Workplace Heterogeneity and the Returns toVersatilityI

August 2017

Damir StijepicJohannes Gutenberg University, Mainz

AbstractIn the present paper, I develop an on-the-job search model in which workers faceboth frictional and structural impediments to sorting. There are two key modelpredictions. First, versatility enhances a person’s ability to sort into the mostproductive firms since a mismatch between the job requirements and the person’sskill set is less likely to occur. Second, the larger the productivity differentialsbetween the firms, the larger the returns to sorting and, hence, versatility. I test thetwo predictions, making use of the 1979 National Longitudinal Survey of Youth.Indeed, I find that a person’s versatility is positively associated with the abilityto reallocate across employers. Furthermore, the wage returns to versatility arehigher in more dispersed industries.

Keywords: versatility, multidimensionality of skills, workplace heterogeneity,productivity dispersion, search and matching, on-the-job search, inter-firmmobility, sorting, wage inequality, skill premiumJEL: J00, I26, J31, J24, J63

II thank Sarra Ben Yahmed, Bjorn Brugemann, Carlos Carrillo-Tudela, Tewodros Dessie,Guido Friebel, Nicola Fuchs-Schundeln, Peter Funk, Terry Gregory, Marten Hillebrand, AndreyLaunov, Jeremy Lise, Alexander Mosthaf, Henning Muller, Jean-Marc Robin, Sonja Settele, IrynaStewen, Reyn van Ewijk, Klaus Walde, the participants of the Chair in Macroeconomics ResearchDay at the Johannes Gutenberg University (Mainz, 2015), the ZEW Research Seminar (Mannheim,2015), and the Jahrestagung des Vereins fur Socialpolitik (Augsburg, 2016) for helpful comments.I gratefully acknowledge financial support from the Fritz Thyssen Foundation under the grant no.40.16.0.028WW. The usual disclaimer applies.

Email address: mail@damir.stijepic.com (Damir Stijepic)

1. Introduction

Wage inequality has risen in many countries over the last decades. Manycountries have also experienced a simultaneous surge in the productivity disper-sion across employers. Dunne et al. (2004) find that the between-plant wageand productivity dispersion substantially increased in U.S. manufacturing from1975 to 1992 and that “virtually the entire increase in overall dispersion in hourlywages for U.S. manufacturing workers from 1975 to 1992 is accounted for by thebetween-plant components” (Dunne et al., 2004, pg. 399). Barth et al. (2014)and Faggio et al. (2010) document similar patterns in other U.S. industries andin several European countries, respectively. Furthermore, recent studies, whichfit linear models with additive employer and employee fixed effects a la Abowdet al. (1999), find that a substantial share of the increase in the wage gap betweenhigher- and lower-educated employees is attributable to a widening in the averageemployer wage premia received by differently educated groups, i.e., increasingemployer heterogeneity and rising assortativeness between high-wage employeesand high-wage employers (see, e.g., Card et al., 2013).1

Yet, little is known about the underlying mechanisms. In the present paper, Ished light on the link between the productivity dispersion across employers andthe skill premium by providing a new perspective that explicitly takes into accountthe multidimensionality of skills. Specifically, I explore how the productivity dis-persion across employers affects the returns to a person’s versatility in the sense ofbeing able to perform various different tasks or activities—eventually even acrossoccupations. My analysis stresses mechanisms relating to employer–employeesorting and rent sharing.

In the theoretical contribution, I develop a parsimonious on-the-job searchmodel that features both frictional and structural impediments to sorting.2 Thekey idea is that, in an environment where jobs differ in requirements, versatilityenhances a person’s ability to sort into the most productive firms since efficient

1Notably, Kambourov and Manovskii (2008) document a substantial increase in worker mobil-ity in the United States over the 1968–1997 period at various levels of occupational and industryaggregation.

2See Stijepic (2015c) for a quantitative analysis based on a richer model. Stijepic (2017d)develops a heterogeneous firm model of intra-industry trade with limited inter-firm mobility ofworkers in order to study the impact of trade liberalization on wage inequality. Trade liberalization(i) amplifies the disparities in profitability between the small and the large firms, (ii) raises thewithin-group wage inequality, and (iii) increases the wage differentials between worker groupswho differ in inter-firm mobility.

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reallocations are less likely to be hindered by unmet job requirements. The returnsto sorting and, hence, versatility are larger, the more pronounced the productivitydifferentials between the firms. Intuitively, if firms are similar in productivity, thereturns from switching firms are low. However, if the disparities between firms aresubstantial, so will be the returns. The wage differential between more versatileand less versatile individuals is amplified as the productivity dispersion acrossfirms rises.

In order to test the empirical content of the model’s predictions, I rely onthe 1979 National Longitudinal Survey of Youth (NLSY). The NLSY is uniquein the sense that it comprises a nationally representative sample of young peopleto whom the Armed Services Vocational Aptitude Battery (ASVAB) was admin-istered. This set of standardized tests assesses the respondents’ knowledge andskills in ten areas and allows me to construct a measure of a person’s versatility.Exploiting the variation in job tenure in 2007, I estimate that a person’s versatil-ity measured by the number of test areas in which the person scores above theaverage is, indeed, positively associated with the ability to reallocate across em-ployers. Exploiting the variation in the log-sales-per-employee standard deviationacross eight broadly defined U.S. industries in 2007, I find that an increase in theproductivity dispersion is, indeed, associated with an increase in the wage returnsto versatility.

The present paper is related to the literature on employer–employee sortingin the labor market (e.g., Abowd et al., 1999; Shimer and Smith, 2000; Atakan,2006; Eeckhout and Kircher, 2011; Lise et al., 2016; Grossman et al., forthcom-ing; de Melo, forthcoming; Hagedorn et al., forthcoming).3 Much of the discus-sion revolves around the conditions that establish positive or negative assortativematching, welfare losses that may occur in the decentralized market equilibrium,and the identification of sorting patterns in the data. Worker characteristics thathelp achieve the optimal allocation have attracted little attention. A partial excep-tion is the work of Bagger and Lentz (2014), who stress the role of differences insearch intensities between skill groups in explaining sorting patterns. However,the literature on employer–employee sorting does not address the concept of ver-satility in the sense of being able to perform a wider range of tasks or activitiesand how the productivity dispersion across employers affects the wage returns tothose skills.

3See also the seminal contribution of Becker (1973, 1974) on assortative mating in the marriagemarket.

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My framework is also related to recent models that stress the multidimension-ality of skills (e.g., Charlot et al., 2005; Lise and Postel-Vinay, 2015; Guvenenet al., 2015; Lindenlaub, forthcoming). In the search and matching model of Char-lot et al. (2005), the individuals’ skills vary in both “adaptability” and “intensity,”i.e., aspects that are related to versatility. However, this strand of the literaturedoes not study how the productivity dispersion across employers affects the wagereturns to versatility.4

This paper is structured as follows. In Section 2, I present the on-the-jobsearch model that features both frictional and structural impediments to sorting—with a particular emphasis on the wage returns to versatility and the impact of theproductivity dispersion across employers on those returns. I assess the empiri-cal relevance and scope of the model in Section 3, studying the relation betweenversatility, job mobility and wages. Section 4 draws some conclusions.

2. Frictional and Structural Impediments to Sorting

Leading economists have argued that trading frictions are an essential charac-teristic of the labor market. It takes time and other resources for a worker to geta job and for a firm to fill a vacancy. Around this concept of trading frictions,a prominent literature on search-theoretic models of the labor market has devel-oped. Search theory readily addresses key labor market phenomena about whichthe usual supply-and-demand paradigm is mostly silent. For instance, why areso many people unemployed at the same time that there is a large number of jobopenings? Rogerson et al. (2005) survey this strand of the literature.

In the present paper, I develop a parsimonious (random) on-the-job searchmodel that features both frictional and structural impediments to sorting. In thecanonical on-the-job search model, firms merely search for a random worker to filla vacancy. In contrast, firms look for specific workers whose skills meet the jobrequirements in the present paper’s model. In particular, it is not sufficient for aworker and a firm to overcome the frictions in the market in order to form a match.Once they meet, there has to be an overlap between the job requirements and the

4The present paper also complements existing models of search and matching that stressthe importance for workers of occupational matching (e.g, Groes et al., 2015; Kambourov andManovskii, 2009), firm matching (e.g, Bagger and Lentz, 2014; Burdett and Mortensen, 1998; Jo-vanovic, 1979), or both occupational and firm matching (e.g, Kramarz et al., 2014; McCall, 1990).Sanders and Taber (2012) review the literature on firm-specific, industry-specific, occupation-specific and task-specific human capital.

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worker’s skills additionally. Burdett and Mortensen (1998) and Bontemps et al.(2000) provide a detailed exposition of the canonical on-the-job search model.

This section is structured as follows. I present the on-the-job search modelwith frictional and structural impediments to sorting in Section 2.1. The charac-terization of the model’s equilibrium is in Section 2.2. In Section 2.3, I analyzethe versatility wage premium with a particular emphasis on the role of the produc-tivity dispersion across employers.

