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FEDERAL RESERVE BANK OF SAN FRANCISCO
WORKING PAPER SERIES

Unemployment Dynamics in the OECD
Michael Elsby
University of Edinburgh and NBER
Bart Hobijn
FRB San Francisco
Aysegül Sahin
FRB New York

February 2011

Working Paper 2009-04
http://www.frbsf.org/publications/economics/papers/2009/wp09-04bk.pdf

The views in this paper are solely the responsibility of the authors and should not be
interpreted as reflecting the views of the Federal Reserve Bank of San Francisco or the
Board of Governors of the Federal Reserve System.

Unemployment Dynamics in the OECD
Michael W. L. Elsby

Bart Hobijn

Ayşegül Şahin

University of Edinburgh and NBER

FRB San Francisco

FRB New York

February 2011

Abstract
We provide a set of comparable estimates for the rates of in‡ow to and out‡ow from
unemployment using publicly available data for fourteen OECD economies. We then
devise a method to decompose changes in unemployment into contributions accounted
for by changes in in‡ow and out‡ow rates for cases where unemployment deviates from
its ‡ow steady state, as it does in many countries. Our decomposition reveals that
‡uctuations in both in‡ow and out‡ow rates contribute substantially to unemployment
variation within countries. For Anglo-Saxon economies we …nd approximately a 15:85
in‡ow/out‡ow split to unemployment variation, while for Continental European and
Nordic countries, we observe much closer to a 45:55 split. Using the estimated ‡ow
rates we compute gross worker ‡ows into and out of unemployment. In all economies
we observe that increases in in‡ows lead increases in unemployment, whereas out‡ows
lag a ramp up in unemployment.
Keywords: Unemployment, Worker ‡ows, Job Finding Rate, Separation Rate.
JEL-codes: E24, J6.
We would like to thank anonymous referees, Regis Barnichon, Shigeru Fujita, Wilbert van der Klaauw,
Emi Nakamura, Simon Potter, Gary Solon, participants at the New York/Philadelphia Workshop on Quantitative Macroeconomics 2008, Midwest Macroeconomics Conference 2009, Recent Developments in Macroeconomics Conference 2009, EEA Conference 2009, CREI/Kiel Conference on Macroeconomic Fluctuations
and the Labor Market 2009 for helpful comments, and Joseph Song for outstanding research assistance. The
views expressed in this paper are those of the authors and do not necessarily re‡ect those of the Federal Reserve Bank of New York, the Federal Reserve Bank of San Francisco or the Federal Reserve System. An Excel
spreadsheet with all the data, calculations, and results presented in this paper is available for download at
http://www.frbsf.org/economics/economists/bhobijn/UnemploymentDynamicsInTheOECD.xlsm. Thanks
to Jonas Staghøj for pointing out a coding error in a previous version of the spreadsheet. E-mail addresses
for correspondence: mike.elsby@ed.ac.uk; bart.hobijn@sf.frb.org; aysegul.sahin@ny.frb.org.

1

1

Introduction

Unemployment rates among developed economies have varied substantially both across time
and across countries over the last 40 years. This variation in unemployment may occur as a
result of variation in the rate at which workers ‡ow into the unemployment pool, variation
in the rate at which unemployed workers exit the unemployment pool, or a combination
of the two. The relative contributions of changes in in‡ow and out‡ow rates to changes
in unemployment have been abundantly documented for the U.S.1 Less is known, however,
about the driving forces of unemployment variation in other countries. Such a question is
of interest because of the considerable variation in unemployment that has been observed
in developed economies in recent decades, notably in Continental Europe. In this paper, we
provide a detailed analysis of unemployment ‡ows for fourteen developed economies using
publicly available data.
In the …rst part of our analysis we describe how it is possible to derive measures of the
rates of in‡ow2 to and out‡ow from the unemployment pool using annual data from the
OECD. To do this, we generalize the method developed by Shimer (2007), which makes use
of time series for the number employed, the number unemployed, and the number unemployed less than …ve weeks to infer ‡ow hazard rates for the U.S. A limitation that arises
when applying this methodology outside the U.S. is that series on short duration unemployment can be noisy for countries in which short durations account for a small proportion
of overall unemployment, such as in Continental Europe. To address this, we develop a
method that exploits additional data on unemployment at higher durations to construct a
set of comparable time series for the unemployment in‡ow and out‡ow rates across countries.
Our measures allow us to document a set of stylized facts on unemployment ‡ows among
developed economies. First, the average level of unemployment in‡ow and out‡ow rates
varies substantially across countries. Interestingly, the results suggest a natural partitioning of economies into Anglo-Saxon, Nordic and Continental European. Anglo-Saxon and
Nordic economies display high exit rates from unemployment, with monthly hazards that
exceed 20 percent. In stark contrast, out‡ow rates among Continental European economies
1

See Elsby, Michaels, and Solon [2009], Fujita and Ramey [2008], Hall [2005a,b], Shimer [2007], and
Yashiv [2007].
2
Some recent literature on unemployment ‡ows has referred to the rate of in‡ow into unemployment as
the “separation rate” (Shimer, 2005a, b; Fujita and Ramey, 2008). We refer to it as the in‡ow rate for
two reasons. First, a separation is typically taken to mean a quit or a layo¤ from an employer. In the
presence of job-to-job transitions, such separations need not lead to an unemployment spell. Second, some
unemployment spells originate from non-participation rather than a separation from employment.

2

are much lower— typically less than 10 percent at a monthly frequency. Symmetrically, unemployment in‡ow rates also vary considerably across countries. Anglo-Saxon and Nordic
countries exhibit in‡ow hazards that exceed 1.5 percent at a monthly frequency. However, as
with the observed levels of out‡ow rates, monthly in‡ow rates among Continental European
economies are again much lower at around 0.5 to 1 percent. These observations con…rm the
diagnosis that European labor markets are sclerotic in the sense that they display much lower
rates of reallocation of labor, as documented in Blanchard and Summers (1986), Bertola and
Rogerson (1997), Blanchard and Wolfers (2000), and Blanchard and Portugal (2001).
In the second part of our analysis, we pose the question of how much of the observed variation in unemployment within each country can be accounted for by variation in the in‡ow
rate into unemployment and variation in the out‡ow rate from unemployment respectively.
To answer this, we provide a method for decomposing changes in the unemployment rate
into contributions due to changes in the ‡ow hazards that can be applied in countries with
very di¤erent unemployment dynamics. Recent literature (Elsby, Michaels, and Solon [2009],
Fujita and Ramey [2009], Petrongolo and Pissarides [2008]) has evaluated these contributions
under the assumption that the unemployment rate is closely approximated by its ‡ow steady
state value. Under this assumption, contemporaneous unemployment variation may be decomposed into contributions related to contemporaneous logarithmic variation in in‡ow and
out‡ow hazards. While this steady state assumption holds as a reasonable approximation
in the U.S., we show that it can be very inaccurate in other developed economies, notably
those of Continental Europe.
Reacting to this we show that, in cases where unemployment deviates from steady state,
current variation in unemployment can be decomposed recursively into contributions due
to current and past logarithmic changes in the in‡ow and out‡ow hazards. Intuitively,
when unemployment is out of steady state, it can vary as a result of contemporaneous
changes in the in‡ow and out‡ow rates, or as a result of dynamics driven by past changes in
these ‡ow hazards. Using our alternative decomposition, we obtain a much more accurate
characterization of changes in unemployment rates across countries.
Application of our decomposition to our estimated time series for the ‡ow hazard rates
provides us with a second stylized fact on unemployment ‡ows. Among all countries that we
consider, ‡uctuations in both in‡ow and out‡ow rates contribute substantially to unemployment variations within countries. The relative contribution of each di¤ers across countries,
however. Among Anglo-Saxon economies we …nd approximately a 15:85 in‡ow/out‡ow split
of unemployment variation, a result that echoes recent …ndings for the U.S. over the same
3

sample period. For Continental European and Nordic countries, however, we observe much
closer to a 45:55 in‡ow/out‡ow split. Thus, a complete understanding of unemployment
variation among our large sample of developed economies requires an understanding of the
determinants of both the in‡ow rate as well as the out‡ow rate.
The …nal part of our empirical analysis uses the estimated ‡ow hazard rates to compute
measures of the number of workers ‡owing in and out of the unemployment pool (as opposed
to the hazard rates for these ‡ows).3 A third stylized fact that emerges from these results is
that a geographical partitioning also applies to average worker ‡ows across countries. AngloSaxon and Nordic countries exhibit annual worker ‡ows in and out of unemployment that
comprise more than 15 percent of the labor force. Among Continental European economies,
on the other hand, worker ‡ows typically involve less than 10 percent of the labor force,
echoing the …ndings of Blanchard and Portugal (2001) and Bertola and Rogerson (1997).
We then analyze the dynamic relationship between these worker ‡ows and unemployment
within each country. Using a simple correlation analysis, we document a fourth stylized fact
on unemployment ‡ows among developed economies: The timing of the contributions of
in‡ows and out‡ows to unemployment variation displays a remarkable uniformity across
countries. In all economies we observe that increases in in‡ows lead increases in unemployment, whereas out‡ows lag a ramp up in unemployment, an observation that has been
highlighted for the U.S. in earlier studies.4
Our …ndings that variation in unemployment in‡ows accounts for a substantial fraction of
unemployment variation and is an important leading indicator for changes in unemployment
dovetails with a recent literature on U.S. unemployment ‡ows. A growing trend in modern
macroeconomic models of the aggregate labor market has been to assume that the in‡ow rate
into unemployment is acyclical (Hall [2005a,b], Shimer [2005] among others). Reacting to
this, a number of recent studies has cautioned against this trend by documenting evidence for
systematic countercyclical movements in unemployment in‡ows in U.S. data.5 Our …ndings
3

