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Federal Reserve Bank of Chicago

Establishments Dynamics and
Matching Frictions in Classical
Competitive Equilibrium
Marcelo Veracierto

WP 2007-16

Establishments Dynamics and Matching
Frictions in Classical Competitive Equilibrium∗
Marcelo Veracierto
Federal Reserve Bank of Chicago
August 2007
Abstract: This paper develops a Walrasian equilibrium theory of establishment level dynamics and matching frictions and uses it to evaluate the effects of
congestion externalities in the matching process and determine the government
interventions that are needed to implement a Pareto optimal allocation. The
optimal policy, which involves a tax on the creation of help-wanted ads and an
unemployment subsidy, is highly contractionary. However, it leads to large welfare
gains. The policy also plays an important role in dampening the response of the
economy to aggregate productivity shocks.
Keywords: Firm dynamics, matching, unemployment, business cycles.
JEL classification: E32, J63, J64.

∗

This paper originated in a conversation with Randall Wright and was heavily influenced
by it. I have also benefited from the comments of seminar participants at the Federal Reserve
Bank of Atlanta, the Federal Reserve Bank of Philadelphia, the Federal Reserve of Chicago, the
2007 Summer Camp in Macroeconomics and the 2007 NBER Summer Institute. All remaining
errors are solely mine. The views express here do not necessarily reflect the position of the
Federal Reserve Bank of Chicago or the Federal Reserve System. Address: Federal Reserve
Bank of Chicago, Research Department, 230 South LaSalle Street, Chicago, IL 60604. E-mail:
mveracierto@frbchi.org. Phone: (312) 322-5695.

1. Introduction
This paper develops a Walrasian theory of establishment level dynamics and matching frictions and
uses it to evaluate the effects of congestion externalities in the matching process. The theory blends
together three important strands in the literature: 1) the Hopenhayn and Rogerson [6] model of
establishment dynamics, 2) the Mortensen and Pissarides [9] matching model, and 3) the Lucas
and Prescott [8] islands model. In my model establishments are similar to those in Hopenhayn
and Rogerson [6] except that the amount of hiring that they can undertake is determined by the
number of help-wanted ads that they posted during the previous period. Similarly to Mortensen
and Pissarides [9] unemployed workers and help-wanted ads meet according to a matching function.
However, wages are determined by Walrasian markets instead of bilateral Nash bargaining and
productions units are constituted by establishments instead of individual jobs. From the Lucas
and Prescott [8] model I retain the directed search specification but assume that the search costs
are incurred by the establishments instead of the unemployed workers. These modelling choices
give rise to a unified framework for analyzing establishment dynamics, vacancies, unemployment
and matching frictions that fully relies on classical price theory. An important goal of the paper
is to evaluate if this type of framework can explain the behavior of U.S. labor markets both at
growth-trend and business cycle frequencies.
The economy is populated by a representative household constituted by a continuum of members
that value consumption and leisure. Household members differ in their employment histories but
obtain full insurance within the household. The consumption good is produced by a large number of
spatially separated establishments that operate a decreasing returns to scale technology using labor
as the only input of production. The establishments are subject to idiosyncratic productivity shocks
that induce them to expand and contract over time. In order to hire a worker an establishment
needs to have a hiring opportunity. In the same vein, an unemployed workers needs to have a job
opportunity in order to become employed. Hiring opportunities and job opportunities are jointly
produced: They are obtained when an unemployed worker meets the help-wanted ad posted by an
establishment. The rate at which a help-wanted ad meets unemployed workers is determined by
the aggregate number of help-wanted ads and unemployed workers entering a constant returns to
scale matching technology. In order to retain a Walrasian market structure I assume that any of
the unemployed workers with a job opportunity can be hired by any of the establishments with a
hiring opportunity.

I analyze this economy in a number of ways. First, I solve the social planner’s problem and
characterize the efficient allocation. Second, I describe a competitive equilibrium that attains the
Pareto optimum allocation. The decentralization requires a large number of competitive matching
companies operating the constant returns to scale matching technology at a reduced scale. This
equilibrium is efficient because the matching companies fully internalize the congestion effects that
unemployed workers and help-wanted ads generate. Third, I describe a competitive equilibrium
with matching externalities. This type of equilibrium, which is standard in the matching literature,
specifies that the search technology can only be operated at the aggregate level and that establishments and unemployed workers have free access to it. Since no decision maker regulates the
operation of the matching technology, congestion externalities arise and the competitive equilibrium is inefficient. Fourth, I characterize the government interventions needed to attain the Pareto
optimal allocation in the competitive equilibrium with matching externalities. The optimal policy,
which implements a version of Hosios’ condition, involves a subsidy to unemployed workers and a
tax to the creation of help-wanted ads.
The quantitative results indicate that the competitive equilibrium with congestion externalities
is quite succesful in replicating the behavior of U.S. labor markets. In particular, parameter values
can be chosen to reproduce important long-run establishment level observations (e.g. the size
distribution of establishments, job creation and destruction rates, etc.) as well as aggregate labor
market statistics (e.g. the unemployment rate, the hazard rate of unemployment, the elasticity
of the hazard rate of unemployment with respect to market tightness, etc.). More importantly,
when aggregate productivity shocks of empirically plausible magnitude are introduced, the model
is found to replicate the observed business cycle behavior of output, employment, unemployment
and vacancies. Given the empirical success of this version of the model, it becomes important
to evaluate the magnitude of the congestion externalities underlying the matching process. I find
that the externalities are quite large: Undoing them require a tax on help-wanted ads of 267%
and a subsidy to unemployed workers equal to 4% of wages. Moreover, introducing the optimal
policy reduces output by 6.2%, consumption by 5.5% and employment by 9.9%. Although the
policy is contractionary, the increase in leisure more than compensates the drop in consumption
and a steady state welfare gain of 0.8% in terms of permanent consumption is obtained. Once
transitionary dynamics are considered the welfare gain increases to 1.1% in terms of consumption.
The paper is organized as follows. Section 2 describes the economy. Section 3 describes the set
of feasible allocations. Section 4 characterizes a Pareto optimal allocation. Section 5 describes the

2

competitive equilibrium that decentralizes the optimal allocation. Section 6 describes a competitive
equilibrium with matching externalities. Section 7 characterizes the government intervention that
attains the Pareto optimal allocation in a competitive equilibrium with matching externalities.
Section 8 calibrates the steady state competitive equilibrium with matching externalities. Finally,
Section 9 presents the results.

2. The economy
The economy is populated by a measure one of households, each composed by a unit interval of
members called workers. Labor is indivisible: Workers can be either employed or unemployed,
and employed workers must spend a larger amount of time in market activities than unemployed
workers. The preferences of the representative household are given by:
∞
X
t=0

β

t

∙

¸
−1
c1−σ
t
+ ϕUt ,
1−σ

(2.1)

where ct is consumption, Ut is unemployment, ϕ > 0, σ > 0 and 0 < β < 1. The parameter ϕ is
positive since the household is assumed to value leisure.
The consumption good is produced by a large number of spatially separated establishments.
Each establishment has a production function given by
yt = st F (nt ) ,
where st ∈ S = {0, s1 , s2 , ..., smax } is an idiosyncratic productivity shock, nt is labor, and F is a
twice continuously differentiable, strictly increasing, and strictly concave function with limn→0 F 0 (n) =
+∞ and limn→∞ F 0 (n) = 0. The idiosyncratic productivity shock st follows a finite Markov process
with monotone transition matrix Q. Realizations of st are assumed independent across all establishments and st = 0 is assumed to be an absorbing state. Since there are no fixed costs of operation,
exit takes place only when the idiosyncratic productivity level becomes zero. In every period, a
measure ς of new establishments is exogenously born. Their distribution over initial productivity
shocks is given by ψ.
Establishments can hire workers in a central island called the hiring market. However, the number of workers that an establishment can hire is constrained by the number of hiring opportunities
mt that the establishment has available at the beginning of the period. An establishment receives

3

a hiring opportunity when one of its posted help-wanted ads meets an unemployed worker. Since
workers are assumed to quit at the exogenous rate δ, an establishment’s employment level nt is
constrained as follows:
nt ≤ (1 − δ) nt−1 + mt .
All workers that separate from an establishment (either because of quits or firings) join the pool of
unemployment.
Unemployed workers have the possibility of becoming employed in the hiring market, but only
if they have a job opportunity. An unemployed worker receives a job opportunity when he meets a
help-wanted ad posted by some establishment. Once in the hiring market, any unemployed worker
with a job opportunity can be hired by any establishment with a hiring opportunity.
The matching technology, which jointly produces job and hiring opportunities, is described as
follows. Let At be the total number of help-wanted ads in the matching technology, and let Ut
be the total number of unemployed workers in the matching technology. The number of hiring
opportunities obtained by an establishment that created at help-wanted ads is given by:
mt+1 = at m(At , Ut ),

(2.2)

where m is assumed to be strictly concave, strictly decreasing in A, strictly increasing in U and
homogeneous of degree zero. The total number of job opportunities obtained by unemployed
workers is then equal to
Mt+1 = M (At , Ut ) ,
i.e. it is given by the total number of hiring opportunities

3. Feasibility
In what follows, it will be convenient to index establishments by the date j of their creation, by their
history of idiosyncratic shocks stj = (sj , sj+1 ..., st−1 , st ) ∈ S t−j+1 since the date of their creation
and by the number of workers e that they were endowed with at the time of their creation. Only
establishments created at t = 0 are allowed to have a positive initial endowment of workers e.
Establishments created after t = 0 have a zero initial endowment of workers.1
1

The “initial endowment” variable e is introduced to avoid carrying separate notation for incumbent establishments
at t = 0 and establishments created after t = 0.

