelo Veracierto
Cornell University and
Federal Reserve Bank of Chicago
April, 1998
Abstract: We construct a general equilibrium model to evaluate the quantitative e¤ects of severance payments in the presence of contracting and reallocational frictions. Key elements of the model are: 1) establishment level dynamics,
3) imperfect insurance markets, and 4) variable search decisions. Contrary to previous studies that analyzed severance payments in frictionless environments, we
…nd that severance payments reduce unemployment, produce negative insurance
e¤ects and improve welfare levels.
¤
We thank the comments of participants at the 1995 NBER Small Group Meeting, the
1996 Canadian MSG meetings, the 1996 North American Summer Meetings of the Econometric
Society, the 1996 SEDC meetings, University of Texas-Austin, Texas A&M, SUNY-Bu¤alo,
University of Rochester, University of Iowa, SMU, Universidad Carlos III , Universidad Torcuato
Di Tella, Cem…, the macro group of the Wharton School, and the Cornell-PSU macro group. The
views expressed herein are those of the authors and not necessarily those of the Federal Reserve
Bank of Chicago or the Federal Reserve System. E-mail addresses: f-alvarez1@uchicago.edu and
mveracie@aruba.frbchi.org.
1. Introduction
Many countries have implemented policies intended to provide workers with higher jobsecurity levels. A common practice in Europe is the imposition of mandated severance
payments.1 The objective of severance payments is not only to provide unemployment compensation to workers, but to deter employers from …ring workers too often. While severance
payments can considerably improve job-security levels by lowering …ring rates, their implications for insurance, output, unemployment and welfare are less clear. The purpose of this
paper is to develop a framework that can be used to evaluate the consequences of severance
payments, weighing both potential costs and potential bene…ts.
An early investigation of the e¤ects of severance payments was undertaken by Bentolila
and Bertola [3], who analyzed the partial equilibrium problem of a monopolist facing stochastic demand shocks. They found the …ring costs had larger e¤ects on the propensity to
…re than to hire, increasing the average employment of the monopolist.
Later on, Hopenhayn and Rogerson [6] performed a general equilibrium analysis. They
considered an economy where output was produced by a large number of establishments
subject to idiosyncratic productivity shocks, and analyzed the e¤ects of a …ring tax that was
rebated to households as a lump sum transfer. Since they considered a frictionless world with
perfect insurance markets, their equilibrium allocation without government interventions was
Pareto optimum. As a consequence, …ring taxes had no potential bene…ts: they could only
distort the job creation and destruction process. Since households valued leisure and the
distortions introduced decreased the productivity of establishments, agents responded to the
1
Lazear [7] reports that mandated severance payments (for blue collar workers with ten years of tenure)
exceed one year of wages in several European countries.
…ring taxes by substituting away from market activities. As a consequence, …ring taxes
decreased output, consumption, employment and welfare. In fact, Hopenhayn and Rogerson
reported that …ring taxes equal to one year of wages had large negative e¤ects: they decreased
employment by 2.5%, consumption by 4.4% and welfare by 2.8%.2
This paper extends Hopenhayn and Rogerson [6] analysis by evaluating the e¤ects of
severance payments in an economy with frictions.3 In particular, the economy embodies key
elements for weighing potential costs against potential bene…ts of severance payments: 1)
establishment level dynamics, 2) reallocation frictions, and 3) absence of insurance contracts.
Similarly to Hopenhayn and Rogerson [6], output is produced by a large number of
establishments that receive idiosyncratic productivity shocks. This induce them to expand
and contract over time, leading to labor and capital reallocation across establishments. But
contrary to Hopenhayn and Rogerson, the reallocation process is costly: workers become
unemployed when separated from establishments. Unemployed individuals do not receive
wages and must search to …nd new employment. The probability that an unemployed agent
…nds a new job depends on his individual search intensity. There are no insurance markets
available, and the particular class of labor contracts we allow for precludes workers from
obtaining any type of insurance from their own employers. However, individuals can save
and accumulate an interest bearing asset which can be used to smooth consumption across
2
Three features of the Hopenhayn-Rogerson analysis suggest that this welfare cost may be overestimated:
1) the analysis focused on steady state comparisons, 2) it excluded (mobile) physical capital as an alternative
factor of production, and 3) there were no potential bene…ts of …ring taxes. Veracierto [14] shows that the
…rst two features aren’t crucial for the results they obtained. This paper explores the importance of the
third.
3
Our work is closely related to Millard and Mortensen [10], who used the Mortensen and Pissarides
[11] matching model to evaluate the e¤ects of alternative labor market policies. Four important di¤erences
are that we emphasize individual search decisions instead of an aggregate matching process, our wages are
determined by competitive labor markets instead of bilateral bargaining, our agents are risk averse instead
of risk neutral, and we emphasize involuntary layo¤s instead of quits.
2
employment states. Since agents are risk averse and there are no insurance markets, the
idiosyncratic risk that they face can result in considerable welfare losses. In this framework,
we introduce severance payments and evaluate their e¤ects both on allocations and welfare.
The model is calibrated to match U.S. observations from the National Income and Product Accounts, features of the job creation and destruction process reported by Davis and
Haltiwanger [4], the elasticity of the hazard rate with respect to unemployment bene…ts as
measured by Meyer [9], and the average duration of unemployment spells. This is done
under policy parameters chosen to reproduce important features of the U.S. unemployment
insurance system, such as its replacement ratio, the average duration of bene…ts, the fraction
of laid-o¤ workers that become covered by the system, and its degree of experience rated.
We …nd that severance payments have the following e¤ects in our economy. First, (similarly to Hopenhayn and Rogerson [6]) productivity is negatively a¤ected. Second, there are
no insurance gains. All the contrary, severance payments reduce the stock of assets that
agents have for smoothing consumption across employment states. Third, unemployment
decreases substantially: both establishments decrease their layo¤ rates and agents search
more intensively. And fourth, welfare improves dramatically: even though average consumption is negatively a¤ected, welfare increases because agents transit fewer times through
unemployment.
The paper is structured as follows. The economy is introduced in Section 2. Competitive equilibrium is de…ned in Section 3. Section 4 describes the parametrization of the
model. Section 5 compares the U.S. policy regime with laissaiz-faire and alternative European regimes. Section 6 analyzes the e¤ects of severance payments. Section 7 discusses
the role of unemployment insurance in generating high unemployment rates in Europe. And
3
Section 8 concludes the paper. An algorithm to compute steady state equilibria is provided
in the Appendix.
2. The economy
The economy is populated by a measure one of agents every period. Agents experience
stochastic lifetimes, evolving from active life to retirement and eventually to death.4 The
probability that an active agent retires is exogenously given by ³. Once an agent retires
he faces a constant probability # of surviving to the following period. With probability
(1 ¡ #) the retired agent dies, and is immediately replaced by an o¤spring who starts life
as an active (unemployed) person. Retirement and death realizations are assumed to be
independent across agents, leading to a constant number of active agents and retirees over
time.5
Active agents are either employed or unemployed at any point in time. Unemployed
agents become employed depending on their individual search intensities. Agents like to
consume, dislike to search, and are indi¤erent about the well being of their o¤springs. Specif4
Retirement makes an agent unproductive for the rest of his life
The life cycle element is introduced to the model economy to improve its performance in two important
dimensions. First, it leads to more realistic savings behavior, which is key for evaluating the bene…ts of job
security provisions (savings are an important source of self-insurance for agents). Second, it dramatically
improves the accuracy of our numerical computations (which requires a high willingness to save from agents).
5
4
ically, their preferences are described by the following utility function:6
E
1
X
t=0
¯ t [ln ct + u (1 ¡ ´t )]
(1)
where 0 < ¯ < 1 is the discount factor, ct is consumption, 0 < ´ t < 1 is the search intensity,
and u is given by:
u (1 ¡ ´ t ) = ®
(1 ¡ ´ t )¿ ¡ 1
; with ® > 0, ¿ > ¡1;
¿
(2)
Consumption possibility sets are such that both employed agents and retirees cannot search
(i.e. their ´ t must be zero)7 .
Output is produced by a large number of establishments that use capital and labor as
factors of production. To motivate the search frictions in the economy, we assume that
establishments must produce grouped together at a single geographical location. Every
period a new production site is randomly determined and establishments must move as a
group to the new location. Unemployed agents ignore the production site of establishments,
so they need to search to …nd it.8 The probability » that an unemployed agent …nds the
6
Preferences were selected to be consistent with the following stylized growth fact: unemployment has no
long run-trend while wages grow steadily over time. This requires that income and substitution e¤ects exactly
o¤set each other. Within this class of preferences, a separable utility function is needed to avoid the counterfactual implication that unemployed agents consume more than employed agents. These considerations
led to our choice of log utility in consumption.
Observe that these preferences imply a coe¢cient of relative risk aversion equal to one, which is in the lower
range of the most commonly used values. However, our model time period is relatively short, half-a-quarter.
As a consequence, a higher elasticity of intertemporal substitution is called for.
7
Note that (for a same level of consumption) employed agents enjoy as much utility as unemployed agents
that do not search. This feature will guarantee the absence of voluntary quits in the competitive equilibrium
studied below, simplifying the analysis substantially.
8
As will be made clear below, while this …ction introduces search frictions in the environment, it will allow
for perfectly competitive labor markets. As a consequence, many complicated bargaining issues between
workers and establishments will be avoided.
5
location of establishments depends on his own search intensity level according to the following
relation:
» = ´ ¾ ; where 0 · ¾ · 1.