Our analysis is not the …rst to estimate worker ‡ows across countries. Other studies that examine worker
‡ows for a subset of European countries include Albaek and Sørensen (1998) for Denmark; Bauer and Bender
(2004) and Bachmann (2005) for Germany; Bertola and Rogerson (1997) for Canada, Germany, Italy, the
U.K., and the U.S.; Burda and Wyplosz (1994) for France, Germany, Spain, and the U.K.; Petrongolo and
Pissarides (2008) for France, Spain and the U.K.; and Pissarides (1986), Bell and Smith (2002), and Gomes
(2008) for the U.K. Reichling (2005) reports estimates of the separation rate for a set of countries (see his
Table 5) and also emphasizes that the separation rate is lower in European countries than in the U.S.
4
See Darby, Haltiwanger, and Plant [1985, 1986], Blanchard and Diamond [1990], Davis [2006], Fujita
and Ramey [2008].
5
Recent studies that have emphasized this fact include Braun, De Bock, and DiCecio (2006); Davis (2006);
Elsby, Michaels, and Solon (2009); Fujita and Ramey (2008); Kennan (2006); and Yashiv (2008). Older

4

show that this caution resonates all the more if we wish to understand the considerable
variation in unemployment rates observed outside the U.S.
The remainder of the paper is organized as follows. In section 2 we summarize the OECD
data that we use throughout our analysis. In section 3, we describe our methodology for
inferring the rates of in‡ow to and out‡ow from the unemployment pool using the OECD
data. Application of this methodology provides individual time series for the unemployment
‡ow hazards for each of the fourteen countries in our sample. In section 4, we pose the
question of how much of the variation in unemployment within countries can be accounted
for by changes in the in‡ow and out‡ow rates respectively. To answer this question, we
derive a decomposition of unemployment variation that allows for unemployment to deviate
from steady state. We show that allowing for such deviations is critical for understanding
unemployment ‡uctuations outside the U.S. Section 5 presents evidence on the number of
workers ‡owing in and out of unemployment, and documents stylized facts on the timing
of the impact of worker ‡ows on unemployment changes. Section 6 summarizes and o¤ers
conclusions.

2

Data

Since a large part of our analysis is informed by the available data, we start by discussing
the OECD samples that we use. These are taken from two di¤erent sources. First, we
use annual measures of the unemployment stock by duration, taken from OECD (2010a).6
We then supplement these data with quarterly measures of the aggregate unemployment
rate, taken from OECD (2010b). Both slices of data are based on the labor force surveys
conducted in each of the countries in our sample.
The fourteen economies that we focus on are: Australia, Canada, France, Germany,
Ireland, Italy, Japan, New Zealand, Norway, Portugal, Spain, Sweden, United Kingdom,
and the United States. For all countries relatively long historical quarterly time series are
available for the unemployment rate. Our focus on these economies is primarily driven by
the length of the available requisite series for unemployment by duration. Throughout, we
denote the fraction of the labor force in an unemployment spell of less than d months in
<1
<3
<6
<12
7
month t by u<d
.
t . For our analysis we use annual time series for ut , ut , ut , and ut
studies that have documented this include Perry (1972); Marston (1976); Blanchard and Diamond (1990);
and Baker (1992).
6
The data are also publicly available on the web from http://stats.oecd.org.
7
For many countries, data on unemployment duration initially were collected only once a year. More

5

Note that we de…ne these categories inclusively, in the sense that u<3
includes u<1
t
t , and so
on. The starting year for the available series varies between 1968 (for the U.S.) and 1986
(for New Zealand and Portugal).8 For all countries, the data end in 2009.
An important advantage of using data from the OECD is that, even though the labor force
surveys of these countries have di¤erent structures, the OECD data have been standardized
to adhere to the same structure. This aids cross-country comparisons of our results.9

3

The Ins and Outs of Unemployment in the OECD

At the heart of our analysis is a set of estimated annual time series of ‡ow hazard rates into
and out of unemployment for fourteen OECD countries. These time series are estimated using
an extension of the method that Shimer (2007) developed for the United States. Shimer’s
method cannot be applied directly to other OECD countries because the required data are
not available. The extension that we introduce allows us to overcome this limitation and to
produce annual time series for the rates of in‡ow to and out‡ow from the unemployment
pool for a large subset of OECD countries.

3.1

Analytical Framework

The evolution over time of the unemployment rate, which we denote by ut , can be written
as:10
dut
= st (1 ut ) ft ut ;
(1)
dt
where st is the monthly rate of in‡ow into unemployment, ft is the monthly out‡ow rate
from unemployment, and t indexes months.11 As mentioned above, the data that we use in
recently, mainly due to the standardization of Labor Force Surveys in the European Union, countries are
collecting these data at a quarterly frequency. Because our aim is to construct historical time series that are
as long as possible, we focus on annual time series.
8
The initial year in the sample for each country is listed in Table 2.
9
While the OECD goes to some lengths to standardize their unemployment measures, their procedures
may not be perfect. For example, it is possible that workers who de…ne themselves as out of the labor force
in e.g. the U.S. might de…ne themselves as unemployed in Europe. Addressing these important issues of
standardization is beyond the scope of this paper.
10
It is important to note that equation (1) implicitly assumes that all of the in‡ow into unemployment
originates from employment. We have calculated a set of results taking into account non-participation.
Except for the level of the average in‡ow rate, these results were very similar to those we present here.
Details of these results, as well as an explanation of why this is the case are provided in the Appendix.
11
We de…ne the ‡ow hazards st and ft in monthly terms to aid comparison with estimates reported in
U.S. studies of unemployment ‡ows.

6

the remainder of the paper allow us to infer unemployment ‡ows at an annual frequency.
Thus, we would like to relate the continuous time evolution of unemployment in equation (1)
to the unemployment rates that we observe at discrete annual intervals. Assuming that the
‡ow hazards are constant within years,12 and solving equation (1) forward one year allows
us to do this:
(2)
ut = t ut + (1
t )ut 12 ,
where
ut =

st
st + ft

(3)

denotes the ‡ow steady-state unemployment rate, and
t

=1

e

12(st +ft )

(4)

is the annual rate of convergence to steady state. In this way we can relate variation in
the unemployment stock ut in a given country over the course of a year to variation in
the underlying ‡ow hazards, st and ft .13 To implement this, however, we need to obtain
estimates of these ‡ow hazards, to which we now turn.
Our method for estimating the out‡ow rate ft is an extension of the method popularized
by Shimer (2007). In his study of U.S. unemployment ‡ows, he infers the monthly out‡ow
probability Ft using the identity that the monthly change in the unemployment stock is given
by
ut+1 ut = u<1
Ft ut .
(5)
t+1
Here u<1
t+1 denotes the stock of unemployed workers with duration less than one month, and
hence re‡ects the ‡ows into unemployment; Ft ut re‡ects the ‡ows out of unemployment.
12

This assumption does lead to some smoothing out of high frequency variation in the ‡ow hazards that
we estimate. As many U.S. studies of unemployment ‡ows have shown, and as we will con…rm in our cross–
country estimates, it is predominantly the in‡ow rate st that displays such high frequency variation. It
follows that annual smoothing is likely to lead to an overstatement of the contribution of changes in the
out‡ow rate ft to unemployment variation. This works against a key …nding of this paper that variation in
the in‡ow rate st accounts for a substantial fraction of unemployment variation.
13
For simplicity, we abstract from labor force growth in equations (1) through (4). It is straightforward
to show, however, that if the labor force grows at monthly rate gt , then ut = st =(st + ft + gt ) and t =
1 e 12(st +ft +gt ) . In our sample, gt averages around 0.001 on a monthly basis. In contrast, the average value
of (st + ft ) in our sample is on the order of 0.2. This point also extends to speci…c countries and periods in
which labor force growth accelerates. For example, gt rose in the 2000s in Spain up to 0.003 on a monthly
basis. However, over the same period, we observe that (st + ft ) averages around 0.1 in Spain. Consequently,
allowing for labor force growth does not a¤ect our results in a quantitatively important way.

7

Solving for the monthly out‡ow probability, one obtains14
Ft = 1

u<1
t+1

ut+1
ut

.

(6)

The monthly out‡ow probability is then related to the associated monthly out‡ow hazard
rate, ft<1 , through
ft<1 = ln(1 Ft ).
(7)

3.2

Estimation of Flow Hazard Rates

Duration Dependence and Estimation of the Out‡ow Rate In what follows we will
see that the estimate of the out‡ow rate implied by equation (6) works well for countries
in which the out‡ow rate from unemployment is relatively high, such as the U.S. However,
in countries that exhibit low exit rates, such as those of Continental Europe, estimates
based on equation (6) can be substantially noisy. The simple reason is that low out‡ow
rates imply that very few unemployed workers at a point in time are in their …rst month of
unemployment, which increases the sampling variance of the estimate of u<1
t+1 , and in turn
15
leads to noisy estimates of ft .
Our approach to this problem is to use the additional unemployment duration data
available from the OECD to increase the precision of our estimate of ft in countries where
the out‡ow rate is low. To see how this may be done recall that the OECD data also report
the unemployment stock at durations higher than one month. It follows that, analogous to
the method detailed above, it is possible to write the probability that an unemployed worker
14

Since the OECD database reports only quarterly data on the aggregate unemployment rate, we compute
ut by interpolating quarterly data.
15
For example, the OECD data for the U.S. are based on the Current Population Survey, which surveys
around 130,000 individuals each month. In the U.S., the labor force participation rate averaged 47.9 percent,
6.1 percent of which were unemployed, 43.3 percent of which were unemployed for less than one month. This
suggests around 130; 000 0:479 0:061 0:433 1; 645 respondents have been unemployed less than one
month in each month’s survey. In contrast, each survey for Germany includes around 165,000 respondents,
with an average participation rate of 48.5 percent, 8.3 percent of which were unemployed, but only 6.9
percent of which were unemployed for less than one month. This implies that only around 458 respondents
have been unemployed for less than one month in each survey for Germany. This simple comparison would
suggest that the sampling variance of the estimate of short-term unemployment in each survey in Germany
will be 3.6 times its U.S. equivalent. In addition, this calculation becomes much more extreme when one
accounts for the fact that the OECD data for the U.S. are annual averages of monthly data, while those
for Germany correspond to just one month, April. Similar calculations for other European countries yield
similar conclusions.

8

exits unemployment within d months as
Ft<d

=1

u<d
t+d

ut+d
ut

.