4

The number of establishments μ0 (0, s0 , e) created at t = 0 with initial productivity s0 and
h
i
initial endowment of workers e, is given. For t ≥ 1, the number of establishments μt j, stj , e with

creation date j ≤ t, history stj and initial endowment of workers e satisfies the following equations:
μt (t, st , 0) = ςψ (st ) ,
μt (t, st , e) = 0, for e > 0,
μt [j, (sj , sj+1 ..., st−1 , st ) , e] = μt−1 [j, (sj , sj+1 ..., st−1 ) , e] Q (st−1 , st ) , for 0 ≤ j < t.
Aggregate consumption is given by

ct ≤

t XX
X
£ ¡
¢¤
¢¤ ¡
¢
£
¡
st F nt j, stj , e − kat j, stj , e μt j, stj , e ,
j=0

stj

(3.1)

e

³
´
³
´
where at j, stj , e are the help-wanted ads created by an establishment of type j, stj , e . This

equation states that aggregate consumption is equal to the sum of output net of help-wanted ad
costs across all types of establishments.
Aggregate help-wanted ads are given by:
t XX
X
j=0 stj

e

¢ ¡
¢
¡
at j, stj , e μt j, stj , e ≤ At ,

(3.2)

i.e. it is the sum of help-wanted ads across all type of establishments. Unemployment is given by:

Ut ≤ 1 −

t XX
X
j=0 stj

e

¢ ¡
¢
¡
nt j, stj , e μt j, stj , e ,

(3.3)

i.e. it is the total number of agents that do not work.
Employment feasibility at the establishment level is described as follows. For j = t,
¢
¡
nt j, stj , e ≤ e,

(3.4)

since at the time of their creation establishments cannot employ more than their initial endowment
of workers. For j < t:
´
´
³
³
¢
¡
t−1
,
e
+
a
,
e
m [At−1 , Ut−1 ] .
j,
s
nt j, stj , e ≤ (1 − δ)nt−1 j, st−1
t−1
j
j
5

(3.5)

That is, the employment level of an establishment cannot exceed the sum of its previous employment
level net of quits and the number of hiring opportunities that it has at the beginning of the period.

4. Pareto optimal allocations
The social planner’s problem is to maximize (2.1) subject to equations (3.1)-(3.5). Since the
utility function in equation (2.1), the production function F and the matching function M are
concave, this is a standard problem. An analysis of its first order conditions leads to the following
characterization.
An efficient allocation can be described by a sequence {ct , At , Ut , vt , nt , at , θt , γ t , μt }∞
t=0 . The
elements vt , nt , and at are functions of the state of an establishment (x, s), where x are the units
of labor available for employment at the beginning of the period and s is the current productivity
level. The number vt (x, s) is the date t shadow value of a worker at an establishment of type
(x, s), the number nt (x, s) is the date t employment level at an establishment of type (x, s), and
the number at (x, s) are the date t help-wanted ads created by an establishment of type (x, s). The
elements θt and γ t are numbers: θt is the date t shadow value of a worker in the pool of aggregate
unemployment and γ t is the shadow value of a next-period hiring opportunity.2 Finally, the element
μt is the date t measure of establishments across states (x, s). To represent an efficient allocation,
the sequence must satisfy the following conditions.
The shadow value of a worker at an establishment of type (x, s) must satisfy the following
equation:
½
µ
¶
ct σ
0
δθt+1
(4.1)
vt (x, s) = max θt , sF (x) + β
ct+1
)
µ
¶
X
£
¤ ¡ 0¢
ct σ
0
+β
(1 − δ)
vt+1 (1 − δ) x + at (x, s) m [At , Ut ] , s Q s, s
.
ct+1
0
s

This equation is quite intuitive. The shadow value vt (x, s) cannot be less than the social value
of sending an additional worker to the pool of unemployment θt . Otherwise, welfare could be
improved by reducing the employment level of the establishment. If the shadow value vt (x, s)
exceeds the value of unemployment, the planner retains all workers available to the establishment
x. In this case, the flow shadow value of a worker is given by the marginal productivity sF 0 (x).

2

All shadow values are expressed in terms of the consumption good.

6

With probability δ the worker quits and his continuation value is the discounted shadow value
θt+1 of having an additional worker in the pool of unemployment at the beginning of the following
period. With probability (1 − δ) the worker does not quit the following period, and his continuation
value is equal to the expected discounted shadow value vt+1 of beginning the following period in an
establishment with (1 − δ) x + at (x, s) m [At , Ut ] workers available for employment. Observe that
the social planner discounts next period values using the product of the discount factor β and the
intertemporal marginal rate of substitution (ct /ct+1 )σ .
The optimal number of help-wanted ads created by an establishment of type (x, s) is characterized by the following condition:
β

µ

ct
ct+1

¶σ X
s0

£
¤ ¡
¢
vt+1 (1 − δ) nt (x, s) + at (x, s) m (At , Ut ) , s0 Q s, s0 ≤ γ t + β
with equality if at (x, s) > 0.

µ

ct
ct+1

¶σ

θt+1 ,
(4.2)

That is, if the establishment creates a positive number of help-wanted ads it must be the case
that the expected discounted shadow value of a worker at the establishment vt+1 is equal to the
shadow value of a next-period hiring opportunity γ t plus the discounted shadow value of a nextperiod unemployed worker θt+1 . This conditions is also intuitive. If β (ct /ct+1 )σ E [vt+1 ] > γ t +
β (ct /ct+1 )σ θt+1 , the value of increasing the establishment’s next-period hiring opportunities by
one unit exceeds the opportunity cost. As a consequence, welfare could be improved by realizing
this increase. If β (ct /ct+1 )σ E [vt+1 ] < γ t + β (ct /ct+1 )σ θt+1 even when zero hiring opportunities
are created, the social planner stays at the corner solution of at (x, s) = 0.
Substitution equation (4.2) in equation (4.1) gives
½
µ
¶
ct σ
0
θt+1
vt (x, s) = max θt , sF (x) + δβ
ct+1
" µ
#)
µ
¶
¶
£
¤ ¡ 0¢
ct σ X
ct σ
0
+ (1 − δ) min β
vt+1 (1 − δ) x, s Q s, s , γ t + β
θt+1
.
ct+1
ct+1
0
s

The optimal employment rule nt (x, s) is then easily obtained. It is characterized by a threshold
level x̄t (s) that satisfies the following condition:
0

µ

ct

¶σ

θ = sF (x̄t (s)) + δβ
θt+1
(4.3)
ct+1
( µ
)
µ
¶
¶
£
¤ ¡ 0¢
ct σ X
ct σ
0
+ (1 − δ) min β
vt+1 (1 − δ) x̄t (s) , s Q s, s , γ t + β
θt+1 .
ct+1
ct+1
0
s

7

That is, x̄t (s) is the unique value of x at which the social planner is indifferent between leaving
the marginal worker at the establishment and sending him to the pool of unemployment.
The optimal employment rule is then given by:
nt (x, s) = min {x̄t (s) , x} .

(4.4)

That is, if x > x̄t (s), the shadow value of a worker in an establishment of type (x, s) is less than
the shadow value of unemployment. As a consequence, the social planner reduces the employment
level of the establishment to the point at which he is indifferent between making a further reduction
in employment or not.
The optimal help-wanted ads creation rule at (x, s) is also easily obtained. It is characterized
by a threshold level xt (s) that satisfies the following condition:
β

µ

ct
ct+1

¶σ X
s0

£
¤ ¡
¢
vt+1 (1 − δ) xt (s) , s0 Q s, s0 = γ t + β

µ

ct
ct+1

¶σ

θt+1 .

(4.5)

⎫
⎬

(4.6)

The help-wanted ads creation rule is then given by

at (x, s) m (At , Ut ) =

⎧
⎨

0, if min {x̄t (s) , x} > xt (s)

⎩ (1 − δ) [x (s) − min {x̄ (s) , x}] , otherwise ⎭
t
t

.

The shadow value of a next-period hiring opportunity γ t satisfies the following condition:
γt =

k
.
m (At , Ut ) + At mA (At , Ut )

(4.7)

Observe that m + A.mA > 0 is the marginal product of a help-wanted ad in creating next-period
hiring opportunities. Since k is the cost of creating a help-wanted ad, equation (4.7) states that
the shadow value of a next-period hiring opportunity equals its cost of production.
The shadow value of an unemployed worker θt is given by
θt =

cσt ϕ + γ t At mU

(At , Ut ) + β

µ

ct
ct+1

¶σ

θt+1 .

(4.8)

Observe that AmU is the marginal product of an unemployed worker in creating next-period hiring
opportunities, which are valued at the shadow price γ t . Thus equation (4.8) states that the shadow
value of an unemployed worker θt is equal to his value of leisure expressed in consumption units

8

cσt ϕ, plus his shadow value in creating next period hiring opportunities γ t At mU , plus the discounted
shadow value of being an unemployed worker during the following period.
Consumption ct is given by
ct =

X
s

[st F [nt (x, s)] − kat (x, s)] μt (dx, s) ,

(4.9)

aggregate help-wanted ads At are given by
At =

X

at (x, s) μt (dx, s) ,

(4.10)

s

and aggregate unemployment Ut is
X

Ut = 1 −

nt (x, s) μt (dx, s) .

(4.11)

s

Finally, the sequence of measures μt must satisfy
¡
¢ X
μt+1 X 0 , s0 =
s

Z

Bt (s)

¡ ¢ ¡ ¢
Q(s, s0 )dμt + ςψ s0 I X 0 ,

(4.12)

where I (X 0 ) is an indicator function that takes a value equal to one if 0 ∈ X 0 and a value of zero,
otherwise, and Bt (s) is the set of all x such that (1 − δ) x + at (x, s) m (At , Ut ) lies in the Borel set
X 0.
An efficient allocation is a sequence {ct , At , Ut , vt , nt , at , θt , γ t , μt }∞
t=0 such that equations (4.1)(4.12) hold, with μ0 given. Observe that, from the concavity of the planner’s problem, a unique
efficient allocation exists.

5. A competitive equilibrium
In what follows I specify a competitive equilibrium in which workers are bought and sold as capital
goods.3 Establishments buy workers in the hiring market, sell them in the firing market and
buy hiring opportunities from matching companies. Households buy workers in the firing market,
sell them in the hiring market, rent unemployed workers to the matching companies, and receive

3

I choose this unusual specification because it easy to describe. It turns out that it is equivalent to a much
more complicated specification in which households and establishments trade binding state contingent employment
contracts (see Alvarez and Veracierto [1] for this alternative formulation).

