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Federal Reserve Bank of Chicago

On the Cyclical Behavior of
Employment, Unemployment and
Labor Force Participation
Marcelo Veracierto

REVISED February, 2008
WP 2002-12

On the cyclical behavior of employment,
unemployment and labor force participation∗
Marcelo Veracierto
Federal Reserve Bank of Chicago
February, 2008

Abstract: In this paper I evaluate to what extent a real business cycle (RBC)
model that incorporates search and home production decisions can simultaneously
account for the observed behavior of employment, unemployment and out-of-thelabor-force. This contrasts with the previous RBC literature, which analyzed
employment or hours fluctuations either by lumping together unemployment and
out-of-the-labor-force into a single non-employment state or by assuming a fixed
labor force. Once the three employment states are explicitly introduced I find
that the RBC model generates highly counterfactual labor market dynamics.

∗

I thank Fernando Alvarez, Bob Hall, Richard Rogerson and Ivan Werning for very useful
comments, as well as seminar participants at the Federal Reserve Bank of Chicago, Northwestern University, Purdue University, University of Illinois at Urbana-Champaign, Universidad de
Navarra (Spain), the 2002 SED Meetings, the 2002 NBER Summer Institute, the 2003 Midwest
Macro Conference and the 2003 NBER EFGR Meeting in San Francisco. The views expressed
here do not necessarily reflect the position of the Federal Reserve Bank of Chicago or the Federal
Reserve System. Address: Research Department, Federal Reserve Bank of Chicago, 230 South
LaSalle Street, Chicago, IL 60604. E-mail: mveracierto@frbchi.org.

1. Introduction
This paper is motivated by a very basic set of facts: that employment varies 60 percent
as much as output and is highly procyclical, that unemployment varies 6 times more than
output and is countercyclical, and that the labor force varies only 20 percent as much as
output and is weakly procyclical. The purpose of this paper is to evaluate to what extent a
real business cycle (RBC) model can jointly account for these observations.
Standard RBC models are not designed to address this type of evidence. These models
typically lump together unemployment and out-of-the-labor-force into a single nonemployment state and analyze variations in employment and hours worked by either studying a
work-leisure decision (e.g. Hansen, 1985, and Prescott, 1986) or a work-home production
decision (e.g. Greenwood and Hercowitz, 1991, and Benhabib, Rogerson, and Wright, 1991).
Given their assumption of frictionless labor markets, standard RBC models cannot be used
to analyze unemployment fluctuations.
In recent years, a number of papers have introduced search frictions into RBC frameworks,
some of them (like Andolfatto, 1996, Merz, 1995, 1999, and Den Haan, Ramey and Watson, 2000) using the Mortensen-Pissarides (1994) matching framework, others (like Gomes,
Greenwood and Rebelo, 2001) using the Lucas-Prescott (1974) islands framework. A common finding in this literature is that a RBC model that incorporates search frictions can
account for salient features of U.S. business cycles and even outperform the standard model
in several ways. While this is an important result, none of the above papers attempted to
explain the joint behavior of employment, unemployment and out-of-the-labor-force: Merz
(1995, 1999) and Gomes, Greenwood and Rebelo (2001) assumed a fixed labor force, while
Andolfatto (1996) and Den Haan, Ramey and Watson (2000) lumped together unemployment and out-of-the-labor-force into a single nonemployment state.1
Explaining the joint behavior of employment, unemployment and labor force participation
is important not only to obtain a better understanding of labor market dynamics, but to
test the empirical plausibility of the search and leisure/home-production decisions embodied
1

Strictly speaking, Den Haan, Ramey and Watson (2000) lumped together unemployment and out-ofthe-labor-force workers that claim to want a job.

in a model. Consider, for example, the models by Merz (1995, 1999) or Gomes, Greenwood
and Rebelo (2001) that allow agents to search and enjoy leisure while they are unemployed
but that restrict them to stay in the labor force. If the main reason why agents become
unemployed in those models is to enjoy leisure (i.e. if intertemporal substitution in leisure is
the main factor driving employment fluctuations), a significant number of agents would want
to leave the labor force in order to enjoy even more leisure if they were given the chance.
Thus, most of the flows from employment to unemployment during a recession could end up
being flows from employment to out-of-the-labor-force once a labor force participation margin
is allowed for, generating highly counterfactual behavior. Lumping together unemployment
and out-of-the-labor-force into a single nonemployment state (as in Andolfatto, 1996, and
Den Haan, Ramey and Watson, 2000) may hide similar problems.
A first attempt to evaluate this possibility was made by Tripier (2003), who analyzed an
eﬃcient RBC version of the Mortensen-Pissarides matching model that makes an explicit
distinction between employment, unemployment and out-of-the-labor-force.2 His main finding was that the model fails to reproduce the countercyclical unemployment rate observed
in U.S. data. While this result suggests that RBC models can have serious diﬃculties in
generating empirically reasonable labor market dynamics, it was obtained under two restrictive assumptions: 1) that workers accept the first job-oﬀer that they receive (since all jobs
have the same productivity level), and 2) that jobs are destroyed at a constant rate. Given
these assumptions, the main mechanism that can give rise to a significant increase in aggregate employment level after a positive productivity shock hits the economy is an increase in
labor force participation.3 Since new market participants must search for a job before they
become employed, it is not surprising that this mechanism will give rise to a pro-cyclical
2

Greenwood, MacDonald and Zhang (1996) also analyzed a RBC model that incorporates the three
employment states (but no search frictions). However, their focus was on the cyclical behavior of job creation
and job destruction instead of decomposing the cyclical behavior of non-employment into unemployment
and out-of-the-labor-force. Other papers that have explicitly modeled the three employment states include
Alvarez and Veracierto (2000), Andolfatto and Gomme (1996), Garibaldi and Wasmer (2005), Kim (2004),
Moon (2005), Pries and Rogerson (2004) and Veracierto (2007a), but none of them analyzed business cycle
dynamics.
3

In principle, a higher employment level could also be obtained by increasing the number of vacancies
posted. However, eﬃcient versions of the Mortensen-Pissarides model fail to generate large fluctuations in
vacancies (see Shimer, 2005).

unemployment rate. This paper extends Tripier’s analysis by introducing endogenous jobacceptance and job-separation decisions. Incorporating these margins is important because
a higher aggregate employment level can now be obtained by increasing the job-acceptance
rate or by decreasing the job-separation rate, without having to increase the size of the labor
force. Thus, contrary to Tripier’s analysis, the theory is given a fair chance at generating a
counter-cyclical unemployment rate.
The benchmark model considered is a version of one used by Alvarez and Veracierto
(2000), which in turn is based on the Lucas and Prescott (1974) equilibrium search model.
Output, which can be consumed or invested, is produced by a large number of islands
using capital and labor. Contrary to the deterministic steady state analysis of Alvarez and
Veracierto (2000), the islands are subject both to idiosyncratic and aggregate productivity
shocks. Once the shocks are observed, agents must decide whether to work in the islands
where they are currently located or to leave. The reallocation of workers across islands is
subject to search frictions. An important diﬀerence with Lucas and Prescott (1974) is that
search is undirected, leading to an endogenous average duration of unemployment. Another
diﬀerence is that an explicit out-of-the-labor-force margin is introduced: Agents are allowed
to obtain more home production leaving the labor force than becoming unemployed.
Parameter values are chosen so that the deterministic steady state of the model economy
reproduces important observations from the National Income and Product Accounts (NIPA)
and some key labor market statistics. Aggregate productivity shocks in turn are selected
to match the behavior of measured Solow residuals. Under such parametrization, I find
that the model fails to account for the joint behavior of employment, unemployment and
out-of-the-labor-force. The search and home production decisions embodied in this version
of the neoclassical growth model generate drastically counterfactual behavior, mainly: 1)
unemployment fluctuates as much as output while in the data it is six times more variable,
2) unemployment is weakly procyclical while in the data it is strongly countercyclical, 3)
employment fluctuates as much as the labor force while in the data it is three times more
variable, and 4) the labor force is strongly procyclical while it is weakly procyclical in the
actual economy. These results are robust to a wide variety of specifications for the search
technology.

