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Finance and Economics Discussion Series
Divisions of Research & Statistics and Monetary Affairs
Federal Reserve Board, Washington, D.C.
What Drives Matching Efficiency? A Tale of Composition and
Dispersion
Regis Barnichon and Andrew Figura
2011-10
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
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acknowledgement) should be cleared with the author(s) to protect the tentative character of these papers.
What Drives Matching E¢ ciency?
A Tale of Composition and Dispersion
Regis Barnichon
Federal Reserve Board
Andrew Figura
Federal Reserve Board
January 9, 2011
Abstract
This paper presents a framework to study movements in the matching e¢ ciency of
the labor market and highlights two observable factors a¤ecting matching e¢ ciency: (i)
unemployment composition and (ii) dispersion in labor market conditions, the fact that
tight labor markets coexist with slack ones. Using CPS micro data over 1976-2009, we
…nd that composition is responsible for most of the movements in matching e¢ ciency until
2006. In 2008-2009, only forty percent of an exceptionally low matching e¢ ciency can be
attributed to composition. New highly disaggregated data on vacancies and unemployment
show that the unexplained decline in matching e¢ ciency coincides with an increase in
dispersion.
JEL classi…cations: J6, E24, E32
Keywords: Matching Function, Matching E¢ ciency, Composition E¤ ect, Mismatch.
We thank Shigeru Fujita, Bart Hobijn, Rob Valletta, William Wascher and seminar participants at the
Chicago Fed, the National Bank of Hungary, the New York Fed and the San Francisco Fed. We thank Peter
Chen for excellent research assistance. The views expressed here do not necessarily re‡ those of the Federal
ect
Reserve Board or the Federal Reserve System. Any errors are our own.
1
1
Introduction
The unemployment rate is a major 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. An important determinant of the
unemployment rate is the ability of the labor market to match unemployed workers to jobs.
If aggregate matching e¢ ciency declines, i.e. if fewer job matches are formed each period
conditional on unemployment and vacancies, the unemployment rate increases with adverse
e¤ects on welfare and possibly in‡
ation. Further, the e¤ects of a decline in matching e¢ ciency
on the economy will depend on the forces behind this decline. A larger share of long-term
unemployed, a larger fraction of permanent layo¤s, geographic mismatch, skill mismatch, or
more generous unemployment bene…ts can all lower aggregate matching e¢ ciency but with
di¤ering degrees of persistence.
In this paper, we study the determinants of aggregate matching e¢ ciency ‡
uctuations over
the last four decades.
As a …rst pass towards capturing changes in aggregate matching e¢ ciency, we estimate an
aggregate matching function tying levels of vacancies and unemployment to the job …nding rate.
While the matching function appears relatively stable over time, a testimony of the success
of the matching function, the regression residual, or aggregate matching e¢ ciency, displays a
cyclical pattern, increasing in the later stages of expansions, and declining in the early stages
of recoveries. In the 2008-2009 recession however, the decline in aggregate matching e¢ ciency
started before the recession and was a lot more pronounced, adding an estimated 1 1 percentage
2
points to the unemployment rate (Barnichon and Figura, 2010).
The …rst contribution of this paper is to present an empirical framework to study movements
in aggregate matching e¢ ciency. Under fairly general assumptions, we link movements in
aggregate matching e¢ ciency to two measurable factors: (i) composition of the unemployment
pool, and (ii) dispersion in labor market conditions. First, if composition changes, and a group
with a lower than average job …nding probability (such as workers on permanent layo¤) becomes
over-represented among the unemployed, the average job …nding probability will decline more
than what a matching function would imply. Second, changes in the location and nature (e.g.,
skill requirements) of new jobs can lead to a misallocation of jobs and workers across labor
markets and generate dispersion in labor market conditions as tight labor markets coexist
with slack labor markets. Because of the concavity of the matching function, an increase in
dispersion in labor market conditions will lower matching e¢ ciency. Moreover, the e¤ect of
higher dispersion on matching e¢ ciency may be exaggerated if workers can …nd a job outside of
their local labor market (Abraham, 1991). To address this little studied issue, we introduce the
2
concept of "permeability" between labor market segments. With higher permeability, workers
are more likely to cross local labor market barriers and …nd a job in a di¤erent labor market
segment, and dispersion has a weaker e¤ect on matching e¢ ciency.
The second contribution of this paper is to use matched CPS micro data on unemploymentemployment transitions over four decades to estimate a model of job …nding probability and
to empirically relate aggregate matching e¢ ciency to composition and dispersion. In addition,
because the e¤ect of misallocation on matching e¢ ciency is a function of dispersion in labor
market conditions across segments, it is crucial to observe segments at a high level of disaggregation in order to correctly assess the extent of dispersion. We thus separately consider
shorter datasets that allow us to probe dispersion across more re…ned labor market segments.
In particular, we present a new dataset on labor market tightness by occupation and geographic
location covering a total of 564 segments, a 55-fold improvement over publicly available data
such as the Job Openings and Labor Turnover Survey (JOLTS). Further, because 564 segments
may still be well below the true number of segments in the US, we propose a method using
UK data to scale up our measure of dispersion over 564 segments to a more realistic number
of labor market segments.
Our main …ndings can be summarized as follows: (1) Changes in composition are important
and generate non-trivial cyclical movements in matching e¢ ciency. Because cyclical movements
in composition are positively correlated with aggregate labor market tightness, regressions that
do not control for composition estimate the matching function elasticity with an upward bias.
(2) Movements in composition are mostly due to two factors: (i) an increase in the fraction
of long-term unemployed during recessions, and (ii) a larger fraction of unemployed workers
on permanent (rather than temporary) layo¤ during recessions. (3) Until 2006, changes in
composition are responsible for most of the cyclical movements in matching e¢ ciency, while
dispersion appears to have played a modest role. (4) Since 2006, composition explains only
40 percent of a dramatic decline in matching e¢ ciency. Instead, the unexplained decline
coincides with an increase in dispersion in labor market conditions. Quantitatively, dispersion
may account for a quarter, and perhaps more, of the unexplained decline in matching e¢ ciency.
(5) Extended unemployment bene…ts, reduced worker mobility caused by a distressed housing
market or industry speci…c shocks do not seem to have signi…cantly lowered matching e¢ ciency.
This paper builds on a large literature studying the matching function (see Petrongolo and
Pissarides (2001) for a review) and extends Bleakley and Fuhrer (1997) to identify changes
in matching e¢ ciency. While that latter study focuses on aggregate labor market tightness
as the main explanatory variable of the aggregate job …nding rate, we emphasize that the
aggregate job …nding probability is an average of probabilities across heterogeneous workers
working in di¤erent segments of the labor market. Baker (1992) studies the role played by
3
composition in explaining the counter-cyclicality of average unemployment duration. This
paper extends Baker (1992) by presenting a model of job …nding probability based on the
concept of a matching function that takes into account individual characteristics as well as
local labor market characteristics. Finally, the literature on mismatch has typically relied on
a variety of dispersion measures (Padoa Schioppa, 1991, Layard, Nickell and Jackman, 2005)
to capture the extent of misallocation of jobs and workers, and absent a unifying framework,
there was no consensus on the most appropriate measure. This paper …lls the gap by providing
a dispersion measure, the variance of labor market tightness across labor market segments,
that can be analytically related to matching e¢ ciency and to the equilibrium unemployment
rate.1
The next section takes a …rst pass at capturing changes in matching e¢ ciency with an
aggregate matching function regression. Section 3 presents a more re…ned empirical framework
to identify the driving forces of matching e¢ ciency, and Section 4 uses micro data to estimate
that framework and discuss the results. Section 5 estimates the extent of dispersion across
labor market conditions at a high disaggregation level and evaluates the e¤ect on matching
e¢ ciency. Section 6 concludes.
2
A …rst look at changes in matching e¢ ciency
The matching function relates the ‡ of new hires to the stocks of vacancies and unemployow
ment. Like the production function, the matching function is a convenient device that partially
captures a complex reality with workers looking for the right job and …rms looking for the right
worker. In a continuous time framework, the ‡ of hires can be modeled with a standard
ow
Cobb-Douglas matching function with constant returns to scale, and we can write
mt = m0t Ut Vt1
(1)
with mt , the number of new hires at instant t, Ut the number of unemployed, Vt the number
of vacancies, and m0t aggregate matching e¢ ciency.2
Since the job …nding rate jft is the ratio of new hires to the stock of unemployed, we have
jft =
mt
Ut
so that jft = m0t
1
t
v
with = u the aggregate labor market tightness, u=U=LF ,
v=V =LF and LF the labor force. To identify m0t , a simple approach is thus to estimate
an aggregate matching function and interpret movements in the residual as movements in
1
In recent work, Sahin, Song, Topa, and Violante (2010) address the issue with a di¤erent approach, by
constructing mismatch indices based on a theoretical framework of mismatch.
2
The Cobb-Douglas matching function is used in almost all macroeconomic models with search and search
and matching frictions (e.g., Pissarides, 2001).
4
matching e¢ ciency. Speci…cally, we regress
ln jft = (1
) ln
t
+ ET (ln m0t ) +
t
(2)
with ET (:) denoting the average over the estimation period so that ET (ln m0t ) denotes the
intercept of the regression. Deviations of aggregate matching e¢ ciency from its average level
are then given by
t
= ln m0t
ET ln m0t :
(3)
We measure the job …nding rate jft from unemployment-employment transitions from the
Current Population Survey (CPS), and we use the composite help-wanted index presented
in Barnichon (2010) as a proxy for vacancy posting.3 We use non-detrended quarterly data,
allow for …rst-order serial correlation in the residual and estimate (2) over 1976-2007. Table 1
presents the results. The elasticity is estimated at 0:67. Using lagged values of vt and ut as
instruments gives similar results, and the elasticity is little changed at 0:66.
Figure 1 plots the empirical job …nding rate, its …tted value, and the residual of equation
(2), i.e.,
t;
the movements in aggregate matching e¢ ciency. A …rst observation is that the
matching function appears relatively stable over time, a corollary of the success of the matching
function. However, aggregate matching e¢ ciency displays a clear cyclical pattern, and typically
lags the business cycle, increasing in the later stages of expansions, peaking in the late stages of
recessions or the early stages of recoveries, and declining thereafter. In the 2008-2009 recession
however, the decline in matching e¢ ciency occurred earlier than in previous recessions and
was a lot more pronounced. In the fourth quarter of 2009, the residual reached an all time
low of four standard-deviations.4 The expansion period preceding the 2008-2009 recession
also appears peculiar, because the increase in matching e¢ ciency that typically occurs before
recessions was a lot more muted.
3
A framework to study movements in matching e¢ ciency
In this section, we present a general framework to investigate the factors responsible for movements in aggregate matching e¢ ciency. In particular, we identify two observable factors that
a¤ect aggregate matching e¢ ciency: the composition of the unemployment pool, and the
3
A measurement issue is that vacancies are not only …lled from the unemployed pool (U) but also from the
employment pool (E) and individuals outside the labor force (NLF). As a robustness check, we proceeded as
in Blanchard and Diamond (1989) and estimated a regression over 1994-2009 of the sum of E-U ‡
ows, NLF-E
‡
ows and E-E ‡
ows (Fallick and Fleischman, 2004) on vacancies and the number of unemployed and individuals
outside the labor force willing to work. The behavior of m0t was broadly unchanged.