9

job-opportunities for free. Since at every period of time, there is always some positive number
of establishments that do not use all the hiring opportunities available to them (because their
productivity shocks have changed), the price of a worker in the hiring market is always brought
down to the price in the firing market. Hereon, I will refer to this single price as the price of a
worker pw
t in the labor market.
The date t problem of an establishment that has e workers carried over from the previous period,
m hiring opportunities and current productivity level s is given by:
Jt (e, m, s) =

max

nt ,mt+1 ,ht ,ft

n
h
sF (nt ) + pw
t (ft − ht ) − qt mt+1

£
¤ ¡
¢
1
1 X
Jt+1 (1 − δ) nt , mt+1 , s0 Q s, s0 +
pw δnt
+
1 + it 0
1 + it t+1
s

(5.1)
)

subject to
nt = e + ht − ft
ht ≤ m
h
where pw
t is the price of a worker, qt is the price of a hiring opportunity in the next period, nt is the

employment level of the establishment, ht is the amount of hiring, ft is the amount of firing, mt+1
is the number of hiring opportunities that the establishment purchases, it is the interest rate, and
Jt (e, m, s) is the present expected discounted value at date t of an establishment of type (e, m, s)
after quits have taken place. Observe that an establishment maximizes the present discounted value
of its profits, which are given by the sum of its output and its net sale of workers, minus the value
of the hiring opportunities that the establishment buys in the matching market. Also observe that
the amount of hiring cannot exceed the number of hiring opportunities available at the beginning
of the period.
It is straightforward to show that Jet = Jmt + pw
t . Moreover, Jet and Jmt depend on (e, m) only
through the sum x = e+m. Using these properties, the first order conditions for the establishment’s
problem can be written as follows:
½
0
Jet (x, s) = max pw
t , sF (x) +
+ (1 − δ)

1
1 + it

1
pw δ
1 + it t+1

)
X
£
¤
¡
¢
Je,t+1 (1 − δ) x + mt+1 (x, s) , s0 Q s, s0 ,
s0

10

(5.2)

and
£
¤ ¡
¢
1 X
1
Je,t+1 (1 − δ) nt (x, s) + mt+1 (x, s) , s0 Q s, s0 ≤ qth +
pw ,
1 + it 0
1 + it t+1

(5.3)

s

with equality if mt+1 (x, s) > 0.

The establishment’s employment rule nt (x, s) is similar to that of the social planner. It is
characterized by a threshold level x̄t (s) that satisfies the following condition:
1
pw δ
(5.4)
1 + it t+1
"
#
£
¤ ¡
¢
1 X
1
+ (1 − δ) min
Je,t+1 (1 − δ) x̄t (s) , s0 Q s, s0 , qth +
pw .
1 + it 0
1 + it t+1

= sF 0 (x̄t (s)) +
pw
t

s

The optimal employment rule is then given by
nt (x, s) = min {x̄t (s) , x} .

(5.5)

The optimal hiring opportunities creation rule is also easily obtained. It is characterized by a
threshold level xt (s) that satisfies the following condition:
£
¤ ¡
¢
1 X
1
Je,t+1 (1 − δ) xt (s) , s0 Q s, s0 = qth +
pw .
1 + it 0
1 + it t+1

(5.6)

s

The hiring opportunities creation rule is given by

mt+1 (x, s) =

⎧
⎨

0, if min {x̄t (s) , x} > xt (s)

⎫
⎬

⎩ (1 − δ) [x (s) − min {x̄ (s) , x}] , otherwise ⎭
t
t

.

(5.7)

The problem of a household that had ut−1 unemployed workers during the previous period and
that during the current period has jt job opportunities and bt bond holdings is the following:
Ht (ut−1 , jt , bt ) = max

½

¾
−1
c1−σ
t
+ ϕut + βHt+1 (ut , jt+1 , bt+1 )
1−σ

11

subject to
w
ct + bt+1 ≤ pm
t ut + pt (ht − ft ) + (1 + it−1 ) bt + Πt

ut = (ut−1 − jt ) + ft + (jt − ht )
ht ≤ jt
ft ≤ 1 − ut−1
Mt+1
jt+1 = ut
Ut
where ut is the number of unemployed members during the current period, ht are the household
members sold in the hiring market, ft are the household members bought in the firing market and
Πt are the profits of all the establishments in the economy. The first constraint is the household’s
budget constraint. Observe that the household receives income from renting unemployed members
w
to the matching companies pm
t ut , from the selling of workers in the hiring market pt ht , from

interest and principal payments on its bond holdings (1 + it−1 )bt and from the establishments’
profits Πt . The household spends its income in purchasing workers in the firing market pw
t ft ,
on consumption ct and on next period bond holdings bt+1 .The second constraint states that the
number of unemployed members during the current period ut is given by the number of unemployed
members in the previous period that were left unmatched ut−1 − jt , by the household members
bought in the firing market ft , and by the household members left unsold in the hiring market
jt − ht . The third constraint states that the number of household members sold in the hiring
market ht cannot exceed the job-opportunities available to the household at the beginning of the
period jt . The fourth constraint states that the number of household members bought in the firing
market ft cannot exceed the number of household members that were employed during the previous
period 1 − ut−1 . The last constraint states that the number of job opportunities that the household
will have the following period is given by the number of unemployed members during the current
period times the rate at which the representative firm creates job-opportunities.
Observe that the third and fourth constraints must hold with strict inequality at equilibrium.
For these constraints not to bind, the household must view its problem as being independent of its
job-opportunities jt . This requires that
pw
t

=

cσt ϕ + pm
t

+β

12

µ

ct
ct+1

¶σ

pw
t+1 .

(5.8)

This condition states that the household must be indifferent between selling workers in the hiring
market and keeping them unemployed. The left hand side is the price pw
t that the household can
get by selling an unemployed worker in the hiring market. The right hand side is the sum of the
value of leisure expressed in consumption units cσt ϕ, the rental price of an unemployed worker in the
matching industry pm
t , and the savings from buying one less unemployed worker in the firing market
´σ
³
ct
pw
at the beginning of the following period (expressed in current consumption units) β ct+1
t+1 .
Also observe that the solution to the household’s problem requires that
1
=β
1 + it

µ

ct
ct+1

¶σ

,

(5.9)

i.e. that the interest rate be equal to the marginal rate of substitution between current consumption
and future consumption.
The date t problem of the representative matching company is given by:
o
n
max qth Mt+1 − pm
t Ut − kAt
subject to
Mt+1 = At m(At , Ut ).
That is, the matching company obtains revenues qth Mt+1 from selling next period hiring opportunities, pays pm
t Ut for renting unemployed workers and pays kAt for creating help-wanted ads. The
first order conditions to this problem are the following:

qth [m(At , Ut ) + At mA (At , Ut )] = k,
qth At mU (At , Ut ) = pm
t .

(5.10)
(5.11)

The first equation states that the marginal revenue product of a help-wanted ad equals its marginal
cost k. The second equation states that the marginal revenue product of an unemployed worker
equals its marginal cost pm
t .

©
ª∞
h m
A competitive equilibrium is a sequence ct , bt , At , Ut , Jet , nt , at , mt+1 , pw
t , qt , pt , it , μt t=0 such

that bt = 0,

at (x, s) =

mt+1 (x, s)
,
m (At , Ut )

13

and equations (5.2)-(5.11) and (4.9)-(4.12) are satisfied every period t, with μ0 given.
The following proposition states that every competitive equilibrium allocation is efficient.
ª∞
©
h m
Proposition 5.1. (First Welfare Theorem) Let ct , bt , At , Ut , Jet , nt , at , mt+1 , pw
t , qt , pt , it , μt t=0

be a competitive equilibrium. Let

θ t = pw
t ,
vt = Jet ,
γ t = qth .
Then, {ct , At , Ut , vt , nt , at , θt , γ t , μt }∞
t=0 is an efficient allocation.
Since there is a unique efficient allocation, a corollary of this proposition is that there is a unique
competitive equilibrium. The following proposition states that the Second Welfare Theorem also
holds.
Proposition 5.2. (Second Welfare Theorem) Let {ct , At , Ut , vt , nt , at , θt , γ t , μt }∞
t=0 be an efficient
allocation. Let
= θt ,
pw
t
qth = γ t ,
= γ t At mU (At , Ut )
pm
t
Jet = vt
mt+1 (x, s) = at (x, s) m (At , Ut )
bt = 0
1
1 + it

= β

µ

ct
ct+1

¶σ

ª∞
©
h m
Then, ct , bt , At , Ut , Jet , nt , at , mt+1 , pw
t , qt , pt , it , μt t=0 is a competitive equilibrium.
Both propositions follow from comparing first order conditions for the social planner’s problem
and the competitive equilibrium.

14

6. A competitive equilibrium with congestion externalities
This section describes the standard notion of equilibrium considered by the matching literature:
One in which the matching process is subject to congestion externalities. In particular, the matching
technology is now assumed to operate only at the aggregate level. Moreover, all help-wanted ads
and all unemployed workers in the economy are assumed to be inputs to it. Since no decision
maker internalizes the operation of the matching technology, standard congestion externalities
arise. Establishments buy workers in the hiring market, sell them in the firing market and buy
help-wanted ads from job-posting companies. Households buy workers in the firing market and sell
them in the hiring market. Since not all hiring opportunities are used in equilibrium, the price of
a worker pw
t must be the same in the hiring market and in the firing market.
The date t problem of an establishment that has e workers carried over from the previous period,
m hiring opportunities and current productivity level s is given by
Jt (e, m, s) =

max

nt ,ht ,ft ,at

a
{sF (nt ) + pw
t (ft − ht ) − pt at

£
¤ ¡
¢
1 X
1
+
Jt+1 (1 − δ) nt , mt+1 , s0 Q s, s0 +
pw δnt
1 + it 0
1 + it t+1
s

)

subject to
nt = e + ht − ft
ht ≤ m
mt+1 = at m(At , Ut )
where ht is the number of workers bought in the hiring market, ft is the number of workers sold in
the firing market, at is the number of help-wanted ads purchased, pat is the price of a help-wanted
ad, it is the interest rate and mt+1 is the number of hiring opportunities that the establishment
generates. Observe that the number of hiring opportunities that the establishment generates mt+1
is proportionate to the number of help-wanted ads purchased at , with constant of proportionality
given by the aggregate effectiveness of help-wanted ads in generating hiring opportunities m(At , Ut ).
The establishment takes At and Ut as given. Also, observe that the amount of hiring ht cannot
exceed the hiring opportunities available to the establishment at the beginning of the period.
It is straightforward to show that Jet = Jmt + pw
t . Moreover, Jet and Jmt depend on (e, m) only

15

through the sum x = e+m. Using these properties, the first order conditions for the establishment’s
problem can be written as follows:
½
0
Jet (x, s) = max pw
t , sF (x) +
+ (1 − δ)

1
1 + it

1
pw δ
1 + it t+1

(6.1)

)
X
£
¤
¡
¢
Je,t+1 (1 − δ) x + at (x, s) m(At , Ut ), s0 Q s, s0
s0

and
£
¤ ¡
¢
1 X
Je,t+1 (1 − δ) nt (x, s) + at (x, s) m(At , Ut ), s0 Q s, s0 ≤
1 + it 0
s

1
pat
+
pw
m(At , Ut ) 1 + it t+1

with equality if at (x, s) > 0.