(8)

As before, this can be mapped into an out‡ow rate estimate given by
ft<d =

ln(1

Ft<d )=d:

(9)

Given the available data, we can estimate ft<d for d = 1; 3; 6; 12.16
It is important to clarify the interpretation of the out‡ow rate measures ft<d . It is
tempting to interpret ft<d as the out‡ow rate for unemployed workers of duration d. However,
that is not an accurate interpretation. Rather, it is the hazard rate associated with the
probability that an unemployed worker at time t completes her spell within the subsequent
d months.
These four measures, ft<1 ; ft<3 ; ft<6 ; and ft<12 , are not necessarily estimates of the same
out‡ow rate. Only in the case where the out‡ow hazard is unrelated to the duration of an
unemployment spell, i.e. if there is no duration dependence in out‡ow rates, are all four
measures consistent estimates of the aggregate out‡ow rate from unemployment, de…ned
as the average out‡ow rate among the entire unemployed population. However, if there is
duration dependence in unemployment out‡ow rates in a given country, then estimates based
on durations of unemployment greater than one month, ft<3 ; ft<6 ; and ft<12 , will not yield
consistent estimates of the average out‡ow rate among the unemployed.
For example, imagine that there exists negative duration dependence whereby the out‡ow
rate declines with duration.17 In such an environment, we would expect to observe ft<1 >
ft<3 > ft<6 > ft<12 . To see why, consider the version of equation (8) which expresses the
fraction of the unemployment stock in month t that exits within the next three months.
The remaining unemployed workers that do not exit over these subsequent three months
increasingly will be comprised of unemployed workers with low out‡ow rates, i.e. the high
duration unemployed. This process of dynamic selection will imply that excessive weight
will be placed on the low out‡ow rates of high duration unemployed workers in the estimate
of ft<3 , generating a downward bias in its estimate of ft . This argument applies even more
16

The appendix contains a detailed description on how we estimate these rates combining the annual and
quarterly data available.
17
In the U.S., for example, the …nding of substantial negative duration dependence in unemployment exit
rates has been widely documented since Kaitz (1970). Most recently, Shimer (2008) has emphasized this
stylized fact for the U.S.

9

strongly to the estimates of ft<6 and ft<12 .18
In light of this, we formally test for the presence of duration dependence in out‡ow rates
by testing the hypothesis that ft<1 = ft<3 = ft<6 = ft<12 . The formal details are described
in the Appendix, but our general approach is as follows. First, we derive the asymptotic
distribution of the unemployment rates by duration as well as for the unemployment rates.
We then apply the Delta method to compute the joint asymptotic distribution of the out‡ow
rate estimates ft<d with d = 1; 3; 6; 12. This allows us to formulate a simple Chi-squared test
of the null hypothesis of no duration dependence.
It should be noted that we test for a very broad de…nition of duration dependence.
As has been emphasized since Kaitz (1970), duration dependence can arise through two
channels. “True”duration dependence refers to the case where unemployment duration has
a causal e¤ect on the out‡ow rates of individual workers. In contrast, “spurious” duration
dependence refers to the process of dynamic selection whereby workers with high exit rates
leave unemployment faster than those with low exit rates, thereby generating a negative
correlation between duration and out‡ow rates (Salant, 1977). Our hypothesis test is not
intended to distinguish between these two sources of duration dependence, but rather to
test for whether the alternative measures of the out‡ow rate derived above are signi…cantly
di¤erent from one another. Thus, the duration dependence we test for can arise due to either
dynamic selection or true duration dependence or both.
For those countries for which we reject the hypothesis of no duration dependence, we
follow the recent U.S. literature in using ft<1 as our estimate of the unemployment out‡ow
rate, as this measure provides the most accurate estimate of the average out‡ow rate in the
presence of duration dependence. For countries with weak evidence for duration dependence
for which we do not reject the null, we make use of all the additional information on the
out‡ow rate contained in ft<3 ; ft<6 ; and ft<12 in order to obtain a more precise estimate of ft .
Speci…cally, we use our estimates of the asymptotic distribution of the out‡ow rate estimates,
ft<1 ; ft<3 ; ft<6 ; and ft<12 to compute an optimally weighted estimate of the out‡ow rate that
minimizes the mean squared error of the estimate.19
The results of the hypothesis test are reported in Table 2. While we …nd signi…cant
evidence of duration dependence in Anglo-Saxon and Nordic countries and Japan, we do not
observe signi…cant evidence among the Continental European countries in our sample.20 It is
By the same token, the estimate of ft<1 that has been widely used in recent literature is also subject to
this drawback, just to a lesser degree than the other three measures.
19
The construction of these optimal weights is detailed in the Appendix.
20
While our hypothesis test provides a natural rule of thumb, we implicitly rule in favor of the null when
18

10

natural to ask whether this conclusion is supported by the results of microeconometric studies
that estimate duration dependence for speci…c European economies. A particularly useful
summary of this literature is reported by Machin and Manning (1999, Table 6). They show
that the evidence for duration dependence among European economies is quite inconclusive.
Estimates of duration dependence in Germany and Spain, for example, di¤er across studies,
with evidence found for negative, positive and negligible duration dependence reported. Our
conclusion of limited evidence for duration dependence lies at the midpoint of this array.
A clearer consensus emerges for France and the U.K. For France, the literature …nds very
little evidence for duration dependence, at least within the …rst year of the unemployment
spell. In contrast, for the U.K., the literature in general …nds evidence for negative duration
dependence. Our estimates are in line with these conclusions.
Our results are also consistent with other work that has estimated duration dependence
across countries. In their own analysis, Machin and Manning (1999) …t a Weibull duration model to the duration structure of unemployment across countries. They report weak
negative duration dependence in France and Spain in the 1990s, but strong negative duration dependence in Australia, the U.K. and the U.S. in the 1980s and 1990s. Using a
similar approach on OECD data, Hobijn and Şahin (2009) also …nd little evidence of duration dependence among Continental European economies, but substantial evidence among
economies with high unemployment out‡ow rates. The result of our hypothesis test is that
we use ft<1 as our estimate of the out‡ow rate for the Anglo-Saxon countries in our sample
and the optimally weighted average of ft<1 ; ft<3 ; ft<6 ; and ft<12 for the remaining countries.
Temporal Aggregation Bias and Estimation of the In‡ow Rate Given our estimate
of the out‡ow rate, we compute the in‡ow rate st using the method pioneered by Shimer
(2007). In particular, note that the expression for the annual unemployment rate in equation
(2) is simply a nonlinear equation in the unemployment rates, ut+12 and ut , and the ‡ow
hazard rates, st and ft . We can thus solve equation (2) for the in‡ow rate.
As emphasized by Shimer (2007) and subsequent work based on his method, this estimate
of the in‡ow rate is robust to temporal aggregation bias in the measurement of unemployment
in‡ows. In particular, since equation (2) is inferred from solving forward the continuous-time
di¤erential equation for the evolution of the unemployment rate, it accounts for the fact that
the hypothesis of no duration dependence cannot be rejected. This raises the question of the power of the
test. In results that can be replicated in the spreadsheet that accompanies this paper, we observe that the
test does indeed have high power among the Continental European economies for which we fail to reject the
null, in the sense that the estimates of ft<d are similar for all durations d.

11

workers who ‡ow into unemployment after one period’s survey may exit prior to the next
period’s survey, ‡ows that would be missed in discrete-time data. Correcting for temporal
aggregation bias in the in‡ow rate is particularly important the context of the OECD data,
since the data are available at an annual frequency, in contrast to the monthly data that are
available for the U.S.21
A natural question is whether a symmetric bias a¤ects estimation of the out‡ow rate.
Interestingly, time aggregation causes relatively little bias in the out‡ow rate, for two reasons.
First, consider the measure of the out‡ow probability in equation (6). This is just the
complement of the probability that those unemployed at time t remain unemployed by time
t + 1. If there were a time aggregation problem, the concern would be that the data fail to
pick up on workers who exit unemployment after one period’s survey, but who re-enter prior
to the next period’s survey. However, the measure of the out‡ow probability in equation (6)
does not miss such transitions: Any worker who followed this path would be identi…ed as
short-term unemployed in the second survey, and therefore correctly counted as an out‡ow.
Second, it still could be the case that the measure of the out‡ow probability in equation (6)
misses multiple exits from unemployment within the period (e.g. out after …rst survey, in
again, out again, in again prior to next survey). However, we will see that the in‡ow rate in
practice is very small in comparison to the out‡ow rate for all countries in our sample, so
that the probability of such multiple transitions is likely to be miniscule.22

3.3

Evidence from OECD Data

The average unemployment in‡ow and out‡ow hazards over the sample periods for the whole
sample of countries are reported in Table 2. A striking observation from these results is the
substantial cross-country variation in both st and ft . A particularly useful illustration of
this point is in Figure 1, which displays the average values of st and ft from Table 2 in graph
form. Interestingly, one can discern a natural partition of developed economies between
Anglo-Saxon, Nordic and Continental European economies.
Figure 1 reveals very high out‡ow rates among the Anglo-Saxon and Nordic economies.
21

The magnitude of the correction for time aggregation bias in in‡ow rates also will vary across countries. In
European economies with sclerotic unemployment ‡ows, we will see that the out‡ow rate from unemployment
ft is low. As a result, the correction for time aggregation bias is smaller for these countries, as a lower
proportion of in‡ows into unemployment after one survey will exit unemployment prior to the next survey.
22
Shimer (2007) makes a similar point. In his words: “Because the probability of losing a job during the
month that it is found is comparatively small, time aggregation causes relatively little bias in the job …nding
rate.”

