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Federal Reserve Bank of Chicago

Labor Market Policies in an
Equilibrium Search Model
Fernando Alvarez and Marcelo Veracierto

WP 1999-10

Labor Market Policies in an Equilibrium Search
Model¤
Fernando Alvarez
University of Chicago, Universidad T. Di Tella and NBER
Marcelo Veracierto
Federal Reserve Bank of Chicago
June, 1999

Abstract. We explore to what extent di¤erences in employment and unemployment across economies can be generated by di¤erences in labor market
policies. We use a version of the Lucas-Prescott equilibrium search model with
undirected search and endogenous labor-force participation. Minimum wages, degree of unionization, …ring taxes, and unemployment bene…ts are introduced and
their e¤ects analyzed. When the model is calibrated to US observations it reproduces several of the elasticities of employment and unemployment with respect
to changes in policies reported in the empirical literature. We …nd that: i) minimum wages have small e¤ects; ii) …ring taxes have similar e¤ects to those found
in frictionless general equilibrium models; iii) unions have large and negative effects on employment, unemployment, and welfare; and iv) unemployment bene…ts
substantially increase unemployment and reduce welfare.
¤

Prepared for the 1999 NBER Macroeconomics Annual. We thank Je¤ Campbell, Larry
Jones, Alan Krueger, Robert Lucas, Giuseppe Moscarini, Julio Rotemberg, Nancy Stokey and
Edward Prescott for their comments, as well as seminar participants at Carnegie-Mellon, Duke,
Northwestern, ITAM, Federal Reserve Bank of Chicago, University of Chicago, and the 1999
NBER Macro Annual Conference. We also thank Enric Fernandez for excellent research assistance. The views express here do not necessarily re‡ect the position of the Federal Reserve
Bank of Chicago or the Federal Reserve System.

1

Introduction

Labor markets perform quite di¤erently across countries. An often cited example is the sharp contrast in unemployment rates between Europe and the
U.S. There are large and persistent di¤erences in labor market policies as
well.1 The goal of this paper is to explore to what extent di¤erences in labor market policies can generate di¤erences in labor market performance. In
particular, the paper builds a general equilibrium model to evaluate the aggregate e¤ects and welfare consequences of a variety of labor market policies
and institutions; mainly: minimum wages, …ring restrictions, unemployment
insurance and unions. The model embodies a McCall search model in a general equilibrium production economy by modifying the Lucas and Prescott
[15] islands model to incorporate undirected search and out-of-the-labor-force
participation.
Production takes place in a large number of separate locations called
islands which use labor as an input of production in a decreasing returns to
scale technology. In each island there is a …xed number of …rms which share
a common productivity shock. Productivity shocks follow a Markov process,
and are identically and independently distributed across islands. At the
beginning of a period, there is a given distribution of agents across islands.
After shocks are realized, agents decide whether to leave their islands and
become non-employed, or stay and work. Non-employed agents must decide
whether to search or engage in home production. If an agent searches, he is
randomly assigned to an island the following period. In this sense search is
undirected.
Labor markets are competitive within each island: …rms and workers take
the process for spot wages as given. We also assume that …rms and workers
have access to a complete set of state contingent securities indexed by the
shocks to each island. Given this market structure, workers and …rms maximize the expected discounted value of their earnings. The model abstracts
from any insurance role of labor market policies. In Alvarez and Veracierto
[1] we analyzed unemployment insurance and severance payments in a model
with incomplete markets and found that the insurance role of these policies
was quantitatively very small.2 Their welfare implications were dominated
by their e¤ects on productivity, search decisions and …rm dynamics. Those
1
This has been documented in a number of OECD Jobs Studies and surveyed and
analyzed by Nickel [5], among others.
2
Also see Costain [10], Hansen and Imrohoroglu [12], and Valdivia [26].

1

…ndings motivate our current assumption of complete markets: it considerably simpli…es the analysis, allowing us to analyze a richer set of policies
while still capturing most of the e¤ects of these policies.
The model is general equilibrium in the sense that: 1) wages are consistent with market clearing in each island, 2) the cross sectional distribution
of employment and wages is endogenous, 3) the endogenous distribution of
wages across islands is consistent with the incentives to search, and 4) aggregate employment is consistent with the number of workers that search and
the aggregate labor supply.
The model is closely related to two strands in the literature. First, it
incorporates important elements of industry equilibrium models where the
job creation and destruction process is determined by changes in the labor
demand of …rms. Examples of these models include Bertola and Caballero
[6], Bentolila and Bertola [4], Hopenhayn and Rogerson [13], Campbell and
Fisher [7], and Veracierto [24]. Second, it incorporates features of standard
search models where the job creation and destruction process is determined
by the accept-reject decisions of workers. Examples of these models include
McCall [17], Mortensen [20], Wolpin [25], and Lundqvist and Sargent [16].
Industry equilibrium models (e.g. Hopenhayn and Rogerson [13]) have
typically abstracted from unemployment decisions, focusing on the employment /non-employment decision. Most equilibrium models of unemployment
that have been used for policy analysis (e.g. Millard and Mortensen [19])
have abstracted from the employment/non-employment decision and studied
production units that consist of single workers. The model in this paper
incorporates all three margins: 1) the employment decision of …rms, which
allows to study …rms dynamics; 2) home vs. market production decisions,
which allows to analyze labor force participation; and 3) the search decisions
of workers, which allows to study unemployment.3 In fact, the labor market
policies that we analyze will have important consequences on all of these
margins.
We start by considering a laissez-faire regime. Since this is an economy
where the laissez-faire equilibrium is e¢cient (despite of the search frictions),
we use it as a benchmark when comparing the e¤ects of di¤erent policies.
We show how to modify the basic environment to introduce minimum wages,
unions, …ring taxes and unemployment bene…ts. In all cases, we consider
3

On the other hand, our model abstracts from entry and exit and from any search done
by …rms, two margins that have been analyzed in previous studies.

2

stationary equilibria only. We select parameters values by matching model
moments with selected U.S. statistics under a stylized version of U.S. policies.
Minimum wages are introduced as in text-book analyses: if equilibrium
wages in a given island are lower than the minimum wage, jobs must be
rationed in some way until wages equal the minimum wage. We experiment
with di¤erent ways of rationing the supply of workers. For instance, we
allow for a distinction between “insiders” and “outsiders”. We …nd that the
aggregate e¤ects of minimum wages are extremely small in all the cases.
We introduce unions, by assuming that the workers in a certain fraction
of the islands sector are unionized. As in textbook analyses, unions restrict
employment in order to increase total wage earnings. As a consequence,
unionized islands generate higher unemployment rates than competitive islands. We consider two models of unions, with quite di¤erent implications.
In one version, a union is constituted by the coalition of all workers present
in the island at a given period of time. The workers collude to extract rents
from the …xed factor, sharing the bene…ts equally among themselves. In the
other version, the union is dominated by a “union boss” who appropriates
all the rents from the …xed factor, and pays workers their opportunity cost.
We …nd that in the coalitions model of unions, higher degrees of unionization
increases the unemployment rate and decreases welfare levels substantially.
This is due to the incentives to search for a unionized island in order to appropriate rents. The rationing of employment in unionized islands contribute
to larger ‡ows into unemployment as well.
Following Bentolila and Bertola [4] and Hopenhayn and Rogerson [13],
we introduce …ring restrictions as a tax on employment reductions. This
tax makes the …rms employment decision dynamic, since increasing current
employment exposes …rms to future …ring costs. Firms react to the …ring
taxes by …ring and hiring workers less often, leading to higher unemployment
duration and lower unemployment incidence. Under our parametrization, the
decrease in unemployment incidence dominates the increase in unemployment
duration. As a consequence, …ring taxes reduce the unemployment rate in the
economy. Similarly to previous studies, we …nd that …ring taxes equivalent to
one year of wages have large negative welfare e¤ects. However, …ring taxes of
similar magnitudes as the severance payments observed in OECD countries
produce relatively small negative e¤ects.
Finally, we model unemployment insurance bene…ts as payments that accrue to workers after a job separation. In our model, unemployment bene…ts

3

have similar e¤ects as …ring subsidies.4 In particular, agents chose to stay
out of the labor force and not search as long as they are eligible for UI bene…ts. We …nd that UI bene…ts have large e¤ects on unemployment rates since
they increase both the duration and the incidence of unemployment. For instance, doubling the present value of UI bene…ts (from U.S. values) increases
unemployment rates by about 1 per cent.
Our quantitative analysis indicates that the responses of the unemployment rate and employment to changes in UI bene…ts, degree of unionization,
minimum wages and …ring taxes are broadly consistent with estimates in the
empirical literature (Nickel [5], for example). This provides some con…dence
about the structure of our model economy and the welfare results obtained.
The paper is organized as follows. Section 2 describes the economy. Section 3 describes that laissez-faire equilibrium. Section 4 introduces di¤erent
policies/institutions into the basic model. Section 5 explains our choice of parameter values. Section 6 describes the e¤ects of the di¤erent policies in the
calibrated economy. Finally, Section 7 compares these e¤ects with estimates
provided by the empirical literature.

2

The economy

The economy is populated by a measure one of ex-ante identical agents with
preferences given by:
·µ 1¡°
¶
¸
1
X
ct ¡ 1
t
E
¯
+ ht
1
¡
°
t=0

where ct is consumption of market goods, ht is consumption of home goods,
° ¸ 0, and 0 < ¯ < 1.
The market good is produced in a continuum of islands. Each island has
a production technology given by:
yt = F (zt ; gt ) ´ zt gt®
where yt is output, gt is the labor input, zt is an idiosyncratic productivity
shock and 0 < ® < 1. The productivity shock zt evolves according to the
following AR(1) process:
ln zt+1 = a + ½ ln zt + "t+1
4

In fact, they are completely equivalent when the UI bene…ts are small.

4

where "t+1 s N (0; ¾ 2 ), and 0 < ½ < 1. Realizations of zt are assumed to be
independent across islands. Throughout the paper we will refer to Q as the
corresponding transition function for zt , and to f (gt ; zt ) = @F (zt ; gt ) =@gt as
the marginal productivity of labor.
Home goods are produced in a non-market activity which requires labor
as an input of production. If an agent spends a period of time at home, he
obtains wh units of the home good. Home and market activities are mutually
exclusive: agents cannot engage in both at the same time.
At the beginning of every period there is a given distribution of agents
across islands. An island cannot employ more than the total number of agents
xt present in the island at the beginning of the period. If an agent stays in
the island he is currently located, he produces market goods and starts the
following period in that same location. Otherwise, the agent leaves the island
and becomes non-employed.
A non-employed agent has two alternatives. First, he can leave the labor
force and engage in home production during the current period. The following period the agent will remain non-employed. The second alternative is to
search. If the agent searches, he obtains zero home production during the
current period but becomes randomly assigned to an island at the beginning
of the following period. A key feature of the search technology is that agents
have no control over which island they will be assigned to, i.e. search is
undirected. In particular, we assume that searchers arrive uniformly across
all islands in the economy.
Hereon, we refer to agents doing home production as being “out of the
labor force”, agents working in the islands sector as “employed”, and agents
searching as “unemployed”.
We now describe feasibility for stationary allocations.5 An island is indexed by its current productivity shock z and the total number of agents x
available at the beginning of the period. Feasibility requires that the island’s
employment level, denoted by g(x; z), cannot exceed the number of agents
initially available:
g (x; z) · x
The number of agents in the island at the beginning of the following period,
denoted by x0 , is given by:
x0 = U + g (x; z)
5

Since our analysis will focus on steady state equilibria, we restrict our discussion of
feasibility to stationary allocations.