4
Elsby, Hobijn and Sahin (2010) report a similar …nding using the unemployment out‡ rate, and Davis,
ow
Faberman and Haltiwanger (2010) also report a dramatic decline in the vacancy yield using JOLTS data.
5
amount of dispersion in labor market conditions. The former arises if the characteristics of
the unemployed change throughout the cycle, making job …nding more or less likely, while the
latter is caused by the concavity of the matching function and arises if tight labor markets
coexist with slack labor markets.
3.1
Composition and dispersion
Denote JFij;t the job …nding probability of an individual of type j in labor market segment i.5
A labor market segment can be de…ned by its geographic location, industry group or occupation
group. The labor market segment i of individual type j can then be thought of as the labor
market in which individual j is most likely to look for work and to …nd a job. Typically, this
will be proxied by his location and past employment history. Individual type j is de…ned by
n o
a vector of K characteristics xk , and labor market segment i is characterized by its labor
jt
market tightness (or vacancy-unemployment ratio)
it .
Because an unemployed worker may
also look outside of his labor market segment, his job …nding probability may also depend on
the aggregate labor market tightness
6
t.
Thus, we postulate that the job …nding probability of individual type j in labor market i
can be written
JFij;t = JF (Xjt ;
it ; t )
(4)
so that the average job …nding rate is given by
JFt =
X Uij;t
Ut
i;j
JFij;t :
(5)
To highlight the e¤ects of composition and dispersion on the average job …nding probability,
we take a second-order Taylor of expansion of JFij;t with respect to it around t and Xjt
X
1
around X = T:J
Xjt with Xjt = [1; x1 ; :::; xK ] and xk the kth observable characteristics of
jt
jt
jt
t;j
5
The job …nding rate jf and the the job …nding probability JF can be related from jf = ln (1 JF ).
Two other plausible determinants of the job …nding probability are the search intensity of workers and the
recruiting intensity of …rms. These parameters can easily be incorporated in our framework, but we preferred
to leave them out for two reasons. First, such concepts are di¢ cult to implement empirically as measuring
workers’ search intensity or …rms’ recruiting intensity is notoriously di¢ cult (See Davis, Faberman and Haltiwanger, 2010 for promising work in this direction). Second, as we report below, our framework without varying
search/recruiting intensities can successfully capture job …nding probability movements over 1976-2006. This
suggests that aggregate labor market tightness (or sectoral tightness) can proxy for varying intensities and that
our framework provides a good reduced-form approximation of a model of job …nding probability with varying
intensities. After 2006, varying intensities could have played a larger role, and we separately estimate the e¤ect
of extended unemployment bene…ts on workers’search intensity.
6
6
individual j, and we get7
JFt = JF t ( t ) +
X
JFtk
it
M Mt
+
t
k
t:
(6)
The …rst term in (6), JF t ( t ) = JFij;t (X; t ; t ), is the average job …nding rate absent workers
heterogeneity and dispersion.
The second term in (6),
Composition:
X
JFtk , captures the total composition e¤ect with
k
JFtk , the contribution of a given characteristic k to the average job …nding probability8
JFtk =
X Uj;t @JF
Ut @xk
jt
j
xk
jt
xk :
(7)
t ;X
The composition e¤ect arises because of worker heterogeneity. If the share
Uj;t
Ut
of a de-
mographic group (e.g. job losers) with a lower than average job …nding probability (i.e.,
@JF
@xk
jt
xk
jt
xk < 0) increases in recessions, then the average job …nding probability will
t ;X
decline without any change in individuals’job …nding probabilities.
Dispersion:
The third term in (6) captures the e¤ect of dispersion in labor market conditions
on the average job …nding probability with
M Mt
it
= M M0 ( t )
t
X Ui;t
i
= M M0 ( t ) var
it
Ut
2
1
(8)
t
it
t
and M M0 ( t ) =
2
1 2 @ JFij;t
2 t
@ 2
it
t ;X
.9 Dispersion in labor market tightness across segments will
negatively a¤ect the average job …nding probability if the individual job …nding probability is a
concave function of
it
(as would be the case with a matching function). With
@ 2 JFij;t
@ 2
it
t ;X
< 0,
an increase in dispersion across labor market segments, i.e., an increase in misallocation of
7
The cross-order term between Xjt X and it 1 is omitted and only described in the Appendix. This is
t
done for clarity of exposition as that term is empirically very small at the level of disaggregation permitted by
our data on labor market segments.
8
We omitted the second-order term for clarity of exposition, but incorporated the (small) second-order term
in all our calculations.
XU
XU
9
j;t @JF
ij;t
The term corresponding to it ,
( it
t ), is nil because t =
it :
Ut @ it
Ut
i;j
t ;X
i;j
7
jobs and workers, decreases the average job …nding probability. For example, if some segments
(such as health care) display a relatively tight labor market and some segments (such as
manufacturing) display a slack labor market, the average job …nding probability will be lower
than in an economy where labor market tightness is identical across segments.
Postulating a functional form for JFij;t
3.2
To bring our framework to the data, we need to posit a functional form for the job …nding
probability JFij;t . We adopt a logistic functional form
(1
JFij;t
1 em0 it
ln
= Xjt + ln
(1
)!
1 JFij;t
em0 it
with
it
=
vit
uit ,
)! (1
t
(1
t
)(1 !)
)(1 !)
+
(9)
ij;t
Xjt = [1; x1 ; ::; xK ] ! 2 [0; 1], and m0 a constant term. This expression has two
jt
jt
constant terms: m0 and the constant term in Xjt . To enable the estimation of m0 , we demean
the Xjt variables before estimating equation (9).
This speci…cation has a number of advantages:
First, a logistic functional form is consistent with the fact that the job …nding probability
falls between 0 and 1.
Second, in the absence of worker heterogeneity (Xjt = X) and labor market dispersion
(
it
=
t ),
(9) reduces to JFij;t = 1
e
m0
1
t
, the reduced-form aggregate speci…cation (2)
with m0t = m0 .
Third, to relate
it
and
t
to the job …nding probability of individual type j, we assume
that the job …nding probability is a geometric average of local labor market tightness
the aggregate labor market tightness
t.
it
and
Put di¤erently, we allow for the possibility that a
worker crosses barriers between labor market segments, so that his job …nding probability is
not solely a function of tightness in his local labor market. To get some intuition, consider
the simpler case without worker heterogeneity. The job …nding rate of a worker in segment i
becomes jfit = m0
(1
it
)! (1
t
)(1 !)
, i.e. a weighted (geometric) average of the segment labor
market tightness and the aggregate labor market tightness. The weight ! 2 [0; 1] captures the
impermeability of the local labor market. If ! = 1, labor market segments are impossible to
cross, and aggregate labor market tightness has no impact on the local job …nding rate. In
contrast, if there are no barriers between labor markets, ! = 0, a worker’ job …nding rate only
s
depends on the aggregate labor market tightness.
8
3.3
A decomposition of aggregate matching e¢ ciency
Thanks to our decomposition (6), we can now link movements in aggregate matching e¢ ciency
to the composition of the unemployment pool and the amount of dispersion in labor market
conditions. After some manipulation of (6) left for the Appendix,
t
= ln m0t ET ln m0t , the
deviations of aggregate matching e¢ ciency from its average value, can be written
t
with
and
1
mmt = !(1
2
em0
'
m0
1
t
1
t
) (1
X
JFtk
mmt +
t:
(10)
k
!(1
) 1
m0
1
t
var
it
(11)
t
mmt = mmt ET mmt with ET (:) denoting the average over the estimation period.
Aggregate matching e¢ ciency m0t is a function of the distribution of individual characteristics and labor market segments’ tightness. Movements in aggregate matching e¢ ciency
can be decomposed into a composition e¤ect, the …rst term on the right-hand side of (10),
a dispersion (or misallocation) e¤ect, the second term, and an unexplained component (that
includes the approximation error), the last term.
Expression (11) describes the e¤ect of misallocation (also called mismatch) on aggregate
matching e¢ ciency. Three observations are worth noting. First, the e¤ect of misallocation
is roughly proportional to the variance of labor market tightness, so that one can readily estimate the e¤ect of misallocation by looking at the dispersion in labor market conditions.10
The literature on mismatch has used various measures to quantify the e¤ect of misallocation
X
Ui
Vi
on the unemployment rate. For example, some use
(e.g., Jackman and Roper
U
V
i
X
1987, Franz 1991, Brunello 1991), others unemployment rate dispersion measures
u2 or
i
i
X
ui 2
(e.g., Jackman, Layard and Savouri (1991), Attanasio and Padoa Schioppa (1991)),
u
i
others
X
Ui Vi
U V
1=2
(Bean and Pissarides, 1991), and others
i
X
Ei
E
Ui =Ei
U=E
Vi =Ei
V =E
2
(Layard,
i
Nickell and Jackman, 1991) with Ei the number of employed workers in segment i and E the
total number of employed workers. Some measures were constructed using employment or
labor force weights (but surprisingly, rarely unemployment weights), but other measures did
not weight observations. While all these measures capture the extent of dispersion across labor
markets, absent a unifying framework, there was no consensus on the most appropriate measure. The measure we propose has an important advantage over these other measures: It can
10
The coe¢ cient of proportionality does depend on
t
9
but its e¤ect is small.
be directly related to aggregate matching e¢ ciency and thus to the equilibrium unemployment
rate (Barnichon and Figura, 2010).11
Second, while the mismatch literature imposes tight labor market segments boundaries,
our framework allows for some permeability between labor market segments. The e¤ect of
dispersion on the average job …nding rate and matching e¢ ciency depends on !. For the range
of plausible values for
and m0
1
t
, the e¤ect of dispersion increases with barriers between
labor market segments (i.e. when ! increases) and is strongest when labor market segments’
barriers are in…nite. Conversely, with higher permeability, workers are more likely to cross local
labor market barriers and …nd a job in a di¤erent labor market, and this possibility weakens
the e¤ect of dispersion on aggregate matching e¢ ciency.
Finally, because average dispersion is positive (var
on aggregate matching e¢ ciency movements
but by
4
t
it
t
0, 8t), the e¤ect of misallocation
is not given by mmt , the level of dispersion,
mmt , the deviations of dispersion from its average level.
Empirical results
4.1
Estimation
We use matched data from the Current Population Survey (CPS) covering January 1976 to
December 2007 to estimate the Unemployment-Employment (UE) transition probability for
an individual j in labor market market segment i. We restrict the estimation to pre-2008 data
so that any changes in matching e¢ ciency post 2007 do not a¤ect our coe¢ cient estimates. In
1994, a major redesign of the CPS survey was implemented and introduced breaks in many
important variables, such as reason for unemployment and duration of unemployment.12 To
control for these breaks, we estimate separate coe¢ cients for the pre and post redesign periods.
Our whole sample contains about 1.2 million observations.
In this section, we present the individual characteristics that in‡
uence the job …nding
probability, discuss our method for measuring labor market tightness by segment, and present
results.