(3)
Feasibility allows to allocate any of the agents that …nd the production site of the economy
to any of the existing establishments. However, once an agent joins an establishment he
gets attached to it: if for any reason the agent separates (or gets separated) from this
establishment, the agent becomes unemployed.
The production function of an individual establishment is given by:
yt = st ktµ n°t
(4)
where µ > 0, ° > 0, µ +° < 1, kt is capital, nt is labor, and st is an idiosyncratic productivity
shock. The idiosyncratic shock st takes a …nite number of values and follows a …rst order
Markov process with transition function Q. This process is assumed to be such that: 1)
starting from any initial value, with probability one st reaches zero in …nite time, and 2)
once st reaches zero, there is zero probability that st will receive a positive value in the
future. Given these assumptions, it is natural to identify a zero value for the productivity
shock with the death of an establishment. The evolution of the idiosyncratic productivity
shocks determine the expansion and contraction of establishments over time.
A technology to create new establishments is assumed to be freely available. The technology speci…es that if ¹ units of the consumption good are allocated to it, a new establishment
is created the following period. Initial productivity shocks st for the newly created estab-
6
lishments are randomly drawn from a common distribution Ã.
Finally, output can be either consumed, invested in establishment creation, or invested
in physical capital. The technology to accumulate capital is given by:
Kt+1 = (1 ¡ ±)Kt + It
(5)
where Kt is capital, It is investment and 0 < ± < 1 is the depreciation rate.
3. Competitive equilibrium
This section describes a competitive equilibrium characterized by a complete lack of private
insurance markets. The only way agents can privately smooth consumption across employment states is by saving in an interest bearing asset - borrowing is not permitted -. In
addition, the particular class of labor contracts we allow for preclude agents from obtaining
any insurance from their own employers. The absence of private insurance arrangements
combined with the search frictions that plague the environment will open a potentially important role for government interventions.
In this framework we introduce a number of labor market policies commonly observed in
actual countries. The …rst is an unemployment insurance system …nanced both with regular
payroll taxes and …ring taxes. Firing taxes are paid by employers to the government whenever
they lay o¤ workers. In addition, employers are required to make severance payments directly
to workers at the time of their dismissal (the main focus of the paper will be the analysis of
this particular policy). We now turn to a detailed description of the steady state competitive
equilibria.
7
3.1. Labor contracts
Labor contracts are restricted to be of the following form: 1) they specify a constant wage
rate to be paid as long as the employment relation lasts, and 2) they give the employer the
ability to terminate the employment relation at any time (after payment of any severance
and …ring taxes imposed by the government). Note that these labor contracts provide no
insurance to workers.9
To simplify the analysis, we assume that before a worker joins any particular establishment its individual state is unveri…able to the worker. This guarantees that at equilibrium
the same wage rate will be o¤ered by all hiring establishments. Once a worker joins an
establishment, its individual state is revealed to the worker but the wage rate cannot be
renegotiated. Under these assumptions the market for new hires will be perfectly competitive since: 1) agents are identical from the point of view of establishments that hire, 2)
establishments that hire are ex-ante identical from the point of view of agents, and 3) a large
number of unemployed agents …nd the labor market and a large number of establishments
hire workers at any point in time.
9
Lazear [7] has noted that if contracts were perfect, severance payments would be neutral: if a government
forced employers to make payments to workers at the time of their dismissal, perfect contracts would undo
these transfers by specifying opposite payments from workers to employers. In order for severance payments
to have any type of e¤ects, some form of incompleteness must be introduced.
The extreme form of rigid labor contracts assumed not only has the advantages of precluding insurance
arrangements and making the analysis tractable, but is a natural benchmark to analyze in the absence of
an obvious intermediate case. In particular, our results can be interpreted as an ”upper bound” estimate
for the potential e¤ects of …ring restrictions (since more ‡exible contracts would presumably decrease their
e¤ects).
Observe that most previous studies have avoided this di¢culty by modelling severance payments as …ring
taxes. Since in this case payments go to a third party (the government), their e¤ects cannot be undone by
private arrangements.
8
3.2. Establishments’ problem
Under the …ring penalties imposed by the government, the individual state of an establishment is given by its current productivity shock s and its previous period employment level e.
We assume that establishments have access to markets to diversify the risk induced by the
idiosyncratic productivity shocks s, and hence seek to maximize expected discounted pro…ts.
The maximization problem of an establishment of type (e; s) is described by the following
Bellman equation:
V (e; s) = MAX
{s k n
µ °
¡ w ¤ n ¡ rk ¡ -(e; n) +
}
1 X
V (n; s0 )Q(s; s0 )
1 + i s0
(6)
where w¤ is the before payroll tax wage rate, r is the rental price of capital, i is the interest
rate, and -(e; n) is a …ring cost function given by:
-(e; n) = (" + ¸)w ¤ max [e(1 ¡ ³) ¡ n; 0]
(7)
Note that whenever the number of workers the establishment currently employs n is smaller
than the previous period employment net of retirements e(1¡³), the establishment dismisses
workers. In this case the establishment must pay "w ¤ +¸w ¤ as …ring penalties for each worker
it …res. The …rst term is paid to the government as …ring taxes while the second term is
paid directly to the worker as severance (after payroll taxes). Both the …ring tax factor "
and the severance payments factor ¸ are policy parameters exogenously determined by the
government.
For future reference we denote by n (e; s) and k (e; s) the current employment and capital
9
optimal decision rules for an establishment with state (e; s) :
In what follows, we describe the problems faced by employed, unemployed and retired
agents. In solving their problems, households take the decision rules of …rms, prices and
government policy parameters as given.
3.3. Employed agents’ problem
Recall that agents learn the individual state of their employers as soon as they get hired.
This is important information to an agent because the probability of being …red depends
on the state of the establishment he is employed with. The individual state of an employed
agent is then given by his current assets level a and the state of the establishment he works
for (e; s). His optimization problem is described by the following Bellman equation:
H(a; e; s) =
{ ln c + ¯³R (a ) + ¯ (1 ¡ ³) X H(a ; e ; s )¤(e ; s )Q(s; s ) +
X
¯ (1 ¡ ³)
[(1 ¡ ·) U (a ; 0; 1) + ·U (a ; 1; 1)] [1 ¡ ¤(e ; s )] Q(s; s )} (8)
0
M AX
0
0
0
0
0
0
s0
0
0
0
0
0
s0
where e0 is given by:
e0 = n (e; s)
and the problem is subject to:
c + a0 · (1 + i) a + w
(9)
a0 ¸ 0
(10)
10
Note from the budget constraint (9) that an employed agent receives income both from
interest payments (1 + i) a and wages w (net of payroll taxes). Also note that equation
(10) imposes a borrowing constraint to the agent. The agent derives utility from current
consumption ln c and discounts next period’s payo¤s at the rate ¯. Next period’s value
is given as follows. With probability ³ the agent retires, obtaining a value R(a0 ). With
probability 1 ¡ ³ the agent does not retire, but is subject to losing his job. Let:
(
n (e; s)
¤(e; s) = min 1;
(1 ¡ ³)e
)
(11)
be the probability of continuing employed that a worker at an establishment of type (e; s)
faces at the beginning of the period (where n (e; s) is the current employment decision and e
is the past employment of the establishment). Note that agents are …red only when current
employment n(e; s) is smaller than previous period employment net of retirements (1 ¡ ³)e.
For an agent who is currently employed at an establishment of state (e; s), then:
(
n (e0 ; s0 )
¤ (e ; s ) = min 1;
(1 ¡ ³)e0
0
0
)
, where e0 = n (e; s) ,
gives the probability of continuing employed the following period if a shock s0 is realized.
Since the state of the establishment would be (e0 ; s0 ) in this case, the value obtained by the
agent would be given by H(a0 ; e0 ; s0 ). Similarly, 1 ¡ ¤(e0 ; s0 ) gives the probability of being
…red the following period if a shock s0 is realized. In this case the agent faces an expected
value given by (1 ¡ ·) U (a0 ; 0; 1) + ·U (a0 ; 1; 1), an expression to be described next.
11
3.4. Unemployed agents’ problem
The function U (a; b; m) gives the value of being unemployed to an agent with current state
(a; b; m), where a are the current assets of the agent, b is an indicator of whether the agent is
eligible for unemployment bene…ts or not (b = 1 meaning that the agent is eligible), and m is
an indicator of whether the agent receives severance payments or not (m = 1 meaning that
the agent receives severance). At the time an agent gets …red he receives severance payment
from his former employer and becomes eligible for unemployment bene…ts with a probability
given by · (a policy parameter for the government). Consequently (1 ¡ ·) U (a0 ; 0; 1) +
·U (a0 ; 1; 1) in equation (8) is the expected value that an agent faces at the time of being
…red. Since severance payments are given once and for all at the time of the …ring, m becomes
zero after that period. Even though an unemployed agent may be eligible for bene…ts at any
given period, the government cancels his eligibility for the following period with probability
1¡Á. Once an agent loses his eligibility he cannot regain it during the current unemployment
spell.
