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Long-Term Unemployment and the Great Recession: Evidence from UK Stocks and Flows


Abstract and Figures

Long-term unemployment more than doubled during the United Kingdom's Great Recession. Only a small fraction of this persistent increase can be accounted for by the changing composition of unemployment across personal and work history characteristics. Through extending a well-known stocks-flows decomposition of labour market fluctuations, the cyclical behaviour of participation flows can account for over two-thirds of the high level of long-term unemployment following the financial crisis, especially the procyclical flow from unemployment to inactivity. The pattern of these flows and their changing composition suggest a general shift in the labour force attachment of the unemployed during the downturn.
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Carl Singleton*
Long-term unemployment more than doubled during the United Kingdom’s Great
Recession. Only a small fraction of this persistent increase can be accounted for
by the changing composition of unemployment across personal and work history
characteristics. Through extending a well-known stocks-flows decomposition of
labour market fluctuations, the cyclical behaviour of participation flows can
account for over two-thirds of the high level of long-term unemployment following
the financial crisis, especially the procyclical flow from unemployment to inactiv-
ity. The pattern of these flows and their changing composition suggest a general
shift in the labour force attachment of the unemployed during the downturn.
The main aim of this article was to describe how the persistent rise in long-
term unemployment (LTU) during the United Kingdom’s Great Recession
came about (Figure 1).
This countercyclical rise in average duration, which
typically persists even after unemployment has begun to fall rapidly, has long
been of interest to those studying European labour markets.
Renewed inter-
national interest has been driven by the significant and less usual rise in US
unemployment durations since the 20082009 downturn, where LTU rose to
its highest post-war level, and persisted even after short-term unemployment
had largely subsided.
Using the Labour Force Survey (LFS), I first discuss
how much of the recent UK experience can be accounted for by changes to
the composition of the unemployment pool, i.e. by the prevalence of personal
*University of Edinburgh
Throughout this article, and as most commonly defined in the United Kingdom, this
refers to those unemployed and looking for work for at least 12 months.
See for a comprehensive review Machin and Manning (1999).
Examples for the US case include: Elsby et al. (2011), Kroft et al. (2013), Krueger et al.
(2014) and Kroft et al. (2016). A discussion of the features of LTU in several European
countries during the Great Recession is provided by a collection of essays in Bentolila and
Jansen (2016). Through the case of Spain, Bentolila et al. (2017) have assessed the possible
role of institutional factors in accounting for the unprecedented rise in LTU in Southern
European countries.
Scottish Journal of Political Economy, DOI: 10.1111/sjpe.12139, Vol. 65, No. 2, May 2018
©2017 Scottish Economic Society.
and work history characteristics among the unemployed. I then identify which
of the flows between employment, inactivity and unemployment durations can
account for LTU’s rise and persistence.
I find that LTU’s rise, from 2007 to its prolonged peak in 20102013, can-
not be accounted for in any large part by changes in the prevalence of observ-
able characteristics among those looking for work: including the industry and
occupation of previous employment, the reasons for leaving a job, and
whether an individual was most recently otherwise employed or out of the
labour force. This mirrors similar results from Kroft et al. (2016) for the Uni-
ted States over the same period.
A notable recent literature has added to earlier work by Clark and Sum-
mers (1979) highlighting the cyclical importance of fluidity at the participation
margin. Most prominently, Elsby et al. (2015) (henceforth referred to as EHS)
have demonstrated that a third of historical US unemployment rate variation
can be accounted for by the cumulative influence of monthly changes in the
transition hazard rates between unemployment and inactivity. Applications of
their methodology to flows estimates obtained from the LFS have demon-
strated that this result generalises to the United Kingdom, for a period includ-
ing the Great Recession (Borowczyk-Martins and Lal
e, 2016; Razzu and
Singleton, 2016). Specifically for long-term unemployment changes, Krueger
et al. (2014) and Kroft et al. (2016) have identified the importance of cyclical
patterns in participation flows using calibrated matching models. Both find
that allowing for duration dependence in exit rates to employment, as well as
Figure 1. UK unemployment rate and LTU, 19972015.
Source: Labour Market Statistics, Office for National Statistics, ages 1664, accessed
November 2015; shaded area denotes UK officially defined recession, 2008q22009q2.
[Colour figure can be viewed at]
Scottish Journal of Political Economy
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transitions between inactivity and unemployment, is crucial in matching the
rise and level of US LTU post 2008. Instead of similarly calibrating these
models to the UK labour market, I explore thoroughly the underlying flows
data and how they have determined patterns of LTU over the past two dec-
I do this by extending EHS’s stocks-flows decomposition from three to
five labour market states: employment, short, medium- and long-term unem-
ployment, and inactivity.
It is not a priori obvious that results for the United Kingdom during the
Great Recession will be similar to those found in the aforementioned studies
of US LTU. There are notable differences in how OECD countries experi-
enced the Great Recession. The reduction in UK GDP, accounting for pre-
recession trends, was roughly twice as great as in the United States by the end
of 2011, but the United States nonetheless experienced a greater rise in unem-
ployment (Hoffmann and Lemieux, 2016). The United Kingdom’s experience
was not only distinct from the United States but also something of an outlier
both across countries and compared with past UK recessions. Thus, in the
context of what has become the ‘The UK Productivity Puzzle’ (Barnett et al.,
2014; Bryson and Forth, 2015), it would be striking if the determinants of the
recent cyclical and persistent level of LTU in the United States and United
Kingdom were similar.
To preview the results, aggregate transition rates from unemployment exhi-
bit substantial negative duration dependence.