5

where U is total unemployment in the economy. Note that this equation
uses the fact that unemployed agents become uniformly distributed across
all islands in the economy.
The law of motion for x and the Markov process for z generate an invariant
distribution ¹ which satis…es:
Z
0
0
¹ (X ; Z ) =
Q (z; Z 0 ) ¹ (dx £ dz)
f(x;z): g(x;z) + U 2 X 0 g

for all X 0 and Z 0 : This equations states that the total number of islands with
a number of agents in the set X 0 and a productivity shock in the set Z 0 is
given by the sum of all islands that transit from their current shocks to a
shock in Z 0 and chose an employment level such that x0 is in X 0 :
Aggregate employment N is then given by:
Z
N = g (x; z) ¹ (dx £ dz)
and aggregate consumption by:
Z
c = F (g (x; z) ; z) ¹ (dx £ dz) :
Both expressions are obtained by adding the corresponding magnitudes across
all islands in the economy.
Finally, the number of agents that stay out-of-the-labor-force cannot be
negative:
1 ¡ U ¡ N ¸ 0:

3

Laissez-Faire Competitive Equilibrium

In this section we describe a competitive equilibrium with complete markets.
For expositional purposes, we …rst discuss the case where the market good
and the home good are perfect substitutes, i.e. where ° = 0. The case
° > 0 will be discussed at the end of the section. When both goods are
perfect substitutes agents seek to maximize the expected discounted value of
their wage earnings and home production. We assume competitive spot labor
markets in every island. As a consequence wages are given by the marginal
productivity of labor f .
6

Let consider the decision problem of an agent that begins a period in an
island of type (x; z) and must decide whether to stay or leave, taking the
employment level of the island g(x; z) and the aggregate unemployment level
as given. If the agent decides to stay, he earns the competitive wage rate
f (g(x; z); z) and begins the following period in the same island. If the agent
decides to leave, he becomes non-employed and obtains a value of µ (to be
determined below). His problem is then described by the following Bellman
equation:
½
¾
Z
0
0
v(x; z) = max µ; f (g(x; z); z) + ¯ v (g(x; z) + U; z ) Q (z; dz )
(1)
where v(x; z) is the expected value of beginning a period in an island of type
(x; z).
At equilibrium, the employment rule g(x; z) must be consistent with individual decisions. In particular,
(i) if v(x; z) > µ (agents are strictly better-o¤ staying than leaving):
g(x; z) = x

(2)

(ii) if v(x; z) = µ (agents are indi¤erent between staying or leaving):
g(x; z) = g¹ (z)

(3)

where g¹ (z) satis…es:
µ = f (¹
g (z) ; z) + ¯

Z

v (¹
g (z) + U; z 0 ) Q (z; dz 0 ) :

(4)

Figure 1 illustrates the labor market within an island. Between 0 and
x, the labor supply is in…nitely elastic at µ since at that value agents are
indi¤erent between staying or leaving. For values larger than µ all agents
prefer to stay, so the labor supply becomes inelastic at x. For values lower
than µ all agents prefer to leave, so the labor supply becomes inelastic at
zero.
The downward sloping curve is the marginal value of a worker at the
island, which can be interpreted as a demand function for labor. If the
intersection of both curves occurs at the left of x, the equilibrium employment
level is g¹ (z) : Otherwise, the equilibrium employment level is x.
Figures 2 and 3 depicts the equilibrium values v(x; z) and equilibrium
employment g(x; z) that correspond to Figure 1. If x is larger than g¹ (z) the
7

equilibrium employment is g¹ (z) and the equilibrium value is µ. If x is smaller
than g¹ (z) the equilibrium employment is x and the equilibrium value is the
marginal value of labor evaluated at x.
Let now consider the problem of a non-employed agent who must decide
whether to go home and obtain home production or search for a job. If the
agent chooses to stay out of the labor force, he obtains wh of home goods
during the current period but remains non-employed the following period. If
the agent decides to search, he obtains no home production during the current
period but gets a new draw at the beginning of the following period from
the invariant distribution of islands ¹. Thus the problem of a non-employed
agent is described by the following equation:
½
¾
Z
h
µ = max w + ¯µ; ¯ v(x; z)¹(dx; dz)
(5)
R
If wh + ¯µ < ¯ v(x; z)¹(dx; dz) (non-employed agents strictly prefer to
search than stay at home) no one stays at home and employment feasibility
becomes:
Z
U + g (x; z) ¹ (dx £ dz) = 1
(6)
R
If wh + ¯µ = ¯ v(x; z)¹(dx; dz) (non-employed agents are indi¤erent
between searching and staying at home) some agents may stay out-of-thelabor-force and employment feasibility becomes:
Z
U + g (x; z) ¹ (dx £ dz) · 1
(7)
R
The inequality wh + ¯µ > ¯ v(x; z)¹(dx; dz) implies that U = 0, which
is inconsistent with an equilibrium (see Alvarez and Veracierto [2]). It follows
that:
Z
µ = ¯ v(x; z)¹(dx; dz):
(8)
In Alvarez and Veracierto [2] we show that despite the search frictions,
this is an economy where the Welfare Theorems hold: laissez-faire competitive allocations coincide with the stationary solutions to a Pareto problem.
We also establish the existence and uniqueness of stationary competitive
equilibria. Moreover, our proof provides an e¢cient algorithm to compute
the unique steady state equilibrium.
8

When ° > 0 market goods and home goods are imperfect substitutes,
which is the preference speci…cation used by Hopenhayn and Rogerson [13]
to analyze the employment and welfare e¤ects of …ring taxes. Following
them, we assume that agents have access to employment lotteries and …nancial markets where they can diversify the income risk associated with search
and employment histories.6 The employment lotteries are not realistic. Nevertheless we think that the tractability that they bring to the problem more
than outweigh their lack of realism.
The case of ° > 0 requires only minor modi…cations to the equilibrium
conditions presented above. If µ is interpreted as the present value of search
in terms of market goods, equation (8) is satis…ed by de…nition and the functional equation (1) still describes optimal behavior by agents and …rms within
the islands sector. The only equilibrium condition that must by modi…ed is
the one that determines the optimal mix of agents between market and home
activities. The new relevant condition is:
wh
· c¡° µ
1¡¯
The left hand side of this equation gives the present value gain of increasing by one unit the number of agents in the home sector. The right hand
side represents the present value loss of decreasing by one unit the number
of agents that search: it is the present value of forgone wages in terms of
consumption goods, µ, times the marginal utility of consumption, c¡° . At
equilibrium, both sides must be equal if there is a positive number of agents
at home. If the right-hand-side is larger than the left-hand-side, no one must
be at home in equilibrium.
In Alvarez and Veracierto [2] we show that the equilibrium unemployment
rate is independent of the value of °. Instead ° determines the elasticity of
the labor supply, with ° = 0 corresponding to an in…nitely elastic labor
supply and a large ° corresponding to a low elasticity.
In the description that follows of the equilibrium conditions for the di¤erent policies we focus on the case where ° = 0 to simplify the exposition. The
case where ° > 0 would require modi…cations to the optimal non-employment
decisions analogous to the ones just described.
6

Prescott and Rios-Rull [23] show how to use classical competitive equilibrium analysis
to study a similar economy by using lotteries.

9

4

Labor Market Policies

In this section we introduce a variety of labor market policies and institutions
to our model economy, in particular, we consider minimum wages, unions,
…ring taxes, and unemployment insurance.

4.1

Minimum wages

The …rst labor market policy we consider is a minimum wage legislation. If
equilibrium wages in an island are lower than the mandated minimum wage
w, employment must be rationed. In this case, a lottery determines who
becomes employed. The losers of the lottery are forced to leave the island
and become non-employed.7 Throughout the section we denote x
e(z) to be
the maximum employment level consistent with w and z, i.e.
w = f (e
x(z); z):

Let consider the problem of an agent that begins a period in an island of
type (x; z). If g(x; z) < x~ (z), the minimum wage does not bind in the island
and the problem of the agent is similar to laissez faire:
½
¾
Z
0
0
v(x; z) = max µ; f (g(x; z); z) + ¯ v (g(x; z) + U; z ) Q (z; dz )
But if g(x; z) = x~ (z), the minimum wage binds and an employment lottery
takes place. Since the lottery treats all agents the same way, the probability
that the agent wins is given by x
e(z)=x. In that case he receives the minimum
wage w during the current period and begins the following period in the same
island. His expected value is then given by:8
·
¸
Z
x
e(z)
x¡x
e(z)
0
0
v(x; z) =
µ
f(e
x(z); z) + ¯ v(~
x (z) + U; z )Q(z; dz ) +
x
x
7

In actual computations we allow the losers of the lotteries to stay in the islands if they
so desire. But (except for extreme cases) we found that they always preferred to leave
than to stay without working. As a consequence, here we describe the more restrictive but
simpler case where agents are forced to leave. In Alvarez and Veracierto [2] we discuss the
more general case.
R
8
In Alvarez and Veracierto [2] we show that f(e
x(z); z)+¯ v(~
x (z)+U; z 0 )Q(z; dz 0 ) > µ:
agents always prefer to go through the employment lottery than to leave directly.

10

Figure 4 illustrates the labor market when the minimum wage binds. At
the equilibrium employment level, wages are lower than the minimum wage.
Hence, the labor supply must be rationed down to x~ (z) workers.
The decision problem of non-employed agents as well as the rest of the
equilibrium conditions are the same as under laissez-faire.
4.1.1

Insider-Outsider model of minimum wages

We explore a variation on the previous case in order to capture the distinction between “insiders” and “outsiders”. In this case we assume that when
the minimum wage is binding, the rationing scheme gives priority to the
previously employed agents. More speci…cally, the agents that worked in the
island last period (the “insiders”, of which there are x¡U), are given priority
over the ones that searched last period and just arrived (“the outsiders”, of
which there are U ). We assume that if rationing must take place, one of the
following two cases applies: either 1) all “insiders” stay employed and the
remaining x~ (z) ¡ x ¡ U positions are rationed between the U “outsiders”,
or 2) the available x~ (z) positions are rationed between the x ¡ U “insiders”
and none of the U “outsiders” are employed.
The analysis of minimum wages for this case is similar to the previous one,
but it requires some additional notation to consider the di¤erent problems
of “outsiders” and “insiders”. The details of the analysis can be found in
Alvarez and Veracierto [2].