2.1. The ModelConsider a random on-the-job search model with continuous ex-ante firm het-

erogeneity a la Burdett and Mortensen (1998). Let p denote a firm’s productivity,which I assume to be Pareto distributed in the economy, i.e., Γp0(p) = 1 − (p0/p)z

for z > 2, p0 > 0 and p ≥ p0. Firms post job offers that are associated withfixed wage contracts, w.5 Furthermore, firms are bound by an equal treatmentconstraint. A firm must pay all of its workers (of the same type) the same wage,irrespective of when they were hired, from where, and of the outside offers thatsome of them may have received. In particular, a firm does not respond to outsideoffers to its employees, but lets them go if they receive a higher wage offer.6

Workers are contacted by firms according to a Poisson process at rate λ > 0.In contrast to the so-called competitive search models or directed search models(see, e.g., Delacroix and Shi, 2006; Shi, 2009), the probability of being contactedby firms of a specific productivity is independent the worker’s state. In particu-lar, the probability does not depend on the productivity of the worker’s currentemployer. A worker is either employed or unemployed. In the former case, theworker receives the wage offered by the respective firm; in the latter case, I nor-malize the flow income enjoyed by the worker to zero. Workers and firms are bothrisk neutral. Without loss of generality, let the measures of the sets of workers andfirms equal unity.

I extend the Burdett and Mortensen (1998) framework by assuming that jobsdiffer in task requirements and that the jobs’ task requirements may change overtime. Specifically, there is a continuum of tasks in the economy. The task as-sociated with a job is randomly and uniformly reassigned according to a Poisson

5Shimer (2006) studies bargaining in an otherwise standard Burdett and Mortensen (1998)model. Cahuc et al. (2006) allow for bargaining in the Postel-Vinay and Robin (2002) model.

6Postel-Vinay and Robin (2002) consider a setup where firms condition their wage offers on aworker’s outside option and incumbent firms may match outside offers. See Moscarini (2008) forfurther reading.

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process at rate δ > 0. In particular, the distribution of task requirements is uniformand independent of the firm productivity in the steady-state equilibrium. Hence,all tasks are equally valuable ex ante. The share of tasks that a worker is ableto perform is denoted by α ∈ (0, 1). I abstract from the specific composition oftasks in a worker’s skill set, assuming that the tasks that the workers are able tofulfill are uniformly distributed in the population. This is a rational equilibriumoutcome provided that the following assumptions hold. First, all tasks are equallycostly to learn. Second, workers determine their sets of tasks that they are able toperform before entering the labor market. Third, workers cannot adapt their setsof tasks once on the labor market. Under the stated assumptions, workers are exante indifferent between the tasks that they are able to perform and the tasks thatthey are not able to perform since the distribution of the tasks required by jobs isuniform and independent of the firm productivity.

The match surplus is negative if the task required by the job is not part of thetasks that the worker is able to perform. Furthermore, it is not possible to delayagreement in anticipation that the match surplus may turn positive at a future pointin time. Therefore, the only matches formed are those in which the worker is ableto fulfill the task required by the respective job. Similarly, if the task requiredby the job changes and the worker is not able to fulfill the new task, the matchis dissolved. The resulting model is isomorphic in terms of worker flows to thecanonical on-the-job search model, where the worker’s offer-arrival rate, λ, andthe job-destruction rate, δ, are given by λ = αλ and δ = (1 − α)δ, respectively.Let κ denote the ratio of the effective job-finding rate, λ, to the separation rate intounemployment, δ, i.e., κ = λ/δ.

The ratio of the effective job-finding rate to the separation rate into unemploy-ment, κ, is a key parameter in the Burdett and Mortensen (1998) framework. Ahigher κ induces first-order stochastic dominance in the distribution of workersover firms. In other words, the higher is this ratio, the larger is the share of work-ers employed at the productive firms. Intuitively, separations into unemploymentrepresent negative mobility shocks. The more pronounced the shocks, the lesslikely are individuals to sort into a specific firm. Therefore, the job-finding rateis to be scaled by the separation rate into unemployment in order to obtain anadequate measure of the workers’ ability to reallocate across firms.

2.1.1. WorkersWhen information about a new job opportunity with suitable task requirements

arises, the unemployed workers’ optimal behavior is to accept any positive wageoffers since their flow income is zero. Let u denote the measure of the set of

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unemployed workers in the steady-state equilibrium. In the steady state, the flowof workers into employment, λu, equals the flow into unemployment, δ(1 − u).Therefore, the steady-state measure of the set of unemployed workers is u = 1/(1+κ).

When information about a new job opportunity with suitable task requirementsarises, the employed workers’ optimal behavior is to quit their current job andto move to the new one provided that the new wage offer exceeds the currentone. Let F(w) denote the steady-state equilibrium proportion of firms offering awage no greater than w, henceforth referred to as the wage-offer distribution. Inote that the support of the wage-offer distribution is connected in equilibriumsince otherwise firms could increase profits by lowering their wage offers withoutreducing their workforce. Furthermore, the equilibrium wage-offer distributioncannot exhibit mass points since otherwise firms could significantly increase theirworkforce and, hence, profits by marginally increasing their wage offers.7 LetG(w) denote the steady-state equilibrium proportion of workers receiving a wageno greater than w, henceforth referred to as the cross-sectional wage distribution.In the steady state, the flow of unemployed workers into firms offering a wage nogreater than w, λF(w)u, equals the flow of employed workers into unemployment,δG(w)(1 − u), and into higher paid jobs, λ(1 − F(w))G(w)(1 − u). Therefore, thesteady-state cross-sectional wage distribution is G(w) = F(w) /(1 + κ(1 − F(w))) .8

2.1.2. FirmsA firm with a workforce of mass l and offering a wage w loses workers when

they separate into unemployment, δl, or are poached by other firms that offerhigher wages, λ(1 − F(w))l. The firm attracts workers who are unemployed, λu,or poaches workers from firms that offer lower wages, λG(w)(1 − u). Hence, thefirm’s steady-state workforce is l(w) = κ (1 + κ(1 − F(w)))−2. Following Burdettand Mortensen (1998), I assume that firms maximize their steady-state profits:

π(p) ≡ maxw{(p − w)l(w)} (1)

The firm’s optimization problem consists in the trade-off that is induced by theambivalent effect of the offered wage on profits. On the one hand, a higher wagedecreases the profits per worker. On the other hand, a higher posted wage allowsthe firm to attract and to retain more workers.

7See Bontemps et al. (2000) for formal proofs.8Alternatively, one may derive the law of motion for the cross-sectional wage distribution by

the Fokker–Planck formalism (see, e.g., Stijepic, 2015b; Bayer and Walde, 2010).

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2.2. Equilibrium CharacterizationFirms of equal productivity choose the same wage strategy in equilibrium.

Hence, there is no wage dispersion among equally productive firms. Intuitively,a continuous productivity distribution leaves no room for wage dispersion amongequally productive firms. In the case of a discrete productivity distribution, firmsof the same productivity typically do not choose the same wage posting strat-egy. Furthermore, more productive firms offer higher wages in equilibrium. Intu-itively, more productive firms enjoy higher marginal revenues for a given postedwage. Hence, they find it optimal to offer wages that exceed those posted by lessproductive firms in order to attract and to retain more workers. Formally, thereexists a non-decreasing equilibrium wage-offer function, denoted by w(p), so thatF(w(p)) = Γp0(p).9

2.2.1. WagesIn this section, I derive the workers’ average wage, w. The first-order condi-

tion with respect to the posted wage, w, for the firm’s maximization problem, asdescribed by Equation (1), is (p − w)dl/dw(w) = l(w). Exploiting the equilibriumrelation F(w(p)) = Γp0(p), one obtains

2κγp0(p)(p − w(p))1 + κ(1 − Γp0(p))

=dwdp

(p), (2)

where γp0(p) denotes the density that is associated with the productivity distribu-tion, Γp0(p). This is a linear differential equation. With the boundary conditionw(p0) = 0, it admits the solution

w(Γ) = 2p0κ (1 + κ(1 − Γ))2∫ Γ

0

(1 − x)−1/z

(1 + κ(1 − x))3 dx, (3)

where I use a change of variables formula in order to rewrite wages in terms ofthe firm’s productivity rank, Γ.10 It follows for the workers’ average wage

w =∫ 1

0w(Γ)dG(Γ) = 2p0κ(1 + κ)

∫ 1

0

(1 − x)1−1/z

(1 + κ(1 − x))3 dx, (4)

where G(·) denotes the steady-state distribution of workers over firm-productivityranks, i.e., G(Γ) = Γ /(1 + κ(1 − Γ)) .

9See Bontemps et al. (2000) for a formal proof.10It is optimal for the least productive firm to offer a wage of zero. Otherwise, the firm could

decrease its wage offer without reducing its steady-state workforce and, hence, increase its profits(see, e.g., Bontemps et al., 2000).

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2.2.2. TenureIn this section, I am interested in the distribution of tenure in the population,

i.e., the spell duration of the job at the worker’s current employer. Workers em-ployed at firms offering the wage w quit their current job in the event of a taskmismatch, δ, or if they find higher paid jobs, λ (1 − F(w)). Therefore, the sep-aration rate conditional on the wage w is given by δ + λ (1 − F(w)). While alljob transition processes are Poisson, all corresponding distributions are exponen-tial. The steady-state distribution of tenure t has, conditional on the wage w, thedensity

h(t | w) = (δ + λ(1 − F(w))) e−(δ+λ(1−F(w)))t, (5)

where the wage w is distributed in the population of employed workers accordingto the cross-sectional wage distribution G(w) = F(w) /(1 + κ(1 − F(w))) . I treatthe wage as unobserved heterogeneity and integrate it out from the joint likelihoodof w and t. The unconditional likelihood of tenure is

h(t) =∫ ∞

0h(t | w)dG(w) = δ(δ + λ)

∫ 1

0

e−(δ+λ(1−x))t

δ + λ(1 − x)dx, (6)

where the second equality follows from a change of variables formula.