Flows at the margin between
inactivity and unemployment are important in explaining LTU’s rise since
2008, and account for as much as half of its variation since 1998. The relative
importance of the procyclical unemployment to inactivity flow is especially
robust to the alternative methods used here to estimate transition rates. The
pattern of how unemployment exit rates account for LTU in the Great Reces-
sion is suggestive of shifts in the composition of the unemployment pool, with
regard individuals’ attachment to the labour force. These exit rates signifi-
cantly depend on what state individuals entered unemployment from. But
more generally, like the stock, the recessionary decrease in transitions from
unemployment to inactivity cannot be described by the greater prevalence of
characteristics in the unemployment pool that one would expect to be corre-
lated with attachment.
The remainder of the article is arranged as follows. Section II details a
counterfactual exercise on whether or not the changing composition of the
unemployment pool accounts for the Great Recession’s rise in LTU. Sec-
tion III outlines the methodology used to estimate transition rates, discusses
their time series, and briefly gives some detail of the extended EHS stocks-
As such, this article relates to several others that have used the LFS to characterise the
fluidity of the UK labour market, detailing its advantages and limitations in this regard:
Gomes (2012), Sutton (2013) and Carrillo-Tudela et al. (2016).
I use the term duration dependence here more loosely than in the specialist literature,
which applies this only to the exit probability of individuals. Duration dependence in the
United Kingdom has been identified and studied at length previously by among others van
den Berg and van Ours (1994).
Scottish Journal of Political Economy
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flows decomposition method. Section IV discusses results using this decompo-
sition, and gives additional focus to the unemployment to inactivity transition
rate. Finally, Section V summarises the results and offers some further discus-
sion and implications for future research.
Before studying the flows data, I assess the possibility that the changing com-
position of unemployment could account for LTU over the cycle. This could
help to nuance any later flows-based conclusions. For instance, if the rise in
LTU was accounted for by a collapse in outflows from unemployment at long
durations to inactivity, this could be wrongly attributed to a collapse in indi-
vidual worker hazard rates, when in truth the composition of the long-term
unemployed may have shifted towards those who are more attached to the
labour market, such as those who were made redundant instead of having
resigned from their last job.
I use the Annual Population Survey (ONS, 2004, 2007, 2010, 2013), restrict-
ing attention to the historical UK definition of working-age.
Short-, medium-
and long-term unemployment are defined by those who have been unemployed
for up to 3, between 3 and 12, and over 12 months, denoted respectively by S,
M, and L.
I consider the change in unemployment over three periods: first
20072010, i.e. before the Great Recession to the peak rise in LTU, second
20072013, to assess the possibility that composition might have had a greater
role during the persistent phase of unemployment, and third 20042007, to serve
as a baseline. I define types of the unemployed over sex, age groups, region of
residence, industry and occupation of the last job, reason for leaving previous
employment, type of employment sought, and the time since leaving the last job
relative to the length of the current unemployment spell. These types address
individuals who have never worked nor had paid employment. Relative to 2004
and 2007, I construct a counterfactual unemployment pool, holding constant
the distribution over {S,M,L}for each type of the unemployed, but applying
the aggregate level of unemployment and its distribution over the different types
for 2007, 2010 and 2013. That is, the counterfactual for 2010 only differs from
the actual observed unemployment pool in one respect: types are apportioned
to {S,M,L}according to their 2007 shares thereof.
Male 1664, female 1659. This is also consistent with the age groups for which it is
possible to extract a consistent series of gross flows from published Two-Quarter Longitudi-
nal LFS (ONS, 19972014) datasets.
Only these three duration types are considered to be consistent throughout with the set
of labour market transition rates that I can reliably estimate from longitudinal survey data
later. These particular duration band choices also have the nice result of roughly splitting the
unemployment pool evenly, on average, over the period studied, 19972014.
See Online Appendix A for a more detailed description of the data, variables and
methodology used in this analysis, as well as full counterfactual results for the baseline 2004
2007 case and long-term shares of unemployment across the various personal characteristics
accounted for.
Scottish Journal of Political Economy
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Table 1 demonstrates the results of this analysis between 2007 and 2010/13
(see also Online Appendix Figure A2), showing actual and counterfactual
levels of LTU, and changes in the share of those unemployed over 12 months.
Each row addresses a single type characteristic in the composition of unem-
ployment, including its interaction with both sex and age group types. The
final row interacts more characteristics.
The changing composition of the unemployed was not significant in
accounting for the rise in the long-term share of unemployment from around
a quarter to a third since 2008.
For example, although LTU’s share of unem-
ployment increased 12 percentage points between 2007 and 2013, the change
in composition along the reason for leaving a previous job, sex and age
groups accounts for only one point. Similarly, other characteristics only
account for a small fraction of the increase. In terms of the level of LTU, by
2013 the counterfactuals leave an increase of over 250,000 unaccounted for.