1. Controlling for individual characteristics
The CPS data provides information allow-
ing us to control for changes in the characteristics of the unemployed. We use three main types
of information: demographic, reason for unemployment and duration of unemployment, and
11
See also the recent work by Sahin, Song, Topa, and Violante (2010) who develop mismatch indices based
on a theoretical framework of mismatch.
12
See, for example, Polivka and Miller (1998).
10
we include a set of monthly dummies to control for seasonality in job …nding probabilities.13
Demographic information includes the age and sex of the unemployed individual. We model
the e¤ect of age on the job …nding probability using a quadratic in age. The CPS distinguishes
between 5 main reasons for unemployment: permanent layo¤, temporary layo¤, new labor force
entrant, reentering the labor force, and quit job. We use dummy variables for each reason. The
CPS records the duration (in weeks) of individuals’current spells of unemployment, which we
allow to linearly a¤ect the probability of exit.
Prior research suggests that the job …nding probability declines with duration, and two
reasons are often cited. First, prolonged unemployment may lower individuals’skills relative
to other job seekers, making them less desirable to employers, or it may reduce their contacts in
job–
…nding networks, making it harder to …nd employment. Henceforth, we describe this e¤ect
as scarring. Second, prolonged unemployment may signal that the individuals have unobserved
characteristics that make it di¢ cult to …nd employment. Prolonged unemployment may also
capture unobserved circumstances. For instance, an individual may be looking for work in a
too narrow (relative to data availabilities), and hence unobservable, labor market segment with
a very low vacancy-to-unemployment ratio. As such workers remain in the unemployment pool
longer, the unobserved circumstances will be correlated with unemployment duration. Thus,
unobserved characteristics or circumstances may be responsible for duration’ ability to predict
s
the job …nding probability.
Average unemployment duration is also likely a¤ected by aggregate labor market conditions. When labor demand is low, it typically takes unemployed individuals longer to …nd jobs,
and durations rise. Thus, the signal about job …nding prospects from an individual’ unemploys
ment duration may be weaker when average durations are higher. To allow the signal from an
individual’ unemployment duration to change as aggregate conditions change, we interact an
s
individual’ duration with the average duration, which is highly countercyclical. In e¤ect, this
s
speci…cation allows the slope of the relationship between job …nding and duration to change
as aggregate conditions change.
2. Measuring labor market tightness by segment
in
it
To estimate the e¤ect of dispersion
on aggregate matching e¢ ciency, we need vacancy posting data by industry and region
going back to 1976. Moreover, since the e¤ect of misallocation arises out of the concavity of
the matching function, it is important to reach a good level of disaggregation as dispersion
increases with the number of observed segments. Unfortunately, the two data sources with
vacancy posting data, the JOLTS and the Help-Wanted Indexes (HWI) from the Conference
13
We also experimented with education level and race/ethnicity but found that these characteristics play little
role in the cyclicality of matching e¢ ciency, consistent with the …ndings of Baker (1992). We thus omitted these
characteristics for clarity of exposition.
11
Board do not satisfy these criteria. JOLTS is only available since December 2000, and while
the JOLTS measure of job openings can be disaggregated into 10 industry groups, the survey’
s
sample size is too small to allow for a disaggregation by regions and industries.14 The HWI
can be disaggregated by regions (the nine US Census divisions), but not by industry.
Instead, we use the unemployment rate to proxy for the labor market tightness in a particular segment. Regional and industry data on vacancy posting from the JOLTS over 2000-2010
show that vacancies and unemployment rates are highly negatively correlated across regions
or industries, and that
2009.15
uit
ut
is a very good proxy for
it
t
with no apparent break over 2008-
We use the CPS micro data to estimate unemployment rates for each segment. Since
new entrants to the labor force cannot be easily classi…ed in a particular industry, we use the
average unemployment rate in their state of residence. While the CPS sample is large (about
60,000 households) and allows for a higher level of disaggregation over 1976-2009 than available
vacancy data, we nonetheless face some limitations regarding the degree of disaggregation we
can achieve. We de…ne 150 segments based on the cross product of 50 states and three broad
industry groups.16 Our three broad industry groups roughly correspond to goods producing,
business/health care/educational services, and other services.17
Accordingly, we estimate the slightly modi…ed form of equation (9)
JFij;t
1
ln
= Xjt + ln
UE
1 JFij;t
by maximum likelihood with
=
(1
m0
e
uit
ut
uit
ut
1
t
1
t
+ "ijt
(12)
) !. To be able to infer an estimate of permeability,
!, from our estimate , we will posit that
range of our estimates for
m0
e
=
1:5, a value in the middle of the plausible
.18
14
The JOLTS is produced by the BLS and contains monthly data on job openings from 16,000 establishments
since December 2000.
15
Formally, we used JOLTS and Conference Board vacancy data by region or industry to regress ln it =
t
ln uit + . The regression results are shown in Table A1 in the Appendix.
ut
16
At the level of disaggregation permitted by the CPS, initial regressions and dispersion indexes by industry or
state suggest that state di¤erences in unemployment have much stronger e¤ects on job …nding probabilities than
di¤erences across industries. Therefore, we allow for as much state-level unemployment variation as possible.
17
De…ning segments by occupation rather than industry does not qualitatively change our results. The
industry groups are (1) manual workers-agriculture, mining, construction, manufacturing, transportation and
public utilities, (2) professional workers-…nance, professional and business services, health care and education,
information and public sector, and (3) service workers-retail and wholesale trade, leisure and hospitality services,
other services.
18
The value of only matters for our estimate of ! . Using the extreme values of 1.7 and 1.3 makes little
di¤erence to our conclusions, with ! ranging from 0.35 to 0.45.
12
4.2
4.2.1
Results
Coe¢ cient estimates
Table 2 reports our coe¢ cient estimates. The coe¢ cient on the aggregate vacancy-unemployment
ratio is highly signi…cant but is lower than the coe¢ cient estimated in Section 2 using only
aggregate labor market tightness. This suggests that characteristics and/or dispersion are on
average procyclical, and that failing to control for those parameters biases estimates of the
aggregate matching function elasticity upward.
The impermeability coe¢ cient of labor market segments is signi…cantly smaller than one
(! = :16=(1:5 :28) ' 0:4). While barriers between labor market segments appear to be non
trivial, they are also not insurmountable. As a result, the e¤ect of labor market tightness on
exit hazards within a segment (!(1
market tightness ((1
)(1
) = 0:16) is not as great as the e¤ect of aggregate labor
!) = 0:22).
Turning to individual characteristics, JF is decreasing in unemployment duration. Using (6)
and (7), the coe¢ cient on unemployment duration implies that having a spell of unemployment
lasting 6 months is associated with a decrease in an individual’ job …nding probability of about
s
1
1-1 2 percentage point. However, the coe¢ cient on the interaction of individual and aggregate
duration implies that this e¤ect is mitigated if the average unemployment duration is also high.
In other words, the slope of the relationship between job …nding and unemployment duration
becomes ‡
atter in downturns. As a result, increases in duration in a cyclical downswing do not
send as strong a signal about reduced job …nding probabilities as in other periods because these
increases re‡
ect, in part, changes in aggregate conditions, which we have already controlled
for.
The estimates of the e¤ect of the reason for unemployment on the job …nding probability
are relative to that of a job leaver. The estimates reveal that it is particularly di¢ cult for
permanent job losers and new entrants to the labor force to …nd employment. Unsurprisingly,
workers on temporary layo¤ have an easier time becoming reemployed. As expected, the
CPS redesign, by restricting temporary layo¤s to individuals expecting to be recalled within
6 months, increased the di¤erence in exit hazards for permanently and temporarily laid o¤
workers.
Turning to demographics, the coe¢ cient on the male dummy indicates that males are more
likely to …nd jobs than females. However, a comparison of the pre and post redesign coe¢ cients
shows that this relative advantage has lessened over time. The estimated coe¢ cients on the
age variables indicate that the probability of job …nding initially increases and then decreases
with age. In the pre redesign period, the age with the highest job …nding probability is around
30. In the post redesign period, it is close to 17.
13
4.2.2
The e¤ect of individual characteristics and dispersion on the job …nding
probability
Next, we use our decomposition (6) to estimate the e¤ect of individual characteristics and
labor market dispersion on the average job …nding probability over 1976-2009. Figure 2 graphs
JFtk , the contributions of characteristics –
reason for unemployment, unemployment duration, demographics– and M Mt , the contribution of dispersion in labor market tightness, to
,
JFt .
The contribution of reason for unemployment is procyclical, falling in recessions and rising
in recoveries. This pattern owes, in part, to an increasing share of permanent job losers and
a declining share of temporary job losers during recessions. The contribution of duration is
also procyclical. Although the coe¢ cient on the interaction term suggests that the e¤ect of
duration on job …nding probabilities is reduced in recessions, longer duration always implies a
lower job …nding probability. This indicates that some of the increase in individual durations
during cyclically weak periods re‡
ects scarring or unfavorable unobserved circumstances.
Demographics generate a downward trend in the average job …nding probability over the
sample period, as the labor force ages and women’ share of the labor force increases, before
s
leveling out at the end of the sample, as the share of men in the unemployment pool increases.
Consistent with Baker (1992), demographic characteristics have little in‡
uence on the cyclical
behavior of the job …nding probability. Finally, the e¤ect of dispersion on the job …nding
probability, given by (8), is very small because the cross-sectional variance of relative labor
market tightness is too small, at least for the segments we observe, for misallocation to have a
noticeable e¤ect on aggregate matching e¢ ciency.
4.2.3
Movements in aggregate matching e¢ ciency
Using decomposition (10), the lower panel of Figure 2 presents movements in aggregate matching e¢ ciency, in a similar fashion to Figure 1, but allowing for a richer speci…cation than the
reduced-form approach (2) from Section 2. The plain thick line is analogous to the residual of
Figure 1 and shows
t,
the total movements in aggregate matching e¢ ciency, given by (10).
X
m0 1
t
The plain thin line plots e 1
JFtk
mmt , the e¤ect of composition and dispersion on
m
0 t
t.
k
Finally, the dotted line plots the di¤erence between the two other lines, i.e.
t,
the changes
in aggregate matching e¢ ciency that cannot be accounted for by composition or dispersion.
Up until 2006, composition accounted for most of the cyclical movements in aggregate
matching e¢ ciency. Changes in composition make aggregate matching e¢ ciency procyclical
because, as noted above, (i) the fraction of long-term unemployed increases during recessions,
and (ii) a larger fraction of unemployed workers is on permanent layo¤ during recessions.
14
Interestingly, the muted increase in aggregate matching e¢ ciency in the run-up to the 20082009 recession can also be explained by composition, with both (i) and (ii) playing a role and
demographics contributing to a downward trend in matching e¢ ciency. Prior to 1994, the
ability of composition to account for matching e¢ ciency movements is not as good, and this
is probably due to the quality of the data and the loose distinction between temporary and
permanent layo¤ before 1994.19
Since 2007, a large fraction of the decline in aggregate matching function e¢ ciency has
been due to unobserved factors. Initially, the deterioration in late 2007 and 2008 owed almost
entirely to unobservable factors, as observable components were relatively constant. Thereafter,
observable factors, especially unemployment duration and reason for unemployment, began to
contribute to the deterioration, and this contribution has grown steadily, while the unexplained
component has been relatively constant. As a result, as of 2009Q4, observable factors account
for about 40 percent of the decline in aggregate matching e¢ ciency since 2007, while unobserved
factors account for the remainder.
