THE CYCLICALITY OF SEPARATION AND JOB FINDING RATES

INTERNATIONAL ECONOMIC REVIEWVol. 50, No. 2, May 2009

THE CYCLICALITY OF SEPARATION AND JOB FINDING RATES∗

BY SHIGERU FUJITA AND GAREY RAMEY1

Federal Reserve Bank of Philadelphia, U.S.A.;University of California–San Diego, U.S.A.

This article uses CPS gross flow data to analyze the business cycle dynamicsof separation and job finding rates and quantify their contributions to overallunemployment variability. Cyclical changes in the separation rate are negativelycorrelated with changes in productivity and move contemporaneously with them,whereas the job finding rate is positively correlated with and tends to lag pro-ductivity. Contemporaneous fluctuations in the separation rate explain between40 and 50% of fluctuations in unemployment, depending on how the data aredetrended. This figure becomes larger when dynamic interactions between theseparation and job finding rates are considered.

1. INTRODUCTION

The empirical behavior of U.S. job loss and hiring over the business cycle remainsan elusive and controversial subject, despite decades of research. Although muchof the early work considered gross flows of workers and jobs, more recent papershave stressed the importance of transition rates faced by individual workers.2

Furthermore, researchers have highlighted the variability of unemployment as akey measure of aggregate labor market activity.3

In this article, we assess the cyclical behavior of worker transition rates intoand out of unemployment for the aggregate U.S. labor market. We focus on twospecific dimensions of cyclical behavior. First, how do separation and job finding

∗ Manuscript received December 2006; revised August 2007.1 For helpful comments, we thank Bjorn Brugeman, Francisco Covas, Steve Davis, Wouter Den

Haan, Bruce Fallick, Marjorie Flavin, Iourii Manovskii, Ronni Pavan, Vincenzo Quadrini, ValerieRamey, numerous anonymous referees, and seminar participants at Bank of Canada, Federal Re-serve Banks of Philadelphia, Richmond, and San Francisco, USC, and UCSD. We are also gratefulto Rob Shimer for making his series readily available at his Web page. Jacob Goldston provided ex-cellent research assistance. The views expressed here are those of the authors and do not necessarilyrepresent the views of the Federal Reserve Bank of Philadelphia or the Federal Reserve System.Please address correspondence to: Shigeru Fujita, Research Department, Federal Reserve Bank ofPhiladelphia, Ten Independence Mall, Philadelphia, PA 19106, U.S.A. Phone: 215-574-3957. E-mail:[email protected].

2 For analyses of gross worker and job flows, see Poterba and Summers (1984, 1986), Abowdand Zellner (1985), Darby et al. (1986), Davis (1987), Blanchard and Diamond (1989, 1990), Davisand Haltiwanger (1992), Davis et al. (1996), Bleakley et al. (1999), Fallick and Fleischman (2004),Nagypal (2004), Fujita and Ramey (2006, 2007), Fujita et al. (2007), and Yashiv (2006, 2007). Transi-tion hazard rates have been considered in Nagypal (2004), Hall (2005b), Shimer (2005a, 2005b), Elsbyet al. (2009), Fujita and Ramey (2006, 2007), Fujita et al. (2007), and Yashiv (2006, 2007).

3 Hall (2005a) and Shimer (2005a) stress the salience of unemployment variability as a statistic forevaluating job matching models.

415C© (2009) by the Economics Department of the University of Pennsylvania and the Osaka UniversityInstitute of Social and Economic Research Association

416 FUJITA AND RAMEY

rates comove with the business cycle? Second, to what extent do movements inthese rates contribute to overall unemployment variability?4

These questions are central to evaluating the relative roles of separation versusjob finding activity in explaining unemployment movements. Higher unemploy-ment during downturns might be triggered by higher separation rates, which gen-erate waves of job loss. Alternatively, an initial phase of low job finding rates maydrive unemployment upward. Sorting out the timing and magnitude of these chan-nels is important for understanding the mechanisms that underlie unemploymentfluctuations.