(6.2)

The establishment’s employment rule nt (x, s) has the same form as in the previous sections. It
is characterized by a threshold level x̄t (s) that satisfies the following condition:
pw
= sF 0 (x̄t (s)) +
t
+ (1 − δ) min

1
pw δ
1 + it t+1
"
1 X
1 + it

s0

£
¤ ¡
¢
Je,t+1 (1 − δ) x̄t (s) , s0 Q s, s0 ,

1
pat
+
pw
m(At , Ut ) 1 + it t+1

(6.3)
#

The optimal employment rule is then given by
nt (x, s) = min {x̄t (s) , x} .

(6.4)

The optimal hiring opportunities creation rule also has the same form as before. It is characterized by a threshold level xt (s) that satisfies the following condition:
£
¤ ¡
¢
1 X
1
pat
+
Je,t+1 (1 − δ) xt (s) , s0 Q s, s0 =
pw .
1 + it 0
m(At , Ut ) 1 + it t+1

(6.5)

s

The help-wanted ads creation rule is given by

at (x, s) m(At , Ut ) =

⎧
⎨

0, if min {x̄t (s) , x} > xt (s)

⎫
⎬

⎩ (1 − δ) [x (s) − min {x̄ (s) , x}] , otherwise ⎭
t
t

16

.

(6.6)

The representative job-posting company solves the following static profit maximization problem:
max {pat At − kAt } .
where pat is the price of a help-wanted ad, k is the cost of producing a help-wanted ad, and At are
the total help-wanted ads produced. Thus, at equilibrium we must have that
pat = k

(6.7)

The date t problem of a household that had ut−1 unemployed workers during the previous
period and that during the current period has jt job opportunities and bt bond holdings is given by
Ht (ut−1 , jt , bt ) = max

½

¾
−1
c1−σ
t
+ ϕut + βHt+1 (ut , jt+1 , bt+1 )
1−σ

subject to
ct + bt+1 ≤ pw
t (ht − ft ) + (1 + it−1 ) bt + Πt
ut = (ut−1 − jt ) + ft + (jt − ht ) ,
ht ≤ jt ,
ft ≤ 1 − ut−1 ,
Mt+1
jt+1 = ut
Ut
where ut is the number of unemployed members during the current period, ht are the household
members sold in the hiring market, ft are the household members bought in the firing market, and
Πt are the profits of all the establishments in the economy. The household takes the aggregate
effectiveness at which unemployed workers reach the hiring market.Mt+1 /Ut as given. Observe
that the third and fourth constraints must hold with strict inequality at equilibrium. For these
constraints to be non-binding at every period t, the household must view its problem as being
independent of its job-opportunities jt . This requires that
pw
t

=

cσt ϕ

+β

µ

ct
ct+1

¶σ

pw
t+1

(6.8)

for every t. This condition states that the household must be indifferent between selling workers in

17

the hiring market and keeping them unemployed. Also observe that the solution to the household’s
problem requires that
1
=β
1 + it

µ

ct
ct+1

¶σ

.

(6.9)

A competitive equilibrium with congestion externalities is a sequence {ct , bt , At , Ut , Jet , nt , at ,
a
∞
pw
t , pt , it , μt }t=0 such that bt = 0 and equations (6.1)-(6.9) and (4.9)-(4.12) are satisfied every

period t, with μ0 given.
6.1. A myopic-planner characterization
Consider the problem of a social planner that maximizes (2.1) subject to equations (3.1)-(3.4) and
the following employment feasibility condition at the establishment level:
³
³
´
´
¢
¡
t−1
nt j, stj , e ≤ (1 − δ)nt−1 j, st−1
j,
s
,
e
+
a
,
e
m̄t−1 , for j < t.
t−1
j
j

(6.10)

The planner takes the sequence {m̄t }∞
t=0 as given. Observe that equation (6.10) is identical to
equation (3.5) except that that the arguments of m are taken as given. Given that this social
planner does not take into account how his decisions affect m, I will refer to him as a myopicplanner.
A solution to the myopic planner’s problem can be described by a sequence {ct , At , Ut , vt , nt ,
at , θt , μt }∞
t=0 that satisfies the following conditions.
The shadow value of a worker at an establishment of type (x, s) must satisfy the following
equation:
½
µ
¶
ct σ
0
θt+1
vt (x, s) = max θt , st F (x) + δβ
ct+1
)
µ
¶
£
¤ ¡ 0¢
ct σ X
0
+ (1 − δ) β
vt+1 (1 − δ) x + at (x, s) m̄t , s Q s, s
ct+1
0

(6.11)

s

The optimal number of help-wanted ads created for an establishment of type (x, s) is characterized by the following condition:
β

µ

ct
ct+1

¶σ X
s0

£
¤ ¡
¢
vt+1 (1 − δ) nt (x, s) + at (x, s) m̄t , s0 Q s, s0 ≤

k
+β
m̄t

with equality if at (x, s) > 0.

18

µ

ct
ct+1

¶σ

θt+1 ,
(6.12)

The optimal employment rule nt (x, s) is characterized by a threshold level x̄t (s) that satisfies
the following condition:
µ

0

ct

¶σ

θt+1
(6.13)
θt = st F (x̄t (s)) + δβ
ct+1
" µ
#
µ
¶
¶
¡ 0¢ k
ct σ
ct σ X
vt+1 [(1 − δ) x̄t (s)] Q s, s ,
+β
θt+1 .
+ (1 − δ) min β
ct+1
m̄t
ct+1
0
s

The optimal employment rule is then given by
nt (x, s) = min {x̄t (s) , x} .

(6.14)

The optimal hiring opportunities creation rule at (x, s) is characterized by a threshold level
xt (s) that satisfies the following condition:
β

µ

ct
ct+1

¶σ X
s0

£
¤ ¡
¢
k
vt+1 (1 − δ) xt (s) , s0 Q s, s0 =
+β
m̄t

µ

ct
ct+1

¶σ

θt+1 .

(6.15)

The help-wanted ads creation rule is given by
⎧
⎨

at (x, s) m̄t =

0, if min {x̄t (s) , x} > xt (s)

⎫
⎬

⎩ (1 − δ) [x (s) − min {x̄ (s) , x}] , otherwise ⎭
t
t

.

(6.16)

The shadow value of an unemployed worker satisfies that
θt =

cσt ϕ

+β

µ

ct
ct+1

¶σ

θt+1 , for t ≥ 0

(6.17)

∞
A myopically-efficient allocation with respect to {m̄t }∞
t=0 is a sequence {ct , At , Ut , vt , nt , at , θ t , μt }t=0

such that equations (6.11)-(6.17) and (4.9)-(4.12) hold, with μ0 given.
In what follows, I provide a modified version of the Welfare Theorems, which I will refer to as
the Myopic Welfare Theorems.
∞
a
Proposition 6.1. (First Myopic Welfare Theorem) Let {ct , bt , At , Ut , Jet , nt , at , pw
t , pt , it , μt }t=0 be

19

a competitive equilibrium with congestion externalities. Let
m̄t = m(At , Ut )
θt = pw
t ,
vt = Jet
∞
Then, {ct , At , Ut , vt , nt , at , θt , μt }∞
t=0 is a myopically-efficient allocation with respect to {m̄t }t=0 .

Proposition 6.2. (Second Myopic Welfare Theorem) Let {ct , At , Ut , vt , nt , at , θt , μt }∞
t=0 be a myopicallyefficient allocation with respect to {m̄t }∞
t=0 . Suppose that

m̄t = m(At , Ut ), for every t.
Let
= θt ,
pw
t
Jet = vt
pat = k
bt = 0
1
1 + it

= β

µ

ct
ct+1

¶σ

∞
a
Then, {ct , bt , At , Ut , Jet , nt , at , pw
t , pt , it , μt }t=0 is a competitive equilibrium with congestion exter-

nalities
The characterization of a competitive equilibrium with congestion externalities as a myopicefficient allocation will turn out to be extremely useful in computations.

7. The optimal policy regime
In this section I introduce government policies to the competitive equilibrium with congestion
externalities of the previous section. In particular, I introduce a tax τ t to help-wanted ads and
a subsidy ρt to unemployed workers. Any negative (positive) difference between the tax revenues
and the subsidy payments associated with those tax rates are rebated (taxed) to households in a
lump-sum way. The purpose is to look for government interventions that will attain the first best

20

allocation described in Section 4.
The date t problem of an establishment that has e workers carried over from the previous period,
m hiring opportunities and current productivity level s is now given by
Jt (e, m, s) =

max

nt ,ht ,ft ,at

a
{sF (nt ) + pw
t (ft − ht ) − (1 + τ t ) pt at

£
¤ ¡
¢
1 X
1
+
Jt+1 (1 − δ) nt , mt+1 , s0 Q s, s0 +
pw δnt
1 + it 0
1 + it t+1
s

)

subject to
nt = e + ht − ft
ht ≤ m
mt+1 = at m(At , Ut )
where the purchases of help-wanted ads are now taxed at the rate τ t .
The first order conditions for the establishment’s problem are the following:
½
0
Jet (x, s) = max pw
t , sF (x) +

1
pw δ
1 + it t+1

(7.1)

)
£
¤ ¡ 0¢
1 X
0
+ (1 − δ)
Je,t+1 (1 − δ) x + at (x, s) m(At , Ut ), s Q s, s
1 + it 0
s

and
£
¤ ¡
¢
1 X
Je,t+1 (1 − δ) nt (x, s) + at (x, s) m(At , Ut ), s0 Q s, s0 ≤
1 + it 0
s

1
(1 + τ t ) pat
+
pw
m(At , Ut )
1 + it t+1

with equality if at (x, s) > 0

(7.2)

The establishment’s employment rule nt (x, s) has the same form as in the previous sections. It
is characterized by a threshold level x̄t (s) that satisfies the following condition:
1
pw δ
(7.3)
1 + it t+1
#
"
a
£
¤
¡
¢
1 X
1
)
p
(1
+
τ
t
t
+
Je,t+1 (1 − δ) x̄t (s) , s0 Q s, s0 ,
pw
+ (1 − δ) min
1 + it 0
m(At , Ut )
1 + it t+1

pw
= sF 0 (x̄t (s)) +
t

s

21

The optimal employment rule is then given by
nt (x, s) = min {x̄t (s) , x} .