12

Among these countries the average monthly unemployment out‡ow hazard exceeds 20 percent. The economies of Continental Europe stand in stark contrast. Unemployment out‡ow
rates in these economies lie below 10 percent at a monthly frequency. A similar picture
develops for the estimates of the in‡ow rates in Figure 1. We observe high unemployment
in‡ow hazards among the Anglo-Saxon and Nordic economies, which typically lie above 1.5
percent on a monthly basis. Likewise, in‡ow rates among the European economies are again
much lower at around 0.5 to 1 percent per month.
Figure 1 also shows that there are both extremes and intermediate cases that are understated in this Anglo-Saxon/Nordic/Continental Europe taxonomy. For Japan, while the
average unemployment out‡ow rate of 19 percent is similar to those in Anglo-Saxon and
Nordic economies, its in‡ow rate is more comparable to those of Continental Europe. Another intermediate case is the U.K., which displays unemployment ‡ows that lie halfway
between the Anglo-Saxon and the Continental European models. Perhaps the most striking
observation, however, is the outlier status of the U.S. With an average monthly unemployment out‡ow rate of nearly 60 percent and an average in‡ow rate of 3.5 percent, it exhibits
transition rates at least 50 percent larger than the remainder of our sample of countries.
Figures 2 and 3 display the time series for the in‡ow and out‡ow hazards for each country
in our sample. The transition rates are plotted on log scales since, as emphasized in the
literature on unemployment ‡ows, and as we will con…rm in what follows, it is the logarithmic
variation in st and ft that places them on an equal footing with respect to ‡uctuations in
the unemployment rate.
Figures 2 and 3 reveal that, in addition to signi…cant cross-country variation in unemployment ‡ows, there is also substantial variation in unemployment ‡ow hazards over time
within countries. Although there is a great deal of information contained in these …gures,
a number of observations come to light. First, there are important di¤erences in the frequency of ‡uctuations in unemployment ‡ows across economies. Among the Anglo-Saxon
economies, a clear cyclical pattern is present, suggesting a substantial high frequency component to unemployment ‡uctuations in these countries. Among other economies, however,
the variation in st and ft occurs at a much lower frequency, and it is hard to di¤erentiate
cycle from trend.
Figures 2 and 3 are also indicative of how the relative contributions of variation in the
in‡ow and out‡ow rates di¤er across countries. Speci…cally, the Anglo-Saxon economies
appear to display relatively more variation in the out‡ow rate from unemployment, a point
that has been emphasized in recent literature for the U.S. However, inspection of the time
13

series for the Nordic and European economies reveals greater variation in the in‡ow rate,
suggesting about an equal contribution of the ins and the outs to unemployment variation
in these countries.
Figures 2 and 3 also provide a sense of the degree to which these stylized facts have held
true in the most recent recession. In many respects, historical di¤erences in unemployment
dynamics between Anglo-Saxon and Continental European economies have been echoed in
recent data. Inspection of the time series for the ‡ow hazards after 2007 reveals that, as in the
past, the recent rise in unemployment has been associated more with rises in unemployment
in‡ows in Continental European economies, and with declines in rates of out‡ow in AngloSaxon countries. Figures 2 and 3 do point to one stark feature of the recession, however:
The out‡ow rate from unemployment in the U.S. fell precipitously to reach a historic low,
a point noted by many observers of the Great Recession in the U.S. (see Elsby, Hobijn and
Şahin [2010], for example). An advantage of the cross-country estimates in Figures 2 and 3
is that they provide a useful perspective on this phenomenon. Despite the record decline in
rates of exit from unemployment in the U.S., the level of the out‡ow rate witnessed recently
in the U.S. still dwarfs those observed in Continental Europe.
Of course, this visual impression is only suggestive of the relative contributions of the
in‡ow and out‡ow hazards to unemployment variation; we address this issue more formally
in section 4. Before we do so, we …rst compare our estimates of unemployment transition
rates with those reported in related literature.

3.4

Relation to Existing Evidence

Unemployment ‡ows for the U.S. have been extensively studied in the literature. Almost all
of these studies, including Elsby, Michaels, and Solon (2009), Fujita and Ramey (2009) and
Shimer (2007), are based on data from the Current Population Survey. Since the OECD
data that we use are also based on the same survey data, the levels of our estimated ‡ow
hazards are in line with these previous estimates.23
The cross-country analysis of ‡ow rates that is most closely related to the results in
this paper is Hobijn and Şahin (2009). They use GMM to estimate average job-…nding and
separation rates for a broader sample of countries. Since they focus on average ‡ow hazards,
their analysis does not address the dynamic properties of the evolution of unemployment in
23

One exception is Hall [2005], who employs a broader de…nition of unemployment than the usual Current
Population Survey de…nition. Consequently he estimates a lower out‡ow rate.

14

these countries. The average ‡ow transition rates that they obtain using their estimation
method are almost identical to those documented in Table 2.
The time series plotted in Figures 2 and 3 for countries other than the U.S. also are
qualitatively similar to previous results based on microdata for individual countries. Our
estimates for the U.K. are consistent with the declining employment to unemployment (E–
U) and rising unemployment to employment (U–E) transition rates estimated using U.K.
Labour Force Survey data from the early 1990s on (Bell and Smith [2002], Gomes [2008],
and Petrongolo and Pissarides [2008]). The trends we …nd for Germany are consistent with
Bachmann (2005) who uses German social security data to estimate a sharp rise in the E–U
transition rate and a decline in the U–E hazard in the early 1990s. In addition, the estimated
time series for Spain correspond very closely to those reported in Petrongolo and Pissarides
(2008) using Spanish Labor Force Survey data. Reichling (2005) reports estimates of the
separation rate for a set of countries (see his Table 5) and also emphasizes that the separation
rate is lower in European countries than in the U.S.
There are also several cross-country studies that provide structural estimates of search
models that include estimated ‡ow hazards. Two examples of these are Ridder and van
den Berg (2003) and Jolivet, Postel-Vinay and Robin (2006). Because they are based on
structural models, the estimated transition rates in these papers do not correspond exactly to
the ‡ow rate concept we use here. However, the qualitative ranking of countries in terms of
the levels of in‡ow and out‡ow rates are very similar to ours. For example, Italy is estimated
to have the smallest out‡ow rate, the U.S. the highest, with the U.K lying between the U.S.
and the Continental European countries.

4

Decomposing Unemployment Fluctuations

In this section, we formulate and apply a formal decomposition of changes in unemployment
into parts due to changes in the in‡ow and out‡ow rates for each country. Our decomposition
allows for deviations of the actual unemployment rate from its ‡ow steady-state value. We
show that allowing for such deviations is important for understanding unemployment ‡uctuations in many, especially European, countries. We use the annual time series on in‡ow
and out‡ow rates, presented above, to conduct this decomposition. Because we use annual
data in what follows, time, t, is denoted in years rather than months in the remainder of
this paper.

15

4.1

Analytical Framework

As mentioned above, an important aim of this paper is to understand the proximate driving
forces behind variation in unemployment rates across countries. As previous literature has
shown, such a task is relatively straightforward for the U.S.24 The reason is that unemployment dynamics are uncommonly rapid in the U.S.— that is, st + ft is a relatively large
number in the U.S. The formal implication of this is that the rate of convergence of the
unemployment rate to its ‡ow steady state value in equation (2), t = 1 e 12(st +ft ) , is
very close to one in the U.S. In this case, the unemployment rate can be approximated very
closely by its ‡ow steady state value,
ut

ut =

st
, and
st + ft

t

1:

(10)

As emphasized in Elsby, Michaels and Solon (2009), log di¤erentiation of the latter implies
d ln ut

(1

ut )[d ln st

d ln ft ]:

(11)

Thus, in countries with labor markets characterized by fast unemployment dynamics, a
simple decomposition of unemployment variation presents itself: The relative contributions
of the in‡ow and out‡ow rates to unemployment variation can be gleaned from comparing
the contemporaneous logarithmic variation in the two ‡ow hazard rates.
Based on the evidence we found above, one might anticipate that the approximations
that underlie the decomposition of unemployment variation based on (11) work well among
the Anglo-Saxon and Nordic economies, which display relatively high rates of in‡ow and
out‡ow. However, the evidence also suggests that there is good reason to hesitate in applying
equation (11) as a decomposition of unemployment variation in Continental Europe. The
reason is that the unemployment ‡ow hazards in these economies are very low, especially
relative to the U.S. Inspection of equation (2) reveals that, for Continental Europe, the ‡ow
steady-state unemployment rate is therefore likely to be a poor approximation to the actual
unemployment rate.
Reacting to this, we devise a decomposition of unemployment changes that holds even
when unemployment is out of steady state. Our approach uses equation (2) as its starting
point. We show in the Appendix that a log-linear approximation to (2) allows us to express
24

See Elsby, Michaels and Solon (2009), Fujita and Ramey (2009) and Pissarides (2009), among others.

16

the log change in the unemployment rate recursively as
ln ut

t 1

1

ut

1

[ ln st

ln ft ] +

1

t 2

ln ut

1

.

(12)

t 2

This decomposition distinguishes between changes in the steady state due to current changes
in the in‡ow and out‡ow rates, and changes in the unemployment rate due to deviations
from the steady state caused by past changes in the ‡ow rates.
A number of aspects are worth noting about equation (12). First, if unemployment
dynamics are very fast, so that st + ft is high and t is close to one for all t, then equation
equation (12) reduces to the steady-state decomposition implied by (11). In addition, a
particularly intuitive way of understanding (12) is to consider the case where t = for
all t. In that case, the log change in the unemployment rate in (12) is a distributed lag of
contemporaneous and past log changes in the in‡ow rate st and the ft . This highlights a
potential pitfall of applying the steady-state decomposition in (11) to unemployment ‡ows
in economies, such as those of Continental Europe, with slow unemployment dynamics:
Out of steady state, contemporaneous variation in the unemployment rate is driven both
by contemporaneous as well as lagged variation in the ‡ow hazards. We will see that, by
ignoring these lag e¤ects, the steady-state decomposition can lead to misleading conclusions
on the relative contributions of the in‡ow and out‡ow rate to changes in unemployment.
In principle, the non-steady-state decomposition in equation (12) can be used to assess the
relative contributions of in‡ow and out‡ow rates for any given change in the unemployment
rate at any time for any given country. Clearly, however, given the wealth of information in
our dataset, performing such a decomposition for every unemployment episode in every country would be excessive. Thus, we need a method of summarizing the relative contributions
of the ins and outs of unemployment.
Fujita and Ramey (2009) formulate such a summary method for the U.S. using the
steady-state decomposition. Speci…cally, they compute the following values:

f

=

cov( ln ut ; (1 ut 1 ) ln ft )
and
var( ln ut )

s

=

cov( ln ut ; (1 ut 1 ) ln st )
;
var( ln ut )

(13)

where a superscript indicates that these are based on the assumption that observed unemployment is closely approximated by its steady-state value. If this assumption holds, f
and s should approximately sum to one.
We extend Fujita and Ramey’s s to the decomposition of unemployment changes out
17

of steady state based on equation (12). In particular, for each country in our sample we
compute
f

=

cov ( ln ut ; Cf t )
,
var( ln ut )

s

=

cov ( ln ut ; Cst )
, and
var( ln ut )

0

=

cov ( ln ut ; C0t )
,
var( ln ut )

(14)

where Cf t , Cst , and C0t denote the respective cumulative contributions of contemporaneous
and past variation in the in‡ow rate, the out‡ow rate, as well as the initial deviation from
steady state at time t = 0. Consistent with (12), they are de…ned recursively by
Cf t =
Cst =

t 1

ut 1 ) ln ft +

(1

t 1

(1

ut 1 ) ln st +

and
C0t =

t 1

(1

t 2)

1

Cf t

1

with Cf 0 = 0,

(15)

t 2

1

C0t

t 2

t 2

Cst

1

with Cs0 = 0,

(16)

t 2

1

with C00 =

ln u0 .