This article addresses these issues by analyzing gross flow data from the CurrentPopulation Survey (CPS) over the 1976–2005 period. The data are adjusted formargin error in line with the approach of Abowd and Zellner (1985). We mea-sure quarterly separation and job finding hazard rates using Shimer’s (2005b) timeaggregation correction. Comovement is analyzed by considering the correlationsbetween the two hazard rates and labor productivity at various leads and lags.In order to quantify the contributions of separation and job finding rates, we de-compose total unemployment variations into components that depend separatelyon each rate. We consider both HP filtering and first differencing as methods fordetrending the data.

Our results show that the separation rate is highly countercyclical, having apeak correlation with productivity of −0.58 in the HP filtered data, and −0.22 inthe first differenced data.5 Moreover, the peaks are achieved at a lag of zero, andthe correlations at other horizons are roughly symmetric about zero. This meansthat changes in the separation rate occur contemporaneously with productivity.For the job finding rate, in contrast, the correlations are positive, and their peakoccurs at leads of two to three quarters, meaning that the job finding rate tends totrail the cycle.6

In order to evaluate the direct comovement between the separation and jobfinding rates, we evaluate their cross correlations. Peaks are attained when theseparation rate is lagged by one quarter, at values of roughly −0.7 and −0.4 in theHP filtered and first differenced data, respectively. Thus, the separation rate leadsthe job finding rate.

In order to analyze the contributions of the hazard rates to unemploymentvariability, we follow Shimer (2005b) by approximating the unemployment rateusing the theoretical steady-state value associated with the contemporaneous sep-aration and job finding rates. This allows unemployment variability to be readilydecomposed by means of a conventional factor analysis. In the HP filtered data,fluctuations in the separation rate relative to trend explain 41% of overall fluctu-ations in unemployment. The figure rises to 51% in the first differenced data. We

4 Throughout the article, we use the terms “separation” and “job finding” to denote movements ofworkers out of and into employed status. Thus, we do not consider movements directly between jobs.

5 Note that it is natural for the correlations to be smaller in magnitude when the first differencefilter is used.

6 We also consider cross correlations between the hazard rates and unemployment. We find thatthe separation rate leads unemployment, whereas the job finding rate moves contemporaneously withit. This is consistent with our productivity results, since unemployment tends to lag productivity.

SEPARATION AND JOB FINDING RATES 417

conclude that both job finding and separation rates are important in accountingfor unemployment variability.

We also consider the contributions of the separation and job finding rates since1985. For this subsample, we find that the separation rate explains 34% and 46% ofunemployment fluctuations under the respective filtering methods. Thus, althoughthe separation rate explains a smaller proportion in recent decades, its contributionremains substantial.

The aforementioned decompositions abstract from dynamic interactions. Assuch, they may understate the role of the separation rate, since fluctuations inthe separation rate are negatively correlated with future changes in the job find-ing rate and thus with future unemployment fluctuations. In order to investigatethis effect, we recast our decompositions to reflect the contributions of currentand past variations in the separation and job finding rates to unemployment vari-ability. In this case, the proportion of unemployment variability explained bythe separation rate rises to 60–70% over the full sample. Thus, the contempo-raneous decompositions may understate the true importance of the separationrate.

Our findings bear on the current debate over the cyclical behavior of the separa-tion rate. Using both gross flow- and unemployment duration-based data derivedfrom the CPS, Shimer (2005b) argues that once time aggregation bias is taken intoaccount, measured separation rates are nearly acyclic and play a small role in ex-plaining unemployment fluctuations. We find, however, that the separation rate ishighly countercyclical, even when we consider Shimer’s own data. Shimer modelsunemployment variability by constructing “counterfactual” unemployment ap-proximations that hold the separation or the job finding rates constant at theirhistorical averages. Our method, on the other hand, decomposes unemploymentfluctuations into two linear terms, corresponding to the respective contributionsof the separation and job finding rates. This allows us to carry out a variancedecomposition of unemployment fluctuations in a systematic manner. When ourmethod is applied to Shimer’s data sets, we find that the separation rate explainsbetween 28 and 56% of unemployment variability. Thus, the explanatory powerof the separation rate is substantial by any measure.

