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

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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

Federal Reserve Board

Andrew Figura

Federal Reserve Board

20 August 2010

Abstract

This paper presents a framework to interpret movements in the Beveridge curve and

analyze unemployment áuctuations. We decompose the unemployment rate into three main

components: (1) a component driven by changes in labor demand ñmovements along the

Beveridge curve and shifts in the Beveridge curve due to layo§sñ (2) a component driven

by changes in labor supply ñ shifts in the Beveridge curve due to quits, movements inand-out of the labor force and demographicsñ and (3) a component driven by changes in

the e¢ ciency of matching unemployed workers to jobs. We Önd 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 classiÖcations: 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 reáect 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 áuctuations and their impact on welfare, as well as assessing ináationary 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

ìequilibriumîor ìstructuralîunemployment, 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) Örm-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 Örst contribution of this paper is to present a framework to rigorously study movements

in the Beveridge curve. We accomplish our Beveridge curve decomposition by Örst isolating the

ináows and outáows of unemployment, following Shimer (2007). Using an aggregate matching

function tying vacancy posting and unemployment to transitions from unemployment into

employment, we decompose the outáow 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 ináows 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 Önd that labor demand and

labor supply contribute approximately equally to unemploymentís 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 unemploymentís

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 áuctuations. However, movements in-and-out of the labor force explain close to a quarter of unemploymentís 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

1

2

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 Örms 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 Önd little evidence of any trend in labor demand. In contrast, unemploymentís 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 womenís 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 Örst strand investigates the

relative responsibility of unemployment ináows and outáows in accounting for changes in unemployment.1 We take this literature one step further by decomposing the labor market áows

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 áuctuations into three categories; changes in labor demand ñmovements along the Beveridge curve and shifts in the Beveridge curve due to layo§sñ,

changes in labor supply ñshifts in the Beveridge curve due to quits and movements in and out

of the labor forceñ, 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 = 

EU

t Et + 

IU

t

It  (

UE

t + 

UI

t

)Ut

E_

t = 

UE

t Ut + 

IE

t

It  (

EU

t + 

EI

t

)Et

_It = 

EI

t Et + 

UI

t Ut  (

IE

t + 

IU

t

)It

(1)

As Örst 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 u

ss

t

so that

ut '

st

st + ft

 u

ss

t

(2)

with st and ft deÖned by2

8

><

>:

st = 

EU

t +



EI

t 

IU

t

1

II

t

ft = 

UE

t +



UI

t 

IE

t

1

II

t

:

2.2 Modeling 

UE with a matching function

The job Önding rate is deÖned as the ratio of new hires to the stock of unemployed, so that

the job Önding 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 speciÖcation widely used in the search and matching literature (see e.g. Pissarides, 2001),

2Expression (2) generalizes the simpler two-states case without movements in-and-out of the labor force in

which u

ss

t =



EU

t

EU

t +UEt

: 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 Örst leaving the labor force (U-I) and then by Önding a job directly

from inactivity (I-U). ft, the ìU-E transition probabilityî that matters for steady-state unemployment rate is

then a weighted average of 

UE

t and 

UI

t 

IE

t

, with weights of 1 and 1

1II

t

, the average time that an inactive

worker spends in I. st has a similar expression.

6
we can express mt as

mt = m0u



t

v

1

t

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 Önding rate 

UE

t as

ln 

UE

t = (1  ) ln vt

ut

+ m0 + t: (3)

where t allows the e¢ ciency of matching workers to Örms to vary over time.

2.3 Decomposing movements in the Beveridge curve

Writing the steady-state approximation for unemployment (2) and modeling the job Önding

rate with a matching function, we can write

u

ss

t 

st

st +



UI

t 

IE

t

1

II

t

+ 

UE

t

'

st

st + 

UIE

t + m0



vt

u

ss

t

1

(4)

with 

UIE

t =



UI

t 

IE

t

1

II

t

. 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 Örms 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 

UIE

t moves.