4.2

Unions

We assume that a fraction ¸ of the islands are unionized. In these islands a
union determines the total labor supply, taking the wages of the rest of the
economy as given. Once the union decides how many agent to work in the
island, there is a competitive market where workers are paid their marginal
productivity. Agents that are restricted from entering this competitive labor
market leave the island and become non-employed. We explore two extreme
assumptions on the distribution of the rents generated by the union. In the
…rst case, which we label the “coalition model”, we assume that they are
shared equally among all current union members. In the second case, which
we label the “union-boss model”, we assume that they are entirely captured
by one individual.

11

We use a simple story to illustrate the two models. Consider an economy
made out a large number of piers, where cargo must be unloaded from ships,
and where the number of ships arriving to each pier is random. Workers are
distributed across piers, and take one period to move between them. There is
a gate in each pier on the other side of which ship managers hire workers in a
competitive spot market. The two model of unions di¤er on the assumption
about the control over the gate. In the coalition model the gate is controlled
by all the workers present in the pier at the beginning of the period. In the
union-boss model the gate is controlled by a union boss.
4.2.1

The coalition model

We denote the total expected discounted earnings of the coalition in an island of type (x; z) by u(x; z). Since we assume that the monopoly rents of
the coalition are shared equally among all workers in the island, each agent
receives a value u(x; z)=x. The union maximizes the expected discounted
value of earnings of its current members. Hence, u satis…es:
Z
g
u (x; z) = max f f (g; z) g + µ [x ¡ g] + ¯
u (g + U; z 0 ) Q (z; dz 0 ) g
0·g·x
g+U
(9)
where g is the number of agents that the union allows to work -i.e. those
allowed to cross the gate-. The present discounted value of total earnings
of the agents that leave the island equals µ [x ¡ g]. On the other hand,
the total current wage earnings of the agents that become employed equal
f (g; z) g. Each of these agents receive a value u (g + U; z 0 ) =(g + U ) starting
the following period, since they will form a coalition with the new U agents
that will arrive to the island. The total expected discounted value of the g
members that are allowed to stay is given by last term in equation (9).
The Bellman equation in (9) has a non-standard structure due to the
g
endogenous discount factor ¯ g+U
: However, in Alvarez and Veracierto [2] we
show that a unique value function u satis…es this Bellman equation, that
it is concave and di¤erentiable, and that its optimal employment policy is
described by a threshold rule of the same form that in the competitive islands.
Competitive islands behave exactly the same as under laissez-faire. The
employment decision rule of unionized islands generates an invariant distribution ¹u , while the employment decision rule of competitive islands generate
an invariant distribution ¹. The decision problem of non-employed agents is
12

then given by:
½
¾
Z
Z
u (x; z) u
h
µ = max w + ¯µ; ¯¸
¹ (dx £ dz) + ¯ (1 ¡ ¸) v (x; z) ¹ (dx £ dz)
x
Note that agents that search have no control whether they will arrive to
a unionized island or not. As in the previous cases, if the right hand side
of this expression is larger than the left hand side, no-one stays out-of-thelabor-force.
4.2.2

The union boss model

In a unionized island a union boss acts as a monopolist with respect to the
competitive …rms and as a monopsonist with respect to the workers. The
union boss maximizes his own expected discounted revenue net of payments
to workers, so he solves:
½
¾
Z
0
0
V (x; z) = max f (g; z) g ¡ gµ (1 ¡ ¯) + ¯ V (g + U; z ) Q (z; dz )
0·g·x

(10)
where g is the number of workers that he allows to work. Letting µ denote
the equilibrium non-employment value for a worker, note that a worker is
indi¤erent between working at the wage µ (1 ¡ ¯) and leaving the island.
The union boss can then charge an access fee to workers, so that after paying
this fee they only receive µ (1 ¡ ¯) : In Alvarez and Veracierto [2] we show
that the optimal employment policy is described by a threshold rule similar
to that which characterizes employment in competitive islands.
Letting ¹u and ¹ be the invariant distribution corresponding to unionized
and competitive islands, optimality of search decisions requires that,
½
¾
h
w
+
¯µ;
R
µ = max
(1 ¡ ¸) ¯ v (x; z) ¹ (dx; dz) + ¸¯µ
where we use the fact that the value for a worker of arriving to an unionized
island is µ.

4.3

Firing taxes

In this section we consider a competitive equilibrium with …ring taxes: whenever a …rm reduces employment below its previous period level the …rm must
13

pay a tax ¿ per unit reduction in employment. The proceeds are rebated as
lump sum transfers.
Because of the …ring cost ¿ , the …rms’ maximization problem now becomes
dynamic. The individual state of a …rm is given by (x; n; z), where n is its
previous period employment level. The …rms’s problem is described by the
following Bellman equation:
R (x; n; z) = max f F (g; z) ¡ w (x; z) g ¡ ¿ max fn ¡ g; 0g
g¸0
Z
+¯ R (G (x; z) + U; g; z 0 ) Q (z; dz 0 ) g

(11)

where g is current employment, F (g; z) is output, and ¿ max fn ¡ g; 0g are
the …ring taxes. The …rm behaves competitively, taking the equilibrium
employment level of the island G (x; z), the equilibrium wage rate w (x; z),
and the number of agents that search U as given. We denote the optimal
employment decision rule for this problem by g (x; n; z).
Note that at equilibrium, the islands’ employment rule must be generated
by the individual decisions of …rms. In particular,
g (x; x ¡ U; z) = G (x; z) , for all x; z ;
where x ¡ U is the previous period employment level of the island.
The problem of a worker in an island of type (x; z) is given by the following
Bellman equation:
½
¾
Z
0
0
H (x; z) = max w (x; z) + ¯ H (G (x; z) + U; z ) Q (z; dz ) ; µ
(12)
where µ is the value of non-employment. The worker chooses to leave the
island whenever the expected discounted value of wages in the island is less
than the value of non-employment. Similarly to …rms, workers behave competitively taking the island’s employment level G (x; z), the equilibrium wage
rate w (x; z), and the number of agents that search U as given.
Figure 5 illustrates the behavior of an island’s labor market under …ring
taxes. The supply curve is similar to that under laissez faire: it is in…nitely
elastic at µ, and becomes inelastic at x for values larger than µ. On the
contrary, the demand for labor is substantially di¤erent. In particular, the
…ring tax introduces a wedge between the marginal value of hiring and the
marginal value of …ring a worker. This translates into a jump of size ¿ at
14

the previous period employment level n, which in equilibrium equals x ¡ U .
Note that only large enough shocks induce …rms to hire or …re workers. For
intermediate shocks, …rms will leave their labor force unchanged.
The decision problem of non-employed agents as well as the rest of the
equilibrium conditions are the same as under laissez-faire, so we omit them.
Note that equilibrium wages w (x; z) are not equal to marginal productivities
f (g (x; z) ; z). Instead wages have to be lower than marginal productivities,
e¤ectively making workers pre-pay the …ring taxes.
In Alvarez and Veracierto [2] we show that a competitive equilibrium with
…ring taxes coincide with the stationary solution to a constrained Pareto
problem, where the planner treats the employment separation costs as technological. This is an important result. It establishes that the spot labor
contracts considered above are su¢cient to exploit all mutually bene…cial
trades, even in the presence of search frictions and …ring taxes. We also
show that the equilibrium described above coincides (except for equilibrium
wages) with a competitive equilibrium where the …ring taxes are paid directly
by the workers. The advantage of this alternative decentralization is that it
is much simpler to analyze, since it only requires a small variation on the
arguments used in the laissez-faire case.

4.4

Unemployment Insurance

In this section we introduce an unemployment insurance system in which
the government pays unemployment bene…ts b to eligible agents, …nancing
the system with lump sum taxes. Non-employed agents may or may not
be eligible for bene…ts. Whenever an agent leaves an island where he was
employed during the previous period, he becomes eligible for bene…ts with
probability ·. Eligible agents lose their eligibility for the following period
with probability Ã. Agents that lose their bene…ts cannot regain eligibility
within the same spell of unemployment.9
Given the nature of the unemployment insurance system we must keep
track not only whether non-employed agents are out-of-the-labor-force or
unemployed, but whether they are eligible for bene…ts or not.
Let µ0 be the expected value of being non-employed without bene…ts, µ1
the value of being non-employed with bene…ts, U0 the new arrivals (i.e. the
9

We model the eligibility and duration of the bene…ts as stochastic to reduce the dimension of the state in the agent’s problem.

15

number of agents that searched during the previous period) which are not
eligible for bene…ts during the current period, and U1 the new arrivals which
are eligible for bene…ts during the current period. Note that U = U0 + U1 .
Agents learn whether they are eligible for bene…ts or not at the beginning of
the period.
The problem of an agent that was employed during the previous period
in an island with current state (x; z) is described by the following Bellman
equation:
½
¾
Z
0
0
v(x; z) = max ·µ1 + (1 ¡ ·)µ0 ; f (g(x; z); z) + ¯ v (g(x; z) + U; z ) Q (z; dz )
where g(x; z) and U are taken as given by the agent.
The problem of an agent that searched the previous period, has UI eligibility i and arrives to an island with current state (x; z) is given by:
½
¾
Z
0
0
ui (x; z) = max µi ; f(g(x; z); z) + ¯ v (g(x; z) + U; z ) Q (z; dz )

where i = 1 if the agent is eligible for bene…ts, and i = 0 otherwise.
We now consider the non-employment decisions of eligible and ineligible
agents. If an agent not eligible for UI bene…ts decides to stay at home, he
obtains home production wh during the current period. The following period
he will be non-employed and ineligible for bene…ts, obtaining a value µ0 . If
he decides to search, he will draw an island of type (x; z) under the invariant
distribution, obtaining a value u0 (x; z). His problem is then described by:
½
¾
Z
h
µ0 = max w + ¯µ0 ; ¯ u0 (x; z)¹ (dx; dz) :

If an agent eligible for UI bene…ts decides to go home, he obtains home
production wh during the current period. The following period he will become
ineligible for bene…ts with probability (1 ¡ Ã) and will still be eligible for
bene…ts with probability Ã;obtaining values µ1 and µ0 respectively. If the
agent decides to search he will draw an island type (x; z) under the invariant
distribution, obtaining a value u0 (x; z) with probability (1 ¡ Ã) and a value
u1 (x; z) with probability Ã, depending whether the agent loses his eligibility
for UI bene…ts or not. His decision problem is then described by the following
equation:
½
¾
h
w
+
¯
[õ
+
(1
¡
Ã)
µ
]
;
1
0
R
µ1 = b + max
¯ fÃu1 (x; z) + (1 ¡ Ã)u0 (x; z)g ¹(dx; dz)
16

