A Matthew Effect in Occupational Skill Content

Status-Sorted Diffusion Reproduces Occupational Hierarchy

Roberto Cantillan & Mauricio Bucca

Department of Sociology | Pontificia Universidad Católica de Chile

Occupations Are in Constant Transformation

Occupational titles may remain stable while their content changes.

• Tasks and skill requirements are continually reorganized
• Some requirements are adopted, retained, or abandoned

Labor markets also change through the recomposition of existing occupations.

Weeden & Grusky 2005; Labussière & Bol 2026

Technological Change Raises the Pressure to Update

• Technological change (and, more recently, AI) has increased the returns to cognitive and analytical capabilities
• It has contributed to occupational polarization and the hollowing of routine middle-skill work

Technological change makes the recomposition of occupational content consequential for inequality.

Autor, Levy & Murnane 2003; Acemoglu & Autor 2011; Goos, Manning & Salomons 2014; Eloundou et al. 2024

Upskilling Pressure May Be Strongest at the Bottom

• Lower-status occupations face greater pressure to adapt to replacement and devaluation
• Recent job-posting evidence finds substantial skill diversification in low-wage jobs

But realized occupational updating may be heterogeneous.

Autor 2015; Acemoglu & Restrepo 2020; Tong, Wu & Evans 2025; Han & Cheng 2026

Heterogeneity Depends on Skill Type and Specialization

Changes in occupational content may be contingent on the functional domain and functional specificity of the skills involved.

Functional domain
Socio-cognitive vs. sensory-physical
Polarization

• Socio-cognitive: high education, high wages
• Sensory-physical: lower education, lower wages

Alabdulkareem et al. 2018

Functional specificity
General vs. specialized
Hierarchical organization

• General skills scaffold many occupational profiles
• Specialized skills are narrower and more dependent

Hosseinioun et al. 2025

I. Skill Diffusion

Skill Diffusion Is Directional Updating

What we observe

Occupations gain and lose skill requirements over time.

What makes the change relational

Each changing skill is already held by a set of other occupations.

What we compare

The changing occupation’s position relative to those current holders.

Skill diffusion is the changing distribution of skill requirements across occupations, traced through gains and losses relative to the skill’s current holders.

Current holders are plausible sources for adoption and positional referents for abandonment; we do not observe direct transmission. Strang & Meyer 1993; Wimmer 2021

Proximity Facilitates Diffusion

• Related occupational profiles are more likely to borrow skills from one another.

Task-profile proximity

Unsigned, symmetric distance: \(\mathrm{dist}_{ij}=\mathrm{dist}_{ji}\)

Standard gravity structure: interaction increases with origin and destination mass and decreases with their separation.

Gravity models: Tinbergen 1962; Kolaczyk & Csárdi 2020. Symmetric relatedness measure: Hidalgo et al. 2007.

Status Governs Diffusion Direction

• Nurses and doctors have one symmetric task-profile proximity.
• But each source → target ordering has a different signed status gap, so diffusion may be asymmetric.

Opposite directions, opposite status gaps: \(G_{ij}=-G_{ji}\)

Our main argument: skill diffusion is status-sorted and asymmetric.

Proximity and prestige in diffusion: Bail, Brown & Wimmer 2019.

We Ask Two Descriptive Questions

1. Symmetry

Is realized skill updating symmetric with respect to occupational status, or is it status-directed?

2. Direction

If updating is status-directed, do skills flow predominantly upward or downward—and does this differ by skill type?

We do not adjudicate among the mechanisms directly. We establish whether updating is asymmetric and identify its predominant direction.

II. Data and Research Design

Data

• O*NET skill profiles, 2015–2024
• 741 occupations × 160 requirements
• Skill specialization defined by RCA \(\geq 1\)

Baseline occupational status

• 2015 BLS wages
• Required education
• Cognitive task content

We observe how occupational skill portfolios change over a decade.

Dependent Variables

Holders: occupations that already have a skill.
Target: the occupation whose content changes.

Adoption: the target gains a skill its holders already have.
Abandonment: the target sheds a skill its holders retain.

Conceptual precedent for joint trajectories of adoption and abandonment: Strang & Macy 2001.