Even though the paper fails to account for U.S. observations, it fails in an informative
way. The paper finds that the empirical performance of an RBC model can become quite
poor once unemployment and endogenous labor force participation are explicitly introduced.
Thus, the paper questions the ability of previous RBC models to account for labor market
fluctuations. Moreover, the paper suggests that a successful business cycle model, whatever
that may end up being, will have to give a much more important role to fluctuations in
search decisions than to fluctuations in home production or leisure.
The paper is organized as follows: Section 2 describes the model economy. Section 3
describes a competitive equilibrium. Section 4 parameterizes the model. Section 5 presents
the results. Section 6 discusses the role played by worker flows. Finally, Section 7 concludes
the paper. An appendix describes the computational algorithm.

2. The benchmark economy
The economy is populated by a representative household constituted by a unit measure of
members. Each household member is endowed with one unit of time and has preferences
described by:

(∞ "
!#)
Ã
1−φ
X
−
1
h
t
,
β t ln ct + A
E0
1
−
φ
t=0

(2.1)

where ct is consumption of a market good, ht is consumption of a home good, 0 < β < 1 is the
subjective time discount factor, φ > 0 and A > 0. The household serves as a full insurance
mechanism, pooling the resources of all its individual members. Thus, all household members
obtain an identical consumption bundle (ct , ht ).
The market good, which can be consumed or invested, is produced by a measure one of
spatially separated islands. Each island has a production function given by
yt = e(1−ϕ)at zt ltγ ktϕ ,
where yt is production, lt is the labor input, kt is the capital input, zt is an idiosyncratic
productivity shock, at is an aggregate productivity level common to all islands, γ > 0, ϕ > 0,

and γ + ϕ < 1.4 The idiosyncratic productivity shock zt follows a finite Markov process with
transition matrix Q, where Q(z, z 0 ) is the probability that zt+1 = z 0 conditional on zt = z.
Realizations of zt are assumed to be independent across islands. The aggregate productivity
level evolves according to the following AR(1) process:
at+1 = ρa at + εt+1 ,

(2.2)

where 0 < ρa < 1 and εt+1 is i.i.d., normally distributed, with variance σ 2a and zero mean.
Capital is freely mobile across islands but not labor, which is subject to search frictions.
At the beginning of every period household members diﬀer in terms of their physical
locations: Some of them are distributed across islands and some others are located outside
the islands sector. The household must decide how to allocate its members across diﬀerent
activities.5 If a household member is initially located in an island, the household has two
alternatives: To order him to stay or to order him to leave. If the household member is
ordered to stay he produces the market good and starts the following period at that same
location. If the household member is ordered to leave he becomes non-employed.
The total number of non-employed household members is given by the sum of all the
household members that are ordered to leave and all the household members that are located
outside the islands sector at the beginning of the period. The household allocates nonemployed members into two mutually exclusive activities: To search or to specialize in home
production. If a household member is ordered to search for a new employment opportunity,
he arrives to an island at the beginning of the following period with probability p.6 Since
search is undirected, all the household members that arrive to the islands sector become
uniformly distributed across all the islands in the economy. If a household member is ordered
4
The assumption of a fixed factor of production in each island (implicit in the decreasing returns to scale
assumption) is made for computational reasons: It guarantees that the labor and capital inputs of all islands
remain positive at all times. The linear computational method used in this paper is well designed to handle
this case.
5

This decision is made after all productivity shocks for the current period (both idiosyncratic and aggregate) are observed.
6

A later specifications of the model will allow this probability to vary endogenously over time.

to specialize in home production, he devotes his full time endowment to that end.
Household members that search or work also contribute to home production, but in a
more restricted way. In particular, the total amount of home production obtained by the
household is given by
ht = 1 − π U Ut − π N Nt ,

(2.3)

where Nt is the number of household members that work (i.e. that are employed), Ut is
the number of household members that search (i.e. that are unemployed), π N is the fixed
length of the workweek, π U is the fixed amount of time required by the search technology,
and 0 < π U ≤ π N ≤ 1.7 Observe that household members generate more home production
being out-of-the-labor-force than searching and that they generate more home production
searching than being employed.

3. Competitive equilibrium
In order to describe a competitive equilibrium, I will index islands according to their history of
idiosyncratic shocks z t = (z0 , z1 , ..., zt ) and their number of agents available at the beginning
of date zero, x0 . Hereon, I will denote the time t distribution of islands across these variables
by qt (z t , x0 ). Observe that qt+1 (z t+1 , x0 ) must satisfy that:
qt+1 ((z t , zt+1 ), x0 ) = qt (z t , x0 )Q(zt , zt+1 )
for every z t and zt+1 .To simplify notation, I will assume that q0 has a finite support over the
pairs (z0 , x0 ).
Since capital if freely movable, there is a single rental rate of capital rt in the whole
economy8 . On the contrary, because of the search frictions, each type of island (z t , x0 ) has
its own wage rate wt (z t , x0 ). The representative firm in an island of type (z t , x0 ) solves the
7

Hereon, I will refer to household members that specialize in home production as being “out-of-the-laborforce”. The total number of household members that are out-of-the-labor-force is given by 1 − Ut − Nt .
8

For convenience, the dependence of all variables on the history of aggregate productivity shocks at =
(a0 , a1 , ..., at ) will be suppressed from the notation.

following static maximization problem:
¡
¢
©
¡
¢
ª
Πt z t , x0 = max e(1−ϕ)at zt ltγ ktϕ − wt z t , x0 lt − rt kt ,

(3.1)

where wt and rt are taken as given. Since the representative firm behaves competitively, it
equates rental prices to marginal productivities:
¡
¢
¡
¢γ−1 ¡ t ¢ϕ
wt z t , x0 = e(1−ϕ)at zt γlt z t , x0
kt z , x0 ,
¡
¢γ
¡
¢ϕ−1
.
rt = e(1−ϕ)at zt lt z t , x0 ϕkt z t , x0

(3.2)
(3.3)

The total number of household members that the representative household puts to work
in islands of type (z t , x0 ) is denoted by nt (z t , x0 ). This number is constrained by the total
number of household members located in islands of type (z t x0 ) at the beginning of the period.
At date zero, this constraint takes the simple form
n0 (z0 , x0 ) ≤ x0 q0 (z0 , x0 ),

(3.4)

where the right hand side is the number of islands of type (z0 , x0 ) multiplied by the number
of agents present in each of these islands at the beginning of date zero, x0 . In all other dates,
the constraint becomes:
¡
¢
¡
¢
¡
¢
nt z t , x0 ≤ nt−1 z t−1 , x0 Q (zt−1 , zt ) + pUt−1 qt z t , x0 .

(3.5)

Observe that, in this case, the total number of household members located in islands of type
(z t x0 ) at the beginning of the period is given by the sum of two terms. The first term is
the total number of household members that were put to work in islands of type (z t−1 , x0 )
in the previous period and their locations transited from zt−1 to zt . The second term is
the total number of household members that were put to search during the previous period
Ut−1 , times the fraction that arrived to the islands sector p, times the fraction that arrived
to an island of type (z t , x0 ). Observe that this second term takes into account the fact that
search is undirected: Unemployed agents that arrive to the islands sector become uniformly

distributed across all the islands in the economy.
The total number of household members that work is given by
Nt =

z t ,x0

¡
¢
nt z t , x0 ,

(3.6)

i.e. it is the sum of nt (z t , x0 ) across all the diﬀerent types of islands in the economy.
The problem of the representative household is to maximize the utility function (2.1)
subject to equations (2.2), (2.3), (3.4)-(3.6) and the following budget constraint:
ct + Kt+1 − (1 − δ) Kt ≤ rt Kt +

z t ,x0

¡
¢ ¡
¢ X ¡ t ¢ ¡ t ¢
wt z t , x0 nt z t , x0 +
Πt z , x0 qt z , x0 , (3.7)
z t ,x0

where Kt is the stock of capital owned by the household at the beginning of the period.
Equation (3.7) states that the value of consumption and investment cannot exceed total
income, which is given by the sum of capital rental income, total wage earnings and total
profits. Observe that the last term in equation (3.7) implicitly assumes that the representative household owns one share of each island in the economy. Also observe that the household
takes rt , wt (z t , x0 ), Πt (z t , x0 ), qt (z t , x0 ), K0 and a0 as given.
The optimal household decisions are easily characterized. The investment decisions must
satisfy a standard Euler equation:
1 = βEt

∙

ct
ct+1

¸
(rt+1 + 1 − δ) .