(17)

t 2

If the decomposition fully captures ‡uctuations in the unemployment rate then
1.

4.2

s+ f + 0

=

Accounting for Unemployment Fluctuations in the OECD

In order to illustrate why it is important to take into account deviations from steady state
for many countries, consider Figure 4. This plots the actual unemployment rate, ut , as well
as the ‡ow-steady-state unemployment rate, ut , for the four countries that are studied by
Petrongolo and Pissarides (2008), namely France, Spain, the U.K., and the U.S. As has been
emphasized in the recent literature, for the U.S. the actual unemployment rate is virtually
identical to the steady-state unemployment rate. However, we observe that this is not the
case for the other three countries.
Another way of seeing this is to look at the second column of Table 3. This lists the
standard deviation of the logarithmic deviation of unemployment from steady state for each
of the countries in our sample. Table 3 reveals that these deviations tend to be small among
Anglo-Saxon economies which have high in‡ow and out‡ow rates, with the exception of
the U.K. All other countries exhibit substantial deviations of unemployment from its ‡owsteady-state value.
To see what happens when one applies the decomposition based on the steady-state
18

assumption to a country that substantially deviates from steady state, consider the top panel
of Figure 5. It depicts the steady-state decomposition of ln ut into parts due to changes in
the in‡ow rate, the out‡ow rate, and a residual part that is due to approximation error for
France. As can be seen from this …gure, the residuals from the steady-state decomposition
are very large. In fact, in this case we observe that f + s = 1:37 rather than 1. Thus, if one
calculates s and imputes f = 1
s , then one would underestimate f by 0:37 because of
the approximation error induced by deviations from steady state.25
The bottom panel of Figure 5 depicts the non-steady-state decomposition for France.
As this …gure shows, the residuals are very small and the magnitudes of the parts due to
the ‡ow rates decrease relative to the steady-state decomposition. In the …rst …ve years of
the sample a non-trivial part of unemployment ‡uctuations in France was due to the labor
market not being in steady state in 1976. This is re‡ected by the contribution of the initial
value to the changes in the unemployment rate.
The results of our non-steady-state decomposition based on equations (12), (14) and (15)
for each country are presented in Table 3. For purposes of comparison, we also include the
results from applying the steady-state decomposition. The results in Table 3 are notable
from a number of perspectives. First, as anticipated above, we observe that the steady-state
decomposition in equation (13) works quite well for economies with fast unemployment
dynamics, such as the Anglo-Saxon and Nordic economies, in the sense that s and f
approximately sum to one for these economies. In contrast, the steady-state decomposition
performs very poorly among economies with slow unemployment dynamics: The sum of the
estimated s and f consistently lies above one for these countries, rendering the steady-state
decomposition uninformative in determining the driving forces of unemployment variation.26
As anticipated by the results for France in Figure 5, the results of our non-steady-state
decomposition reveal that this problem is substantially reduced when we take into account
the lag structure of the e¤ects of changes in in‡ow and out‡ow rates on unemployment:
The residual variance of log changes in unemployment is closer zero for all countries, and
especially so among economies with slow unemployment dynamics. Thus, taking account of
the dynamic e¤ects of changes in the unemployment ‡ow hazards on the unemployment rate
25

In their analysis, Petrongolo and Pissarides (2008) implicitly acknowledge this drawback by eliminating
the periods for which the deviation of the unemployment rate from its ‡ow steady state value is large.
26
The main reason that the steady-state decomposition consistently explains more than 100% of unemployment variation is that contemporaneous changes in log ‡ow hazards in reality have only a partial contemporanous e¤ect on current unemployment, determined by t 1 < 1 (see equation (12)). The steady-state
decomposition erroneously attributes their full e¤ect contemporaneously.

19

is important for inferring the proximate driving forces of unemployment ‡uctuations. In this
way, the non-steady-state decomposition summarized in equations (12), (14) and (15) is a
useful contribution to the analysis of unemployment ‡ows across countries.
The formal results of the non-steady-state decomposition in Table 3 in many ways con…rm
the suggestive picture that one can discern from the time series in Figure 2 and 3. Among
the Anglo-Saxon economies of Australia, Canada, New Zealand, the U.K. and the U.S., we
observe that variation in the out‡ow rate accounts for the majority (though not all) of the
variation in the unemployment rate over the respective sample periods. In particular, we
…nd something like a 15:85 in‡ow/out‡ow accounting for unemployment variation for these
economies.
However, variation in the in‡ow rate plays a much larger role among other economies. In
fact, we …nd much closer to a 45:55 in‡ow/out‡ow split for the Continental European, Nordic
and Japanese economies. These observations are an interesting addition to the debate that
has progressed for the U.S. Recent studies have cautioned against the neglect of variation
in unemployment in‡ows as an important driving force for changes in unemployment in the
U.S. context.27 The results summarized in Table 3 show that this caution resonates all the
more if we wish to understand the considerable variation in unemployment rates outside of
the U.S.
The latter point is important for our understanding of the economics of unemployment.
The relative abundance and ease of access to relevant data for the U.S. have led to a wealth of
research that documents the proximate driving forces for variation in the U.S. unemployment
rate. However, the variation in unemployment in the U.S., though substantially cyclical, is
dwarfed by the unemployment experiences among many European economies. A prominent
example is Spain, which faced unemployment rates that varied from below 5 percent in
the 1970s to 25 percent in the 1990s (see Figure 4). Our results suggest that, in order to
understand the substantial variation in unemployment rates among European economies, it
is necessary to understand both the variation in the out‡ow rate from unemployment as well
as the in‡ow rate.

4.3

Relation to Existing Evidence

A number of studies have documented the contributions of changes in in‡ow and out‡ow rates
to unemployment variation in the U.S. (see Elsby, Michaels and Solon, 2009; Shimer, 2007;
27

See Braun, De Bock and DiCecio (2006), Elsby, Michaels and Solon (2009), Fujita and Ramey (2009),
and Yashiv (2008).

20

and Fujita and Ramey, 2009). A natural question is whether the results of our decomposition
are similar to these related …ndings. Recall from Table 3 that we …nd approximately a 15:85
in‡ow/out‡ow contribution to unemployment variation in the U.S. over the period 1968 to
2009 covered by our data. At …rst blush, this …nding can seem di¤erent from those reported
in prior research.28 Fujita and Ramey (2009), for example, report a greater role for in‡ows,
accounting for as much as 56 percent of unemployment ‡uctuations.
The most comparable previous estimates of in‡ow and out‡ow rates to the ones we
present here are those derived by Elsby, Michaels and Solon (2009). Using their quarterly
analogs of our annual estimates yields an estimated in‡ow contribution of 27 percent over
the period 1968 to 2004, a little larger than our estimates based on annual data. This
con…rms the intuition foreshadowed in footnote 12 that the use of annual data leads to some
smoothing of high frequency ‡uctuations in the in‡ow rate, leading to an understatement
of the in‡ow contribution to unemployment variation. However, the understatement is not
nearly as severe as one might imagine from a simple comparison with Fujita and Ramey
(2009).29
Comparatively little research has studied the contributions of the changes in the in‡ow
and out‡ow rates to the ‡uctuations in unemployment across countries. A notable exception is Petrongolo and Pissarides (2008), who study the dynamics of unemployment in three
European countries: the U.K., France and Spain. They implement a di¤erent method for
treating deviations of actual unemployment from its ‡ow steady state, by dropping observations for which that deviation is large. Despite this, our results line up well with their
…ndings for the U.K. and Spain. Using U.K. Labor Force Survey microdata for the period
1993 to 2005, they report an in‡ow contribution of 0.48. Over the same period, we estimate
a steady state in‡ow contribution of 0.43 for the U.K. Similarly, using Spanish Labor Force
survey data for the period 1987 to 2006, Petrongolo and Pissarides report an average in‡ow
28

An exception is Shimer (2007) who reports an in‡ow contribution of 18 percent for the period 1967
to 2007 using a slightly di¤erent decomposition method (see his Table 1, column 2). Shimer’s method
is analogous to ours, except that he uses the sample average ‡ow hazards as the expansion point for his
approximation. Speci…cally, he computes two counterfactual unemployment rates. The …rst …xes the in‡ow
rate at its sample average and allows the out‡ow rate vary as it did in the data; the second does the opposite.
He then decomposes the variance of unemployment into components related to these two counterfactuals.
29
The relatively large in‡ow contributions reported by Fujita and Ramey can be traced to a number
of factors. First, their larger estimated in‡ow contributions are based on di¤erent data sources that use
longitudinally linked monthly microdata from the Current Population Survey (the so-called gross ‡ows
data). Second, Fujita and Ramey decompose changes in steady-state unemployment rather than the realized
unemployment series, which in practice accentuates the estimated in‡ow contribution. Third, the sample
periods reported by Fujita and Ramey do not coincide with ours. Relaxing all these di¤erences yields an
in‡ow contribution of 27 percent.