Three Skill Classes Capture Function and Specificity

Crossing domain x specificity yields three functional classes

Domain: Alabdulkareem et al. 2018  ·  Nestedness/specificity: Hosseinioun et al. 2025

• General socio-cognitive (49 skills): \(c_s\) at/above within-domain median — broad, scaffolding
• Specialized socio-cognitive (48 skills): \(c_s\) below median — narrower, dependent
• Sensory-physical (63 skills): \(c_s < 0\) throughout — high-nestedness cell empirically absent

An Asymmetric Gravity Model for Skill Diffusion

\[ \Lambda^f_{ijs} \propto \frac{M_i M_j}{D^f_{ij}} \]

NUMERATOR

\(M_i M_j\)

\(\downarrow\)

Occupational masses

May capture occupational size, centrality, or baseline propensity to send/receive.

Absorbed by endpoint fixed effects in our specifications

DENOMINATOR

\(D^f_{ij}\)

Effective separation has two components in our model:

i ⟷ jProfile distance
distᵢⱼ = distⱼᵢ · symmetric proximity

i ⟶ jSigned status gap
Gᵢⱼ = σⱼ − σᵢ = −Gⱼᵢ · directional

The extension is asymmetric because \(G_{ij}=-G_{ji}\), even when profile distance is unchanged.

Estimation

How likely is target occupation \(j\) to adopt or abandon skill \(s\)?

\[ \operatorname{cloglog}\Pr(Y^f_{ijs}=1) = \underbrace{\alpha_s+\alpha^{(p)}_{e}}_{\text{fixed effects}} + \underbrace{\delta^f_g\,\mathrm{dist}_{ij}}_{\text{profile relatedness}} + \color{#b33a3a}{ \underbrace{\beta^f_g\,G_{ij}}_{\text{directional status association}} }, \qquad G_{ij}=\sigma_j-\sigma_i \]

• \(f \in \{\text{adoption},\text{abandonment}\}\); coefficients vary by skill class \(g\)
• \(\beta^f_g\) is the parameter of interest: it identifies whether diffusion is directed upward or downward
• Complementary source + skill and target + skill fixed-effect specifications

III. Findings

Panel A: Skill Diffusion Is Directed Around Fixed Sources

\(x<0\): target below source   |   \(x>0\): target above source

Socio-cognitive skills are adopted and retained upward; sensory-physical skills are adopted and retained downward.

Panel B: The Same Diffusion Pattern Holds Around Fixed Targets

Holding the target and skill fixed, identification comes from comparing sources above and below the same target.

The signs are unchanged: the directional pattern is not a by-product of which occupations tend to change more.

The Pattern Cannot Be Reduced To…

Occupational characteristics

Size, centrality, and baseline propensity to send or receive skills cannot account for the result.

Endpoint fixed effects absorb these characteristics in complementary specifications.

Intrinsic skill characteristics

Prevalence, diffusibility, and other stable properties of the skill cannot account for the result.

Skill fixed effects compare relations involving the same skill.

The same domain reversal survives both fixed-effect comparisons.

The Signed-Gap Model Recovers the Status Gradient

The directional status-gap model recovers the observed gradient; the symmetric and distance-only models do not.

IV. Discussion

Takeaways

• Occupational content changes through two margins: adoption (the target adds a skill) and abandonment (the target sheds a skill).

• Both margins are systematically directed by baseline occupational status.

• Higher-status occupations disproportionately adopt and retain general and specialized socio-cognitive skills.

• Lower-status occupations disproportionately adopt and retain sensory-physical skills.

• The directional pattern remains when baseline status is constructed without cognitive content.

Together, these results reveal a Matthew-effect pattern in occupational skill diffusion: changing skill content accumulates along the preexisting occupational hierarchy.

External validation. ESCO partially reproduces the pattern with independently constructed skill data; OOH provides a complementary check against independently measured labor-market outcomes.