Note that the agent receives UI bene…ts independently of whether he stays
out-of-the-labor-force or searches.
We denote by Ái 2 [0; 1] the fraction of non-employed agents with eligibility i = 0; 1 that decide to search. The equilibrium values of Ái must be
consistent with the optimal non-employment decision described above. In
particular,
Z
h
w + ¯µ0 > ¯ u0 (x; z)¹ (dx; dz) ) Á0 = 0
Z
h
w + ¯µ0 < ¯ u0 (x; z)¹ (dx; dz) ) Á0 = 1

and correspondingly for Á1 :
To describe aggregate consistency, it is useful to introduce the following
notation. Let Hi be the number of non-employed agents that stayed home
during the previous period and have eligibility i during the current period,
and let Di be the total number of agents with eligibility i that leave the islands during the current period. Note that D1 includes two types of agents:
1) agents that searched during the previous period, their bene…ts have not
expired during the current period, and reject employment, and 2) all previously employed agents that decide to leave their islands and gain eligibility.
In particular:10
Z
D1 =
min [U1 ; x ¡ g(x; z)] ¹(dx; dz) +
Z
· max fmin [x ¡ U1 ¡ U0 ; x ¡ U1 ¡ g(x; z)] ; 0g
On the other hand, D0 consists of: 1) all new arrivals without bene…ts that
decide not to accept employment, and 2) all previously employed agents that
leave and do not gain eligibility:
Z
D0 =
max [U0 ¡ g (x; z) ; 0] ¹(dx; dz) +
Z
(1 ¡ ·) max fmin [x ¡ U1 ¡ U0 ; x ¡ U1 ¡ g(x; z)] ; 0g :
10

Since µ1 > µ 0 , the …rst agents to leave an island are those who have just arrived
and are eligible for bene…ts, the second group to leave are those that were employed the
previous period, and the last agents to leave are those who have just arrived and are not
eligible for bene…ts.

17

In steady state, U0 , U1 , H0 and H1 satisfy their laws of motion:
U0
U1
H0
H1

=
=
=
=

Á0 (D0 + H0 ) + (1 ¡ Ã) Á1 (D1 + H1 ) ;
ÃÁ1 (D1 + H1 ) ;
(1 ¡ Á0 ) (D0 + H0 ) + (1 ¡ Ã) (1 ¡ Á1 ) (D1 + H1 ) ;
Ã(1 ¡ Á1 ) (D1 + H1 )

The market clearing condition is given by:
Z
U0 + H0 + U1 + H1 + g(x; z)¹(dx; dz) = 1:
4.4.1

UI bene…ts, …ring subsidies, …ring taxes and severance payments

We conclude this section with a brief analysis of the relationship between UI
bene…ts, …ring taxes, …ring subsidies and severance payments. De…ne p as the
expected discounted payments that an agent is entitled after a job separation,
contingent on not becoming employed until the expiration of bene…ts, so that
p=·

b
:
1 ¡ ï

(13)

In Alvarez and Veracierto [2] we show that non-employed agents with bene…ts
search (Á1 > 0) only if all non-employed agents without bene…ts search (Á0 =
1). Moreover, we establish that for small values of p, equilibria with UI
bene…ts have Á1 = 0 and 0 < Á0 < 1. In words, agents that receive UI
bene…ts do not search, and agents that have no UI bene…ts are indi¤erent
between searching and staying out-of-the-labor-force. It follows that the
only feature that is important from the UI bene…ts system is the expected
discounted value of payments p; regardless of the particular combination of
duration Ã; bene…ts per period b, and eligibility ·. Since agents eligible for
bene…ts do not search, this results shows that in our model UI bene…ts are
equivalent to a …ring subsidy by the amount p.
The previous result has the following two important corollaries about the
combined e¤ects of …ring taxes and UI bene…ts, whose proofs can be found in
Alvarez and Veracierto [2]. First, these policies can be summarized by a single
number: the expected discounted value of UI bene…ts minus of the value of
…ring taxes. In particular, if p0 ´ p ¡ ¿ > 0, then the equilibrium is the same
18

that with a …ring subsidy of p0 : Alternatively, if p0 < 0 the equilibrium is
the same than with a …ring tax of size p0 : Second, if we interpret severance
payments as a tax to the …rms proportional to the employment reductions
and a simultaneous subsidy to each worker that leaves the …rm, then one
obtains that severance payments have no e¤ect. This is a known result for
competitive markets, see for example Lazear [14]. What is interesting is that
it holds even in the presence of the search frictions.

5

Calibration

To explore the e¤ects of the labor market policies described above, we parametrize the economy in the following way. There are six structural parameters to determine: 1) the Cobb-Douglas parameter ®, 2) the time discount
factor ¯, 3) the home productivity w h , 4) the curvature parameter in the
utility function °, 4) the persistence of productivity shocks ½, and 5) the
variance of the innovations ¾ 2 . Additionally we have to chose the model
period. Parameter values are chosen to reproduce selected U.S. observations
under a policy regime that resembles the U.S. unemployment insurance system. We select a model period of one and a half months as a compromise
between computational costs and our interest to be able to match the short
average duration of unemployment in the U.S.
A characteristic of the U.S. system is that it is …nanced by experience
rated taxes. Experience rated taxes work as …ring taxes: they increase the
tax liabilities of employers when workers are …red. Anderson and Meyer [3]
report that they are quite substantial in magnitude: for each dollar that the
government pays as unemployment insurance, about 60 cents are paid by
employers as experience rated taxes. For this reason we want to consider a
policy regime both with unemployment insurance and experience rated taxes.
We use the property of the model described in Section 4.4.1 to introduce both
policies in a parsimonious way. We interpret the experience rated UI tax as
a …ring tax and set the UI bene…ts in the model to be equal to the present
value of the UI bene…ts net of this …ring tax. In particular, we consider
the “net” UI bene…ts to be 40 percent of the US unemployment insurance
bene…ts.
In a sample of agents that collected UI bene…ts between 1978 and 1983,
Meyer [18] found an average replacement ratio of about 66%. Given Anderson
and Meyer’s estimate of experience rated taxes and our previous discussion,
19

we select a replacement ratio which is 60% of Meyer’s: 26%. Meyer [18] also
reported that the average duration of agents in his sample is 13 weeks. Since
we are proceeding under the assumption that agents that collect bene…ts do
not search, we identify the 13 weeks with the average duration of UI bene…ts.
Given a model period of 6 weeks, this translates to a persistence of UI bene…ts
à of about 0.50.
The probability · that an agent becomes eligible for UI bene…ts at the
start of an unemployment spell is chosen as follows. Let h be the escape
rate from unemployment and I the ‡ow out of employment. Then in steady
state:
hU = I:
(14)
Let H1 be the number of agents that stay out-of-the-labor-force collecting UI
bene…ts. Note that:
(1 ¡ Ã)H1 = ·I;
(15)

since the ‡ow out of H1 is given by the number of agents that lose their
bene…ts, and the ‡ow into H1 is equal to a fraction · of the ‡ow out of
employment. At steady state both ‡ows must be equal. Substituting (14) in
(15) we obtain:
(1 ¡ Ã) H1
·=
h
U
H1
Note that U is the ratio of agents that receive UI bene…ts to the total number
of agents that are unemployed. In OECD [21], Table 8.4, we …nd that this
ratio is about 0.35 for the U.S. economy. On the other hand, a 4 months
average duration of unemployment in the U.S. suggests a value of 1=h equal
to 2.66 model periods. The value of · consistent with these magnitudes is
0.50.
The Cobb-Douglas parameter ® was set to match a labor share of 0.64,
which is the value implicit in the NIPA accounts. The discount factor ¯
was selected so that its inverse reproduces an annual interest rate of 4%, a
compromise between the return on equity and the return on bonds.
Given the all the previous choices, the persistence of the productivity
shocks ½ and the variance of its innovations ¾ 2 were selected to generate an
average duration of unemployment equal to 4 months and an unemployment
rate of 6.2%. Note that there is no analytical relation between these parameters and the corresponding observations; we experimented until a good …t
was obtained.
20

In Alvarez and Veracierto [2] we show that the productivity of home
production wh a¤ects only the labor force participation ratio, leaving all
other ratios unchanged. The productivity wh was then selected to reproduce
a labor force participation of 0.79, which is the ratio of labor force to working
age population in the U.S. (OECD [21], Table 8.4).
The curvature parameter ° in the utility function determines the degree
of substitutability between home goods and market goods, but has no e¤ects
on steady state observations (it only a¤ects the value of w h that is needed
to reproduce a given labor force participation). However, ° is an important
determinant of the elasticity of labor supply. In particular, it can be shown
that the elasticity of labor force participation with respect to labor taxes is
equal to:
1
¿
"=¡
(16)
1 ¡ ® ¡ ®° 1 ¡ ¿
where ¿ is the labor tax.
One way of selecting ° is then to use equation (16) to calibrate to some
empirical estimate of the elasticity ". The regression coe¢cients in Nickell
[5], Table 7, indicate that a cross-country elasticity " equal to 0.18 is not
unreasonable. Since the average labor tax in Nickell’s sample is about 50%,
our choice of ® requires a value of ° equal to 8 to reproduce such elasticity.
Another way of selecting ° is to use macro observations. One stylized fact
that has been emphasized in the macroeconomic literature is that wages have
increased substantially over long period of times, while total hours worked
have displayed no trend. To reconcile this observation with the theory, preferences where income and substitution e¤ects cancel each other are needed.
This requires a choice of ° = 1 under our preference speci…cation. This parameter value is not only consistent with macro secular observations (and consequently is common in the macroeconomic literature), but is what Hopenhayn
and Rogerson [13] have used to estimate the welfare costs of …ring taxes. As
a consequence we will treat it as our benchmark, but we will also report
results under ° = 0 and ° = 8.
Table 1 reports selected parameter values under the benchmark case.11
11

Parameter values under ° = 0 and ° = 8 are available upon request.

21

6

Experiments

This section analyzes the e¤ects of the labor market policies and institutions
introduced above for the parameters selected in the previous section. In each
subsection we report how the corresponding policy a¤ects laissez-faire, which
serves as our benchmark case.
Tables 2 through 5 show the results. To illustrate the role of the elasticity
of labor supply, the tables report results for di¤erent values of °. The e¤ects
on the unemployment rate, the average duration of unemployment, and the
rate of incidence into unemployment are presented in the …rst panels of the
tables since they are independent of °. The second panels show results under
° = 0 (the case where home and market goods are perfect substitutes), the
third panels report results under ° = 1 (our benchmark log utility case),
and the fourth panels present results under ° = 8 (the low elasticity of
labor supply case). For each of these panels we report the following: 1)
total unemployment (i.e. the total number of agents U that search in the
model economy), 2) total employment, 3) total market output, and 4) total
home output. Each of these numbers is normalized by its corresponding
laissez-faire value. Additionally a welfare measure is provided. It is de…ned
as the permanent increase in consumption that must be given to agents in
the laissez-faire economy to attain the same utility level as under the policy
considered.