In evaluating Shimer’s duration-based findings, Elsby et al. (2009) interpretthe first differences of separation and job finding rates as a decomposition ofunemployment variability. Their evidence suggests a more substantial role forseparation rates than that suggested by Shimer, particularly when job loss is dis-tinguished from labor force entry. We build on their approach by developing anexact decomposition of unemployment variability and extending the method tofluctuations in the unemployment level. Yashiv (2006, 2007) carefully analyzesseveral existing data sources to discern the cyclical properties of U.S. gross workerflows and transition hazard rates. Among other findings, he shows that separationrates are strongly countercyclical and job finding rates are strongly procyclicalwhen real GDP is used as the cyclical indicator.

The article proceeds as follows. Section 2 describes the data construction, Sec-tion 3 evaluates comovement, Section 4 considers the decomposition of unem-ployment variability, and Section 5 concludes.


2. DATA

We consider measures of separation and job finding rates derived using monthlydata from the CPS for the period 1976–2005. Month-over-month transitions by in-dividual workers between employed, unemployed, and not-in-labor-force (NILF)status can be measured by matching workers who are sampled in consecutivemonths. Owing to sample rotation and temporary absences of individuals, transi-tion information is unavailable for a substantial subset of the sample. This failureto match individual workers across months is referred to as margin error, and itleads to omission of possible transitions from the survey data.

The most common correction for margin error, the missing-at-random (MAR)method, simply drops the missing observations and reweights the transitions thatare measured. This procedure leads to biases, however, if types of transitionsdiffer in their likelihood of omission. Following the important work of Abowdand Zellner (1985), we use an alternative correction that employs information onworker stocks. In particular, the MAR-based worker flow measures are reweightedin a manner that minimizes the discrepancies between officially reported stocks ofworkers and the stocks that would be imputed from the flow measures. See Fujitaand Ramey (2006) for details of our margin error correction.

A second problem with the data concerns the point-in-time measurement ofworker status, which fails to capture transitions that are reversed within the month.In order to correct for this, we use the method suggested by Shimer (2005b), whichlinks the month-over-month gross flow measures to underlying continuous-timeadjustment equations.7 Let eut and uet denote the margin error-adjusted grossflows from employment to unemployment and from unemployment to employ-ment, respectively, and let et−1 and ut−1 indicate the measured stocks of employedand unemployed workers, respectively. Then, the average monthly separation andjob finding rates are determined by

st = eut

et−1, f t = uet

ut−1.(1)

Assume that actual worker transitions are determined by a continuous-time pro-cess under which separation and job finding events arrive at constant rates withinthe month. The continuous-time separation and job finding hazard rates, denotedby st and f t , will satisfy

st = st(1 − e−(st + ft )

)st + ft

, f t = ft(1 − e−(st + ft )

)st + ft

.(2)

We use formulas (1) and (2) to compute our hazard rate series st and f t fromthe adjusted CPS data. These monthly series are then converted to quarterly fre-quency by simple averaging. The resulting series cover the sample period 1976Q1–2005Q4.

7 See Shimer (2005b), footnote 9.


For comparison purposes, we consider two additional sets of measures con-structed by Shimer, based on CPS gross flow and unemployment duration data,respectively. In his gross flow-based series, margin error is handled using the MARprocedure, whereas time aggregation error is corrected using the method discussedabove. His duration-based series are adjusted for time aggregation error using arelated method. See Shimer (2005b) for further details concerning his data con-struction.8

3. BUSINESS CYCLE COMOVEMENT

In this section, we assess the dynamic relationships at business cycle frequenciesbetween the separation and job finding rates, st and f t , and labor productivity.9

The dynamic relationships are measured in terms of cross correlations at variousleads and lags. We consider both HP filtering and first differencing. For the HPfilter, we use the standard smoothing parameter of 1600.

Results for the two detrending methods are shown in Figure 1. For HP filtereddata, the separation rate and productivity achieve a peak correlation of −0.58at a lag of zero. Moreover, the correlations at other leads and lags are roughlysymmetric about zero. This means that the separation rate is highly countercyclicaland adjusts contemporaneously with the cycle. When the first difference filter isused, the magnitudes of the correlations are naturally reduced. However, onecan see in the upper right panel of the figure that the same dynamic pattern ispreserved.