The problem of an unemployed agent with current state (a; b; m) is then described by the
following equation:
U(a; b; m) = M AX
{ ln c
+ u(1 ¡ ´) + ¯³R (a0 ) + ¯ (1 ¡ ³) ´ ¾
¯ (1 ¡ ³) (1 ¡ ´ ¾ )
subject to:
12
X
b0
X
H(a0 ; e0 ; s0 )¡(e0 ; s0 ) +
e0 ;s0
}
U(a0 ; b0 ; 0)P (b; b0 )
(12)
c + a0 · (1 + i) a + ½wÂ(b = 1) + ¸wÂ(m = 1)
(13)
a0 ¸ 0
(14)
Equation (13) is the budget constraint of an unemployed agent, Â being an indicator function which is equal to one if its argument is true and zero otherwise. The budget constraint
restricts consumption and savings to be less than the sum of interest income (1 + i) a, unemployment bene…ts ½w (if b = 1 ), and severance payments ¸w (if m = 1). The agent
derives utility ln c from current consumption, utility u(1 ¡ ´) from current search e¤ort and
discounts next period’s payo¤s at the rate ¯. Next period’s expected value is given as follows.
With probability ³ the agent retires, obtaining a value R(a0 ). With probability 1 ¡ ³ the
agent does not retire and may become employed with a probability which depends on his
current search intensity ´. With probability ´ ¾ the agent …nds the labor market, in which
case the agent joins some randomly determined establishment among those that hire. We
use ¡(e0 ; s0 ) to denote the fraction of total hiring done by establishments of type (e0 ; s0 ): Then
P
e0 ;s0
H(a0 ; e0 ; s0 )¡(e0 ; s0 ) is the expected value to the agent of …nding the labor market10 . With
probability (1 ¡ ´¾ ) the agent does not …nd the market and continues unemployed, obtaining
a value which depends on wether the agent is eligible for bene…ts or not. Let the matrix
P describe the transition probabilities between eligibility and ineligibility for unemployment
insurance, i.e.
10
To simplify notation from now on, we treat all the variables, including e and a as if they can take only
a …nite number of values and write summations instead of integrals.
13
0
1
0
B P (b = 0; b0 = 0) P (b = 0; b0 = 1) C
B 1
C
B
P =B
B
C=B
@
A
@
0
0
Then,
P
b0
0 C
C
1¡Á Á
P (b = 1; b = 0) P (b = 1; b = 1)
1
C
A
(15)
U (a0 ; b0 ; 0)P (b; b0 ) gives the expected value of continuing unemployed the following
period.
3.5. Retirees’ problem
The state of a retiree is simply given by his current assets level a. His problem is described
by the following Bellman equation:
R(a) =MAX
0
c;a
{ ln c + ¯#R(a )}
0
(16)
subject to:
c + a0 · (1 + i) a
(17)
a0 ¸ 0
(18)
The budget constraint (17) states that the only income that a retiree receives is interest from
previously accumulated assets. The agent derives utility ln c from current consumption and
discounts next period’s payo¤s at the rate ¯. With probability # the agent survives into
the following period, obtaining a value R(a0 ). With probability (1 ¡ #) the agent dies and
obtains a value which we normalize to zero. When the agent dies any remaining assets left
behind are immediately inherited by his o¤spring.
14
For future reference we denote g H (a; e; s), cH (a; e; s), g U (a; b; m), cU (a; b; m), ´ (a; b; m),
g R (a) and cR (a) to be the optimal saving and consumption decision rules for employed and
unemployed agents, the optimal search decision rule for unemployed agents, and the optimal
saving and consumption decision rules for retired agents, respectively.
3.6. Banks
A competitive banking sector accepts deposits from households at the interest rate i and holds
physical capital and establishments as counterpart. Capital is rented to establishments at
the rental rate r. Since there are no costs of intermediation, at equilibrium we must have
that:
r =i+±
(19)
where ± is the depreciation rate of capital.
In addition, since banks can create new establishments according to the technology described in the previous section, the following free entry condition must be satis…ed at equilibrium:
¹=
1 X
V (0; s0 )Ã(s0 )
1 + i s0
(20)
where ¹ is the …xed input of goods required to create an establishment and à is the distribution function over initial productivity shocks. Equation (20) states that the expected
discounted value of a newly created establishment must be equal to the …xed entry cost.
Note that new establishments arrive with zero previous period employment.
15
3.7. Aggregate consistency
To de…ne a steady state we need to keep track of the cross sectional distributions of establishments and households. These distributions are generated by the corresponding optimal
decision rules, as we describe in this section.
At steady state a time invariant measure x describes the number of establishments across
individual states (e; s). If º is the number of establishments being created then x must satisfy:
x (e0 ; s0 ) =
X
x (e; s) Q(s; s0 ) + Ã(s0 )ºÂ(e0 = 0)
(21)
e;s: n(e;s) = e0
Equation (21) states that the number of establishments that next period have past employment e0 and current shock s0 is equal to the sum of two terms: 1) all those establishments
that currently chose employment e0 and transit from their current s to the shock s0 , and 2) all
those establishments that are created with initial productivity s0 (this term must be included
only if e0 = 0, given that new establishments arrive with zero previous period employment).
At this point it is useful to recall Bellman equation (12) which describes the problem
of unemployed agents. In that problem a distribution ¡ of new hires across establishment
types was used to form expectations about the value of …nding the location of the labor
market. At equilibrium this distribution must be consistent with the employment decisions
of establishments and with the measure x described above. In particular, the fraction of
total hiring done by establishments of type (e0 ; s0 ) must be given by :
max [0; n (e0 ; s0 ) ¡ (1 ¡ ³)e0 ] x (e0 ; s0 )
¡(e0 ; s0 ) = P
max [0; n (e; s) ¡ (1 ¡ ³)e] x (e; s)
e;s
16
(22)
where n (e; s) is the optimal employment decision of an establishment of type (e; s).
The cross sectional distribution of households is characterized by time invariant measures
y H (a; e; s), y U (a; b; m), and y R (a) describing the number of employed, unemployed and retired agents across individual states. These measures are those implied by the optimal search
rule ´(a; b; m) and the optimal saving rules g H (a; e; s), g U (a; b; m), and g R (a). In particular,
the number of agents that are employed next period in state (a0 ; e0 ; s0 ) is given by the sum
of two terms:
y H (a0 ; e0 ; s0 ) =
X
a;e;s: g H (a;e;s) = a0 and n(e;s) = e0
X
a;b;m: g U (a;b;m) = a0
(1 ¡ ³) y H (a; e; s)Q(s; s0 )¤(e0 ; s0 ) +
(1 ¡ ³) y U (a; b; m)´(a; b; m)¾ ¡(e0 ; s0 )
(23)
The …rst term are all currently employed agents that do not retire, save a0 , do not get …red
at the beginning of the following period, and their employers chose current employment e0
while they transit to the shock s0 . The second term are all currently unemployed agents
that do not retire, save a0 , …nd the labor market, and get hired by an establishment of type
(e0 ; s0 ).
The number of unemployed agents in state (a0 ; b0 ; m = 1) is given by:
y U (a0 ; b0 ; 1) =
a;e;s:
X
g H (a;e;s)
=
a0
(1 ¡ ³) y H (a; e; s) [1 ¡ ¤(n (e; s) ; s)] ·(b0 )
(24)
That is, the number of unemployed agents which receive severance payments and have employment eligibility b0 is given by all currently employed agents that do not retire, save a0 ,
get …red at the beginning of the following period, and start their unemployment spell under
17
eligibility b0 . Abusing notation, we used ·(b0 ) to be equal to · if b0 = 1 and 1 ¡ ·, otherwise.
On the other hand, the number of unemployed agents in state (a0 ; b0 ; m = 0) is given by
the following expression:
y U (a0 ; b0 ; 0) =
X
a;b;m: g U (a;b;m) = a0
X
a: g R (a) = a0
(1 ¡ ³) y U (a; b; m) [1 ¡ ´(a; b; m)¾ ] P (b; b0 ) +
(1 ¡ #) y R (a) Â (b = 0)
(25)
The …rst term are all currently unemployed agents that do not retire, save a0 , do not …nd
the labor market, and transit from their current eligibility b to b0 . The second term are all
those retirees which save a0 and die. These agents are replaced by o¤springs that inherit
their assets and start life being unemployed without bene…ts, which adds to y U (a; b; m) only
when b speci…es no bene…ts and m speci…es no severance payments.
Finally, the number of retirees with asset levels a0 is given by the sum of three terms:
y R (a0 ) =
X
a;e;s: g H (a;e;s) = a0
X
³y H (a; e; s)+
a;b;m: g U (a;b;m) = a0
³y U (a; b; m)+
X
#y R (a)
a: g R (a) = a0
(26)
The …rst term are all those employed agents that retire and save a0 , the second term are all
those unemployed agents that retire and save a0 , and the last term are all retired agents that
save a0 and do not die.
18
3.8. Government budget constraint
We consider steady state equilibria without public debt. Hence in an equilibrium the government must satisfy the following (‡ow) budget constraint:
½w
X
a;m
y U (a; 1; m) = (w¤ ¡ w)
X
y H (a; e; s) +
(27)
a;e;s
["w¤ + ¸(w ¤ ¡ w)]
X
e;s
max [0; (1 ¡ ³)e ¡ n (e; s)] x (e; s)
The left hand side is the total amount of bene…ts ½w paid by the government to eligible
unemployed agents. The right hand side is the total amount of revenues collected by the
government. Revenues consist of two categories: 1) payroll taxes w ¤ ¡ w received from
employed agents, and 2) …ring taxes "w¤ plus taxes on severance payments ¸(w ¤ ¡w) received
from total …rings.