6.1

Minimum wages

Table 2a describes the e¤ects of minimum wages. The second column corresponds to laissez-faire, while the third and fourth columns correspond to
minimum wages equivalent to 85% and 90% of average wages, respectively.
In the …rst case only 5% of employed agents receive the minimum wage; in
the second case the fraction is 27%.
We see in Table 2a that introducing a minimum wage to an otherwise
laissez-faire economy increases the incidence of agents into unemployment.
The reason is that employment must now be rationed in islands where the
minimum wage becomes binding. For the same reason it becomes more
di¢cult for unemployed agents to …nd employment. As a consequence the
average duration of unemployment increases. Both e¤ects tend to increase
the unemployment rate relative to laissez-faire. However, we …nd that the
e¤ects are small: a minimum wage equal to 85 percent of average wages
22

increases the unemployment rate only from 5.3 percent to 5.4 percent. Higher
minimum wages can increase the unemployment rate further. But even a
minimum wage which is large enough so that 27 percent of employed agents
receive it, only increases the unemployment rate from 5.3 percent to 6.6
percent, a small e¤ect compared to other policies.
The minimum wage regulation has the e¤ect of increasing average wages.
As a result, the number of agents that search for a job (U ) increases until
indi¤erence between working at home and at the market is restored (i.e.
until equality in equation 8 is obtained). Table 2a shows that when home
and market goods are perfect substitutes (° = 0), a minimum wage equal
to 90 percent of average wages increases the number of agents unemployed
(U) by 24.7 percent. However, employment falls by 1.9 percent because
the increase in the unemployment rate is large relative to the increase in
the number of agents unemployed. The fall in employment dominates the
increase in unemployment and labor force participation decreases. This leads
to an increase in home output of 1.8 percent and a decrease in market output
of 0.5 percent.
On the other extreme when ° = 8, the e¤ects are quite di¤erent. The
fall in market output increases the marginal utility of market goods so much
that agents respond by substituting away from home activities towards market activities. As a consequence, the labor force participation increases and
home production decreases. Employment still decreases because the increase
in labor force participation is small compared to the increase in the unemployment rate. However, the fall in market output now becomes negligible.
The welfare e¤ects of minimum wages are extremely small. Even for a
minimum wage equal to 90 percent of average wages, the welfare cost is only
about 0.2 percent in terms of consumption.
In Table 2b we compute the e¤ects of minimum wages when the employment rationing scheme gives priority to “insiders” over “outsiders”. This
feature could potentially increase the duration of unemployment, since “outsiders” –i.e. agents that search- are rationed more often. However the results
are virtually the same: we still …nd small e¤ects of minimum wages.

6.2

Unions

Table 3a reports the e¤ects of the coalition model of unions. Table 3b reports
the e¤ects of the union boss model. In both cases we compare laissez faire,
with economies that have 20, 40, 60 and 80 percent of their islands unionized.
23

We describe the coalition model of unions …rst. Recall that unions obtain
monopolistic rents from the …xed factor by restricting the labor supply of its
members. As a consequence, unionized islands have higher unemployment
rates than competitive islands (for instance with 20 percent of the labor
force unionized, the unemployment rate is 4 percentage points smaller in
the competitive sector than in the unionized sector). As the number of
unionized islands increases, the aggregate unemployment rate of the economy
then increases due to a composition e¤ect. Moreover, as the size of the
unionized sector becomes larger the average duration of unemployment and
the incidence into unemployment in both sectors tend to increase. The reason
is that agents demand better conditions to become and remain employed
since it is easier for them to …nd monopolistic rents somewhere else. As a
consequence, a larger unionized sector unambiguously increases the aggregate
unemployment rate in the economy. In fact Table 3.a shows that the e¤ects
of unions are surprisingly large. When 60 percent of the islands become
unionized the unemployment rate increases from 5.3 percent to 12.5 percent.
Since unions extract rents from the …xed factor, average wages increase
with the size of the union sector (since the opportunity cost of becoming employed in the competitive sector increases, wages increase in the competitive
sector as well). When home and market goods are perfect substitutes and 60
percent of the islands become unionized, the number of agents unemployed
(U) must increase by 115.9 percent before agents again become indi¤erent
between participating in market activities and working at home (i.e. before equality in equation 8 is restored) . However, the unemployment rate
increases so much that employment falls by 16.1 percent. The fall in employment dominates the increase in the number of agents unemployed, leading
to a decrease in labor force participation and a consequent increase in home
production of 28.4 percent. Market output falls by 9.3 percent because of
the large fall in employment. Note that the e¤ects of unions are qualitatively
similar to those of minimum wages since both regimes transfer rents from
…rms towards workers. However, the e¤ects of unions are much larger since
a minimum wage legislation extracts rents only when the minimum wage
becomes binding (i.e. only wages in the lower tail of the distribution are
a¤ected) while unions extract rents at all levels.
When ° = 8, the marginal utility of home goods increases so much when
market output falls, that agents substitute away from home activities to
sustain the level of market output. In this case, the labor force participation
increases and home output consequently falls by 17.1 percent. The increase
24

in labor force is not enough to outweigh the higher unemployment rate, and
employment still falls by 3.3 percent. However, market output now decreases
only by 0.7 percent.
We …nd that the welfare cost of unions is extremely large: when ° = 1
and 60 percent of the islands become unionized, the welfare loss is 3.5 percent
in terms of consumption.
We now turn to the results under the union-boss model, as described in
Table 3.b. We see that the e¤ects are very di¤erent from the coalitions model:
larger unionized sectors lead to lower unemployment rates. To understand
this di¤erence, notice that in this case it is the “union boss” the one who
retains all monopolistic rents: workers in the union sector are merely paid
their opportunity cost. As a consequence, average wages fall as the size of the
unionized sector increases. With lower average wages, both union bosses and
competitive …rms hire more workers and unemployment rates decrease in each
sector. Observe that the unemployment rate is always higher in the unionized
sector than in the competitive sector, since union bosses restrict the labor
supply. However, the composition e¤ect doesn’t dominate: unemployment
rates fall so rapidly in each sector as the degree of unionization increases
that the economy-wide unemployment rate decreases. In fact, as the fraction
of islands unionized increases to 60 percent, the unemployment rate decreases
from 5.3 percent to 3.5 percent.
When home goods and market goods are perfect substitutes (° = 0),
the fall in average wages is so large when 60 percent of the islands become
unionized, that the number of agents that search (U) must fall by 53.9 percent
before agents again become indi¤erent between working at home and working
in the market (i.e. before equality in equation 8 is restored). The fall in
unemployment is so large that employment decreases by 29 percent, despite
the fall in the unemployment rate. The consequent reduction in labor force
participation leads to an increase of 93.7 percent in home output. On the
contrary, market output decreases by 21.4 percent.
When ° = 8, the fall in market output increases marginal utility of market
goods so much, that agents substitute away from home activities to sustain
the level of market output. Even though this e¤ect is large enough to increase employment by 1 percent, it is not enough to increase the labor force
participation: home output still increases, but only by 3.6 percent. As a
counterpart, market output decreases by merely 1.6 percent.
Notice that even though unemployment rates are lower, the negative welfare e¤ects of unions are quite large. For instance, with 60 percent of the
25

labor force unionized the welfare cost of unions is equivalent to a 1.5 percent
permanent reduction in consumption under ° = 1.
Since the two models of unions predict such di¤erent e¤ects on unemployment rates, it is important to discuss what evidence favors one type of model
over the other. Note that in the coalitions model of unions, union members
receive higher wages than workers in the competitive sector. The opposite is
true in the union-boss model. Thus, an indirect test of the relative relevance
of the two models would be provided by the sign of the union wage premium
in the data. Card [8] provides such evidence. Using panel data from the
1987 and 1988 Current Population Surveys, he reported that the union wage
premium is about 15 percent in the U.S. economy. The sign of this premium
favors the coalitions model of unions over the union-boss model. However,
the evidence in favor is stronger than this. In order to obtain a wage premium
of the magnitude reported by Card, about 20 percent of the islands must be
unionized (the generated wage premium is 12.5 percent). Under this degree
of unionization we verify that 13 percent of the workforce is employed in
the unionized sector. This is surprisingly close to the empirical counterpart
of 15.6 percent reported by Nickell[5], providing additional con…dence about
the quantitative relevance of the coalitions model of unions.

6.3

Firing taxes

Table 4 shows the e¤ects of …ring taxes that range between 3 months and
12 months of average wages. To understand these results, note that in the
presence of …ring taxes …rms change their behavior in two important ways:
1) they become less willing to …re workers (as they try to avoid current
taxes), and 2) they become less willing to hire workers (as they try to avoid
future taxes). These e¤ects tend to reduce the incidence of unemployment
and increase the average duration of unemployment, respectively. Depending
on which e¤ect is larger, the unemployment rate can decrease or increase.
Under our choice of parameter values we …nd that the e¤ect on the …ring
rate dominates: the unemployment rate decreases from 5.3 to 3.7 percent
with …ring taxes equal to 12 months of wages.
The distortions in the …ring and hiring process introduced by the …ring
taxes reduce the productivity in the islands sector quite substantially. As
a consequence wages fall considerably. When home and market goods are
perfect substitutes (° = 0) , this induces the number of agents that search
for employment to decrease by 40 percent before agents become indi¤erent
26

between searching and staying at home. The fall in the total number of
agents unemployed is so dramatic that drags employment with it, despite
the decrease in the unemployment rate. In particular, employment decreases
by 13.9 percent. The consequent fall in labor force participation increases
home output by 47.3 percent. On the other hand, market output decreases
by 12 percent both because of the decrease in employment and the distortions
introduced in the job reallocation process.
When ° = 8, the decrease in market output is so large that the marginal
utility of market goods increases quite dramatically. This induces agents to
substitute away from home activities towards market activities. As a consequence the total number of agents unemployed only falls by 16.7 percent.
This is a small decrease compared to the fall in the unemployment rate, leading to an increase in employment of 3.9 percent. Labor force participation
increases so much that home output falls by 7.2 percent. As a counterpart,
market output falls only by 0.8 percent.
It is interesting to compare our results with those obtained by Hopenhayn and Rogerson [13] who calculated the costs of …ring taxes in a frictionless economy without unemployment, where labor could freely reallocate
across production units. Since they considered log preferences we restrict our
discussion to the ° = 1 case.
Table 3 in Hopenhayn and Rogerson [13] reports that a …ring tax equivalent to one year of wages lowers output by 4.6 percent, decreases employment
by 2.5 percent, and lowers welfare by 2.8 percent in terms of consumption
in their model economy. Table 4 in this paper shows that the same policy
produces a fall of 4.5 percent in output, a decrease in employment of 2.1
percent and a welfare cost of 2.3 percent in our model economy. These results are surprisingly similar and consequently, they are robust to the search
frictions introduced. However they are not robust to the preference parameter °: As in Hopenhayn and Rogerson [13] the e¤ects of …ring taxes on
employment and output depend on the income and substitution e¤ects on
the labor supply. If the substitution e¤ect dominates –as in the ° = 0 case–
employment decreases, if the income e¤ect dominates –as in the case ° = 8
case– employment increases.