The correlation between the job finding rate and productivity peaks at 0.60 ata lead of two to three quarters in the HP filtered data. Thus, the job finding rateis highly procyclical and trails the cycle. A similar pattern may be observed in thefirst differenced data.

In order to assess the robustness of these findings to the choice of cyclical indi-cator, Figure 2 repeats the exercise using unemployment in place of labor produc-tivity. The correlation between the separation rate and unemployment lies above0.50 at lags of zero to four quarters in the HP filtered data, whereas the correlationbetween unemployment and the future separation rate reaches almost 0 after fourquarters. Thus, the separation rate leads unemployment. This dynamic pattern ispreserved in the first differenced data. The job finding rate and unemploymentexhibit strong negative correlation, and the job finding rate moves roughly con-temporaneously with unemployment. These results conform to the preceding onesin that unemployment is a lagging indicator of the business cycle. We concludethat the separation rate is highly countercyclical and moves contemporaneouslywith the cycle, whereas the job finding rate is highly procyclical and trails thecycle.

8 Sample periods are 1967Q2–2004Q4 for the gross flow-based data and 1951Q1–2004Q4 for theduration-based data. The data are available at Shimer’s Web page, http://robert.shimer.googlepages.com/flows.

9 We measure labor productivity as GDP divided by the number of employed persons reported inthe CPS.


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Correlations between prodt and sep. rate

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NOTES: Sample covers 1976Q1–2005Q4. Transition rate series are adjusted for margin error and timeaggregation error. See Fujita and Ramey (2006) for data construction details. Labor productivity ismeasured as real GDP divided by the number of employed persons reported in the CPS. HP filter usessmoothing parameter of 1600.

FIGURE 1

CROSS CORRELATIONS BETWEEN LABOR PRODUCTIVITY AND TRANSITION HAZARD RATES

Figure 3 reports the cross correlations between the separation and job findingrates under the two filtering methods. These provide a direct assessment of co-movement between the two rates themselves. Observe that the HP filtered ratesare strongly negatively correlated at lags of zero to four quarters, whereas thefirst differenced rates exhibit strong negative correlation at a lag of one quarter.It follows that declines in the job finding rate tend to be preceded by increases inthe separation rate.

In Figures 4–6, we replicate this analysis using Shimer’s gross flow- and duration-based data sets. The results are essentially unaltered except for the first differencedduration data, in which a backward phase shift in the unemployment–job findingcorrelations may be observed. We favor the gross flow-based findings since theyare derived from direct measurements of the flows between employment and un-employment. In the duration data, these flows are confounded with flows betweenNILF and unemployment, leading to less reliable measures of separation and jobfinding rates.


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NOTES: Sample covers 1976Q1–2005Q4. Series are adjusted for margin error and time aggregationerror. See Fujita and Ramey (2006) for data construction details. HP filter uses smoothing parameterof 1600.

FIGURE 2

CROSS CORRELATIONS BETWEEN UNEMPLOYMENT RATE AND TRANSITION HAZARD RATES

4. CONTRIBUTIONS TO UNEMPLOYMENT VARIABILITY

We now quantify the contributions of separation and job finding rates to overallunemployment variability. Shimer (2005b) argues that the measured magnitudesof the two hazard rates make it reasonable to use the following approximation:

ut � st

st + ft≡ uss

t .

This approximation may also be applied to the trends. Let ut , st , and f t denotethe trend components of the three series obtained via the HP filter. We then have

ut � st

st + f t≡ uss

t .

Log-linearizing usst around the trend values uss

t yields the following decomposition:


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NOTES: Sample covers 1976Q1–2005Q4. Series are adjusted for margin error and time aggregationerror. See Fujita and Ramey (2006) for data construction details. HP filter uses smoothing parameterof 1600.