After controlling for dispersion and observed characteristics, the unexplained decline in
matching e¢ ciency amounts to about 0:15 log points in end 2009, compared to 0:20 log points
(Figure 1) using a reduced-form regression (2) that only conditioned on aggregate labor market
tightness. It is perhaps surprising that the di¤erence between these two numbers is not larger
given that changes in the composition of the unemployed have led to a deterioration in matching
e¢ ciency and are responsible for 40 percent of the total decline. The reason is that the
deterioration in matching e¢ ciency caused by changes in observed characteristics is in line
with what one would have predicted conditioning on aggregate labor market tightness. As a
result, these e¤ects were already captured (in a reduced form sense) by the aggregate matching
function regression. As mentioned above, the coe¢ cient in the aggregate regression is larger
than in a regression using micro data, because it re‡
ects the correlation between aggregate
labor market tightness and the characteristics of the unemployed.
4.2.4
Digging further: matching e¢ ciency in the 2008-2009 recession
To try to understand the unexplained portion of the recent decline in aggregate matching
e¢ ciency, we explore several other estimation speci…cations.
Allowing for a break after 2007 First, we estimate (12) over 1976-2009 and allow for
breaks in the coe¢ cients on the right-hand-side variables after 2007. Speci…cally, each right19
The CPS redesign, by restricting temporary layo¤s to individuals expecting to be recalled within 6 months,
made the distinction a lot sharper (as seen from the evolution of the coe¢ cient on temporary layo¤s pre and
post-1994 in Table 2), which certainly improved our measure of composition.
15
hand-side variable is interacted with a dummy variable equal to 1 after 2007. If the deterioration in matching e¢ ciency is related to a larger contribution of permanent job losers or
older workers, for example, then the post-2007 coe¢ cients on permanent job loss or age should
change to re‡ this fact. If, however, the deterioration is not related to the observed charect
acteristics of the unemployed, then it will be re‡
ected by changes in the coe¢ cients of the
aggregate matching function.
Table 3 shows our estimation results, while Figure 3 shows the contributions of the righthand-side variables after allowing for a break in the post 2007 coe¢ cients. The deterioration in
matching e¢ ciency appears mostly as a higher aggregate elasticity (from 0.28 to 0.36) and as a
larger e¤ect of unemployment duration. As shown in Figure 3, the increase in unemployment
duration has been associated with a large decrease in matching e¢ ciency. The coe¢ cient on the
interaction between average duration and individual duration has decreased signi…cantly post
2007. Whereas in previous recessions, the contribution of individual duration to a reduction
in job …nding was attenuated (because it likely re‡
ected aggregate labor market conditions,
already controlled for, rather than individual circumstances) in the most recent recession, this
was not the case and the e¤ect of duration on matching e¢ ciency was stronger. Changes in
other characteristics have had little e¤ect.
The lower panel of Figure 3 repeats the lower panel of Figure 2, which shows the explained
and unexplained components of the deterioration in matching e¢ ciency, except that Figure 3
includes in the explained component the part explained by a break in post-2007 coe¢ cients.
The explained component now accounts for somewhat more (50 versus 40 percent) of the
deterioration in matching e¢ ciency. Moreover, the fraction of explained variation seems to
grow overtime, due largely to the duration component. This pattern suggests that duration
is capturing the e¤ect of unobserved circumstances, rather than scarring, on the job …nding
probability. Indeed, if unobserved circumstances lowered the job …nding probability of some
individuals, the contribution of the unexplained component to lower matching e¢ ciency would
be large initially. But with time, it would fade as the (increasing) unemployment duration of the
a¤ected individuals began to capture the e¤ect of the unobserved circumstances. This pattern
is not what one would expect, however, if scarring were the explanation for the explanatory
power of duration.
The e¤ect of extended emergency unemployment bene…ts
Next, we study whether
the increases in the maximum length of eligibility for unemployment insurance, which went
into e¤ect at the onset of the recession, have had any e¤ect on worker’ search intensity and
s
thus on matching e¢ ciency. To identify the e¤ect of extended and emergency unemployment
bene…ts (EEB) on job …nding probabilities, we follow a strategy used by Kuang and Valletta
16
(2010) who note that job losers are predominantly eligible for unemployment insurance (UI)
bene…ts while job leavers and new labor force entrants are not. While Kuang and Valletta
(2010) study the e¤ect of EEB on unemployment durations, we identify the e¤ect of EEB on
the job …nding probability by interacting a job loser dummy with a post-2008 dummy (the
period when EEB was in full e¤ect) in our regression (12). We …nd that EEB has little e¤ect
on job …nding probabilities.20 The coe¢ cient on the interaction between the job loser dummy
and the post 2008 dummy is nearly identical to that on the interaction between the other
unemployed dummy and the 2008 dummy.
Is the deterioration in matching e¢ ciency concentrated by sector or region?
Next,
we look at whether the deterioration in matching e¢ ciency has been concentrated by industry
or by location.21 To do so, we estimate two separate speci…cations of (12), where we interact a
post-2007 dummy with, respectively, dummies for an individual’ last industry of employment,
s
and dummies for an individual’ current state of residence. If the deterioration in matching
s
e¢ ciency is concentrated, then there will be signi…cant di¤erences in the interaction coe¢ cients
across industries or states. One can think of these interaction terms as shifts in local labor
market or industry Beveridge curves.
Turning …rst to concentration by industry, we …nd that there is no signi…cant di¤erence
across our three broad industry categories. The coe¢ cients on the post-2007 interaction terms
are almost identical, and the decline in matching e¢ ciency appears to be present in all industry
groups.
In contrast, there are statistically signi…cant di¤erences in the deterioration in matching
e¢ ciency across states. However, there is no apparent pattern to the di¤erences. The top
5 states (in terms of deterioration) are (in order) Florida, South Carolina, New Hampshire,
Minnesota, and Missouri. The presence of Florida is perhaps unsurprising as that state has
su¤ered a large drop in home prices and a large number of foreclosures. The drop in home prices
may have increased the number of homeowners who are underwater on their mortgages and
20
The results are reported in Table A2 in the Appendix. Our results do not necessarily contradict Kuang
and Valletta’ …ndings or Mo¢ tt (1985), Katz and Meyer (1990) and Meyer (1990) conclusion that extending
s
bene…ts does increase unemployment duration. The reason is that unemployment duration is determined by the
unemployment-employment (UE) transition rate and by the unemployment-nonparticipation (UN) transition
rate. In the Appendix, we also estimate a logistic regression for the UN transition probability after controlling
for characteristics of the unemployed. We do …nd a signi…cant e¤ect of EEB on UN transitions as job losers’
probability of remaining in the labor force increased signi…cantly more than the UN probability of other unemployed after 2008. See also Fujita (2010) who uses a di¤erent identi…cation scheme than Kuang and Valetta and
…nds that EEB signi…cantly lowered male workers’job …nding probability in the 2008-2009 recession.
21
The results are shown in Table A3 and Table A4 in the Appendix. We also looked at education groups.
While higher educational attainment is generally associated with higher job …nding probabilities, the change in
job …nding probability after 2007 was fairly widespread. All categories except the least educated (less than high
school degree) and the most educated (graduate degree) su¤ered signi…cant declines in job …nding probabilities.
17
therefore less mobile than other households. At the same time, large numbers of foreclosures
may signal the presence of many homeowners with scarce …nancial resources and little ability
to borrow, which might also impede mobility. Still, three other states often mentioned with
Florida as states with particularly bad housing markets, Nevada, Arizona and California, are
not in the top 10 (Nevada is 14th, Arizona 18th and California 28th), and the remaining states
in the top 5 have no apparent similarities.22
Discussion
From these results we take away two main conclusions. First, many of the
popular explanations for the deterioration in aggregate matching e¢ ciency …nd little support
in the data. For example, some observers have speculated that job …nding di¢ culties of
unemployed workers from the construction industry, which was particularly hard hit in the
last recession, were behind the deterioration in matching e¢ ciency. We …nd the deterioration
in matching e¢ ciency to be widespread across industries, consistent with Barnichon, Elsby,
Hobijn and Sahin’ (2010) …ndings based on JOLTS data that the decline in the vacancy
s
yield is relatively broad-based across industries. Other observers suggested that underwater
mortgages and their detrimental e¤ect on mobility were responsible for the deterioration in
match e¢ ciency. Although Florida, a state with particularly hard hit real estate markets, did
appear to su¤er particularly large deteriorations in matching e¢ ciency, three other states with
problem real estate markets— Nevada, Arizona and California— did not. More generally, the
geographic distribution of match e¢ ciency did not suggest real estate, or any other factor, as
a single cause. Finally, the advent of EEB does not appear responsible for the deterioration in
matching e¢ ciency, although it does appear to have dissuaded some individuals from dropping
out of the labor force.
Second, much of the deterioration in aggregate matching e¢ ciency seems to be associated
with long-duration spells of unemployment. Moreover, the timing pattern of the decline in e¢ ciency, in which the fraction of the decline that is unexplained has rapidly decreased over time,
suggests that unobserved characteristics, rather than scarring, explain the correlation between
duration and deterioration in matching e¢ ciency. These unobserved characteristics could be
related to a mismatch between workers’skills and location and the skills/location required by
available jobs. Although we have found little evidence of misallocation, our dispersion measure
has been highly aggregated, and dispersion may be occurring at a much more disaggregated
level. We explore this possibility in the next section.
22
Farber (2010), Molloy, Smith and Wozniac (2010) and Kaplan and Schulhofer-Wohl (2010) also …nd little
evidence that a "house-lock" is impeding migration or driving up unemployment.
18
5
More evidence on dispersion
Our empirical exercise has so far relied on the unemployment rate by state and industry to
proxy for labor market tightness and capture the extent of dispersion across labor market
segments. In this section, we instead use direct measures of vacancy posting, and, using three
di¤erent datasets, we consider three measures of dispersion: (i) dispersion by industry, (ii)
dispersion by region, and (iii) dispersion by occupation and geographic location.
Available dispersion measures are confronted with two limitations. First, not all hires occur
with the formal posting of a vacancy, and the fraction of informal hiring is not necessarily
identical across occupation, industry or geographic location. As a result, dispersion in labor
market tightness need not solely capture misallocation of jobs and workers but also the fact
that some segments have a higher level of informal hiring than others. Second, the level of
disaggregation allowed by direct measures of labor market tightness is probably too coarse to
capture the full extent of dispersion. To address these two measurement issues, we rely on a
simpler framework which abstracts from worker heterogeneity and allows us to (i) estimate the
fraction of informal hiring by segment, and (ii) use UK data to infer the extent of dispersion
at a very …ne level of disaggregation.