2.3. Qualitative AnalysisIn this section, I compare the economic outcomes of a high-versatility worker

group to those of a low-versatility worker group, subscripted by H and L, respec-tively. The two groups differ only in the share of the tasks that they are able toperform, i.e., αH > αL. In particular, all workers are equally productive condi-tional on the productivity of the firm. The key implication is that κH > κL. In thefollowing analysis, I focus on the mechanisms that generate the versatility wagepremium and the impact of the productivity dispersion across employers on thatwage premium.

2.3.1. The Versatility Wage PremiumIn order to shed light on the mechanisms that generate the versatility wage

premium, I study two counterfactual wage premia. Let wL(·) and wH(·) denotethe equilibrium wage-offer functions for the low-versatility workers and for thehigh-versatility workers, respectively. GL(·) and GH(·) are the steady-state dis-tributions over firm-productivity ranks of the low-versatility workers and of thehigh-versatility workers, respectively. Let wi j =

∫ 1

0wi(Γ)dG j(Γ) for i, j ∈ {L,H}

be the average wage of a hypothetical worker group that faces the wage-offer

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function wi(·) and whose steady-state distribution over firm-productivity ranks isG j(·). Note that wLL and wHH are simply the average wages of the low-versatilityworkers and of the high-versatility workers, i.e., wL and wH, respectively.

The first counterfactual wage premium wHH/wLH imposes the same distribu-tion over firms on both worker groups, i.e., the average wage of the high-versatilityworkers is measured relative to the average wage of the low-versatility workersthat would have arisen if the low-versatility workers were matched with firms asthe high-versatility workers. Therefore, the difference in the average wage be-tween the two groups would then be solely due to differences in the wage-offerfunction between the two groups. Henceforth, I refer to this counterfactual wagepremium as the appropriation wage premium.

The second counterfactual skill premium wHH/wHL imposes the same wagewithin firms on both worker groups, i.e., the high-versatility workers’ averagewage is measured relative to the low-versatility workers’ average wage that wouldhave arisen if the low-versatility workers were paid the same wage as the high-versatility workers in each firm. Therefore, the difference in the average wagewould then be solely determined by differences in the distribution over firms.Henceforth, I refer to this counterfactual wage premium as the allocation wagepremium.

Proposition 1 (Allocation Premium). In the steady state, the average wage ofthe high-versatility group exceeds that of the low-versatility group even condi-tional on the firms’ wage offers, i.e., the allocation wage premium is positive(wHH/wHL > 1).

PROOF. A higher κ induces first-order stochastic dominance in the steady-stateequilibrium distribution of workers over the firm-productivity classes, G(Γ) =Γ /(1 + κ(1 − Γ)) . Since the posted wage is increasing in the firm’s productivity,Proposition 1 follows. �

The ratio of the effective job-finding rate to the separation rate into unemploy-ment, κ, plays a key role in determining the distribution of workers over firms.A higher κ induces fist-order stochastic dominance in the distribution of workersover the firm-productivity classes. This is associated, ceteris paribus, with a higheraverage match productivity. The allocation of resources across economic activitiesis an important determinant of aggregate productivity. Hsieh and Klenow (2009)analyze the resource allocation across firms in a cross-country study. They arguethat aggregate productivity could rise by as much as 50 percent in China and 60

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percent in India if resources were as efficiently allocated in those countries as inthe United States. Lentz and Mortensen (2008) estimate a Schumpeterian growthmodel using Danish data. They find that more than one-half of the aggregategrowth is accounted for by the resource reallocation from less to more productivefirms.

Provided that wages depend positively on the match productivity, a higher ra-tio of the effective job-finding rate to the separation rate into unemployment, κ,induces also higher wages by increasing the average match productivity. This im-pact of sorting on wages is prominently analyzed within the Abowd et al. (1999)framework with additive employee and employer wage fixed effects.11 For in-stance, Card et al. (2016) find that the under-representation of women at firms thatoffer higher wage premia to both gender groups explains about 15 percent of theoverall 23 log-point gender wage gap in Portugal.

Proposition 2 (Appropriation Premium). In the steady state, the average wageof the high-versatility group exceeds that of the low-versatility group even con-ditional on the workers’ distribution over firms, i.e., the appropriation wage pre-mium is positive (wHH/wLH > 1).

PROOF. In order to prove Proposition 2, I show that wH(Γ) ≥ wL(Γ) for allΓ ∈ [0, 1] and for some Γ with strict inequality. By Equation (3), the differen-tial equation for the wage as a function of a firm’s productivity rank is

dwdΓ

(Γ) =2κ

1 + κ(1 − Γ)(p0(1 − Γ)−1/z − w(Γ)

). (7)

If wH(Γ) = wL(Γ) < p0(1 − Γ)−1/z, then dwH/dΓ(Γ) > dwL/dΓ(Γ) since κH > κL.Note that wH(0) = wL(0) = 0. �

The high-versatility and the low-versatility workers are equally productive ata given firm. Hence, the differences in wages within firms solely reflect the differ-ences in the rent share that the workers are able to appropriate. Following Burdettand Mortensen (1998), I do not assume the workers’ rent share to be an exogenousconstant, but motivate it by the workers’ search for better jobs while employed.Indeed, Cahuc et al. (2006) estimate the workers’ exogenous rent share to be only

11Eeckhout and Kircher (2011) discuss the methodological challenges of identifying assortativematching in the data.

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modest or not significant at all once it is accounted for the between-firm competi-tion resulting from on-the-job search. Differences between worker groups in theiremployers’ monopsonistic power play a potentially important role in explainingrelative wages. For instance, Ransom and Oaxaca (2010) estimate labor supplyelasticities at the firm level in the U.S. retail grocery industry. They find thatthe difference in the firm-level labor-supply elasticities between women and menexplains well the lower relative pay of women.12

Proposition 3 (Versatility Premium). In the steady state, the average wage ofthe high-versatility group exceeds that of the low-versatility group, i.e., the versa-tility wage premium is positive ( wH/wL > 1).

PROOF. Proposition 3 follows from the proofs of Propositions 1 and 2. �

In conclusion, versatility increases the workers average wage by enhancingtheir ability to allocate to the most productive firms and by reducing the employ-ers’ monopsonistic power. In order to numerically illustrate this section’s mainresults, I set the shape parameter of the Pareto distribution, z, to three, implyinga coefficient of variation of 0.58. The scale parameter, p0, is normalized to unity.Figure 1 depicts the versatility wage premium and the two counterfactuall wagepremia in percentage points for a range of values of the high-versatility workers’ratio of the job-finding rate to the separation rate into unemployment, κH, wherethe low-versatility workers’ κL is set to one. All of the premia are increasing inthe high-versatility workers’ κH. I note that Cahuc et al. (2006) estimate the ra-tio of the job-finding rate to the separation rate into unemployment, κ, to be 1.02and 3.95 among the lowest and the highest of their four skill groups in Frenchmanufacturing, respectively.

2.3.2. The Impact of the Productivity Dispersion across EmployersLet the mean-preserving spread of the firm-productivity distribution, Γp0(·), be

denoted by Γ∗p∗0(·). Specifically, I assume the firm productivities above the thresh-old px ∈ (p0,∞) to increase by a factor of P > 1. Furthermore, I rescale theinitial productivities by the factor p∗0/p0. The parameter p∗0 is implicitly definedby∫ ∞

p∗0xdΓ∗p∗0(x) =

∫ ∞p0

xdΓp0(x), so that the average firm productivity is unaltered.Hence, the transformed productivities, p∗, as a function of the initial productivi-ties, p, are p∗(p) = P1{p>px}(p∗0/p0)p, where 1{p > px} is an indicator function that

12See Manning (2003) for a detailed exposition of the dynamic monopsony model.

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Figure 1: Versatility wage premium (wH/wL, solid line), the allocation wage premium (wH/wHL,dotted line), and the appropriation wage premium (wH/wLH , dashed line) in percentage pointsagainst the high-versatility workers’ ratio of the job-finding rate to the separation rate into unem-ployment, κH , where the low-versatility workers’ κL is set to one. The shape parameter, z, and thescale parameter, p0, of the productivity distribution are set to three and one, respectively.

equals one if p > px but is zero otherwise. Therefore, the mean-preserving spreadof the productivity distribution is

Γ∗p∗0(p∗) =

1 −( p∗0

p∗/P

)zif p∗ > Pp∗x

1 −( p∗0

p∗x

)zif Pp∗x ≥ p∗ ≥ p∗x

1 −( p∗0

p∗

)zif p∗x > p∗ ≥ p∗0

0 otherwise

. (8)

All variables under the mean-preserving productivity spread, Γ∗p∗0(·), are denotedby an asterisk.