6.4

Unemployment insurance

In Table 5 we analyze the e¤ect of introducing unemployment compensations
with di¤erent expected discounted value of bene…ts into the laissez-faire econ27

omy. We measure the generosity of the UI system by the present value of
b
UI bene…ts p, given by · 1¡¯Ã
; where · is the fraction of separations that
quali…ed for UI bene…ts, b are the bene…ts per period, Ã is the per period
probability of maintaining the UI bene…ts, and ¯ is the reciprocal of the gross
interest rate. In Table 5 we calculate the equilibrium for di¤erent values of p,
starting with the one that corresponds to our depiction of U.S. policies (see
the section on calibration for the details). Recall that for the U.S. we select
p to be 0.28 of average model period wages, where the model period equals
one and a half months. The other values of p considered are 0.5, 0.75, 1.0,
and 1.25 model period of wages.
As the size of the UI bene…ts increase, workers are more willing to leave
an island after a bad shock. This increases the rate of incidence into unemployment. On the other hand, there are two e¤ects on the average duration
of unemployment. First, agents tend to accept employment more easily since
they obtain eligibility for UI bene…ts. This leads to a decrease average duration. Second, since searching for a job becomes more attractive than staying
at home without UI bene…ts, the number of agents that search (U) must
increase until agents are once again indi¤erent between both activities (i.e.
equality in equation 8 is restored). This leads to an increase in the average
duration of unemployment. In Table 5 we observe that this general equilibrium e¤ect dominates: larger UI bene…ts increase the average duration of
unemployment. Since both the rate of incidence and the average duration
of unemployment increase, the unemployment rate increases quite substantially. We see that a present value of UI bene…ts equivalent to one model
period of wages increases the unemployment rate from 5.3 percent to 11.9
percent.
When market goods and home goods are perfect substitutes ( ° = 0 ),
the general equilibrium e¤ect described above is large: the total number of
unemployed (U) increases by 179.4 percent when moving from laissez faire
to a present value of UI bene…ts equivalent to 1 model period of wages. This
increase in the total number of unemployed is so important that employment
increases by 15.2 percent despite the increase in the unemployment rate. This
leads to such an increase in labor force participation that home output falls
by 73.5 percent. As a counterpart, market output increases by 12.1 percent.
Under ° = 8, the higher market output decreases the marginal utility
of market goods inducing agents to substitute away from market activities.
As a consequence, the total number of unemployed (U ) increases by a more
moderate 136.4 percent and employment falls by 2.5 percent. The lower labor
28

force participation dampens the fall in home output to only 17.5 percent. On
the other hand, market output increases by merely 0.8 percent.
The welfare costs of introducing UI bene…ts are quite large: a present
value of UI bene…ts equivalent to 1 model period of wages reduces welfare by
2.5 percent in terms of consumption under ° = 1.

7

A comparison with the empirical evidence

We end the paper by contrasting our results with some of the empirical
evidence available on the e¤ect of di¤erent policies/regimes.

7.1

Minimum wages

While empirical studies for the U.S. economy have traditionally found that
minimum wages a¤ect teenage employment with an elasticity of about ¡0:1,
the evidence has become more tenuous over time (see Card and Krueger
[9]). The evidence that minimum wages a¤ect adult employment is even
weaker, suggesting that minimum wages have little impact on the aggregate
unemployment rate and employment level.
Card and Krueger [9] observe that in the U.S. economy only 5 percent
of workers are paid the minimum wage. Since in Table 2a the economy
with a minimum wage equal to 80 percent of average wages generates a
similar proportion of recipients, we identify it with the U.S.12 Given the
little di¤erences between that economy and laissez-faire, we …nd our results
to be broadly consistent with the empirical evidence.
While a large empirical literature has investigated the e¤ects of minimum
wages on income inequality, we consider that our model is not well suited
to address those issues. The only heterogeneity that our model generates is
due to time variation in wages: all agents face the same stochastic process
for wages. As a consequence, the wage distribution that the model produces
is too concentrated compared to the data (the standard deviation of wages
in the benchmark US case is only 13%). To analyze distributional issues we
12

In order for 5 percent of workers to be subject to the minimum wage, the minimum
wage has to be 80 percent of average wages in the model economy. In the U.S. the minimum
wage is only 26 percent of average wages (see Card and Krueger [9]). The reason for the
di¤erence is that the wage distribution is too concentrated in the model compared to the
data. See the comments in the next paragraph.

29

would have to incorporate di¤erent income groups, but that would complicate
the model considerably and is outside the scope of this paper.

7.2

Unions

In Section 6.2 we argued in favor of the coalitions model of unions over
the union-boss model due to its ability to jointly generate an empirically
relevant union wage premium and degree of unionization. We now compare
its predictions with some of the estimates found in the empirical literature.
Nickell [5] reports that union densities vary widely across countries: from
9.8 percent in France and 11 percent in Spain, up to 72 percent in Finland
and 82.5 percent in Sweden. Table 3.a. considered degrees of unionization
within this empirical range and found that unions produce large variations
in unemployment rates: from 7.1 percent to 16.3 percent. We consider the
magnitude of these e¤ects to be consistent with empirical …ndings. In particular, the coe¢cients in Nickell’s regressions indicate that the elasticity of
the unemployment rate with respect to union density is about 0.48. The
corresponding elasticity underlying Table 3.a is 0.38, which is very close to
Nickell’s estimate.13
Nickell’s regression coe¢cients also indicate an elasticity of employment
relative to union density of about -0.05. Di Tella and MacCulloch [11] provide
a similar estimate. As has been previously discussed, the corresponding
elasticity in the model economy depends on the substitutability between
home and market goods given by the parameter °. For ° = 1 the model
elasticity is -0.03 which is also close to Nickell’ s estimate.

7.3

Firing taxes

Table 4 reported the e¤ects of …ring taxes between three months and one
year of wages. We saw that …ring taxes equal to one year of wages decreased
the unemployment rate from 5.3 percent to 3.7 percent and decreased employment by 2.1 percent in the benchmark case (° = 1). These are large
e¤ects. However, …ring taxes equal to one year of wages are large compared
to observed policies in OECD countries. Table 6 reports the sum of advance
notice and severance payments (adjusted by tenure) as multiples of average
13

We calculated each of the elasticities of change relative to the economy with 20 percent
of unionization, and then we averaged them.

30

model period wages. According to this measure, one year of …ring taxes
(equal to 8 model periods) is at the upper end of what is observed.14
The sign of the relation between unemployment rate and …ring taxes in
the model economy is consistent with Nickell’s results: in his regression of
unemployment rate he …nds a negative coe¢cient on a measure of employment protection. On the other hand, Lazear [14] reports a positive coe¢cient
for severance payments. Neither of the two coe¢cients are statistically signi…cantly di¤erent from zero. Di Tella and MacCulloch [11] …nd a negative
e¤ect of labor market ‡exibility on unemployment rate controlling for random e¤ects, but the result are not signi…cant when they control for both
country and year …xed e¤ects.
Nickell [5], Lazear [14] and Di Tella and MacCulloch [11] …nd that larger
employment protection reduces aggregate employment. In our model economy, the sign of that relation depends on the degree of substitution between
home and market goods. However, for the benchmark economy (° = 1) we
…nd a negative relation. Lazear [14] reports that moving from laissez faire
to three months of severance payments reduces the employment-population
ratio by about 1 percent. In our benchmark case of ° = 1 we …nd that
three months of severance payments reduce the employment to population
ratio from 73.6 percent to 72.7 percent, which is consistent with Lazear’s
estimate.

7.4

Unemployment Insurance

Table 5 reported how changes in the present value of UI bene…ts a¤ect unemployment rates and employment levels. We found large e¤ects. But the
present values considered ranged up to 5 times the benchmark value for the
U.S. economy. While we evaluated relatively large present values of UI bene…ts, we consider that the responsiveness of the model to UI bene…ts is within
what the empirical evidence suggests.
Nickell [5] reports regression coe¢cients that imply an elasticity of the
14

Moreover, as explained at the end of the section on unemployment insurance, in the
model economy severance payments can be undone perfectly. To the extent that in actual
economies severance payments can be partially undone, the relevant measure of …ring
taxes would be lower than those shown in Table 6. For instance, if severance payments
can be undone perfectly, …ring taxes would only include expected legal costs of litigation.
For Germany, Italy, France and UK, Bentolila and Bertola [4] report that these costs are
well below one month of wages.

31

unemployment rate with respect to UI bene…ts replacement ratio of about
0.62. The average elasticity in Table 5 is 0.34, which is smaller than Nickell’s
estimate, but is of the right order of magnitude. Observe that our theory
predicts that the elasticity of the unemployment rate with respect to the replacement ratio is the same as with respect to bene…ts duration (see equation
13). The elasticity that Nickell reports with respect to bene…ts duration is
about 0.20, which is lower than his estimated elasticity with respect to the
replacement ratio. However, his coe¢cient on bene…ts duration is estimated
with a larger standard deviation.
The elasticity of employment with respect to UI bene…ts in Nickell’s calculations is -0.02.15 While the results in the model economy depend on the
substitutability between market and home goods, for the benchmark economy (° = 1) the average elasticity in Table 5 is -0.01. This elasticity is lower
than Nickell’s estimate but again is of the correct order of magnitude.

References
[1] Alvarez, F. and Veracierto, Marcelo, “Search, Self-Insurance and Job
Security Provisions,” Working Paper 98-2, Federal Reserve Bank of
Chicago, April 1998.
[2] Alvarez, F. and Veracierto, Marcelo, “Equilibrium search and labor market policies: a theoretical analysis”, working paper, 1999.
[3] Anderson, P. and Meyer, B., “The E¤ects of Unemployment Insurance
Taxes and Bene…ts on Layo¤s Using Firm and Individual Data”, Working Paper, Northwestern University, 1993.
[4] Bentolila, S. and Bertola, Giuseppe, “Firing Costs and Labour Demand:
How Bad Is Eurosclerosis?,” Review of Economic Studies, v57 n3 July
1990, pp.381-402.
[5] Nickell, S., “Unemployment and Labor Market Rigidities: Europe versus North America,” Journal of Economic Perspectives v11 n3 Summer
1997, pp. 55-74.
15

Di Tella and MacCulloch [11] also estimate negative elasticities.

