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Anatomy of Non-Employment Risk

Carolina Fugazza

Abstract

This paper investigates how job separation and job-finding probabilities shape the non-employment risk across ages and working group characteristics. Improving on current methods, I estimate duration models for employment and non-employment separately. I then use the results to derive the individual age profiles of conditional transitions in and out of non-employment as well as the unconditional non-employment risk profile over the whole working life. This approach allows me to apply the decomposition of changes in individual non-employment risk. To date, this type of decomposition has only been used to study aggregate non-employment dynamics. I find that differences in job separation rates across ages underlie the observed age differences in non-employment risk. When differences between working groups are under consideration, the job finding probability is just as important as the job separation probability.

JEL Classification: C53; E24; J64

Acknowledgements

I would like to thank Christian Bartolucci, John.V. Duca, Chirstopher Flinn, Stefan Hochguertel, Francis Kramarz, Costas Meghir, Claudio Michelacci, Raffaele Miniaci, Giovanna Nicodano, Lia Pacelli, Nicola Pavoni, Roberto Quaranta, Alessandro Sembenelli, Konstantinos Tatsiramos, Benjamin Villena-Roldan, Claudia Villosio and Mathis Wagner for their helpful discussions and comments. I would also like to thank the participants at Cognetti’s Lunch Seminar, the Institute for Employment Research (IAB) Workshop, the ESPE 2011 Annual Congress, the AIEL 2011 Annual Congress, IFS and IZA workshops. Grateful thanks are given for the financial support from CINTIA-Italy and the Piedmont Region. The usual disclaimers apply.

A Non-employment Risk Decompositions

A.1 Shimer’s (2007) Approach

Following Shimer (2007), I consider for each working group g at age t, the comparison between the steady state non-employment risk, ug,tss (see eq. (6) in the text), with the counterfactual non-employment risk determined by fixing, one at a time, the job finding and job exiting probability at the average values over working life and across working groups.

In particular, to evaluate the role of the job separation probability in shaping the non-employment risk, I fix the job finding rate at its average over working life and across working groups, f, (i.e. f=g=1Gt=1Tfg,t) and take the actual job separation rates, st,g to determine, for each working group g at each age t, the counterfactual the non-employment risk:

(7)ug,ts=sg,tsg,t+f

Similarly, to evaluate the role of the job finding probability, I fix the job separation at its average over working life and across working groups, s, (i.e. s=g=1Gt=1Tsg,t) and take the actual job finding rates, ft,g, to determine the counterfactual the non-employment rate for each group g at each age t:

(8)ug,tf=sˉsˉ+fg,t

Following Shimer (2007), I evaluate the contribution of the two transition distributions by regressing the two counterfactual non-employment risk series, ug,ts and ug,tf, on the steady-state approximation of the actual non-employment risk, ug,tss, obtaining:

(9)cs=cov(ug,tss,ug,ts)var(ug,tss);cf=cov(dug,tss,ug,tf)var(ug,tss)

where cs and cf are respectively the contributions of variations of job separations and findings across ages and working groups to the heterogeneity of the non-employment risk observed across ages and working groups.

A.2 Fujita and Ramey’s (2009) Approach

As robustness check, I consider an extension of the approach introduced by Fujita and Ramey (2009).[30] This approach is based on the log-linearisation of ug,tss around its average over ages and across working groups denoted as:

(10)uss=sˉsˉ+fˉ

where s and f denote the job separation and job finding probabilities averaged over working life and across all working groups (see above). By log-linearising ug,tss around uss, I obtain the following decomposition (see Fujita and Ramey 2009):

(11)dug,tss=lnug,tssug,tss=(1ug,tss)lnsg,ts(1ug,tss)lnfg,tf+ϵg,t

where ϵg,t is a residual term.

Equation (11) shows that deviations of job separation and job finding probabilities from their average (over ages and working groups) contribute separately to deviations of the non-employment risk from its own average (over ages and working groups). Equation (11) is restated as:

(12)dug,tss=dug,ts+dug,tf+ϵg,t

Fujita and Ramey (2009) show that the linear decomposition can be used to quantitatively assess the effects of the transition rates on non-employment risk variability. Following Fujita and Ramey (2009), I express these contributions through

(13)βs=cov(dug,tss,dug,ts)var(dug,tss);βf=cov(dug,tss,dug,tf)var(dug,tss);βϵ=cov(dug,tss,dϵg,t)var(dug,tss)

where βs+βf+βϵ=1 (see Fujita and Ramey 2009). In particular, βs is the coefficient in a linear regression of dug,ts on dug,tss, which applies correspondingly to the other betas. The betas can be interpreted as the contribution of job separation and job finding probabilities to total variability of the non-employment risk across ages and working group characteristics.