(3.8)

This condition states that the cost of investing in one unit of capital must be equal to
its expected discounted return, where date t and date t + 1 consumption units are valued
according to their marginal utilities.
The optimal labor allocation decision can be described in terms of the value ξ t (z t , x0 ) ≥ 0

of having a worker in an island of type (z t , x0 ) at the beginning of period t.9 This value must
9

Actually, ξ 0 (z0 , x0 ) and ξ t (z t , x0 ) are the Lagrange multipliers of constraints (3.4) and (3.5), respectively.

satisfy the following condition:
¡
¢
ξ t (z t , x0 ) ≤ wt z t , x0 − π N A (1 − π U Ut − πN Nt )−φ ct
"
#
£ t
¤
ct X
ξ t+1 (z , zt+1 ), x0 Q(zt , zt+1 ) ,
+βEt
ct+1 z

(3.9)

t+1

with equality if nt (z t , x0 ) > 0. Since nt (z t , x0 ) is always positive in equilibrium, equation
(3.9) states that ξ t (z t , x0 ) must be equal to the expected discounted surplus value of having
a household member permanently employed in the island instead of permanently specialized
in home production.
In addition, the following complementary slackness conditions must hold:
£
¡
¢
¡
¢
¡
¢¤
ξ t (z t , x0 ) nt−1 z t−1 , x0 Q (zt−1 , zt ) + pUt−1 qt z t , x0 − nt z t , x0
= 0,
ξ 0 (z0 , x0 ) [x0 q0 (z0 , x0 ) − n0 (z0 , x0 )] = 0.

(3.10)
(3.11)

These equations state that whenever the surplus value of having a worker permanently
employed in an island is strictly positive, the household puts to work all the workers available
in that island at the beginning of the period. The household orders some of its members to
leave only when it is indiﬀerent between letting them work in the island and taking them
out-of-the-labor-force.
The last decision variable for the household is the number of household members to put to
search Ut . Assuming an interior solution, this decision must satisfy the following condition:
⎡

πU A (1 − π U Ut − π N Nt )−φ ct = pβEt ⎣

z t+1 ,x0

⎤
£
¤
¡
¢
ct
ξ t+1 z t+1 , x0 qt+1 z t+1 , x0 ⎦

ct+1

(3.12)

The left-hand-side is the amount of home production foregone by putting a household member to search instead of keeping him out-of-the-labor-force. The right-hand-side is the probability that the unemployed worker will arrive to the islands sector p, times the expected
discounted value of obtaining one additional household member at some randomly determined island. Observe that this expected value reflects the undirected nature of search.

Because of the search frictions, each type of island (z t , x0 ) has its own labor market
clearing condition:
¡ t ¢
nt (z t , x0 )
=
l
z , x0 .
t
qt (z t , x0 )

(3.13)

The left-hand-side is the number of household members that the representative household
puts to work in each island of type (z t , x0 ). The right-hand-side is the quantity of labor
demanded by the representative firm in an island of type (z t , x0 ).
Because capital is fully flexible there is a single market clearing condition for the whole
economy:
Kt =

z t ,x0

¡
¢ ¡
¢
kt z t , x0 qt z t , x0 ,

(3.14)

This equation states that the capital supplied by the representative household must be equal
to the total quantity demanded by all the islands in the economy.
Finally, the market clearing for the consumption good is given by:
ct + Kt+1 − (1 − δ) Kt =

z t ,x0

¡
¢
e(1−ϕ)at zt lt (z t , x0 )γ kt (z t , x0 )ϕ qt z t , x0 .

(3.15)

That is, the sum of consumption and investment must be equal to the aggregate output
produced by all the islands in the economy.
A competitive equilibrium is a stochastic process {ct , Kt+1 , nt , Ut , Nt , ht , ξ t , lt , kt , wt ,

rt , Πt }∞
t=0 such that equations (2.2)-(3.15) are satisfied, with a0 , K0 and q0 given. Since
the economy is convex, the Welfare Theorems hold. Thus a competitive equilibrium can
be obtained by solving the social planner’s problem, which is to maximize equation (2.1)
subject to equations (2.2), (2.3), (3.4), (3.5), (3.6), (3.13), (3.14) and (3.15), taking a0 , K0
and q0 as given. The appendix describes the algorithm used to compute the solution to this
social planner’s problem.

4. Parameterization
This section describes the observations used to calibrate the steady state of a deterministic
version of the competitive equilibrium described in the previous section, in which the aggre-

gate productivity shock at is set to its unconditional mean of zero. The curvature of home
production in the utility function (φ) and the time requirements for search and employment
(π U and π N ), will be taken as free parameters in the experiments below. The parameters
to be calibrated are β, A, γ, ϕ, δ, the values for the idiosyncratic productivity shock z, the
transition matrix Q, and the parameters determining the driving process for the aggregate
productivity shock a. The time period selected for the model is one month. A short time period is called for in order to reproduce the relatively short average duration of unemployment
observed in U.S. data.
The stock of capital in the market sector K is identified with business capital, that
is, with plant, equipment and inventories. As a result, investment in business capital I is
associated in the National Income and Product Accounts with fixed private non-residential
investment plus changes in business inventories. Considering that the depreciation rate is
related to steady state I and K according to
δ=

I
,
K

the average I/K ratio over the period 1967:Q1 to 1999:Q4 gives a monthly depreciation rate
δ = 0.0066.
In turn, consumption c is identified with consumption of non-durable goods and services
(excluding housing services). Output is then defined as the sum of these consumption and
investment measures. The average monthly capital-output ratio K/Y corresponding to the
period 1967:Q1 to 1999:Q4 is 25.8.
The interest rate in the model economy is given by
1+i=

1
.
β

As a consequence β = 0.9967 is chosen to reproduce an annual interest rate of 4 percent,
roughly the average between the return on equity and the return on treasury bills in the U.S.
economy.
The Cobb-Douglas production function and the competitive behavior assumption implies

that ϕ equals the share of capital in output. That is,
µ

1
−1+δ
β

Given the previous values for β, δ, and

K
,
Y

K
= ϕ.
Y

it follows that ϕ = 0.2554. On the other hand,

γ = 0.64 is selected to reproduce the labor share in National Income.
The idiosyncratic productivity levels z and the transition matrix Q are chosen to approximate (by quadrature methods) the following AR(1) process:
log zt+1 = ρz ln zt + εzt+1 ,
where εzt+1 is i.i.d., normally distributed, with zero mean and variance σ 2z .10 Since the
stochastic process for the idiosyncratic productivity shocks is a crucial determinant of the
unemployment rate and the average duration of unemployment, ρz and σ 2z will be selected to
reproduce an unemployment rate of 6.2 percent and an average duration of unemployment
equal to one quarter, which correspond to U.S. observations. The weight of home production
in the utility function A in turn will be selected to reproduce a labor force participation equal
to 74 percent (the average ratio between the size of the labor force and total population
between 16 and 65 years old). The actual values for ρz , σ 2z and A will depend on the values
for π U and π N , which are taken as free parameters.
Finally, using the measure of output described above and a labor share of 0.64, measured Solow residuals are found to be as highly persistent but somewhat more variable than
Prescott (1986): the standard deviation of quarterly technology changes is 0.009 instead of
0.0076. As a consequence, ρa = 0.98 and σ 2a = 0.0092 /3 are chosen here.
Table 1 reports parameter values for all the specifications that will be considered later
on.
10

Only three values for z will be allowed in the computations. While this may not seem a large number, it
leads to a considerable amount of heterogeneity: The support of the invariant distribution of islands across
employment levels will be over one thousand points in most of the experiments reported below.