21

contribution of 0.43. The corresponding value in our calculations is 0.40. It is reassuring
that these two perspectives on the data yield similar answers: The OECD data for the U.K.
and Spain are annual measures based on the respective quarterly labor force surveys that
Petrongolo and Pissarides use. This suggests that there is little slippage in using annual
data to measure the ‡ow contributions to unemployment ‡uctuations for these European
countries.30

5

Worker Flows

So far, we have focused on the ‡ow hazard rates for worker transitions in and out of unemployment. These ‡ow rates, in turn, generate actual worker ‡ows into and out of unemployment.
In this …nal part of our analysis, we construct annual time series of worker ‡ows for the
fourteen OECD countries in our sample. We use these time series to uncover a very robust
stylized fact across countries: In‡ows lead changes in unemployment, while out‡ows lag.

5.1

Analytical Framework

The annual ‡ow hazard rates that we presented before can be used to compute the total
out‡ows out of unemployment and in‡ows into unemployment. Let Ft be the total number
of workers that ‡ows out of the unemployment pool in year t as a fraction of the labor force,
and let St be the total in‡ows into unemployment.
Given (1), these ‡ows can be written as31
Ft = 12ft ut +

t

(1

ut ) (ut

ut ) , and St = 12st (1

ut )

t ut

(ut

ut ) .

(18)

By construction, the ‡ows are such that the increase in the unemployment rate is the di¤er30

Petrongolo and Pissarides’results for France based on unemployment claims data do not line up as well
with our estimates. They report an in‡ow contribution of 0.2 for the years 1991 to 2007, smaller than our
analogous estimate of 0.5. We suspect that this discrepancy arises because the OECD data that underlie our
estimates are based on French Labor Force Survey data, rather than the claimant data used by Petrongolo
and Pissarides. This is consistent with results reported by Petrongolo and Pissarides’ for the U.K. Their
measured in‡ow contribution based on U.K. unemployment claims data for the period 1993Q2 to 2005Q3 is
0.25, much less than their estimate of 0.48 based on the U.K. Labor Force Survey.
R t+12
31
The total in‡ow into unemployment can be derived as St = st t
[1 u ( )] d
=
R t+12
st t
1 ut e (st +ft ) (ut ut ) d = 12st (1 ut )
u
(u
u
),
where
the
second
equality
follows
t t
t
t
from solving the di¤erential equation for the unemployment rate (1) forward. Analogously, the total outR t+12
R t+12
‡ow from unemployment can be derived as Ft = ft t
u ( ) d = st t
ut + e (st +ft ) (ut ut ) d =
12ft ut + t (1 ut ) (ut ut ).

22

ence between the in‡ows and the out‡ows, i.e.
ut = St

Ft .

(19)

A large number of studies (Darby, Haltiwanger, and Plant [1986], Davis [1987, 2006],
Blanchard and Diamond [1990], Merz [1999], and Fujita and Ramey [2009]) has noted two
key stylized facts about worker ‡ows in the U.S. The …rst is that gross ‡ows increase when
unemployment increases. The second is that changes in in‡ows, St , tend to lead the changes
in out‡ows, Ft , as well as changes in the unemployment rate, ut . In what follows, we
con…rm that these stylized facts for the U.S. also hold for many other developed economies.

5.2

Evidence on Worker Flows in the OECD

Figures 6 and 7 depict the time series for our estimates of the number of workers ‡owing into
unemployment, St , and the number ‡owing out, Ft , together with the unemployment rate
for each country in our sample. In line with the di¤erences in the ‡ow hazard rates st and
ft between Anglo-Saxon Countries and Continental Europe, we …nd very large di¤erences
in average worker ‡ows between these groups of countries as well. The second column of
Table 4 contains the average worker ‡ows for all countries in our sample. These echo the
stark geographical partitioning of labor market ‡ows that we detailed above for the ‡ow
hazard rates across countries. Anglo-Saxon countries exhibit annual worker ‡ows in and out
of unemployment that comprise more than 15 percent of the labor force. The U.S. is once
more a conspicuous outlier with average annual worker ‡ows of 40 percent of the labor force.
At the opposite end of the spectrum again lie the economies of Continental Europe with
worker ‡ows that typically account for less than 10 percent of the labor force.
In addition, a prominent visual pattern to the timing of changes in these ‡ows emerges
from Figures 6 and 7. It can be seen that increases in the unemployment rate are often
preceded by rises in the number of workers ‡owing into the unemployment pool, followed
by a commensurate rise in the out‡ow. Thus, in most countries we observe that gross ‡ows
increase when unemployment rises, and that in‡ows tend to lead out‡ows, just as observed
in U.S. data.
This observation can be seen more formally using a simple correlation analysis. The
last six columns of Table 4 report the contemporaneous, lead, and lag correlations between
the changes in the ‡ows and changes in the unemployment rate. These correlations tell the
following story. In the year prior to a rise in unemployment, in‡ows into the unemployment
23

pool rise— the one year lead correlation between changes in in‡ows and contemporaneous
changes in unemployment is positive in almost all economies. Moreover, in‡ows remain high
in the year that unemployment rises— the contemporaneous correlation between changes in
in‡ows and changes in unemployment are positive for all countries. In the year following
an unemployment ramp up, out‡ows begin to rise— the one year lag correlation between
changes in out‡ows and contemporaneous changes in unemployment is positive in almost all
economies.
Thus, just like studies that use monthly data for the U.S., we …nd that changes in
in‡ows tend to lead changes in the unemployment rate in the annual data we use. What
emerges from our results on worker ‡ows is that, even though the OECD economies have very
di¤erent levels of ‡ows, the cyclical behavior of worker ‡ows across countries is very similar.
Economic downturns, in which the unemployment rate increases, …rst see an increase in
workers ‡owing into unemployment, rather than a decline in the number of workers ‡owing
out of it. Subsequently, the out‡ows increase as the economy recovers.
These results have stark implications for popular models of the aggregate labor market.
An important recent trend in these models has been to assume that in‡ow rate st into
unemployment is constant over the business cycle (Hall [2005a,b], Blanchard and Gali
[2006], Gertler and Trigari [2006], Krusell, Mukoyama, and Şahin [2010], for example). In
the context of these models, increases in unemployment during recessions are driven entirely
by declines in the job …nding hazard, ft .
This assumption has important implications for the dynamic properties of worker ‡ows
over the cycle. A rich literature on unemployment ‡ows in the U.S. has emphasized that
such models imply that increases in the unemployment rate are preceded by reductions in
the number of workers ‡owing out of the unemployment pool, Ft (Darby, Haltiwanger, and
Plant, 1985, 1986; Blanchard and Diamond, 1990; Davis, 2006). Consequently, reductions
in out‡ows are predicted to lead increases in the unemployment rate in this class of models.
In addition, because the in‡ow rate st is assumed constant, these models also imply that the
number of workers ‡owing into the unemployment pool St will decline modestly in the wake
of a recession as the employment rate 1 ut falls, so that changes in St lag changes in the
unemployment rate. Thus, models that assume a constant in‡ow rate have two important
predictions with regard to worker ‡ows: (i) when unemployment goes up gross worker ‡ows
decline, and (ii) out‡ows lead changes in unemployment, while in‡ows lag.
The studies of worker ‡ows in the U.S. cited above have established that neither of these
theoretical implications is borne out by the data for the U.S. This has led researchers to
24

challenge the empirical relevance of such models in the U.S. context (Davis [2006]; Fujita
and Ramey [2009]; Ramey [2008]). Our results reveal that the observation of increased
in‡ows as a leading indicator of increased unemployment, far from being unique to U.S.
data, is something close to a stylized fact for all modern developed labor markets.
These results con…rm and reinforce earlier …ndings based on earlier periods for subsets
of the European countries that we study. Using Portuguese microdata from the early 1990s,
Blanchard and Portugal (2001) emphasize that the levels of worker ‡ows are much lower in
Portugal relative to the U.S. Similar …ndings are reported by Bertola and Rogerson (1997,
Table 3) who document reduced worker ‡ows in Italy and Germany relative to Anglo-Saxon
counterparts using OECD data for 1988. Using data from France, Germany, Spain, and the
U.K. up to the early 1990s, Balakrishnan and Michelacci (2001) and Burda and Wyplosz
(1994) have highlighted that both in‡ows and out‡ows increased as European unemployment
soared in the 1970s and 1980s, with increased in‡ows leading increased unemployment.

6

Conclusion

Our analysis of publicly available data from the OECD provides four contributions to our
understanding of unemployment ‡ows. First, we present a method of estimating the ‡ow
hazard rates for entering and exiting unemployment across fourteen developed economies,
building on the method pioneered by Shimer (2007) for the U.S. An important bene…t of
this methodology is that it can be extended to estimate unemployment ‡ows for additional
economies over longer time periods as more data becomes available.
Application of this method to fourteen OECD countries uncovers a stark contrast in average ‡ow hazard rates between Anglo-Saxon, Nordic, and Continental European countries.
Anglo-Saxon and Nordic labor markets are characterized by high unemployment in‡ow and
out‡ow rates, while these ‡ow hazard rates in Continental European economies are generally
less than half of those in their Anglo-Saxon counterparts. Notably, results for the U.S. which
have received much attention in recent literature are a conspicuous outlier among developed
economies, with in‡ow and out‡ow rates that are at least …fty percent larger than the remaining economies in our sample. These results strengthen and extend earlier work that has
diagnosed European labor markets as sclerotic based on similar …ndings for subsets of the
economies we study.
Our second contribution is to devise a decomposition of unemployment ‡uctuations into
parts due to changes in in‡ow and out‡ow rates that can be applied to countries with very
25

di¤erent unemployment dynamics. Conventional decompositions applied to U.S. data have
exploited the fact that unemployment is closely approximated by its steady-state value in
the U.S. (Elsby, Michaels, and Solon [2009]; Fujita and Ramey [2009]). For many OECD
countries outside the U.S., however, we demonstrate that unemployment deviates considerably from its steady-state level. Consequently we show that conventional decompositions
lead to misleading results on the relative importance of ‡uctuations in in‡ow and out‡ow
rates for the dynamics of the unemployment rate. The results from applying our alternative
decomposition reveal approximately a 15:85 in‡ow/out‡ow contribution to unemployment
variation among Anglo-Saxon countries, whereas in most European countries the split is
much closer to 45:55.
Our third contribution is based on a simple correlation analysis of changes in worker
‡ows and changes in the unemployment rate over time. For all countries in our sample,
worker ‡ows tend to increase when unemployment increases. Moreover, we …nd that, in
almost all countries in our sample, changes in in‡ows into unemployment lead changes in
the unemployment rate, while changes in out‡ows tend to lag unemployment variation.
This con…rms and reinforces the conclusions of previous literature based on a smaller set of
countries, suggesting that these …ndings for worker ‡ows are a stylized fact of modern labor
markets.
Stepping back, our empirical …ndings provide an important perspective on the theoretical
literature on unemployment ‡ows that has evolved in recent years. Much of this recent
literature has assumed the in‡ow rate into unemployment to be an exogenous constant. As
a reaction to this, a number of studies of U.S. unemployment ‡ows has cautioned against
this trend (Elsby, Michaels, and Solon [2009], Fujita and Ramey [2009], and Yashiv [2007]).
A fourth contribution of the results of this paper is that the same conclusion extends to the
analysis of labor markets in a wide range of developed economies, and especially so if one is
interested in understanding the substantial changes in unemployment rates in Europe.