The equilibrium wage-offer function under the mean-preserving productivityspread is

w∗(Γ∗) = 2p∗0κ (1 + κ(1 − Γ∗))2∫ Γ∗

0

P1{x>Γ∗x}(1 − x)−1/z

(1 + κ(1 − x))3 dx for Γ∗ ∈ [0, 1], (9)

where 1{x > Γ∗x} is an indicator function that equals one if x > Γ∗x ≡ Γ∗p∗0(p∗x) butis zero otherwise. Note that the equilibrium wage-offer function is necessarilycontinuous. Otherwise, a firm above the discontinuity could decrease its wageoffer without reducing its steady-state workforce and, hence, increase its profits.

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The average wages and the counterfactual average wages are

w∗i j = 2p∗0κi(1 + κ j)∫ 1

0

(1 − x)−1/zφ(x, i, j)(1 + κi(1 − x))3 dx

+ (P − 1)2p∗0κi(1 + κ j)∫ 1

Γ∗x

(1 − x)−1/zφ(x, i, j)(1 + κi(1 − x))3 dx, (10)

for i, j ∈ {L,H}, where φ(x, i, j) =∫ 1

x(1 + κi(1 − y))2/(1 + κ j(1 − y))2dy. The first

term on the right-hand side is simply (p∗0/p0)wi j. Let the second term be denotedby (p∗0/p0)(P − 1)w′i j.

In order to shed light on the mechanisms that generate the positive relation be-tween the productivity dispersion across employers and the versatility wage pre-mium, I first study the impact of the mean-preserving productivity spread on theappropriation premium, wHH/wLH, and on the allocation premium, wHH/wHL. Theproofs in this section and the proof of Proposition 5 in Stijepic (2017d) share thesame basic structure. Jensen (2017, forthcoming) provides a detailed expositionof the underlying concepts.

Proposition 4 (Allocation Premium and Productivity Dispersion). The alloca-tion wage premium under the mean-preserving firm-productivity spread, w∗HH/w

∗HL,

exceeds that under the initial firm-productivity distribution, wHH/wHL, in the steadystate.

PROOF. Proposition 4 claims, equivalently, w′HH/wHH > w′HL/wHL. This inequal-ity is implied by∫ 1

Γ∗x

(1 − x)−1/zφ(x,H,H)(1 + κH(1 − x))3 dx

/∫ 1

0

(1 − x)−1/zφ(x,H,H)(1 + κH(1 − x))3 dx

>

∫ 1

Γ∗x

(1 − x)−1/zφ(x,H, L)(1 + κH(1 − x))3 dx

/∫ 1

0

(1 − x)−1/zφ(x,H, L)(1 + κH(1 − x))3 dx, (11)

where the inequality follows from κH > κL. �

Proposition 4 states that if both the high-versatility and the low-versatilityworkers would be offered the same wage within each firm, the high-versatilityworkers’ relative wage would, nevertheless, increase as the productivity disper-sion across firms rises. Intuitively, the rising productivity gap between the low-productivity firms and the high-productivity firms amplifies the wage disparities

14

between those firms. Since high-versatility workers, due to their higher κ, rep-resent a disproportionately large share of the workforce at the high-productivityfirms, their relative wage rises.

This sorting effect is also prominently analyzed within the Abowd et al. (1999)framework. For instance, Card et al. (2013) fit linear models with additive em-ployee and employer fixed effects for West Germany for the years 1985–2009.They find that two-thirds of the increase in the wage gap between the lower-educated and the higher-educated workers are attributable to a widening in theaverage employer wage premia received by differently educated groups.

Proposition 5 (Appropriation Premium and Productivity Dispersion). The ap-propriation wage premium under the mean-preserving firm-productivity spread,w∗HH/w

∗LH, exceeds that under the initial firm-productivity distribution, wHH/wLH,

in the steady state.

PROOF. Proposition 5 claims, equivalently, w′HH/wHH > w′LH/wLH. This inequal-ity is implied by∫ 1

Γ∗x

(1 − x)−1/zφ(x,H,H)(1 + κH(1 − x))3 dx

/∫ 1

0

(1 − x)−1/zφ(x,H,H)(1 + κH(1 − x))3 dx

>

∫ 1

Γ∗x

(1 − x)−1/zφ(x, L,H)(1 + κL(1 − x))3 dx

/∫ 1

0

(1 − x)−1/zφ(x, L,H)(1 + κL(1 − x))3 dx, (12)

where the inequality follows from κH > κL. �

Proposition 5 states that if the high-versatility and the low-versatility work-ers would be matched with the firms exactly in the same way, the high-versatilityworkers’ relative wage would still rise as the productivity dispersion across firmsincreases. The intuition is as follows. First, note that κ is the average number ofoutside contacts per employment spell. The more firms are expected to interactduring an employment spell, the lower is the employers’ monopsonistic power.Hence, the higher is the rent share that the workers are able to appropriate. Sec-ond, the workers’ outside option, i.e., the flow income of zero while unemployed,is an important determinant of the wages at the low-productivity firms. However,it is predominantly κ, i.e., the fierceness of the between-firm competition, thatdetermines the wages at the high-productivity firms. Therefore, a high κ, as in-duced by a high versatility, is crucial in order to appropriate some of the additional

15

relative match surplus at the firms with the relative productivity gains.13

The following proposition is the present paper’s main theoretical contribution.It establishes the positive relation between the productivity dispersion across firmsand the versatility wage premium.

Proposition 6 (Versatility Premium and Productivity Dispersion). The versa-tility wage premium under the mean-preserving firm-productivity spread, w∗H/w

∗L,

exceeds that under the initial firm-productivity distribution, wH/wL, in the steadystate.

PROOF. Proposition 6 claims w∗H/w∗L > wH/wL, which is equivalent to w′HH/wHH >

w′LL/wLL. The latter inequality is implied by∫ 1

Γ∗x

(1 − x)1−1/z

(1 + κH(1 − x))3 dx/∫ 1

0

(1 − x)1−1/z

(1 + κH(1 − x))3 dx

>

∫ 1

Γ∗x

(1 − x)1−1/z

(1 + κL(1 − x))3 dx/∫ 1

0

(1 − x)1−1/z

(1 + κL(1 − x))3 dx, (13)

where the inequality follows from κH > κL. �

In conclusion, the versatility wage premium increases in the productivity dis-persion across firms for two reasons. First, the high-versatility workers representa disproportionately large share of the workforce at the firms with the relativeproductivity gains. Second, the high-versatility workers are able to appropriatea larger share of the additional relative match surplus at those firms. In orderto numerically illustrate the effect of the mean-preserving productivity spread onwages, I set the firm-productivity threshold, px, to 1.5 so that 30 percent of thefirms experience relative productivity gains. Consistent with the first numericalexercise, the shape parameter, z, and the scale parameter, p0, of the productivitydistribution are three and one, respectively. Broadly in line with the estimates ofCahuc et al. (2006), the low-versatility and the high-versatility workers’ ratios ofthe job-finding rate to the separation rate into unemployment, κL and κH, are one

13Stijepic (2016b) documents the comovement of the skill premium with the differentialemployer-size wage premium between high-skill and low-skill workers in U.S. manufacturingduring the postwar era. Most notably, the surge in the skill premium in the 1980s and in the 1990scoincides with the surge in the differential size premium. This suggests that differences betweensmall employers and large employers play a potentially important role in explaining the recentincreases in wage inequality.

16

Figure 2: Percentage-point change in the versatility wage premium (w∗H/w∗L, solid line), the al-

location wage premium (w∗H/w∗HL, dotted line), and the appropriation wage premium (w∗H/w

∗LH ,

dashed line) against the relative productivity gains, P. The low-versatility and the high-versatilityworkers’ ratios of the job-finding rate to the separation rate into unemployment, κL and κH , are oneand four, respectively. The productivity threshold, px, is 1.5. The shape parameter, z, and the scaleparameter, p0, of the productivity distribution are three and one, respectively.

and four, respectively. Figure 2 depicts the percentage-point change in the versa-tility wage premium and in the two counterfactual wage premia against the relativeproductivity gains, P. All of the premia are increasing in the relative productivitygains, P.14

3. Empirical Relevance and Scope

The random on-the-job search model is a workhorse model in modern laboreconomics and its predictions have proven fruitful in various applications. Nu-merous economists have studied the model’s mechanisms that affect allocations

14Stijepic (2016c) shows that, by weakening the competition between employers, a mean-preserving spread of the employers’ productivity distribution decreases the share of the productionoutput that the workers receive in the canonical on-the-job search model. This result is particu-larly intriguing in light of the rising productivity dispersion and the declining labor share in manycountries (see, e.g., Dunne et al., 2004; Faggio et al., 2010; Barth et al., 2014; Piketty and Zucman,2014; Karabarbounis and Neiman, 2014). Notably, the stability of the labor’s share of income hasbeen a fundamental feature of macroeconomic models at least since the work of Kaldor (1957).Most of the theoretical literature on structural change and growth focuses on paths that are char-acterized by a constant aggregate labor share of income (e.g., Kongsamut et al., 2001; Ngai andPissarides, 2007; Foellmi and Zweimuller, 2008). See Stijepic (2015a, 2017b, forthcoming) for ageometrical approach to structural change modeling.

