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Job Mobility and Sorting

Theory and Evidence

Damir Stijepic

Abstract

Motivated by the canonical (random) on-the-job search model, I measure a person’s ability to sort into higher ranked jobs by the risk ratio of job-to-job transitions to transitions into unemployment. I show that this measure possesses various desirable features. Making use of the Survey of Income and Program Participation (SIPP), I study the relation between human capital and the risk ratio of job-to-job transitions to transitions into unemployment. Formal education tends to be positively associated with this risk ratio. General experience and occupational tenure have a pronounced negative correlation with both job-to-job transitions and transitions into unemployment, leaving the risk ratio, however, mostly unaffected. In contrast, the estimates suggest that human-capital concepts that take into account the multidimensionality of skills, e.g. versatility, play a prominent role.

JEL Classification: J60; J63; J24; I24; I26

Acknowledgements

I thank Björn Brügemann, Carlos Carrillo-Tudela, Tewodros Dessie, Guido Friebel, Nicola Fuchs-Schündeln, Peter Funk, Pawel Gola, Marten Hillebrand, Christian Holzner, Andrey Launov, Jeremy Lise, Alexander Mosthaf, Henning Müller, Jean-Marc Robin, Sigrid Röhrs, Sonja Settele, Iryna Stewen, Denis Stijepic, Huzeyfe Torun, Reyn van Ewijk, Klaus Wälde, Peter Winker, two anonymous referees, and the participants of the Annual Conference of the Royal Economic Society (Manchester, 2015), the Annual Conference of the Search and Matching Network (Aix-en-Provence, 2015), the Annual Conference of the German Economic Association (Münster, 2015), the NASM of the Econometric Society (Philadelphia, 2016) and the Annual Conference of the European Association of Labour Economists (Ghent, 2016) for helpful comments. I gratefully acknowledge financial support from the Interdisciplinary Public Policy (IPP) Research Unit at the Johannes Gutenberg University and from the Fritz Thyssen Foundation under the grant no. 40.16.0.028WW. The usual disclaimer applies.

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Appendix

A Theory

I rely on the canonical on-the-job search model to motivate the empirical analysis (see e.g. Cahuc and Zylberberg, 2004).

A.1 Assumptions

Let the mass of the set of workers be normalized to unity. Both unemployed and employed workers find jobs according to a Poisson process at rate λ. There is a continuum of jobs in the economy. Furthermore, there exists a ranking of jobs that reflects a person’s preferences over these jobs.[11] Specifically, let p∈[0,1] denote a person’s ranking of a given job. The ranking of jobs may be based on differences in pay between jobs, but may also take into account other job characteristics, e.g. working conditions. I also assume that jobs are sufficiently heterogeneous so that the jobs between which a person is indifferent do not have a non-zero mass.

Job offers are randomly drawn from a sampling distribution F( · ), i.e. F(p) is the share of offers associated with jobs ranked p or lower. The sampling distribution F( · ) reflects the directedness of a person’s search and need not coincide with the actual distribution of jobs. In particular, a person may find it optimal to oversample preferred jobs. For instance, consider the two sampling distributions F( · ) and F˜(). Let F( · ) first-order stochastically dominate F˜(), i.e. F(p)F˜(p) for all admissible job ranks and with strict inequality for some ranks. Hence, offers are associated with higher job ranks under the distribution F( · ) than under the distribution F˜() in expectations. In other words, a person’s search is more directed towards highly ranked jobs under F( · ) than under F˜(). I assume the distribution F( · ) to be continuously differentiable, excluding, in particular, cases in which a person dedicates a non-zero mass of sample draws to jobs of a specific rank. In other words, a person’s search for jobs is sufficiently diversified.[12] Finally, once a person accepts a job, the match is at risk of being dissolved at rate δ.

A.2 Sorting

The workers’ optimal behavior is as follows. When information about a new job opportunity arises, workers quit their current job and move to the new one provided that the rank of the new job exceeds that of the current one. Without loss of generality, I assume that unemployed workers are at least indifferent between unemployment and the least preferred job in the economy. Therefore, unemployed workers accept all job offers.

Let u denote the steady-state unemployment rate and G(p) the steady-state proportion of employed workers in jobs of rank p or lower. I refer to G( · ) as the workers’ cross-sectional job distribution. Finally, let κ=λ/δ denote the ratio of the job-finding rate to the transition rate into unemployment. The following proposition establishes a link between the cross-sectional job distribution, G( · ), and the ratio of the job-finding rate to the transition rate into unemployment, κ.