A.3 Differences Across Ages

In this section, I focus solely on age heterogeneity in the non-employment risk. In particular, I consider at each age t the non-employment risk averaged across working groups:

(14)ututss=stst+ft

where st=g=1Gsg,t and ft=g=1Gfg,t, are the job separation and the job finding faced by all representative workers on average at age t. The aim is to determine the respective role of job separations and job findings in shaping age differences in the non-employment risk.

Shimer’s (2007) approach

In this subsection, following Choi, Janiak, and Villena-Roldan (2015), I adapt the Shimer’s (2007) approach to explain differences in the non-employment risk across ages.

To determine the contribution of the job finding and the job separation rates to differences across ages, I compare the average non-employment risk at age t, utss, with the counterfactual non-employment risk determined by fixing, one at a time, the job finding and job exiting probability at their average over working life and across working groups, f(f=t=1Tft) and s(s=t=1Tst) , respectively.

By fixing the job finding at the average over working life and across working groups, f, and taking the job separation rates at each age averaged across working groups, st , I determine the hypothetical life cycle non-employment rate:

(15)uts=stst+f

By fixing the job separation at the average over working life, s, and taking the job finding rates at each age t averaged across working groups, ft, I determine the hypothetical life cycle non-employment rate:

(16)utf=sˉsˉ+ft

Following Shimer (2007), the contribution of the two transition distributions is measured by the regression coefficients of uts and utf on utss:

(17)cs(t)=cov(utss,uts)var(utss)cf(t)=cov(utss,utf)var(utss)

where cs(t) and cf(t) are the contributions of the variability of job separations and findings across ages to the difference of the non-employment risk over working life.

Fujita and Ramey’s (2009) approach

As robustness check, I consider the extended approach based on Fujita and Ramey (2009). Following this approach, I capture the role of age variations in the job finding and job separation rates in explaining the deviations of the non-employment risk faced by the average at each age, utss, from its own trend uss (i.e. the average non-employment risk across ages):

(18)uss=sˉsˉ+fˉ

where f(f=t=1Tft) and s(s=t=1Tst) denote, for the average worker, the job separation and job finding probabilities averaged over the working life. The approach is based on the log-linearisation of the average non-employment risk at age t, utss, around the overall mean, uss. From the log-linearisation, the following decomposition can be obtained (see Fujita and Ramey 2009):

(19)dutss=lnutssuss=(1uss)lnsts(1uss)lnftf+ϵt=duts+dutf+ϵt

where ϵt is a residual term.

The relative importance of the two transition distributions, st and ft, is expressed through:

(20)βs(t)=cov(dutss,duts)var(dutss);βf(t)=cov(dutss,dutf)var(dutss);βϵ(t)=cov(dutss,dϵt)var(dutss)

where βs(t)+βf(t)+βϵ(t)=1, βs(t) and βf(t) are the contributions of age variations in job separations and job findings to age differences in the non-employment risk faced by the average worker.

A.4 Differences Across Working Groups

Shimer’s (2007) approach

Following the approach of Shimer (2007) adopted in the previous subsection, I focus on explaining the differences in the non-employment risk across working groups:

(21)ugugss=sgsg+fg

where sg=t=1Tsg,t and fg=t=1Tfg,t.

I consider the comparison between the ugss for the working group g with the counterfactual non-employment risk (22 and 23) determined by fixing, one at a time, the job finding and job exiting probabilities at their averages across all working groups and ages.

Firstly, I fix the job finding at the average over all groups and ages, f and take the actual job separation rate at group level g, sg, to determine the hypothetical life cycle non-employment rate:

(22)ugs=sgsg+fˉ

Moreover, I fix the job separation at the average across groups, s, and take the actual job finding rates at group level g, fg to determine the hypothetical non-employment risk:

(23)ugf=sˉsˉ+fg

Following Shimer (2007), the contribution of the two transition distributions is measured as the regression coefficients of ugs and ugf, respectively, on ugss:

(24)cs(g)=cov(ugss,ugs)var(ugss)cf(g)=cov(ugss,ugf)var(ugss)

Fujita and Ramey’s (2009) approach

As a robustness check, I extend the approach introduced by Elsby, Hobijn, and Sahin (2013) and Fujita and Ramey (2009). This extended approach is based on the decomposition of the log-linear approximation of ugss around the average across working groups and ages, denoted as uss:

(25)dugss=lnugssuss=(1uss)lnsgs(1uss)lnfgf+ϵg=dugs+dugf+ϵg

where ϵg is a residual term.

As in the previous subsection, the relative importance of the two transition distributions is assessed by evaluating

(26)βs(g)=cov(dugss,dugs)var(dugss);βf(g)=cov(dugss,dugf)var(dugss);βϵ(g)=cov(dugss,dϵg)var(dugss)

where βs(g)+βf(g)+βϵ(g)=1, βs(g) and βf(g) are the contributions of the variations in job separations and job findings to differences in the non-employment risk across groups, faced at a given age.

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Published Online: 2019-05-24

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