FIGURE 3

CROSS CORRELATIONS BETWEEN JOB FINDING RATE AT t AND SEPARATION RATE AT t + i

ln(

usst

usst

)= (1 − uss

t ) ln(

st

st

)− (1 − uss

t ) ln(

ft

f t

)+ εt .(3)

Observe that (3) expresses the deviations of unemployment from trend as a sumof factors that depend separately on the deviations of separation and job findingrates from trend, together with a residual term.

In the case of first differencing, the trend components are given by usst−1, st−1,

and f t−1, and the decomposition becomes

� ln usst = (

1 − usst−1

)� ln st − (

1 − usst−1

)� ln ft + εt .(4)

Equations (3) and (4) may be expressed generically as

dusst = dusr

t + dujfrt + εt .(5)

Figure 7 plots the factors dusrt and dujfr

t together with the unemployment devia-tions duss

t under each of the filtering methods. Under HP filtering, the factor dusrt is

somewhat less variable than dujfrt , whereas the variabilities are comparable under

first differencing. In either case, both factors display substantial variability relativeto duss

t throughout the sample period.


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Shimer Gross FlowShimer Duration

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NOTES: Samples cover 1967Q2–2004Q4 for Shimer gross flow-based data and 1951Q1–2004Q4 forShimer duration-based data. Series are adjusted for time aggregation error. See Shimer (2005b) fordata construction details. Labor productivity is measured as real GDP divided by the number ofemployed persons reported in the CPS. HP filter uses smoothing parameter of 1600.

FIGURE 4

CROSS CORRELATIONS BETWEEN LABOR PRODUCTIVITY AND TRANSITION HAZARD RATES: SHIMER DATA

The linear decomposition (5) makes possible a quantitative assessment of un-employment variability in terms of the separate contributions of separation andjob finding rates. Note that the variance of duss

t may be written as

Var(duss

t

) = Var(dusr

t

) + Var(dujfr

t

) + Var(εt )

+ 2Cov(dusr

t , dujfrt

) + 2Cov(dusr

t , εt) + 2Cov

(dusr

t , εt)

= Cov(duss

t , dusrt

) + Cov(duss

t , dujfrt

) + Cov(duss

t , εt).

(6)

The term Cov(dusst , dusr

t ) gives the amount of variation in dusst that derives from

variation in dusrt , both directly and through its correlations with dujfr

t and εt . Thismay be expressed as a proportion of total variation,


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NOTES: Samples cover 1967Q2–2004Q4 for Shimer gross flow-based data and 1951Q1–2004Q4 forShimer duration-based data. Series are adjusted for time aggregation error. See Shimer (2005b) fordata construction details.

FIGURE 5

CROSS CORRELATIONS BETWEEN UNEMPLOYMENT RATE AND TRANSITION HAZARD RATES: SHIMER DATA

βsr = Cov(duss

t , dusrt

)Var

(duss

t

) .

Observe that βsr is formally equivalent to the concept of beta in finance. Corre-spondingly, the proportions of variation in duss

t that derive from dujfrt and εt are

given by

β jfr = Cov(duss

t , dujfrt

)Var

(duss

t

) , βε = Cov(duss

t , εt)

Var(duss

t

) .

From (6), we have 1 = βsr + β jfr + βε . Thus, the three betas serve to decompose thetotal variation in duss

t into the separate components that derive from fluctuationsin separation and job finding rates, together with a residual component.

Panel A of Table 1 reports the values of betas calculated under the two filteringmethods. In the HP filtered data, fluctuations in the separation rate relative to


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i=


NOTES: Samples cover 1967Q2–2004Q4 for Shimer gross flow-based data and 1951Q1–2004Q4 forShimer duration-based data. Series are adjusted for time aggregation error. See Shimer (2005b) fordata construction details.

FIGURE 6

CROSS CORRELATIONS BETWEEN JOB FINDING RATE AT t AND SEPARATION RATE AT t + i: SHIMER DATA

trend explain 41% of overall fluctuations in unemployment. The figure rises to51% in the first differenced data. We conclude that separation and job finding ratesaccount for comparable proportions of unemployment variability. In particular,cyclical fluctuations in the separation rate explain between 40 and 50% of thefluctuations in unemployment.

