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Finance and Economics Discussion Series
Divisions of Research & Statistics and Monetary Affairs
Federal Reserve Board, Washington, D.C.
What Drives Movements in the Unemployment Rate? A
Decomposition of the Beveridge Curve
Regis Barnichon and Andrew Figura
2010-48
NOTE: Staff working papers in the Finance and Economics Discussion Series (FEDS) are preliminary
materials circulated to stimulate discussion and critical comment. The analysis and conclusions set forth
are those of the authors and do not indicate concurrence by other members of the research staff or the
Board of Governors. References in publications to the Finance and Economics Discussion Series (other than
acknowledgement) should be cleared with the author(s) to protect the tentative character of these papers.
What drives movements in the unemployment rate?
A decomposition of the Beveridge curve.
Regis Barnichon
Andrew Figura
Federal Reserve Board
Federal Reserve Board
20 August 2010
Abstract
This paper presents a framework to interpret movements in the Beveridge curve and
analyze unemployment ‡uctuations. We decompose the unemployment rate into three main
components: (1) a component driven by changes in labor demand –movements along the
Beveridge curve and shifts in the Beveridge curve due to layo¤s– (2) a component driven
by changes in labor supply – shifts in the Beveridge curve due to quits, movements inand-out of the labor force and demographics– and (3) a component driven by changes in
the e¢ ciency of matching unemployed workers to jobs. We …nd that cyclical movements
in unemployment are dominated by changes in labor demand, but that changes in labor
supply due to movements in-and-out of the labor force also play an important role. Further,
cyclical changes in labor demand lead cyclical changes in labor supply. Changes in matching
e¢ ciency generally play a small role but can decline substantially in recessions. At lowfrequencies, labor demand displays no trend, and changes in labor supply explain virtually
all of the secular trend in unemployment since 1976.
JEL classi…cations: J6, E24, E32
We would like to thank Alessia Campolmi, Shigeru Fujita, Bart Hobijn, Chris Nekarda, Rob Valletta and
seminar participants at the Chicago Fed, the National Bank of Hungary, the New York Fed and the San Francisco
Fed. The views expressed here do not necessarily re‡ect those of the Federal Reserve Board or of the Federal
Reserve System. Any errors are our own.
1
Keywords: Gross Worker Flows, Job Finding Rate, Employment Exit Rate, Matching
Function.
2
1
Introduction
The unemployment rate is an important indicator of economic activity. Understanding its
movements is useful in assessing the causes of economic ‡uctuations and their impact on welfare, as well as assessing in‡ationary pressures in the economy. The Beveridge curve captures
the downward sloping relationship between the unemployment rate and the job vacancy rate
and is widely used as an indicator of the state of the labor market. Movements along the
Beveridge curve, i.e., changes in unemployment due to changes in vacancies, are typically interpreted as cyclical movements in labor demand. However, shifts in the Beveridge curve are
di¢ cult to interpret. While they are sometimes seen as indicating movements in the level of
“equilibrium”or “structural”unemployment, they can in fact be caused by a number of diverse
factors; changes in the intensity of layo¤s and quits, changes in labor force participation, or
changes in the e¢ ciency of matching workers to jobs.
In this paper, we present a framework to isolate the di¤erent components of the Beveridge
curve, and we use that framework to decompose unemployment rate movements into three
categories: (1) …rm-induced changes in unemployment, i.e. movements in labor demand, (2)
worker-induced changes in unemployment, i.e. movements in labor supply, and (3) changes in
the e¢ ciency of matching unemployed workers to jobs.
The …rst contribution of this paper is to present a framework to rigorously study movements
in the Beveridge curve. We accomplish our Beveridge curve decomposition by …rst isolating the
in‡ows and out‡ows of unemployment, following Shimer (2007). Using an aggregate matching
function tying vacancy posting and unemployment to transitions from unemployment into
employment, we decompose the out‡ow component into a component driven by changes in
vacancies, i.e. movements along a stable Beveridge curve, and a component driven by changes
in the e¢ ciency of matching workers to jobs. We interpret movements along a stable Beveridge
curve as changes in labor demand. To interpret the in‡ows of unemployment, we use CPS
micro data to distinguish movements in layo¤s, i.e. changes in labor demand, from changes in
demographics, quits or movements in-and-out of the labor force, i.e. changes in labor supply.
3
The second contribution of this paper is to provide a comprehensive decomposition of the
unemployment rate covering all frequencies over 1976-2009. We …nd that labor demand and
labor supply contribute approximately equally to unemployment’s variance, but that these two
forces play very di¤erent roles at di¤erent frequencies.
At business cycle frequencies, labor demand accounts for three quarters of unemployment’s
variance, a result in line with the approach taken by the search literature and the canonical Mortensen-Pissarides (1994) model to focus on vacancy posting and job separation when
studying unemployment ‡uctuations. However, movements in-and-out of the labor force explain close to a quarter of unemployment’s variance, a result at odds with the conventional
wisdom that movements in-and-out of the labor force played little role at business cycle frequencies (see e.g. Hall, 2005, Shimer, 2007, and Elsby, Michaels and Solon, 2009). Finally,
changes in matching e¢ ciency play on average a small role but can decline substantially in
recessions. For instance, in the 2008-2009 recession, lower matching e¢ ciency added about 1 12
percentage points to the unemployment rate.
We also study the timing of the di¤erent forces moving the unemployment rate. At the
beginning of a recession, the Beveridge curve shifts out because of an increase in temporary
layo¤s. A quarter later, unemployment moves along the Beveridge curve as …rms adjust vacancies. The Beveridge curve also shifts out further because of an increase in permanent layo¤s.
Then, another quarter later, labor supply responds to the economic situation; the Beveridge
curve shifts in slightly because quits decline but shifts out further as workers display a stronger
attachment to the labor force. While only suggestive, this chain event could indicate that labor
supply responds to labor demand at cyclical frequencies.
At low frequencies, we …nd little evidence of any trend in labor demand. In contrast, unemployment’s trend since 1976 can be entirely accounted for by secular changes in labor supply,
in particular the aging of the baby boom, the increase in women’s labor force participation
and the increasing attachment of women to the labor force. The secular leftward shift in the
Beveridge curve since 1976 correlates with a decline in the time-series volatility of business
4
growth rates since 1976 and a decline in the job destruction rate (Davis, Faberman, Haltiwanger, Jarmin and Miranda, 2010). Thus, our results suggest that an explanation of these
phenomena lies with secular changes in labor supply rather than with secular changes in labor
demand.
Our paper is related to two strands in the literature. The …rst strand investigates the
relative responsibility of unemployment in‡ows and out‡ows in accounting for changes in unemployment.1 We take this literature one step further by decomposing the labor market ‡ows
into economically meaningful components that allow us to say something about the economic
forces driving movements in unemployment. Our use of an aggregate matching function and
the Beveridge curve to accomplish this decomposition harks back to an earlier strand in the
literature (e.g. Lipsey, 1965, Abraham, 1987, Blanchard and Diamond, 1989) that relied on
the Beveridge curve to distinguish between changes in labor demand (movements along the
Beveridge curve) and shifts in sectoral reallocation (shifts in the Beveridge curve). We build
on this literature to better identify causes of Beveridge curve shifts.
The next section lays the theoretical groundwork for our decomposition. Section 3 estimates an aggregate matching function and decomposes changes in the unemployment rate
into changes in labor demand, changes in labor supply, and changes in the matching function.
Section 4 discusses the implications of our results. Section 5 concludes.
2
A Beveridge curve decomposition
In this section, we present a method to quantitatively decompose movements in the Beveridge
curve. We decompose unemployment ‡uctuations into three categories; changes in labor demand –movements along the Beveridge curve and shifts in the Beveridge curve due to layo¤s–,
changes in labor supply –shifts in the Beveridge curve due to quits and movements in and out
of the labor force–, and changes in matching e¢ ciency.