5.1
A simpler empirical framework
To explore whether dispersion can account for the 0.15 log points decline in matching e¢ ciency
not accounted for by composition, we simplify our empirical framework by considering the case
without worker heterogeneity but using the elasticity estimated after controlling for composition, i.e.,
=0:72. Without worker heterogeneity, the job …nding rate in segment i absent
worker heterogeneity is given by
jfit = m0
!(1
it
) (1 !)(1
t
)
(13)
and the e¤ect of dispersion on aggregate matching e¢ ciency movements is given by
1
mmt ' !(1
2
5.2
)(1
!(1
)) var
it
t
ET var
it
:
(14)
t
Data on labor market tightness by segment
We consider three datasets. First, the JOLTS measure of job openings can be disaggregated
into 10 industry groups over 2000-2010.23 Second, the Conference Board Help-Wanted Index
23
These groups are Trade (wholesale and retail), Information, Construction, Manufacturing, Professional/Business Services, Education and Health, Leisure and Hospitality, Financial Activities, Transportation.
19
originally proxied for the number of help-wanted advertisements in 51 major newspapers.
While the print index is not disaggregated by industries, the index can be disaggregated by
region, and an index of newspaper help-wanted advertising for the nine US census divisions is
available. These newspaper indexes have become increasingly unrepresentative with the advent
of online advertising, and the Conference Board began collecting data on online job posting in
2005.24 By splicing the regional print help-wanted indexes with online job openings by regions
as in Barnichon (2010), we build composite indexes of print and online vacancy posting for the
nine US census divisions over 2000-2010.
Third, since November 2006, the Conference Board has published the number of helpwanted online ads by state and occupation, as well as the number of ads by metropolitan
statistical areas (MSA) and occupation. The coverage of these two datasets is unique as it
allows us to build a direct counterpart of
vit
uit
at a high level of disaggregation. To the best
of our knowledge, these datasets are the …rst ones to contain information on vacancy posting
in the US by occupation and geographic location. Moreover, we expand the coverage of each
dataset by combining the state-level information with the MSA-level information to produce
series of vacancy posting by occupation and geographic areas across the US. With 50 states
and 52 MSAs, we get a total of 94 geographic areas.25 The Conference Board reports online
ads for six occupation groups.26 After combining these vacancy series with the number of
unemployed by geographic area and occupation estimated from the CPS, we can survey the
extent of dispersion over 94 6 = 564 labor market segments during the 2008-2009 recession.
One concern about using vacancy data by segment is that some segments may have a higher
share of informal hiring. For example, it is likely that a lot of hiring in construction occurs
without the formal posting of a vacancy. While the aggregate vacancy-unemployment ratio
from Conference Board data averaged 1.1 in 2006, the vacancy-unemployment ratio averaged
0.5 in construction and maintenance but about 4 in management and business/…nancial. Similarly, because a broad industry group may contain industries with di¤erent levels of informal
hiring, the levels of job openings may not be comparable across regions with di¤erent industry
24
The online data collected by the Conference Board correspond to the number of new, …rst-time online jobs
and jobs reposted from the previous month on more than 1200 major Internet job boards. These data provide
a direct measure of online job posting.
25
More speci…cally, we proceed as follows: when a state comprises n MSAs, we decompose the number of ads
for that state into n + 1 geographic areas. The additional area is the di¤erence between total ads in the state
and the total number of ads across the MSAs from that state. We obtain less than 50+52 areas because some
MSAs span di¤erent states (such as New York City). When this is the case, we group these states together.
The additional area is then the di¤erence between total ads in those states and the total number of ads in the
MSAs of those states. A list of the geographic areas is presented in Table A5 in the Appendix.
26
These groups are Management & Business/Financial, Professional & Related, Services, Sales & O¢ ce, Construction & Maintenance, Production & Transportation. They correspond to the SOC high level aggregations,
except Management & Business/Financial and Professional & Related which split the high-level aggregation
group "Management, Business, Science and Arts" into two subgroups.
20
specializations. For example, labor market tightness in services is on average three times higher
in Denver than in New York. Similarly, rural areas and urban areas need not display the same
fraction of informal hiring.
Because of such di¤erences in informal hiring, dispersion in observed labor market tightness
need not solely capture misallocation of jobs and workers but also the fact that some segments
have a higher level of informal hiring than others. Formally, informal hiring is akin to measurement error in vacancy posting, as we do not measure it but ~it with it = i ~it and i the share
P
P
of formal hiring.27 With t = i Uit it , we then get t = 0t ~t with 0t = i Vit i . According
Ut
Vt
to (14), the e¤ect of dispersion on matching e¢ ciency is thus a function of var
To estimate
i
0t
can back-out ln
~it
~t
.
for each dataset, we use data on the job …nding rate by segment. Taking
the log of jfit = m0
i
1
i
0t
!(1
it
) (1 !)(1
t
)
for segment i and an arbitrarily chosen segment 1, we
from the regression
ln jfit
ln jf1t = !(1
) ln
i
+ !(1
) ln ~it
ln ~1t +
1
(15)
t
where we take the log-di¤erence between two segments to remove the non-observable parameter
P Uit i
i
i
0t
0t
0t
0t : We then obtain 1 from 1 =
i Ut 1 , and we get 0t = 1 = 1 . For the online helpwanted ads by occupation and geography, the level of disaggregation is such that the sample size
of the CPS is a limitation and the monthly measures of the job …nding rate and unemployment
over 564 segments are noisy. We thus use variables at their average values over 2006-2010 and,
assuming a value for !(1
5.3
) (we take !=0.4 and =0.72), we can compute
i
1
from (14).28
Dispersion measures
Figure 4 plots the dispersions in labor market tightness over 2000-2010 using our three data
sources. JOLTS data indicate that dispersion across ten industry groups increased in the 20082009 recession by about twice as much as during the 2001 recession, but that it receded in
2009. Dispersion across the 9 census divisions also rose in the 2008-2009 recession, but the
increase started in late 2006, earlier than for sectoral dispersion. In comparison, the increases
in regional dispersion in the 2001 recession were small.
Dispersion by geography and occupation shows a clear increase in the 2008-2009 recession,
27
We assume that, apart from measurement error, there are no di¤erences in matching e¢ ciency across
occupation and geographic area so that mi = m0 , 8i (an assumption we implicitly made in Section 3 with our functional form (9)). With di¤erent matching e¢ ciency levels, (13) becomes jfit =
) (1 !)(1
)
!(1
) ~!(1
) ~(1 !)(1
mi i
: With i and mi both a¤ecting matching e¢ ciency in observationit
t
0t
ally equivalent, it is not possible to disentangle the two phenomena from information on the job …nding rate
and measured labor market tightness alone.
28
Using a di¤erent value for ! makes little di¤erence to our results.
21
and Figure 4 shows that the behavior of the series matches very well with the behavior of
the unexplained component of Figure 2. In fact, the correlation between the two series is
high at 0:82. Over 2007-2008, the increase in dispersion coincides with the decline in match
e¢ ciency, while composition was ‡ (Figure 2). In 2009, both dispersion and the unexplained
at
component of matching e¢ ciency peaked before declining slightly.
Geography/occupation dispersion was constant in 2009 while both dispersion across regions
and dispersion across industry groups declined. These di¤erent results highlight the importance
of looking simultaneously at geography and occupation or industry when studying the e¤ect
of dispersion. Thus in the rest of the paper, we will concentrate on dispersion by geography
and occupation, which we think provides the most accurate description of dispersion in labor
market conditions.
5.4
Inferring the true amount of dispersion from UK data
Because the e¤ect of dispersion arises out of the concavity of the matching function, it is crucial
to reach a good level of disaggregation. Our highest level of disaggregation covers only 564
labor market segments, probably a small amount compared to the true number of segments in
the US. As Shimer (2007) emphasized, the Occupational Employment Statistics (OES) counts
about 800 occupations, and there are 362 metropolitan statistical areas and 560 micropolitan
statistical areas, so a total of about 740,000 labor market segments.29
Thus, we now present a method using UK data to scale up our measure of dispersion over
564 segments to a more realistic number of labor market segments. De…ne an elementary labor
market segment as the smallest segment in which the matching function is still well described
by (13). We will refer to an elementary segment as a unit. The e¤ect of misallocation on
matching e¢ ciency is thus given by the dispersion in labor market conditions across such
units. We cannot observe labor market tightness at the unit level. Instead, we observe jt =
1 P
N
i s over segment j, consisting of m
jk t , the average value of the
m
N units indexed
jk 2Ij
by Ij = fj1 ; ::; jm g
[1; N ] with N the total number of units and N the number of observed
(larger) segments. Thus, we cannot measure var
can measure varn
N
N
n
jt
t
it
t
, the dispersion over the N units, but we
, the variance in labor market tightness over N larger segments with
1.30
To relate these two quantities and get an estimate of var
it
t
from varn
jt
t
, we turn
29
740,000 is an extreme example used for illustration as dispersion across that many segments would exaggerate
the e¤ect of mismatch. When the set of classi…cations is too …ne, the boundaries between segments are less
clearly de…ned, and workers are more likely to cross segments to …nd a job.
30
As we re…ne the level of disaggregation and n= N ! 1, varn
N
22
j
t
! var
it
t
:
to UK data. Unlike the US, the UK public employment o¢ ce collects vacancies by occupation
and geography at very di¤erent levels of disaggregation, from low levels of disaggregation to
very high levels of disaggregation (as high as 80,000 segments). These numbers can in turn
be matched to the number of job seekers’allowance claimants to construct measures of labor
market tightness across various occupation and geographic segments.31 With these data, we
can then establish an empirical “scaling law”that captures how varn
jt
t
increases when we
raise the number of observations N and consider smaller labor market segments.
The UK data by occupation are available at the one- to four- digits SOC levels, consisting
of respectively 9, 25, 81 and 353 groups, and we use data by geographic region at three
disaggregation levels; government o¢ ce regions (11 segments), Job Center plus Districts (48
segments), and Travel to Work Areas (232 segments). Thanks to these di¤erent levels of
jt
disaggregation, we can probe how varn
from N = Nocc
Ngeo = 9
t
varies as we increase the precision of observations
11 = 99 segments to 353
232 = 81; 896 segments. To increase
the sample size, we took averages of unemployment and vacancy data over the whole sample
period July 2006-July 2010.32
A simple theoretical framework left for the Appendix shows that we could expect a relation
of the form
varn
jt
= var
t
with f (ngeo ; nocc )
it
f (ngeo ; nocc )
with ngeo =
t
Ngeo
Nocc
; nocc =
Ngeo
Nocc
(16)
1, f (:) increasing and f ! 1 when (ngeo ; nocc ) ! (1; 1), and where f (:)
can be assumed to be time invariant.
Empirically, a power law ln varn (
extremely well with an
R2
jt
t
) = ln a0 + a1 ln ngeo + a2 ln nocc …ts the UK data
of 0:98 (Table 4).33 This encouragingly suggests that one need
not probe the data at a very high level of disaggregation to estimate the e¤ect of dispersion
on matching e¢ ciency, but can instead use f (ngeo ; nocc ) = na1 na2 to scale up our estimate
geo occ
varn
jt
t
. To illustrate the empirical relation, Figure 5 plots the relationship between the
jt
total number of observed segments and varn
t
as we increase the number of occupation
categories from 9 (comparable with the 6 occupations observed using Conference Board data)
to 353, and holding the number of geographic areas constant at 48 (comparable with the 94
areas observed using Conference Board data).
