Accessible Unlicensed Requires Authentication Published online by De Gruyter August 20, 2021

Workplace Heterogeneity and the Returns to Versatility

Damir Stijepic

Abstract

In the canonical random on-the-job search model with continuous firm heterogeneity, I show that a mean-preserving spread of the firm-productivity distribution raises the returns to mobility, i.e., the inter-firm mobility of workers as measured by the number of outside contacts per employment spell. Both sorting and rent-share mechanisms play a role. In a further contribution, I distinguish frictional and structural impediments to mobility in order to establish a link between mobility and skills via the concept of versatility. Versatility enhances a person’s mobility since a mismatch between job requirements and the person’s skill set is less likely to occur. I provide some statistics in support of the discussed mechanisms. The findings are particularly intriguing in light of the concurrent rise in the productivity dispersion across firms and in the skill premium in many countries.

JEL Classification: J22; J24; J31; J62; J63; I26; E24

Corresponding author: Damir Stijepic, Johannes Gutenberg University, Mainz, Germany, E-mail:

Acknowledgments

I thank Sarra Ben Yahmed, Björn Brügemann, Carlos Carrillo-Tudela, Tewodros Dessie, Guido Friebel, Nicola Fuchs-Schündeln, Peter Funk, Terry Gregory, Marten Hillebrand, Andrey Launov, Jeremy Lise, Alexander Mosthaf, Henning Müller, Jean-Marc Robin, Sonja Settele, Iryna Stewen, Reyn van Ewijk, Burkhard Schipper, Klaus Wälde, four anonymous referees, and the participants of the Chair in Macroeconomics Research Day at the Johannes Gutenberg University (Mainz 2015), the ZEW Research Seminar (Mannheim 2015) and the Jahrestagung des Vereins für Socialpolitik (Augsburg 2016) for helpful comments. I gratefully acknowledge the financial support provided by the Fritz Thyssen Foundation under the grant No. 40.16.0.028WW and by the German Research Foundation (DFG) under the grant No. 433336278. The usual disclaimer applies.

Appendix A. Empirical Relevance and Scope

The random on-the-job search model is a workhorse model in modern labor economics and its predictions have proven fruitful in various applications. Numerous economists have studied the model’s mechanisms that affect allocations or rent sharing. In this appendix, I directly explore the empirical relevance and scope of the predictions derived in the main text, making use of the 1979 National Longitudinal Survey of Youth (NLSY). An overview of the data is in Appendix 1. I study how versatility is related to job mobility and to wages in Appendix 2. A summary of the empirical findings is in Appendix 3.

A.1 The National Longitudinal Survey of Youth

The following analysis is based on the 1979 NLSY. The NLSY follows a sample of the American youth born in 1957–1964. The first round of interviews was in 1979. By the year 2012, 25 interview rounds had been completed. I study the labor-market outcomes in 2007. I note that all survey participants are in their 40s in that year. The NLSY is unique in the sense that it comprises a nationally representative sample of young people to whom the Armed Services Vocational Aptitude Battery (ASVAB) was administered. This set of standardized tests assesses knowledge and skills in several areas, allowing me to construct a measure of a person’s versatility. The ASVAB was administered to a total of 11,914 NLSY participants in 1980, representing a completion rate of approximately 94 percent. The testing was conducted according to standard ASVAB procedural guidelines. 5–10 participants were tested at more than 400 test sites. The NLSY participants were paid 50 US-dollars for completing the test in order to compensate them for their time and travel expenses.

The ASVAB consists of a battery of ten subtests that assess knowledge and skills 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 is fitted separately to an item response curve psychometric model: a three-parameter logistic model for the power subtests and a Poisson model for the speeded subtests. The final knowledge and skill estimates are standardized within each ASVAB subtest to population means of zero and standard deviations of one. I winsorize each ASVAB subtest score at the 1st percentile and at the 99th percentile. Furthermore, I rely on two attitudinal scales as a measure of non-cognitive abilities. The Rotter Locus of Control Scale measures the extent to which individuals 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 external control, while the minimum possible score is four, indicating a high internal control. The Rosenberg Self-Esteem Scale describes the degree of approval or disapproval towards oneself (Rosenberg 1965). The maximum possible score is 30, while the minimum possible score is zero. A higher score designates a higher self-esteem. I standardize each attitudinal scale to a mean of zero and a standard deviation of one in the sample.

In line with Guvenen et al. (2020), I construct three skill categories: mathematical, verbal and social skills. Mathematical skills are the principal component of the ASVAB test scores in the areas of arithmetic reasoning and mathematics knowledge. Verbal skills are the principal component of the ASVAB test scores in the areas of word knowledge and paragraph comprehension. Social skills are the principal component of the Rosenberg Self-Esteem Scale and the inverse Rotter Locus of Control Scale. I measure a person’s versatility by the number of skill domains with above-median scores. For instance, if a person scores above the median in the mathematical and in the verbal domain but below the median in the social domain, the person has two skills domains with above-median scores overall, i.e., a versatility of two.