1
See, e.g., Shimer (2007), Elsby, Michaels and Solon (2009), Fujita and Ramey (2009), Elsby, Hobijn and
Sahin (2009).
5
2.1
Steady-state unemployment
Let Ut ; Et ; and It denote the number of unemployed, employed and inactive (out of the labor
force) individuals, respectively, at instant t 2 R+ . Letting
AB
t
denote the hazard rate of
transiting from state A 2 fE; U; Ig to state B 2 fE; U; Ig, unemployment, employment and
inactivity will satisfy the system of di¤erential equations
8
>
>
U_ t =
>
>
<
E_ t =
>
>
>
>
: I_t =
EU
t Et
+
IU
t It
(
UE
t
+
UI
t )Ut
UE
t Ut
+
IE
t It
(
EU
t
+
EI
t )Et
EI
t Et
+
UI
t Ut
(
IE
t
+
IU
t )It
(1)
As …rst argued by Shimer (2007), the magnitudes of the hazard rates is such that the half-life
of a deviation of unemployment from its steady state value is about a month. As a result,
at a quarterly frequency, the unemployment rate ut =
Ut
LFt
is very well approximated by its
steady-state value uss
t so that
ut '
with st and ft de…ned by2
2.2
Modeling
UE
8
>
< st =
>
: ft =
st
st + ft
EU
t
+
UE
t
+
uss
t
EI IU
t
t
II
t
U I IE
t
t
1 II
t
(2)
1
:
with a matching function
The job …nding rate is de…ned as the ratio of new hires to the stock of unemployed, so that
the job …nding rate can be written as
UE
t
=
mt
ut
with mt the number of new matches at
instant t: By modeling mt with a constant returns to scale Cobb-Douglas matching function,
a speci…cation widely used in the search and matching literature (see e.g. Pissarides, 2001),
2
Expression (2) generalizes the simpler two-states case without movements in-and-out of the labor force in
which uss
t =
EU
t
EU + U E
t
t
: With movements in-and-out of the labor force, workers can transition between U and
E either directly (U-E) or in two steps by …rst leaving the labor force (U-I) and then by …nding a job directly
from inactivity (I-U). ft , the “U-E transition probability” that matters for steady-state unemployment rate is
E
I IE
then a weighted average of U
and U
, with weights of 1 and 1 1 II , the average time that an inactive
t
t
t
t
worker spends in I. st has a similar expression.
6
we can express mt as
mt = m0 ut vt1
with m0 a positive constant, vt the number of job openings and ut the number of unemployed.
In this context, we can model the job …nding rate
ln
where
2.3
t
UE
t
= (1
) ln
UE
t
as
vt
+ m0 +
ut
t:
(3)
allows the e¢ ciency of matching workers to …rms to vary over time.
Decomposing movements in the Beveridge curve
Writing the steady-state approximation for unemployment (2) and modeling the job …nding
rate with a matching function, we can write
uss
t
with
U IE
t
=
U I IE
t
t
II
t
1
st
st +
U I IE
t
t
1 II
t
+
UE
t
'
st
st +
U IE
t
+ m0
vt
uss
t
1
(4)
. Expression (4) is the theoretical underpinning of the Beveridge curve,
the downward sloping relation between unemployment and vacancy posting. Steady-state
unemployment moves along the Beveridge curve as …rms adjust vacancies. In contrast, as
illustrated in Figure 1, the Beveridge curve shifts because of layo¤s, quits or movements in and
out of the labor force, i.e. when st or
U IE
t
moves.
However, while the matching function is remarkably successful at modeling the job …nding
rate, the relation
UE
t
= m0
vt
ut
1
is not exact, and the labor market may temporarily
deviate from its average matching e¢ ciency. To separate movements along the Beveridge
curve from shocks to the matching function, we de…ne uss;bc
as the steady-state unemployment
t
rate implied by a stable Beveridge curve, i.e. by a stable matching function. Formally, uss;bc
t
7
is de…ned by
st
uss;bc
=
t
:
1
U IE
t
st +
(5)
vt
+ m0
uss;bc
t
1
UE
Denoting ^ t = m0
vt
the job …nding rate predicted by a stable matching func-
uss;bc
t
tion, we can rewrite (4) as
uss
t =
where "t = ln
UE
t
UE
ln ^ t
st
st +
U IE
t
(6)
UE
+ ^ t e"t
captures deviations of the job …nding rate from the value implied
by a stable Beveridge curve, i.e. a stable relationship between unemployment and vacancies.3
Log-linearizing (2) around the mean of the hazard rates gives us:4
d ln uss
=
t
EI
d ln
IE
with
AB
EI
t
d ln
IU
+
IE
t
d ln
UI
IU
t
d ln
+
UI
t
EU
d ln
UE
EU
t
UE
t
d ln
some positive constants depending on the mean of
AB
t
(7)
+
t
.5 In this context, we
can decompose unemployment movements in a Beveridge curve framework from
shif ts
f
bc
d ln uss
+ d ln uef
+
t = d ln ut + d ln ut
t
U E d ln ^ U E
t
where d ln ubc
t
f
eridge curve, d ln uef
t
=
U E d"
t
U E (1
)d ln
vtU E
uss;bc
t
(8)
t
represents movements along the Bev-
captures the shifts in the Beveridge curve caused by changes
3
Note that "t is di¤erent from t . While (3) is useful to highlight movements in matching e¢ ciency, this
regression conditions on actual unemployment, not the unemployment that would have prevailed had there been
no changes in matching e¢ ciency. To properly identify changes in matching e¢ ciency, one needs to determine
IE
uss;bc
; the unemployment rate implied by a stable matching function and the current levels of st and U
.
t
t
ss;bc
Deviations of the actual job …nding rate from the job …nding rate implied by ut
can then be interpreted as
due to a change in matching e¢ ciency.
4
A …rst-order approximation is very good on average, but t can become non-negligible during episodes of
high unemployment rate. Thus, for our quantitative exercises, we rely on a second-order approximation, which
performs extremely well. The expressions for the second-order coe¢ cients are shown in the Appendix.
EI IU
IU U E
IE EU
U I IE
5
+ IE U E
+ IE U E
Formally, EI = (1 uss ) s , U E =
, IE =
(1 uss )
,
s+f
s
s+f
UI
=
UI
IE
s+f
,
EU
= (1
uss )
IE
EU
+ IU EU
s
,
IU
= (1
8
uss )
EI
IU
+ IU EU
s
IU
UE
s+f
:
in matching e¢ ciency, and shifts in the Beveridge curve are given by
t
d ln ushif
t
EU
d ln
EU
t
+
EI
d ln
EI
t
+
IU
d ln
IU
t
IE
d ln
IE
t
UI
d ln
UI
t
Shifts in the Beveridge curve can occur through changes in workers’attachment to the labor
force or through changes in the probability that workers separate from their job and join the
unemployment pool, either through a layo¤ or through a quit. Finally, the residual term
t
corresponds to the approximation error.
We can then assess the separate contributions of di¤erent movements in the Beveridge
curve by noting as Fujita and Ramey (2009) that
shif ts
ef f
ss
bc
ss
ss
V ar (d ln uss
)+Cov(d ln uss
t ) = Cov(d ln ut ; d ln ut )+Cov(d ln ut ; d ln ut
t ; d ln ut )+Cov(d ln ut ;
(9)
so that, for example,
ss
Cov(d ln ubc
t ;d ln ut )
var(d ln uss
)
t
measures the fraction of unemployment’s variance due
to movements along the Beveridge curve:
2.4
Interpreting shifts in the Beveridge curve
The Beveridge curve can shift if the employment-unemployment transition probability changes.
