Research ArticleSOCIAL SCIENCES

The value of complementary co-workers

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Science Advances  18 Dec 2019:
Vol. 5, no. 12, eaax3370
DOI: 10.1126/sciadv.aax3370
  • Fig. 1 Educational synergy and substitutability networks.

    Who works with whom? Who can substitute whom? Educational tracks are connected if they often co-occur in economic establishments (A) or give access to the same occupations (B). In both cases, connections predominantly form between educational tracks with similar content areas (colors) or, albeit less so, similar levels (shapes). The highlighted community in the synergy network consists of health care–related educations. In the substitutability network, this community is distributed across several tighter substitutability communities, showing how both networks differ: Although medical secretaries and doctors complement each other, they cannot replace one another. Definition of metrics. (C) Synergy: Educations e, e, and e′′ are overrepresented in establishment p, creating co-occurrences e−e, e−e′′, and e−e′′ that are scaled by the total number of co-occurrences (here, three) in p. The synergy between e and e is defined as the pairs’ overrepresentation in these co-occurrences across establishments. Last, the homogeneous transformation from c to c reduces distributional skew. (D) Substitutability: Workers with educations e and e choose different occupations. The substitutability between these educations is defined as the correlation between their occupational profiles. Heterogeneity in levels (E) and content areas (F) of educational tracks in synergy (blue) and substitutability (red) communities. Vertical lines: Average effective number of educational tracks per community in units of SDs of a simulated benchmark (shown in kernel density plots, details are provided in section SB.4). Synergy communities are less homogeneous in educational levels than substitutability communities, but both are similarly heterogeneous in content.

  • Fig. 2 Average co-worker synergy and substitutability.

    (A) Average co-worker synergy against average co-worker substitutability by occupation. The gray line represents a linear regression fit. The distance to this fit can be interpreted as the average co-worker complementarity in the occupation. Complementarity is particularly high not only among professionals and associate professionals but also among technicians and crafts persons. (B) Idem (A), with averages over industries instead of occupations. A high average co-worker synergy means that industries combine workers with skills that are often found in the same work places; a high average substitutability that industries employ homogeneous workforces. Complementarity (the distance to the regression line) is particularly high not only in skill-intensive industries, such as health care and R&D in natural sciences, but also in crafts-based industries like construction.

  • Fig. 3 Career paths.

    Table: Linear probability models of workers’ switching establishments in a given year (column 1) or remaining for at least 2, 3, or 4 years with the same establishment (columns 2 to 4). The units of observation are worker-year combinations in column (1) and worker-establishment combinations in columns (2) to (4). “Base probability” provides estimated probabilities of switching or reaching long tenures for the average worker. SEs, clustered at the worker level (column 1) or at the establishment level (columns 2 to 4), in parentheses. The estimates show strong positive associations of employee retention rates with having synergistic co-workers and negative associations with having substitutable co-workers. (A) Average co-worker complementarity, m̂wpwt, as in Eq. 6 in blue, and wage residual, ω̂wpwt, as in Eq. 7 in red, against work experience. Co-worker complementarity rises as work experience increases in a way that is closely tracked by a worker’s wage. (B) Change in co-worker complementary, Δm̂wpwt, for workers who change jobs. In both graphs, vertical bars represent 95% confidence intervals based on 1.96 times the SEMs.

  • Fig. 4 Educational premiums.

    Table: OLS regressions of log10(wage). Columns correspond to subsamples of workers with different levels of education. SEs, clustered at the worker level, are provided in parentheses. As educational attainment rises, co-worker synergy becomes more important for workers’ wages. (A) Returns to schooling by complementarity quintile (coded bottom to top from dark blue to dark red) in log10 points over the omitted category (workers with primary education, bottom complementarity quintile). Estimates are based on regression models that interact educational levels with complementarity quintile dummies while controlling for establishment age and size. Ninety-five percent confidence intervals use SEs clustered at the worker level. Returns to education rise markedly with co-worker complementarity. The range they cover among workers with college degrees is wider than the difference between the returns to college and secondary education. Estimates in (B) control for worker fixed effects and thus only compare wages of the same individual across time. These estimates show that results are not simply driven by complementarity-rich establishments hiring more able workers.

  • Fig. 5 Wage premiums.

    (A) Effect of co-worker complementarity, m̂wpt, on wages in establishments of different sizes while controlling for workers’ age and educational level. As establishments become larger, the estimated benefits of having complementary co-workers increase. (B) Idem, adding worker fixed effects. (C) Estimated LPP for workers with different levels of education using no control variables (blue bars), controlling for the weighted average co-worker synergy and substitutability of Eqs. 4 and 5 (light red) and controlling for the logarithms of the number of co-workers that are highly synergistic or close substitutes (dark red). The figure shows that, although the benefits of working in large establishments cannot be explained by workers’ average co-worker synergy and substitutability, for workers with over upper secondary schooling, they can be fully explained by the greater number of highly complementary co-workers in large plants. (D) UWPs by complementarity quintile, estimated by regressing the logarithm of wages on the logarithm of total employment in a labor market area. The UWP rises from below 1% to above 9% for each doubling of a region’s size when comparing workers in the bottom to workers in the top complementarity quintile. (E) Idem, adding worker fixed effects. (F) Idem (C), but now for the UWP. The worker-count controls can account for 21% of the UWP for workers with postsecondary degrees, 34% for college-educated workers, and 74% for workers with postgraduate degrees. This shows that, especially for higher educated workers, an important part of the high wages earned in large cities can be attributed to the co-worker environments these cities offer.