3.9. Market clearing
Markets must clear at equilibrium. In the goods market, consumption plus investment in
physical capital, plus investment in new establishments must equal the total amount of
output produced by establishments. In particular,
X
C + ±K + ¹º =
s n (e; s)° k (e; s)µ x (e; s)
(28)
e;s
where C is aggregate consumption, K is the aggregate stock of capital, º is creation of new establishments, and n (¢) and k (¢) are the employment and capital decisions of establishments.
19
Note that aggregate consumption is given by :
C=
X
X
cH (a; e; s) y H (a; e; s)+
a;e;s
cU (a; b; m) y U (a; b; m)+
X
cR (a) y R (a)
(29)
a
a;b;m
where cH , cU , and cR are the optimal consumption decisions of employed, unemployed and
retired agents respectively.
In the labor market, the number of unemployed agents which …nd the labor market must
equal the total amount of hiring done by establishments:
X
a;b;m
(1 ¡ ³) y U (a; b; m)´(a; b; m)¾ =
X
e;s
max [0; n (e; s) ¡ (1 ¡ ³)e] x (e; s)
(30)
In the market for capital we must have that the aggregate stock of capital supplied by
banks must equal the total amount of capital demanded by establishments:
X
K=
(31)
k (e; s) x (e; s)
e;s
Finally, the asset market must also clear. This condition becomes redundant by Walras
law, but is described for sake of completeness. It means that the total amount of savings
(deposits) made by households S must equal the total value of the assets A owned by the
banking sector, where:
S=
X
a;e;s
a y H (a; e; s)+
X
a y U (a; b; m)+
a;b;m
20
X
a
a y R (a)
(32)
and:
A=K+
Ph
e;s
i
s k µ n° ¡ w ¤ n ¡ rk ¡ -(e; n) x (e; s) ¡ º¹
i
(33)
Note that the assets owned by banks consist of the aggregate stock of capital K and the
value of the aggregate portfolio of establishments x, which is obtained by capitalizing pro…ts
minus the cost of creation .
3.10. De…nition of equilibrium
We are now in condition to de…ne a competitive equilibrium. An equilibrium is a set of prices
fi; r; w¤ ; wg, a set of functions {V (e; s), n (e; s), k (e; s), H(a; e; s), g H (a; e; s), U (a; b; m),
g U (a; b; m), ´(a; b; m), R(a), g R (a)}, a set of time invariant measures {x (e; s), y H (a; e; s),
y U (a; b; m), y R (a)}, a level of establishments creation º, a distribution function ¡(e; s), and
a probability function ¤(e; s) such that:
1) given i, r, and w¤ : V (e; s) is the value function of establishments and n (e; s) and
k (e; s) are the associated optimal employment and capital decisions,
2) given i, w, ¤ and ¡: H(a; e; s), U (a; b; m), and R(a) are the value functions of
employed, unemployed and retired agents respectively, g H (a; e; s), g U (a; b; m), g R (a) and
cH (a; e; s), cU (a; b; m), and cR (a) are their corresponding optimal saving and consumption
decision rules, and ´(a; b; m) is the optimal search decision rule of unemployed agents,
3) the measure x (e; s) across establishment types, the distribution function ¡(e; s), and
the probability function ¤(e; s) are consistent with the individual decisions of establishments
and the level of establishments creation º as given in equations (21), (22), and (11),
4) the measures y H (a; e; s); y U (a; b; m); y R (a) are consistent with the individual decisions
21
of households as given in equations (23), (24), (25) and (26),
5) the government budget constraint (27) is balanced,
6) the market clearing conditions (28), (30), and (31) hold, and
7) the no arbitrage conditions (19) and (20) are satis…ed.
A recursive algorithm to compute such a competitive equilibrium is described in detail
in the appendix.
4. Calibration
Fixing a time period of half-a-quarter, parameters were selected to reproduce important
features of the U.S. economy (Table 1 summarizes the calibrated values). We start by
describing our choice of policy parameters.
Analyzing a sample of unemployed agents which collected unemployment insurance bene…ts between 1978 and 1983 in twelve U.S. states, Meyer [9] reported that on average people
spend about 13 weeks before they either lose their bene…ts or …nd employment. We select
the persistence of U.I. bene…ts Á so that agents in our model economy spend about 9 weeks
unemployed and collecting bene…ts. This shorter duration is chosen over the 13 weeks reported by Meyer because of the high unemployment rate (8.7 percent) during his sample
period.11
Evidence presented by Blank and Card [2] suggests that about 50% of laid o¤ workers
do not qualify or do not apply for unemployment insurance bene…ts. In line with this
11
In periods of high unemployment, both agents remain unemployed longer and UI bene…ts are extended
over longer periods. This suggests that 13 weeks probably overestimates the duration in normal times. Since
we calibrate our model to an unemployment rate of 5.7 percent, a shorter duration is used.
22
observation, · was set to 0.50. Anderson and Meyer [1] report that for each dollar paid by
the government as unemployment insurance, 60 cents are paid by employers as experience
rated taxes. Since these taxes work as …ring taxes, " was chosen so that 60% of total
unemployment insurance bene…ts are …nanced with …ring taxes. On the other hand, the
replacement ratio ½ was selected to be 66% which is the value reported by Meyer. Finally,
since there are no mandated severance payments in the U.S. economy, ¸ was set to zero.
The number of parameters to determine on the …rms side depends critically on the number
of values that the idiosyncratic productivity shock s is allowed to take. Tractability requires
considering only three values. Normalizing the lowest positive productivity shock to one, we
let s take values in the set f0; 1; sg. Under this number of shocks, only a few parameters must
be determined: one in the initial distribution Ã, four in the transition matrix Q, the …xed
entry cost ¹, and the highest productivity shock s. Since these parameters are important
determinants of the establishment dynamics implied by the model, their values were selected
to reproduce important features of U.S. establishment dynamics.
In practice, the transition matrix Q was restricted to be of the following form:
0
B 1
B
B
B
Q=B
B ¼
B
B
@
0
0
!(1 ¡ ¼)
¼ (1 ¡ !)(1 ¡ ¼)
1
C
C
C
C
(1 ¡ !)(1 ¡ ¼) C
C
C
C
A
!(1 ¡ ¼)
i.e. a process that treats the low and the high productivity shocks symmetrically. The
parameters ¼, !, and s were selected to reproduce important observations on job creation
and job destruction reported by Davis and Haltiwanger [4]. These are (1) that the average job
23
creation rate due to births and the average job destruction rate due to deaths are both about
0.73% a quarter, (2) that the average job creation rate due to continuing establishments and
the average job destruction rate due to continuing establishments are both about 4.81% a
quarter, and (3) that the annual persistence of both job creation and destruction is about
75%. On the other hand, the …xed entry cost parameter ¹ was chosen so that the average
establishment size in the model economy is about 62 employees, same magnitude as in the
data.
We must also select Ã(1) which determines the distribution over initial productivity
shocks. If we would allow for a large number idiosyncratic productivity shocks it would be
natural to chose à to reproduce the same size distribution of establishments as in the data.
With only two values for s this approach does not seem restrictive enough, since we could
pick any two arbitrary employment ranges in the actual size distribution to calibrate to. For
this reason we chose to follow the same principle as in the choice of Q and pick à = (0:5; 0:5),
i.e. a distribution that treats the low and the high productivity shocks symmetrically. Note
that under these choices of Q and Ã, there will be as many establishments in the low shock
as in the high shock at steady state.
The remaining parameters to calibrate are ¯, ®, ¿ , ¾, ³, #, °, µ, and ±. The stock of capital
in the model economy was identi…ed with plant, equipment and inventories. Consequently,
physical investment was associated in the National Income and Product Accounts with nonresidential investment plus changes in business inventories. The empirical counterpart of
consumption was identi…ed with personal consumption expenditures in non-durable goods
and services. Measured output was then de…ned to be the sum of these investment and
consumption measures. For simplicity we assumed that the entrepreneurial investment in
24
new establishments goes unmeasured in the National Income and Product Accounts. At
steady state, investment is given by I = ±K. Using an annual capital-output ratio of 1.7 and
an investment-output ratio of 0.15, the half-a-quarter depreciation rate ± was then estimated
to be 0.011.
The annual interest rate was selected to be 4 per cent . This is a compromise between
the average real return on equity and the average real return on short-term debt for the
period 1889 to 1978 as reported by Mehra and Prescott [8]. Given the interest rate i and the
depreciation rate ±, the capital share parameter µ was selected to match the capital-output
ratio in the U.S. economy. The labor share parameter ° was in turn selected to replicate
a labor share in National Income of 0.64 (this is the value commonly used in the business
cycles literature).
With respect to the demographics of the model, the probability ³ that an active agent
retires the following period was selected so that the average duration of active life is 40
years. The probability # that a retired person survives into the following period was in turn
selected to deliver an average duration of retirement of 15 years.
A crucial observation for the analysis of labor market policies is the elasticity of the
hazard rate with respect to unemployment bene…ts. Meyer [9] estimates that a 1% increase
in the replacement ratio is associated with a 0.9% decrease in the hazard rate of agents that
collect insurance. To obtain such a large response in the model economy both the search
technology and preferences must be close to linear. In particular, values of ¾ and ¿ equal to
0.98 were needed to reproduce Meyer’s observation. In turn, the preference parameter ® was
chosen to generate an average duration of unemployment spells equal to 1 quarter, about
the same magnitude observed in the U.S. economy. Finally, the discount rate factor ¯ was
25
selected to obtain an equilibrium at the annual interest rate of 4% …xed above.