Not only is this an observed fact of the initial stage of the downturn to 2010,
where we might expect composition to have had a more minor role, but is
also the case as LTU persisted through to 2013 and the beginning of the
labour market recovery. This is in spite of large pre-recession differences in
the likelihood of different types finding themselves in LTU (Online
Appendix Table A2). This conforms with the findings of Kroft et al. (2016)
for the United States over the same period. In addition to the characteristics
accounted for by Kroft et al., the length of time since an individual left their
last job, relative to the duration of their current unemployment spell, cannot
Table 1
Counterfactual levels and increases in the share of the unemployed who are long-term, 2007
Number over 12 months
(000s) Increase in share
2007 2010 2013 20072010 20072013
Actual 370 740 850 0.08 0.12
Counterfactuals: composition change only
1. Region 590 580 0.01 0.01
2. Prev. job industry 570 0.01
3. Prev. job occupation 570 0.01
4.Reason left prev. job 580 580 0.01 0.01
5. Type of job sought 600 580 0.02 0.01
6. When left last job 580 570 0.01 0.01
Characteristics 1. & 46. 560 590 0.00 0.01
Notes: Counterfactuals give levels and increases in shares for 2010 and 2013 holding constant the distribu-
tion over {S,M,L}for each stated type of heterogeneity, interacted with sex and age groups, from 2007,
and applying the overall distribution of types in the unemployment pool from 2010 or 2013. Source:
Author calculations using UK Annual Population Survey, ages 1664/59, JanuaryDecember 2007, 2010
and 2013.
See Online Appendix A for confirmation that this is not an anomalous result for this
time period. LTU during more normal times, 20042007, is similarly uninfluenced by the
composition of those looking for work.
Scottish Journal of Political Economy
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explain a perceptible part of the rise in the LTU share. In other words,
changes in the extent to which the unemployed entered form employment or
inactivity are not significant.
However, this is not to say that the participa-
tion margin is not important, only that changing the composition along where
individuals enter unemployment from cannot alone explain recessionary LTU.
A concern of this analysis, and how to interpret the results, is that upon
conditioning on some observable characteristics, those who are long-term
unemployed will become increasingly characterised by something unobserv-
able which tends towards longer spells of unemployment. And given that
average durations rise in recessions, dynamic selection of the unemployment
pool in this regard will also be cyclical. In spite of this, it remains a surpris-
ing result that so little of the change in the distribution of unemployment
across {S,M,L} can be accounted for by observables. Ahn and Hamilton
(2016) have provided a methodology to potentially address the role of unob-
served heterogeneity. They conclude that the employment history characteris-
tics of the unemployed are likely to explain more of the rise in average
duration than coarser observable information. I have found that this is not
the case in so far as employment history can be observed in the LFS. EHS
have shown that during recessions, the US unemployment pool does shift
towards consisting of those who are more attached to the labour force, such
as job losers rather than labour force entrants, and that this is at least a rel-
evant factor in explaining cyclical patterns in exit rates, especially the flow
to inactivity. A cautious look at the distribution of personal characteristics
across unemployment durations over time, combined with the results of the
counterfactual exercise, suggest that recessionary LTU in the United King-
dom is not so discriminating.
So far I have shown that changes in the composition of unemployment alone
cannot account for recent changes in UK LTU. By identifying the flows and
specific transition rates between labour market states which do account for
these changes, I can develop a more complete picture of LTU in the Great
I derive estimates of quarterly gross flows between five labour market states
from the Two Quarter Longitudinal LFS datasets, between the fourth quar-
ters of 1997 and 2014.
The five states are defined as follows: employment,
inactivity, short-, medium- and long-term unemployment, denoted by X2{E,
N,S,M,L}. The LFS has a five wave rotational structure, such that in any
The duration of unemployment in the LFS is derived from the minimum response to
when an individual left their last job and the stated length of time looking for work. Where
these differ it is implied that an individual has been economically inactive since leaving their
last job. In practice this also includes new entrants to the working-age labour force at age
16, who directly become unemployed, though this should be accounted for by age group and
never having had paid employment characteristics.
These are subsequently seasonally adjusted. See Online Appendix B for adjustment
Scottish Journal of Political Economy
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quarter the labour market status of roughly 80% of respondents can be com-
pared with their record from the previous quarter. I use population weights
provided by the ONS which address non-response bias in the longitudinal
sample. Simple transition rates can be estimated, for example from employ-
ment to short-term unemployment, as ~
Et1, where
EStis the gross
number of transitions, and where
EXtgives an estimate of the stock
in employment.
Employment status classification errors
A major concern when estimating flows by unemployment duration is that the
data are potentially rife with classification errors. If labour market status was
recorded accurately and conclusively, from one quarter to the next, then zero
gross flows from employment to LTU should be observed, or from long- to
medium-term unemployment for example. These measured flows in labour
force surveys are typically significantly different from zero.
This could be
explained by the incorrect recollection on the part of respondents regarding
the length of time they have been employed or unemployed, or that their own
interpretation of their past state is different from the International Labour
Organization (ILO) definition assigned to their previous responses. My own
reading of the data is that the first explanation is unlikely, as individuals who
remain in the same state provide very few duration inconsistencies. There is
also no concentration of inconsistent transitions with unemployment dura-
tions of 45 months. Furthermore, flows between employment and unemploy-
ment have relatively few inconsistencies compared with those at the
participation margin.
For robustness, I address this empirical phenomenon and consistency con-
cerns in reported transitions in three ways. Actual stocks are obtained from
national labour market statistics and are given by the state vector
t, with lower case denoting population rates, and where the state
space is reduced by noting that the population rates across all five states sum
to one. First, I measure transition rates as they are given directly by the data,
and make only the standard adjustment that they should support the observed
quarterly change in z
, abstracting from entry to and exit from the working-age
In what follows this is referred to as the ‘na
ıve’ approach, or
specification (I). Second, using the measured rates, I compute the aggregate
state-transition matrices for every quarter which are not only consistent with
the observed actual changes in stocks but also conform to restrictions that
These gross flows within the US Current Population Survey (CPS), and their cyclical
behaviour, are discussed in Elsby et al. (2011). Also, the matching model calibrated in Kroft
et al. (2016) recognises this and allows for empirically observed flows into unemployment at
longer durations. See Clarke and Tate (1996) for a thorough analysis of inconsistencies
between recorded states and subsequent duration responses in early panels of the LFS.