However, while the matching function is remarkably successful at modeling the job Önding

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 deÖne u

ss;bc

t

as the steady-state unemployment

rate implied by a stable Beveridge curve, i.e. by a stable matching function. Formally, u

ss;bc

t

7
is deÖned by

u

ss;bc

t =

st

st + 

UIE

t + m0



vt

u

ss;bc

t

1

: (5)

Denoting ^

UE

t = m0



vt

u

ss;bc

t

1

the job Önding rate predicted by a stable matching function, we can rewrite (4) as

u

ss

t =

st

st + 

UIE

t + ^

UE

t

e

"t

(6)

where "t = ln 

UE

t  ln ^

UE

t

captures deviations of the job Önding 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 u

ss

t = 

EId ln EI

t + 

IU d ln IU

t + 

EU d ln EU

t

(7)



IEd ln IE

t  

UId ln UI

t  

UEd ln UE

t + t

with 

AB	

some positive constants depending on the mean of 

AB

t

	

.

5

In this context, we

can decompose unemployment movements in a Beveridge curve framework from

d ln u

ss

t = d ln u

bc

t + d ln u

shif ts

t + d ln u

ef f

t + t

(8)

where d ln u

bc

t  

UEd ln ^

UE

t = 

UE(1  )d ln v

UE

t

u

ss;bc

t

represents movements along the Beveridge curve, d ln u

ef f

t  

UEd"t captures the shifts in the Beveridge curve caused by changes

3Note 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

u

ss;bc

t

; the unemployment rate implied by a stable matching function and the current levels of st and 

UIE

t

.

Deviations of the actual job Önding rate from the job Önding rate implied by u

ss;bc

t

can then be interpreted as

due to a change in matching e¢ ciency.

4A Örst-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.

5Formally, EI = (1  uss)



EI IU

s

, 

UE =



IU UE+IEUE

s+f

, 

IE =



IEEU

s

(1  u

ss) 



UIIE+IEUE

s+f

,



UI =



UIIE

s+f

, 

EU = (1  uss)



IEEU +IU EU

s

, 

IU = (1  uss)



EI IU +IU EU

s 



IU UE

s+f

:

8
in matching e¢ ciency, and shifts in the Beveridge curve are given by

d ln u

shif t

t  

EU d ln EU

t + 

EId ln EI

t + 

IU d ln IU

t  

IEd ln IE

t  

UId ln UI

t

Shifts in the Beveridge curve can occur through changes in workersíattachment 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

V ar (d ln u

ss

t

) = Cov(d ln u

ss

t

; d ln u

bc

t

)+Cov(d ln u

ss

t

; d ln u

shif ts

t

)+Cov(d ln u

ss

t

; d ln u

ef f

t

)+Cov(d ln u

ss

t

; t):

(9)

so that, for example, Cov(d ln u

bc

t

;d ln u

ss

t

)

var(d ln u

ss

t

) measures the fraction of unemploymentís 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 Örm-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

workersíattachment 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
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: u

p

i

;

u

t

i

, u

q

i

and u

o

i

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) satisÖed by the number of unemployed

Uit, employed Eit and inactive Iit in demographic group i becomes

8

>>>>>>><

>>>>>>>:

U_

j

it = 

Ej

it Eit  (

jE

it + 

jI

it )U

j

it, j 2 fp; t; qg

U_ o

it = 

Io

it Iit  (

oE

it + 

oI

it )U

o

it

E_

it = 

pE

it U

p

it + 

tE

it U

t

it + 

qE

it U

q

it + 

oE

it U

o

it + 

IE

it Iit  (

El

it + 

Eq

it + 

EI

it )Eit

_Iit = 

EI

it Eit + 

oI

it U

o

it  (

IE

it + 

Io

it )Iit

(10)

With Ut =

X

N

i=1



U

p

it + U

t

it + U

q

it + U

o

it

, the aggregate steady-state unemployment rate u

ss

t

satisÖes (2) with the average transition rates given by

8

>>>>>>>>>><

>>>>>>>>>>:



UB

t =

X

N

i=1

X

j2fp;t;q;og

U

j

it

Ut



jB

it , B 2 fE; Ig



EU

t =

X

N

i=1

X

j2fp;t;qg

Eit

Et



Ej

it and 

EI

t =

X

N

i=1

Eit

Et



EI

it



IU

t =

X

N

i=1

Iit

It



Io

it and 

IE

t =

X

N

i=1

Iit

It



IE

it

(11)

10
Using the steady-state approximations, we can approximate (11) with

8

>>>>>>>>>><

>>>>>>>>>>:



UB

t '

X

N

i=1

X

j2fp;t;q;og

!it

u

j;ss

it

u

ss

t



jB

it , B 2 fE; Ig



EU

t '

X

N

i=1

X

j2fp;t;qg

!it

e

ss

it

e

ss

t



Ej

it and 

EI

t '

X

N

i=1

!it

e

ss

it

e

ss

t



EI

it



IU

t '

X

N

i=1

!it

i

ss

it

i

ss

t



Io

it and 

IE

t '

X

N

i=1

!it

i

ss

it

i

ss

t



IE

it

(12)

where !it =

LFit

LFt

is the share of group i in the labor force and u

ss

it ; essit and i

ss

it denote respectively the steady-state unemployment rate, employment rate and inactivity rate of group i.

The steady-state unemployment rate for category i satisÖes u

ss

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 

EU

t

d ln 

EU

t =

X

N

i=1

!i

e

ss

i

e

ss



EU

i



EU 

d ln 

EU

it + d ln 

!it

e

ss

it

e

ss

t

 = d ln ~

EU

t + d ln 

EU;demog

t

(13)

and similarly for the other transition rates.7 The Örst term corresponds to movements in

~

EU

t 

X

N

i=1

!i

e

ss

i

e

ss 

EU

it , the hazard rate that holds the share of each demographic group constant.

The second term, d ln 

EU;demog

t 

X

N

i=1

!i

e

ss

i

e

ss



EU

i



EU d ln !it

e

ss

it

e

ss

t

, corresponds to movements in the

relative size of the labor force in each group !it, as well as changes in the share of each group

in the employment pool ( e

ss

i

e

ss ).

Finally, to separate quits from layo§s, note that 

EU

t =

X

j2fp;t;qg



Ej

t

and 

Ej

t =

X

N

i=1

!it

e

ss

it

e

ss

t



Ej

it ,

8j 2 fp; t; qg.

6

See the Appendix for analytical expressions of the steady-state values.

7Throughout the paper, we present the derivations to a Örst-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

t

in (12), and we split the contributions of the cross-order terms in half between each two

components.

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

d ln u

ss

t = d ln u

bc

t + d ln u

shif ts;layof fs

t

| {z }

Ld

+d ln u

shif ts;quits

t + d ln u

shif ts;LF NLF

t + d ln u

demog

t

| {z }

Ls

+d ln u

ef f

t +t

:

(14)

where8

8

>>>>>>>>>>>>>><

>>>>>>>>>>>>>>:

d ln u

bc

t = 

UEd ln ^

UE

t

d ln u

shif ts;layof fs

t = 

EU 

d ln ~

Ep

t + d ln ~

Et

t



and d ln u

shif ts;quits

t = 

EU d ln ~

Eq

t

d ln u

shif ts;LF NLF

t = 

EId ln ~

EI

t + 

IU d ln ~

IU

t  

IEd ln ~

IE

t  

UId ln ~

UI

t

d ln u

demog

t = 

EId ln 

EI;demog

t + 

IU d ln 

IU;demog

t + 

EU d ln 

Eq;demog

t



IEd ln 

IE;demog

t  

UId ln 

UI;demog

t

d ln u

ef f

t = 

UEd"t  UEd ln 

UE;demog

t

:

We group the Örmsí induced movements in unemployment (due to vacancies or layo§s)

under the heading "labor demand" and the workersí 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 ináuence the other. Rather, we

think of the labor demand/labor supply classiÖcation as a useful framework to think about

the mechanisms (changes in Örmsíbehavior or changes in workersíbehavior) at play behind

unemployment áuctuations.