(7.4)

The optimal hiring opportunities creation rule also has the same form as before. It is characterized by a threshold level xt (s) that satisfies the following condition:
£
¤ ¡
¢ (1 + τ t ) pat
1
1 X
+
Je,t+1 (1 − δ) xt (s) , s0 Q s, s0 =
pw
1 + it 0
m(At , Ut )
1 + it t+1

(7.5)

s

The help-wanted ads creation rule is given by

at (x, s) m(At , Ut ) =

⎧
⎨

0, if min {x̄t (s) , x} > xt (s)

⎫
⎬

⎩ (1 − δ) [x (s) − min {x̄ (s) , x}] , otherwise ⎭
t
t

.

(7.6)

The representative job-posting company solves the following static profit maximization problem:
max {pat At − kAt } .
where pat is the price of a help-wanted ad, k is the cost of producing a help-wanted ad, and At are
the total help-wanted ads produced. Thus, at equilibrium we must have that
pat = k

(7.7)

The date t problem of a household that had ut−1 unemployed members during the previous
period and that during the current period has jt job opportunities and bt bond holdings is given by
Ht (ut−1 , jt , bt ) = max

½

¾
−1
c1−σ
t
+ ϕut + βHt+1 (ut , jt+1 , bt+1 )
1−σ

22

subject to
ct + bt+1 ≤ ρt ut + pw
t (ht − ft ) + (1 + it−1 ) bt + Πt + Tt
ut = (ut−1 − jt ) + ft + (jt − ht ) ,
ht ≤ jt ,
ft ≤ 1 − ut−1 ,
Mt+1
jt+1 = ut
Ut
where unemployed workers are now subsidized at the rate ρt and the household now faces a lumpsum tax Tt . Since the second and third constraints must hold with strict inequality at equilibrium,
the price of a worker must satisfy the following condition:
pw
t

=

cσt ϕ

+ ρt + β

µ

ct
ct+1

¶σ

pw
t+1 .

(7.8)

Also observe that the solution to the household’s problem requires that
1
=β
1 + it

µ

ct
ct+1

¶σ

.

(7.9)

The government balances its budget period-by-period. This means that the lump-sum taxes Tt
must be given by
Tt = ρt Ut − τ t pat At .

(7.10)

A competitive equilibrium with externalities and policy intervention is a sequence {ct , bt , At , Ut ,
a
∞
Jet , nt , at , pw
t , pt , it , μt , τ t , ρt , Tt }t=0 such that bt = 0 and equations (7.1)-(7.10) and (4.9)-(4.12)

are satisfied every period t, with μ0 given.
The following proposition characterizes the optimal policy intervention, i.e., the policy regime
that attains the first best allocation.
Proposition 7.1. (Necessity of optimal policy regime) Let {ct , At , Ut , vt , nt , at , θt , γ t , μt }∞
t=0 be the

23

unique efficient allocation (as defined in Section 4). Define,
At mA (At , Ut )
,
m (At , Ut ) + At mA (At , Ut )
kAt mU (At , Ut )
,
=
m (At , Ut ) + At mA (At , Ut )
= 0

τt = −
ρt
Tt

= θt
pw
t
pat = k
Jet = v
bt = 0
1
1 + it

= β

µ

ct
ct+1

¶σ

∞
a
Then, {ct , bt , At , Ut , Jet , nt , at , pw
t , pt , it , μt , τ t , ρt , Tt }t=0 is a competitive equilibrium with external-

ities and policy intervention.
The converse is also true.
a
Proposition 7.2. (Sufficiency of optimal policy regime) Let {ct , bt , At , Ut , Jet , nt , at , pw
t , pt , it ,

μt , τ t , ρt , Tt }∞
t=0 be a competitive equilibrium with externalities and policy intervention such that
At mA (At , Ut )
,
m (At , Ut ) + At mA (At , Ut )
kAt mU (At , Ut )
,
=
m (At , Ut ) + At mA (At , Ut )
= 0

τt = −
ρt
Tt

(7.11)

Let
θ t = pw
t
k
m (At , Ut ) + At mA (At , Ut )
= Jet

γt =
vt

Then, {ct , At , Ut , vt , nt , at , θt , γ t , μt }∞
t=0 is the unique efficient allocation
Observe that the optimal policy regime is fully funded: It does not require lump-sum taxes or
subsidies to implement it. It is also straightforward to verify that when the matching function has

24

the following Cobb-Douglas functional form
Mt = ΩUtφ A1−φ
,
t

(7.12)

the optimal policy simplifies to:
φ
,
1−φ
φ At
= k
.
1 − φ Ut

τt =

(7.13)

ρt

(7.14)

That is, while the optimal tax rate on help-wanted ads is constant, the unemployment subsidy
varies directly with the degree of market tightness.
This characterization of the optimal policy in the Cobb-Douglas case is closely related to Hosios’
efficiency condition in the context of bilateral Nash bargaining (Hosios [7]). To see this, observe that
Jet − pw
t can be interpreted as the surplus associated with the marginal worker. Hosios’ condition
states that the employer must receive a fraction 1 − φ of this surplus in order to achieve efficiency.
Since in a Walrasian equilibrium the employer receives all of this surplus, a fraction φ must be taxed
away and be given to the workers in the form of an unemployment subsidy, effectively mimicking a
higher Nash bargaining weight for the workers. An inspection of equations (7.2) and (7.13) indicates
that this exactly what the optimal policy achieves.

8. Calibration
Given that the preponderant view in the literature is that the matching process is subject to
congestion externalities, in this section I calibrate the steady state of the competitive equilibrium
with externalities and no policy interventions described in Section 6 to long-run U.S. observations.4
The following section will explore the business cycle properties of this economy as well as the effects
of introducing the optimal policy regime.
I choose the model time period to be two-weeks to accommodate for the relatively short average
durations of unemployment and vacancies in the U.S. economy. Calibrating to an annual interest
rate of 4 percent, which is a standard value in the macro literature, then requires a time discount
factor β equal to 0.99835.

4

A future version of the paper will also consider an efficient competitive equilibrium scenario.

25

The preference parameter σ, which determines the elasticity of intertemporal substitution, is
taken as a free parameter. However, I will restrict attention to two values: σ = 0 and σ = 1.
The first value is often used in the search literature based on the Mortensen and Pissarides [9]
model (e.g. Hall [5], Hagedorn and Manovskii [4] and Shimer [11]). The second value, which is
consistent with the stylized growth facts, is generally used in the macro literature. In what follows,
I describe the calibration strategy assuming that σ = 0. At the end of the section, I discuss how
to accommodate the other case.
It is straightforward to verify that doubling the utility of leisure ϕ, the values of all idiosyncratic
productivity levels z, and the cost of creating a help-wanted ad k doubles the units in which
consumption and output are measured but leaves all other equilibrium variables unchanged. As a
consequence, I normalize the utility of leisure ϕ to one.
I assume that the production function has the following functional form:
yt = st nαt ,
where 0 < α < 1. Following the macro literature I choose the curvature parameter α to reproduce
a labor share in National Income (1 − β)pw N/Y equal to 0.64.
The values for the idiosyncratic productivity levels s, the distribution over initial productivity
levels ψ and the transition matrix Q are key determinants of the job-flows generated by the model.
As a consequence I choose them to reproduce observations from the Business Employment Dynamics
(BED) data set, which is a virtual census of establishments level dynamics. Since BED data across
establishment sizes can be found for the nine employment ranges shown in the first column of Table
1, I restrict the idiosyncratic productivity levels s to take nine positive values and choose them so
that all establishments with a same idiosyncratic productivity level choose employment levels in
the same range.
The average size of new entrants can be obtained by dividing the total gross job gains at opening
establishments by the total number of opening establishments. Using data between 1992:Q3 and
2005:Q4, I find that the average size of new entrants is equal to 5.3 employees. Since this is a small
number, I restrict the distribution over initial productivity levels ψ to put positive mass on only
the two lowest values of s and choose ψ (s1 ) to reproduce that average size.
Similarly, the average size at exit can be obtained by dividing the total gross job losses at closing
establishments by the total number of closing establishments. Using data for the same time period

26

as above, I find that the average size at exit is equal to 5.2 employees. Since this is also a small
number, I restrict the probabilities of transiting to a zero productivity level Q(s, 0) to take positive
values only at the two lowest values of s and choose Q(s1 , 0)/Q(s2 , 0) to reproduce that average
size. The level for Q(s1 , 0) is then chosen to reproduce the average quarterly rate of gross job losses
due to closing establishments (JLD) over the same time period, which is equal to 1.6%.5
The rest of the transition matrix Q is parameterized with enough flexibility to reproduce important establishment level observations. The only restriction that I impose is that Q (si , sj ) > 0
only if j = i − 1, j = i or j = i + 1. Since the rows of Q add to one this introduces 16 parameters
(2 parameters each, for i = 2, ..., 8, and 1 parameter each, for i = 1, 9). Eight of these parameters
are chosen to reproduce the shares in total employment across size classes (which provide eight
independent observations). The other eight parameters are chosen to reproduce the shares in total
gross job gains across size classes (which also provide eight independent observations). I must point
out that the BED does not tabulate statistics across size classes in its regular reports. However,
these statistics can be found in Okolie [10] (Tables 1 and 3) for the first two quarters of 2000.
These statistics together with the corresponding model statistics are shown in the first panel of
Table 1. The second panel reports the average sizes at entry and exit both in the model and the
data. We see that the model does a good job at reproducing these observations. As a test of the
model, Table 1 also includes the shares in total gross job losses across size classes for the first two
quarters of 2000 in Okolie [10], and the average quarterly rates of gross job gains due to expanding
establishments (JGE), gross job gains due to opening establishments (JGB), gross job losses due
to contracting establishments (JLC), and exit rates reported by the BED for the period 1992:Q32005:Q4. Although the fit is not perfect, we see that the model also does a good job at reproducing
these statistics.6
The exogenous separation rate δ and the number of establishments created every period ς are
important determinants of the worker flows in and out of unemployment, so I calibrate them to
reproduce this type of observations. In particular, I target an average monthly separation rate from
employment equal to 3.5% and an average monthly hazard rate from unemployment equal to 46%,

5
Since the model is bi-weekly, monthly and quarterly statistics are constructed following establishments over two
and six consecutive time periods, respectively.
6
The main discrepancy is with the shares in total gros job losses for the size ranges (5, 10) and (10, 20), which are
too large in the first case and too small in the second. This could be remedied by allowing for a postivive Q(s3 , 0)
and by lowering Q(s2 , 0), since the range (5, 10) accounts for a large fraction of the establishments closings. However,
I do not expect that such modification would affect the main results in the paper.