See Razzu and Singleton (2016) for a version of the EHS decomposition which does not
abstract from working-age entry and exit: the different stocks individuals enter to or exit
from can potentially affect the cyclical behaviour of those stocks, though in practice this is
Scottish Journal of Political Economy
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some of the quarterly transition probabilities ought to have been zero:
=0. In what follows this is referred to
as the ‘restricted’ approach, or specification (II) . Third, based on an assump-
tion that the ILO employment status is most likely to have been recorded accu-
rately, some observed transitions are reassigned before computing alternative
estimates of the gross flows and transition rates. The latter are then adjusted as
per (II) and subsequently referred to as ‘cleaned’, or specification (III).
A further concerning source of potential classification errors is not
addressed by (III). Using re-interview surveys of the CPS, Abowd and Zellner
(1985) found that flows between unemployment and inactivity are the most
likely source of these errors in individuals’ longitudinal records. This was also
corroborated by Clarke and Tate (1996) within the LFS, who further noted
that inconsistencies are greater for groups with characteristics which are likely
to be correlated with lower labour market attachment. This latter point is of
particular concern when conducting a cyclical analysis of flows, as the compo-
sition of the inactive and unemployed pools can be expected to change over
the economic cycle, thus leading to correlation between changes in these clas-
sification errors and labour market stock measures, potentially biasing any
results substantially. EHS suggested a robustness check to demonstrate the
direction and potential magnitude of this bias. They referred to this as ‘de-
NUN-ification’. Monthly transitions between unemployment and inactivity are
ignored in what would otherwise have been continuous spells in one state or
the other over 4 months. I carry out a similar recoding procedure using up to
four consecutive quarters of observations for an individual, but only where it
is unambiguous that transitions could not be genuine. For example, an indi-
vidual who is observed as NNSN is not re-assigned to continuous inactivity,
whereas individual NNLN is. This procedure is carried out subsequent and in
addition to the recoding exercise described for (III), and transition rates are
again adjusted as per (II). This is referred to in what follows as the ‘deNUN
approach, or specification (IV).
In each specification the adjusted rates are
then used to populate a state-transition matrix P
. For completeness, a set of
continuous time equivalent hazard rates, adjusted to account for potential
time aggregation bias, are also estimated using a standard procedure.
This is
referred to in what follows as specification (V).
Transition rate time series and interpretation
Figure 2 compares the estimated exit rate series from LTU across specifica-
tions. The restrictions imposed on the non-na
ıve specifications imply a signifi-
cant decrease in the level of exits, to off-set the lack of entries other than
from medium-term unemployment. Despite this, the qualitative pattern since
See Online Appendix B for more details of these adjustments, or Borowczyk-Martins
and Lal
e (2016) and EHS for similar applications.
Online Appendix Tables B1B3 give details on the extent and effect of the recoding in
(III) and (IV) on the measured numbers of gross flows.
See for example Shimer (2012) and also some discussion in Online Appendix B.
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the Great Recession remains similar. Specifications (III) and (IV) do not sub-
stantially alter the estimated series relative to (II), especially with regard to
their cyclical pattern. The level adjustments in estimated transition rates of
the ‘restricted’ specifications are somewhat extreme. It is impossible to identify
whether the adjustment is mainly driven by incorrect duration records, or an
individual having a different interpretation of their previous labour market
status as compared with the statistical agency. Adjustments of this kind rely
on arbitrary assumptions and only provide a sense of the direction or size of
any classification error bias in results. As such, despite some impossible
observed transitions, in what follows the na
ıvely estimated transition rates are
mainly studied.
Figure 3 compares the estimated exit rates from specification (I) across
unemployment durations, where Umore generally denotes unemployment.
For p
, exits to employment decline steeply across all durations in 2008,
but although there is some recovery for long-term rates, this is less appar-
ent at shorter durations, where the decline appears to have been more per-
sistent. The levels of these aggregated transition rates suggest negative
duration dependence. Further, this appears to reduce during the downturn.
This is consistent with the predictions of screening models, where during a
downturn the length of an unemployment spell becomes a less informative
signal of a worker’s unobservable productivity (Kroft et al., 2013). The
estimated levels of transition rates for medium and long-term unemployed
to inactivity are close, and their patterns since 2008 are similar. These rates
declined in 2008, but remained persistently low thereafter, and began to
recover from 2013 onwards. However, the exit rate to inactivity for the
short-term unemployed, being over twice as high as at longer durations
pre-recession, saw a sharp decrease in 2011, before recovering to its pre-
recession level by 2014.
Interpretation of these exit rates is not straightforward. Although the com-
position of the unemployment pool does not generally explain the rise in
(a) pLE (b) pLN
Figure 2. Estimated long-term unemployment exit rates, 19982014: comparison of
Source: Author calculations using Two Quarter Labour Force Survey, ages 1664/59,
1997q22015q2, after seasonal adjustment, and with a centred moving average to smooth.
[Colour figure can be viewed at]
Scottish Journal of Political Economy
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LTU, this conclusion cannot simply be extended to these exit rates. Besides
personal characteristics and employment history changes there is a more obvi-
ous composition challenge. Even if the unemployed were identical other than
their duration, given the theoretical negative duration dependence of exits,
and how {S,M,L} are defined, the average rise in durations during a recession
would contribute to some of the observed fall in measured transition rates
within the grouped duration states.