Betas for the post-1985 subsample are also reported. The contribution of theseparation rate falls to 34 and 46% under the respective filtering methods. Thus,although the separation rate explains a smaller proportion of unemployment fluc-tuations in recent decades, its contribution remains substantial.

Results obtained using the Shimer data sets are reported in panel B of Table 1.The proportions explained by the separation rate are somewhat greater in hisgross flow-based data, which are not corrected for margin error. In his duration-based data, the proportion explained by the separation rate drops to 28% underHP filtering and 40% under first differencing. The proportions for the post-1985subsample lie in a range of 15–42%, with lower values associated with the dura-tion data. Again, we favor the gross flow-based findings since they directly isolatethe flows between employment and unemployment. In the duration data, theseflows are confounded with flows between NILF and unemployment. As demon-strated by Elsby et al. (2009), rates of unemployment inflow from employmentare more countercyclical than overall unemployment inflow rates. In any event,all three data sets show that the separation rate makes an important contributionto unemployment variability.


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0.4Contribution of the Separation rate (HP filtered)

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0.4Contribution of the Job Finding Rate (First Differenced)

NOTES: Solid lines indicate dusrt AND dujfr

t . Dashed lines indicate dusst . See text for definitions. Sample

period is 1976Q1–2005Q4. Shaded areas indicate NBER-dated recessions.

FIGURE 7

CONTRIBUTIONS OF SEPARATION AND JOB FINDING RATES TO BUSINESS CYCLE MOVEMENTS

OF UNEMPLOYMENT RATE

4.1. Dynamic Decomposition. The foregoing analysis decomposes unem-ployment variability in terms of contemporaneous deviations of the separationand job finding rates from trend. As demonstrated in Section 3, however, the sep-aration rate is strongly negatively correlated with the job finding rate in futureperiods. This suggests that deviations of the separation rate may play a somewhatlarger role than what the preceding analysis indicates in that they influence futurejob finding rates and thus future unemployment variability.

In order to assess the potential quantitative importance of this dynamic channel,we represent the factors dusr

t and dujfrt in the standard moving average form,

dusrt = εsr

t +∞∑

k=1

(akε

srt−k + bkε

jfrt−k

),(7)

dujfrt = ε

jfrt +

∞∑k=1

(ckε

srt−k + dkε

jfrt−k

),(8)


TABLE 1CONTRIBUTIONS TO UNEMPLOYMENT FLUCTUATIONS

Full Sample Post-1985

HP Filter First Difference HP Filter First Difference

A. Fujita–Ramey dataβsr 0.405 0.507 0.344 0.457β jfr 0.587 0.494 0.659 0.543βε 0.008 −0.001 −0.003 0.000

B. Shimer dataGross flow

βsr 0.409 0.555 0.274 0.417β jfr 0.579 0.447 0.729 0.583βε 0.012 −0.002 −0.003 0.000

Durationβsr 0.280 0.400 0.150 0.321β jfr 0.708 0.603 0.856 0.679βε 0.012 −0.003 −0.006 0.000

NOTES: See text for definitions of βsr , β jfr, and βε . Full samples cover 1976Q1–2005Q4 forFujita–Ramey data, 1967Q2–2004Q4 for Shimer gross flow-based data, and 1951Q1–2004Q4for Shimer duration-based data. Post-1985 results are based on the samples starting at 1985Q1.Fujita–Ramey series are adjusted for margin error, and all series are adjusted for time ag-gregation error. See Fujita and Ramey (2006) and Shimer (2005b) for data constructiondetails.

where εsrt and ε

jfrt are variations in dusr

t and dujfrt that are uncorrelated over time, but

can be correlated contemporaneously. Ignoring the residual term εt for simplicity,the variance of duss

t may be written as

Var(duss

t

) = Var(dusr

t + dujfrt

)= Var

(εsr

t

) + Var(ε

jfrt

) + 2Cov(εsr

t , εjfrt

) + srt +

jfrt ,

(9)

where

srt =

∞∑k=1

[(ak + ck)2Var

(εsr

t−k

) + (ak + ck)(bk + dk)Cov(εsr

t−k, εjfrt−k

)],

jfrt =

∞∑k=1

[(bk + dk)2Var

(ε

jfrt−k

) + (ak + ck)(bk + dk)Cov(εsr

t−k, εjfrt−k

)].