17

or rent sharing. In this section, I directly investigate the empirical relevance andscope of the predictions derived in the present paper in order to provide furthersupporting evidence. An overview of the data sets including summary statistics isin Section 3.1. I study the relation between versatility and the mobility parametersof the on-the-job search model in Section 3.2. First evidence supporting a posi-tive relation between the versatility wage premium and the productivity dispersionacross employers is in Section 3.3.

3.1. Data Sets and Summary StatisticsThe following analysis is based on a subsample of the 1979 National Longi-

tudinal Survey of Youth (NLSY). The NLSY follows a sample of the Americanyouth born in 1957–1964. The first round of interviews was in 1979 when the sur-vey participants were of ages 14–22. By the year 2012, 25 interview rounds hadbeen completed. The National Longitudinal Survey of Youth is unique in the sensethat it comprises a nationally representative sample of young people to whom theArmed Services Vocational Aptitude Battery (ASVAB) was administered. Thisset of standardized tests assesses the respondents’ knowledge and skills in severalareas and allows me to construct a measure of a person’s versatility.

I focus on the participants’ labor market outcomes in 2007. The sample selec-tion is as follows. First, I restrict the study to private for-profit employees, sincewage setting and mobility patterns in the government sector or in non-profit ac-tivities may be partially affected by non-market considerations. Second, the finalsample encompasses only white men since non-white individuals’ and women’sopportunities and decisions may also be partially influenced by non-market con-siderations.15 Third, I only consider individuals born in the United States in orderto improve the quality of the education measures. Fourth, I exclude respondentsif irregularities occurred during the Armed Services Vocational Aptitude Batterytesting procedure. The final sample encompasses 823–1,067 individuals, depend-ing on the number of missing values in other variables.

The statistics on the productivity dispersion across establishments within in-dustries are form the Economic Census. The Economic Census collects infor-mation on the U.S. economy once every five years, combining both administra-tive records and establishment surveys. The scope of the Economic Census hasevolved over the years. Since 1992, the industries covered by the program account

15For instance, firms’ discrimination against specific worker groups due to distaste a la Becker(1971), i.e., a concept of discrimination that is not dictated by profit maximization, is a potentialsource of differences in labor market outcomes.

18

for more than 98 percent of the gross domestic product. I make use of EconomicCensus statistics from 2007 reported by Barth et al. (2014).

3.1.1. Standard VariablesThe hourly wage is defined as the annual wage and salary income divided by

the total hours worked in that year. I winsorize the computed hourly wage atthe 1st percentile and at the 99th percentile. The sample includes survey partic-ipants who worked only few hours over the year due to, e.g., part-time work orprolonged periods of unemployment. In order to limit the impact of observationsbased on short employment spells, I make use of weights in all wage regressions.Specifically, I weight the observations by total hours worked winsorized at the99th percentile. The weighted average of the hourly wage in the sample amountsto 32.66 US-Dollars. I measure a person’s job tenure by the number of weeksduring which the person has been working for the current employer. On average,a survey participant has 9.12 years of tenure, where a year is defined to contain 52weeks.

Respondents are grouped into five education categories according to their ed-ucational attainment: individuals who have completed at most the 12th gradeand have no high-school diploma (no high school), high-school graduates (highschool), individuals with some college but either no degree or else an associate de-gree (some college), individuals with a bachelor’s degree (college), and individualswith a master’s, professional school or doctoral degree (advanced). I distinguishfour regions of residence: the northeastern, the northern central, the southern, andthe western region of the United States. The full set of controls also includesfour-digit Census-2003 occupation-level and industry-level fixed effects.

Following Barth et al. (2014), I define eight major industries: (i) mining,construction, utilities, and transport, (ii) manufacturing, (iii) wholesale and re-tail trade, (iv) information and communication, (v) finance, insurance, and realestate, (vi) business services, (vii) health, education, and social services, and (viii)personal services. I use the standard deviation of log-sales-per-employee acrossestablishments from 2007, computed by Barth et al. (2014) based on EconomicCensus data, as a measure of the productivity dispersion within the eight majorindustries.

I also exploit interview questions from various survey years that provide in-formation on the respondents’ attitudes and traits. Since the questions are admin-istered at various points in time, I only have the complete list of variables for 823individuals who participated in the survey in all the relevant years. In order to inferrisk attitudes, the survey participants are asked whether they are generally fully

19

prepared to take risks or whether they try to avoid taking risks. The maximumpossible score is ten, indicating the full preparedness to take risks, and the mini-mum possible score is zero, indicating the unwillingness to take any risks. Trustis measured on the basis of the question of how often you can trust other people.The possible answers range from one, indicating always, to five, indicating never.

The Rotter Locus of Control Scale measures the extent to which individu-als believe that they have control over their lives through self-motivation or self-determination as opposed to the extent that the environment controls theirs lives(Rotter, 1966). The maximum possible score is 16, indicating a high externalcontrol, while the minimum possible score is four, indicating a high internal con-trol. The Rosenberg Self-Esteem Scale describes the degree of approval or dis-approval towards oneself (Rosenberg, 1965). The maximum possible score is 30,while the minimum possible score is zero. A higher score designates a higherself-esteem. The Pearlin Mastery Scale describes the extent to which individualsperceive themselves in control of the forces that significantly impact their lives(Pearlin et al., 1981). The total score may range from 7 to 28. Higher scoresrepresent greater mastery.

3.1.2. Skills and VersatilityThe Armed Services Vocational Aptitude Battery (ASVAB) was administered

to a total of 11,914 National Longitudinal Survey of Youth respondents in 1980,representing a completion rate of approximately 94 percent. The testing was con-ducted according to standard ASVAB procedural guidelines. Five to ten personswere tested at more than 400 test sites, including hotels, community centers andlibraries throughout the United States and abroad. The NLSY participants werepaid 50 US-Dollars for completing the test in order to compensate them for theirtime and travel expenses.

The ASVAB consists of a battery of ten subtests that assess knowledge andskills in the following areas: (i) general science, (ii) arithmetic reasoning, (iii)word knowledge, (iv) paragraph comprehension, (v) numerical operations, (vi)coding speed, (vii) auto and shop information, (viii) mathematics knowledge, (ix)mechanical comprehension, and (x) electronics information. Each subtest hasbeen fitted separately to an item response curve psychometric model: a three-parameter logistic model for the power subtests and a Poisson model for thespeeded subtests. When the logistic model is estimated, it is capable of account-ing for the facts that (i) some subjects perform better than others on the itemsin the subtest, (ii) some items in the subtest are easier than others, (iii) someitems measure the underlying ability more precisely than others, and (iv) subjects

20

02

46

810

1214

1618

2022

perc

ent

0 1 2 3 4 5 6 7 8 9 10

Figure 3: Respondents’ number of ASVAB subtests with above-mean scores. Sample restrictedto white male private for-profit employees ages 25-55 and born in the United States. Author’scalculations based on the 1979 National Longitudinal Survey of Youth.

can occasionally answer any item correctly by guessing since the test items aremultiple choice. In order to recover the respondents underlying ability, the Pois-son model is fitted under the two assumptions that (i) the item content within asubtest is homogeneous, and that (ii) a subtest is infinitely long. The final knowl-edge and skill estimates have been standardizes within each ASVAB subtest toweighted population means of zero and standard deviations of one. I winsorizeeach ASVAB subtest score at the 1st percentile and at the 99th percentile.

I measure the survey participants’ versatility by the number of ASVAB sub-tests in which they achieved scores above the mean. Figure 3 displays the distri-bution of the number of above-mean scores in the sample. Of course, not all skillsare equally relevant on the labor market. In order to take into account further dif-ferences in the survey participants’ skills, I additionally include controls for allthe ten ASVAB subtest scores in all the following regressions. On average, therespondents obtain above-mean scores in 6.3 subtests.

3.1.3. Summary StatisticsTable 1 presents summary statistics for the overall sample and separately by

education. The number of subtests in which the respondents have above-meanscores is increasing in educational attainment. On the one hand, high-schooldropouts perform above the mean in only 1.7 subtests. On the other hand, respon-dents with advanced education have above-mean scores in 9.1 subtests. I notethat education is positively associated with the respondents’ willingness to trustother people, i.e., smaller values of the displayed trust measure. Table 2 displays

21

Overall No high High Some College Advancedschool school college

Share (in %) 100 7.22 43.96 16.12 20.90 11.81(0.79) (1.52) (1.13) (1.25) (0.99)

Above-mean scores 6.27 1.68 5.05 6.76 8.43 9.14(0.10) (0.22) (0.14) (0.22) (0.13) (0.11)

Rotter locus of control 8.50 9.35 8.95 8.57 7.82 7.44(0.07) (0.29) (0.11) (0.18) (0.15) (0.20)

Rosenberg self-esteem 22.70 20.81 21.92 23.14 23.52 24.66(0.12) (0.46) (0.17) (0.31) (0.28) (0.32)

Pearlin mastery 22.47 20.74 21.85 22.60 23.61 23.64(0.09) (0.30) (0.13) (0.26) (0.19) (0.29)

Trust attitude 2.78 3.26 2.94 2.78 2.57 2.31(0.03) (0.12) (0.04) (0.07) (0.05) (0.06)

Risk attitude 5.22 4.83 4.74 5.25 5.98 5.86(0.08) (0.35) (0.13) (0.19) (0.15) (0.16)

Tenure (in years) 9.12 7.01 9.62 8.72 9.39 8.65(0.25) (0.79) (0.41) (0.61) (0.52) (0.67)

Hourly wage 32.66 17.94 21.53 29.18 46.74 60.70(0.92) (2.15) (0.67) (1.68) (2.46) (3.58)

Table 1: Summary statistics for white male private for-profit employees ages 25-55 and born in theUnited States. Standard errors in parentheses. Author’s calculations based on the 1979 NationalLongitudinal Survey of Youth.

summary statistics by industry. The log-sales-per-employee standard deviationsubstantially varies across industries. Education, health, and social services is theleast dispersed industry with a standard deviation of 73 log-points. Finance, in-surance, and real estate is the most dispersed industry with a standard deviation of120 log-points.