Decomposition method
I can also derive statistics to assess the relative importance of each transition
rate in explaining the change in the observed labour market stocks. The
stocks-flows decomposition used here is directly extended to five states from
EHS. This method has the advantage over others in so far as it does not rely
on an approximation of the labour market to its steady state.
Whilst this
simplification might be valid for the United States, it is decreasingly so for less
fluid labour markets such as the United Kingdom, or for LTU, which could
be persistently away from the steady state stocks implied by current estimated
transition rates. Relative to other methods used to account for the flows based
rise in LTU, such as by Kroft et al. (2016), this decomposition approach has
one clear advantage. It requires no structure, being a pure mathematical
accounting exercise; there is no need to define a matching framework or tech-
nology, with some pre-determined structure for any estimated duration depen-
dence in transition rates. There is also a clear disadvantage. The lack of
structure limits the possible extent of any counterfactual analysis. It is a fur-
ther disadvantage that due to small cell sizes in the data, I restrict attention to
three broad duration states of unemployment. Thus, I can only account for
the partial role of changes in aggregate duration dependence, not being able
(a) pUE (b) pUN
Figure 3. Estimated unemployment exit rates by duration using specification (I), 19982014.
Source: Author calculations using Two Quarter Labour Force Survey, ages 1664/59,
1997q22015q2, after seasonal adjustment, and with a centred moving average to smooth the
series. [Colour figure can be viewed at]
See for such examples Solon et al. (2009); Shimer (2012); Gomes (2012). For an alterna-
tive non-steady state decomposition, using flows estimates from the British Household
Panel Survey, see Smith (2011).
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to account for any changes which occur within these three unemployment
Given the estimated transition rates populating P
for each specification,
the reduced form of the Markov process governing a five state labour market
is given by
pEM pNM 1P
pEL pNL pSL pNL 1P
I exclude p
, as otherwise the variation in these unemployment
survival rates could largely obscure the role of entries and exits at shorter
durations in the evolution of LTU. However, p
then still has a somewhat
strange interpretation and cannot be trivially excluded. Although the process
is memoryless, its effect on long-term unemployment is similar to a decline in
exit rates, in so far as it then captures a rise in average duration within M,
and the mass of workers here moving closer to L, i.e. then experiencing a p
transition. The steady-state of (1) is given by
The change in the labour market state can be re-written as a weighted sum of
its lagged value and the change in the present steady state;
Iterating (3) back to some initial value of the labour market state, z
, and
using a Taylor expansion around each transition rate contained in Π
, with
easily obtained analytical derivatives, the change in labour market state can
approximately be written as
where c
is a vector containing the independent contribution of past and pre-
sent changes in transition rate p
to the current change in each labour market
state, and cz0;tis the contribution of some initial state value.
In practice I
also distribute the contribution from Dp
, noting that it ought to be in real-
ity a function of changes in gross flows from between 3 to 9 months
To improve accuracy additional polynomial terms are included in the expansion though
cross-derivatives are set to zero.
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unemployed to states {E,N,S}; i.e. for contributions to Dztfrom {Dp
I use
cMS þð1aME aMN ÞcMM
where values for each acan be estimated using gross flows data from the
As well as being able to study the outcome of this decomposition over
specific time periods, a more general measure of each transition rate’s impor-
tance in determining the change in the stocks can be derived with a variance
decomposition. For example, the share of the variance of changes in long-
term unemployment explained by its covariance with {c
(i.e. the fourth
row element of the vector c
; the contribution of past and present changes
in p
) is given by
ES ¼covðDlt;fcES;tg4Þ
Given (4), the sum of the b
’s for each transition rate contained in Π
, in addi-
tion to the variance shares accounted for by the contribution of the initial
labour market state and approximation errors, will necessarily sum to one.
Using (46) it is straightforward to similarly derive the contributions of transi-
tion rates to changes in other labour market variables, such as the overall
unemployment population share and its rate of the economically active, by
adding rows and linearising. A continuous time equivalent decomposition for
use with the estimated hazard rates of specification (V) is a trivial extension of
the above.
I implement the EHS style decomposition described above for quarterly
changes between the second quarter of 1998 and the fourth of 2014, with the
initial value of the labour market state being the first quarter of 1998.
Variance decomposition
Table 2 gives the complete variance decomposition results for quarterly
changes in LTU’s population share, and other labour market stocks, for the
ıve and restricted specifications of estimated transition rates: i.e. values for
the b
described above. The Online Appendix B contains equivalent results
for specifications (IIIV), which are viewed as robustness checks. The final
rows sum unemployment flow contributions across all durations; i.e. Dp
gives the contribution from quarterly changes in the aggregate transition rate
For example, the share attributed to the exit rate p
is estimated as the centred median
over nine quarters of ~
MÞt. I take the median over a range
of tbecause the series for ~
aME;tcontains outliers which could distort the decomposition, due
to the denominator occasionally being very small. I experimented with several ways to make
this approximation, but the variance decomposition results were not sensitive to these.
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from employment to all unemployment durations. Initially focusing on the
ıve results, Dp
and Dp
together explain a third of the variation of
changes in LTU. When combined with changes in transition rates between
inactivity and other unemployment durations, i.e. Dp
and Dp
, this
increases to almost a half. This is especially accounted for by the pro-cyclical
. These same flows changes account for less than a third of total unem-
ployment’s fluctuations. Contrasting the cyclical importance of Dp
, the former is approximately half as important than the latter for total
unemployment. This relative difference is however reversed for LTU. Thus,
the participation margin appears relatively more important in accounting for
the cyclical behaviour of long-term unemployment than the total level.