5. Results
In order to evaluate the behavior of the model economy, Table 2 reports quarterly U.S. business cycle statistics. Before any statistics were computed, all time series were logged and
detrended using the Hodrick-Prescott filter. The empirical measures for output Y , consumption c, investment I and capital K reported in the table correspond to the measures described
in the previous section, and cover the period between 1967:Q1 and 1999:Q4. The table shows
some well known facts about U.S. business cycle dynamics: that consumption and capital
are less variable than output while investment is much more volatile, and that consumption
and investment are strongly procyclical while capital is acyclical. The variability of labor
relative to output (0.57) is lower than usual because it refers to employment instead of total
hours worked. What is important in Table 2 is the variability of unemployment, which is 6.25
times the variability of output, and the variability of the labor force, which is only 0.20 times
the variability of output. While employment is strongly procyclical, labor force participation
is only weakly procyclical. On the contrary, unemployment is strongly countercyclical: its
correlation with output is -0.83. Note that even though unemployment is a small fraction
of the labor force, its behavior is key in generating a much larger variability in employment
than in labor force participation.
In what follows I report results for diﬀerent versions of the model economy. The analysis
will relate the paper to the previous literature and show the robustness of the results to
diﬀerent specifications of the search technology. In all cases the free parameter φ, which
determines the curvature of home production in the utility function, will be chosen to reproduce the standard deviation of employment observed in the U.S. economy. This will give
the model the best chances at mimicking observed labor market dynamics. Despite of this,
we will see that the model performs quite poorly.
5.1. Home production while unemployed
This section reports the main results of the paper: It shows that the model economy is unable
to reproduce the joint behavior of employment, unemployment and labor force participation
observed in U.S. data. In order to make the results more transparent, I will assume that all

agents that search arrive to the islands sector with probability one, i.e. p = 1. Later on, I
will relax this assumption.
Since there is no reliable data on the amount of time that unemployed agents spend
searching, this section will show results for diﬀerent values of π U . The only restriction that I
will impose is that total hours spent in market activities π U U + π N N must be equal to 0.33,
which is the magnitude commonly used in the RBC literature.
5.1.1. Case π U = π N
To start with, let consider the case in which π U = π N . This case is important because agents
obtain the same amount of home production being unemployed than being employed: The
only way that they can obtain additional home production is by leaving the labor force. The
first column of Table 3 (“π U = π N , flexible labor force”) reports the results for this case. The
statistics correspond to averages across 100 simulations of 408 periods each (corresponding
to the 136 quarters of data). Before computing these statistics, the monthly data generated
by the model was aggregated to a quarterly time period and then logged and detrended
using the Hodrick-Prescott filter. Comparing the business cycles generated by this version
of the model with those of the U.S. economy, we see that consumption fluctuates less than
output in both economies but that it is considerably smoother in the model than in the
U.S.: its relative volatility is 0.32 instead of 0.57. Investment is about 4.5 times as variable
as output in both economies, and it is strongly procyclical in both. Employment fluctuates
the same amount in the model as in the data (parameter values were selected to generate
this result) and is strongly procyclical in both economies. Thus we see that the model, in
principle, has the same ability of reproducing standard business cycle statistics as previous
RBC models. However the model fails badly in terms of the labor market dynamics that it
generates. There are four main problems: 1) unemployment is only slightly more variable
than output while it is six times more volatile than output in the data, 2) unemployment is
weakly procyclical while it is strongly countercyclical in the U.S., 3) employment fluctuates
as much as the labor force while employment is three times more variable than the labor
force in the U.S. economy, and 4) labor force participation is strongly procyclical while it is
weakly procyclical in the actual economy.

To shed light on these model statistics Figure 1 shows diﬀerent impulse responses to
a positive aggregate productivity shock equal to one standard deviation.11 The variables
reported are employment (Nt ), unemployment (Ut ), labor force (Ut +Nt ), the job acceptance
t
t
rate ( Hiring
), and the job separation rate ( FNiring
). The basic intuition for these responses
pUt−1
t−1

can be obtained from considering the social planner’s problem. When the aggregate shock
hits the economy the social planner wants to increase employment as soon as possible.
However, on impact this can be achieved only by decreasing the job separation rate or by
increasing the job acceptance rate: The number of workers present in the islands sector is
initially predetermined. The gains from decreasing the separation rate turn out to be very
small. The reason is that, at steady state, most of the job separations already take place in
islands with very low idiosyncratic productivity levels. As a consequence, the social planer
generates most of the initial increase in aggregate employment through a large increase in
the job acceptance rate. It is important to observe that this spike in the job acceptance rate
reduces the initial average idiosyncratic productivity of employed workers.
In order to take advantage of the persistent aggregate productivity shock the social
planner also decides to increase the size of the labor force. Given that there are no adjustment
costs in this margin, the full adjustment takes place as soon as the aggregate shock hits the
economy. This has important implications for unemployment. Since workers enter the labor
force as searchers, the sudden increase in labor force participation generates a large initial
increase in unemployment in spite of the spike in the job acceptance rate.
In subsequent months, the social planner continues to bring workers from unemployment
into employment but trying to achieve a more eﬃcient allocation of workers across islands.
This is clearly seen during the first month after the aggregate shock: Since the average idiosyncratic productivity of employed workers had decreased significantly during the previous
month, the social planner takes corrective actions by sharply reducing the job acceptance
rate and by slightly increasing the job separation rate. The social planner can aﬀord to pursue a more eﬃcient allocation of labor because of the large number of workers that he now
has arriving to the islands sector. As the eﬀects of the aggregate shock die oﬀ, the higher
11

Observe that the month in which the aggregate productivity shock hits the economy is labelled “month
0” in Figure 1.

desire for eﬃciency gets reinforced by a lower desired level for aggregate employment.12 As
a result, the social planner keeps reducing the job acceptance rate and keeps raising the
job separation rate over time, reallocating workers from low productivity islands to high
productivity islands and reducing the size of the labor force. In the long run all variables
end-up reverting to their initial steady state levels.13
It is important to point out that there are two channels driving the employment fluctuations reported above. The first channel is the standard one: When there is a good aggregate
productivity shock it is a bad time to do home production, so the social planner instructs
agents to substitute home goods intertemporally and supply more employment. The second
channel arises from the timing of the search decisions: When there is a good aggregate shock
it is a bad time to search for a good idiosyncratic productivity shock, so the social planner instructs agents to accept employment more easily and leave the islands less frequently.
Since the business cycle behavior of employment and labor force participation are almost
identical, the results so far suggest that the first channel is the most important: Fluctuations
in the decisions to reallocate workers across islands seem to play a small role in aggregate
dynamics.
To verify that this is indeed the case I consider a modified version of the economy in
which households are subject to a large disutility cost from changing the size of the labor
force. This disutility cost does not aﬀect the steady state of the economy but has large
eﬀects on the business cycle dynamics. In particular, since additional home production can
only be obtained by leaving the labor force, this term kills the intertemporal substitution in
home goods as a source of employment fluctuations: Changes in the decisions to reallocate
workers across islands (the second channel mentioned above) becomes the only source of
employment fluctuations. The second column of Table 3 (“π U = π N , fixed labor force”)
shows the results for this case. Not surprisingly we see that when the labor force is eﬀectively
fixed unemployment becomes countercyclical, since recessions are good periods to search for
better idiosyncratic shocks. However, we see that this channel is not an important source
12

Aggregate employment actually peaks two months after the aggregate shock.

This long-run trend cannot be observed in Figure 1 since it shows too few periods.

of employment fluctuations: Compared with the original case (in which both channels are
present), the relative standard deviation of employment drops from 57% to 3% while the
relative standard deviation of unemployment drops from 147% to 41%. We conclude that
intertemporal substitution in home production is, by far, the most important mechanism
generating employment fluctuations in the model economy. This will represent a fundamental
problem: In all cases considered it will make employment follow labor force participation
too closely, generating highly counterfactual business cycle statistics.
5.1.2. Case π U = 0.01π N
Let now consider the other extreme: The case in which searching for a job takes only 1%
as much time as being employed. Observe that in this case agents obtain almost the same
amount of home production being unemployed as being out-of-the-labor-force.14 As a consequence, the utility weight of home goods A must be increased in order to match the same
labor force participation rate. Also, since agents obtain plenty of home production while
being unemployed, the variance σ 2z and persistence ρz need to become much smaller in order
to generate the same unemployment rate and average duration of unemployment.
It will be convenient to start the analysis by considering the case of a large disutility cost
to changing the labor force. The fourth column in Table 3 (“π U = 0.01π N , fixed labor force”)
shows the results. We see that, when the labor force is eﬀectively fixed, the cyclical behavior
of employment generates a highly variable and countercyclical unemployment level.15 This
result was also obtained by papers that introduced search into RBC models, but that fixed
the labor force and allowed agents to enjoy leisure while unemployed (e.g. Merz 1995,
1999, Gomes, Greenwood and Rebelo, 2001). However, we’ll see that this apparent success
relies on a strong home-good intertemporal substitution eﬀect and on the fixed labor force
assumption. When the labor force is allowed to change the model will generate implausible
dynamics.
14

The case π U = 0 cannot be considered since no agent would be out-of-the-labor-force.

Actually a bit too variable and countercyclical compared to the data: 7.84 versus 6.25 and -0.97 versus
-0.83, respectively.