Assuming that f (:) is similar in the UK and in the US (i.e. that the scaling law parameters
31
See Sahin, Song, Topa, and Violante (2010) for a detailed study of mismatch in the UK.
We do not use data prior to May 2006 because of a break in methodology.
33
Estimating the scaling law using only yearly data (and leaving out the highest disaggregation levels Nocc =
353) gives similar a1 and a2 but di¤erent intercepts a0 , supporting our assumption that f (:) is time invariant.
32
23
a1 and a2 are not country speci…c)34 and given an estimate of the number of labor market
units Ngeo and Nocc , we can use the UK scaling law to build an estimator of var
v arn
d
t
f (ngeo ; nocc )
t
:
jt
varn
it
it
t
:
(17)
Assuming that there are 353 distinct occupations in the US and 232 geographic segments,
probably a conservative estimate given Shimer’ (2007) aforementioned observation and the
s
94
6
fact that the US is, geography-wise, much larger than the UK, we get that f ( 232 ; 353 ) ' 1=20,
so that an increased in measured dispersion in online HWI from 0:25 to 0:5 between November
2006 and December 2009 for (Nocc =6, Ngeo =94) translates into an increase from 5 to 10 when
(Nocc =353, Ngeo =232).
5.5
E¤ects of dispersion on matching e¢ ciency
To translate our estimated increase in dispersion into lower matching e¢ ciency, we need to
address one …nal issue. The previous section suggests that the increase in dispersion in labor
market conditions lead to a high value of var
it
t
at about 10 in 2009. With such high
dispersion, the Taylor expansion (14) need not provide a good approximation of the e¤ect of
dispersion on matching e¢ ciency.
Instead, we resort to numerical simulations to calculate the exact e¤ect of dispersion on
matching e¢ ciency. If the job …nding rate in segment i is described by (13), mm, the e¤ect
of dispersion on matching e¢ ciency is given by the di¤erence in the average job …nding rate
when
i
always equals 1 and when
mm = ln
X Ui
i
and we calculate mm = mm(
E =1 and var( )=
i
i
2.
i
2)
U
is distributed with variance
m0
!(1
i
) (1 !)(1
by positing that ln
Figure 6 shows how changing
)
ln m0
N(
i
2
2.
Speci…cally,
1
ln(1+
2
(18)
2
)
; ln 1 +
2
), so that
a¤ects mm and aggregate matching
e¢ ciency. Moreover, because it is di¢ cult to estimate the permeability of labor market segments, Figure 6 also plots the e¤ect of ! on the relationship between dispersion and matching
e¢ ciency. That way, we can report the e¤ect of dispersion on matching e¢ ciency for di¤erent
values of !:
With the variance of
it
t
increasing from about 5 in November 2006 to about 10 in December
34
In the Appendix, we show that one can apply the UK scaling law to US data if the average correlation in
labor market conditions within an occupation group and/or a geographic area is similar in both countries.
24
2009, misallocation can explain 26 percent (0:04 log-points out of the 0:15 unexplained logdecline in jf , cf. Figure 2) of the decline in matching e¢ ciency when ! = 0:4, about 36 percent
(:055 log points) when ! = 0:6, and about 20 percent (:03 log-points) when ! = 0:3:35 As a very
conservative estimate, we can take the increase in dispersion from online HWI at face value (an
increase from 0.25 to 0.5) and not use the UK scaling law. In that case, dispersion accounts
for about 10 percent (0.015 log-points) of the unexplained decline in matching e¢ ciency (using
! = 0:4).
Thus, we conclude that an increase in labor market dispersion likely led to a noticeable
decline in matching e¢ ciency, though a signi…cant fraction of the overall decline remains unexplained.36
5.6
Taking stock
It is di¢ cult to estimate the e¤ect of dispersion on matching e¢ ciency because data on vacancies and unemployment at high levels of disaggregation are not available. However, with
some assumptions, one can use the available data to estimate the e¤ect of dispersion at high
levels of disaggregation. These assumptions are: (1) most of the di¤erences in matching ef…ciency across segments are due to di¤erent fractions of informal hiring, (2) the UK scaling
relationship linking var
it
t
, the actual dispersion in labor market conditions, to varn
jt
t
,
the dispersion measured over a number of larger segments, is time invariant and can be applied
to the US. Given these assumptions, it is likely that greater dispersion has accounted for a
substantial portion –
about a quarter but possibly more–of the unexplained drop in matching
e¢ ciency over the past three years.
6
Conclusion
In this paper, we study the determinants of aggregate matching e¢ ciency ‡
uctuations over the
last four decades.
35
While these numbers are derived using Nocc =353 and Ngeo =232, in practice, for N large enough, the
choice of N makes little di¤erence to our conclusion. Doubling the number of units (i.e., setting Nocc =706
and Ngeo =464) only increases the contribution of misallocation from 26 to 27 percent, while halving N only
decreases it to 24 percent.
36
Note that our calculation implicitly assumed that the estimated value of var
it
t
in November 2006
corresponds to ET var it , the average dispersion level over 1976-2007. This seems plausible given that
t
Figures 1 and 2 show that aggregate matching e¢ ciency was at its average level in late 2006, suggesting that
dispersion was at its average level. Interestingly, if the average level of dispersion is given by the November 2006
reading of 5, this implies that, on average, dispersion in labor market conditions depresses the US job …nding
rate by about 15 percent (using ! = 0:4 and Figure 6).
25
Under fairly general assumptions, we link movements in aggregate matching e¢ ciency to
two measurable factors: (i) composition of the unemployment pool, and (ii) dispersion in labor market conditions. We also show that the e¤ect of misallocation on aggregate matching
e¢ ciency is a function of the dispersion in conditions across labor markets segment and of the
segments’permeability. While a number of dispersion measures have been proposed in the literature, our framework provides a dispersion measure – variance of labor market tightness–
the
that can be analytically related to matching e¢ ciency and to the equilibrium unemployment
rate.
Using CPS micro data over 1976-2009, we …nd that changes in composition of the unemployment pool generate non-trivial procyclical movements in matching e¢ ciency, implying that
estimates of the aggregate matching function elasticity are biased upwards. Until 2006, the
composition of the unemployment pool (mostly the share of job losers on permanent layo¤s
and the share of long-term unemployed) is responsible for most of the cyclical movements in
matching e¢ ciency, while dispersion in labor market conditions appears to have played a modest role. Since 2006, composition explains only 40 percent of a dramatic decline in matching
e¢ ciency. Instead, the behavior of the unexplained decline is highly (negatively) correlated
with dispersion in labor market conditions. Quantitatively, misallocation of workers and jobs
may account for a quarter, and perhaps more, of the unexplained decline. We also test a
number of popular explanations but …nd no evidence that matching e¢ ciency was a¤ected by
the extension of unemployment coverage, by a “house-lock” or by industry speci…c shocks.
A remaining question is what accounted for the remaining unexplained decline in matching e¢ ciency. An obvious possibility, given the di¢ culty to assess dispersion at high levels
of disaggregation, is that our UK scaling law lead us to understate the extent of the increase
in dispersion and hence the e¤ect of dispersion on matching e¢ ciency. Another possibility,
not tested in this paper, is that part of the decline in matching e¢ ciency was caused by a
compositional change in vacancy posting. For example, because the construction sector has a
high fraction of informal hiring (and hence an apparently high matching e¢ ciency), a decline
in the fraction of construction ads among vacancies will lower matching e¢ ciency. However,
Barnichon, Elsby, Hobijn and Sahin (2010) do not …nd that vacancy composition signi…cantly
contributed to the decline in the vacancy yield. A related hypothesis raised by Davis, Faberman and Haltiwanger (2010) is that …rms vary recruiting intensity during recessions. Despite
the fact that our empirical framework does not allow for varying recruiting intensity, it can
successfully capture job …nding probability movements over 1976-2006. This suggests that aggregate labor market tightness (or sectoral tightness) can proxy for varying recruiting intensity
over that period. Thus, if the recent unexplained decline in matching e¢ ciency was caused
by lower recruiting intensity, this would imply that recruiting intensity was exceptionally low
26
in the current recession. Assessing this hypothesis would be an interesting goal for future
research.
27
References
[1] Abraham, K. “Mismatch and Labour Mobility: some …nal remarks,” in Mismatch and
Labor Mobility, Cambridge, Cambridge University Press, 1991.
[2] Attanasio, O. and F. Padoa Schioppa. “Regional Inequalities, migration and mismatch in
Italy, 1690-86,”in Mismatch and Labor Mobility, Cambridge, Cambridge University Press,
1991.
[3] Baker, M. “Unemployment Duration: Compositional E¤ects and Cyclical Variability,”
American Economic Review, 1992.
[4] Barnichon, R. “Building a composite Help-Wanted index,” Economics Letters, 2010.
[5] Barnichon, R., M. Elsby, B. Hobijn, A. Sahin. “Which Industries are Shifting the Beveridge
Curve? Working Paper, 2010.
[6] Barnichon, R. and A. Figura. “What Drives Movements in the Unemployment Rate? A
Decomposition of the Beveridge Curve,” FEDS Working Paper, 2010.
[7] Bean, C. and C. Pissarides. “Skill shortages and structural unemployment in Britain:
a (mis)matching approach,” in Mismatch and Labor Mobility, Cambridge, Cambridge
University Press, 1991.
[8] Bleakley H. and J. Fuhrer. Shifts in the Beveridge Curve, Job Matching, and Labor Market
Dynamics,” New England Economic Review, 1997.
[9] Brunello, G. “Mismatch in Japan,” in Mismatch and Labor Mobility, Cambridge, Cambridge University Press, 1991.
[10] Davis, S., J. Faberman and J. Haltiwanger. “The Establishment-Level Behavior of Vacancies and Hiring,” NBER Working Paper, 2010.
[11] Elsby, M., B. Hobijn and A. Sahin. “The Labor Market in the Great Recession,”Brookings
Papers on Economic Activity, 1-48, 2010.
[12] Farber, H “Job Loss and Unemployment in the 21st Century: the Great Recession in
Labor Market Perspective,” Industrial Relations Section , Princeton University Working
Paper,560, 2010.
[13] Franz, W. “Match and mismatch on the German labour market,”in Mismatch and Labor
Mobility, Cambridge, Cambridge University Press, 1991.
28
[14] Fujita, S. “E¤ects of the UI Bene…t Extensions: Evidence from the Monthly CPS,”
Philadelphia Fed Working Paper 10-35, 2010.
[15] Jackman, R. and S. Roper. “Structural Unemployment,” Oxford Bulletin of Economics
and Statistics, 49(1), 9-36, 1987.
[16] Jackman, R., R. Layard, and S. Savouri. “Mismatch: a framework for thought,” in Mismatch and Labor Mobility, Cambridge, Cambridge University Press, 1991.
[17] Layard R., S. Nickell, and R. Jackman. Unemployment: Macroeconomic Performance and
the Labour Market, 2nd Edition, Oxford University Press, 2005.