Table 2
Stocks-flows decomposition: ‘na
ıve’ and ‘restricted’ transition rates, 1998q2-2014q4
rate DlDeDuDuz
rate Dl
0.25 0.26 0.03 0.25 0.34 0.34 0.08
0.06 0.08 0.08 0.01
0.00 0.02 0.02 0.06
0.16 0.00 0.00 0.00 0.16 0.01 0.01 0.01
0.07 0.10 0.10 0.02 0.06 0.08 0.08 0.00
0.00 0.00 0.00 0.01 0.03 0.05 0.05 0.07
0.00 0.00 0.00 0.04
0.00 0.08 0.07 0.01 0.01 0.06 0.05 0.00
0.12 0.14 0.14 0.14 0.14 0.19 0.20 0.25
0.00 0.00 0.00 0.01 0.00 0.00 0.00 0.09
0.00 0.05 0.04 0.11 0.01 0.07 0.07 0.15
0.07 0.08 0.09 0.10 0.10 0.14 0.14 0.15
0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.01
0.00 0.00 0.00 0.04
0.00 0.04 0.04 0.21 0.01 0.09 0.08 0.12
0.30 0.01 0.03 0.00 0.32 0.00 0.03 0.00
0.00 0.04 0.04 0.01 0.01 0.08 0.07 0.01
0.02 0.07 0.06 0.02
0.01 0.03 0.02 0.13
Initial val. 0.01 0.01 0.01 0.03 0.01 0.02 0.02 0.05
Approx. err. 0.02 0.01 0.01 0.01 0.08 0.12 0.12 0.00
0.27 0.36 0.36 0.10 0.25 0.34 0.34 0.08
0.26 0.32 0.32 0.26 0.30 0.41 0.41 0.40
0.00 0.17 0.15 0.33 0.02 0.22 0.20 0.28
0.03 0.14 0.12 0.16 0.01 0.08 0.07 0.01
0.00 0.01 0.01 0.10 0.03 0.05 0.05 0.15
ıve’ transition probabilities, i.e. with no zero value restrictions when adjusting
/t(see Online
Appendix B).
Transition probabilities adjusted according to restrictions p
Interpretation: Share of variance in the quarterly change in the employ-
ment rate accounted for by past and present quarterly changes in p
(or hazard rate equivalent), i.e.
EU ¼covðDet;fcEU;tg1Þ
Source:Author calculations using Two Quarter Longitudinal Labour Force Survey & Labour Market
Statistics, ages 1664/59.
Scottish Journal of Political Economy
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Comparing results using the estimated restricted transition rates, in terms
of accounting for the unemployment rate, the ‘outs’ become more dominant,
explaining 60% of the variation in the stock. This is driven by the restriction
that all gross flows must enter short-term unemployment. These restrictions
do not affect the combined importance of the participation margin, but give
more weight to Dp
. Results for the change in LTU with the restricted set of
possible transitions do differ more substantially from the na
ıve. Instead of
explaining almost a half of the variance, transitions between inactivity and
unemployment account for less than a third. This difference is mostly
explained by a greater relative importance of Dp
. The importance of Dp
though remains unchanged.
The additional reassignment of some gross flows data to assess the role of
possible classification errors have anticipated effects on the results (Online
Appendix Table B4). With regard to the unemployment rate, the effect of
using the ‘cleaned’ flows series is to marginally reduce the importance of the
participation margin. This is further reduced through ‘de-NUN-ification’.
However, through all specifications the pro-cyclical Dp
(and Dp
) remains
a major factor, explaining a third of the variance in LTU’s changes in the past
16 years to 2015.
As a further robustness check, I compare results using na
ıve transition rates
with those using their time aggregation bias adjusted hazard rate equivalents
(Online Appendix Table B5). With regard to the unemployment rate, the
share of the variance attributed to changes in the exit rates rises relative to
the non-adjusted baseline, from a half to two-thirds, in line with the expected
direction of the bias. But addressing this does not alter the principal qualita-
tive result: the participation margin is crucial in accounting for LTU varia-
Focusing on the great recession
Figure 4 plots the cumulative rise in the working-age LTU population share
from the final quarter of 2007, and the estimated contributions from past and
present changes in the underlying na
ıve transition rates, using equations (4)
and (5). By the beginning of 2012 the population share had reached a peak of
2.5%, more than doubling with an increase of 1.4 percentage points. The
majority of the initial rise in 2008 is explained by the pro-cyclical Dp
. How-
ever, this contribution disappears by 2010, and by 2012 changes in the exit
rates to employment alone would have implied a lower long-term level than
pre-recession, despite the actual level being at its peak. Entries to unemploy-
ment from employment contribute a small amount, but this is never substan-
tial. Conversely, by 2010 entries from inactivity can explain almost half a
percentage point of the increase, though this subsequently declines to pre-
recession levels even as LTU persists. To account for the majority of the per-
sistent and prolonged rise in LTU we must focus on the decline in exit rates
to inactivity.
Scottish Journal of Political Economy
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These flows patterns, and their contributions to the stock of long-term
unemployed, would strongly suggest a compositional change in the unemploy-
ment pool. Intuitively, the initial fall in the exit rate to employment affected
the already unemployed going into the Great Recession. However, as the
downturn persisted, the composition of this pool shifted towards individuals
with higher job finding rates. Similarly, these displaced workers are likely to
have had a stronger attachment to the labour force, potentially accounting for
the procyclical exit rate to inactivity.
Duration dependence or participation flows?