Proposition 1

[Sorting].   For κ>κ˜>0, let G( · ) and G˜() denote the corresponding cross-sectional job distributions. For a given sampling distribution, F( · ), it follows that G( · ) first-order stochastically dominates G˜(). That is: G(p)G˜(p) for all p∈[0,1] and G(p)<G˜(p) for some p∈[0,1].

Proof 1

In a steady-state equilibrium, the flow of workers into employment, λu, equals the flow into unemployment, δ(1u). Therefore, the steady-state unemployment rate is u=δ/(δ+λ). Furthermore, the flow of unemployed workers into jobs with a rank no greater than p, λF(p)u, equals the flow of employed workers into unemployment, δG(p)(1u), and into higher ranked jobs, λ(1F(p))G(p)(1u). Hence, the steady-state cross-sectional job distribution is G(p)=F(p)(1+κ1F(p). It immediately follows that a higher κ induces first-order stochastic dominance.   □

Workers sort into highly ranked jobs by moving from lower ranked to higher ranked jobs. Job-separation shocks prevent workers from staying employed in the highly ranked jobs. For a given sampling distribution, F( · ), it is the ratio of the job-finding rate to the transition rate into unemployment, κ, that reflects how effectively workers sort into highly ranked jobs.

A.3 Worker flows

Workers employed in jobs ranked p quit their current job in the event of a separation shock, δ, or if they find higher ranked jobs, λ1F(p). Hence, the separation rate conditional on the job rank is δ+λ1F(p). The following proposition provides an analytical expression for the unconditional steady-state risk ratio of separating to another job to transitioning into unemployment, denoted by κˉ. I note that this risk ratio coincides with the ratio of the unconditional steady-state separation rate to another job, denoted by λˉ, to the transition rate into unemployment, δ.

Proposition 2

[Job Mobility].   The unconditional steady-state risk ratio of separating to another job to transitioning into unemployment, κˉ, is

(3)κˉ=λˉ/δ=1+κκln1+κ1.

[13]

Proof 2

Integrating the conditional separation rate, δ+λ1F(p), over the cross-sectional job distribution, G( · ), yields

(4)δ+λˉ=01δ+λ1F(p)dG(p)==01δ(δ+λ)δ+λ1F(p)dF(p)=δ(δ+λ)λlnδ+λδ,

where the first equality follows from an application of a change of variables formula, using the steady-state relation G(p)=F(p)(1+κ1F(p). Equation (3) immediately follows from Equation (4).   □

I note that the unconditional steady-state separation rate to another job, λˉ, does not depend on the sampling distribution, F( · ); nor does the unconditional steady-state risk ratio of separating to another job to transitioning into unemployment, κˉ. Intuitively, workers who direct their search towards top-ranked jobs are more likely to obtain better offers while at a given job. Therefore, they are more likely to separate from that job. However, workers who direct their search towards top-ranked jobs are more likely to be in top-ranked jobs, so that there are only few preferred jobs. Therefore, they are less likely to separate from a job. The positive and negative effects of the directedness of a person’s search on the unconditional separation rate exactly cancel.

The unconditional steady-state risk ratio of separating to another job to transitioning into unemployment, κˉ, is the principal measure of job mobility in the empirical analysis.[14] This risk ratio is an appealing measure of job mobility for at least three reasons. First, κˉ is solely a function of the model’s primitive mobility parameters, i.e. κ. Furthermore, κˉ is increasing in κ for κ > 0. Hence, ordinality is preserved. Therefore, realized mobility patterns, κˉ, allow of directly inferring the underlying mobility characteristics, κ.

Second, κˉ reflects a person’s ability to sort into highly ranked jobs. Since κˉ is an ordinal transformation of κ, Proposition 1 applies to κˉ as well. Therefore, the higher is κˉ, the more likely is a person to be employed in top-ranked jobs. In an environment where more productive firms offer, ceteris paribus, higher wages–-which is both an equilibrium outcome in this framework and in line with empirical evidence–-κˉ also reflects the ability to allocate to the more productive firms in the economy.[15] As stressed in the introduction, the resource allocation across firms is an important determinant of aggregate productivity.

Third, κˉ reflects the fierceness of the competition between firms for workers. κ, of which κˉ is an ordinal transformation, is the average number of outside contacts per employment spell. The more firms are expected to interact during an employment spell, the lower is the employers’ monopsonistic power. Hence, the larger is the rent share that the workers are able to appropriate.[16] Differences between worker groups in their employers’ monopsonistic power play a supposedly important role in explaining relative wages. For instance, Ransom and Oaxaca (2010) estimate labor supply elasticities at the firm level in the U.S. retail grocery industry, finding that the difference in the supply elasticities between women and men explains well the gender pay gap.[17]

A.4 Sensitivity analysis

I this section, I relax several assumptions of the canonical on-the-job search model in order to study the robustness of the main theoretical findings.