26

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30

A

Mathematical details

Estimation of Out‡ow Rates. De…ne the fraction of the labor force that has been unemployed
in month t for less than a month as u1;t , more than one but less than three months as u3;t , more
than three but less than six months as u6;t , more than six but less than twelve months u12;t , and
<3
more than 12 months as u1;t . Then u<1
t = u1;t , ut = u1;t +u3;t , etc. Given this data and quarterly
data for the unemployment rate, the four estimates of the out‡ow rate are
ft<1 =

ln (u3;t + u6;t + u12;t + u1;t ) +

ft<3 =

(ln (u6;t + u12;t + u1;t )

ft<6
ft<12

=
=

(ln (u12;t + u1;t )

(ln (u1;t )

ln ut

ln ut

ln ut

2
1
ln (u1;t + u3;t + u6;t + u12;t + u1;t ) + ln ut
3
3

3

,

3 ) =3,

6 ) =6,

and

12 ) =12.

(20)

In practice, we have annualized data for the duration distribution of unemployment for which
we do not know in which month of the year they are measures. Therefore, for our estimates of the
out‡ow rates average the lagged unemployment rates, ut 3 , ut 6 , and ut 12 over the four quarters
in the year for which the out‡ow rate is estimated.
Asymptotic Distribution of Out‡ow Rate Estimates. We do not observe the u1;t , u3;t ,
u6;t , u12;t , and u1;t . Instead we observe their sample approximations based on the labor force
surveys of the di¤erent countries. Let the sample size of the labor force survey be nt and let u
bd;t
d = 1; 3; 6; 12; 1 be the estimated fractions from the labor market survey. Moreover, we also observe
the estimated unemployment rate u
bt , not only at t but also at u
bt 3 , u
bt 6 , and u
bt 12 . We assume
that the sample of individuals in the labor force survey is independent across these realizations of
the unemployment rate and is of the same size nt = nt s where s = 3; 6; 12 and the sample sizes
are as given in Table 1.
These sample approximations have a joint multinomial distribution, such that
E (b
ud;t ) = ud;t and E (b
ut
and
var (b
ud;t ) =
as well as
var (b
ut

s)

=

1
ut
n

1
ud;t (1
n

s (1

ut

s)

ut =

= ut

s

for s = 0; 3; 6; 12.

ud ) and cov (b
ud ; u
bd0 ) =

and
De…ne the vector

s)

cov (b
ut ; u
bt

and cov (b
ud;t ; u
bt
s)

Vt =

"

(d)

Vt
03

1
u
bd u
bd0
n

(22)

= 0 for s = 3; 6; 12,

= 0 for s 6= 0.

u1;t u3;t u6;t u12;t u1;t ut

and the covariance matrix

s)

(21)

5

31

05 3
(u)
Vt

#

3

,

(23)
(24)

ut

6

ut

12

0

(25)

(26)

where

(d)
Vt

and

2

6
6
=6
6
4

u1;t (1 u1;t )
u1;t u3;t
u1;t u6;t
u1;t u12;t
u1;t u1;t
u1;t u3;t
u3;t (1 u3;t )
u3;t u6;t
u3;t u12;t
u3;t u1;t
u1;t u6;t
u3;t u6;t
u6;t (1 u6;t )
u6;t u12;t
u6;t u1;t
u1;t u12;t
u3;t u12;t
u6;t u12;t
u12;t (1 u12;t )
u12;t u1;t
u1;t u1;t
u3;t u1;t
u6;t u1;t
u12;t u1;t
u1;t (1 u1;t )
(u)

Vt

2

=4

ut

3 (1

ut

3)

0
0

0
ut

6 (1

ut

0
0

6)

0

ut

12 (1

ut

12 )

3
5

3

7
7
7 , (27)
7
5
(28)

and the o¤-diagonal zero matrices re‡ect that we assume independence of di¤erent samples in the
labor force surveys.
Assuming a relatively large sample of the labor force survey, nt , we can approximate
p

nt (b
ut

D

ut ) ! N (0; Vt )

(29)

1
Vt
nt

(30)

such that
bt
u

N

ut ;

We are not interested in this distribution. Instead, we are interested in three estimates of the out‡ow
rate, each of which is a consistent estimate if there is no duration dependence in the out‡ow rate
during the …rst year of unemployment. De…ne the vector
ft =

ft<1 ft<3 ft<6 ft<12

0

(31)

then we will use the Delta-method to derive the asymptotic distribution of b
f for n ! 1.32 In order
to do so, we consider the following gradient.
2
30
2
0
0
0
3ut
1
6 2
7
0
0
0
6 3ut ut u<1
7
t
6 2
7
1
1
6 3u
7
0
0
3(ut u<3
6 t ut u<1
7
t
t )
6 2
7
1
1
1
0
6
7
<1
<3
<6
@ft
3u
t
u
u
3
u
u
6
u
u
t
( t t )
( t t )
7
t
= 6
(32)
Df;t =
0
6
7
2
1
1
1
1
@ut
6 3ut ut u<1
7
<3
<6
<12
3(ut ut )
6(ut ut )
12(ut ut ) 7
t
6
1
1
6
7
0
0
6
7
3ut 3
3ut 3
6
7
1
0
0
0
4
5
6ut 6
1
0
0
0
12ut 12
This allows us to write the approximate distribution of b
ft as
32

b
ft

N

1
ft ; Df;t Vt D0f;t
n

(33)

Note that we assume that the level of unemployment, ut , is measured without any measurement error.

32

It is this distribution that we are going to use for the derivation of our hypothesis test as well as for
the calculation of the "optimal" weighting of the di¤erent out‡ow rate estimates for our estimated
out‡ow rate.
Hypothesis Test for No Duration Dependence. If there is no duration dependence, then it
is the case that
H0 : ft = f , where f is scalar and is a vector with ones
(34)
which is the null-hypothesis of interest. For our
2
1
Mf = 4 0
0

test, we de…ne the matrix
3
0 0
1
1 0
1 5
0 1
1

Under the null-hypothesis, it is the case that
Mf b
ft

N

1
0; Mf Df;t Vt D0f;t M0f
n

(35)

(36)

De…ne the Choleski-decomposition matrix C as
Mf Df;t Vt D0f;t M0f = Ct C0t
Then

p

nCt 1 Mf b
ft

(37)

N (0; I3 )

(38)

Remember that the sum of squares of 3 independent standard normally distributed random variables
is chi-squared distributed with 3 degrees of freedom. Hence, when we de…ne
gt = nb
ft0 M0f C0t

1

Ct 1 Mf b
f

= nb
ft0 M0f Mf Df;t Vt D0f;t M0f

then, under the null it is the case that

gt

2

(3) .

(39)
1

Mf b
ft
(40)

Optimal Weighting of Estimated Out‡ow Rates. For those countries for which we do not
reject the null-hypothesis for reasonably large sample sizes and for the majority of the years, we
then have to decide on the optimal weighting of the estimated …nding rates. That is, we want to
…nd vector with weights, w, and estimate

such that

fbt = wt0 b
ft
wt0 = 1

33

(41)

(42)

and that, given this constraint, w minimizes
Vf;t = wt0 Df;t Vt D0f;t wt

(43)

Let us …rst take care of the restriction. For this purpose, de…ne

such that

2

3 2
0
6 0 7 6
7 6
= 6
4 0 5+4
1
et
= e1 + Mw w

wt

0

wt<1 wt<3 wt<6

et =
w

1
0
0
1

(44)

3
0
0 7
7w
e
1 5 t
1

0
1
0
1

(45)
(46)

Then the objective function can be written as

et + w
e t0 M0w Df;t Vt D0f;t Mw w
et
Vf;t = e01 Df;t Vt D0f;t e1 + 2e01 Df;t Vt D0f;t Mw w

(47)

which yields that the set of optimal weights is
et =
w

and thus

wt = e1

1

M0w Df;t Vt D0f;t Mw

M0w Df;t Vt D0f;t e1
1

Mw M0w Df;t Vt D0f;t Mw

(48)

M0w Df;t VD0f;t e1

(49)

Note, this only imposes that the weights add up to one but not that they are positive.
Dynamic Decomposition of Changes in Unemployment. Note that the unemployment rate
at the end of year t evolves according to
ut =

t ut

+ (1

t ) ut 1 ;

(50)

where t
1 e 12(st +ft ) is the annual rate of convergence to steady state, ut
st = (st + ft ) is
the steady state unemployment rate, and st and ft are respectively the monthly unemployment
in‡ow and out‡ow hazard rates in year t. A log–linear approximation to (50) around st = st 1 ,
ft = ft 1 , and ut 1 = ut 1 is given by
ln ut

ln ut

1

+

t 1

ln ut

ln ut

ln ut

1

+

t 1

1

1

ut

[

1

+ (1

ln st

t 1)

ln ut

ln ft ] + (1

1

ln ut

t 1)

(51)

1

ln ut

1

ln ut

1

:

(52)

If unemployment is always in steady state, then
ln ut =

ln ut

1

ut

1

[

ln st

ln ft ]

(53)

However, if unemployment deviates from steady state, then this approximation is not appropriate.