Table 3 shows the principle component analysis of the ten ASVAB subtestscores, i.e., the leading eigenvalues and eigenvectors from the eigen decomposi-tion of the correlation matrix. The objective of the principle component analysisis to find unit-length linear combinations of the (standardized) variables with thegreatest variance. The first principal component has maximal overall variance.The second principal component has maximal variance among all unit-lengthlinear combinations that are uncorrelated to the first principal component, etc.All principal components combined contain the same information as the original(standardized) variables.

The first principle component of the ASVAB subtest scores has an eigenvalueof 6.3, i.e, it explains 63 percent (6.3/10) of the overall variance of the ten stan-dardized ASVAB subtest scores. The second principle component has an eigen-value of 1.2, explaining 12 percent (1.2/10) of the overall variance. The first and

22

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Tabl

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Sum

mar

yst

atis

tics

byin

dust

ryfo

rwhi

tem

ale

priv

ate

for-

profi

tem

ploy

ees

ages

25-5

5an

dbo

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the

Uni

ted

Stat

es.V

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tility

wag

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man

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per-

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les-

disp

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tics

from

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2014

).

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Num

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90.

121

−0.1

400.

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308

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Tabl

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Prin

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the second component together account for roughly three-quarters ((6.3+1.2)/10)of the overall variance. The entries of the eigenvector of the first principle compo-nent, which are the loadings multiplying the standardized ASVAB subtest scores,are positive for all subtests and of roughly equal size. Hence, the first componentcan be interpreted as a person’s overall skill level. The eigenvector of the sec-ond principle component has, in particular, negative loadings on numeracy skills,e.g., arithmetic reasoning, numerical operations, coding speed and mathematicalknowledge. Hence, the second principle component tends to distinguish numeracyskills from other skills.

3.2. Mobility and VersatilityInterestingly, the literature typically finds a positive correlation between the

ratio of the job-finding rate to the separation rate into unemployment, κ, and ed-ucational attainment. Cahuc et al. (2006) estimate the transition parameters ofan on-the-job search model for four skill groups in four French industries, findingthat the ratio of the job-finding rate to the separation rate into unemployment tendsto increase with a person’s skill level. For instance, they estimate this ratio to be1.02 for the lowest skill category and 3.95 for the highest skill category in Frenchmanufacturing.

Making use of the Current Population Survey, Fallick and Fleischman (2004)document monthly gross worker flows for the United States in 1994–2003, find-ing that while individuals with higher educational attainment separate less oftento another employer, they are disproportionately less likely to separate into unem-ployment. For instance, 8.6 percent of employed high-school dropouts separateinto unemployment or leave the labor force each month. Another 3.4 percentchange employers. In contrast, 2.0 percent of persons with advanced educationchange employers, but only 1.9 percent separate into unemployment or leave thelabor force.16 Therefore, the risk ratio of an employer–employer transition to aseparation into unemployment is increasing in education. I note that the risk ratioof separating to another employer to separating into unemployment is an ordi-nal transformation of the ratio of the job-finding rate to the separation rate intounemployment in the canonical on-the-job search model (see Stijepic, 2016a).

Relying on the 1996 Panel of the Survey of Income and Program Partici-pation, Stijepic (2016a) studies the determinants of the risk ratio an employer–

16Overall, Fallick and Fleischman (2004) report that 2.6 percent of employed workers separateto another employer, 1.3 percent separate into unemployment, and 2.7 percent leave the labor forceeach month.

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employer transition to a separation into unemployment. Formal education tends tobe positively correlated with this risk ratio. General experience and accumulatedoccupation-specific human capital substantially reduce both job-to-job transitionsand separations into unemployment, leaving the risk ratio, however, mostly un-affected. In contrast to other studies, Stijepic (2016a) constructs a proxy for aperson’s versatility based on the number of different courses that the person at-tended in high school. Above-median versatile individuals are estimated to be 1.6times more likely to separate to another employer than into unemployment rela-tive to below-median versatile individuals. The effect is similar in magnitude tothat of a college degree on a high-school dropout’s risk ratio. Notably, Stijepic(2016a) finds a positive correlation between the employed versatility measure andthe standard measures of education.17

Following Ridder and van den Berg (2003) and Cahuc et al. (2006), I maxi-mize the unconditional likelihood of job tenure in the sample in order to estimatethe job-finding rate and the separation rate into unemployment. Specifically, thelikelihood function is based on Equation (6) derived in Section 2.2.2. I adjust thelikelihood to account for the fact that job tenure is available at weekly intervals.Furthermore, I censorize job tenure at three years, where a year is defined to con-tain 52 weeks, following Cahuc et al. (2006). I extend the estimation procedureby assuming that the job-finding rate and the separation rate into unemploymentare log-linear in the relevant covariates, denoted by xi for i ∈ {1, ..., n}, i.e.,

δ = eδ0+∑n

i=1 δi xi and λ = eλ0+∑n

i=1 λi xi , (14)

where the coefficients δi and λi for i ∈ {0, ..., n} are to be estimated.The set of covariates contains the number of above-mean ASVAB subtest

scores as a measure of a person’s versatility. In order to control for skill dif-ferences beyond the mere number of above-mean scores, I would ideally includeeach of the ten ASVAB subtest scores into the set of covariates so that the num-ber of above-mean scores captures predominately the diversity within each skillportfolio and not its composition. Unfortunately, the sample is not large enoughand the likelihood function does not exhibit sufficient curvature in order to iden-

17Stijepic (2017c,a) studies the relation between cognitive skills and employment, making useof an international survey that directly assesses participants’ cognitive skills in several domains.Notably, the risk ratio of exiting to entering unemployment is positively correlated with a country’saverage worker versatility as measured by the number of skill domains in which a worker hasabove-median scores, suggesting that it is essential to acquire a certain level of proficiency in askill domain in order to get a job and to stay employed.

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λi δi λi − δi

Above-mean scores 1.830∗∗ −0.213∗∗ 2.044∗∗∗(0.763) (0.088) (0.791)

Principle com-ponents of scores

First −2.221∗∗ 0.162 −2.384∗∗(0.888) (0.114) (0.926)

Second 0.070 0.008 0.062(0.661) (0.080) (0.708)

Third 3.277∗ −0.416∗∗∗ 3.693∗∗(1.708) (0.100) (1.720)

Constant −8.656∗∗ −1.775∗∗∗ −6.881(4.094) (0.587) (4.422)

Table 4: Maximum-likelihood estimates of the effects of the displayed variables on the job-findingrate per annum and the separation rate into unemployment per annum. Log-likelihood: −2,310.Observations: 1,051. Sample restricted to white male private for-profit employees ages 25-55 andborn in the United States. Standard errors in parentheses. Statistical significance at the 10, 5, and1 percent level denoted by ∗, ∗∗, and ∗∗∗, respectively. Author’s calculations based on the 1979National Longitudinal Survey of Youth.

tify all of the parameters reliably. Therefore, I make instead use of the first threeprinciple components of the ten ASVAB subtest scores, which capture 81 percentof the overall variance of the standardized scores. Additionally controlling forthe fourth principle component and the fifth principle component does not sizablyaffect the point estimate on the number of above-mean ASVAB subtest scores.Table 4 displays the maximum-likelihood estimates.

I note that the principle components of the ASVAB scores are zero for a personwho performs on average in all ASVAB subtests. Hence, a person who scoresclose to the mean in all subtests and slightly above the mean in four subtests isestimated to have a job-finding rate, λ, of 0.26 (exp(4 · 1.8 − 8.7)), implying anaverage spell between job offers of 3.80 years (1/λ). The separation rate intounemployment, δ, is estimated to be 0.07 (exp(4 · (−0.2) − 1.8)), implying anaverage employment spell of 13.83 years (1/δ). Hence, the ratio of the job-findingrate to the separation rate into unemployment, κ, is 3.64, i.e., the person obtains3.64 job offers per employment spell.

An additional above-mean score is estimated, ceteris paribus, to increase thejob-finding rate by a factor of 6.2 (exp(1.8)) and to decrease the separation rateinto unemployment by a factor of 0.8 (exp(−0.2)). Therefore, the ratio of thejob-finding rate to the separation rate into unemployment rises by a factor of 7.7(exp(1.8 + 0.2)). The effects are statistically significant at the five percent level.All in all, the estimates of the impact of versatility on the job-finding rate, λ, and

27

on the separation rate into unemployment, δ, are in line with the on-the-job searchmodel imposing structural impediments to sorting presented in Section 2.