However, an employed worker can join the unemployment pool for two reasons: a layo¤ or a
quit. While a layo¤ is a …rm-induced movement in unemployment, a quit is a decision of
the worker. Thus, from a conceptual point of view, it is important to distinguish these two
concepts empirically. In addition, shifts in the Beveridge curve can occur through changes in
workers’attachment to the labor force. Thus, to identify and interpret the di¤erent forces that
can shift the Beveridge curve, we separate job leavers, job losers and labor force entrants, and
we classify jobless workers according to the event that led to their unemployment status: a
permanent layo¤ p, a temporary layo¤ t, a quit q and a labor force entrance o.
Further, a number of researchers (e.g. Abraham and Shimer, 2001) emphasize that changes
in demographics have been an important force behind the secular trend in unemployment. In
9
t ):
particular, as the labor force gets older, the average turn-over rates declines, and the unemployment rate goes down. Thus, to better interpret the low-frequency shifts in the Beveridge
curve, we extend our decomposition (8) and isolate the direct e¤ect of demographics on unemployment.
Formally, for each demographic group i, there are four unemployment rates by reason: upi ;
uti , uqi and uoi and the associated hazard rates f
jE
i ;
Ej
i ;
jI
i g;
j 2 fp; t; qg and f
oE
i ;
Io
i ;
oI
i g.
In this case, the system of di¤erential equations (1) satis…ed by the number of unemployed
Uit , employed Eit and inactive Iit in demographic group i becomes
8
>
>
U_ itj =
>
>
>
>
>
< U_ o =
it
>
>
E_ it =
>
>
>
>
>
: I_ =
it
With Ut =
Ej
it Eit
(
Io
it Iit
(
pE p
it Uit
EI
it Eit
N
X
+
+
jE
it
oE
it
+
j 2 fp; t; qg
oI
o
it )Uit
+
tE t
it Uit
oI o
it Uit
jI
j
it )Uit ,
+
(
qE q
it Uit
IE
it
oE o
it Uit
+
+
IE
it Iit
+
(
El
it
+
Eq
it
(10)
+
EI
it )Eit
Io
it )Iit
Uitp + Uitt + Uitq + Uito , the aggregate steady-state unemployment rate uss
t
i=1
satis…es (2) with the average transition rates given by
8
>
>
>
>
>
>
>
>
>
>
<
>
>
>
>
>
>
>
>
>
>
:
UB
t
=
N
X
X
j
Uit
Ut
jB
it ,
B 2 fE; Ig
i=1 j2fp;t;q;og
EU
t
IU
t
=
=
N
X
X
Eit
Et
i=1 j2fp;t;qg
N
X
Iit Io
It it and
i=1
Ej
it
and
EI
t
=
N
X
i=1
IE
t
=
N
X
i=1
10
Iit
It
IE
it
Eit
Et
EI
it
(11)
Using the steady-state approximations, we can approximate (11) with
8
>
>
>
>
>
>
>
>
>
>
<
where ! it =
LFit
LFt
UB
t
EU
t
>
>
>
>
>
>
>
>
>
>
:
IU
t
N
X
'
'
'
X
! it
uj;ss
it
uss
t
jB
it ,
B 2 fE; Ig
and
EI
t
i=1 j2fp;t;q;og
N
X
X
ess
! it eit
ss
t
i=1 j2fp;t;qg
N
X
iss Io
! it iit
ss it
t
i=1
and
Ej
it
IE
t
'
N
X
'
N
X
iss
! it iit
ss
t
ess
! it eit
ss
t
EI
it
(12)
i=1
IE
it
i=1
ss
ss
is the share of group i in the labor force and uss
it ; eit and iit denote respec-
tively the steady-state unemployment rate, employment rate and inactivity rate of group i.
The steady-state unemployment rate for category i satis…es uss
it =
sit
sit +fit
since the system of
di¤erential equations (10) holds independently for each demographic group.6
To isolate the direct e¤ect of demographics, we log-linearize (12) and get for
d ln
EU
t
=
N
X
i=1
!i
ess
i
ess
EU
i
EU
d ln
EU
it
+ d ln ! it
ess
it
ess
t
EU
= d ln ~ t
+ d ln
EU
t
EU;demog
t
(13)
and similarly for the other transition rates.7 The …rst term corresponds to movements in
N
X
ess
~ EU
! i eiss EU
it , the hazard rate that holds the share of each demographic group constant.
t
i=1
The second term, d ln
EU;demog
t
N
X
ess
i
! i ess
EU
i
EU
ess
d ln ! it eit
ss , corresponds to movements in the
t
i=1
relative size of the labor force in each group ! it , as well as changes in the share of each group
ess
in the employment pool ( eiss ).
Finally, to separate quits from layo¤s, note that
EU
t
=
X
j2fp;t;qg
8j 2 fp; t; qg.
6
Ej
t
and
Ej
t
=
N
X
ess
! it eit
ss
t
Ej
it ,
i=1
See the Appendix for analytical expressions of the steady-state values.
Throughout the paper, we present the derivations to a …rst-order for clarity of exposition. However, for
the quantitative results, we used a second-order approximation. For instance, for EU , we took a second-order
expansion of ln EU
in (12), and we split the contributions of the cross-order terms in half between each two
t
components.
7
11
2.5
A labor demand/labor supply decomposition
Using (13), we isolate the contribution of demographics to movements in unemployment and
separate layo¤s from quits and movements in-and-out of the labor force and rewrite (8) as
shif ts;layof f s
ts;quits
ts;LF
bc
d ln uss
+d ln ushif
+ d ln ushif
t = d ln ut + d ln ut
t
t
|
{z
} |
{z
Ls
Ld
N LF
f
+ d ln udemog
+d ln uef
t
t + t:
}
(14)
where8
8
>
U E d ln ^ U E
>
d ln ubc
>
t =
t
>
>
>
>
Eq
Ep
Et
ts;layof f s
ts;quits
>
>
and d ln ushif
d ln ushif
= EU d ln ~ t + d ln ~ t
= EU d ln ~ t
>
t
t
>
>
>
>
IE d ln ~ IE
U I d ln ~ U I
< d ln ushif ts;LF N LF = EI d ln ~ EI + IU d ln ~ IU
t
t
t
t
t
>
Eq;demog
IU;demog
EI;demog
demog
EU
IU
EI
>
+
d ln t
+
d ln t
=
d ln t
d ln ut
>
>
>
>
>
>
IE d ln IE;demog
U I d ln U I;demog
>
>
t
t
>
>
>
>
ef f
U E;demog
U
E
U
E
:
d ln ut =
d"t
d ln t
:
We group the …rms’ induced movements in unemployment (due to vacancies or layo¤s)
under the heading "labor demand" and the workers’ induced movements in unemployment
(due to quits, movements in and out of the labor force and changes in demographics) under
the heading "labor supply". Importantly, we do not presume that labor demand and labor
supply are independent forces as changes in one factor could in‡uence the other. Rather, we
think of the labor demand/labor supply classi…cation as a useful framework to think about
the mechanisms (changes in …rms’ behavior or changes in workers’ behavior) at play behind
unemployment ‡uctuations.
8
AB
See the Appendix for the exact expressions for ~ t , d ln
12
AB;demog
t
or d ln
U A;reason
:
t
3
Empirical results
3.1
Measuring individuals’transition rates
To identify the individuals’transition rates, we use CPS gross ‡ows measuring the number of
workers moving from state A 2 S to state B 2 S each month. We classify jobless workers
according to the event that led to their unemployment status: a permanent layo¤, a temporary
layo¤, a quit and a labor force entrance.9 Further, we split workers into N = 8 categories;
male vs. female in the three age categories 25-35, 35-45, 45-55, and male and female together
for ages 16-25 and over 55.