27

which were estimated by Shimer [12] using CPS data between 1948 and 2004. Since the separation
rate of 3.5% is significantly larger than the rate of job losses experienced by establishments, I select
a positive value of δ to reproduce the excess worker reallocation.7 Also, observe that the separation
and hazard rates estimated by Shimer [12] imply a steady state unemployment rate equal to 7.1%.
The average size of establishments implied by the shares in total employment in Table 1 thus
determine the entry rate of establishments ς needed to generate an aggregate employment level N
equal to 0.929.
I assume that the matching function takes the Cobb-Douglas form in equation (7.12). The
matching parameters Ω and φ together with the cost of posting a help-wanted ad k are important
determinants of the role that vacancies play in the model economy. In fact, one of these parameters
entails a mere normalization: It is easy to show that dividing k by a factor λ, and dividing Ω by
a factor λ1−φ leaves the equilibrium unchanged except that the units in which vacancies A are
measured are multiplied by the factor λ. Given this result, I normalize Ω so that the units in which
vacancies are measured are such that the vacancy rate A/(A + N ) of continuing establishments
equals 2.2%, which is the the average between 2000 and 2005 in the JOLTS dataset.8 This normalization allows me to identify k with the cost of creating a vacancy. Since Hagedorn and Manovskii
[4] estimate that the flow cost of posting a vacancy is 60% of the wage rate and since the wage rate
in my model economy is ϕ = 1, I calibrate k to 0.60. In turn, I calibrate the curvature parameter
φ in the matching function (7.12) to 0.72 which is the elasticity estimated by Shimer [11].
As a test of the model Table 2 reports a set of basic monthly statistics both for JOLTS and the
model economy that were not used as calibration targets.9 We see that the model does a reasonable
job at reproducing the hiring and separation rates for continuing establishments, the vacancy yield
rate (i.e. the hires per vacancy), the fraction of vacancies with zero hirings and the fraction of
hires with zero vacancies. Time aggregation plays an important role in generating a vacancy yield
rate greater than one and the large fraction of hires with zero vacancies since, following JOLTS,
vacancies are measured at the end of a period and hirings are measured over the two subsequent
periods. The low rate of exogenous separations δ explains the model’s success in reproducing the

7
Not surprisingly, my calibrated value of δ is smaller than the quit rate of workers measured by JOLTS, since
many of those separations entail job-to-job transitions that the model abstracts from.
8

I restrict attention to continuing establishments because this is the only type of establishments included in JOLTS.

9

JOLTS statistics are from Davis et al. [?, ?].

28

fraction of vacancies with zero hirings. The reason is that a significant number of establishments
reach the lower thresholds x (s) and start hiring just enough workers to replenish the exogenous
separation of workers. Since the monthly rate of exogenous separation is less than 1%, following
Davis et al. [?, ?], I classify these establishments (and their corresponding vacancies) as having
zero hirings. Observe that the model performs less satisfactorily in reproducing the fraction of
establishments with zero vacancies and the fraction of establishments with zero hiring. The small
number of idiosyncratic productivity levels that I allow for explains this result since they lead to a
large number of inactive establishments. Introducing more idiosyncratic productivity level would
generate smaller and more frequent adjustments and improve the performance of the model in this
dimension. However, I do not expect that this modification to change the main results in the paper.
Table 3 displays all calibrated parameter values for the case of linear preferences, i.e. for the
case σ = 0. The other case is easily handled since at steady state the curvature parameter σ
only enters equation 6.8. In particular, when σ is greater than zero I leave all parameter values
unchanged except for the utility of leisure ϕ (σ) which I set to
φ (σ) = ϕ (0) c (0)−σ ,

(8.1)

where c(0) and ϕ (0) are the steady state consumption level and the utility of leisure in the case
σ = 0. This choice of ϕ (σ) leaves the calibrated steady state allocation unchanged across the
different values of σ. The values that satisfy equation (8.1) turn out to be ϕ (1) = 0.6846 when σ
is equal to one.

9. Results
Before analyzing the effects of introducing the optimal policy regime to the calibrated economy of
the previous section, I evaluate the empirical plausibility of that economy by contrasting its business
cycle fluctuations with those of the U.S. I do this by introducing an aggregate productivity shock
common to all establishments. In particular, I modify the production function of establishments
to the following:
yt = ezt st nαt ,
where zt is an aggregate productivity shock that evolves according to a standard AR(1) process
zt+1 = ρz zt + εt+1 ,

29

and εt+1 is an i.i.d. normally distributed innovation, with zero mean and standard deviation σ ε .
I choose ρz and σ ε to reproduce the empirical behavior of Solow residuals in the U.S. economy
measured at quarterly frequencies. Using GDP and civilian employment data between 1951:1 and
2004:4 I find that the logarithm of these residuals are highly persistent and that their changes
have a standard deviations of 0.008.10 It turns out that values of ρz = 0.96 and σ ε = 0.0044 are
needed to reproduce this type of behavior for the Solow residuals measured from the artificial data
generated by the model economy.
The first panel of Table 4 reports business cycle statistics between 1951:1 and 2004:4 for GDP
(Y), civilian employment (N), civilian unemployment (U), the help-wanted ads index (A), market
tightness (A/U) and average labor productivity (Y/N). Before any statistics were computed all the
time series were logged and detrended using a Hoddrik-Prescott filter with smothing parameter
1,600. The statistics are the vector of standard deviations and the correlation matrix. We see that
employment and average productivity fluctuate 0.60% as much as output, while unemployment
and help-wanted ads fluctuate about 8 times as much. Market tightness is even more variable: it
fluctuates 16 times as much as output. All variables are strongly procyclical except for unemployment, which is strongly contercyclical. We also see that the data displays a clear Beveridge curve:
Unemployment and help-wanted ads are strongly negatively correlated. The correlation of unemployment with market tightness is also close to -1 while the correlation with average productivity
is much weaker: only -0.46.
The second panel of Table 4 describes analogous statistics from the model economy with linear
preferences.11 We see that the model generates only a slightly smaller standard deviation of output
than the data and that the standard deviations of all variables relative to output have the correct
magnitude. The correlations of all variables with output have the correct sign but they are a bit
too strongly correlated. We also see that the model generates the Beveridge curve, although the
correlation between unemployment and help-wanteed ads is a bit weaker than in the data. The
corelation of unemployment with market tightness is as strong as in the U.S. economy while its
correlation with average productivity is a touch weaker. Overall, we see that the model reproduces
U.S. business cycle statistics surprisingly well.

10

Solow residuals were constructed using a labor share of 64%.

11

The model with log preferences generates virtually no employment fluctuations. Actually, if the cost of creating
help-wanted ads was ezt k, i.e. if it was perfectly correlated with the aggregate productivity shock, the economy with
log preferences would generate zero employment fluctuations.

30

Having established the empirical relevance of the equilibrium with externalities, I now turn
to measure the consequences of the congestion effects. In particular, I evaluate the effects of
introducing the optimal policy characterized by Propositions 7.1 and 7.2. It turns out that the
optimal policy is given by a tax of 257% on the creation of help-wanted ads and an unemployment
subsidy equal to 4.4% of the wage rate (i.e. of the user cost of labor (1 − β)pw ). Table 5 reports the
steady-state results. We see that the optimal policy is extremely contractionary: output decreases
by 6.2%, consumption by 5.5%, employment by 9.9%, and vacancies by 91.7%. Matches increase by
13.4% despite the decrease in vacancies because of a sharp increase in unemployment. In fact, the
unemployment rate increases from 7.2% in the steady state with congestion externalities to 16.4%
under the optimal policy regime. Observe that the higher number of matches allow for higher rates
of job gains due to expanding establishments and job losses due to contracting establishments,
leading to a better distribution of workers across establishments. Also observe that the drop in
consumption is more than compensated by the large increase in leisure, and the optimal policy leads
to large welfare gains: Agents in the steady-state of the equilibrium with congestion externalities
would require a 0.8% permanent increase in consumption in order to be indifferent with living in
the efficient steady-state.
Figure 1 shows the transitionary dynamics generated by the optimal policy over the first year
of the reform. There are two important features to observe. First, the transitionary dynamics are
rather slow: Only by the end of the year variables appear to be settling at their stationary values.
Second, unemployment jumps and help-wanted ads plummet immediately after the reform. While
output drops with the initial increase in unemployment, consumption is not very much affected
on impact because of the large savings in help-wanted ads. Since consumption does not initially
change and agents start enjoying a significant amount of leisure right away, there are large welfare
gains early on in the reform. This, coupled with the long transitionary dynamics, imply that the
welfare gains of the reform can be much higher once the transitionary dynamics are considered.
Table 6 shows that this is indeed the case: The welfare gains of the reform increase from 0.8% to
1.1% when the short-run effects are taken into account..
Finally, Table 7 shows how the introduction of the optimal policy affects the business cycle
fluctuations of the economy. The first panel reproduces the business cycle statistics for the equilibrium with congestion externalities. The second panel describes analogous statistics for the efficient
equilibrium. We see that the optimal policy dampens the response of the economy to aggregate
producitivity shocks quite substantially. In particular, the standard deviation of output decreases

31

by 3% and the standard deviation of employment decreases by 17%. However, the largest effects
are in the volatility of unemployment, which plummets by 70%. Despite of this, the correlation matrices indicate that the comovements between the different variables are not significantly affected.
In particular, the correlation between unemployment and help-wanted ads only changes from -0.75
to -0.67, i.e. there are little effects on the slope of the Beveridge curve.