32

[6] Bertola, G. and Caballero, Ricardo J., “Cross-Sectional E¢ciency and
Labour Hoarding in a Matching Model of Unemployment”, Review of
Economic Studies v61 n3 July 1994, pp. 435-56.
[7] Campbell, J. and Fisher, Jonas, “Aggregate Employment Fluctuations
with Microeconomic Asymmetries,” National Bureau of Economic Research Working Paper 5767, September 1996, pp. 23.
[8] Card, D., “The E¤ects of Unions on the Structure of Wages: A Longitudinal Analysis”, Econometrica, v64 n4, July 1996, pp 957-979.
[9] Card, D. and Krueger, A., 1995, “Myth and Measurement: The New
Economics of the Minimum Wage”, Princeton University Press.
[10] Costain, J., “Unemployment Insurance in a General Equilibrium Model
of Job Search and Precautionary Saving”, Ph.D. Thesis, University of
Chicago 1997.
[11] Di Tella, R. and MacCulloch, Robert, 1999, “The Consequences of Labor
Market Flexibility: Panel Evidence Based on Survey Data”, Harvard
Business School.
[12] Hansen, G. and Imrohoroglu, Ayse, “The Role of Unemployment Insurance in an Economy with Liquidity Constraints and Moral Hazard,”
Journal of Political Economy v100 n1 February 1992, pp. 118-42.
[13] Hopenhayn, H. and Rogerson, Richard, “Job Turnover and Policy Evaluation: A General Equilibrium Analysis,” Journal of Political Economy
v101 n5 October 1993, pp. 915-38.
[14] Lazear, E., “Job Security Provisions and Employment,” Quarterly Journal of Economics, v105, pp. 699-726, 1990.
[15] Lucas, R. and Prescott, Edward C. “Equilibrium Search and Unemployment,” Journal of Economic Theory; v7 n2 Feb. 1974, pp. 188- 209.
[16] Lundqvist, L. and Sargent, Thomas J. “The European Unemployment
Dilemma,” Journal of Political Economy v106 n3 June 1998, pp. 514-50.
[17] McCall, J., “Economics of Information and Job Search,” Quarterly Journal of Economics v84 n1 Feb.1970, pp. 113-26.
33

[18] Meyer, B., “Unemployment Insurance and Unemployment Spells”,
Econometrica, v58, pp. 757-782, 1990.
[19] Millard, S. and Mortensen, Dale T. “The unemployment and welfare
e¤ects of labor market policy: a comparison of the U.S. and U.K.” in
[20] Mortensen, D. “Job Search and Labor Market Analysis” in Ashenfelter
and Layard eds., Handbook of labor economics, Elsevier Science, New
York 1986, pp.849-919.
[21] OECD, “Jobs Study”, 1994.
[22] Bene…t recipients per unemployed is from panel B in table 8.4 of OECD
Jobs Study 1994, percentage of unemployment bene…ciaries to LFS unemployment
[23] Prescott, Edward C, and Rios-Rull, Jose-Victor,. “Classical Competitive
Analysis of Economies with Islands” , Journal of Economic Theory, v57
n1 June 1992, pp. 73-98.
[24] Veracierto, M., Essays on Job Creation and Job Destruction, Ph.D.
Thesis, University of Minnesota 1995.
[25] Wolpin, K. “Estimating a Structural Search Model: The Transition from
School to Work,” Econometrica v55 n4 July 1987, pp. 801-17.
[26] Valdivia, V., “Policy Evaluation in Heterogeneous Agent Economies:
The Welfare Impact of Unemployment Insurance,” Ph.D. Thesis, Northwestern University 1996.

34

Table 1

®
¯
°
½
¾2
wh

Parameters
Cobb-Douglas parameter
time preference
substitution between market vs. home goods
persistence of z
innovation variance of z
productivity at home

0.64
0.9951
1
0.98724
0.00838
.817

US Observations
Labor Share
0.64
Interest Rate
4 % (annual)
Employment/Population
0.79
Average Duration of Unemployment 4 months
Unemployment Rate
6.2 %
US Policies
Average duration of U.I. bene…ts collected
U.I. recipients / Unemployed
Replacement Ratio
Experience Rating

35

3 months
35 %
66 %
60 %

TABLE 2.a. MINIMUM WAGES, NO PRIORITY
(AS % OF AVG. WAGES)
Laissez-Faire
Unemployment Rate
Avg. Duration of Unemp.
Incidence of Unemp.

MINIMUM WAGE
85%
90%

5.3
2.4
2.3

5.4
2.4
2.3

6.6
2.8
2.6

100.0
100.0
100.0
100.0
0.0

99.9
102.1
100.0
100.1
0.0

98.1
124.7
99.5
101.8
-0.2

100.0
100.0
100.0
100.0
0.0

99.9
102.1
100.0
100.0
0.0

98.6
125.4
99.8
100.0
-0.2

100.0
100.0
100.0
100.0
0.0

99.9
102.3
100.0
100.0
0.0

98.9
126.0
100.0
99.0
-0.1

Gamma = 0.0
Employment
Unemployment
Market Output
Home Output
Change in Welfare (% of cons. vs. LF)
Gamma = 1.0
Employment
Unemployment
Market Output
Home Output
Change in Welfare (% of cons. vs. LF)
Gamma = 8.0
Employment
Unemployment
Market Output
Home Output
Change in Welfare (% of cons. vs. LF)

TABLE 2.b. MINIMUM WAGES, PRIORITY
(AS % OF AVG. WAGES)
Laissez-Faire
Unemployment Rate
Avg. Duration of Unemp.
Incidence of Unemp.

MINIMUM WAGE
85%
90%

5.3
2.4
2.3

5.4
2.4
2.3

6.6
2.8
2.5

100.0
100.0
100.0
100.0
0.0

100.0
102.3
100.1
99.8
0.0

97.8
124.8
99.3
102.5
-0.2

100.0
100.0
100.0
100.0
0.0

99.9
102.2
100.0
99.9
0.0

98.5
125.7
99.7
100.1
-0.2

100.0
100.0
100.0
100.0
0.0

100.0
101.4
100.1
99.7
0.0

98.9
125.6
100.0
98.9
-0.2

Gamma = 0.0
Employment
Unemployment
Market Output
Home Output
Change in Welfare (% of cons. vs. LF)
Gamma = 1.0
Employment
Unemployment
Market Output
Home Output
Change in Welfare (% of cons. vs. LF)
Gamma = 8.0
Employment
Unemployment
Market Output
Home Output
Change in Welfare (% of cons. vs. LF)

TABLE 3.a. UNIONS AS COALITIONS
Laissez-Faire
Unemployment Rate
Avg. Duration of Unemp.
Incidence of Unemp.

5.3
2.4
2.3

ISLANDS UNIONIZED
20%
40%
60%
80%
7.1
3.0
2.7

9.5
3.6
3.0

12.5
4.5
3.4

16.3
5.5
3.7

12.5

10.9

8.9

6.6

100.0
100.0
100.0
100.0
0.0

96.5
132.8
98.3
105.2
-0.7

91.0
171.7
95.1
114.9
-1.9

83.9
215.9
90.7
128.4
-3.4

75.6
264.5
85.5
144.7
-5.3

100.0
100.0
100.0
100.0
0.0

98.2
135.2
99.4
99.6
-0.7

95.7
180.6
98.2
99.4
-1.9

92.5
238.0
96.6
99.5
-3.5

88.5
309.3
94.5
99.6
-5.6

100.0
100.0
100.0
100.0
0.0

99.0
136.4
99.9
96.5
-0.7

97.9
184.8
99.7
90.9
-1.8

96.7
248.8
99.3
82.9
-3.2

95.0
332.2
98.9
72.5
-4.8

Wage Premium * (in %)
Gamma = 0.0
Employment
Unemployment
Market Output
Home Output
Change in Welfare (% of cons. vs. LF)
Gamma = 1.0
Employment
Unemployment
Market Output
Home Output
Change in Welfare (% of cons. vs. LF)
Gamma = 8.0
Employment
Unemployment
Market Output
Home Output
Change in Welfare (% of cons. vs. LF)

* Average earning per union member / average competitive wages

Table 3.a. (cont.) COMPETITIVE vs. UNIONIZED ISLANDS
ISLANDS UNIONIZED
20%
40%
60%
80%
COMPETITIVE ISLANDS
Unemployment Rate
Avg. Duration of Unemp.
Incidence of Unemp.

6.6
2.7
2.6

8.0
3.1
2.8

9.6
3.6
3.0

11.3
4.0
3.2

10.6
3.8
3.1

13.0
4.4
3.4

15.6
5.1
3.6

18.3
5.8
3.8

7.1
3.0
2.7

9.5
3.6
3.0

12.5
4.5
3.4

16.3
5.5
3.7

UNIONIZED ISLANDS
Unemployment Rate
Avg. Duration of Unemp.
Incidence of Unemp.
WHOLE ECONOMY
Unemployment Rate
Avg. Duration of Unemp.
Incidence of Unemp.

TABLE 3.b. "UNION BOSS" MODEL

Laissez-Faire
Unemployment Rate
Avg. Duration of Unemp.
Incidence of Unemp.

ISLANDS UNIONIZED
20%
40%
60%
80%

5.3
2.4
2.3

4.8
2.3
2.2

4.2
2.2
2.1

3.5
2.0
1.9

2.4
1.7
1.5

100.0
100.0
100.0
100.0
0.0

92.2
83.5
94.4
125.8
-0.3

82.9
65.8
87.6
155.9
-1.0

71.0
46.1
78.6
193.7
-2.2

53.3
23.5
64.1
249.3
-5.2

100.0
100.0
100.0
100.0
0.0

97.6
88.5
97.9
109.9
-0.3

94.6
75.1
95.3
122.3
-0.7

90.4
58.6
91.7
139.1
-1.5

83.1
36.7
85.2
167.1
-3.7

100.0
100.0
100.0
100.0
0.0

100.2
90.8
99.6
101.2
-0.2

100.5
79.8
99.1
102.2
-0.5

101.0
65.5
98.4
103.6
-1.1

101.9
44.9
97.1
104.2
-2.4

Gamma = 0.0
Employment
Unemployment
Market Output
Home Output
Change in Welfare (% of cons. vs. LF)
Gamma = 1.0
Employment
Unemployment
Market Output
Home Output
Change in Welfare (% of cons. vs. LF)
Gamma = 8.0
Employment
Unemployment
Market Output
Home Output
Change in Welfare (% of cons. vs. LF)

Table 3.b. (cont.) COMPETITIVE vs. UNIONIZED ISLANDS
20%

ISLANDS UNIONIZED
40%
60%

80%

COMPETITIVE ISLANDS
Unemployment Rate
Avg. Duration of Unemp.
Incidence of Unemp.