For each demographic group, there are 6 possible states with S = U p ; U t ; U q ; U o ; E; I .
To account for time aggregation bias, we consider a continuous environment in which data are
available at discrete dates t and proceed in a similar fashion to Shimer (2007). Denote NtAB ( )
the number of workers who were in state A at t 2 N and are in state B at t +
and de…ne nAB
t ( )=
Assuming that
N AB ( )
P t AX
Nt (
X2S
AB
t ,
)
with
2 [0; 1]
the share of workers who were in state A at t.
the hazard rate that moves a worker from state A at t to state B at
10
t + 1, is constant from t to t + 1, nAB
t ( ) satis…es the di¤erential equation:
n_ AB
t ( )=
X
nAC
t ( )
CB
t
nAB
t ( )
C6=B
X
C6=B
BC
t ,
8 A 6= B:
(15)
We then solve this system of di¤erential equations numerically to obtain the transition rates
for each demographic group. We use data from the CPS from January 1976 through December
2009 and calculate the quarterly series for the transition rates over 1976Q1-2009Q4 by averaging
the monthly series.
9
To address Shimer’s (2007) worry that the quit/layo¤ distinction may be hard to interpret in the CPS
because a sizeable fraction of households who report being a job leaver in month t subsequently report being
a job loser at t + 1, we discarded all the observations with "impossible" transitions (such as job leaver to job
loser).
10
Because an unemployed worker cannot change reason for unemployment or because a job loser/leaver cannot
be a labor force entrant, some transitions are forbidden, and we impose AB
= 0 for such transitions (for example,
t
pq
= 0, Ip = 0, etc..)
13
3.2
Estimating a matching function
We estimate a matching function by regressing
ln
UE
t
= (1
using our measure of the job …nding rate
) ln
UE
vt
+c+
ut
t
(16)
as the dependent variable.
We estimate (16) with monthly data using the composite help-wanted index presented in
Barnichon (2010) as a measure of vacancy posting. We use non-detrended data over 1967:Q12009:Q4 and allow for …rst-order serial correlation in the residual. To take into account movements in the size of the labor force, we rescale the composite help-wanted index by the size of
the labor force. Table 1 presents the result. The elasticity
value inside the plausible range
is precisely estimated at 0:62, a
2 [0:5; 0:7] identi…ed by Petrongolo and Pissarides (2001). A
legitimate concern with this regression is that equation (16) may be subject to an endogeneity
bias. We then estimate (16) using lagged values of vt and ut as instruments. As column (2)
shows, the endogeneity bias appears to be small as the elasticity is little changed at 0:60. Figure
2 plots the residual of equation (16) estimated over 1967-2009. While the matching function
appears relatively stable over time, a testimony of the success of the matching function, the
residual can become large. In the third quarter of 2009, the residual reached an all time low
of three standard-deviations.
3.3
3.3.1
A decomposition of unemployment ‡uctuations
Aggregate decomposition
In this section, we use (14) to decompose unemployment ‡uctuations into: (i) movements due
to changes in labor demand, (ii) movements due to changes in labor supply, and (iii) changes
in matching e¢ ciency.
To better visualize the contribution of each category in history, we log-linearize unemploy-
14
ment around the base date 2000q3.11 That base date is attractive because it corresponds to
t 12
the highest reading for vacancy posting per capita as well as the lowest value for ln ushif
.
t
Figure 3 plots (log) unemployment and its components relative to their 2000q3 values. To
express the y-axis in units of unemployment rate, we use a logarithmic scale.
Figure 3 suggests that both changes in labor demand and changes in labor supply contribute to unemployment’s ‡uctuations. However, the secular trend in unemployment appears
to originate in changes in labor supply, while changes in labor demand appear to be mainly
cyclical. A variance decomposition con…rms this impression, and Table 2 shows that while
labor demand and labor supply contribute to respectively 50 and 30 percent of unemployment’s variance on average, movements in labor supply account for virtually all the trend in
unemployment since 1976.13 In contrast, changes in labor demand account for 82 percent of
unemployment’s cyclical ‡uctuations (excluding movements due to changes in matching e¢ ciency). Nonetheless, the contribution of changes in labor supply at cyclical frequencies is far
from negligible at 18 percent.
With a contribution of 13 percent, changes in matching e¢ ciency generally have a small
impact on the equilibrium unemployment rate, a corollary of the success of the matching
function in modeling the job …nding rate. However, Figure 3 shows some marked decrease in
matching e¢ ciencies in the aftermath of the 82 peaks in unemployment and during the 20082009 recession. Without any loss in matching e¢ ciency, Figure 3 shows that unemployment
would have been about 50 basis points lower over 1984-1988 and about 150 basis points lower
in 2009.14
11
For a Taylor-expansion around an extremum point such as 2000Q3, we use a second-order approximation
(see the Appendix) to ensure that the approximation remains good. To classify the cross-order terms (in, say,
labor demand versus labor supply), we split their contribution in half between each two components. The
red line in Figure 3 plots the exact value of the steady-state unemployment rate, which is very close to our
approximation.
12
Thus, 2000q3 corresponds to the date with the most leftward Beveridge curve, and that base year can be
used as a reference point from which we can quickly visualize the rise and fall in trend unemployment as well
as the cyclical ‡uctuations over the last 35 years.
13
To separate trend and cyclical unemployment, we decompose changes in unemployment into a trend component (from an HP-…lter, = 105 ) and a cyclical component.
14
In a companion paper (Barnichon and Figura, 2010), we investigate the forces behind changes in matching
e¢ ciency.
15
3.3.2
Digging further
To better interpret changes in labor demand and changes in labor supply, we now study the
behavior of their subcomponents.
Figure 4 and 5 plot the decomposition of labor demand and labor supply following (14).
We can see that there is no clear trend in any of the components of unemployment due to labor
demand. In contrast, labor supply seems responsible for the secular decline in unemployment
since 1976. Table 3 presents the results of a variance decomposition using (14) and con…rms
this visual inspection. While movements along the Beveridge curve, layo¤s and movements
in-and-out of the labor force each account for about a third of unemployment’s variance, the
picture is very di¤erent when one considers high and low-frequency movements separately.
Demographics and movements in-and out of the labor force are the prime driving forces of
secular shifts in unemployment but labor demand (movements along the Beveridge curve and
layo¤s) is the main driving force at business cycle frequencies. We thus discuss each frequency
range separately.
Business cycle ‡uctuations:
As Table 3 shows, movements along the Beveridge curve and
shifts due to layo¤s are the two main determinants of unemployment ‡uctuations and account
for respectively 37 and 46 percent of the cyclical ‡uctuations in unemployment. However, Table
3 shows that the cyclical contribution of movements in-and-out of the labor force is far from
negligible at around 23 percent. Quits have a small but negative contribution of -7 percent, a
result consistent with Elsby, Michaels and Solon’s (2009) …nding using unemployment duration
data that quits to unemployment move countercyclically.
To better interpret these results, Table 4 presents the correlation matrix for the main determinants of unemployment ‡uctuations at business cycle frequencies. Shifts in the Beveridge
curve due to layo¤s and movements along the Beveridge curve are strongly positively correlated, in line with the usual assumption that they both respond to …rms’labor demand. The
correlation with shifts due to temporary layo¤s is less strong, because, as we can see in Figure
16
4, …rms’ increasing reliance on permanent layo¤s at the expense of temporary layo¤s muted
the cyclicality of temporary layo¤s in the second-half of the sample. Shifts in the Beveridge
curve due to movements in-and-out of the labor force are strongly positively correlated with
shifts due to layo¤s and to movements along the Beveridge curve.