8

See the Appendix for the exact expressions for ~

AB

t

, d ln 

AB;demog

t or d ln 

UA;reason

t

:

12
3 Empirical results

3.1 Measuring individualsítransition rates

To identify the individualsítransition rates, we use CPS gross áows 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

; Ut; Uq; Uo; 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 NAB

t

( )

the number of workers who were in state A at t 2 N and are in state B at t +  with  2 [0; 1]

and deÖne n

AB

t

( ) = NAB

t P

()

X2S

NAX

t

()

the share of workers who were in state A at t.

Assuming that 

AB

t

, the hazard rate that moves a worker from state A at t to state B at

t + 1, is constant from t to t + 1, n

AB

t

( ) satisÖes the di§erential equation:10

n_

AB

t

( ) = X

C6=B

n

AC

t

( )

CB

t  n

AB

t

( )

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.

9To address Shimerís (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).

1 0Because 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

t = 0 for such transitions (for example,



pq = 0, Ip = 0, etc..)

13
3.2 Estimating a matching function

We estimate a matching function by regressing

ln 

UE

t = (1  ) ln vt

ut

+ c + t (16)

using our measure of the job Önding rate 

UE 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:Q1-

2009:Q4 and allow for Örst-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  is precisely estimated at 0:62, a

value inside the plausible range  2 [0:5; 0:7] identiÖed 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 A decomposition of unemployment áuctuations

3.3.1 Aggregate decomposition

In this section, we use (14) to decompose unemployment áuctuations 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 unemploy14
ment around the base date 2000q3.11 That base date is attractive because it corresponds to

the highest reading for vacancy posting per capita as well as the lowest value for ln u

shif t

t

.

12

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 unemploymentís áuctuations. 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 conÖrms this impression, and Table 2 shows that while

labor demand and labor supply contribute to respectively 50 and 30 percent of unemploymentís 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

unemploymentís cyclical áuctuations (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 Önding rate. However, Figure 3 shows some marked decrease in

matching e¢ ciencies in the aftermath of the 82 peaks in unemployment and during the 2008-

2009 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

1 1For 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.

1 2Thus, 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 áuctuations over the last 35 years.

1 3To separate trend and cyclical unemployment, we decompose changes in unemployment into a trend component (from an HP-Ölter,  = 105

) and a cyclical component.

1 4 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 conÖrms

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 unemploymentís 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 áuctuations: As Table 3 shows, movements along the Beveridge curve and

shifts due to layo§s are the two main determinants of unemployment áuctuations and account

for respectively 37 and 46 percent of the cyclical áuctuations 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 Solonís (2009) Önding 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 áuctuations 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 Örmsílabor demand. The

correlation with shifts due to temporary layo§s is less strong, because, as we can see in Figure

16
4, Örmsíincreasing 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 speciÖc 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 womenís 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 Örms 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

1 5This could be due to the extension of unemployment beneÖts duration during recessions. In fact, during

the mid-70s and early 80s recessions, there was comparatively little increase in unemployment coverage, and

the large increases in unemployment were not caused by large movements in 

UI

t and 

IU

t

. In contrast, a large

increase in unemployment insurance coverage in the early-90s recession coincided with unusually large increases

in d ln u

UI

t and d ln u

IU

t given the magnitude of the recession.

1 6See Sahin, Song and Hobijn (2009) for a discussion of the added-worker e§ect in the 2008-2009 recession.

1 7This 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) identiÖed 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 womenís 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 conÖrms 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 speciÖc demographics

groups since 1976.

The right panel of Figure 10 plots the trends in d ln u

demog

t

for six demographic groups and

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 boomís e§ect as women historically had a

higher job Önding rate and lower job separation rate than men.