The methodology used here introduces both the limited duration dependence
of unemployment exit rates and the role of participation flows in accounting
for LTU changes. I can assess the importance of each in turn during the
Great Recession. To simplify the problem, for the former I use the restricted
transition rate series. With these, which are consistent with actual changes in
unemployment, I project forwards the LTU population share as if there was
(a) pEU &pNU (b) pUE &pUN
(c) pEN,pNE &pUU
Figure 4. Decomposition of the cumulative change in long-term unemployment, 20082014:
contributions from individual transition rates.
Notes: Series indexed to zero in 2007q4. Interpretation is the cumulative increase in long-
term unemployment’s population share since 2007 accounted for by past and present changes
in transition rates. Flows contributions may not appear to exactly sum to the change in the
stock due to accumulated approximation errors. The initial state value contribution is
Source: Author calculations using Two Quarter Labour Force Survey & Labour Market
Statistics, ages 1664/59. Transition rates calculated using specification (I). [Colour figure can
be viewed at]
Scottish Journal of Political Economy
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in fact no duration dependence. That is, given some initial value for LTU, l
I can recursively update the stock as follows,
where xis the population rate corresponding to the stock X, and Σ
is the total exit rate from unemployment, including restarts. The initial value
is chosen as early as possible, 1998q4. Figure 5 compares the actual cumula-
tive rise in LTU, from 2008, with this ‘no duration dependence’ counterfac-
tual. Clearly the limited aggregate duration dependence studied here is not
significant in matching the counter-cyclical propagation of LTU, as the two
series are almost identical.
Using the full decomposition results with na
ıve transition rates, Figure 5
also demonstrates the implied rise in LTU assuming instead no contempora-
neous or past changes in transition rates between unemployment and inactiv-
ity: i.e. setting Dp
and Dp
equal to zero in all periods. This picture
simply reinforces results already discussed. Over two-thirds of recessionary
LTU is accounted for by changes in flows at the participation margin.
Composition and unemployment to inactivity flows
As previously studied for the stocks above, I can assess the role of composi-
tion along some observable characteristics in accounting for these flows
Figure 5. Cumulative long-term unemployment change and two counterfactuals: no
duration dependence and no changes in participation flows, 20082014.
Notes: Series indexed to zero in 2007q4. Interpretation is the cumulative increase in long-
term unemployment.
Source: Author calculations using Two Quarter Labour Force Survey & Labour Market
Statistics, ages 1664/59. [Colour figure can be viewed at]
Though as in Kroft et al. (2016); Krueger et al. (2014) it is highly significant in terms of
matching levels of LTU over the whole sample period.
Scottish Journal of Political Economy
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patterns. One distinction of interest is whether individuals entered unemploy-
ment from inactivity or employment, as this will correlate strongly with
labour force attachment. Although this could to some extent be observed
using the five successive waves of the LFS, it can be studied for a larger sam-
ple using responses to when an individual left their last job, and whether or
not the time since is strictly greater than the derived unemployment duration.
Due to sample sizes it would not be robust to disaggregate the long-term
unemployed gross flows series further. However, if Sand Mare combined, it
turns out that approximately over the sample period similar numbers in this
combined stock entered from employment and inactivity. The level of those
unemployed 012 months, for whom the time since they left their last job is
strictly greater than these grouped duration categories, is denoted by Sn, and
for those where this matches, by Se. For these two new states, as well as {E,
L,N}, I derive seasonally adjusted gross flows and estimated transition rate
series, which are adjusted to match observed changes in population rates, as
in the na
ıve specification described before.
Figure 6 shows estimated exit rate series for those unemployed for
<12 months, conditional on whether they entered from employment or inac-
tivity. Unsurprisingly, the exit rate to employment is significantly higher for
employment entrants, and vice versa, the exit rate to inactivity is higher for
inactivity entrants. Pre-recession, p
was over twice as high as p
. There-
fore, just through differences in these levels, if the unemployment pool had
shifted during the Great Recession towards entrants from employment, this
could account for some of the importance of changes in the p
rate relative
to p
Specifically with respect to LTU, and the contribution of changes in exit
rates, I can use the gross flows, conditional on point of entry to unemploy-
ment, to test the suspicion that my main results are related to composition
changes. Figure B1 repeats panel (b) of Figure 4, but overlays the share of
(a) pSxE (b) pSxN
Figure 6. Short-term unemployment exit rates conditional on where entered from, 1998
Source: Author calculations using Two Quarter Labour Force Survey, ages 1664/59,
1997q22015q2, after seasonal adjustment, and with a centred moving average to smooth.
Transition rates adjusted to be consistent with observed changes in stocks. [Colour figure can
be viewed at]
Scottish Journal of Political Economy
©2017 Scottish Economic Society
gross flows into LTU which were employed prior to becoming unemployed.
There is a notable increase in this share by 2009 and onwards, which coincides
with the decreasing and increasing contributions of Dp
and Dp
tively. However, we have already seen from the stocks counterfactual exercise
that the composition over this particular employment history characteristic
does not account for LTU and its persistent rise. The implication being that
whilst there is some correlation, much larger shifts in the unemployment pool
along these observables would be required to explain the overall rise of the
stock and the contributing pattern of the flows.