3.3. Productivity Dispersion and the Returns to VersatilityIn this section, I estimate how the returns to versatility depend on the pro-

ductivity dispersion across establishments. Specifically, I exploit variations in thestandard deviation of log-sales-per-employee across eight major U.S. industriesin 2007. Table 5 displays the ordinary least-squares estimates of the effects of thedisplayed variables on the logarithm of the hourly wage. Since the measure ofproductivity dispersion varies only at the major industry level, I adjust the stan-dard errors for clustering at that level. The first specification in Table 5 includesthe number of ASVAB subtests with above-mean scores as a measure of a per-son’s versatility, its interaction with the industry standard deviation of log-sales-per-employee, the industry standard deviation of log-sales-per-employee, and theASVAB subtest scores and their interactions with the industry standard deviationof log-sales-per-employee. An increase in the standard deviation of log-sales-per-employee by ten log-points is associated with an increase in the above-mean scorepremium by 2.9 log-points in the sample. Notably, the standard deviation of log-sales-per-employee ranges from 0.73 in education, health and social services to1.20 in finance, insurance and real estate. Evaluated at this range, the estimate inthe first specification suggests an increase in the above-mean score premium by13.7 log-points (0.29 · (1.20 − 0.73)).

Versatility may be a requirement for some high-paid jobs. Such wage effectsdo not necessarily reflect the mechanisms at work in the on-the-job search modelimposing structural impediments to sorting. Indeed, I assume in Section 2 thatjobs that are suitable for high-versatility workers do not systematically differ fromthe jobs that are suitable for low-versatility workers. Therefore, I also control forcareer choices by including four-digit Census-2003 industry-level fixed effects,four-digit Census-2003 occupation-level fixed effects, and region-of-residence-level fixed effects in the second specification of Table 5. The relation betweenthe versatility wage premium and the industry standard deviation of log-sales-per-employee remains positive and statistically significant at the five percent level.

A prominent strand of the literature stresses the role of non-cognitive skillsin explaining labor market outcomes. For instance, Heckman et al. (2011) studyhigh-school dropouts, who can take the General Educational Development (GED)test to certify to employers and post-secondary institutions that their skills areequivalent to those of high-school graduates. They find that high-school dropouts

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(1) (2) (3) (4)

Above-mean scores −0.283∗ −0.348∗∗∗ −0.329∗∗ −0.318∗∗(0.124) (0.042) (0.099) (0.113)

Above-mean scores and 0.292∗∗ 0.367∗∗∗ 0.331∗∗ 0.318∗∗sales dispersion interacted (0.117) (0.041) (0.099) (0.102)Education

No high school – – – −2.099(1.553)

Some college – – – −0.161(0.768)

College – – – 0.607(0.488)

Advanced – – – 0.506(0.581)

Education and salesdispersion interacted

No high school – – – 1.996(1.620)

Some college – – – 0.238(0.811)

College – – – −0.403(0.534)

Advanced – – – −0.117(0.642)

Sales dispersion −1.314∗∗∗ – – –(0.325)Attitudes and traits,

– – x xand interactions withsales dispersionIndustry, occupation, – x x xand regionASVAB subtest scores,

x x x xand interactions withsales dispersion

R-squared 0.253 0.691 0.747 0.756Observations 916 909 823 823

Table 5: Ordinary least-squares estimates of the effects of the displayed variables on the loga-rithm of the hourly wage. Weights proportional to hours worked used in all calculations. Samplerestricted to white male private for-profit employees ages 25-55 and born in the United States.Standard errors adjusted for clustering at the major industry level in parentheses. Statistical signif-icance at the 10, 5, and 1 percent level denoted by ∗, ∗∗, and ∗∗∗, respectively. Author’s calculationsbased on the 1979 National Longitudinal Survey of Youth. Sales dispersion statistics from Barthet al. (2014).

who pass the GED test perform about as well as high-school graduates on achieve-ment tests but perform much worse in many aspects of life because they lack im-portant personality traits such as persistence, motivation, and reliability. Heckman

29

et al. (2006) estimate both cognitive and non-cognitive skills to be associated withsubstantial wage premia.18 Therefore, I additionally control for the respondents’attitudes and traits as described in Section 3.1.1 in the third specification of Table5. Since the economics literature suggests a prominent role of risk and trust atti-tudes, I generate indicator variables for each of the eleven risk categories and fivetrust categories. All the measures of the respondents’ attitudes and traits are alsointeracted with the industry standard deviation of log-sales-per-employee. Thepositive relation between the versatility wage premium and the industry standarddeviation of log-sales-per-employee persists.

Conventional human capital theory claims that education adds to the pro-ductivity of individual employees and, therefore, increases the market value oftheir labor (Becker, 1964; Mincer, 1974). It does not matter how the productiv-ity is increased, but it is implicitly assumed that students receive skills throughtheir education. Other scholars have pointed out that—due to, e.g., informationalfrictions—the selection, allocation, and rewarding of individual employees alsotakes place on the basis of signals such as formal qualifications (Spence, 1973).In such markets, formal education adds not only to the productivity of individualemployees, but also positively affects the individual employees’ labor market out-comes by serving as a signaling device for their productive capacities. Yet otherscholars argue that education serves as a rationing device, in particular, for highlypaid high-status jobs (Collins, 1979). In order to control for such effects, I alsoinclude the education indicator variables and their interactions with the industrystandard deviation of log-sales-per-employee in the fourth specification of Table5. The relation between the versatility wage premium and the industry standarddeviation of log-sales-per-employee remains positive and statistically significantat the five percent level.

4. Conclusion

For the United States, I document that (i) a person’s versatility measured bythe number of test areas in which the person scores above the average is positivelyassociated with the ability to reallocate across employers and that (ii) the wagereturns to versatility are higher in more dispersed industries. An above-meanscore in an additional test area is estimated to raise the ratio of the job-findingrate to the separation rate into unemployment by a factor of 7.7. An increase in

18Heckman and Kautz (2012) review the evidence on how school grades, the performance inachievement and IQ tests, personality traits and attitudes relate to success in life.

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the standard deviation of log-sales-per-employee by ten log-points is estimated toraise the wage returns to an above-mean score by 2.9–3.7 log-points.

The findings are consistent with a model that features both frictional and struc-tural impediments to sorting. In an environment where jobs differ in requirements,versatility enhances a person’s ability to allocate to the most productive firms sinceefficient reallocations are less likely to be hindered by unmet job requirements.Furthermore, the returns to sorting into the most productive firms and, hence, ver-satility are larger, the more pronounced the productivity differentials between thefirms are. Intuitively, if firms are similar in productivity, the returns from sortinginto more productive firms are low. However, if the disparities between firms aresubstantial, so will be the returns. The wage differential between more versatileand less versatile individuals is amplified.

In view of the surge in the productivity dispersion across employers and thepositive correlation between educational attainment and versatility, the presentpaper’s findings suggest a prominent role of versatility in explaining the rise in thecollege wage premium in the United Sates between the 1970s and the 1990s. Allin all, it is potentially not the specialization into particularly productive specifictasks or activities that allowed college graduates to obtain relative wage raises, butrather the ability to perform various tasks and activities—eventually even acrossoccupations.

31

References

Abowd, J. M., Kramarz, F., Margolis, D. N., 1999. High Wage Workers and High WageFirms. Econometrica 67 (2), 251–334.

Atakan, A. E., 2006. Assortative Matching with Explicit Search Costs. Econometrica74 (3), 667–680.

Bagger, J., Lentz, R., 2014. An Empirical Model of Wage Dispersion with Sorting. NBERWorking Papers 20031, National Bureau of Economic Research, Inc.

Barth, E., Bryson, A., Davis, J. C., Freeman, R. B., 2014. It’s Where You Work: In-creases in Earnings Dispersion across Establishments and Individuals in the U.S. IZADiscussion Papers 8437, Institute for the Study of Labor (IZA).

Bayer, C., Walde, K., 2010. Matching and Saving in Continuous Time: Theory. CESifoWorking Paper Series 3026, CESifo Group Munich.

Becker, G. S., 1964. Human Capital: A Theoretical and Empirical Analysis with SpecialReference to Education. Columbia University Press.

Becker, G. S., 1971. The Economics of Discrimination. University of Chicago Press.

Becker, G. S., 1973. A Theory of Marriage: Part I. Journal of Political Economy 81 (4),813–46.

Becker, G. S., 1974. A Theory of Marriage: Part II. Journal of Political Economy 82 (2),S11–S26.

Bontemps, C., Robin, J.-M., van den Berg, G. J., 2000. Equilibrium Search with Con-tinuous Productivity Dispersion: Theory and Nonparametric Estimation. InternationalEconomic Review 41 (2), 305–58.

Burdett, K., Mortensen, D. T., 1998. Wage Differentials, Employer Size, and Unemploy-ment. International Economic Review 39 (2), pp. 257–273.

Cahuc, P., Postel-Vinay, F., Robin, J.-M., 2006. Wage Bargaining with On-the-Job Search:Theory and Evidence. Econometrica 74 (2), 323–364.

Card, D., Cardoso, A. R., Kline, P., 2016. Bargaining, Sorting, and the Gender Wage Gap:Quantifying the Impact of Firms on the Relative Pay of Women. The Quarterly Journalof Economics 131 (2), 633–686.