The left panel of Figure 10 plots the trends in d ln u

shif ts;LF NLF

t

for six demographic

groups and highlights a downward trend in unemployment caused by a change in the behavior

of women, consistent with the Öndings of Abraham and Shimer (2001). Looking at Figure

6 and the behavior of prime age womenís 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 Önding a job (as is increasingly the case) or by going Örst through the unemployment

pool. Second, women display an increasing attachment to the labor force as 

UI and EI

1 8Abraham and Shimer (2001) also documented these two changes using annual transition probabilities.

18
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 (

IEand 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 áuctuations: 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 unemploymentís variance, (ii) movements in1 9The 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.

2 0This is especially true for women.

2 1Formally, we extrapolated the trend growth rates in labor force participation (IU ; UI

,

EI and IE) for

young and old workers over 2010-2016 using the 2000-2007 average growth rate of the HP-Ölter trends.

19
and-out of the labor force account for a quarter of unemploymentís 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

signiÖcant 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

áuctuations are driven by changes in job posting and job separation. However, considering (ii),

25 percent of unemployment áuctuations 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 áuctuations.

Low-frequency movements: At low-frequencies, our main Önding is the absence of any

signiÖcant 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

2 2The 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 Örmsílabor demand. Davis, Faberman, Haltiwanger, Jarmin and

Miranda (2010) link the secular decline in the job destruction rate to the secular decline in

the unemployment ináow 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 Örms) must also

justify the absence of any signiÖcant 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 áuctuations. We Önd that movements in labor demand are

the main determinants of cyclical áuctuations in unemployment but that movements in-and-out

of the labor force play an important role and account for almost a quarter of unemploymentís

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. Unemploymentís trend since 1976 can be entirely

2 3Of 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 Önd 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 womenís 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

1

2

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

To Önd the steady-state unemployment rate u

ss

it , employment rate e

ss

it and inactivity rate i

ss

it

of each demographic group i, note that nU

j

ito

j2fp;t;q;og

, Uit, Eit and Uit satisfy the system of

di§erential equations (1) so that nU

ss;j

it o

j2fp;t;q;og

, U

ss

it , Essit and I

ss

it are the solutions of the

system

8

>>>>>>>>>>>>>>><

>>>>>>>>>>>>>>>:

X

j2fp;t;q;og

U

ss;j

it 

jE

it + 

IE

it I

ss

it = ( X

j2fp;t;qg



Ej

it + 

EI

it )Eit



EI

it Ess

it +

X

j2fp;t;q;og

U

ss;j

it 

jI

it = (

IE

it + 

Io

it )I

ss

it

U

ss;j

it =



Ej



jE+jI Ess

it , 8 j 2 fp; t; qg

U

ss;o

it =



Io



oE+oI I

ss

it

U

ss

it =

X

j2fp;t;q;og

U

ss;j

it

The steady-state unemployment rate u

ss

it is then obtained from u

ss

it =

Uss

it

LFss

it

and satisÖes

u

ss

it 

sit

sit + fit

22
with sit and fit deÖned by

8

><

>:

st = 

EI

it 

IU

it + 

IE

it 

EU

it + 

IU

it 

EU

it

fit = 

UI

it 

IE

it + 

IU

it 

UE

it + 

IE

it 

UE

it

and where the transition rates are given by

8

>>>>>>>>>>>><

>>>>>>>>>>>>:



UE

it =

X

j2fp;t;q;og

u

ss;j

it

u

ss

it



jE

it



UI

it =

X

j2fp;t;q;og

u

ss;j

it

u

ss

it



jI

it



EU

it =

X

j2fp;t;qg



Ej

it



IU

it = 

Io

it

where u

ss

it =

Uss

it

LFss

it

, u

ss;j

it =

U

ss;j

it

LFss

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 classiÖed 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 Örst 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

2 4Taking 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 ináuence 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 Önding 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 Örst and Öfth 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 signiÖcantly 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 Millerís 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 =