34

In that case, it is worthwhile to realize that
ln ut

ln ut

1

=

t 1

ln ut

ln ut

1

t 1

ln ut

=

t 1

ln ut

ln ut

1

t 1

ln ut

=

t 1 (ln ut

ln ut ) +

t 1 (ln ut

ln ut

1

ln ut
ln ut

1

(54)

1

+

t 1 (ln ut

ln ut

1)

1)

such that
t 1

ln ut

1

and thus
(ln ut

(ln ut

t 1

ln ut ) =

1

ln ut )

(55)

ln ut

(56)

t 1
t 1

Substituting this into (51) we can write
ln ut

t 1

1

ut

1

[

ln st

ln ft ] +

1

t 2

ln ut

1

.

(57)

t 2

Which allows us to do the decomposition out of steady state.
E¤ect of Inclusion of Non-Participants. Equation (1) does not take into account ‡ows that
stem from people that are not-in-the-labor-force (NILF) that start looking for a job and become
unemployed. It also does not include persons that ‡ow out of unemployment as well as out of the
labor force. In addition, it normalizes the size of the labor force to one, thus not taking into account
labor force growth. We have actually calculated a set of results that allow for these things, but for
the sake of clarity have abstracted from them in the analytical framework applied here. It turns
out that including these things does not a¤ect the results much. Below we explain why.
The …rst thing to note is that our estimates of the out‡ow rate out of unemployment solely
use unemployment data and are not a¤ected by the simplifying assumptions described above. The
out‡ow rate basically determines the total out‡ows out of unemployment. Since the change in the
number of unemployed persons is the di¤erence between the in‡ows and the out‡ows, this implies
that the total in‡ows into unemployment are also not sensitive to these simplifying assumptions.
The only thing that is a¤ected is the in‡ow rate. In our framework, the in‡ow rate re‡ects the
fraction of employed persons that ‡ows into unemployment. Without the simplifying assumption
the in‡ow rate would re‡ect the fraction of persons that are either employed or NILF that ‡ow
into unemployment. In e¤ect, if one would drop our simplifying assumption one would …nd a lower
in‡ow rate that is scaled down by the labor force participation rate. For all countries in the sample,
labor force growth is so small that it is swamped by the magnitude of worker ‡ows. Hence, the
results presented here turn out to be almost identical to the ones that take into account labor force
growth.

35

36

http://stats.oecd.org/mei/default.asp?lang=e&subject=10.

Note: Sample sizes include non-labor force members. Information based on metadata for OECD (2008b), available at

United States: Data comes from the monthly CPS. Each month about 60,000 households are interviewed for the survey. (We use n = 130; 000.)

use n = 120; 000.)

United Kingdom: Survey is conducted continuously throughout the year. In any three-month period, 57,000 households are interviewed (120,000 persons). (We

Sweden: Participation is voluntary. Every month about 20,000 persons are included in the sample. (We use n = 20; 000.)

n = 185; 000.)

Spain: Sample includes 74,000 households; however in practice only about 65,000 households (i.e. approximately 185,000 persons) are interviewed. (We use

Portugal: Sample size approximately 21,000 households. (We use n = 52; 500.)

Norway: Sample size is 12,000 households (24,000 persons). Includes all armed forces.(We use n = 24; 000.)

are excluded from the sample. (We use n = 40; 000.)

New Zealand: Obtained from 16,000 private dwellings (approximately 32,000 persons) each quarter. From 2nd quarter of 1995, residents in non-private households

Japan: The survey covers a sample of 40,000 households. (We use n = 100; 000.)

Italy: The sample was doubled in April 1990 from 12,000 to 24,000 households. (We use n = 60; 000.)

Ireland: Sample of 39,000 households is surveyed each quarter. Includes career military living in private households. (We use n = 97; 500.)

Germany: The average quarterly sample in 2005 comprises about 165,000 respondents. (We use n = 165; 000.)

n = 150; 000.)

Previously, the Survey was annual. In March 2001, 75,000 households responded to the survey covering 150,000 persons which includes armed forces. (We use

France: Data are compiled from various sources including the Labor Force Survey (“Employment Survey”). Since 2003, the Survey is quarterly and continuous.

Canada: Approximately 56,000 households since 1976. (We use n = 135; 000.)

Australia: Survey covers about 0.5% of Australia’s population. (We use n = 57; 000.)

Table 1: Approximate sample sizes of Labor Force Surveys

37
1986
1977
1976
1983
1968

Portugal

Spain

Sweden

United Kingdom

United States

0%

0%

0%

0%

0%

0%

1%

1%

5%

2%

3%

0%

0%

0%

included

P-value
f <1

0%

1%

1%

5%

10%

1%

0%

0%

9%

11%

2%

7%

0%

0%

excluded

P-value
f <1
Rejected?

H0

6.1%

7.7%

4.3%

15.4%

6.2%

4.1%

6.4%

3.3%

9.8%

10.8%

8.3%

8.1%

8.5%

7.1%

rate (u)

Unemployment

56.5%

13.9%

29.2%

6.3%

6.3%

38.5%

28.5%

18.9%

4.3%

5.9%

6.0%

7.7%

26.1%

22.8%

rate (f )

Out‡ow

Sample averages

3.6%

1.0%

1.2%

1.1%

0.4%

1.6%

1.7%

0.6%

0.4%

0.6%

0.5%

0.7%

2.4%

1.7%

rate (s)

In‡ow

to

H0 : ft<3 = ft<6 = ft<12 :

H0 : ft<1 = ft<3 = ft<6 = ft<12 :

The hypothesis ‘f <1 excluded’refers
signi…cance level.

The rejection of the null of no duration dependence is based on the second hypothesis and determined at a 1%

the sample size reported in Table 1. The hypothesis ‘f <1 included’refers to

Note: Reported P-values are sample averages for the test for no duration dependence over the sample period, based on the application of

1983

1983

Italy

Norway

1983

Ireland

1986

1983

Germany

New Zealand

1975

France

1977

1976

Japan

1978

Australia

sample

Start of

Canada

Country

Test for no duration dependence

Table 2: Test for no duration dependence and summary statistics on unemployment and ‡ow rates

38
9.0%
1.3%
1.1%
0.4%
13.0%
9.9%
1.5%
3.0%
0.2%

Japan

New Zealand

Norway

Portugal

Spain

Sweden

United Kingdom

United States

8.5%

Germany

Italy

5.1%

France

14.2%

0.6%

Canada

Ireland

1.3%

% dev. from ss

Australia

Country

std. dev. of

0.85

0.91

0.50

0.76

0.94

0.55

0.90

0.61

1.08

0.80

0.92

0.75

0.80

0.96

f

0.16

0.22

0.53

0.50

0.42

0.46

0.13

0.48

0.43

0.77

0.56

0.62

0.24

0.11

s

-0.01

-0.12

-0.03

-0.25

-0.36

0.00

-0.03

-0.09

-0.51

-0.57

-0.48

-0.37

-0.05

-0.07

residual

Steady-state decomposition

0.85

0.85

0.50

0.57

0.68

0.54

0.88

0.56

0.83

0.47

0.56

0.54

0.79

0.93

f

0.16

0.17

0.51

0.43

0.32

0.45

0.13

0.45

0.15

0.55

0.47

0.45

0.23

0.10

s

0.00

0.00

0.00

0.01

0.00

0.01

0.00

0.00

0.05

0.00

0.00

0.02

0.00

0.00

0

-0.01

-0.02

-0.01

-0.01

0.00

0.00

-0.01

-0.01

-0.03

-0.02

-0.03

-0.01

-0.02

-0.03

residual

Non-steady-state decomposition

Table 3: Decompositions of unemployment ‡uctuations

39

Note: The column

1
2

(F + S)

.2

-.4

.0

.1

-.1

.1

.0

.1

-.4

.0

-.1

-.1

-.2

-.6

k=
1

-.1

-.1

.4

-.1

-.2

.3

-.2

.1

-.2

-.2

-.2

-.1

.0

-.4

.3

.4

.8

.5

.6

-.2

.2

.0

.5

.7

.5

.6

.6

.5

k=1

Ft+k )

k=0

corr ( ut ;

.5

-.1

.3

.7

.3

.2

.3

.2

-.1

.3

.6

.2

.0

-.3

k=
1

.4

.2

.7

.6

.5

.4

.2

.3

.2

.6

.5

.7

.3

.2

-.2

.2

.6

.2

.2

-.3

-.1

-.1

.1

.4

-.2

-.1

.3

.1

k=1

St+k )

k=0

corr ( ut ;

list the average of the average in and out‡ow rates over the sample period.

40.0%

United States

17.9%

Norway

11.7%

19.5%

New Zealand

United Kingdom

7.0%

Japan

13.3%

4.8%

Italy

Sweden

6.4%

Ireland

4.6%

5.9%

Germany

10.5%

7.3%

France

Spain

25.9%

Canada

Portugal

18.4%

(F + S)

Australia

Country

1
2

Table 4: Average worker ‡ows and correlations with changes in the unemployment rate

Figure 1: Average in- and out‡ow rates across countries.

40

Figure 2: In- and out‡ow rates (log-scale in percentages) for Anglo-Saxon and Nordic countries, and Japan

41

Figure 3: In- and outlfow rates (log-scale in percentages) for Continental European countries.

42

Figure 4: Actual versus steady state unemployment in four illustrative countries.

43

Figure 5: Steady-state versus non-steady-state decomposition of unemployment ‡uctuations
for France.

44

Figure 6: Unemployment rate and worker ‡ows, Anglo-Saxon and Nordic countries, and
Japan.

45

Figure 7: Unemployment rate and workers ‡ows, Continental European countries.

46