[18] Kaplan, G. and S. Schulhofer-Wohl. “Interstate migration has fallen less than you think:
Consequences of hot deck imputation in the Current Population Survey,”Working Paper,
2010.
[19] Katz, Lawrence, and Bruce Meyer. “The Impact of the Potential Duration of Unemployment Bene…ts on the Duration of Unemployment,” Journal of Public Economics, 41 pp.
45-72, 1991.
[20] Kuang, K. and R. Valletta. “Extended Unemployment and UI Bene…ts,”FRBSS Economic
Letter, 2010.
[21] Meyer, Bruce. “Unemployment Insurance and Unemployment Spells,”Econometrica, 58:4,
pp. 757-82, 1990.
[22] Mo¢ tt, Robert. “Unemployment Insurance and the Distribution of Unemployment
Spells,” Journal of Econometrics, 28, pp. 85-101, 1985
[23] Molloy, R., C. Smith and A. Wozniac. “Internal Migration in the US: Updated Facts and
Recent Trends,” mimeo, University of Notre Dame, 2010.
[24] Padoa Schioppa, F. Mismatch and Labor Mobility, Cambridge, Cambridge University
Press, 1991.
[25] Petrongolo, B. and C. Pissarides. “Looking into the black box: A survey of the matching
function,” Journal of Economic Literature, 39: 390-431, 2001.
[26] Pissarides, C. Equilibrium Unemployment Theory, 2nd ed, MIT Press, 2000.
[27] Sahin A., J. Song, G. Topa, and G. Violante. “Mismatch in the Labor Market: Evidence
from the UK and the US," mimeo, 2010.
[28] Shimer, R. “Mismatch,” American Economic Review, 97(4): 1074-1101, 2007.
29
Appendix
A second-order Taylor expansion of the job …nding probability
Rewriting (9), the individual job …nding probability is given by
1
JFij;t =
(1
it
t
m0
e
)!
e
1
t
(1
it
t
m0
+
JFt = JF t ( t ) +
X
m0
1
Expanding with respect to Xjt around X and
)!
e
!
1
t
Xjt
e
(1
it
t
)!
JFtk
around
t
M Mt
it
1
t
it
!
+
e
Xjt
to a second-order, JFt becomes
+ ft +
t
k
it :
t
with
JFtk = e
m0
1
t
1
e
m0
X Uj;t
1
t
j
+
1X
1
2
2e
m0
k
1
t
Ut
[
xk
jt
k
xk
jt
l
1
1
2
xk
xl
jt
xk
2e
m0
1
t
2
k
xk
jt
xk
2
xl ]
l6=k
the (second-order) composition e¤ect from characteristic k on the average job …nding rate,
it
M Mt
= M M0 ( t )
t
X Ui;t
i
Ut
it
2
1
t
the term capturing the e¤ect of dispersion on the average job …nding rate with M M0 ( t ) =
1
2
+ (1
)m0
ft = !(1
1
t
m0
)
1
t
e
m0
X X Uij;t
i;j
k
Ut
1
t
m0
and
1
t
2m0
1
t
1
it
t
1
k
xk
jt
xk :
capturing the interaction of composition and dispersion.37
37
This e¤ect comes from the concavity of the matching function, as above average workers would have a
stronger positive impact on matching e¢ ciency than below average workers if above average workers were
located in looser labor markets. Interestingly, this also implies that matching e¢ ciency is lower when workers
with above average characteristics are concentrated in tighter labor markets.
30
Decomposing movements in aggregate matching e¢ ciency
To establish a link between aggregate movements in matching e¢ ciency and changes in composition and dispersion, we write the job …nding rate jft as a function of the job …nding
probability JFt , and use (6) to get
jft =
=
ln (1
JFt )
ln 1
JF t ( t ) +
X
JFtk
it
M Mt
=
JF t ( t )
ln 1
' jf ( t ) +
with jf ( t )
ln 1
ln 1
1
X
1
JF t ( t )
1
X
1
JF t ( t )
+
t
t
k
JFtk
!!
JFtk
k
it
M Mt
+
t
t
k
it
M Mt
t
!
+
t
!!
JF t ( t ) :
Using the functional form (9), we have jf ( t ) = m0
1
t
, and taking the log of the previous
expression gives us
ln jft ' ln m0 + (1
) ln
e
+ ln 1 +
m0
' ln m0 + (1
1
t
1
t
X
JFtk
it
M Mt
k
it
M Mt
{z
+
t
t
At
where for the last expression, we used the fact that m0
+
t
k
) ln t
X
JFtk
m0 1
t
e
+
m0
|
t
m0 1
t
1
t
e
m0
1
t
t
!!
!
(19)
}
X
JFtk M Mt
it
t
+
k
t:
Expression (19) has the same form as our aggregate regression (2).
Thus, the deviations of aggregate matching e¢ ciency from its average level can be written
t
= ln m0t
= ln jft
' At
'
ET ln m0t
(1
) ln
t
ET (ln jft
ET At using (19)
X
JFtk
mmt +
1
m0 1
t
e
m0
t
k
31
t
(1
) ln t )
with mmt =
M Mt
it
t
em0
m0
1
t
1
t
M Mt
it
t
mmt = mmt ET mmt .38 Using the expression for
and
, the e¤ect of dispersion on matching e¢ ciency movements is then given by
1
mmt ' !(1
2
) (1
!(1
) 1
1
t
m0
var
it
ET var
t
it
:
t
A theoretical link between actual labor market dispersion and observed dispersion
Assume that the
i
are independently distributed across N elementary labor market segments
of equal size (i.e., with the same number of unemployed). For clarity of exposition, we will
refer to the elementary segments as units. Denote h the distribution of
h( ;
i
2)
(mean
and variance
2)
N segments that consist of m
the
is
recover
units, we observe
2
i:
i
over many units. Speci…cally, for
P
= N
jk , the average value of
N
i
j
jk 2Ij
over segment j indexed by Ij = fj1 ; ::; jm g
observations of
across units so that
with i 2 [1; N ]. We cannot observe the value of
for the N units, but we do observe the average value of
N
N
i
[1; N ], a segment consisting of m =
N
N
To estimate the true amount of dispersion in the labor market, we want to
from the observed variance across larger segments, i.e., var( j ):
If the observed segments were random samples of the
is
(i.e., if the
is
were independently
distributed across units in each observed segment), we would have a linear relation linking the
true dispersion to the observed variance
var( j ) =
which converges to
2
when N ! N .
2N
N
:
In fact, however, the segments that we observe are not random samples of the
(20)
i s.
Instead,
because the segments that we observe correspond to an occupation group or/and a geographic
location, the labor market units inside those segments are likely to be correlated. Denote
the average correlation between labor market units within a segment. Speci…cally,
=
P
is the
m6=n corr( jm ; jn ), and, for simplicity, we assume that the average correlation
1
1
n
same for all observed segments.
is likely to increase as we re…ne our de…nition of a segment.
For example, the average correlation between labor markets across the large US Census region
"West" is certainly lower than the average correlation between labor markets across the city of
38
For the last expression, we assumed that ET
X
JFtk is small, which is empirically the case since the second-
k
order approximation of JFtk is very small and since we demeaned the Xjt variables before estimating (9) so that
the …rst-order term of JFtk is nil.
32
Los Angeles. Denoting Ngeo the number of observed geographic locations and Nocc the number
of observed occupations, we have N = Ngeo Nocc , and we assume that
0
1
> 0,
0
2
> 0 and
N
N
( Ngeo ; Nocc )
geo
occ
Ngeo Nocc
;
) 1
Ngeo Nocc
Ngeo Nocc
2
f(
;
)
Ngeo Nocc
2
=
2
geo
occ
! 1 when N ! N = Ngeo Nocc . A little bit of algebra gives us
var( j ) =
which also converges to
N
= ( Ngeo ; Nocc ) with
N
1+ (
N
N
N
N
(21)
N
when N ! N . With ( Ngeo ; Nocc ) 6= 0, this generalization of (20)
N
geo
occ
N
N
is not linear. Instead, because ( Ngeo ; Nocc ) ! 1 when N ! N , one can show that, as N
geo
converges to N ,
@ 2 var( j )
@N 2
occ
< 0 and the curve ‡
attens out, in line with the UK evidence.
Thus, we can build an estimator of
2
v arn ( i )
d
varn j
:
f (ngeo ; nocc )
(22)
This theoretical framework is useful to clarify what kind of assumptions are necessary to use the
N
UK scaling law and the estimator v arn with US data. Note that f ( Ngeo ; Nocc ) is independent of
d
N
geo
2.
occ
N
Thus, f ( Ngeo ; Nocc ) will be identical in the US and the UK, if both countries have identical
N
N
( Ngeo ; Nocc ),
geo Nocc
geo
occ
i.e., if, within a segment of size
N
Ngeo Nocc ,
the average correlation in labor market
tightness between units of that segment is the same for both countries.39 For example, within
the "West" region of each country, the average correlation between two neighboring geographic
units must be the same in the US and the UK. Or, within the occupation group "Construction",
the average correlation between subcategories of construction must the same. Assuming as a
…rst approximation that the average correlations across occupation and geographic are time
invariant and similar in the US and the UK, we can apply the UK scaling law to US data.
N
2
1 P
Finally, we do not observe var( j ) but the sample variance N
: As a result,
j
j=1
we can only use (22) if N is large enough to ensure
1
N
N
P
j=1
2
j
' var( j ). For low values
of N (as would be the case with JOLTS data with only 10 industry groups and 1 area), the
sample variance may not be a good approximation of the actual variance, and the scaling law
could give misguided results.
39
The condition to use the UK law (21) with US data becomes more stringent as N increases. Since only the
average correlation enters (21), one only needs that, within a segment of size n = N , the average correlation
N
between units is identical in the US and the UK. But as N increases to N , the number of units which one takes
the average gets smaller, and the condition is more restrictive.
33
Figure 1: Empirical job …nding rate, job …nding rate predicted by an aggregate matching
function and (log) aggregate matching e¢ ciency, the (log) di¤erence between the empirical
and the predicted job …nding rate, 1976-2009. For aggregate matching e¢ ciency, the plotted
series is the 4-quarter moving average. Grey bars indicate NBER recession dates.
34
Reason f or Unemployment
Demographics
0.02
Changes in JF probality
Changes in JF probality
0.02
0.01
0
-0.01
-0.02
0.01
0
-0.01
-0.02
1976
1980
1984
1988
1992
1996
2000
2004
2008
1976
1980
1984
1988
Duration
1996
2000
2004
2008
2000
2004
2008
Dispersion
0.02
Changes in JF probality
0.02
Changes in JF probality
1992
0.01
0
-0.01
-0.02
0.01
0
-0.01
-0.02
1976
1980
1984
1988
1992
1996
2000
2004
2008
1976
1980
1984
1988
1992
1996
Decomposition of changes in matching efficiency
0.1
Log points of jf
0.05
0
-0.05
-0.1
Aggregate
Composition/Dispersion
Residual
-0.15
-0.2
-0.25
1976
1980
1984
1988
1992
1996
2000
2004
2008
Figure 2: Upper panel: decomposition of the total e¤ect of composition and dispersion into reason for unemployment, demographics, unemployment duration and dispersion. The dashed line
represents the total e¤ect of composition/dispersion. Lower panel: decomposition of changes in
aggregate matching e¢ ciency into composition e¤ect/dispersion and an unexplained aggregate
e¤ect. Regression estimated over 1976-2007. All series are 4-quarter moving averages.