X

N

i=1

X

j2fp;t;qg

!i

u

j;ss

i

u



jB

i



UB d ln 

jB

it +

X

N

i=1

X

j2fp;t;qg

u

j;ss

uss



jB



UB d ln u

j;ss

t

u

ss

t

+

X

N

i=1

!i

u

ss

i

uss



UB

i



UB d ln !it

u

ss

it

u

ss

t

= d ln ~

UB

t + d ln 

UB;demog

t with d ln 

UB;demog

t =

X

N

i=1

!i

u

ss

i

uss



UB

i



UB d ln !it

u

ss

it

u

ss

t

, B 2 fE; Ig

8

>>><

>>>:

d ln 

EU

t =

X

N

i=1

X

j2fp;t;qg

!i

e

ss

i

e

ss



Ej

i



EU d ln 

Ej

it +

X

N

i=1

X

j2fp;t;qg

!i

e

ss

i

e

ss



Ej

i



EU d ln !it

e

ss

it

e

ss

t

= d ln ~

EU

t + d ln 

EU;demog

t

8

>><

>>:

d ln 

EI

t =

X

N

i=1

!i

e

ss

i

e

ss



EI

i



EI d ln 

EI

it +

X

N

i=1

!i

e

ss

i

e

ss



EI

i



EI d ln !it

e

ss

it

e

ss

t

= d ln ~

EI

t + d ln 

EI;demog

t

8

>><

>>:

d ln 

IB

t =

X

N

i=1

!i

i

ss

i

i

ss



IB

i



IB d ln 

IB

it +

X

N

i=1

!i

i

ss

i

i

ss



IB

i



IB d ln !it

i

ss

it

i

ss

t

= d ln ~

IB

t + d ln 

IB;demog

t

B 2 fE; Ug

where the aggregate hazard rates ~

AB

t

that hold composition (by demographics and unemployment reason) constant are deÖned by

8

>>>>>>>>>><

>>>>>>>>>>:

~

UB

t =

X

N

i=1

X

j2fp;t;qg

!i

u

j;ss

i

uss 

jB

it , B 2 fE; Ig

~

EU

t =

X

N

i=1

X

j2fp;t;qg

!i

e

ss

i

e

ss 

Ej

it and ~

EI

t =

X

N

i=1

!i

e

ss

i

e

ss 

EI

it

~

IU

t =

X

N

i=1

!i

i

ss

i

i

ss 

Io

it and ~

IE

t =

X

N

i=1

!i

i

ss

i

i

ss 

EI

it :

A second-order decomposition

A second-order Taylor expansion of

u

ss

t =

st

st + ft

25
with st and ft deÖned by

8

><

>:

st = 

EI

t 

IU

t + 

IE

t 

EU

t + 

IU

t 

EU

t

ft = 

UI

t 

IE

t + 

IU

t 

UE

t + 

IE

t 

UE

t

gives us

d ln u

ss

t = 

UI dUI

t



UI +

1

2



IE2

(s + f)

2





UI

t  

UI 2

+ (17)



UE dUE

t



UE +

1

2





IU + IE2

(s + f)

2





UE

t  

UE2



IE dIE

t



IE +

1

2

"





EU2

s

2

+





EI + UI + UE2

(s + f)

2

#





IE

t  

IE2

+

EI dEI

t



EI +

1

2

"





IU2

s

2

+



IU2

(s + f)

2

#





EI

t  

EI 2

+

EU dEU

t



EU +

1

2

"







IE + IU 2

s

2

+





IE + IU 2

(s + f)

2

#





EU

t  

EU 2

+

IU dIU

t



IU +

1

2





EI + EU 2

"







EI + EU 2

s

2

+





EI + EU + UE2

(s + f)

2

#





IU

t  

IU 2

+cross-order terms + t

with 

EI = (1uss)



EIIU

s

, 

UE =



IU UE+IEUE

s+f

, 

IE =



IEEU

s

(1u

ss)



UIIE+IEUE

s+f

,



UI =



UIIE

s+f

, 

EU = (1  uss)



IEEU +IU EU

s

, 

IU = (1  uss)



EIIU +IU EU

s 



IU UE

s+f

:

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¢ -

ciency, note that "t = ln 

UE

t  ln ^

UE

t with ^

UE

t = m0



vt

u

ss;bc

t

1

. To a second-order, we

can write d"t =

dUE

t



UE 

d^

UE

t



UE 



dUE2

t



UE2 

d^

UE2

t



UE2



, so that by deÖning d"1

t =

dUE

t



UE 

d^

UE

t



UE and

26
d"2

t =

dUE2

t



UE2 

d^

UE2

t



UE2 , we can replace dUE

t and d





UE

t

2

in (17) using

dUE

t



UE =

d^

UE

t



UE + d"1

t

d





UE

t

2



UE =

d



^

UE

t

2



UE + d"2

t

27
References

[1] Abraham, K. ìHelp-Wanted Advertising, Job Vacancies, and Unemployment,îBrookings

Paper on Economic Activity, 1:207-248, 1987.

[2] Abraham, K. and R. Shimer. ìChanges in Unemployment Duration and Labor-Force Attachment.î 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. ìBuilding a composite Help-Wanted index,îmimeo, 2010.

[4] Barnichon, R. and A. Figura. ìWhat happened to matching e¢ ciency?,îmimeo, 2010.

[5] Blanchard O. and P. Diamond. ìThe Beveridge Curve,î Brookings Paper on Economic

Activity, 1:1-60, 1989.

[6] Davis, Steven J., Jason Faberman, and John Haltiwanger. ìThe Flow Approach to Labor Markets: New Evidence and Micro-Macro Links.îJournal of Economic Perspectives,

20(3), 3-26, 2006.

[7] Duca J. and C. Campbell.ìThe impact of evolving labor practices and demographics on

U.S. ináation and unemployment,îDallas Fed Working Paper, 2007.

[8] Elsby, M. B. Hobijn and A. Sahin. ìUnemployment Dynamics in the OECD,îWorking

Paper, 2008.

[9] Elsby, M. R. Michaels and G. Solon. ìThe Ins and Outs of Cyclical Unemployment,î

American Economic Journal: Macroeconomics, 2009.

[10] Fujita, S. and G. Ramey. ìThe Cyclicality of Separation and Job Finding Rates,îInternational Economic Review, 2009.

28
[11] Lipsey, R. ìStructural and DeÖcient-Demand Unemployment Reconsidered,îin 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, ìThe Unemployment Gender Gap During

the Current Recession, îmimeo, FRB-NY, 2009.

[14] Shimer, R., ìThe Impact of Young Workers on the Aggregate Labor Market,îQuarterly

Journal of Economics, 116, 969-1008, 2001.

[15] Shimer, R. ìReassessing the Ins and Outs of Unemployment,îNBER Working Paper No.

13421, 2007.

29
U

V

Shift in the

Beveridge curve

U=s

t

/(st+λt

UIE+m0

(Vt/Ut)

1- σ

eεt)

- s t or λt

UIE: lay of f s, quits, mv ts LF-NLF

or

- matching efficiency ε

t

Figure 1: Shifts in the Beveridge curve.

-.2

-.1

. 0

. 1

. 2

-2.0

-1.8

-1.6

-1.4

-1.2

-1.0

-0.8

-0.6

1970 1975 1980 1985 1990 1995 2000 2005

Residual

Job finding rate, US data

Job finding rate from matching function

(log) job finding rate

residual

Figure 2: Empirical (log) job Önding rate, model job Önding rate and residual, 1967-2009.

30
1976 1981 1986 1991 1996 2001 2006

0.04

0.05

0.06

0.07

0.08

0.09

0.1

0.11

Percentage points of unemployment

Ls

Ld

sho cks to m atch i ng e ffi ci en cy

Figure 3: Decomposition of unemployment áuctuations 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
1976 1981 1986 1991 1996 2001 2006

0.04

0.05

0.06

0.07

0.08

Percentage points of unemployment

Permanent Layoffs

Temporary Layoffs

Mvts along BC

Ld

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.