The hourly wage is defined as the annual wage and salary income divided by total hours worked. I winsorize the hourly wage at the 1st percentile and at the 99th percentile. The sample includes survey participants who worked only few hours over the year due to, e.g., part-time work or protracted periods of unemployment. In order to limit the impact of observations based on short employment spells, I make use of weights in all wage regressions. Specifically, I weight the observations by total hours worked winsorized at the 99th percentile. I measure a person’s job tenure by the number of weeks during which the person has been working for the current employer.

The statistics on the productivity dispersion across establishments within industries are form the Economic Census. The Economic Census collects information on the U.S. economy once every five years, combining both administrative records and establishment surveys. The scope of the Economic Census has evolved over the years. Since 1992, the industries covered by the program account for more than 98 percent of the gross domestic product. Following Barth et al. (2016), I define eight major industries: (i) mining, construction, utilities and transport, (ii) manufacturing, (iii) wholesale and retail trade, (iv) information and communication, (v) finance, insurance and real estate, (vi) business services, (vii) health, education and social services, and (viii) personal services. I use the standard deviation of log-sales-per-employee across establishments from 2007, computed by Barth et al. (2016) based on Economic Census data, as a measure of the productivity dispersion within the eight major industries.

A.2 Estimates

In Appendix 2.1, I make use of the unconditional likelihood of job tenure in order to shed light on the relation between versatility and job mobility. In Appendix 2.2, I study how the productivity dispersion across employers affects the wage returns to versatility in ordinary least-squares regressions.

A.2.1 Skills and Job Mobility

Following Ridder and van den Berg (2003) and Cahuc, Postel-Vinay, and Robin (2006), I maximize the unconditional likelihood of job tenure in the sample in order to estimate the job-finding rate and the separation rate into unemployment. Specifically, workers employed at firms offering the wage w quit their current job in the event of a task mismatch, δ, or if they find higher paid jobs, λ1F(w). Therefore, the separation rate conditional on the wage w is given by δ+λ1F(w). While all job transition processes are Poisson, all corresponding distributions are exponential. The steady-state distribution of tenure t has, conditional on the wage w, the density h(t|w)=δ+λ(1F(w))exp((δ+λ(1F(w)))t), where the wage w is distributed in the population of employed workers according to the cross-sectional wage distribution G(w) = F(w)/(1 + κ(1 − F(w))). I integrate the wage out of the joint likelihood of w and t, treating it as unobserved heterogeneity. The unconditional likelihood of tenure is

(A.1)h(t)=0h(t|w)dG(w)=δ(δ+λ)01e(δ+λ(1x))tδ+λ(1x)dx,

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

I adjust the likelihood to account for the fact that job tenure is available at weekly intervals in the NLSY. In line with Cahuc, Postel-Vinay, and Robin (2006), job tenure is censored at three years and the sample is restricted to workers with more than three years of experience. In order to take into account the effects of covariates, I extend the estimation procedure by assuming that the job-finding rate and the separation rate into unemployment are log-linear in the relevant covariates, denoted by xi for i ∈{1, …, n}, i.e., δ=exp(δ0+i=1nδixi) and λ=exp(λ0+i=1nλixi), where the coefficients δi and λi for i ∈{0, …, n} are to be estimated. Table A.1 displays the maximum-likelihood estimates.

Table A.1:

Maximum-likelihood estimates of the effects of the displayed variables on the log-risks of obtaining a job offer on the job (λi) and of separating into unemployment (δi) per annum.

(1)(2)
λiδiλiδiλiδiλiδi
Math skills (std)−0.482−0.167−0.315
(0.693)(0.124)(0.792)
Verbal skills (std)−0.5140.167−0.681
(0.475)(0.122)(0.561)
Social skills (std)−0.978**0.118−1.096**
(0.386)(0.080)(0.437)
Above-median skill domains2.666***−0.506***3.172***
(1.000)(0.122)(1.084)
Female0.4670.0330.433
(0.810)(0.147)(0.931)
Constant0.155−2.880***3.035***−4.709**−1.873***−2.837
(0.419)(0.076)(0.483)(1.862)(0.256)(2.079)
Log-likelihood−6035−6016
Observations24812481

  1. Standard errors in parentheses. Statistical significance at the 10, 5, and 1 percent level denoted by *, **, and ***, respectively. Author’s calculations based on the 1979 NLSY.