In the rest of the paper we examine the e¤ects of alternative labor market policies.
In particular, we compare the steady states of economies subject to the same structural
parameters that were determined in this section, but which di¤er in terms of their policy
regimes. We start our analysis by evaluating the consequences of switching from the current
U.S. system to laissez-faire and to labor market policies that resemble European systems.
The objective is not only to determine the relative bene…ts of observed labor market regimes,
but to establish the empirical relevance of our model economy. We then turn to the main
objective of this paper: the analysis of severance payments.
5. Policy Regimes
This section evaluates the current U.S. system versus laissaiz-faire and two policy regimes
which resemble european countries. While laissaiz-faire involves no government interventions, the european regimes have generous unemployment insurance systems and severance
payments. Table 2 describes the policy parameters for each regime considered and Table 3
reports equilibrium statistics.12 .
We see that moving from U.S. policies to laissaiz-faire has a large positive e¤ect in the
job …nding rate of unemployed agents. Since the layo¤ rate increases only slightly, the
unemployment rate declines substantially. The associated increase in aggregate employment
12
We adopt the following conventions for tables describing results in this paper: 1) the benchmark case for
the underlying experiment is indicated in bold letters, 2) statistics without meaningful units of measurement
are normalized to 100 at the steady state of the benchmark case while the rest of the statistics are expressed
in percentages, and 3) the welfare measure reported is the proportionate increase in permanent consumption
needed to make average utility across agents in the benchmark case be the same as in the economy under
consideration.
26
is accompanied by similar e¤ects in output, capital and consumption. Aggregate leisure
remains unchanged despite the decrease in the leisure of job seekers, because of the smaller
number of unemployed agents in the economy. All things considered, welfare is signi…cantly
improved under laissez-faire.
We now analyze the consequences of switching to U.K. policies. The U.K. labor market
regime di¤ers considerably from the U.S (we rely on Millard and Mortensen [10] for our
characterization of U.K policies). In the U.K. the replacement ratio is lower than in the
U.S. (½ = 0:36 instead of ½ = 0:66), but both the duration of unemployment bene…ts
is considerably longer and much more people become eligible for bene…ts when laid-o¤.
Correspondingly, we set · equal to one (all laid-o¤ agents become eligible for bene…ts) and Á
to 0.875 (which delivers an average duration of bene…ts equal to one year). Opposed to the
U.S., the U.K. has no experience rated taxes (" = 0). But employers are required to make
severance payments which average about one month of salary (¸ = 0:67).
Table 3 shows that switching to U.K. policies leaves the layo¤ rate unchanged from its
U.S. level, but the job …nding rate is lowered signi…cantly. As a consequence, the unemployment rate increases from 5.7% to 8.9%. Capital, output and consumption are negatively
a¤ected, but aggregate leisure remains roughly the same (the increase in unemployment
is compensated by the larger amount of leisure enjoyed by the unemployed). As a result,
welfare decreases by 1.8% relative to the U.S.
Compared to other european countries, the U.K. is a relatively mild system. Several
countries have implemented substantially more generous unemployment insurance policies
and severance payments, the utmost example being Spain. To evaluate these rather extreme
cases we analyze a “high” interventions regime. In this case, the replacement ratio is set to
27
0.40, the average duration of unemployment bene…ts to 3 years, severance payments to half
a year of wages, and all laid-o¤ workers become eligible for unemployment bene…ts.
We see from Table 3 that the “high” case gives rise to results which are qualitatively
similar to the U.K. system. However, the e¤ects are much larger: the unemployment rate
increases to 10.9% instead of 8.9% and consumption decreases by 5.5% instead of 3.1%.
Despite the larger drop in consumption, welfare is not substantially reduced from its U.K.
level because of the increase in aggregate leisure.
It is important to note that the unemployment rates predicted by the ”U.S.”, ”U.K.”
and ”high interventions” regimes are in line with their empirical counterparts. Moreover,
the model predicts little variation in job turnover rates across policy regimes as well as a
negative relation between in‡ow rates to unemployment and unemployment durations, which
are patterns observed in cross-country data (see [12] and [13]). The satisfactory performance
of the model economy along these empirical dimensions provides additional support for its
policy implications. With this background, we turn to our analysis of severance payments.
6. Severance payments
This section constitutes the core of the paper. It provides a detailed investigation of the
e¤ects of introducing severance payments into the laissaiz-faire economy.
Table 4 reports results for severance payments ranging between 1 month of wages (¸ =
0:67) and 12 months of wages (¸ = 8:0). It shows that severance payments have a positive
e¤ect in the job-…nding rate and a negative e¤ect in the layo¤ rate. As a consequence, they
lower unemployment. Output and output per employee increase until severance payments
28
reach six months of wages (¸ = 4:0). After that point, they are negatively a¤ected. Consumption follows a similar pattern as output, but becomes considerably more volatile (its
standard deviation increases more than its average). On the other hand, aggregate leisure
increases substantially. In terms of welfare, severance payments are extremely bene…cial.
For instance, severance payments equivalent to one year of wages increase welfare by 3.7%
relative to laissaiz-faire.
To understand the e¤ects of severance payments, it will be useful to view them as a
particular form of unemployment insurance. Instead of giving severance payments directly
to workers when they are laid-o¤, in this alternative policy arrangement establishments pay
…ring taxes to the government who in turn rebates them as one time UI bene…ts to the
recently laid-o¤ agents. More speci…cally, severance payments (at rate ¸) are equivalent to
a UI system with the following properties: 1) all laid-o¤ workers become eligible for bene…ts
(· = 1), 2) bene…ts last for exactly one period (Á = 0), 3) bene…ts are as large as the original
severance payments (½ = ¸), and 4) the system is fully …nanced by …ring taxes (" = ¸). We
refer to 1), 2) and 3) as the unemployment insurance component of severances payments, and
to 4) as the …ring tax component. To evaluate the relative importance of these components,
we analyze them separately.
6.1. The …ring tax component
This sub-section investigates the …ring penalty role of severance payments. To that end, …ring
taxes are introduced to an otherwise laissez-faire economy, where the proceeds are rebated
as employment subsidies to establishments (i.e. as negative payroll taxes). Under this
policy, households receive no payments from either establishments (¸ = 0) or the government
29
(½ = 0), i.e. no form of unemployment compensation is provided.
Three versions of the model are considered: 1) an economy with full-insurance markets
and exogenous job-…nding rates, 2) an economy with no insurance markets and exogenous
job-…nding rates, and 3) an economy with no insurance markets and endogenous job-…nding
rates (our original case). By gradually incorporating the important margins that …ring taxes
can potentially a¤ect (mainly: production e¢ciency, insurance opportunities, and search
decisions) we will be able to determine the e¤ects of …ring taxes in each of those margins.
6.1.1. Full-insurance markets and exogenous job-…nding rate
To isolate the e¤ects of …ring taxes on the labor productivity of employed agents and the
layo¤ decisions of establishments, we simplify the model economy considerably by making the
job-…nding rate exogenous and giving agents full access to insurance markets. In particular,
® is set to zero in equation (2) (the utility function is made independent of the search
intensity ´) and » = ´ ¾ is set to a constant. The particular value selected for » is the job…nding rate underlying the laissez-faire economy of Table 4. Note that since the job-…nding
rate is exogenous, the unemployment rate is completely determined by the layo¤ rate chosen
by establishments. Also observe that (under full insurance), the interest rate is determined
by the discount rate 1=¯ ¡ 1; and consumption equals the expected present value of labor
earnings that agents face at birth.
Table 5 describes the results of this experiment. We see that establishments respond to
…ring taxes by lowering their layo¤ rates substantially. This has a large positive impact on
aggregate employment.13 However, output is negatively a¤ected. For instance, when …ring
13
While aggregate employment is determined by the layo¤ rate of establishments, the number of estab-
30
taxes are set to one year of wages, employment increases by 1.3% but output decreases by
3%.
This should not be surprising: …ring taxes decrease the amount of aggregate output that
can be produced with any amount of aggregate employment. To understand this, note that
output is maximized by equating marginal labor productivities across establishments. This is
what actually happens under laissez-faire. But when …ring taxes are present, establishments
no longer equate wages to marginal labor productivities: they follow (s; S) decision rules.
For small …ring taxes, output remains unchanged since the higher employment level
compensates the decrease in productivity. But for …ring taxes larger than three months
of wages, the productive ine¢ciencies outweigh the positive employment e¤ects and output
decreases substantially. Note that this negative productivity e¤ect of …ring taxes is exactly
the same as that analyzed in Hopenhayn and Rogerson [6]. Similarly to that paper, we …nd
it be important in magnitude. In fact, …ring taxes equal to one year of wages have a similar
welfare e¤ect as in Hopenhayn and Rogerson [6]: they decrease welfare by 2.9% in terms of
consumption and welfare.
6.1.2. Lack of insurance markets and exogenous job-…nding rate
This case evaluates the e¤ects of …ring taxes on the ability of agents to self-insure through
their own savings. For that purpose, we drop the full-insurance assumption from the previous
economy but maintain the hypothesis of an exogenous job-…nding rate. Table 6 describes how
…ring taxes a¤ect this economy. The e¤ects on productivity, layo¤ decisions and aggregate
lishments in the economy is determined by the aggregate employment level and the average employment
size chosen by establishments. Similarly to Bentolila and Bertola [3], the average size of establishments can
increase or decrease with …ring taxes. For our parametrization, we …nd that average size actually increases.