As we can see in Figure 5, movements in-and-out of the labor force contribute to some of
the rise in the unemployment rate in recessions. To visualize the role played by movements
in-and-out of the labor force, Figures 6 to 9 plot the evolution of the four hazard rates related
to movements in-and-out of inactivity for speci…c demographic groups. A general observation
is that attachment to the labor force is countercyclical, with workers more likely to join/stay
in the labor force during recessions. This is particularly true for prime-age females as shown in
Figure 6:15 Comparing prime-age women with prime-age men in Figures 6 and 7, the behavior
of
UI
and
IU
shows that women’s attachment to the labor force more countercyclical than
for men. This phenomenon may be a sign of the added worker e¤ect, according to which
women are more likely to join/remain in the labor force when their husband has lost his job.16
Further, older workers can also experience strong cyclical movements in
IU
(Figure 8).17
Finally, Table 5 reports the timing of the peak correlation between any two series and
shows that changes in unemployment follow a particular chain of events. Temporary layo¤s
lead permanent layo¤s and changes in job posting, which themselves lead quits and movements
in-and-out of the labor force. Thus, at the beginning of a recession, the Beveridge curve
shifts out because temporary layo¤s increase. A quarter later, unemployment moves along the
Beveridge curve as …rms adjust vacancies and the Beveridge curve shifts out further because of
more permanent layo¤s. Then, another quarter later, labor supply responds to the economic
situation; the Beveridge curve shifts in slightly because quits decline but also shifts out further
15
This could be due to the extension of unemployment bene…ts duration during recessions. In fact, during
the mid-70s and early 80s recessions, there was comparatively little increase in unemployment coverage, and
I
the large increases in unemployment were not caused by large movements in U
and IU
t
t . In contrast, a large
increase in unemployment insurance coverage in the early-90s recession coincided with unusually large increases
I
in d ln uU
and d ln uIU
given the magnitude of the recession.
t
t
16
See Sahin, Song and Hobijn (2009) for a discussion of the added-worker e¤ect in the 2008-2009 recession.
17
This is particularly true in the 2008-2009 recession (especially women) and could be due to the nature of
the recession as older workers had to come out of retirement because of large losses in stock market wealth.
17
as workers show a stronger attachment to the labor force. While only suggestive, this chain
event could indicate that labor supply responds to labor demand at cyclical frequencies.
Low-frequency movements:
Shimer (1998, 2001) and Abraham and Shimer (2001) iden-
ti…ed two forces that could be responsible for the low-frequency movements in unemployment
since 1976: the aging of the baby boom and the increase in women’s labor force participation
rate. Consistent with this result, Figure 5 shows that the trend in labor supply originates in
demographics and movements in-and-out of the labor force. Table 4 con…rms this idea quantitatively and shows that the two forces can explain virtually all of the trend in unemployment.
To explore this result in more details, we now look at the behavior of speci…c demographics
groups since 1976.
The right panel of Figure 10 plots the trends in d ln udemog
for six demographic groups and
t
shows that the decline in the share of young workers (male and female) contributed to the trend
in unemployment. Indeed, younger workers have higher turnover and a higher unemployment
rate than prime age or old workers, and a decline in the youth share automatically reduces
the aggregate unemployment rate. At the same time, another demographic change had an
opposite e¤ect on unemployment. The increase in the share of prime age female inside the
labor force until the mid-90s dampened the baby boom’s e¤ect as women historically had a
higher job …nding rate and lower job separation rate than men.
ts;LF
The left panel of Figure 10 plots the trends in d ln ushif
t
N LF
for six demographic
groups and highlights a downward trend in unemployment caused by a change in the behavior
of women, consistent with the …ndings of Abraham and Shimer (2001). Looking at Figure
6 and the behavior of prime age women’s transition rates over 1976-2009, two changes are
apparent.18 First, the secular increase in
IU
until the mid-90s and the secular increase in
IE
captures the fact that women were getting increasingly likely to join the labor force, either by
directly …nding a job (as is increasingly the case) or by going …rst through the unemployment
pool. Second, women display an increasing attachment to the labor force as
18
UI
and
Abraham and Shimer (2001) also documented these two changes using annual transition probabilities.
18
EI
follow downward trends since 1976, meaning that women are increasingly likely to remain in
the unemployment pool after an employment spell rather than drop out of the labor force.
As shown in Figure 5, quits to unemployment present little evidence of a trend, except
perhaps in the last 10-15 years. This trend can be traced back to a secular decline in the rate
of quits to unemployment amongst men and women aged 16 to 35.19
Looking forward, two more recent labor supply trends are worth mentioning. First, Figure
8 plots the transition rates for men and women aged over 55. A trend apparent since the late
90s is that older workers are increasingly likely to join the labor force as
IU
and
IE
are
following upward trends.20 We can also notice an increase in labor force attachment as both
UI
and
EI
are following downward trends. Second, Figure 9 shows that young workers are
less likely to join the labor force (
IE
and
IU
are both on downward trends since the mid-90s).
This could be related to the increase in the number of years of education as young workers
stay longer in school before joining the labor force. Using (14), we can infer the consequence of
such trends in terms of steady-state unemployment. Because of the larger demographic weight
of older people, the contribution older workers is larger and unemployment rate would increase
slightly. Extrapolating the trend in labor force participation behavior since 2000 for young and
old workers implies a steady-state unemployment rate about a quarter of a percentage point
higher in 2015.21
4
Theoretical implications
Business cycle ‡uctuations:
At business cycle frequencies, our results can be summarized
as follows: (i) movements along the Beveridge curve and job separation (layo¤s and quits)
account for a large share (76 percent) but not all of unemployment’s variance, (ii) movements in19
The other demographic groups present little evidence of a trend. See also Duca and Campbell (2007).
While our evidence only pertains to quits to unemployment, it is likely that a similar secular decline occurred
for all quits as Fallick and Fleischman (2004) and Rogerson and Shimer (2010) also report a secular decline in
job-to-job transitions since 1994.
20
This is especially true for women.
21
Formally, we extrapolated the trend growth rates in labor force participation ( IU ; U I , EI and IE ) for
young and old workers over 2010-2016 using the 2000-2007 average growth rate of the HP-…lter trends.
19
and-out of the labor force account for a quarter of unemployment’s variance and lag movements
in layo¤s and vacancy posting by a quarter, (iii) quits are procyclical and lag layo¤s by a
quarter, (iv) changes in matching e¢ ciency are generally small but can at times account for
signi…cant changes in the unemployment rate.
The Mortensen-Pissarides (1994) search and matching model has become the canonical
model of equilibrium unemployment. In that model, and consistent with (i), unemployment
‡uctuations are driven by changes in job posting and job separation. However, considering (ii),
25 percent of unemployment ‡uctuations remains unaccounted for. This result is surprising
given the conventional wisdom that movements in-and-out of the labor force played little role
at business cycle frequencies (see e.g. Hall, 2005, Shimer, 2005, 2007 and Elsby, Michaels
and Solon, 2009). Thus, introducing a labor force participation decision in the model is an
important avenue for future research (see Garibaldi and Wasmer, 2005 and Haefke and Reiter,
2006 for e¤orts in that direction). In addition, accounting for movements in-and-out of the
labor force would help explain some of the unemployment volatility puzzle.22
Moreover, in the MP model, quits and layo¤s are indistinguishable since a match terminates
when it is jointly optimal for both parties to separate. However, in the data, quits and layo¤s
display very di¤erent time series properties: quits are negatively correlated with layo¤s, and
quits lag layo¤s by one quarter.