Implications

• Technological pressure may raise demand for cognitive capabilities without redistributing them evenly across occupations

• Lower-status occupations can face a compounded barrier: greater pressure to adapt, but weaker incorporation and retention of socio-cognitive content

• This pattern is consistent with inequality being reproduced inside occupations, before workers move or jobs disappear

Limitations

• Occupational level: we do not observe individual workers or the organizational decisions behind skill changes

• Observational design: estimates directional associations, not direct pairwise transmission or a unique causal mechanism

• Institutional scope: U.S. occupational data; credentialing, wage-setting, and labor-market institutions may moderate the pattern

Thank You

Roberto Cantillan

Department of Sociology, PUC Chile

rcantillan@uc.cl

Paper and Replication: github.com/rcantillan/skill_diffusion

Backup Slides

B1: Main Threats, Tests, and Results

Threat	How we evaluate it	Result
A target gradient may look relational	Compare source + skill and target + skill fixed effects	The signed-gap pattern remains in both panels
RCA may create mechanical change	Freeze the 2015 denominator; use raw importance change	The central domain-specific directions remain
Skills with many sources may dominate	Give each target-skill opportunity equal total weight	The directional pattern remains; magnitudes change little
A common technological shock may drive change	Permute outcomes within skill-type and source-status strata	The observed gradient lies far outside the shock-based null
Results may depend on the RCA cutoff	Rebuild risk sets at 0.90, 1.00, 1.10, and 1.25	The domain reversal appears at every cutoff
Results may depend on the status measure	Use wage, education, and cognitive content separately	The core directional structure remains
Skill classification may be fragile	Randomly reassign 10% and 20% of skills across classes	The pattern is robust to classification noise
Results may depend on a sample draw	Repeat estimation across independent source samples	Directional signs remain stable across draws
One disruption period may drive the result	Compare 2015-2018, 2019-2021, and 2022-2024	No single period accounts for the domain reversal

Across these checks, the domain-specific directional pattern remains. The evidence still identifies association, not direct transmission or one causal mechanism.

B2: Formal Definitions

Revealed Comparative Advantage:

\[\mathrm{RCA}(j,s) = \frac{\mathrm{onet}(j,s)/\sum_{s'}\mathrm{onet}(j,s')}{\sum_{j'}\mathrm{onet}(j',s)/\sum_{j',s''}\mathrm{onet}(j',s'')}\]

Event definitions for skill s:

• Baseline specialist: RCA \(\geq 1\) at \(t_0=2015\)
• Endline specialist: RCA \(\geq 1\) at \(t_1=2024\)
• Adoption: target crosses from below to above RCA threshold
• Abandonment: target falls from above to below RCA threshold

Directional gaps:

\[G_{ij} = \sigma_j - \sigma_i\]

The linear specification estimates one signed coefficient \(\beta_g\) for each skill class: \(\beta_g>0\) orients change toward higher-status targets; \(\beta_g<0\) orients it toward lower-status targets.

B3: Skill Taxonomy

Functional domain:

• Louvain communities on the 2015 RCA co-specialization network
• Socio-cognitive: 97 skills
• Sensory-physical: 63 skills

Functional specificity:

\[c_s = \frac{\mathrm{NODF}_{\text{obs}} - \mathbb{E}[\mathrm{NODF}^{(s)}_{\text{rand}}]}{\mathrm{sd}[\mathrm{NODF}^{(s)}_{\text{rand}}]}\]

Three-class taxonomy:

• General socio-cognitive: 49 skills
• Specialized socio-cognitive: 48 skills
• Sensory-physical: 63 skills

The high-nestedness sensory-physical cell is empirically absent.

B4: Key Coefficients

Linear signed-gap coefficients, Panel A: source + skill FE

Skill type	Adoption β (SE)	Abandonment β (SE)
General SC	+0.136 (0.031)	−0.238 (0.029)
Specialized SC	+0.210 (0.036)	−0.285 (0.031)
Sensory-physical	−0.205 (0.036)	+0.106 (0.038)

Linear signed-gap coefficients, Panel B: target + skill FE

Skill type	Adoption β (SE)	Abandonment β (SE)
General SC	+0.060 (0.018)	−0.069 (0.016)
Specialized SC	+0.129 (0.023)	−0.107 (0.020)
Sensory-physical	−0.234 (0.029)	+0.227 (0.032)

Cloglog hazard scale. One signed linear coefficient per skill class.