35
Reason for Unemployment
Demographics
0.015
0.015
0.01
Changes in JF probality
Changes in JF probality
0.01
0.005
0
-0.005
-0.01
-0.015
-0.02
0.005
0
-0.005
-0.01
-0.015
-0.02
-0.025
1976
1980
1984
1988
1992
1996
2000
2004
-0.025
1976
2008
1980
1984
1988
Duration
1996
2000
2004
2008
2000
2004
2008
Dispersion
0.015
0.015
0.01
Changes in JF probality
0.01
Changes in JF probality
1992
0.005
0
-0.005
-0.01
-0.015
-0.02
0.005
0
-0.005
-0.01
-0.015
-0.02
-0.025
1976
1980
1984
1988
1992
1996
2000
2004
-0.025
1976
2008
1980
1984
1988
1992
1996
Decomposition of changes in matching efficiency
0.1
Log points of jf
0.05
0
-0.05
-0.1
Aggregate
Composition/Dispersion
Residual
-0.15
-0.2
-0.25
1976
1980
1984
1988
1992
1996
2000
2004
2008
Figure 3: Upper panel: decomposition of the total e¤ect of composition and dispersion into reason for unemployment, demographics, unemployment duration and dispersion. The dashed line
represents the total e¤ect of composition/dispersion. Lower panel: decomposition of changes in
aggregate matching e¢ ciency into composition e¤ect/dispersion and an unexplained aggregate
e¤ect. Regression estimated over 1976-2009, allowing for a break in the coe¢ cients in 2008.
All series are 4-quarter moving averages.
36
Figure 4: Left scale: dispersion in labor market tightness across 9 regions, 10 industry groups
and 564 occupation/region groups. Right scale: Unexplained movements in matching e¢ ciency
(y-axis in reverse order). 2001-2010.
37
Figure 5: Relationship between var( it ) and the number of observed labor market segments in
the UK over 2006-2007, keeping the number of geographic units …xed (48) but increasing the
number of observed occupations (9, 25, 81, 353). Labor market tightness measures constructed
from jobseekers allowance claimants and vacancy posting data from Jobcentre Plus.
0.35
0.3
Units of -log(JF)
0.25
0.2
0.15
0.1
0.05
0
1
8
0.8
6
0.6
Variance θ(i)/θ
4
0.4
2
0.2
Im perm eability ω
0
Figure 6: The e¤ect of labor market tightness dispersion var
matching e¢ ciency.
38
i
and impermeability ! on
Table 1: Estimating a Cobb-Douglas matching function
Dependent variable:
λUE
λUE
Sample
(quarterly frequency)
1976-2007
1976-2007
(1)
OLS
(2)
GMM
1-σ
0.33***
(0.01)
0.34***
(0.01)
R2
0.87
--
Regression
Estimation
Note: Standard-errors are reported in parentheses. In equation (2), we use 3 lags of v and u as instruments. We
allow for first-order serial correlation in the residual.
Table 2 Estimated Coefficients for Job Finding probability regression, 1976-2007
Explanatory Variable
Pre-redesign
1976-1993
Matching Function parameter
Aggregate elasticity: 1-σ
Post-redesign
1994-2007
0.28
(0.01)
Constant: ln(m0)
-1.43
(0.003)
Local elasticity: γ
0.16
(0.01)
Other parameters
0.0026
(0.001)
0.0004
(0.001)
Age squared
-0.0002
(0.00002)
-0.0002
(0.00002)
Male dummy
0.20
(0.01)
0.12
(0.01)
Permanent layoff dummy
-0.27
(0.01)
-0.27
(0.01)
Temporary layoff dummy
0.38
(0.001)
0.67
(0.01)
Reentrant dummy
-0.26
(0.01)
-0.32
(0.01)
New Entrant dummy
-0.58
(0.01)
-0.88
(0.02)
Unemployment duration
-0.025
(0.001)
-0.021
(0.002)
Duration interacted with
average duration
0.0006
(0.0001)
0.0003
(0.0001)
Age
Pseudo R2
0.0455
Note. Explanatory variables also include monthly dummies. All variables, except age after 1993, are significant at conventional levels. Standard errors are in parentheses.
39
Table 3 Estimated Coefficients for Job Finding probability regression, 1976-2009
Explanatory Variable
1976-2007
Post 2007
Aggregate elasticity: 1-σ
0.28
(0.01)
0.36
(0.23)
Constant: ln(m0)
-1.43
(0.002)
-1.54
(0.002)
Local elasticity: γ
0.16
(0.01)
0.19
(0.02)
Matching Function parameter
1994-2007
Other parameters
0.0004
(0.001)
0.0036
(0.002)
Age squared
-0.0002
(0.00002)
-0.0002
(0.0001)
Male dummy
0.12
(0.01)
0.059)
(0.02)
Permanent layoff dummy
-0.28
(0.01)
-0.26
(0.03)
Temporary layoff dummy
0.68
(0.01)
0.93
(0.04)
Reentrant dummy
-0.32
(0.01)
-0.25
(0.04)
New Entrant dummy
-0.88
(0.02)
-0.80
(0.05)
Unemployment duration
-0.021
(0.002)
-0.019
(0.003)
Duration interacted with
average duration
0.0003
(0.0001)
0.0001
(0.0001)
Age
0.0457
Pseudo R
Note. Explanatory variables also include monthly dummies. All variables, except duration interacted with average duration after 2007 and age, are significant at conventional
levels. Standard errors are in parentheses.
Table 4: Estimating a functional form for the UK scaling law
θ
varn jt
Dependent variable:
θ
t
a0
5.08
(0.50)
aocc
0.67
(0.03)
ageo
0.13
(0.04)
R2
0.98
Note: The sample includes 12 observations, with Ngeo=11, 48, 232 and
Nocc=9, 25, 81, 353.
40
Appendix
NOT FOR PUBLICATION
α
Table A1: Proxying θit with uit
θt
ut
θit
θt
θit
θt
θit
θt
θit
θt
2000-2010
2000-2009
2006-2010
2006-2010
JOLTS
Industry groups
JOLTS
US Census Regions
Conference Board
Occupations
Conference Board
State/MSA regions
-1.34***
(0.03)
-1.32***
(0.11)
-1.71***
(0.08)
-1.29***
(0.02)
1170
444
234
3510
0.76
0.73
0.89
0.83
Dependent
variable:
Sample
(quarterly
frequency)
Data source
α
Number of
observations
R2
Note: Standard-errors are reported in parentheses. All panel regressions include industry or region fixed effects. The first two regressions include a quadratic trend. The first
two columns use vacancy measures from the JOLT, and the last two columns use data on online advertising from the Conference Board.
Table A2: Effects of EEB on UE and UN transition probabilities in the 2008-2009 recession
UE probability
Job loser
Non job loser
UN probability
-0.12
(0.02)
-0.16
(0.02)
-0.22
(0.02)
-0.05
(0.02)
Note: The two rows report the coefficients on the interaction term between a post-2008 dummy and, respectively, a job loser and non-job loser dummy. In the first column, the
dependent variable is the UE transition probability, and in the second column, the dependent variable is the UN transition probability.
Table A3: Coefficients on post-2007 last industry of employment dummy
Industry
Goods production
Professional services
Sales and other services
No industry (new entrant)
Coefficients
-0.11
(0.02)
-.13
(0.02)
-0.12
(0.02)
-0.15
(0.04)
Note: Except for the industry dummy, the regression is identical to Table 3. Other coefficients are little changed and are available
upon request.
41
Table A4: Coefficients on post-2007 state of residence dummy
State of
State of
Coefficients
Coefficients
residence
residence
FL
-0.41
KS
-0.16
SC
-0.37
CA
-0.15
NE
-0.30
IL
-0.15
MN
-0.29
HI
-0.15
MO
-0.28
IA
-0.15
UT
-0.28
KY
-0.15
AL
-0.27
TN
-0.12
NH
-0.27
VA
-0.11
IN
-0.26
RI
-0.11
OR
-0.25
WY
-0.09
AR
-0.25
SD
-0.08
OH
-0.25
PA
-0.08
MI
-0.24
MS
-0.07
NV
-0.22
VT
-0.07
GA
-0.22
CT
-0.07
MA
-0.21
ND
-0.01
OK
-0.21
NY
-0.01
AZ
-0.20
ID
0.00
DE
-0.20
TX
0.00
ME
-0.19
NJ
0.01
MD
-0.18
DC
0.02
NC
-0.16
LA
0.06
CO
-0.16
AK
0.06
WI
-0.16
WV
0.06
WA
-0.16
NM
0.14
MT
-0.16
Note: Except for the state of residence dummy, the regression is
identical to Table 3. Other coefficients are little changed and are
available upon request.
42
Table A5: List of geographic areas
AK
Other, AK
FL
LA
AL
New Orleans, LA
Other, WA
Miami, FL
Other, LA
Orlando, FL
Other, AL
Other, FL
AR
Phoenix, AZ
CA
HI
Other, HI
Other, WI
Providence, RI
MD
Other, MD
IN/IL/KS/MO
San Francisco, CA
Chicago, IL
San Jose, CA
Kansas City, MO
Denver, CO
St. Louis, MO
CT
KY/OH
MN
San Antonio, TX
Other, UT
UT
Las Vegas, NV
Salt Lake City, UT
Other, MS
Oklahoma City, OK
Richmond, VA
Virginia Beach, VA
MT
Other, MT
OR
Other, OR
NC/SC
Cleveland, OH
Other, NC/SC
Portland, OR
PA/NJ/NY
Buffalo, NY
ND
New York, NY
NE
Philadelphia, PA
Other, ND
Other, KY/OH
Other, VA
Other, OK
MS
Columbus, OH
VA
OK
Other, CT
DE
Other, TX
NM
Other, MN
Charlotte, NC
Louisville, KY
Houston, TX
Minneapolis-St. Paul, MN Other, NV
Cincinnati, OH
DC
Dallas, TX
NV
Hartford, CT
Washington, DC
TX
Other, NM
Other, MI
Other, IN/IL/KS/MO
Other, CO
Austin, TX
NH
MI
Indianapolis, IN
CO
WY
Other, WV
Other, NH
Detroit, MI
Other, ID
Other, TD
Other, WY
Other, ME
ID
TD
WV
ME
IA
Riverside, CA
San Diego, CA
Nashville, TN
Honolulu, HI
Other, IA
Sacramento, CA
Milwaukee, WI
Baltimore, MD
Los Angeles, CA
Other, CA
Memphis, TN
MA/RI
Atlanta, GA
Other, GA
Tucson, AZ
TN
WI
Other, MA/RI
GA
AZ
Other, SD
Boston, MA
Tampa, FL
Other, AR
Other, AZ
SD
Seattle-Tacoma, WA
Birmingham, AL
Other, DE
WA
Jacksonville, FL
Other, PA/NJ/NY
Other, NE
Pittsburgh, PA
Rochester, NY
43
VT
Other, VT
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