Finally, while shocks to matching e¢ ciency are rarely considered in search models, (iv)
suggests that they may be a useful addition to the set of shocks considered to explain unemployment ‡uctuations.
Low-frequency movements:
At low-frequencies, our main …nding is the absence of any
signi…cant trend in labor demand and the fact that movements in labor supply account for
all of the trend in unemployment. This result suggests that any explanation of the trend in
unemployment since 1976 lies with demographics and changes in workers behavior rather than
22
The unemployment volatility puzzle is the fact that the standard MP model cannot replicate the volatility
of unemployment given productivity shocks of plausible magnitude (Shimer, 2005).
20
with any direct changes in …rms’labor demand. Davis, Faberman, Haltiwanger, Jarmin and
Miranda (2010) link the secular decline in the job destruction rate to the secular decline in
the unemployment in‡ow rate. Since we can attribute all of the latter to demographics and
behavioral changes in labor supply (in particular, a stronger attachment of women to the labor
force), our evidence suggests that the secular decline in job destruction is related to changes
in labor supply rather than to changes in labor demand.23
Davis, Haltiwanger, Jarmin and Miranda (2007) also document a decline in cross-sectional
dispersion of business growth rates and in the time-series volatility of business growth rates
since 1976. Again, the absence of a trend in labor demand suggests that labor supply may
have played an important role here. For example, since older workers have longer tenures and
have a lower turn-over rate than young workers, some of the decline in business growth rate
volatility may be due to the aging of the baby boom. In contrast, any labor demand based
explanation (such as a decline in the variance of idiosyncratic shocks hitting …rms) must also
justify the absence of any signi…cant trend in labor demand (such as why the layo¤ rate did
not decline).
5
Conclusion
This paper presents a framework to interpret movements in the Beveridge curve and decompose
the components of unemployment ‡uctuations. We …nd that movements in labor demand are
the main determinants of cyclical ‡uctuations in unemployment but that movements in-and-out
of the labor force play an important role and account for almost a quarter of unemployment’s
variance. Further, labor demand leads labor supply, possibly indicating a causal interpretation
as workers are more likely to join/stay in the labor force during recessions. Possible explanations include wealth e¤ects and the added-worker e¤ect for spouses. At low-frequencies,
labor demand appears to play no direct role. Unemployment’s trend since 1976 can be entirely
23
Of course, stronger attachment of workers to the labor force could in turn have been triggered by labor
demand changes such as increased economic uncertainty. However, the fact that we …nd no trend in labor
demand suggests a less direct link.
21
accounted for by secular changes in labor supply, in particular the aging of the baby boom, the
increase in women’s labor force participation and the increasing attachment of women to the
labor force. Finally, while changes in matching e¢ ciency generally play a small role, they can
decline substantially in recessions. For instance, in the 2008-2009 recession, lower matching
e¢ ciency added about 1 12 percentage points to the unemployment rate. In a companion paper
(Barnichon and Figura, 2010), we explore the possible mechanisms behind such large changes
in matching e¢ ciency.
Appendix
Analytical expressions for three labor market states
ss
ss
To …nd the steady-state unemployment rate uss
it , employment rate eit and inactivity rate iit
n o
of each demographic group i, note that Uitj
, Uit , Eit and Uit satisfy the system of
j2fp;t;q;og
n
o
di¤erential equations (1) so that Uitss;j
, Uitss , Eitss and Iitss are the solutions of the
j2fp;t;q;og
system
8
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
<
X
Uitss;j
j2fp;t;q;og
EI ss
it Eit
+
jE
it
X
+
IE ss
it Iit
=(
X
Ej
it
+
EI
it )Eit
j2fp;t;qg
Uitss;j jI
it
=(
IE
it
+
Io ss
it )Iit
j2fp;t;q;og
Uitss;j
Ej
= jE + jI Eitss ,
>
>
>
>
>
Io
>
>
Uitss;o = oE + oI Iitss
>
>
>
>
X
>
>
>
Uitss =
Uitss;j
>
:
8 j 2 fp; t; qg
j2fp;t;q;og
ss
The steady-state unemployment rate uss
it is then obtained from uit =
uss
it
sit
sit + fit
22
ss
Uit
ss
LFit
and satis…es
with sit and fit de…ned by
8
>
< st =
>
: fit =
EI IU
it it
+
IE EU
it it
+
IU EU
it it
U I IE
it it
+
IU U E
it it
+
IE U E
it it
and where the transition rates are given by
8
>
>
>
>
>
>
>
>
>
>
>
>
<
where uss
it =
ss
Uit
ss ,
LFit
uss;j
it =
ss;j
Uit
ss .
LFit
>
>
>
>
>
>
>
>
>
>
>
>
:
UE
it
=
X
uss;j
it
uss
it
jE
it
uss;j
it
uss
it
jI
it
j2fp;t;q;og
UI
it
=
X
j2fp;t;q;og
EU
it
=
X
Ej
it
j2fp;t;qg
IU
it
=
Io
it
Correction for the 1994 CPS redesign
As explained in Polivka and Miller (1998), the 1994 redesign of the CPS caused a discontinuity
in the way workers were classi…ed between permanent job losers (i.e. other job losers), temporary job losers (i.e. on layo¤s), job leavers, reentrants to the labor force and new entrants to
the labor force (although we do not distinguish between the last two categories). As a result,
the transition probabilities display a discontinuity in the …rst month of 1994.
To "correct" the series for the redesign, we proceed as follows. We start from the monthly
transition probabilities obtained from matched data for each demographic group. We remove
the 94m1 value for each transition probability (since its value corresponds to the redesigned
survey, not the pre-94 survey), and instead estimate a value consistent with the pre-94 survey.
To do so, we use the transition probability average value over 1993m6-1993m12 (the monthly
probabilities can be very noisy so we average them over 6 months to smooth them out)24 that
24
Taking a the average over 3-months or 12-months does not change the the result.
23
we multiply by the average growth rate of the transition probability over 1994m1-2009. That
way, we capture the long-run trend in the transition probability. Over 1994m2-2009, we simply
adjust the transition probability by the di¤erence between the average of the original values
over 94m1-94m6 (to control for the in‡uence of noise or seasonality) and the inferred 94m1
value.
By eliminating the jumps in the transition probabilities in 1994m1, we are assuming that
these discontinuities were solely caused by the CPS redesign. Thus, the validity of our approach rests on the fact that 1994m1 was not a month with large "true" movements in transition probabilities. We think that this is unlikely because there is no such large movements in
the aggregate job …nding rate and aggregate job separation rate obtained from duration data
(Shimer, 2007 and Elsby, Michaels and Solon, 2009) that do not su¤er from these discontinuities. (these authors treat the 1994 discontinuity by using data from the …rst and …fth rotation
group, for which the unemployment duration measure (and thus their transition probability
measures) was una¤ected by the redesign. Moreover, Abraham and Shimer (2001) used independent data from the Census Employment Survey to evaluate the e¤ect of the CPS redesign
on the average transition probabilities from matched data. They found that only
UI
and
IU
were signi…cantly a¤ected, and that, after correction of these discontinuities (using the CES
employment-population ratio), none of the transition probabilities displayed large movements
in 1994.
Finally, we checked ex-post that our procedure had little e¤ect on the stocks, i.e. on the
measure of the aggregate unemployment rate and on the unemployment rate of each demographic group, consistent with Polivka and Miller’s conclusion (1998) that the redesign did not
a¤ect the measure of unemployment.