  • Table 1 Wage effects.

    Models (1) to (3) show regression analyses of log10(wage) on co-worker synergy and substitutability, and model (4) also controls for a fourth-order polynomial of age, educational levels, and log10(establishment size). All models contain year dummies. Model (4) implies that an increase from the 10th to 90th synergy percentile—a shift comparable to the shift in the educational distribution from primary school to college education—is associated with an increase in wages of 18.1%, whereas the same increase in co-worker substitutability is associated with a decrease in wages of 4.8%.

    Dependent variable: log(wage)
    (1)(2)(3)(4)
    Co-worker synergy0.126***0.371***0.274***
    (0.0025)(0.0036)(0.0030)
    Co-worker
    substitutability
    −0.061***−0.211***−0.044***
    (0.0015)(0.0021)(0.0018)
    Log(establishment
    size)
    0.044***
    (0.0003)
    Fourth polynomial
    of age?
    Yes
    Educational level
    dummies?
    Yes
    R20.0400.0380.0600.300
    # Observations2,144,9652,144,9652,144,9652,144,965
    # Clusters364,642364,642364,642364,642

    ***P < 0.01; **P < 0.05; *P < 0.1, SEs clustered at worker level.

    Supplementary Materials

    • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/5/12/eaax3370/DC1

      Section SA. Data

      Section SB. Definition of measures

      Section SC. Co-worker synergy and substitutability by industry and occupation (Fig. 2)

      Section SD. Wages

      Section SE. Career paths (Fig. 3)

      Section SF. Wage premiums

      Fig. S1. Part-time work in Sweden.

      Fig. S2. Scatter plot of educational synergy against educational substitutability.

      Fig. S3. Educational synergies network.

      Fig. S4. Educational substitutability network.

      Fig. S5. Selected synergy communities in the synergy and substitutability graphs.

      Fig. S6. Nested community structure.

      Fig. S7. Levels and contents of education in synergy and substitutability communities.

      Fig. S8. Co-worker variables and establishment size.

      Fig. S9. Average co-worker synergy and substitutability by industry and occupation.

      Fig. S10. SD synergy (observed versus theoretical).

      Fig. S11. Estimated effect of co-worker synergy by error-variance bin.

      Fig. S12. Estimated effect of co-worker synergy by error-variance bin (homoscedastic case).

      Fig. S13. Co-worker complementarity and work experience.

      Table S1. Sample sizes.

      Table S2. Educational pairs: Top synergy.

      Table S3. Educational pairs: Top substitutability.

      Table S4. Educational pairs: Top synergy, controlling for substitutability.

      Table S5. Descriptive statistics main variables.

      Table S6. Survival analysis.

      Table S7. Co-worker educational fit and wages.

      Table S8. Wage regressions, fixed effects models.

      Table S9. IV regression, first differences.

      Table S10. Wage effects of within-education local supply shifts.

      Table S11. Fixed effects models, within transformation versus first differences.

      Table S12. Errors-in-variables estimates.

      Table S13. Wage regressions: Summary.

      Table S14. Returns to education.

      Table S15. Large-plant premium.

      Table S16. UWP, conditional on co-worker fit.

      References (3540)

    • Supplementary Materials

      This PDF file includes:

      • Section SA. Data
      • Section SB. Definition of measures
      • Section SC. Co-worker synergy and substitutability by industry and occupation (Fig. 2)
      • Section SD. Wages
      • Section SE. Career paths (Fig. 3)
      • Section SF. Wage premiums
      • Fig. S1. Part-time work in Sweden.
      • Fig. S2. Scatter plot of educational synergy against educational substitutability.
      • Fig. S3. Educational synergies network.
      • Fig. S4. Educational substitutability network.
      • Fig. S5. Selected synergy communities in the synergy and substitutability graphs.
      • Fig. S6. Nested community structure.
      • Fig. S7. Levels and contents of education in synergy and substitutability communities.
      • Fig. S8. Co-worker variables and establishment size.
      • Fig. S9. Average co-worker synergy and substitutability by industry and occupation.
      • Fig. S10. SD synergy (observed versus theoretical).
      • Fig. S11. Estimated effect of co-worker synergy by error-variance bin.
      • Fig. S12. Estimated effect of co-worker synergy by error-variance bin (homoscedastic case).
      • Fig. S13. Co-worker complementarity and work experience.
      • Table S1. Sample sizes.
      • Table S2. Educational pairs: Top synergy.
      • Table S3. Educational pairs: Top substitutability.
      • Table S4. Educational pairs: Top synergy, controlling for substitutability.
      • Table S5. Descriptive statistics main variables.
      • Table S6. Survival analysis.
      • Table S7. Co-worker educational fit and wages.
      • Table S8. Wage regressions, fixed effects models.
      • Table S9. IV regression, first differences.
      • Table S10. Wage effects of within-education local supply shifts.
      • Table S11. Fixed effects models, within transformation versus first differences.
      • Table S12. Errors-in-variables estimates.
      • Table S13. Wage regressions: Summary.
      • Table S14. Returns to education.
      • Table S15. Large-plant premium.
      • Table S16. UWP, conditional on co-worker fit.
      • References (3540)

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