31
employment are similar to the previous economy. As a consequence, we concentrate on the
insurance e¤ects of …ring taxes.
The key variable to observe in Table 6 is the aggregate amount of assets in the economy
(capital plus the value of establishments), which is reduced substantially. The reason for this
is that …ring taxes restrict the ability of establishments to adjust to idiosyncratic shocks,
reducing their average pro…ts considerably.14 A similar e¤ect was present in the full-insurance
economy of Table 5. The di¤erence is that in this economy, the lower amount of assets
reduces the self-insurance ability of agents (since agents use their stock of assets to smooth
consumption across employment states). As a result, consumption becomes more variable
and welfare declines to lower levels than those in Table 5.15
6.1.3. Borrowing constraints and endogenous job-…nding rate
To evaluate the total e¤ects of …ring taxes, we drop the exogenous job-…nding rate assumption: market structure, preferences and search technology are made identical to the original
economy of Table 4. Table 7 reports the e¤ects of introducing …ring taxes to this economy.
We …nd two important results: 1) the e¤ects of …ring taxes are extremely similar to the
total e¤ects of severance payments in Table 4, and 2) contrary to the economy of Table 6
(which had no insurance markets and exogenous job-…nding rates), …ring taxes are welfare
improving. These results imply that most of the e¤ects of severance payments are accounted
14
Average pro…ts can decrease even though the free entry condition must be satis…ed, because …ring taxes
occurs later in the life of the establishment while the free entry condition weights the initial periods more
heavily.
15
It is interesting to note that the general equilibrium e¤ects of …ring taxes revert the (partial equilibrium)
intuition of precautionary savings. The decrease in unemployment risk associated with the lower layo¤ rate
of establishments, reduces the willingness of agents to save and tend to push interest rates up. However, the
decrease in the value of establishments reduces so much the demand of banks for assets, that equilibrium
interest rates actually go down.
32
by their …ring tax component, and that search decisions are crucial for understanding them.
In what follows, we explain the reasons.
We focus our discussion on how …ring taxes a¤ect job-…nding rates, since their e¤ects
on productivity, layo¤ decisions and insurance opportunities are similar to the previous two
cases. Table 7 shows that …ring taxes have a large positive e¤ect in the job-…nding rate
of unemployed agents. The reason is that establishments respond to the …ring taxes by
reducing their layo¤ rates, which increases the length of time that agents expect to remain
employed once they get hired. This increases the return to the search activity, and induces
agents to search more intensively16 .
A consequence of the higher job-…nding rate is that employment increases more in Table
7 than in the economy of Table 6 (with exogenous job-…nding rates). This leads to larger
increases in output and consumption. However, the higher consumption levels are not large
enough to account for the large positive welfare e¤ects of …ring taxes: consumption levels
are not substantially di¤erent from Table 6, but welfare levels are. In fact, Table 7 shows
that …ring taxes continue to improve welfare even when consumption is negatively a¤ected.
To understand the welfare bene…ts of …ring taxes, we must consider their e¤ects on leisure.
While the leisure of unemployed agents decrease due to their higher search intensities, …ring
taxes increase aggregate leisure because of the smaller number of unemployed agents in the
economy. For our parametrization, the disutility of search is so large that transiting fewer
times through unemployment increases welfare levels even when consumption is negatively
a¤ected.
16
Firing taxes also a¤ect equilibrium wages. However, preferences were selected so that income and
substitution e¤ects cancel each other exactly. As a consequence, wages have no e¤ects on the search decisions
of agents.
33
Two features of the model economy explain why the laissaiz-faire economy performs so
poorly relative to the economy with …ring taxes: 1) the rigid class of wage contracts considered, which constrain wages to be constant over time, and 2) the information structure
previous to hiring, which leads to a same wage rate being paid across all type of establishments. A consequence of these assumptions is that the laissez-faire economy displays an
excessive amount of job-turnover: establishments adjust continuously to their idiosyncratic
shocks since they face no type of adjustment costs. Firing restrictions play a crucial role in
making employers internalize the social costs of …ring workers too often.
6.2. The unemployment insurance component
We now analyze the unemployment insurance component of severance payments. To this
end, we consider an unemployment insurance system with the following properties: 1) all
laid-o¤ workers become eligible for bene…ts (· = 1), 2) bene…ts last for only one period
(Á = 0), 3) bene…ts are as large as the original severance payments of Table 4, and 4) the
system is fully …nanced by payroll taxes. Observe that under this policy regime there are no
…ring taxes (" = 0) or severance payments (¸ = 0).
To separate the insurance e¤ects from the search e¤ects, we consider two versions of the
model economy: 1) an economy with exogenous job-…nding rates, and 2) an economy with
endogenous job-…nding rates (our original case). Both economies are subject to borrowing
constraints.
34
6.2.1. Exogenous job-…nding rate
To isolate the insurance role of the UI component of severance payments, we make the job…nding rate exogenous as in Section 6.1.2, so ® = 0 and » = ´¾ is set to a constant, equal to
the average job-…nding rate under laissez-faire. Table 8 reports the e¤ects of increasing the
replacement ratio ½.
We see that the aggregate layo¤ rate of the economy is not a¤ected by changes in the
replacement ratio. The reason is that the …ring costs faced by establishments are independent
of ½. Since the job-…nding rate is exogenous and the layo¤ rate is constant, aggregate
employment remains the same.
Replacement ratios have interesting e¤ects in the variability of consumption: for small
values of ½ (less than three months of wages) consumption becomes less variable, but for high
values of ½ it becomes much more volatile. Since the duration of a typical unemployment
spell is short (about two model periods, on average), small values of ½ help agents smooth
consumption over their unemployment periods. But high values of ½ make their income
streams too variable: agents become overinsured.
In fact, when UI bene…ts are larger than four model periods of wages (½ ¸ 4) unemployed
agents end up saving their UI bene…ts to …nance consumption during their employment
periods. For ½ = 8 the increase in savings is so signi…cant that the stock of capital is
positively a¤ected. This gives rise to small increases in output and consumption. However,
welfare is lower due to the larger consumption variability.
35
6.2.2. Endogenous job-…nding rate
We reintroduce endogenous job …nding rates to evaluate how the UI component of severance
a¤ect search decisions: preferences and search technology are made identical to the original
economy of Table 4. Table 9 reports the results.
In addition to the insurance e¤ects analyzed in the previous case, we see that higher
replacement ratios have a negative e¤ect in the aggregate job-…nding rate of the economy.
It is important to note that, since UI bene…ts are paid once and for all at the time that
agents are laid o¤ (Á = 0), agents are not subsidized for staying unemployed. The reason
why search intensities are lower is that agents enter unemployment with higher assets than
before. Since they can a¤ord to remain unemployed longer, they decide to put less e¤ort in
the search activity.
Observe that the smaller job-…nding rate decreases aggregate employment, which has
a negative e¤ect on output and consumption levels. Since aggregate leisure remains the
same (the higher leisure enjoyed by the unemployed is compensated by the larger number
of unemployed agents), welfare is lower than in the previous economy with exogenous job…nding rates (Table 8).
It is important to emphasize that, even though the UI component of severance payments
has negative e¤ects on employment, output, consumption and welfare, the e¤ects are small.
Most of the e¤ects of severance payments are due to their …ring tax component.
36
7. Unemployment insurance
The analysis of the previous two sections leave us with an apparent contradiction. Section 5
established that high unemployment experiences in Europe can be explained by labor market
policies. On the other hand, Section 6 found that severance payments have large positive
e¤ects on aggregate employment. These two …ndings imply that the high unemployment
experiences of Europe must be (over) explained by generous UI systems. The apparent dif…culty is that Section 6.2.2 introduced large UI bene…ts and found small e¤ects in aggregate
employment.
This section shows that a combination of large replacement ratios and duration of bene…ts
can indeed generate high unemployment rates, i.e. that the small e¤ects of UI bene…ts in
Section 6.2.2 were a consequence of the short duration of bene…ts assumed (Á = 0). To
do this, we consider the U.S. regime as our benchmark case and analyze one dimensional
changes in policy parameters. In particular, we analyze changes in the replacement ratio
½ and the persistence of UI bene…ts Á, while all other policy parameters are set to their
benchmark U.S. values. Table 10 shows the results of the experiments.
Similarly to Section 6.2.2, we see that UI bene…ts have no e¤ects on layo¤ rates (since
…ring costs remain the same). On the contrary, higher replacement ratios ½ and longer durations of bene…ts Á have large negative e¤ects on job-…nding rates, producing large increases in
unemployment. Note that these large negative e¤ects on job-…nding rates contrast to those
observed in Table 9 (one period duration of UI bene…ts). This is not surprising. In addition
to the wealth e¤ects captured in Table 9, job-…nding rates decrease due to an important
moral hazard e¤ect: higher UI bene…ts increase the opportunity cost of …nding employment
37
(this is true when UI bene…ts persist over time). Note that changes in the replacement ratio
have much smaller e¤ects than changes in the expected duration of UI bene…ts.
In terms of welfare, we …nd that agents are better o¤ when no UI system is in place than
in any of the UI systems analyzed. On the contrary, Hansen and Imrohoroglu [5] found that
UI bene…ts can potentially increase welfare in each of the economies they considered. There
are two main reasons for this di¤erence. First, we allowed a life cycle motive for savings,
which is absent in Hansen and Imrohoroglu [5]. Agents save so much for retirement that they
can easily …nance their (typically) short unemployment spells without su¤ering substantial
drops in consumption. As a consequence, UI bene…ts play a minor insurance role in this
economy. Second, our model was calibrated to reproduce the large empirical elasticity of the
hazard rate with respect to unemployment bene…ts reported by Meyer [9]. As a result, agents
decrease their search intensities considerably in response to the disincentives introduced by
the UI system. The associated contractionary e¤ects more than outweigh the weak insurance
bene…ts of the UI system, and lead to substantial welfare losses.