4.6
2.2
2.2

3.8
2.0
2.0

2.9
1.8
1.7

1.7
1.5
1.2

6.0
2.6
2.4

5.1
2.4
2.2

4.0
2.1
2.0

2.6
1.7
1.6

4.8
2.3
2.2

4.2
2.2
2.1

3.5
2.0
1.9

2.4
1.7
1.5

UNIONIZED ISLANDS
Unemployment Rate
Avg. Duration of Unemp.
Incidence of Unemp.
WHOLE ECONOMY
Unemployment Rate
Avg. Duration of Unemp.
Incidence of Unemp.

TABLE 4. FIRING TAXES (IN MONTHS OF AVG. WAGES)
FIRING TAX
6.0

Laissez-Faire

3.0

5.3
2.4
2.3

4.6
3.7
1.3

4.2
4.2
1.1

3.7
5.1
0.1

100.0
100.0
100.0
100.0
0.0

93.7
81.0
94.9
121.6
-0.6

90.1
71.5
91.9
133.7
-1.2

86.1
60.0
88.0
147.3
-2.3

100.0
100.0
100.0
100.0
0.0

98.7
85.3
98.1
106.8
-0.6

98.1
77.8
97.0
110.3
-1.2

97.9
68.2
95.5
112.7
-2.3

100.0
100.0
100.0
100.0
0.0

101.2
87.4
99.7
98.5
-0.6

102.1
80.9
99.5
96.6
-1.1

103.9
72.3
99.2
91.8
-2.1

Unemployment Rate
Avg. Duration of Unemp.
Incidence of Unemp.

12.0

Gamma = 0.0
Employment
Unemployment
Market Output
Home Output
Change in Welfare (% of cons. vs. LF)
Gamma = 1.0
Employment
Unemployment
Market Output
Home Output
Change in Welfare (% of cons. vs. LF)
Gamma = 8.0
Employment
Unemployment
Market Output
Home Output
Change in Welfare (% of cons. vs. LF)

TABLE 5. UNEMPLOYMENT BENEFITS (PV, IN MODEL PERIODS OF AVG. WAGES)
Laissez-Faire

0.28

PV OF UNEMP.BENEFITS
0.50
0.75
1.00

1.25

5.3
2.4
2.3

6.2
2.7
2.5

7.3
2.9
2.7

9.1
3.4
2.9

11.9
4.1
3.3

15.0
5.0
3.6

100.0
100.0
100.0
100.0
0.0

105.0
125.5
103.8
81.2
0.0

108.0
153.3
106.2
68.0
-0.3

111.6
201.9
109.2
49.5
-1.2

115.2
279.4
112.1
26.5
-3.0

118.5
377.8
114.7
0.7
-5.6

100.0
100.0
100.0
100.0
0.0

101.2
120.9
101.4
92.4
0.0

101.7
144.3
102.2
86.5
-0.3

102.2
184.9
103.2
77.2
-1.0

102.7
249.2
104.2
63.7
-2.5

103.3
329.2
105.1
47.2
-4.6

100.0
100.0
100.0
100.0
0.0

99.4
118.8
100.2
98.7
0.0

98.9
140.3
100.4
96.4
-0.2

98.2
177.6
100.6
91.6
-0.8

97.5
236.4
100.8
82.5
-2.1

97.0
309.0
100.9
70.2
-3.6

Unemployment Rate
Avg. Duration of Unemp.
Incidence of Unemp.
Gamma = 0.0
Employment
Unemployment
Market Output
Home Output
Change in Welfare (% of cons. vs. LF)
Gamma = 1.0
Employment
Unemployment
Market Output
Home Output
Change in Welfare (% of cons. vs. LF)
Gamma = 8.0
Employment
Unemployment
Market Output
Home Output
Change in Welfare (% of cons. vs. LF)

Figure 1
Employment Determination, Laissez-Faire

θ

f(g,z2)+βΕzv(g+U,z’)

f(g,z1)+βΕzv(g+U,z’)

g(z1)

x

g

v

Figure 2
Value Function, Laissez-Faire

θ

f(x,z)+βΕzv(x+U,z’)

x
g(z)

Figure 3
Employment Policy, Laissez-Faire
g(x,z)

g=x

g(x,z)

x
g(z)

Figure 4
Employment Determination, Minimum Wages

“Excess Supply”

θ

f(g,z)+βΕzv(g+U,z’)

~
x(z)

g(z)

x

g

Figure 5
Employment Determination, Firing Taxes (firms pay tax)

τ

R2(x,g,z1)
θ

τ

R2(x,g,z2)

x-U

x

g

Working Paper Series
A series of research studies on regional economic issues relating to the Seventh Federal
Reserve District, and on financial and economic topics.
FDICIA After Five Years: A Review and Evaluation
George J. Benston and George G. Kaufman

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Money, Sticky Wages, and the Great Depression
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Price Pass-Through and Minimum Wages
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Habit Persistence and Asset Returns in an Exchange Economy
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North-South Terms of Trade: An Empirical Investigation
Michael A. Kouparitsas

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Interactions Between the Seasonal and Business Cycles
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WP-97-6

ΑPeso Problem≅ Explanations for Term Structure Anomalies
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The Big Problem of Small Change
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Bank Capital Standards for Market Risk: A Welfare Analysis
David Marshall and Subu Venkataraman

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Monetary Policy and the Term Structure of Nominal Interest Rates:
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Charles L. Evans and David A. Marshall

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Employer Learning and Statistical Discrimination
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WP-97-11

A Model of Commodity Money, With Applications to Gresham=s Law
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The Evolution of Small Change
Thomas J. Sargent and François R. Velde

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The Role of Credit Market Competition on Lending Strategies
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Algorithms for Solving Dynamic Models with Occasionally Binding Constraints
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Modeling Money
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Monetary Policy Shocks: What Have We Learned and to What End?
Lawrence J. Christiano, Martin Eichenbaum and Charles L. Evans

WP-97-18

Volunteer Labor Sorting Across Industries
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WP-97-19

Would Freetrade Have Emerged in North America without NAFTA?
Michael A. Kouparitsas

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The Role of the Financial Services Industry in the Local Economy
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WP-97-21

The Trojan Horse or the Golden Fleece? Small Business Investment
Companies and Government Guarantees
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WP-97-22

Temporary Services Employment Durations: Evidence from State UI Data
Lewis M. Segal and Daniel G. Sullivan

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The Determinants of State Food Manufacturing Growth: 1982-92
Mike Singer

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Requiem for a Market Maker: The Case of Drexel Burnham Lambert
and Below-Investment-Grade Bonds
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Plant Level Irreversible Investment and Equilibrium Business Cycles
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WP-98-1

Search, Self-Insurance and Job-Security Provisions
Fernando Alvarez and Marcelo Veracierto

WP-98-2

Could Prometheus Be Bound Again? A Contribution to the Convergence Controversy
Nicola Cetorelli

WP-98-3

The Informational Advantage of Specialized Monitors:
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Robert DeYoung, Mark J. Flannery, William W. Lang and Sorin M. Sorescu

WP-98-4

Prospective Deficits and the Asian Currency Crisis
Craig Burnside, Martin Eichenbaum and Sergio Rebelo

WP-98-5

Stock Market and Investment Good Prices: Implications of Microeconomics
Lawrence J. Christiano and Jonas D. M. Fisher

WP-98-6

2

Working Paper Series (continued)
Understanding the Effects of a Shock to Government Purchases
Wendy Edelberg, Martin Eichenbaum and Jonas D. M. Fisher

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A Model of Bimetallism
Francois R. Velde, and Warren E. Weber

WP-98-8

An Analysis of Women=s Return-to-Work Decisions Following First Birth
Lisa Barrow

WP-98-9

The Quest for the Natural Rate: Evidence from a Measure of Labor Market Turbulence
Ellen R. Rissman

WP-98-10

School Finance Reform and School District Income Sorting
Daniel Aaronson

WP-98-11

Central Banks, Asset Bubbles, and Financial Stability
George G. Kaufman

WP-98-12

Bank Time Deposit Rates and Market Discipline in Poland:
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Thomas S. Mondschean and Timothy P. Opiela

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Projected U.S. Demographics and Social Security
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WP-98-14

Dynamic Trade Liberalization Analysis: Steady State, Transitional and
Inter-industry Effects
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WP-98-15

Can the Benefits Principle Be Applied to State-local Taxation of Business?
William H. Oakland and William A. Testa

WP-98-16

Geographic Concentration in U.S. Manufacturing: Evidence from the U.S.
Auto Supplier Industry
Thomas H. Klier

WP-98-17

Consumption-Based Modeling of Long-Horizon Returns
Kent D. Daniel and David A. Marshall

WP-98-18

Can VARs Describe Monetary Policy?
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WP-98-19

Neighborhood Dynamics
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WP-98-20

Inventories and output volatility
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WP-98-21

Lending to troubled thrifts: the case of FHLBanks
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WP-98-22

3

Working Paper Series (continued)
Wage Differentials for Temporary Services Work:
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WP-98-23

Organizational Flexibility and Employment Dynamics at Young and Old Plants
Jeffrey R. Campbell and Jonas D. M. Fisher

WP-98-24

Extracting Market Expectations from Option Prices:
Case Studies in Japanese Option Markets
Hisashi Nakamura and Shigenori Shiratsuka

WP-99-1

Measurement Errors in Japanese Consumer Price Index
Shigenori Shiratsuka

WP-99-2

Taylor Rules in a Limited Participation Model
Lawrence J. Christiano and Christopher J. Gust

WP-99-3

Maximum Likelihood in the Frequency Domain: A Time to Build Example
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WP-99-4

Unskilled Workers in an Economy with Skill-Biased Technology
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Product Mix and Earnings Volatility at Commercial Banks:
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School Choice Through Relocation: Evidence from the Washington D.C. Area
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Asset Price Fluctuation and Price Indices
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Labor Market Policies in an Equilibrium Search Model
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Hedging and Financial Fragility in Fixed Exchange Rate Regimes
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Habit Persistence, Asset Returns and the Business Cycle
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Working Paper Series (continued)
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WP-99-16

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WP-99-18

Fiscal Shocks in an Efficiency Wage Model
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WP-99-19

Thoughts on Financial Derivatives, Systematic Risk, and Central
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Testing the Stability of Implied Probability Density Functions
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A Note on the Benefits of Homeownership
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WP-99-23

The Earned Income Credit and Durable Goods Purchases
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WP-99-24

Globalization of Financial Institutions: Evidence from Cross-Border
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Intrinsic Bubbles: The Case of Stock Prices A Comment
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WP-99-31

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Working Paper Series (continued)
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WP-99-32

6