B5: Complete Gravity Model Derivation

Step 1: Classic Gravity \[T_{ij} = k \cdot \frac{M_i M_j}{D_{ij}^{\gamma}} \quad \Rightarrow \quad \log \mathbb{E}[T_{ij}] = \beta_0 + \alpha_i + \beta_j - \gamma \log D_{ij}\]

Step 2: Triadic Extension \[\Lambda^f_{ijs} \propto \frac{M_i \cdot M_j \cdot S_s}{D_{ij}}\]

Step 3: Signed Status Friction \[G_{ij}=\sigma_j-\sigma_i\]

Step 4: Flow-specific distance \[-\log D^f_{ij} = \beta_g G_{ij} + \delta_g \mathrm{dist}_{ij}\]

Step 5: Full Specification \[\operatorname{cloglog}\big(P(Y^f_{ijs}=1)\big) = \alpha_{\mathrm{FE}} + \alpha_s + \beta_g G_{ij} + \delta_g\mathrm{dist}_{ij}\]

B6: Key Magnitudes

Main signed-gap gradients:

Flow	Socio-cognitive	Sensory-physical
Adoption	Positive β	Negative β
Abandonment	Negative β	Positive β

Interpretation:

• Cognitive content accumulates at the top through gains and retention
• Physical content accumulates below through gains and retention
• The signed gradient persists under source + skill and target + skill FE

B7: Occupational Status — PCA Construction

B8: Possible Pathways Behind Status-Directed Diffusion

Competing directional expectations are consistent with different possible mechanisms.

Downward diffusion

Doctor holder \(\longrightarrow\) Nurse target

• Bottom-up pressure: lower-status occupations face stronger replacement pressure.
• Emulation: lower-status occupations borrow cognitive skills from occupations above.

Strang & Macy 2001; Autor 2015; Tong et al. 2025; Han & Cheng 2026.

Upward diffusion

Nurse holder \(\longrightarrow\) Doctor target

• Selective adoption: absorptive capacity and valuation favor higher-status adopters.
• Closure: licensing and credential boundaries restrict downward borrowing.

Cohen & Levinthal 1990; Abbott 1988; Weeden 2002; Kleiner 2013; Deming 2017.

These are interpretive possibilities, not mechanisms we identify directly.

B9: From Occupational Data to Directed Risk Sets

01
Occupational data

• O*NET skill profiles, 2015–2024
• 741 occupations × 160 requirements
• 2015 BLS wages plus O*NET education and cognitive content define baseline status

02
Directed design

• Directed unit: source \(i\) × target \(j\) × skill \(s\)
• Source: holds the skill at baseline
• Target: may change by 2024
• RCA \(\geq 1\) defines skill specialization

03
Flow-specific risk sets

• Adoption: source holds; target does not (21.5M)
• Abandonment: both hold (18.6M)
• Outcome: target moves into or out of specialization

The target changes. The source locates that change relative to current holders.

Risk-set construction follows the source–target logic of directional diffusion: Bail, Brown & Wimmer 2019.

B10: Reading Panels A and B

Panel A: Source + Skill FE

• Holds the source and skill fixed
• Compares targets above and below the same source
• Absorbs source characteristics and stable skill diffusibility

Panel B: Target + Skill FE

• Holds the target and skill fixed
• Compares sources above and below the same target
• Absorbs target characteristics and stable skill diffusibility

\(x<0\): target below source   |   \(x>0\): target above source

\(y\): relative hazard minus one, compared with an equal-status pair

The two panels change which endpoint is held fixed; they test the same signed source–target status association.

External Validation: ESCO & OOH

• Independent classification. ESCO provides occupational–skill relations across releases from 2018 to 2024.

• Independent construction. Skill communities and functional classes are reconstructed entirely within ESCO, without using O*NET classifications or labels.

• Same design. We reproduce the directed source–target–skill opportunity design, using baseline ISEI-08 status.

• Patterns reproduced so far. Higher-status occupations disproportionately adopt general and specialized socio-cognitive skills, while sensory-physical content is consolidated among lower-status occupations through abandonment toward the top.

• Patterns not yet reproduced. Socio-cognitive abandonment and sensory-physical adoption gradients are not estimated precisely.

• Complementary OOH analysis. BLS Occupational Outlook Handbook (OOH) outcomes provide independently measured external criteria. This evaluates labor-market concordance rather than independently measuring skill change.

ESCO provides partial external validation; OOH provides a complementary check against independently measured labor-market outcomes.