24
Analytical expressions for the Beveridge curve decomposition
8
>
>
>
>
d ln
>
<
>
>
>
>
>
:
UB
t
=
N
X
X
uj;ss
! i iu
jB
i
UB
d ln
jB
it
+
UB
X
jB
uj;ss
uss
UB
d ln
uj;ss
t
uss
t
+
U B;demog
t
+ d ln
with d ln
U B;demog
t
=
N
X
uss
! i uiss
UB
i
UB
i=1
8
>
>
>
< d ln
>
>
>
:
8
>
>
< d ln
>
>
:
EU
t
=
N
X
X
ess
i
! i ess
i=1 j2fp;t;qg
EU
= d ln ~ t + d ln
8
>
>
< d ln
>
>
:
IB
t
=
N
X
EI
t
=
N
X
ess
EI
i
EI
IB
i
IB
IB
d ln ~ t
+ d ln
N
X
UB
i
UB
IB
it
+
+
N
X
N
X
iss
IB
i
IB
! i iiss
X
ess
! i eiss
Ej
i
EU
ess
! i eiss
EI
i
EI
uss
t
ess
d ln ! it eit
ss
t
ess
t
iss
it
d ln ! it iss
t
B 2 fE; U g
AB
where the aggregate hazard rates ~ t that hold composition (by demographics and unem-
ployment reason) constant are de…ned by
8
N
X
X
>
UB
uj;ss
jB
>
i
~
>
B 2 fE; Ig
=
!
>
i
t
uss it ,
>
>
>
i=1 j2fp;t;qg
>
>
>
N
N
<
X
X
X
EI
ess
ess
Ej
i
~ EU =
~
!
and
=
! i eiss
i ess it
t
t
>
>
i=1 j2fp;t;qg
i=1
>
>
>
>
N
N
>
X iss
> ~ IU X iss
EI
>
i
~ IE
>
! i iiss Io
! i iss
: t =
it and t =
it :
i=1
A second-order decomposition
A second-order Taylor expansion of
uss
t =
st
st + ft
25
t
d ln ! it uit
ss , B 2 fE; Ig
d ln ! it eit
ss
i=1
IB;demog
t
i=1
uss
it
d ln ! it uss
i=1
EI;demog
t
EI
d ln
EI
it
d ln
= d ln ~ t + d ln
iss
+
EU;demog
t
i=1
! i iiss
Ej
it
d ln
uss
! i uiss
i=1 j2fp;t;qg
! i eiss
i=1
=
Ej
i
EU
N
X
i=1
i=1 j2fp;t;qg
i=1 j2fp;t;qg
= d ln ~ t
N
X
EI
it
with st and ft de…ned by
8
>
< st =
>
: ft =
gives us
d ln uss
t
UI
UI d t
UI
=
EI IU
t
t
+
IE EU
t
t
+
IU EU
t
t
U I IE
t
t
+
IU U E
t
t
+
IE U E
t
t
2
IE
1
+
2 (s + f )2
UI 2
UI
t
+
(17)
2
1 IU + IE
UE
UE 2
+
t
2 (s + f )2
"
#
EI
UI
UE 2
IE
EU 2
+
+
d
1
t
IE
IE 2
IE
+
+
t
IE
2
2
2
s
(s + f )
"
#
EI
IU 2
IU 2
1
EI d t
EI
EI 2
+
+
+
t
EI
2
s2
(s + f )2
"
#
IE
IU 2
IE
IU 2
EU
+
+
1
d
t
EU
EU 2
+
+ EU EU +
t
2
2
2
s
(s + f )
"
2
EI
EI
IU
+ EU
+ EU + U E
1 EI
IU d t
EU 2
+
+
+
+
IU
2
s2
(s + f )2
UE
UE d t
UE
+cross-order terms +
with
UI
=
EI
U I IE
s+f
EI IU
= (1 uss )
,
EU
s
,
uss )
= (1
2#
IU 2
IU
t
t
UE
IU
=
IE EU
+
s
UE
+ IE
s+f
IU
EU
,
UE
IU
,
IE
= (1
=
IE EU
uss )
s
U I IE
+ IE
s+f
(1 uss )
EI IU
+
s
IU
EU
IU
UE
s+f
UE
,
:
To classify the cross-order terms (in, say, labor demand versus labor supply), we split their
contribution in half between each two components.
Finally, to separate movements along the Beveridge curve from changes in matching e¢ UE
t
ciency, note that "t = ln
can write d"t =
d
UE
t
UE
UE
d^t
UE
UE
UE
ln ^ t with ^ t = m0
d
U E2
t
U E2
U E2
d^t
U E2
26
1
vt
uss;bc
t
. To a second-order, we
, so that by de…ning d"1t =
d
UE
t
UE
UE
d^t
UE
and
d"2t =
d
U E2
t
U E2
U E2
d^t
U E2
, we can replace d
d
d
UE
t
UE
t
UE
UE 2
t
UE
UE 2
t
and d
in (17) using
UE
=
=
d^t
UE
+ d"1t
UE
d ^t
UE
27
2
+ d"2t
References
[1] Abraham, K. “Help-Wanted Advertising, Job Vacancies, and Unemployment,” Brookings
Paper on Economic Activity, 1:207-248, 1987.
[2] Abraham, K. and R. Shimer. “Changes in Unemployment Duration and Labor-Force Attachment.” In The Roaring Nineties: Can Full Employment Be Sustained?, ed. Alan B.
Krueger and Robert M. Solow, 367-420. New York: Russell Sage Foundation and Century
Foundation Press, 2001.
[3] Barnichon, R. “Building a composite Help-Wanted index,” mimeo, 2010.
[4] Barnichon, R. and A. Figura. “What happened to matching e¢ ciency?,” mimeo, 2010.
[5] Blanchard O. and P. Diamond. “The Beveridge Curve,” Brookings Paper on Economic
Activity, 1:1-60, 1989.
[6] Davis, Steven J., Jason Faberman, and John Haltiwanger. “The Flow Approach to Labor Markets: New Evidence and Micro-Macro Links.”Journal of Economic Perspectives,
20(3), 3-26, 2006.
[7] Duca J. and C. Campbell.“The impact of evolving labor practices and demographics on
U.S. in‡ation and unemployment,” Dallas Fed Working Paper, 2007.
[8] Elsby, M. B. Hobijn and A. Sahin. “Unemployment Dynamics in the OECD,” Working
Paper, 2008.
[9] Elsby, M. R. Michaels and G. Solon. “The Ins and Outs of Cyclical Unemployment,”
American Economic Journal: Macroeconomics, 2009.
[10] Fujita, S. and G. Ramey. “The Cyclicality of Separation and Job Finding Rates,” International Economic Review, 2009.
28
[11] Lipsey, R. “Structural and De…cient-Demand Unemployment Reconsidered,” in Employment Policy and the Labor Market, ed. Arther M. Ross, 210-255, UC Berkeley Press,
1965.
[12] Pissarides, C. Equilibrium Unemployment Theory, 2nd Edition, MIT Press, 2001
[13] Sahin, Aysegul, Joseph Song, and Bart Hobijn, “The Unemployment Gender Gap During
the Current Recession, ” mimeo, FRB-NY, 2009.
[14] Shimer, R., “The Impact of Young Workers on the Aggregate Labor Market,” Quarterly
Journal of Economics, 116, 969-1008, 2001.
[15] Shimer, R. “Reassessing the Ins and Outs of Unemployment,”NBER Working Paper No.
13421, 2007.
29
U=s /(s +λ
t
V
t
UIE
1- σ ε
+m (V /U ) e t)
t
0 t t
- s or λ
t
UIE
:
t
lay of f s, quits, mv ts LF-NLF
or
- matching ef f iciency ε
t
Shif t in the
Bev eridge curv e
U
Figure 1: Shifts in the Beveridge curve.