A.4.1 State-dependent sampling distribution

Let the sampling distribution, F( · ), depend on a person’s employment status. Specifically, the sampling distribution of unemployed workers is denoted by Fu() and that of employed workers by Fe(). The steady-state cross-sectional distribution is G(p)=δFu(p)/(δ+λ(1Fe(p))). It immediately follows that a higher κ induces first-order stochastic dominance. Let the sampling distribution of unemployed workers be, for instance, a power function of that of employed workers, i.e. Fu()=Feα() for α∈(0,1). Therefore, the steady-state risk ratio of separating to another employer to transitioning into unemployment is

κˉ=01αx1α+κxα1+κ(1x)dx1.

Conditional on the distributional parameter α, κˉ is increasing in κ for κ > 0. Hence, ordinality is preserved. However, if the distributional parameter α is a function of the mobility parameters, i.e. α(λ,δ), the realized mobility patterns, κˉ, do not necessarily allow of directly inferring the underlying mobility characteristics, κ.

A.4.2 State-dependent mobility

In the canonical on-the-job search model, the job-finding rate of employed workers, λe, typically differs from that of unemployed workers, λu. The job-finding rate of unemployed workers, λu, and the transition rate into unemployment determine the steady-state unemployment rate, i.e. u=δ/(δ+λu). However, the steady-state cross-sectional job distribution is independent of the job-finding rate of unemployed workers, i.e. G(p)=δF(p)/(δ+λe(1F(p))).

In a further extension, let the transition rate into unemployment and the job-finding rate be functions of the job rank. Specifically, δ(p)=δˆρ(p) and λ(p)=λˆρ(p), where 01ρ(p)dG(p)=1 and ρ(p) > 0 for all p∈[0,1]. The normalization of the function ρ( · ) implies that the parameters δˆ and λˆ are the average transition rate into unemployment and the average job-finding rate, respectively. If ρ( · ) is a decreasing function in the job rank, workers in highly ranked jobs are less likely to transition into unemployment due to, e.g. a larger match surplus, and workers in highly ranked jobs are also less likely to obtain a job offer due to, e.g. lower search efforts.

In a steady-state equilibrium, the cross-sectional job distribution satisfies the condition 0pρ(x)dG(x)=δˆF(p)/(δˆ+λˆ(1F(p))). Conditional on the sampling distribution, F( · ), and the the mobility differences between jobs, ρ( · ), a higher κ=λˆ/δˆ continues to induce first-order stochastic dominance. The unconditional steady-state risk ratio of separating to another employer to transitioning into unemployment is

κˉ=1+κκln1+κ1.

The risk ratio of separating to another employer to transitioning into unemployment, κˉ, is solely a function of the model’s primitive mobility parameters, i.e. κ. Furthermore, κˉ is increasing in κ for κ > 0. Hence, ordinality is preserved.

All in all, the main theoretical results may also hold in an environment with state-dependent mobility. I note that, in the present setup, the sorting of workers into jobs depends on four factors: (i) the workers’ ranking of jobs, p, (ii) the degree of job mobility, i.e. the workers’ ability to reallocate themselves from one job to another, κ, (iv) the mobility differences between jobs, ρ( · ), and (iv) the directedness of job mobility, i.e. the degree to which the mobility is directed towards highly ranked jobs, F( · ).

A.4.3 Convergence to steady state

Let the initial cross-sectional distribution be equal to the sampling distribution, i.e. Gt()=F(). Furthermore, unemployment is in its steady state. Hence, the cross-sectional job distribution at the point in time τ > t is

Gτ(p)=F(p)1+κ(1F(p))+κF(p)(1F(p))1+κ(1F(p))eδ(1+κ(1F(p)))(τt),

where κ=λ/δ. A higher κ does not necessarily induce first-order stochastic dominance at an arbitrary point in time τ. The absolute values of the transition rate into unemployment, δ, and the job-finding rate, λ, also play a role.

It immediately follows that the unconditional risk ratio of a job-to-job transition to a transition into unemployment, κˉ, continues to be independent of the workers’ ranking of jobs, p, and of the directedness of their job mobility, F( · ). However, the unconditional risk ratio of a job-to-job transition to a transition into unemployment, κˉ, is not necessarily increasing in κ at an arbitrary point in time τ. The absolute values of the transition rate into unemployment, δ, and the job-finding rate, λ, also play a role.