1976 1981 1986 1991 1996 2001 2006

0.04

0.05

0.06

0.07

Percentage points of unemployment

Quits

Mvts LF-NLF

Demographics

Ls

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
1976 1981 1986 1991 1996 2001 2006 0. 2

0.25

0. 3

0.35

0. 4

0.45 λUI

1976 1981 1986 1991 1996 2001 2006 0.04

0.05

0.06

0.07

0.08 λI E

1976 1981 1986 1991 1996 2001 2006 0.02

0.025

0.03

0.035

0.04

0.045 λEI

1976 1981 1986 1991 1996 2001 2006

0.04

0.045

0.05

0.055

0.06 λI U

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-Ölter trend ( = 105).

1976 1981 1986 1991 1996 2001 2006 0.05

0.1

0.15

0.2

0.25 λUI

1976 1981 1986 1991 1996 2001 2006

0.08

0.09

0.1

0.11

0.12 λI E

1976 1981 1986 1991 1996 2001 2006 0.006

0.008

0.01

0.012

0.014 λEI

1976 1981 1986 1991 1996 2001 2006 0.06

0.08

0.1

0.12

0.14

0.16 λI U

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-Ölter trend ( = 105).

33
1976198119861991199620012006 0.2

0.3

0.4

0.5

0.6

0.7 λU I

Hazard rate

1976198119861991199620012006 0.014

0.016

0.018

0.02 λIE

Hazard rate

1976198119861991199620012006

0.04

0.045

0.05

0.055

0.06 λEI

Hazard rate

1976198119861991199620012006 1

2

3

4

5

6 x 10-3 λIU

Hazard rate

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-Ölter trend ( = 105).

1976 1981 1986 1991 1996 2001 2006 0.35

0.4

0.45

0.5

0.55 λUI

Hazard rate

1976 1981 1986 1991 1996 2001 2006 0.06

0.08

0.1

0.12

0.14

0.16

λIE

Hazard rate

1976 1981 1986 1991 1996 2001 2006 0.06

0.065

0.07

0.075

0.08

0.085

λEI

Hazard rate

1976 1981 1986 1991 1996 2001 2006 0.06

0.08

0.1

0.12

0.14

0.16 λIU

Hazard rate

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-Ölter trend ( = 105).

34
1976 1981 1986 1991 1996 2001 2006 -0.04

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0.04

dlnui

shifts, LF-NLF

ln(Xt/E X )

1976 1981 1986 1991 1996 2001 2006 -0.06

-0.04

-0.02

0

0.02

0.04

0.06

0.08

0.1

dlnui

demog

ln(Xt/E X )

w1625

w2555

w5485

m1625

m2555

m5485

w1625

w2555

w5485

m1625

m2555

m5485

Figure 10: HP-Ölter 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
35

Table 1: Estimating a Cobb-Douglas matching function 

Dependent variable: UE  UE 

Sample 

(quarterly frequency) 1967-2009 1967-2009 

Regression (1) (2) 

Estimation OLS GMM 

σ 0.62*** 

(0.01) 

0.61*** 

(0.01) 

 

R2 0.89 -- 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 

 

Raw data 0.59 0.31 0.10 

Trend component 0.16 0.84 -- 

Cyclical component 0.68 0.19 0.13 

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 

 Raw data Trend 

component 

Cyclical 

component 

Ld Mvts along BC 0.24 -0.13 0.37 

Layoffs 0.25 0.05 0.46 

Ls

Quits -0.04 0.06 -0.07 

Mvts LF-NLF 0.28 0.61 0.23 

Demographics 0.12 0.42 0.02 

Matching efficiency 0.13 -- -- 

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 0.56 0.54 -0.52 0.42 

Permanent layoffs - 1 0.88 -0.65 0.71 

Mvts along BC - - 1 -0.68 0.71 

Quits - - - 1 -0.62 

Mvts LF-NLF - - - - 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 0 1 1 2 2 

Permanent layoffs - 0 0 0 1 

Mvts along BC - - 0 0 1 

Quits - - - 0 0 

Mvts LF-NLF - - - - 0 

Note: The table reports the value of j for which corr(Xt,Yt+j) is highest (in absolute value).