The decomposition (9) expands on (6) by expressing the variance in terms ofintertemporally uncorrelated changes in the factors dusr

t and dujfrt . The terms sr

t

and jfrt capture the effects of past changes in the separation and job finding rates

on current unemployment. The betas are now calculated as


TABLE 2DYNAMIC DECOMPOSITIONS

Full Sample Post-1985

HP Filter First Difference HP Filter First Difference

A. Fujita–Ramey dataβsr 0.669 0.614 0.680 0.516β jfr 0.331 0.386 0.320 0.484

B. Shimer dataGross flow

βsr 0.465 0.596 0.709 0.560β jfr 0.535 0.404 0.291 0.440

Durationβsr 0.311 0.405 0.467 0.287β jfr 0.689 0.596 0.532 0.713

NOTES: See text for definitions of βsr and β jfr. Full samples cover 1976Q1–2005Q4 for Fujita–Ramey data, 1967Q2–2004Q4 for Shimer gross flow-based data, and 1951Q1–2004Q4 forShimer duration-based data. Post-1985 results are based on the samples starting at 1985Q1.Fujita–Ramey series are adjusted for margin error, and all series are adjusted for time aggre-gation error. See Fujita and Ramey (2006) and Shimer (2005b) for data construction details.

βsr = Var(εsr

t

) + Cov(εsr

t , εjfrt

) + srt

Var(duss

t

) ,

β jfr = Var(ε

jfrt

) + Cov(εsr

t , εjfrt

) + jfrt

Var(duss

t

) .

We can readily estimate the coefficients of (7) and (8) and the variance-covariance matrix of εsr

t and εjfrt and thus compute the betas.10 The results are

shown in Table 2. In nearly all cases, the separation rate explains a substantiallygreater proportion of overall unemployment fluctuations in comparison to thefigures given in Table 1. For the full sample of the Fujita–Ramey data, in particu-lar, the past and current movements in the separation rate explain nearly 70% ofunemployment variability in the HP filtered data, and roughly 60% in the first dif-ferenced data. This demonstrates that the contemporaneous decomposition maysignificantly understate the true contribution of the separation rate.

5. CONCLUSION

Drawing on CPS gross flow data, adjusted for margin error and time aggregationerror, we demonstrate that cyclical changes in the separation rate are negativelycorrelated with changes in labor productivity and tend to move contemporane-ously with them, whereas the job finding rate is positively correlated with and tends

10 We first estimate a vector autoregression (VAR) of dusrt and dujfr

t and then invert it into theinfinite-order moving average representation (7) and (8). The lag length of the VAR is set to eightquarters. Varying the lag length has little effect on our findings.


to lag productivity by two to three quarters. Moreover, the separation rate accountsfor between 40 and 50% of unemployment variability when dynamic interactionsare not considered. These conclusions are robust to the detrending method, andthe basic pattern holds when unemployment is used in place of productivity asan indicator of the business cycle. The conclusions also hold for Shimer (2005b)gross flow-based data. Although his duration-based data yield a somewhat smallercontribution of the separation rate when the HP filter is adopted as a detrendingmethod (28%), this data set suffers from problems in identifying flows betweenunemployment and employment. The gross flow-based data, in contrast, providedirect measures of these flows. Finally, accounting for dynamic interactions be-tween the separation and job finding rates substantially increases the importanceof the separation rate in explaining unemployment variability.

Our results suggest that in analyzing unemployment adjustment over the busi-ness cycle, researchers should consider fluctuations at both the separation andthe job finding margins. The commonly made assumption of constant separationrates cannot be justified on grounds of empirical realism or quantitative rele-vance. Moreover, since declines in the job finding rate tend to be preceded byincreases in the separation rate, abstracting from cyclical adjustment in the sep-aration rate may distort the analysis of unemployment dynamics in importantways.

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THE CYCLICALITY OF SEPARATION AND JOB FINDING RATES

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