To see this more generally, I consider whether the changing composition of
the unemployment pool can explain the procyclical p
and p
rates. I derive counterfactual series of these rates that would have occurred
had the exit rates of types of unemployed, defined by all possible combina-
tions of some personal and work history characteristics, remained at pre-reces-
sion levels, but only the composition of unemployment changed. I estimate
these pre-recession exit rates for each type as the arithmetic mean of raw
unadjusted quarterly transition rates observed for 20062007. I use character-
istics and categories considered in the counterfactual exercise in Section II:
sex, age groups, type of employment sought, reason for leaving last job, and
when the individual left their last job relative to the reported length of the
unemployment spell. Figure 7 plots the actual estimated transition rate series
along with these counterfactuals. Although the actual unemployment to inac-
tivity transition rate declined steadily from around 0.2 to 0.15 between 2008
and 2011, the counterfactual series only shows a small decline in 2009 and
2010, but thereafter is approximately at pre-recession levels. The long-term to
inactivity rate demonstrates a similar pattern. The counterfactual also initially
matches the actual series, but cannot then match a greater decrease from 2011
(a) pUN (b) pLN
Figure 7. Counterfactual unemployment exit rates to inactivity: changing the composition
of unemployment only, 20062013.
Notes: Using raw transition rates, not seasonally adjusted but smoothed using centred four
quarter moving average. Personal characteristics accounted for in counterfactual: sex, age
groups, type of employment sought, reason left previous employment and when left last job
relative to length of unemployment spell. See Online Appendix A for details and derived
categories of these characteristics.
Source: Author calculations using Two Quarter Labour Force Survey, ages 1664/59,
1997q22015q2. [Colour figure can be viewed at]
Scottish Journal of Political Economy
©2017 Scottish Economic Society
onwards. Thus, the changing composition of the unemployment pool across
these particular characteristics, which are strongly correlated with labour force
attachment in terms of the levels of stocks and flow rates, cannot account for
the cyclical importance of unemployment to inactivity flows.
It is possible that changes in UK Government labour market policy during
the Great Recession are responsible for some of the results here. However, in
Online Appendix C I demonstrate that changes to the eligibility of welfare
payments, which could potentially affect flows between active and inactive
types, cannot account for the procyclical p
Some observed and derived facts discussed in this article regarding long-term
unemployment and the UK labour market during the Great Recession are as
(1) The changing composition of unemployment, along relevant observable
personal and employment history characteristics, cannot account for the
significant and persistent rise in LTU since 2008.
(2) Changes in transition rates between unemployment and inactivity can
explain as much as half of the variation in LTU between 1998 and 2014.
The flow from unemployment to inactivity’s relative importance is robust
to various different approaches used to estimate these transition rates.
(3) Despite (1), the pattern of how changes to flows contributed to the rise in
LTU remains consistent with an unemployment pool which shifted
towards workers more attached to the labour force.
(4) Unemployment exit rates exhibit both level and cyclical dependence on
whether workers entered from employment or inactivity.
(5) However, procyclical transition rates from unemployment to inactivity
are mostly not accounted for by changes to the observable composition
of the unemployment pool.
A significant challenge to the validity of these results remains the longitudi-
nal inconsistencies between states and durations in the LFS. However, it
seems a reasonable stance, as others have taken in the literature, to in the first
instance take these simply as given, and then for robustness study in what
direction any measurement errors would tend to bias results. One way to cor-
roborate them would be using administrative claimant flows data for those
receiving out of work payments from government. But at least so far as the
United Kingdom is concerned, the available data are typically incomplete,
and thus prone to sampling bias, and individuals claiming most major benefits
do not fall strictly within ILO employment status definitions.
This article reinforces that the participation margin is likely to be crucial in
accounting for the observed amplification of long-term unemployment during
recessions, as demonstrated in Krueger et al. (2014) and Kroft et al. (2016 for
the US experience of the Great Recession). An interesting extension of the
matching models in these aforementioned studies would be the inclusion of
Scottish Journal of Political Economy
©2017 Scottish Economic Society
exit rate dependence on employment history, namely depending on which
state workers entered unemployment from. As shown here, this could be sig-
nificant. The shift of the unemployment pool towards entrants from employ-
ment in recessions could potentially off-set a stronger procyclical response and
importance of negative duration dependence.
The results of the flows decomposition lead to a strong suspicion that a
shift in the composition of the unemployment pool, towards more attached
workers, could explain the United Kingdom’s rise in LTU. However, the
counterfactual analyses of the stock and contributing flows, along some
observed characteristics expected to be correlated with attachment, have not
shown this. This points towards the likelihood that levels of attachment are
challenging to identify from observables. Alvarez et al. (2016) have modelled
transitions between employment and non-employment and found that unob-
served heterogeneity across workers, affecting their degrees of negative dura-
tion dependence in exit likelihood, and the resulting dynamic selection of the
stocks over time, must play a significant role in accounting for the evolution
of the aggregate job finding rate from non-employment. Using a similar
model, it would be an interesting direction for future research to consider
whether this extends to unemployment to inactivity flows, and how in this
way we might account for LTU increases during recessions.
I am grateful for helpful comments from Mike Elsby, Giovanni Razzu, Daniel
Schaefer and Andy Snell, and for financial support by the Economic and
Social Research Council (UK) under Grant No. ES/J500136/1. The data used
are accessible from the UK Data Service, having been collected by the Office
for National Statistics (ONS). Neither the collectors of the data nor the Data
Service bear any responsibility for the analysis and discussion of results in this
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Additional Supporting Information may be found in the online version of this
Appendix S1. (a) Composition of the unemployment pool data and method-
(b) Labour market flows data & adjustments
(c) The potential role of labour market policy changes
Date of receipt of final manuscript: 4 June 2017
Scottish Journal of Political Economy
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... 18 I will sidestep the issue of time aggregation here but will address this in the next subsection. 19 SeeElsby et al. (2015),Razzu and Singleton (2016) and Lale and Borowczyk-Martins (2019) for the US using the CPS and Smith (2012),Gomes (2012),Elsby et al. (2016),Singleton (2017) and Lale and Borowczyk-Martins (2019) for the UK. ...
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