The third column in Table 3 (“π U = 0.01π N , flexible labor force”) reintroduces the labor
force participation margin, i.e. it sets the disutility cost of changing the labor force to
zero. In this case, employment becomes as variable as in the data (parameter values were
selected to deliver this result) and continues to be strongly procyclical. However, the model
displays the same problems as in the previous section: Unemployment fluctuates too little
and is weakly procyclical, and the labor force varies as much as employment and is strongly
procyclical.
To understand this result, observe that calibrating this version of the model requires that
the productivity diﬀerences across islands be small (low σ2z ) and that these diﬀerences be
quite transitory (low ρz ). As a result, the social planner becomes quite indiﬀerent about
the distribution of agents across islands and the home-good intertemporal substitution eﬀect
becomes the only source of employment fluctuations (fluctuations in the reallocation of agents
across islands play virtually no role). Given that it is relatively easy to re-employ workers
(the arrival rate p is equal to one and all islands look roughly the same) and given that the
aggregate productivity shock is highly persistent, during recessions the social planner sends
agents outside the labor force (in order to obtain the additional amount of home production)
instead of into unemployment. Thus, labor force participation follows the cyclical behavior
of employment too closely.
5.2. Low arrival rates
This section explores how the business cycles of the model economy are aﬀected when the
arrival rate p is allowed to take values less than one. Table 4 shows results for p equal to 1,
0.75 and 0.50.16
Before describing the results it is important to point out that reducing the arrival rate
p increases the average duration of unemployment. Also, since a lower value of p makes it
more diﬃcult to become re-employed, workers reduce their job separation rate. Thus, in
order to match the same unemployment rate and average duration of unemployment as in
16

Throughout the rest of the paper I will assume that πU = 0.5π N . This is between the two extremes
considered in the previous section and is the case analyzed by Andolfatto (1996). However, similar results
are obtained when π U = π N or π U = 0.01π N are used instead.

the U.S. economy, the persistence ρz and the variance σ 2z of the idiosyncratic shocks must be
recalibrated. In particular, the persistence ρz must be lowered and the variance σ 2z must be
increased quite significantly (see Table 1). The increase in σ 2z has an important consequence
for business cycle fluctuations: It substantially reduces the variability of the job acceptance
rate. The reason is that as the islands become characterized by either very small or very
large idiosyncratic productivity levels, the realization of the aggregate productivity shock
becomes less relevant for determining which islands workers should join.
Given that the arrival rate is fixed and that the job acceptance rate becomes less responsive to an aggregate shock, obtaining a same increase in aggregate employment now
requires a larger increase in the number of agents that search. This in turn requires a larger
increase in labor force participation. As a consequence we see in Table 4 that, as the arrival
rate p decreases, unemployment and labor force participation become more volatile while
the variability of employment remains the same. Also observe that with a lower value of p a
smaller fraction of the labor force entrants arrive to the islands sector, but those that arrive
are more likely to accept employment right away.17 Thus, the labor force entrants that do
not arrive to the islands sector are soon no longer needed and are quickly sent back to being
out-of-the-labor-force. This eﬀect is reflected in Table 4, which shows that unemployment
and labor force participation become less procyclical as the arrival rate p decreases.
While the larger variability of unemployment and the lower procyclicality of unemployment and labor force participation may be seen as improvements over the p = 1 case, the
eﬀects are small and they come at the expense of increasing the volatility of labor force participation (which was already too high). Thus, lowering the arrival rate p does not improve
the ability of the model to account for the cyclical behavior of U.S. labor markets.
5.3. Endogenous search intensity
In what follows, three diﬀerent ways of endogenizing the arrival rate p will be considered. In
the first specification p will depend on the amount of goods spent in the search process, in
17

With a lower arrival rate p the job acceptance rate must be higher in order to match the same average
duration of unemployment

the second specification p will depend on the amount of time spent in the search process, and
in the third specification p will depend on the amount of eﬀort spent in the search process.
5.3.1. Search requires goods
In this section, the probability p that an unemployed workers arrives to the islands sector is
given by
pt = Ωsηt ,

(5.1)

where st is the amount of consumption goods that the worker spends in the search activity
and 0 ≤ η < 1.
Under this specification, the feasibility condition for the consumption good (3.15) becomes the following:
ct + Kt+1 − (1 − δ) Kt +

Its

≤

e(1−ϕ)at zt nt (x, z)γ kt (x, z)ϕ μt (dx, dz),

(5.2)

where Its is the total amount of consumption goods invested in the search process, i.e.
Its = st Ut .

(5.3)

All other feasibility conditions remain unchanged.18 The implicit assumption in equation
(5.3), that each unemployed worker spends the same amount of goods st , is justified by the
concavity of the search technology.19
Table 5 shows the business cycle fluctuations for this modified economy under η = 0,
η = 0.25 and η = 0.50. Observe that the η = 0 case is identical to the economy with fixed
18

Observe that equations (5.1) and (5.3) imply that the rate at which unemployed workers meet employment opportunities pt depends positively on the ratio of total search investment Its to total unemployment
Ut . This feature is shared by the Mortensen-Pissarides model, in which Its is determined by the total number
of vacancies. However, there is a key diﬀerence between both models: While in Mortensen-Pissarides the
arrival of workers to specific production units can be directed by posting vacancies, in this paper search is
undirected. For an islands economy with vacancy posting and matching, see Veracierto (2007b).
19

To see this, let ζ t be any distribution of unemployed workers across searchR intensity levels. Consider an
alternative distribution ψ t that puts all its mass at the search intensity level sdζ t . From the concavity of
equation (5.1) it follows that ψ t would use the same amount of consumption goods as ζ t but increase the
total number of arrivals to the islands sector.

arrival rate p. The other two cases capture the eﬀects of a time varying arrival rate. In all
cases the search productivity parameter Ω is adjusted to generate a steady state arrival rate
p equal to 0.75.20
As η increases, three diﬀerent eﬀects take place. The first eﬀect arises from the fact
that search becomes costly not only in terms of the foregone home production, but in terms
of the consumption goods required by the search process. In response to this additional
cost, the social planner decides to increase the job acceptance rate and decrease the job
separation rate, lowering the average duration of unemployment and the unemployment
rate. Thus, in order to reproduce U.S. observations, the persistence ρz and the variance
σ 2z of the idiosyncratic shocks must be increased. For the same reasons as in the previous
section, this reduces the variability of the job acceptance rate over the business cycle, which
in turn reduces the variability of employment and unemployment.
The second eﬀect is more straightforward. As η increases, a given increase in search intensity has a larger eﬀect on the arrival rate of agents to the islands sector. As a consequence,
employment increases more rapidly (and unemployment decreases more rapidly) after a positive aggregate hits the economy. This makes employment behave more procyclically and
unemployment more countercyclically.
The combination of the first two eﬀects can be clearly seen when the preferences are
extended to include a large penalty for changing the labor force (i.e. when the labor force is
eﬀectively fixed). In this case, Table 5 shows that increasing η reduces the variability of employment and unemployment, and makes employment more procyclical and unemployment
more countercyclical.
The third eﬀect arises from a change in the variability of labor force participation. Observe that, during a recession, agents reduce their search intensity in order to avoid paying
the search costs. When η is large, this decreases the arrival rate of unemployed agents to the
islands sector quite significantly, reducing the benefits of remaining unemployed compared
to leaving the labor force (and obtaining more home production). As a consequence, when
η increases, part of the flows from employment to unemployment during a recession become
20

Similar results are obtained when Ω is chosen to generate a steady state arrival rate p equal to 0.50.

flows from employment to out-of-the-labor-force. This makes labor force participation more
variable and unemployment more variable and procyclical.
Not only each of the above eﬀects is small, but the third eﬀect works in opposite direction
to the previous two. Thus, when the adjustment costs to changing the labor force are
removed, i.e. when the labor force becomes fully flexible, Table 5 shows that the eﬀects of
increasing η are extremely small. We conclude that introducing a search intensity margin
(asuming that search requires goods) does not improve the ability of the model to reproduce
U.S. labor market dynamics.
5.3.2. Search requires time
In this section, the probability p that an unemployed workers arrives to the islands sector is
given by
p = b(s − smin )
where s ≥ smin is the amount of time that the worker spends in the search activity, 0 ≤ b ≤

1, b0 > 0 and b00 < 0.