32

References
[1] Alvarez, F. and M. Veracierto, M. 2006. Fixed-Term Employment Contracts in an Equilibrium
Search Model. NBER Working Paper.
[2] Bentolila, S. and G. Bertola. 1990. Firing Costs and Labor Demand: How Bad is Eurosclerosis?
Review of Economic Studies, 57, 381-402.
[3] Davis, D., Faberman J. and J. Haltiwanger. 2006. The Flow Approach to Labor Markets: New
Data Sources and Micro-Macro Links. Journal of Economic Perspectives, Summer, 3-26.
[4] Hagedorn M. and I. Manovskii. 2006. The Cyclical Behavior of Equilibrium Unemployment
and Vacancies Revisited. Mimeo.
[5] Hall R. 2005. Employment Fluctuations with Equilibrium Wage Stickiness. American Economic
Review, 95(1), 50-65.
[6] Hopenhayn, H. and R. Rogerson. 1993. Job Turnover and Policy Evaluation: A General Equilibrium Analysis. Journal of Political Economy, 101, 915-38.
[7] Hosios, A. 1990. On the Efficiency of Matching and Related Models of Search and Unemployment. Review of Economic Studies, 57, 279-98.
[8] Lucas, R. and E. C. Prescott. 1974. Equilibrium Search and Unemployment. Journal of Economic Theory, 7, 188-209.
[9] Mortensen, D. and C. Pissarides. 1994. Job Creation and Job Destruction in the Theory of
Unemployment. Review of Economic Studies, 61, 397-415.
[10] Okolie, C. 2004. Why size class class methodology matters in analyses of net and gross job
flows. Monthly Labor Review, July, xx-xx.
[11] Shimer, R. 2005. The Cyclical Behavior of Equilibrium Unemployment and Vacancies. American Economic Review, 95(1), 25-49.
[12] Shimer, R. 2005. Reassessing the Ins and Outs of Unemployment. University of Chicago,
mimeo.

33

Table 1
Quarterly observations

Panel A: BED data, March 2000 to June 2000
Size

Data

Model

Classes∗

Shares in

Shares in

Shares in

Shares in

Shares in

Shares in

(employees)

Employment

Job Gains

Job Losses

Employment

Job Gains

Job Losses

[1, 5)

6.4%

16.9%

9.7%

7.6%

15.0%

7.5%

[5, 10)

8.1%

13.1%

11.6%

6.6%

15.7%

20.5%

[10, 20)

10.7%

14.9%

13.7%

11.0%

16.3%

4.2%

[20, 50)

16.6%

18.3%

18.2%

17.1%

17.1%

16.9%

[50, 100)

13.1%

11.6%

12.6%

12.5%

11.7%

14.4%

[100, 250)

16.5%

11.9%

14.6%

16.8%

12.5%

13.6%

[250, 500)

9.8%

5.9%

8.5%

9.5%

5.0%

11.5%

[500, 1000)

7.3%

3.5%

5.4%

7.5%

6.9%

5.6%

[1000, ∞)

11.6%

4.2%

5.9%

11.3%

0.0%

5.9%

Panel B: BED data, 1992:Q3 to 2005:Q4
Data

Model

size at entry

5.3

4.7

size at exit

5.2

4.8

JGB

1.7%

1.6%

JGE

6.2%

6.2%

JLD

1.6%

1.6%

JLC

6.0%

6.2%

Exit Rate

5.2%

6.9%

(∗): The classification of establishments into size classes is as follows: Continuing establishments
between t and t + 1 are classified according to their size at t, opening establishments at t + 1 are
classified according to their size at t + 1, closing establishments at t + 1 are classified according to
their size at t.

34

Table 2
Monthly observations

Panel A: CPS data, 1948-2004
Data

Model

Separation rate

3.5%

3.6%

Hazard rate

46%

46%

Panel B: JOLTS data, 2000-2005
Data

Model

Vacancy rate

2.2%

2.2%

Hiring rate

3.2%

3.0%

Separation rate

3.1%

3.0%

Vacancies yield rate

1.3

1.3

% Vacancies with zero hiring

18.7%

19.0%

% Hiring with zero vacancies

42.3%

58.1%

% Establishments with zero hiring

81.6%

90.0%

% Establishments with zero vacancies

87.6%

95.0%

35

Table 3
Parameter values (σ = 0)

General Parameters:
β

ϕ

α

δ

ς

k

Ω

φ

0.9984

1.0

0.64

0.0045

0.0006

0.61

1.493

0.219

Productivity levels:
s0

s1

s2

s3

s4

s5

s6

s7

s8

s9

0.0

2.19

3.33

4.0

5.71

7.16

10.24

13.33

16.38

20.0

Distribution over initial productivity levels:
ψ (s0 )

ψ (s1 )

ψ (s2 )

ψ (s3 )

ψ (s4 )

ψ (s5 )

ψ (s6 )

ψ (s7 )

ψ (s8 )

ψ (s9 )

0.0

0.017

0.983

0.0

0.0

0.0

0.0

0.0

0.0

0.0

Transition matrix Q:
s00

s01

s02

s03

s04

s05

s06

s07

s08

s09

s0

1.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

s1

0.0007

0.8677

0.1317

0.0

0.0

0.0

0.0

0.0

0.0

0.0

s2

0.038

0.1384

0.82

0.0036

0.0

0.0

0.0

0.0

0.0

0.0

s3

0.0

0.0

0.0071

0.98

0.0129

0.0

0.0

0.0

0.0

0.0

s4

0.0

0.0

0.0

0.0223

0.953

0.0247

0.0

0.0

0.0

0.0

s5

0.0

0.0

0.0

0.0

0.0529

0.94

0.0071

0.0

0.0

0.0

s6

0.0

0.0

0.0

0.0

0.0

0.0165

0.971

0.0125

0.0

0.0

s7

0.0

0.0

0.0

0.0

0.0

0.0

0.0414

0.95

0.0086

0.0

s8

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.022

0.955

0.023

s9

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.024

0.976

36

Table 4
Business Cycles (HP smoothing parameter = 1,600)

Panel A: Data (1951:1-2004:4)
Standard deviations
Y

N

U

A

A/U

Y/N

1.58

1.00

12.32

13.95

25.71

0.99

Correlations

Y

Y

N

U

A

A/U

Y/N

1.00

0.81

-0.84

0.90

0.89

0.79

1.00

-0.87

0.88

0.89

0.26

1.00

-0.91

-0.98

-0.46

1.00

0.98

0.54

1.00

0.51

N
U
A
A/U
Y/N

1.00

Panel B: Model w/externalities (linear preferences)
Standard deviations
Y

N

U

A

A/U

Y/N

1.51

0.84

11.78

11.82

22.11

0.76

Correlations

Y
N
U

Y

N

U

A

A/U

Y/N

1.00

0.95

-0.93

0.85

0.95

0.94

1.00

-0.99

0.71

0.91

0.77

1.00

-0.75

-0.94

-0.75

1.00

0.93

0.90

1.00

0.89

A
A/U
Y/N

1.00

37

Table 5
Steady state results

Linear Preferences

Log Preferences

Externalities

Efficiency

Externalities

Efficiency

output

100.0

93.8

100.0

95.6

consumption

100.0

94.5

100.0

96.3

employment

100.0

90.1

100.0

93.0

unemployment

100.0

227.6

100.0

190.9

vacancies

100.0

18.9

100.0

23.3

matches

100.0

113.4

100.0

105.9

vacancies/unemployment

100.0

8.3

100.0

12.2

output/employment

100.0

104

100.0

102.8

quarterly JGB

1.6%

1.7%

1.6%

1.6%

quarterly JBE

6.2%

7.4%

6.2%

6.9%

quarterly JLD

1.6%

1.7%

1.6%

1.6%

quarterly JLC

6.2%

7.4%

6.2%

6.9%

vacancies tax rate

0.0%

257%

0.0%

257%

UI replacement ratio

0.0%

4.4%

0.0%

6.5%

Steady state welfare gains

0.0%

0.8%

0.0%

0.7%

38

FIGURE 1

2.5

2

1.5

1

0.5

0
-1

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

periods since reform
consumption

unemployment

help-wanted ads

matches

19

20

21

22

23

24

Table 6
Welfare effects

Linear Preferences

Log Preferences

Externalities

Efficiency

Externalities

Efficiency

Steady state welfare gains

0.0%

0.8%

0.0%

0.7%

Transitionary dynamics welfare gains

0.0%

1.1%

0.0%

1.1%

39

Table 7
Business Cycles Effects of Optimal Policy (Linear preferences)

Panel A: Externalities
Standard deviations
Y

N

U

A

A/U

Y/N

1.51

0.84

11.78

11.82

22.11

0.76

Correlations

Y

Y

N

U

A

A/U

Y/N

1.00

0.95

-0.93

0.85

0.95

0.94

1.00

-0.99

0.71

0.91

0.77

1.00

-0.75

-0.94

-0.75

1.00

0.93

0.90

1.00

0.89

N
U
A
A/U
Y/N

1.00
Panel B: Efficiency
Standard deviations
Y

N

U

A

A/U

Y/N

1.46

0.70

3.60

8.50

11.22

0.86

Correlations

Y
N
U

Y

N

U

A

A/U

Y/N

1.00

0.92

-0.92

0.91

0.98

0.95

1.00

-1.00

0.67

0.83

0.75

1.00

-0.67

-0.83

-0.75

1.00

0.97

0.99

1.00

0.99

A
A/U
Y/N

1.00

40

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Not Working: Demographic Changes, Policy Changes,
and the Distribution of Weeks (Not) Worked
Lisa Barrow and Kristin F. Butcher

WP-04-23

The Role of Collateralized Household Debt in Macroeconomic Stabilization
Jeffrey R. Campbell and Zvi Hercowitz