8. Conclusions
We have constructed a general equilibrium model that captures important features for the
analysis of job security provisions, mainly: 1) endogenous establishment level dynamics, 2)
imperfect insurance markets, and 3) endogenous search decisions. The model was used to
evaluate the e¤ects of severance payments.
The main result of the paper is that severance payments can have large positive e¤ects on
employment and welfare (contrary to previous studies that analyzed severance payments in
38
frictionless environments). As a consequence, the high unemployment experiences of Europe
cannot be explained (in the context of our model) by large severance payments, but by
generous UI systems (in particular, by long durations of bene…ts). Interestingly, we …nd that
the …ring penalty component of severance payments is crucial for understanding their total
e¤ects.
It is important to emphasize the central role that endogenous search decisions have played
in our analysis. Severance payments not only decreased unemployment rates due to their
negative e¤ects on layo¤ rates, but because of their positive e¤ects on job-…nding rates:
agents increased their search intensities substantially in response to the longer employment
spells they faced.
Endogenous search decisions were also crucial for generating large welfare bene…ts. When
search produced no disutility (job-…nding rates were exogenous) severance payments gave rise
to substantial welfare losses through two important mechanisms: 1) a negative productivity
e¤ect, and 2) a decrease in the value of establishments (which reduced the amount of assets
available for smoothing consumption across employment states). On the contrary, when
search produced disutility (job-…nding rates were endogenous) severance payments increased
welfare levels because agents transited fewer times through unemployment.
It is important to note several quali…cations to our analysis. First, we restricted ourselves
to long-run comparisons. Welfare results may di¤er substantially once transitional dynamics
are considered. Second, by abstracting from voluntary quits and emphasizing involuntary
layo¤s, we may have overestimated the welfare costs of unemployment. Therefore, we may
have overemphasized the welfare role of severance payments in reducing unemployment rates.
Finally, we analyzed an extremely rigid class of labor contracts. More ‡exible contracts would
39
tend to (partly) internalize the social costs of …ring workers too often, reducing the role for
mandated severance payments.
Regarding these quali…cations, we view our results as being indicative of the type of
e¤ects that are missed when abstracting from search frictions and contractual rigidities:
the above elements should be incorporated to the analysis before reaching de…nite policy
recommendations.
40
A. Appendix
This appendix describes an algorithm to compute steady state equilibria. The problem will
be reduced to solving one equation in one unknown: the interest rate i. The algorithm is
given by the following steps:
1) Fix the interest rate at some arbitrary value i.
2) Given this interest rate and the rental rate r obtained from equation (19), …x the
wage rate w¤ to some arbitrary value and solve the establishments’ problem (6) to get the
corresponding value function V (e; s) and optimal decision rules k (e; s) and n (e; s) (all as
function of w¤ ). Then, …nd the w¤ that gives the free entry condition (20).
3) Fix the establishments creation º to one. Given the decision rules of establishments
obtained in step 2, iterate with the law of motion for x in equation (21) to …nd the stationary
distribution x (e; s) across establishment types. Note that this x (e; s) is correct up to the
yet unknown proportional scaling factor º.
4) Use the distribution x (e; s) found in step 3 and the decision rule n (e; s) found in step
2 to construct the probabilities ¤ in (11) and the distribution ¡ in (22). Note that this ¡ is
correct since x enters both in its numerator and denominator (the still unknown proportional
scaling factor of x cancels out).
4) Fix the after payroll tax wage rate w to one. Then, solve by value function iteration
the problems of employed, unemployed and retired agents given by equations (8), (12) and
(16). This delivers the saving decision rules g H (a; b; m), g U (a; b; m), and g R (a), as well as
the consumption decision rules cH (a; b; m), cU (a; b; m), and cR (a), and the search decision
rule ´(a; b; m). Given these decision rules, we …nd the stationary distributions y H (a; e; s),
41
y U (a; b; m), and y R (a) iterating with equations (23), (24), (25) and (26).
5) Note that under the preferences we use, search decisions are homogenous of degree
zero with respect to w. It follows that the left hand side of equation (30) gives the correct
number of agents arriving to the labor market every period. Consequently, equation (30) is
used to solve for the correct scaling factor º for x as follows:
º=
a;b;m:
P
g U (a;b;m)
P
e;s
=
a0
(1 ¡ ³) y U (a; b; m)´(a; b; m)¾
max [0; n (e; s) ¡ (1 ¡ ³)e] x (e; s)
(34)
The correct measure across establishments types is then obtained by multiplying x by the
scaling factor º.
6) Given the correct x obtained in the previous step, the aggregate stock of capital K is
obtained from equation (31).
7) Given w¤ , x, y H , and y U , the government budget constraint (27) is used to solve for
the correct after payroll tax wage rate w.
8) Since under the preferences we use consumption decisions are homogeneous of degree
one with respect to w, the aggregate consumption obtained from equation (29) is multiplied
by the w found in step 7 to obtain the correct amount of aggregate consumption C:
9) Finally, we check if the interest rate i guessed in step 1 is an equilibrium interest rate
by verifying that the market clearing condition for consumption (28) is satis…ed. Steps 1
through 9 are repeated under a new guess for the interest rate i.
42
References
[1] Anderson, P. and Meyer, B. 1993. The E¤ects of Unemployment Insurance Taxes and
Bene…ts on Layo¤s Using Firm and Individual Data. Working Paper, Northwestern
University.
[2] Blank, R. M. and Card, D. 1988. Recent Trends in Insured and Uninsured Unemployment: Is There an Explanation? Manuscript, Princeton University.
[3] Bentolila and G. Bertola, 1990. Firing Cost and Labour Demand : How Bad is Eurosclerosis”, Review of Economic Studies, 57, 381-402.
[4] Davis, S. and Haltiwanger, J. 1990. Gross Job Creation and Destruction: Microeconomic
Evidence and Macroeconomic Implications. NBER Macroeconomics Annual, V, 123-168.
[5] Hansen, G. and Imrohoroglu, A. 1992. The Role of Unemployment Insurance in an
Economy with Liquidity Constraints and Moral Hazard. Journal of Political Economy,
100, 110-142.
[6] Hopenhayn, H. and R. Rogerson. 1993. Job Turnover and Policy Evaluation: A General
Equilibrium Analysis. Journal of Political Economy, 101, 915-938.
[7] Lazear, E. 1990. Job Security Provisions and Employment. Quarterly Journal of Economics, 105, 699-726.
[8] Mehra, R. and Prescott, E. 1985. The Equity Premium: A Puzzle. Journal of Monetary
Economics, 15, 145-161.
43
[9] Meyer, B. 1990. Unemployment Insurance and Unemployment Spells. Econometrica, 58,
757-782.
[10] Millard, S. and Mortensen, D. 1994. The Unemployment and Welfare E¤ects of Labour
Market Policy: A Comparison of the U.S. and the U.K. Mimeo, Northwestern University.
[11] Mortensen, D. and Pissarides, C. 1994. Job Creation and Job Destruction in the Theory
of Unemployment. Review of Economic Studies, 61, 397-415.
[12] Employment Outlook. 1994. OECD. Paris
[13] Facts, Analysis, Strategy. Paris, 1994.
[14] Veracierto, M. 1996. Policy Analysis in an Aggregate Model of the Employment Creation
and Destruction Process. CAE Working Paper #96-12. Cornell University.
44
TABLE 1
BENCHMARK PARAMETER VALUES
Preferences
$ = 0.994248
Time discount
" = 15.5
Share search disutility
J = 0.98
Curvature search disutility
Technology
2 = 0.19
Capital share
( = 0.58
Labor share
* = 0.011
Dep. rate
µ = 1950.0
Fixed entry cost
F = 0.98
Curv. Search Tech.
Productivity Shocks
s0 = 0.0
Exit shock
s1 = 1.0
Low productivity
s2 = 2.12
High productivity
Distribution over Initial Productivity Shocks
R1 = 0.50
Fraction with s1
R2 = 0.50
Fraction with s1
Transition Matrix for Productivity Shocks
B = 0.0037
Exit rate
T = 0.973
Persistence
Demographics
. = 0.0031
Retirement rate
h = 0.9917
Survival rate (retirees)
Policy parameters (benchmark economy)
8 = 0.0
Severance
g = 0.30
Firing tax
D = 0.66
Replacement ratio
45
N = 0.50
Duration UI
6 = 0.50
Eligibility UI
TABLE 2
POLICY PARAMETERS :
Unemployment Benefits
Replacement
Ratio : D
Duration:
1/(1-N)
Job Security
Fraction
eligible : 6
Severance :
8
Firing tax :
,
Laissez Faire
0.00
0.0
0.0
0.00
0.00
US
0.60
1 quarter
0.50
0.0
0.30
Europe UK
0.36
1 year
1.00
0.67 (1 mo.)
0.00
Europe High
0.40
3 years
1.00
4.0 ( ½ year )
0.00
46
TABLE 3
POLICY REGIMES
U.S.
Laissezfaire
European Job-Protection
U.K.