A straightforward consequence of the strict concavity of b is that the household never
chooses to distribute its members across diﬀerent search intensity levels. To see this, let
Ut be the number of household members that search and ζ t be a distribution of household
members across search intensity levels. Observe that the household’s total amount of home
production is given by
ht = 1 − Ut

sdζ t − π N Nt ,

(5.4)

and that the total number of arrivals is given by
Mt = Ut

b(s − smin )dζ t .

(5.5)

Thus, choosing the same number of searchers Ut but picking an alternative distribution ψt
R
that puts all its mass at the search intensity level sdζ t would generate the same amount
of leisure as before but produce a higher Mt .

Another important property of this search specification is that the optimal search inten-

sity level is constant over time and across states. To see this, substitute equation (5.5) in
equation (5.4) and use the fact that the optimal distribution of household members across
search intensity levels is degenerate, to obtain that
ht = 1 − Mt

st
− πN Nt ,
b(st − smin )

where st is the search intensity level of all household members. Thus, given any desired
value for the total arrivals Mt , the household can increase its amount of home production
by choosing st to maximize:
b(st − smin )
,
st

(5.6)

a choice which is independent of the time and the state.
We conclude that the search specification considered in this section is observationally
equivalent to the benchmark specification, in which the arrival probability p is constant and
search requires a fixed amount of time π U : Given arbitrary values for p and π U , the function
b can always be chosen so that the search intensity s that maximizes equation (5.6) satisfies
that p = b(s) and s = π U . Thus, when search requires time the endogenous search intensity
margin does nothing to improve the ability of the model to reproduce U.S. labor market
dynamics.
5.3.3. Search requires eﬀort
Similarly to the benchmark economy, this section assumes that search requires a fixed amount
of time π U . However, the probability that a household member arrives to the islands sector
is now given by:
pt = Ωsηt
where st is the amount of eﬀort that the worker spends in the search activity, 0 ≤ η < 1, and
Ω > 0. Observe that the assumption that search requires eﬀort is not unreasonable: It is
quite plausible that finding a job requires not only time, but putting attention into writing
eﬀective resumes, putting the correct attitude in the job interviews, etc.
The representative household values consumption and home production but dislikes to

have its members exert search eﬀort. Its utility function is now given by:
∞
X
E βt
t=0

(

ln ct + A

−1
h1−φ
t
1−φ

− BSt

)

where B > 0 and St = Ut st is the total amount of eﬀort exerted by its household members.21
The functional form with respect to search eﬀort is, admittedly, ad-hoc. However, it is chosen
to improve the chances of search intensity aﬀecting business cycle dynamics: With the linear
specification, it is very easy for the household to substitute search eﬀort intertemporally and
withstand large changes in this variable. Despite of this, it will be shown below that, even in
this case, modelling endogenous fluctuations in the arrival rate pt does not change the basic
results.
Before proceeding observe that, contrary to the “search requires time” specification, the
arrival rate pt will generally display fluctuations in this “search requires eﬀort” case. To see
this, note that total leisure is still given by equation (2.3) while the total number of arrivals
is now given by
Mt = Ut Ωsηt .

(5.7)

Using equations (2.3) and (5.7), the household’s utility function can now be written as
follows:
∞
X
E βt
t=0

(

ln ct + A

Ã£
1−

πU
Mt s−η
t
Ω

− πN Nt
1−φ

¤1−φ

−1

1
− B Mt s1−η
t
Ω

)

Thus, the optimal choice of search eﬀort st will now depend on the choices for Mt and Nt .
In what follows I consider the cases η = 0, η = 0.25 and η = 0.50. The η = 0 case is
identical to the benchmark economy with fixed arrival rate p. The other two cases are meant
to capture the eﬀects of a time varying arrival rate. In all cases the productivity parameter
Ω is adjusted to generate a steady state arrival rate p equal to 0.75.22 Table 6 shows the
21

Similarly to the previous specifications, it is easy to argue that the representative household will always
choose a degenerate distribution of household members across search eﬀort levels. That is, all searchers exert
the same eﬀort level st .
22

Similar results are obtained when Ω is chosen to generate a steady state arrival rate p equal to 0.50.

results. We see that it makes little diﬀerence whether the search intensity costs are in terms
of goods or in terms of eﬀort: The results in Table 6 are virtually the same as in Table
5. We conclude that the diﬃculty of RBC models to account for labor market dynamics is
independent of the specification for an endogenous search intensity.

6. Worker flows
Before concluding I would like to provide a few remarks about the role and empirical plausibility of the worker flows underlying the model economy. An apparent drawback of the model
is that it does not allow for direct flows from out-of-the-labor-force (OLF) into employment
while these flows are quite large in the U.S. economy (e.g. Blanchard and Diamond, 1990).
However, if the model time period is short relative to the frequency at which workers are
surveyed, positive flows from OLF into employment would be obtained due to time aggregation. Moreover, it wouldn’t be diﬃcult to reproduce the magnitude of the flows observed in
the data. The reason is that worker flows are actually undetermined in the model economy.
The source of the indeterminacy is that all workers become identical once they leave employment: There is nothing pinning down which nonemployed workers leave the labor force and
which go into unemployment. Arbitrary rules about which workers go into unemployment
can then be used to generate any level of OLF-into-employment flows within a wide range.
To be specific, if all searchers are assumed to have been inside the labor force during the
previous period, zero flows from OLF into employment would be obtained. On the other
extreme, if all searchers are assumed to have been OLF during the previous period, large
measured flows from OLF into employment would be obtained after two model periods.
Given this indeterminacy, it is important to observe that the model does not provide
a theory of worker flows across labor market states but a theory of how many people are
employed, unemployed and OLF in any given period of time. In order to pin down worker
flows the model would have to be extended to incorporate heterogenous agents (which would
add an additional layer of complication to the analysis). However, since the model already
fails to reproduce the behavior of labor market stocks when the flows are allowed to be
undetermined, there is little hope that such an extension would improve its business cycle

behavior.
Finally, although we have seen that it is not crucial for reproducing worker flows in U.S.
data, it is natural to wonder about the consequences of modifying the search technology
to allow for direct transitions from OLF into employment. Would it improve the business
cycle performance of the model? The answer to this question, however, is negative: The
business cycle properties of the model would be worsened. The reason is that by making
it easier for people to transit from OLF into employment, there would be even stronger
reasons to move OLF (instead of becoming unemployed) when agents separate from their
jobs. As a consequence, fluctuations in employment would be even more closely mirrored by
fluctuations in OLF, which was already the main reason why the benchmark model failed to
reproduce the observed behavior of U.S. labor markets.

7. Conclusions
In this paper I analyzed a RBC model that makes an explicit distinction between unemployment and out-of-the-labor-force. I found that the model has serious diﬃculties in reproducing
the type of labor market dynamics observed in U.S. data. The model delivers four highly
counterfactual results: 1) unemployment fluctuates as much as output while in the data it
is six times more variable, 2) unemployment is weakly procyclical while in the data it is
strongly countercyclical, 3) employment fluctuates as much as the labor force while in the
data it is three times more variable, and 4) the labor force is strongly procyclical while it
is weakly procyclical in the actual economy. The reason for the poor empirical performance
of the model is that most of the employment fluctuations are the result of strong homegoods intertemporal substitution eﬀects: Fluctuations in the decisions to reallocate workers
across islands play a minor role. Given that aggregate productivity shocks are highly persistent, that agents obtain more home production being out-of-the-labor-force than being
unemployed and that it is relatively easy to find employment, when agents decide to enjoy
home goods they choose to leave the labor force instead of becoming unemployed. As a consequence, most of the variations in employment are reflected in fluctuations in labor force
participation instead of unemployment, generating counterfactual labor market dynamics.