Card, D., Heining, J., Kline, P., 2013. Workplace Heterogeneity and the Rise of WestGerman Wage Inequality. The Quarterly Journal of Economics 128 (3), 967–1015.

Charlot, O., Decreuse, B., Granier, P., 2005. Adaptability, Productivity, and EducationalIncentives in a Matching Model. European Economic Review 49 (4), 1007–1032.

Collins, R., 1979. The Credential Society: An Historical Sociology of Education andStratification. Academic Press.

32

de Melo, R. L., forthcoming. Firm Wage Differentials and Labor Market Sorting: Recon-ciling Theory and Evidence. Journal of Political Economy.

Delacroix, A., Shi, S., 2006. Directed Search On the Job and the Wage Ladder. Interna-tional Economic Review 47 (2), 651–699.

Dunne, T., Foster, L., Haltiwanger, J., Troske, K. R., 2004. Wage and Productivity Dis-persion in United States Manufacturing: The Role of Computer Investment. Journal ofLabor Economics 22 (2), 397–430.

Eeckhout, J., Kircher, P., 2011. Identifying Sorting–In Theory. Review of Economic Stud-ies 78 (3), 872–906.

Faggio, G., Salvanes, K. G., van Reenen, J., 2010. The Evolution of Inequality in Pro-ductivity and Wages: Panel Data Evidence. Industrial and Corporate Change 19 (6),1919–1951.

Fallick, B., Fleischman, C. A., 2004. Employer-to-Employer Flows in the U.S. LaborMarket: The Complete Picture of Gross Worker Flows. Finance and Economics Dis-cussion Series 2004-34, Board of Governors of the Federal Reserve System (U.S.).

Foellmi, R., Zweimuller, J., 2008. Structural Change, Engel’s Consumption Cycles andKaldor’s Facts of Economic Growth. Journal of Monetary Economics 55 (7), 1317–1328.

Groes, F., Kircher, P., Manovskii, I., 2015. The U-Shapes of Occupational Mobility. Re-view of Economic Studies 82 (2), 659–692.

Grossman, G. M., Helpman, E., Kircher, P., forthcoming. Matching, Sorting, and theDistributional Effects of International Trade. Journal of Political Economy.

Guvenen, F., Kuruscu, B., Tanaka, S., Wiczer, D., 2015. Multidimensional Skill Mis-match. NBER Working Papers 21376, National Bureau of Economic Research, Inc.

Hagedorn, M., Law, T. H., Manovskii, I., forthcoming. Identifying Equilibrium Modelsof Labor Market Sorting. Journal of Political Economy.

Heckman, J. J., Humphries, J. E., Mader, N. S., 2011. The GED. Vol. 3 of Handbook ofthe Economics of Education. Elsevier, Ch. 9, pp. 423–483.

Heckman, J. J., Kautz, T., 2012. Hard Evidence on Soft Skills. Labour Economics 19 (4),451–464.

Heckman, J. J., Stixrud, J., Urzua, S., 2006. The Effects of Cognitive and NoncognitiveAbilities on Labor Market Outcomes and Social Behavior. Journal of Labor Economics24 (3), 411–482.

Hsieh, C.-T., Klenow, P. J., 2009. Misallocation and Manufacturing TFP in China andIndia. The Quarterly Journal of Economics 124 (4), 1403–1448.

Jensen, M. K., 2017, forthcoming. Distributional Comparative Statics. Review of Eco-nomic Studies.

33

Jovanovic, B., 1979. Job Matching and the Theory of Turnover. Journal of Political Econ-omy 87 (5), 972–90.

Kaldor, N., 1957. A Model of Economic Growth. The Economic Journal 67 (268), 591–624.

Kambourov, G., Manovskii, I., 2008. Rising Occupational and Industry Mobility in theUnited States: 1968-97. International Economic Review 49 (1), 41–79.

Kambourov, G., Manovskii, I., 2009. Occupational Mobility and Wage Inequality. Reviewof Economic Studies 76 (2), 731–759.

Karabarbounis, L., Neiman, B., 2014. The Global Decline of the Labor Share. The Quar-terly Journal of Economics 129 (1), 61–103.

Kongsamut, P., Rebelo, S., Xie, D., 2001. Beyond Balanced Growth. Review of EconomicStudies 68 (4), 869–882.

Kramarz, F., Postel-Vinay, F., Robin, J.-M., 2014. Occupational Mobility and Wage Dy-namics Within and Between Firms. Mimeo.

Lentz, R., Mortensen, D. T., 2008. An Empirical Model of Growth Through ProductInnovation. Econometrica 76 (6), 1317–1373.

Lindenlaub, I., forthcoming. Sorting Multidimensional Types: Theory and Application.Review of Economic Studies.

Lise, J., Meghir, C., Robin, J.-M., 2016. Matching, Sorting and Wages. Review of Eco-nomic Dynamics 19, 63–87.

Lise, J., Postel-Vinay, F., 2015. Multidimensional Skills, Sorting, and Human CapitalAccumulation. 2015 Meeting Papers 386, Society for Economic Dynamics.

Manning, A., 2003. Monopsony in Motion: Imperfect Competition in Labor Markets.Princeton University Press.

McCall, B. P., 1990. Occupational Matching: A Test of Sorts. Journal of Political Econ-omy 98 (1), 45–69.

Mincer, J. A., 1974. Schooling, Experience, and Earnings. NBER Books. National Bureauof Economic Research, Inc.

Moscarini, G., 2008. Job-to-Job Quits and Corporate Culture: New Results. 2008 MeetingPapers 153, Society for Economic Dynamics.

Ngai, L. R., Pissarides, C. A., 2007. Structural Change in a Multisector Model of Growth.American Economic Review 97 (1), 429–443.

Pearlin, L. I., Lieberman, M. A., Menaghan, E. G., Mullan, J. T., 1981. The Stress Process.Journal of Health and Social Behavior 20, 337–353.

34

Piketty, T., Zucman, G., 2014. Capital is Back: Wealth-Income Ratios in Rich Countries1700–2010. The Quarterly Journal of Economics 129 (3), 1255–1310.

Postel-Vinay, F., Robin, J.-M., 2002. Equilibrium Wage Dispersion with Worker and Em-ployer Heterogeneity. Econometrica 70 (6), 2295–2350.

Ransom, M. R., Oaxaca, R. L., 2010. New Market Power Models and Sex Differences inPay. Journal of Labor Economics 28 (2), 267–289.

Ridder, G., van den Berg, G. J., 2003. Measuring Labor Market Frictions: A Cross-Country Comparison. Journal of the European Economic Association 1 (1), 224–244.

Rogerson, R., Shimer, R., Wright, R., 2005. Search-Theoretic Models of the Labor Mar-ket: A Survey. Journal of Economic Literature 43 (4), 959–988.

Rosenberg, M., 1965. Society and the Adolescent Self-Image. Princeton University Press.

Rotter, J. B., 1966. Generalized Expectancies for Internal Versus External Control of Re-inforcement. Psychological Monographs General and Applied 80 (1).

Sanders, C., Taber, C., 2012. Life-Cycle Wage Growth and Heterogeneous Human Capi-tal. Annual Review of Economics 4 (1), 399–425.

Shi, S., 03 2009. Directed Search for Equilibrium Wage-Tenure Contracts. Econometrica77 (2), 561–584.

Shimer, R., 2006. On-the-Job Search and Strategic Bargaining. European Economic Re-view 50 (4), 811–830.

Shimer, R., Smith, L., 2000. Assortative Matching and Search. Econometrica 68 (2), 343–370.

Spence, M., 1973. Job Market Signaling. The Quarterly Journal of Economics 87 (3),355–374.

Stijepic, D., 2015a. A Geometrical Approach to Structural Change Modelling. StructuralChange and Economic Dynamics 33 (C), 71–85.

Stijepic, D., 2015b. A Note on Laws of Motion for Aggregate Distributions. Available athttp://ssrn.com/abstract=2644742.

Stijepic, D., 2015c. Technology Diffusion, Worker Mobility and the Returns to Skills.Available at http://dx.doi.org/10.2139/ssrn.2635538.

Stijepic, D., 2016a. Job Mobility and Sorting: Theory and Evidence. Available athttp://dx.doi.org/10.2139/ssrn.2635518.

Stijepic, D., 2016b. Small Employers, Large Employers and the Skill Premium. Eco-nomics Bulletin 36 (1), 381–387.

Stijepic, D., 2016c. The Impact of the Productivity Dispersion across Employers on theLabor’s Income Share. Available at http://ssrn.com/abstract=2803460.

35

Stijepic, D., 2017a. A Cross-Country Study of Workers’ Skills and Unemployment Flows.Available at https://ssrn.com/abstract=2903283.

Stijepic, D., 2017b. An argument against Cobb-Douglas production functions (in multi-sector growth modeling). Economics Bulletin 37 (2), 1143–1150.

Stijepic, D., 2017c. Employment Effects of Skills Around the World: Evidence fromPIAAC. Available at http://ssrn.com/abstract=2850550.

Stijepic, D., 2017d. Globalization, Worker Mobility and Wage Inequality. Review of In-ternational Economics 25 (1), 108–131.

Stijepic, D., forthcoming. Positivistic models of long-run labor allocation dynamics. Jour-nal of Economic Structures.

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