High
Job Finding Rate
51.7 %
61.0 %
31.8 %
23.6 %
Layoff Rate
2.8 %
2.9 %
2.8 %
2.6 %
Unemployment Rate
5.7 %
4.9 %
8.9%
10.9 %
Employment
100.0
100.8
96.8
94.7
Output
100.0
100.8
97.0
94.9
Capital
100.0
100.7
97.1
95.8
Consumption
100.0
100.8
96.9
94.5
Std. Dev. Consumption
100.0
100.9
96.1
94.2
Leisure unemployed
100.0
80.9
140.8
157.4
Aggregate leisure
100.0
100.0
100.1
100.3
Welfare
100.0
100.4
98.2
97.8
47
TABLE 4
SEVERANCE PAYMENTS
8 = 0.0
None
8 = 0.67
1 mo.
8 = 2.0
3 mo.
8 = 4.0
6 mo.
8 = 8.0
12 mo.
Job Finding Rate
61.0 %
61.4 %
62.1 %
63.8 %
70.5 %
Layoff Rate
2.9 %
2.8 %
2.8 %
2.6 %
2.1 %
Unemploym. Rate
4.9 %
4.8 %
4.7 %
4.3 %
3.2 %
Employment
100.0
100.1
100.2
100.6
101.7
Output
100.0
100.2
100.5
100.7
99.5
Capital
100.0
100.3
100.8
101.5
101.5
Assets
100.0
99.7
99.0
98.0
94.2
Consumption
100.0
100.1
100.2
100.3
98.7
Std. Dev. Consump.
100.0
100.2
100.7
101.5
102.1
Leisure unemployed
100.0
99.2
97.3
93.1
75.9
Aggregate leisure
100.0
100.0
100.1
100.2
100.5
Welfare
100.0
100.2
100.7
101.6
103.7
Months of wages
48
TABLE 5
FIRING TAXES REBATED AS EMPLOYMENT SUBSIDIES
Complete Insurance Markets, Exogenous Search Intensity
, = 0.0
None
, = 0.67
1 mo.
, = 2.0
3 mo.
, = 4.0
6 mo.
, = 8.0
12 mo.
Job Finding Rate
61.0 %
61.0 %
61.0 %
61.0 %
61.0 %
Layoff Rate
2.9 %
2.8 %
2.8 %
2.6 %
2.0 %
Unemploym. Rate
4.9 %
4.9 %
4.7 %
4.5 %
3.7 %
Interest Rate
4.0 %
4.0 %
4.0 %
4.0 %
4.0 %
Employment
100.0
100.1
100.1
100.4
101.3
Output
100.0
100.0
100.0
99.7
97.0
Capital
100.0
100.0
100.0
99.7
97.0
Assets
100.0
99.3
98.0
95.8
89.1
Consumption
100.0
100.0
100.0
99.7
97.1
Std. Dev. Consump.
100.0
100.0
100.0
100.0
100.0
Leisure unemployed
Not def.
Not def.
Not def.
Not def.
Not def.
Aggregate leisure
Not def.
Not def.
Not def.
Not def.
Not def.
Welfare
100.0
100.0
100.0
99.7
97.1
Months of wages
49
TABLE 6
FIRING TAXES REBATED AS EMPLOYMENT SUBSIDIES
No Insurance, Exogenous Job-Finding Rate
, = 0.0
None
, = 0.67
1 mo.
, = 2.0
3 mo.
, = 4.0
6 mo.
, = 8.0
12 mo.
Job Finding Rate
61.0 %
61.0 %
61.0 %
61.0 %
61.0 %
Layoff Rate
2.9 %
2.8 %
2.8 %
2.6 %
2.0 %
Unemploym. Rate
4.9 %
4.9 %
4.7 %
4.5 %
3.7 %
Interest rate
4.0 %
4.0 %
4.0 %
3.9 %
3.8 %
Employment
100.0
100.1
100.1
100.4
101.3
Output
100.0
100.2
100.4
100.6
98.9
Capital
100.0
100.3
100.8
101.4
100.7
Assets
100.0
99.7
99.1
97.9
93.3
Consumption
100.0
100.1
100.3
100.2
98.3
Std. Dev. Consump.
100.0
100.2
100.7
101.1
100.0
Leisure unemployed
Not def.
Not def.
Not def.
Not def.
Not def.
Aggregate leisure
Not def.
Not def.
Not def.
Not def.
Not def.
Welfare
100.0
100.0
99.7
99.2
96.1
Months of wages
50
TABLE 7
FIRING TAXES REBATED AS EMPLOYMENT SUBSIDIES
No Insurance, Endogenous Job-Finding Rate
, = 0.0
None
, = 0.67
1 mo.
, = 2.0
3 mo.
, = 4.0
6 mo.
, = 8.0
12 mo.
Job Finding Rate
61.0 %
61.7 %
63.3 %
66.2 %
74.6%
Layoff Rate
2.9 %
2.8 %
2.8 %
2.6 %
2.0 %
Unemploym. Rate
4.9 %
4.8 %
4.6 %
4.2 %
3.1 %
Employment
100.0
100.1
100.3
100.7
101.9
Output
100.0
100.2
100.6
100.9
99.5
Capital
100.0
100.4
101.0
101.7
101.2
Assets
100.0
99.8
99.2
98.2
93.8
Consumption
100.0
100.2
100.4
100.6
98.8
Std. Dev. Consump.
100.0
100.3
101.0
101.6
101.0
Leisure unemployed
100.0
98.2
94.2
86.9
65.3
Aggregate leisure
100.0
100.0
100.1
100.2
100.5
Welfare
100.0
100.3
100.8
101.9
104.2
Months of wages
51
TABLE 8
UNEMPLOYMENT INSURANCE WITH DURATION OF BENEFITS
EQUAL TO ONE MODEL PERIOD
Exogenous Job-Finding Rate
D = 0.0
None
D = 0.67
1 mo.
D = 2.0
3 mo.
D = 4.0
6 mo.
D = 8.0
12 mo.
Job Finding Rate
61.0 %
61.0 %
61.0 %
61.0 %
61.0 %
Layoff Rate
2.9 %
2.9 %
2.9 %
2.9 %
2.9 %
Unemploym. Rate
4.9 %
4.9 %
4.9 %
4.9 %
4.9 %
Employment
100.0
100.0
100.0
100.0
100.0
Output
100.0
100.0
100.0
100.0
100.2
Capital
100.0
100.0
100.0
100.0
100.3
Consumption
100.0
100.0
100.0
100.0
100.1
Std. Dev. Consump.
100.0
99.9
99.9
100.2
101.6
Leisure unemployed
Not def.
Not def.
Not def.
Not def.
Not def.
Aggregate leisure
Not def.
Not def.
Not def.
Not def.
Not def.
Welfare
100.0
100.0
100.0
99.9
99.7
Months of wages
52
TABLE 9
UNEMPLOYMENT INSURANCE WITH DURATION OF BENEFITS
EQUAL TO ONE MODEL PERIOD
Endogenous Job-Finding Rate
D = 0.0
None
D = 0.67
1 mo.
D = 2.0
3 mo.
D = 4.0
6 mo.
D = 8.0
12 mo.
Job Finding Rate
61.0 %
60.6 %
59.8 %
58.6 %
56.0 %
Layoff Rate
2.9 %
2.9 %
2.9 %
2.9 %
2.9 %
Unemploym. Rate
4.9 %
4.9 %
5.0 %
5.1 %
5.3 %
Employment
100.0
100.0
99.9
99.8
99.6
Output
100.0
100.0
99.9
99.8
99.8
Capital
100.0
99.9
99.8
99.8
100.0
Consumption
100.0
100.0
99.9
99.8
99.7
Std. Dev. Consump.
100.0
99.9
99.8
100.0
100.9
Leisure unemployed
100.0
101.0
103.0
106.2
112.8
Aggregate leisure
100.0
100.0
100.0
100.0
100.0
Welfare
100.0
100.0
99.9
99.9
99.5
Months of wages
53
TABLE 10
UNEMPLOYMENT INSURANCE
(Variations around US parameters)
DURATION of UI BENEFITS
N = 0.0
½ qtrs
N = 0.50
1 qtrs
N = 0.75
2 qtrs
N = 0.875
4 qtrs
N = 1.0
forever
61.2 %
51.7 %
37.1 %
22.1 %
0.7 %
Unemploym. Rate
4.9 %
5.7 %
7.8 %
12.4 %
81.8 %
Capital
100.8
100.0
97.8
93.1
19.7
Consumption
100.9
100.0
97.8
93.0
19.4
Std. Dev. Consump.
100.9
100.0
97.7
92.9
19.1
Welfare
100.5
100.0
98.5
94.9
24.6
Average duration
UI benefits
Job Finding Rate
REPLACEMENT RATIOS of UI BENEFITS
Replacement ratio
as fraction of wages
D = 0.0
D = 0.25
D = 0.50
D = 0.67
D = 0.75
D = 1.0
Job Finding Rate
61.3 %
57.9 %
54.1 %
51.7 %
50.4 %
47.1 %
Unemploym. Rate
4.8 %
5.1 %
5.4 %
5.7 %
5.8 %
6.2 %
Capital
100.9
100.6
100.2
100.0
99.9
99.4
Consumption
100.9
100.6
100.2
100.0
99.9
99.4
Std. Dev. Consump.
101.0
100.7
100.3
100.0
99.8
99.4
Welfare
100.5
100.3
100.1
100.0
99.9
99.6
54
@FedFRASER