Despite the failure of the model the paper provides an important lesson. It shows that
the empirical performance of a RBC model that relies on persistent aggregate productivity
shocks and a high intertemporal elasticity of substitution in home-goods can become quite
poor once unemployment and endogenous labor force participation are explicitly introduced.
Thus the paper questions the ability of previous RBC models to account for labor market
fluctuations. The fact that the model fails under a wide range of specifications for the search
technology makes its point stronger.
The key question that the paper has left unanswered is “What type of model would
generate empirically reasonable labor market dynamics?”. An obvious answer seems to be a
RBC model with adjustment costs to labor force participation. In fact, it is straightforward
to verify that introducing adjustment costs of this sort to the benchmark model can generate
empirically relevant labor market dynamics. The reason is quite simple: When there is a bad
aggregate productivity shock and agents are willing to substitute towards home production,
the adjustment costs in labor force participation induce agents to become unemployed instead
of leaving the labor force. Under large adjustment costs and a high intertemporal substitution
in home goods, the model behaves quite similarly to the economy “π U = 0.01π N , fixed labor
force” in Table 3, generating empirically reasonable labor market dynamics.
However this answer cannot satisfy us. There are no good economic reasons to justify this
type of adjustment costs in an RBC model. While there may be many out-of-the-labor-force
activities subject to large adjustment costs (such as child rearing), these are not the type
of activities that are relevant for understanding fluctuations at business cycle frequencies.
What matters is the type of activities that unemployed agents undertake when they are
not searching. If a RBC model allows agents to intertemporally substitute these activities
very easily, it is not clear why there should be large costs to stop searching (leaving the
labor force) and doing more of these same activities. Large adjustment costs in labor force
participation and a high intertemporal substitution in home goods appear to be mutually
inconsistent assumptions.
These reasons suggest that a successful model, whatever that may end up being, will have
to shift the source of employment fluctuations from intertemporal substitution in home goods
towards search decisions. If fluctuations in labor force participation are small (because it is

diﬃcult to substitute home goods intertemporally) but search decisions respond to aggregate
shocks in a significant way, the labor market dynamics thus generated would become much
more satisfactory. Finding such a model promises to be a challenging area of research.
One possibility may be to introduce labor market policies that this paper has abstracted
from. An unemployment insurance system seems particularly relevant. Since unemployment
insurance provides agents additional incentives to remain unemployed, the model would not
require a high persistence and variability of idiosyncratic shocks to reproduce the unemployment rate and the average duration of unemployment observed in the U.S. economy, making
the job acceptance rate much more responsive to aggregate shocks. In addition, even under
the low intertemporal substitution in home goods that would be needed to generate the small
observed fluctuations in labor force participation, the shifts from employment to unemployment could become large because agents would be substituting competing sources of income
over time (in particular, relatively constant unemployment benefits against time varying
wages). While introducing unemployment insurance into the model economy may generate
reasonable labor market dynamics, we cannot view this as a plausible explanation. It seems
highly unlikely that removing the unemployment insurance system in the U.S. would make
unemployment fluctuate procyclically. Moreover, there are several countries that have no
unemployment insurance systems but have countercyclical unemployment rates (e.g. Italy,
Argentina, etc).
A more promising route would be to introduce a reallocation shock that changes the
variance of the idiosyncratic productivity shocks over time. Since the distribution of idiosyncratic shocks is an important determinant of search decisions, this type of shocks can lead
to important variations in unemployment that are not the direct consequence of changes in
labor force participation. In particular, if the variance of the idiosyncratic shocks is negatively correlated to the aggregate productivity shock, depressions would be accompanied
by high incentives to search and unemployment fluctuations could become much larger and
countercyclical. In fact, it is not hard to come up with examples where a version of the
benchmark economy subject to both aggregate and reallocation shocks generates empirically
reasonable labor market dynamics. The challenge will be to verify that this holds under an
empirically plausible process for the aggregate and reallocation shocks.

Another promising route is the one proposed by Shimer (2005) and followed by Hall
(2005) and Farmer (2004): To introduce wage rigidities in the Mortensen-Pissarides search
framework. Shimer suggested that the diﬃculties of the Mortensen-Pissarides model to
account for the large observed fluctuations in unemployment and vacancies are due to the
fact that wages are too flexible in that setting. Indeed, Hall (2005) and Farmer (2004) found
that introducing rigid or partially adjusting wages can significantly improve the performance
of that model. However, the analysis so far has been done under the assumption of a
fixed labor force. It would be interesting to evaluate if the success of sticky-wage versions
of the Mortensen-Pissarides model is preserved once a labor force participation margin is
introduced.
Hagedorn and Manovskii (2007) have recently questioned Shimer’s results, showing that
an empirically plausible calibration of the Mortensen-Pissarides model is able to reproduce
U.S. business cycle fluctuations quite closely. This seems to suggest that introducing a
labor force participation margin to their model may be a worthwhile project. However, it
is important to observe that Hagedorn and Manovskii’s calibration is characterized by two
important features: 1) that workers have a very low bargaining power, and 2) that workers
value leisure quite significantly. The low bargaining power of labor leads to small wage
fluctuations in their model, but because leisure is valued so highly even small decreases in
wages are able to generate large inflows into unemployment.23 While the high value of leisure
is a key feature leading to the large unemployment fluctuations in Hagedorn and Manovskii
(2007), this same feature is likely to generate a poor empirical performance once a labor force
participation margin is introduced. The reason is that if workers were allowed to obtain more
of this highly valued leisure being out-of-the-labor-force than being unemployed, a decrease
in wages would induce workers to leave the labor force instead of becoming unemployed,
generating the same problems as those reported in this paper.

Another consequence of the high value of leisure is that profits are small. As a result, vacancies become
very responsive to changes in aggregate productivity.

A. Appendix
This appendix describes the computational algorithm used to solve the social planner’s
problem, which is to maximize utility (2.1) subject to equations (2.2), (2.3), (3.4), (3.5),
(3.6), (3.13), (3.14), and (3.15) taking a0 , K0 and q0 as given.24
It is straightforward to show that if two islands have identical current productivity levels
zt and identical number of agents available at the beginning of the period lt−1 (z t−1 , x0 ) +
pUt−1 , that the social planner will assign identical continuation plans to these islands independently of their previous history z t−1 and initial x0 .25 Thus, all the heterogeneity across
islands that is relevant to the social planner can be summarized by the distribution μt of
islands across pairs (x, z), where x is the number of agents available to an island at the
beginning of the period and z is its current productivity level.
The social planner’s problem in recursive form can then be written as follows:
V (at , μt , Kt ) =

max

{lt ,Ut ,Kt+1 }

ª
©
R (at , μt , Kt , lt , Ut , Kt+1 ) + βEV (at+1 , μt+1 , Kt+1 )

subject to
0

μt+1 (X , Z ) =

{(x,z):lt (x,z)+pUt ∈X 0 }

Q(z, Z 0 )μt (dx, dz),

(A.1)

(A.2)

lt (x, z) ≤ x,

(A.3)

at+1 = ρa at + εt+1 ,

(A.4)

where the return function R describes the utility that can be obtained with the state and
decision variables (at , μt , Kt , lt , Ut , Kt+1 ).
It is also straightforward to show that the optimal labor allocation rule has the following
form:
lt (x, z; at , μt , Kt ) = min {mt (z; at , μt , Kt ), x} ,

(A.5)

where mt (z; at , μt , Kt ) is an employment threshold independent of x. The (S,s) nature of the
24

The computational algorithm is closely related to those in Veracierto (2002, 2008).

This is a direct consequence of convexity.

employment allocation rule, together with the assumption of a finite number of values for
the idiosyncratic productivity level, imply that the steady state distribution μ∗ has a finite
support x∗ .
In what follows, the jth element of x∗ will be denoted by x∗ (j) and the total number of
elements in x∗ will be denoted by J. Moreover, it will be useful to classify the elements of
x∗ into two sets: 1) those that correspond to islands that in the previous period let some
agents go (set G ∗ ), and 2) those that correspond to islands that in the previous period did

not let anybody go (set L∗ ). That is, for j = 1, ..., J:

j ∈ G ∗ , if x∗ (j) = m∗ (z) + pU ∗ for some z
j ∈ L∗ , if x∗ (j) = x∗ (j − 1) + pU ∗

(A.6)

Observe that equation (A.6) implicitly assumes a particular ordering of the elements of x∗ .
If the aggregate productivity shock is small enough that mt and Ut fluctuate in a small
neighborhood of their steady state values m∗ and U ∗ , the distribution μt will have a finite
support xt of dimension J (same dimension as x∗ ) at every date t. Moreover, the support
will evolve as follows:
⎫
⎧
⎨ mt (z) + pUt , if j ∈ G ∗ , ⎬
xt+1 (j) =
, for j = 1, ..., J,
⎩ x (j − 1) + pU , if j ∈ L∗ ⎭
t

(A.7)

where z satisfies that x∗ (j) = m∗ (z) + pU ∗ , and G ∗ and L∗ are defined by equation (A.6).
This allows to reformulate the social planner’s problem as follows:
V (at , xt , Kt ) =

max

{mt ,Ut ,Kt+1 }

subject to (A.4) and (A.7).26

o
n
e (at , xt , Kt , mt , Ut , Kt+1 ) + βEV (at+1 , xt+1 , Kt+1 ) ,
R

(A.8)

The advantages of working with this transformed problem (A.8) instead of the original
problem (A.1) are that it has a finite number of variables and that its constraints describe
26

This reformulation uses the fact that the labor allocation rule lt is completely determined by the employment thresholds mt through equation (A.5).

e take positive values in the
linear laws of motion. Since all the endogenous arguments of R

deterministic steady state, a second order Taylor expansion around the deterministic steady
state can be performed to obtain a quadratic return function. This leaves a standard linearquadratic structure that can be solved using standard techniques. The assumption that at ,

xt , Kt , mt , and Ut fluctuate in a suﬃciently small neighborhood of their deterministic steady
state values is satisfied in all the experiments reported in this paper.

