WORKING PAPER NO. 07-19/R
THE CYCLICALITY OF SEPARATION AND
JOB FINDING RATES
Shigeru Fujita
Federal Reserve Bank of Philadelphia
and
Garey Ramey
University of California, San Diego
January 2008
The Cyclicality of Separation and Job Finding Rates
∗
Shigeru Fujita
†
and Garey Ramey
‡
January 2008
Abstract
This paper uses CPS gross flow data to analyze the business cycle dynamics of
separation and job finding rates and to quantify their contributions to overall unem-
ployment variability. Cyclical change s in the separation rate are negatively corr e lated
with changes in productivity and move contemporaneously with them, while the job
finding rate is positively correla ted with and tends to lag productivity. Contem-
poraneous fluctuations in the separa tion rate explain between 4 0 and 50 percent of
fluctuations in unemployment, depending on how the data are detrended. T his figure
becomes larger when dynamic interactions between the separation and job finding
rates are considered.
JEL codes: J6 3, J64
Keywords: Separation rate, Job finding rate, Unemployment, CPS worker flows
∗
This paper incorporates material from Fujita and Ramey (2006, 2007). For helpful comments, we thank
Bj¨orn Br¨ugeman, Francisco Covas, Steve Davis, Wouter Den Haan, Bruce Fallick, Marjorie Flavin, Iourii
Manovskii, Ronni Pavan, Vincenzo Quadrini, Valerie R amey, numerous anonymous referees, and seminar
participants at Bank of Canada, Federal Reserve Banks of Philadelphia, Rich mond, and San Francisco,
USC, and UCSD. We are also grateful to Rob Shimer for making his series readily available at his webpage.
Jacob Goldston provided excellent research assistance. The views expressed here are those of the authors
and do not necessarily represent the views of the Federal Reserve Bank of Philadelphia or the Federal
Reserve System. This paper is available free of charge at www.philadelphiafed.org/econ/wps/index.html.
†
Federal Reserve Bank of Philadelphia; Email: shigeru.fujita@phil.frb.org
‡
University of California San Diego; Email: gramey@ucsd.edu
1 Introduction
The empirical behavior of U.S. job loss and hiring over the business cycle remains an
elusive and controversial subject, despite decades of research. While much early work
considered gross flows of workers and jobs , more recent papers have stressed the importance
of transition rates faced by individual workers.
1
Furthermore, researchers have highlighted
the variability of unemployment as a key measure of aggregate labor market activity.
2
In this paper we assess the cyclical behavior of worker transition rates into and out of
unemployment for th e aggregate U.S. labor market. We focus on two s pecific dimensions
of cyclical behavior. First, how do separation and j ob finding rates comove with the
business cycle? Second, to what extent do movements in these rates contribute to overall
unemployment variability?
3
These questions are central to evaluating the relative roles of separation versu s job
finding activity in explaining unemployment movements. Higher unemployment during
downturns might be triggered by higher separation rates, which generate waves of job loss.
Alternatively, an initial phase of low j ob fin ding rates m ay drive unemployment upward.
Sorting out the timing and magnitude of these channels is important for understanding
the mechanisms that underlie unemployment fluctuations.
This paper addresses these issues by analyzing gross flow data from the Current Pop-
ulation Survey (CPS) over the 1976-2006 period. The data are adjusted for margin error
in line with the approach of Abowd and Zellner (1985). We measure quarterly separation
and job findin g hazard rates using Shimer’s (2005a) time aggregation correction. Comove-
ment is analyzed by considering the correlations between the two hazard rates and labor
productivity at various leads and lags. To quantify the contributions of separation and job
finding rates, we decompose total unemployment variations into components that depend
separately on each rate. We consider both HP filtering and first differencing as methods
1
For analyses of gross worker and job flows, see Poterba and Summers (1984, 1986), Abowd and Zellner
(1985), Darby et al. (1986), Davis (1987), Blanchard and Diamond (1989, 1990), Davis and Haltiwanger
(1992), Davis et al. (1996), Bleakley et al. (1999), Fallick and Fleisch man (2004), Nagyp´al (2004), Fujita
and Ramey (2006, 2007), Fujita et al. (2007) and Yashiv (2006a,b). Transition hazard rates have been
considered in Nagyp´al (2004), Hall (2005a), Shimer (2005a,b), Elsby et al. (2007), Fujita and Ramey (2006,
2007), Fujita et al. (2007) and Yashiv (2006a,b).
2
Hall (2005b) and Shimer (2005b) stress the salience of unemp loyment variability as a statistic for
evaluating job matching models.