B Data

I form sixteen broad industry categories based on the 1990 Census Industry Classification System (codes in parentheses): agriculture, forestry, fisheries (010–032), mining (040–050), construction (060), manufacturing–-nondurable goods (100–222), manufacturing–-durable goods (230–392), transportation (400–432), communications (440–442), utilities and sanitary services (450–472), wholesale trade–-durable goods (500–532), wholesale trade–-nondurable goods (540–571), retail trade (580–691), finance, insurance, real estate (700–712), business and repair services (721–760), personal services (761–791), entertainment and recreation services (800–810), professional and related services (812–893). I exclude public administration (900–932) and active duty military (940–960) from the final sample.

Similarly, I also form broader occupation categories based on the 1990 Census Occupation Classification System (codes in parentheses): executive, administrative and managerial occupations (003–021), managers and administrators, n.e.c. (022), management related occupations (023–037), architects (043), engineers (044–063), mathematical and computer scientists (064–068), natural scientists (069–083), health diagnosing occupations (084–089), health assessment and treating occupations (095–097), therapists (098–106), teachers, postsecondary (113–154), teachers, except postsecondary (155–163), librarians, archivists, curators (164–165), social scientists and urban planners (166–173), social, recreation and religious workers (174–177), lawyers and judges (178–179), writers, artists, entertainers, athletes (183–199), health technologists and technicians (203–208), engineering and related technologists and technicians (213–218), science technicians (223–225), technicians, except health, engineering and science (226–235), supervisors and proprietors, sales occupations (243), sales representatives (253–259), sales workers (263–274), sales counter clerks, cashiers, streets sales workers, news vendors (275–278), sales related occupations (283–290), supervisors, administrative support occupations (303–307), computer equipment operators (308–309), secretaries, stenographers, typists (313–31), information clerks (316–323), records processing occupations, except financial (325–336), financial records processing occupations (337–344), duplication, mail, communication and other office machine operators (345–353), mail and message distributing occupations (354–357), material recording, scheduling and distribution clerks (359–374), adjusters and investigators (375–378), miscellaneous administrative support occupations (379–391), private household occupations (403–408), protective service occupations (413–427), food preparation and service occupations (433–444), health service occupations (445–447), cleaning and building service occupations, except household (448–455), personal service occupations (456–469), farm operators and managers (473–476), farm occupations, except managerial (477–484), related agricultural occupations (485–489), fishers, hunters, trappers, forestry and logging occupations (494–499), supervisors, mechanics, repairers (503), vehicle and mobile equipment mechanics and repairers (505–519), electric and electronic equipment repairers (523–534), miscellaneous mechanics and repairs (535–549), supervisors, construction occupations (553–558), construction trades, except supervisors (563–599), extractive occupations (613–617), supervisors, production occupations (628), precision metal working occupations (634–655), precision woodworking occupations (656–659), precision textile, apparel and furnishing machine workers (666–674), precision workers, assorted materials (675–684), precision food production occupations (686–688), precision inspectors, testers and related workers (689–693), plant and system operators (694–699), metalworking and plastic working machine operators (703–717), metal and plastic processing machine operators (719–725), woodworking machine operators (726–733), printing machine operators (734–737), textile, apparel and furnishings machine operators (738–749), machine operators, assorted materials (753–779), fabricators, assemblers and hand working occupations (783–795), production inspectors, testers, samplers, weighers (796–799), motor vehicle operators (803–815), rail transportation occupations (823–826), water transportation occupations (828–834), material moving equipment operators (843–865), helpers, construction and extractive occupations (866–874), freight, stock and material handlers (875–890). I exclude infrequent occupations that do not allow a meaningful grouping with adjacent occupations. Only 15 observations are affected. Finally, respondents in military occupations (903–905) also do not enter the final sample.

Occupations are possibly miscoded for multiple job holders in the 1996 Panel of the Survey of Income and Program Participation. For further details see the “1996 Panel Waves 1 – 12 Labor Force User Note” from May 12, 2006. All in all, I obtain similar occupational transition rates as in other studies, e.g. Moscarini and Thomsson (2007), with the exception of the first rotation group in the second wave. For this group, I identify occupational changes with the same employer as spurious if either (i) the occupation is imputed in the subsequent interview, (ii) the start date of the job changes, (iii) the industry code changes, (iv) neither the union membership, the union contract coverage, nor the payment modalities (paid by the hour, frequency of payments, e.g. weekly, monthly, etc.) change, or (v) the wage and hours worked change by less than five percent.

Received: 2018-07-18
Revised: 2018-11-05
Accepted: 2018-01-16
Published Online: 2019-05-29
Published in Print: 2020-01-28

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