-0.6
-0.8
-1.0
-1.2
.2
-1.4
(log) job finding rate
Residual
Job finding rate, US data
Job finding rate from matching function
-1.6
.1
residual
-1.8
-2.0
.0
-.1
-.2
1970
1975
1980
1985
1990
1995
2000
2005
Figure 2: Empirical (log) job …nding rate, model job …nding rate and residual, 1967-2009.
30
0.11
L
d
L
shocks to matching efficiency
0.1
Percentage points of unemployment
s
0.09
0.08
0.07
0.06
0.05
0.04
1976
1981
1986
1991
1996
2001
2006
Figure 3: Decomposition of unemployment ‡uctuations into labor demand movements, labor
supply movements and shocks to matching e¢ ciency over 1976-2009. The y-axis uses a logarithmic scale. The decomposition uses 2000Q3 as the base year. The colored areas sum
to the approximated steady-state unemployment. The dashed red line is the exact value of
steady-state unemployment.
31
0.08
Permanent Layoffs
Temporary Layoffs
Mvts along BC
Percentage points of unemployment
0.07
L
d
0.06
0.05
0.04
1976
1981
1986
1991
1996
2001
2006
Figure 4: Decomposition of labor demand movements into movements along the Beveridge
curve and Beveridge curve shifts from permanent layo¤s or temporary layo¤s, 1976-2009. The
decomposition uses 2000Q3 as the base year. The y-axis uses a logarithmic scale.
0.07
Quits
Mvts LF-NLF
Demographics
Percentage points of unemployment
L
s
0.06
0.05
0.04
1976
1981
1986
1991
1996
2001
2006
Figure 5: Decomposition of labor supply movements into Beveridge curve shifts due to quits,
movements in-and-out of the labor force and demographics, 1976-2009. The decomposition
uses 2000Q3 as the base year. The y-axis uses a logarithmic scale.
32
λ
UI
λ
0.45
0.06
0.4
0.055
0.35
0.05
0.3
0.045
0.25
0.04
0.2
1976 1981 1986 1991 1996 2001 2006
λ
IU
1976 1981 1986 1991 1996 2001 2006
EI
λ
0.045
IE
0.08
0.04
0.07
0.035
0.06
0.03
0.05
0.025
0.02
1976 1981 1986 1991 1996 2001 2006
0.04
1976 1981 1986 1991 1996 2001 2006
Figure 6: Transition rates for in-and-out of the labor force movements for women aged 25-55,
1976-2009. The dashed line represents the corresponding HP-…lter trend ( = 105 ).
λ
UI
λ
0.25
IU
0.16
0.14
0.2
0.12
0.15
0.1
0.1
0.08
0.05
1976 1981 1986 1991 1996 2001 2006
λ
0.06
1976 1981 1986 1991 1996 2001 2006
EI
λ
0.014
IE
0.12
0.11
0.012
0.1
0.01
0.09
0.008
0.08
0.006
1976 1981 1986 1991 1996 2001 2006
1976 1981 1986 1991 1996 2001 2006
Figure 7: Transition rates for in-and-out of the labor force movements for men aged 25-55,
1976-2009. The dashed line represents the corresponding HP-…lter trend ( = 105 ).
33
UI
6
0.6
5
Hazard rate
Hazard rate
λ
0.7
0.5
0.4
x 10
-3
λ
IU
4
3
0.3
2
0.2
1976 1981 1986 1991 19962001 2006
1
1976 1981 1986 1991 1996 2001 2006
λ
EI
IE
λ
0.06
0.02
Hazard rate
Hazard rate
0.055
0.05
0.045
0.018
0.016
0.04
0.014
1976 1981 1986 1991 1996 2001 2006
1976 1981 1986 1991 19962001 2006
Figure 8: Transition rates for in-and-out of the labor force movements for men and women aged
over 55, 1976-2009. The dashed line represents the corresponding HP-…lter trend ( = 105 ).
λ
UI
λ
0.14
0.5
0.45
0.4
0.12
0.1
0.08
0.35
1976 1981 1986 1991 1996 2001 2006
λ
0.06
1976 1981 1986 1991 1996 2001 2006
EI
λ
0.085
0.16
0.08
0.14
0.075
0.07
Hazard rate
Hazard rate
IU
0.16
Hazard rate
Hazard rate
0.55
0.065
IE
0.12
0.1
0.08
0.06
1976 1981 1986 1991 1996 2001 2006
0.06
1976 1981 1986 1991 1996 2001 2006
Figure 9: Transition rates for in-and-out of the labor force movements for men and women
aged 16-25, 1976-2009. The dashed line represents the corresponding HP-…lter trend ( = 105 ).
34
dlnu
shifts, LF-NLF
i
dlnu
0.04
demog
i
0.1
w1625
w1625
w2555
w2555
w5485
w5485
0.03
m1625
0.08
m1625
m2555
m2555
m5485
0.02
0.06
0.01
0.04
ln(X /E X)
0
t
t
ln(X /E X)
m5485
-0.01
0.02
0
-0.02
-0.02
-0.03
-0.04
-0.04
1976
1981
1986
1991
1996
2001
2006
-0.06
1976
1981
1986
1991
1996
2001
2006
Figure 10: HP-…lter trends ( = 105 ) in Beveridge curve shifts due to changes in labor supply
or to changes in demographics, 1976-2009. All variables are expressed as log-deviations from
their average values.
35
Table 1: Estimating a Cobb-Douglas matching function
Dependent variable:
UE
UE
Sample
(quarterly frequency)
1967-2009
1967-2009
(1)
OLS
(2)
GMM
σ
0.62***
(0.01)
0.61***
(0.01)
R2
0.89
--
Regression
Estimation
Note: Standard-errors are reported in parentheses. In equation (2), I use 3 lags of v and u as instruments. I allow
for first-order serial correlation in the residual.
Table 2: Variance decomposition of steady-state unemployment, 1976:Q1-2009:Q4
Changes in Ld
Changes in Ls
Shocks to the
matching function
0.59
0.16
0.68
0.31
0.84
0.19
0.10
-0.13
Raw data
Trend component
Cyclical component
Note: Trend component denotes the trend from an HP-filter (105) and cyclical component the deviation of the raw data from that trend.
Table 3: Variance decomposition of steady-state unemployment, 1976:Q1-2009:Q4
Trend
component
-0.13
0.05
0.06
0.61
0.42
--
Raw data
0.24
0.25
-0.04
0.28
0.12
0.13
Mvts along BC
Layoffs
Quits
Ls
Mvts LF-NLF
Demographics
Matching efficiency
Ld
Cyclical
component
0.37
0.46
-0.07
0.23
0.02
--
Note: Trend component denotes the trend from an HP-filter (105) and cyclical component the deviation of the raw data from that trend. Mvts along BC refers to
movements along the Beveridge curve and Mvts LF-NLF refers to movements in-and-out of the labor force.
Table 4: Correlation matrix of the determinants of cyclical unemployment, 1976-2009
Temporary layoffs
Permanent layoffs
Mvts along BC
Quits
Mvts LF-NLF
Temporary
layoffs
1
-
Permanent
layoffs
0.56
1
-
Mvts along
BC
0.54
0.88
1
-
Quits
Mvts LF-NLF
-0.52
-0.65
-0.68
1
-
0.42
0.71
0.71
-0.62
1
Note: All variables are detrended with an HP-filter (105).
Table 5: Lead-lag structure of the determinants of cyclical unemployment, 1976-2009
Temporary layoffs
Permanent layoffs
Mvts along BC
Quits
Mvts LF-NLF
Temporary
layoffs
Permanent
layoffs
Mvts along
BC
Quits
Mvts LF-NLF
0
-
1
0
-
1
0
0
-
2
0
0
0
-
2
1
1
0
0
Note: The table reports the value of j for which corr(Xt,Yt+j) is highest (in absolute value).
35
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