3
Throughout the paper we use the terms “separation” and “job finding” to d enote movements of workers
out of and into employed status. Thus, we do not consider movements directly between jobs.
1
for detrending the data.
Our results show that the separation rate is highly countercyclical, having a peak cor-
relation with productivity of -0.58 in the HP filtered data, and -0.22 in the first differenced
data.
4
Moreover, the peaks are achieved at a lag of zero, and the correlations at other hori-
zons are roughly sym metric about zero. This means that changes in the separation rate
occur contemporaneously with th e produ ctivity. For the job finding rate, in contrast, the
correlations are positive, and their peak occurs at leads of two to three quarters, meaning
that the job finding rate tends to trail the cycle.
5
To evaluate the direct comovement between the separation and job finding rates, we
evaluate their cross correlations. Peaks are attained when the separation rate is lagged
by one quarter, at values of roughly -0.7 and -0.4 in th e HP filtered and first differenced
data, respectively. Thus, the separation rate leads the job finding rate.
To analyze the contributions of the hazard rates to unemployment variability, we f ollow
Shimer (2005a) by approximating the unemployment rate using th e theoretical steady state
value associated with th e contemporaneous separation and job finding rates. This allows
unemployment variability to be readily decomposed by means of a conventional factor
analysis. In the HP filtered data, fluctuations in the separation rate relative to trend
explain 41 percent of overall fluctuations in unemployment. The figure rises to 51 percent
in the first differenced data. We conclude that both job fi nding and separation rates are
important in accounting for unemployment variability.
We also consider the contributions of the separation and job finding rates since 1985.
For this subsample, we find that the separation rate explains 34 and 46 percent of un-
employment fluctuations under the respective filtering method s . Thus, although the sep-
aration rate explains a smaller proportion in recent decades, its contribution remains
substantial.
The aforementioned decompositions abstract from dynamic interactions. As such, they
may understate the role of the separation rate, since fl uctuations in the separation rate
are negatively correlated with future changes in the job finding rate, and thus with future
unemployment fluctuations. To investigate this effect, we recast our decompositions to
4
Note that it is natural for the correlations to be smaller in magnitude when the first difference filter is
used.
5
We also consider cross correlations between the hazard rates and unemployment. We find that the
separation rate leads unemployment, while the job finding rate moves contemporaneously with it. This is
consistent with our productivity results, since unemp loyment tends to lag productivity.
2
reflect the contributions of current and past variations in the separation an d job finding
rates to unemployment variability. In this case, the proportion of unemployment variability
explained by the separation rate rises to 60-70 percent over the fu ll sample. Thus, th e
contemporaneous decompositions may understate the true importance of the separation
rate.
Our findings bear on the current debate over the cyclical behavior of the separation
rate. Using both gross flow- and unemploy ment duration-based data derived from the CPS,
Shimer (2005a) argues that once time aggregation bias is taken into account, measured
separation rates are nearly acyclic and play a small role in explaining unemployment fluc-
tuations. We find, however, that the separation rate is highly countercyclical, even when
we consider Shimer’s own data. Shimer models unemployment variability by construct-
ing “counterfactual” unemployment approximations that hold the separation or the job
finding rates constant at their historical averages. Our m ethod, on the other hand, decom-
poses unemployment flu ctuations into two linear terms, corresponding to the respective
contributions of the separation and job finding rates. T his allows us to carry out a variance
decomposition of unemployment fluctuations in a s ys tematic manner. When our method
is applied to Shimer’s data sets, we find that the separation rate explains between 28 and
56 percent of unemployment variability. Thus, the explanatory power of the sep aration
rate is substantial by any measure.
In evaluating Shimer’s duration-based findings, Elsby et al. (2007) interpret the first
differences of separation and job finding rates as a d ecomposition of unemp loyment vari-
ability. Their evidence suggests a more substantial role for separation rates than that
suggested by Shimer, particularly when job loss is distinguished from labor force entry.
We build on their approach by developing an exact decomposition of unemployment vari-
ability and extending the method to fluctuations in the unemployment level. Yashiv
(2006a,b) carefully analyzes several existing data sources to discern the cyclical pr oper-
ties of U.S. gross worker flows and transition hazard rates. Among other findings, he
shows that separation rates are strongly countercyclical and job finding rates are strongly
procyclical when real GDP is used as the cyclical indicator.
The paper pr oceeds as f ollows. Section 2 describes the d ata construction, Section 3
evaluates comovement, Section 4 considers the decomposition of unemployment variability,
and Section 5 concludes.
3