In the first specification of Table A.1, I obtain an estimate of 1.17 (exp(0.155)) for the job-finding rate λ, implying an average spell between two job offers of ten months (1/λ). The estimate of the separation rate into unemployment δ is 0.06 (exp(−2.880)), implying an average employment spell of 18 years (1/δ). Hence, the ratio of the job-finding rate to the separation rate into unemployment κ is 21 (exp(0.155 + 2.880)), i.e., a person obtains 21 job offers per employment spell on average. This estimate of the job-mobility measure κ is higher than what is typically found in the literature. However, Ridder and van den Berg (2003), who note that the unconditional-inference method tends to yield high mobility estimates, obtain an unconditional-inference estimate of 20 for the USA. The set of controls in the second specification of Table A.1 additionally includes the skill measures. All in all, the estimates of the impact of versatility on job mobility are in line with the on-the-job search model that features structural impediments to sorting. The number of above-median skills is positively associated with the job-finding rate and it is negatively associated with the separation rate into unemployment. Above-median skills in an additional domain are estimated to increase, ceteris paribus, the ratio of the job-finding rate to the separation rate into unemployment κ by a factor of 24 (exp(3.172)).

A.2.2 Skills and Wages

In this section, I study the wage returns to versatility and other covariates. Table A.2 displays the ordinary least-squares estimates for different sets of control variables. The baseline set of controls includes a second-order polynomial in experience, indicator variables by gender and indicator variables by major industry. The sets of controls for the first four specifications of Table A.2 additionally include one of the four skill measures, respectively. Math skills, verbal skills, social skills and the number of domains with above-median skills are all estimated to be positively associated with wages. All four measures of skills enter the fifth specification. Notably, the number of domains with above-median skills has no statistically significant impact on wages conditional on the skills in the three domains.

Table A.2:

Ordinary least-squares estimates of the effects of the displayed variables on the logarithm of the hourly wage.

(1)(2)(3)(4)(5)(6)
Math skills (std)0.288***0.222***0.222***
(0.027)(0.032)(0.032)
Verbal skills (std)0.258***0.071**0.069**
(0.026)(0.022)(0.021)
Social skills (std)0.176***0.100***0.100***
(0.016)(0.017)(0.016)
Above-median skill domains0.222***−0.024−0.023
(0.024)(0.027)(0.023)
Log-sales-per-employee standard deviation (demeaned)
× Math skills (std)−0.180
(0.199)
× Verbal skills (std)−0.103
(0.139)
× Social skills (std)−0.161
(0.101)
× Above-median skill domains0.278**
(0.104)
Experience (decades)0.305**0.439**0.526**0.469**0.363**0.370**
(0.120)(0.139)(0.182)(0.152)(0.120)(0.121)
Experience2 (decades2)−0.111**−0.157***−0.186***−0.164***−0.128***−0.130***
(0.032)(0.039)(0.051)(0.041)(0.032)(0.033)
Female−0.241******−0.314***−0.317***−0.286***−0.248***−0.248***
Table A.2:

(continued)

(0.041)(0.034)(0.041)(0.033)(0.042)(0.042)
Industry××××××
R20.2890.2560.2040.2610.3080.309
Observations257325732573257325732573

  1. Weights proportional to hours worked used in all calculations. Robust standard errors adjusted for clustering at the industry level in parentheses. Statistical significance at the 10, 5, and 1 percent level denoted by *, **, and ***, respectively. Author’s calculations based on the 1979 NLSY and sales dispersion statistics from Barth et al. (2016).

In order to study how the productivity dispersion affects the versatility wage premium, I exploit variations in the standard deviation of log-sales-per-employee across eight major U.S. industries. Specifically, I add the productivity dispersion measure and its interaction terms with all skill measures to the set of covariates in the sixth specification of Table A.2. The estimate of the impact of the productivity dispersion across employers on the versatility wage premium is in line with the on-the-job search model that features structural impediments to sorting. An increase in the standard deviation of log-sales-per-employee by ten log-points is associated with an increase in the above-median skills premium by three log-points. Notably, the standard deviation of log-sales-per-employee ranges from 0.73 in education, health and social services to 1.20 in finance, insurance and real estate. Evaluated at this range, the point estimate suggests an increase in the above-median skills premium by 13 log-points (0.278 ⋅ (1.20 − 0.73)).

A.3 Summary of the Empirical Evidence

Making use of the 1979 National Longitudinal Survey of Youth (NLSY), I find that versatility as measured by the number of domains in which a person has above-median skills is positively associated with the ratio of the job-finding rate to the separation rate into unemployment. Furthermore, I document that the versatility wage premium is positively associated with the productivity dispersion across employers within industries as measured by the standard deviation of log-sales-per-employee.

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Received: 2019-01-08
Revised: 2021-05-17
Accepted: 2021-07-02
Published Online: 2021-08-20

© 2021 Walter de Gruyter GmbH, Berlin/Boston