WP-04-24

Advertising and Pricing at Multiple-Output Firms: Evidence from U.S. Thrift Institutions
Robert DeYoung and Evren Örs

WP-04-25

Monetary Policy with State Contingent Interest Rates
Bernardino Adão, Isabel Correia and Pedro Teles

WP-04-26

Comparing location decisions of domestic and foreign auto supplier plants
Thomas Klier, Paul Ma and Daniel P. McMillen

WP-04-27

China’s export growth and US trade policy
Chad P. Bown and Meredith A. Crowley

WP-04-28

Where do manufacturing firms locate their Headquarters?
J. Vernon Henderson and Yukako Ono

WP-04-29

Monetary Policy with Single Instrument Feedback Rules
Bernardino Adão, Isabel Correia and Pedro Teles

WP-04-30

2

Working Paper Series (continued)
Firm-Specific Capital, Nominal Rigidities and the Business Cycle
David Altig, Lawrence J. Christiano, Martin Eichenbaum and Jesper Linde

WP-05-01

Do Returns to Schooling Differ by Race and Ethnicity?
Lisa Barrow and Cecilia Elena Rouse

WP-05-02

Derivatives and Systemic Risk: Netting, Collateral, and Closeout
Robert R. Bliss and George G. Kaufman

WP-05-03

Risk Overhang and Loan Portfolio Decisions
Robert DeYoung, Anne Gron and Andrew Winton

WP-05-04

Characterizations in a random record model with a non-identically distributed initial record
Gadi Barlevy and H. N. Nagaraja

WP-05-05

Price discovery in a market under stress: the U.S. Treasury market in fall 1998
Craig H. Furfine and Eli M. Remolona

WP-05-06

Politics and Efficiency of Separating Capital and Ordinary Government Budgets
Marco Bassetto with Thomas J. Sargent

WP-05-07

Rigid Prices: Evidence from U.S. Scanner Data
Jeffrey R. Campbell and Benjamin Eden

WP-05-08

Entrepreneurship, Frictions, and Wealth
Marco Cagetti and Mariacristina De Nardi

WP-05-09

Wealth inequality: data and models
Marco Cagetti and Mariacristina De Nardi

WP-05-10

What Determines Bilateral Trade Flows?
Marianne Baxter and Michael A. Kouparitsas

WP-05-11

Intergenerational Economic Mobility in the U.S., 1940 to 2000
Daniel Aaronson and Bhashkar Mazumder

WP-05-12

Differential Mortality, Uncertain Medical Expenses, and the Saving of Elderly Singles
Mariacristina De Nardi, Eric French, and John Bailey Jones

WP-05-13

Fixed Term Employment Contracts in an Equilibrium Search Model
Fernando Alvarez and Marcelo Veracierto

WP-05-14

Causality, Causality, Causality: The View of Education Inputs and Outputs from Economics
Lisa Barrow and Cecilia Elena Rouse

WP-05-15

3

Working Paper Series (continued)
Competition in Large Markets
Jeffrey R. Campbell

WP-05-16

Why Do Firms Go Public? Evidence from the Banking Industry
Richard J. Rosen, Scott B. Smart and Chad J. Zutter

WP-05-17

Clustering of Auto Supplier Plants in the U.S.: GMM Spatial Logit for Large Samples
Thomas Klier and Daniel P. McMillen

WP-05-18

Why are Immigrants’ Incarceration Rates So Low?
Evidence on Selective Immigration, Deterrence, and Deportation
Kristin F. Butcher and Anne Morrison Piehl

WP-05-19

Constructing the Chicago Fed Income Based Economic Index – Consumer Price Index:
Inflation Experiences by Demographic Group: 1983-2005
Leslie McGranahan and Anna Paulson

WP-05-20

Universal Access, Cost Recovery, and Payment Services
Sujit Chakravorti, Jeffery W. Gunther, and Robert R. Moore

WP-05-21

Supplier Switching and Outsourcing
Yukako Ono and Victor Stango

WP-05-22

Do Enclaves Matter in Immigrants’ Self-Employment Decision?
Maude Toussaint-Comeau

WP-05-23

The Changing Pattern of Wage Growth for Low Skilled Workers
Eric French, Bhashkar Mazumder and Christopher Taber

WP-05-24

U.S. Corporate and Bank Insolvency Regimes: An Economic Comparison and Evaluation
Robert R. Bliss and George G. Kaufman

WP-06-01

Redistribution, Taxes, and the Median Voter
Marco Bassetto and Jess Benhabib

WP-06-02

Identification of Search Models with Initial Condition Problems
Gadi Barlevy and H. N. Nagaraja

WP-06-03

Tax Riots
Marco Bassetto and Christopher Phelan

WP-06-04

The Tradeoff between Mortgage Prepayments and Tax-Deferred Retirement Savings
Gene Amromin, Jennifer Huang,and Clemens Sialm

WP-06-05

Why are safeguards needed in a trade agreement?
Meredith A. Crowley

WP-06-06

4

Working Paper Series (continued)
Taxation, Entrepreneurship, and Wealth
Marco Cagetti and Mariacristina De Nardi

WP-06-07

A New Social Compact: How University Engagement Can Fuel Innovation
Laura Melle, Larry Isaak, and Richard Mattoon

WP-06-08

Mergers and Risk
Craig H. Furfine and Richard J. Rosen

WP-06-09

Two Flaws in Business Cycle Accounting
Lawrence J. Christiano and Joshua M. Davis

WP-06-10

Do Consumers Choose the Right Credit Contracts?
Sumit Agarwal, Souphala Chomsisengphet, Chunlin Liu, and Nicholas S. Souleles

WP-06-11

Chronicles of a Deflation Unforetold
François R. Velde

WP-06-12

Female Offenders Use of Social Welfare Programs Before and After Jail and Prison:
Does Prison Cause Welfare Dependency?
Kristin F. Butcher and Robert J. LaLonde
Eat or Be Eaten: A Theory of Mergers and Firm Size
Gary Gorton, Matthias Kahl, and Richard Rosen
Do Bonds Span Volatility Risk in the U.S. Treasury Market?
A Specification Test for Affine Term Structure Models
Torben G. Andersen and Luca Benzoni

WP-06-13

WP-06-14

WP-06-15

Transforming Payment Choices by Doubling Fees on the Illinois Tollway
Gene Amromin, Carrie Jankowski, and Richard D. Porter

WP-06-16

How Did the 2003 Dividend Tax Cut Affect Stock Prices?
Gene Amromin, Paul Harrison, and Steven Sharpe

WP-06-17

Will Writing and Bequest Motives: Early 20th Century Irish Evidence
Leslie McGranahan

WP-06-18

How Professional Forecasters View Shocks to GDP
Spencer D. Krane

WP-06-19

Evolving Agglomeration in the U.S. auto supplier industry
Thomas Klier and Daniel P. McMillen

WP-06-20

Mortality, Mass-Layoffs, and Career Outcomes: An Analysis using Administrative Data
Daniel Sullivan and Till von Wachter

WP-06-21

5

Working Paper Series (continued)
The Agreement on Subsidies and Countervailing Measures:
Tying One’s Hand through the WTO.
Meredith A. Crowley

WP-06-22

How Did Schooling Laws Improve Long-Term Health and Lower Mortality?
Bhashkar Mazumder

WP-06-23

Manufacturing Plants’ Use of Temporary Workers: An Analysis Using Census Micro Data
Yukako Ono and Daniel Sullivan

WP-06-24

What Can We Learn about Financial Access from U.S. Immigrants?
Una Okonkwo Osili and Anna Paulson

WP-06-25

Bank Imputed Interest Rates: Unbiased Estimates of Offered Rates?
Evren Ors and Tara Rice

WP-06-26

Welfare Implications of the Transition to High Household Debt
Jeffrey R. Campbell and Zvi Hercowitz

WP-06-27

Last-In First-Out Oligopoly Dynamics
Jaap H. Abbring and Jeffrey R. Campbell

WP-06-28

Oligopoly Dynamics with Barriers to Entry
Jaap H. Abbring and Jeffrey R. Campbell

WP-06-29

Risk Taking and the Quality of Informal Insurance: Gambling and Remittances in Thailand
Douglas L. Miller and Anna L. Paulson

WP-07-01

Fast Micro and Slow Macro: Can Aggregation Explain the Persistence of Inflation?
Filippo Altissimo, Benoît Mojon, and Paolo Zaffaroni

WP-07-02

Assessing a Decade of Interstate Bank Branching
Christian Johnson and Tara Rice

WP-07-03

Debit Card and Cash Usage: A Cross-Country Analysis
Gene Amromin and Sujit Chakravorti

WP-07-04

The Age of Reason: Financial Decisions Over the Lifecycle
Sumit Agarwal, John C. Driscoll, Xavier Gabaix, and David Laibson

WP-07-05

Information Acquisition in Financial Markets: a Correction
Gadi Barlevy and Pietro Veronesi

WP-07-06

Monetary Policy, Output Composition and the Great Moderation
Benoît Mojon

WP-07-07

Estate Taxation, Entrepreneurship, and Wealth
Marco Cagetti and Mariacristina De Nardi

WP-07-08

6

Working Paper Series (continued)
Conflict of Interest and Certification in the U.S. IPO Market
Luca Benzoni and Carola Schenone
The Reaction of Consumer Spending and Debt to Tax Rebates –
Evidence from Consumer Credit Data
Sumit Agarwal, Chunlin Liu, and Nicholas S. Souleles

WP-07-09

WP-07-10

Portfolio Choice over the Life-Cycle when the Stock and Labor Markets are Cointegrated
Luca Benzoni, Pierre Collin-Dufresne, and Robert S. Goldstein

WP-07-11

Nonparametric Analysis of Intergenerational Income Mobility
with Application to the United States
Debopam Bhattacharya and Bhashkar Mazumder

WP-07-12

How the Credit Channel Works: Differentiating the Bank Lending Channel
and the Balance Sheet Channel
Lamont K. Black and Richard J. Rosen

WP-07-13

Labor Market Transitions and Self-Employment
Ellen R. Rissman

WP-07-14

First-Time Home Buyers and Residential Investment Volatility
Jonas D.M. Fisher and Martin Gervais

WP-07-15

Establishments Dynamics and Matching Frictions in Classical Competitive Equilibrium
Marcelo Veracierto

WP-07-16

7