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Table 1
Parameter values
σ 2z

Table

Case

πU = πN

0.447 0.447 0.795 0.0223 1.823 0.60

π U = 0.01π N

0.005 0.472 0.553 0.0003 1.852 0.60

p = 1.00

0.231 0.461 0.786 0.0092 1.829 0.60

p = 0.75

0.231 0.461 0.767 0.0127 1.829 0.60

p = 0.50

0.231 0.461 0.720 0.0251 1.829 0.60

η = 0.00

0.231 0.461 0.767 0.0127 1.829 0.60

η = 0.25

0.231 0.461 0.774 0.0181 1.823 0.60

η = 0.50

0.231 0.461 0.781 0.0324 1.811 0.60

πU

πN

ρz

Table 2
U.S. business cycle statistics

Relative standard deviation (σ x /σ Y )
output

1.00

consumption

0.57

investment

4.28

capital

0.43

employment

0.57

unemployment

6.25

labor force

0.20

productivity

0.63

Correlation with output (ρx,Y )
output

1.00

consumption

0.80

investment

0.91

capital

0.05

employment

0.81

unemployment

-0.83

labor force

0.39

productivity

0.84

Table 3
Home production while unemployed
(Fixed and flexible labor force)

Relative standard deviation (σ x /σ Y )
πU = πN

π U = 0.01πN

Flex LF Fixed LF Flex LF Fixed LF
output

1.00

consumption

0.32

0.35

0.31

0.32

investment

4.59

4.37

4.63

4.55

capital

0.32

0.31

0.32

0.31

employment

0.57

0.03

0.57

0.51

unemployment

1.47

0.41

1.22

7.84

labor force

0.58

0.0

0.56

0.0

productivity

0.46

0.98

0.45

0.51

Correlation with output (ρx,Y )
πU = πN

π U = 0.01πN

Flex LF Fixed LF Flex LF Fixed LF
output

1.00

consumption

0.90

0.92

0.89

0.90

investment

0.96

0.99

capital

0.17

0.18

0.17

employment

0.98

0.76

0.98

unemployment

0.38

-0.76

0.30

-0.97

labor force

0.97

0.0

0.97

0.0

productivity

0.97

1.00

0.97

0.98

Table 4
Low arrival rates
(Flexible labor force)

Relative standard deviation (σ x /σ Y )
p = 1.00 p = 0.75 p = 0.50
output

1.00

consumption

0.32

0.31

investment

4.61

capital

0.32

employment

0.56

unemployment

1.76

2.14

3.74

labor force

0.57

0.58

0.59

productivity

0.46

Correlation with output (ρx,Y )
p = 1.00 p = 0.75 p = 0.50
output

1.00

consumption

0.89

investment

0.99

capital

0.17

employment

0.98

unemployment

0.30

0.22

0.12

labor force

0.96

0.95

0.92

productivity

0.97

Table 5
Endogenous search intensity: Search requires goods
(Fixed and flexible labor force)

Relative standard deviation (σ x /σ Y )
Fixed Labor Force

Flexible Labor Force

η = 0.00 η = 0.25 η = 0.50 η = 0.00 η = 0.25 η = 0.50
output

1.00

consumption

0.35

0.31

0.32

0.31

investment

4.39

4.38

4.33

4.61

4.58

4.50

capital

0.30

0.31

0.32

employment

0.09

0.07

0.05

0.56

unemployment

1.39

1.08

0.70

2.14

2.18

2.26

labor force

0.58

0.59

productivity

0.92

0.94

0.96

0.46

Correlation with output (ρx,Y )
Fixed Labor Force

Flexible Labor Force

η = 0.00 η = 0.25 η = 0.50 η = 0.00 η = 0.25 η = 0.50
output

1.00

consumption

0.92

0.89

0.90

investment

0.99

capital

0.18

0.17

0.16

0.15

employment

0.84

0.88

0.97

0.98

unemployment

-0.84

-0.88

-0.97

0.22

0.25

0.29

labor force

0.95

productivity

1.00

0.97

Table 6
Endogenous search intensity: Search requires eﬀort
(Fixed and flexible labor force)

Relative standard deviation (σ x /σ Y )
Fixed Labor Force

Flexible Labor Force

η = 0.00 η = 0.25 η = 0.50 η = 0.00 η = 0.25 η = 0.50
output

1.00

consumption

0.35

0.31

0.32

investment

4.39

4.37

4.61

4.60

capital

0.30

0.31

0.32

employment

0.09

0.08

0.06

0.56

unemployment

1.39

1.15

0.75

2.14

2.11

3.59

labor force

0.58

0.59

productivity

0.92

0.93

0.95

0.46

Correlation with output (ρx,Y )
Fixed Labor Force

Flexible Labor Force

η = 0.00 η = 0.25 η = 0.50 η = 0.00 η = 0.25 η = 0.50
output

1.00

consumption

0.92

0.89

0.90

investment

0.99

capital

0.18

0.17

employment

0.84

0.87

0.98

unemployment

-0.84

-0.88

-0.96

0.22

0.24

0.12

labor force

0.95

0.92

productivity

1.00

0.97

Figure 1
Labor market impulse-response functions
1.08

1.07

1.06

1.05

1.04

1.03

1.02

1.01

0.99
-1

months after aggregate productivity shock
employment

unemployment

labor force

job acceptance rate

job separation rate

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Elijah Brewer III, Douglas D. Evanoff and Jacky So

WP-01-25

Opportunity Cost and Prudentiality: An Analysis of Collateral Decisions in
Bilateral and Multilateral Settings
Herbert L. Baer, Virginia G. France and James T. Moser

WP-01-26

Outsourcing Business Services and the Role of Central Administrative Offices
Yukako Ono

WP-02-01

Strategic Responses to Regulatory Threat in the Credit Card Market*
Victor Stango

WP-02-02

The Optimal Mix of Taxes on Money, Consumption and Income
Fiorella De Fiore and Pedro Teles

WP-02-03

Expectation Traps and Monetary Policy
Stefania Albanesi, V. V. Chari and Lawrence J. Christiano

WP-02-04

Monetary Policy in a Financial Crisis
Lawrence J. Christiano, Christopher Gust and Jorge Roldos

WP-02-05

Regulatory Incentives and Consolidation: The Case of Commercial Bank Mergers
and the Community Reinvestment Act
Raphael Bostic, Hamid Mehran, Anna Paulson and Marc Saidenberg

WP-02-06

Technological Progress and the Geographic Expansion of the Banking Industry
Allen N. Berger and Robert DeYoung

WP-02-07

Choosing the Right Parents: Changes in the Intergenerational Transmission
of Inequality  Between 1980 and the Early 1990s
David I. Levine and Bhashkar Mazumder

WP-02-08

Working Paper Series (continued)
The Immediacy Implications of Exchange Organization
James T. Moser

WP-02-09

Maternal Employment and Overweight Children
Patricia M. Anderson, Kristin F. Butcher and Phillip B. Levine

WP-02-10

The Costs and Benefits of Moral Suasion: Evidence from the Rescue of
Long-Term Capital Management
Craig Furfine

WP-02-11

On the Cyclical Behavior of Employment, Unemployment and Labor Force Participation
Marcelo Veracierto

WP-02-12

Full text of Working Papers (Federal Reserve Bank of Chicago) : On the Cyclical Behavior of Employment, Unemployment and Labor Force Participation, Working Paper 2002-12

FRASER