References — Technological Change and Updating

• Autor, D. H., Levy, F., & Murnane, R. J. (2003). “The Skill Content of Recent Technological Change: An Empirical Exploration.” Quarterly Journal of Economics 118(4):1279–1333. doi:10.1162/003355303322552801.

• Acemoglu, D., & Autor, D. (2011). “Skills, Tasks and Technologies: Implications for Employment and Earnings.” Handbook of Labor Economics 4:1043–1171. doi:10.1016/S0169-7218(11)02410-5.

• Goos, M., Manning, A., & Salomons, A. (2014). “Explaining Job Polarization: Routine-Biased Technological Change and Offshoring.” American Economic Review 104(8):2509–2526. doi:10.1257/aer.104.8.2509.

• Autor, D. H. (2015). “Why Are There Still So Many Jobs? The History and Future of Workplace Automation.” Journal of Economic Perspectives 29(3):3–30. doi:10.1257/jep.29.3.3.

• Eloundou, T., Manning, S., Mishkin, P., & Rock, D. (2024). “GPTs are GPTs: Labor Market Impact Potential of LLMs.” Science 384(6702):1306–1308. doi:10.1126/science.adj0998.

• Tong, D., Wu, L., & Evans, J. A. (2025). “Lower-Skilled Occupations Face Greater Upskilling Pressure in U.S. Job Ads.” Nature Communications 17:1237. doi:10.1038/s41467-025-67992-y.

• Han, S., & Cheng, S. (2026). “Skill Diversification Beyond High-Paying Jobs.” American Journal of Sociology. doi:10.1086/741725.

B12: References — Occupational Structure and Diffusion

• Weeden, K. A., & Grusky, D. B. (2005). “The Case for a New Class Map.” American Journal of Sociology 111(1):141–212.

• Labussière, M., & Bol, T. (2026). “Are Occupations ‘Bundles of Skills’? Identifying Latent Skill Profiles in the Labor Market Using Topic Modeling.” Sociological Science 13:362–407. doi:10.15195/v13.a16.

• Alabdulkareem, A., Frank, M. R., Sun, L., AlShebli, B., Hidalgo, C., & Rahwan, I. (2018). “Unpacking the Polarization of Workplace Skills.” Science Advances 4(7):eaao6030. doi:10.1126/sciadv.aao6030.

• Hidalgo, C. A., Klinger, B., Barabási, A.-L., & Hausmann, R. (2007). “The Product Space Conditions the Development of Nations.” Science 317(5837):482–487. doi:10.1126/science.1144581.

• Tinbergen, J. (1962). Shaping the World Economy: Suggestions for an International Economic Policy. New York: Twentieth Century Fund.

• Kolaczyk, E. D., & Csárdi, G. (2020). Statistical Analysis of Network Data with R. 2nd ed. Cham: Springer. doi:10.1007/978-3-030-44129-6.

• Hosseinioun, M., Neffke, F., Zhang, L., & Youn, H. (2025). “Skill Dependencies Uncover Nested Human Capital.” Nature Human Behaviour. doi:10.1038/s41562-024-02093-2.

• Strang, D., & Meyer, J. W. (1993). “Institutional Conditions for Diffusion.” Theory and Society 22(4):487–511. doi:10.1007/BF00993595.

• Strang, D., & Macy, M. W. (2001). “In Search of Excellence: Fads, Success Stories, and Adaptive Emulation.” American Journal of Sociology 107(1):147–182. doi:10.1086/323039.

• Cheng, S., & Park, B. (2020). “Flows and Boundaries: A Network Approach to Studying Occupational Mobility in the Labor Market.” American Journal of Sociology 126(3):577–631. doi:10.1086/712406.

• Lin, K.-H., & Hung, K. (2022). “The Network Structure of Occupations: Fragmentation, Differentiation, and Contagion.” American Journal of Sociology 127(5):1551–1601. doi:10.1086/719407.

• Bail, C. A., Brown, T. W., & Wimmer, A. (2019). “Prestige, Proximity, and Prejudice: How Google Search Terms Diffuse across the World.” American Journal of Sociology 124(5):1496–1548. doi:10.1086/702007.

• Wimmer, A. (2021). “Domains of Diffusion: How Culture and Institutions Travel around the World and with What Consequences.” American Journal of Sociology 126(6):1389–1438. doi:10.1086/714273.