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Structurally Conditioned Diffusion Reproduces Skills-Based Stratification

Roberto Cantillan, Mauricio Bucca

Abstract

Occupational hierarchies remain strikingly stable even as job content changes rapidly. We ask whether skill requirements propagate directionally along the wage hierarchy or follow symmetric diffusion. Using O*NET 2015-2024, we analyze 17.3 million directed diffusion opportunities linking 873 occupations and 161 skills. We show that propagation obeys an Asymmetric Trajectory Channeling (ATC) rule: the same requirement spreads differently upward and downward, and the asymmetry depends on skill domain and on the architecture of skill dependencies. Two mechanisms generate ATC. Directional incorporation asymmetry implies that wage gradients create distinct receiving environments: upward-moving socio-cognitive requirements encounter complementary infrastructure, whereas upward-moving sensory/physical requirements face structural indifference. Structural portability constraints imply that dependency position governs portability: requirements anchoring long prerequisite chains carry co-adoption burdens that restrict diffusion regardless of destination. Consistent with these mechanisms, socio-cognitive requirements propagate upward more often than downward (20.7% vs 14.9%), while sensory/physical requirements exhibit the mirror pattern (19.5% downward vs 10.3% upward). Nestedness amplifies these asymmetries in opposite directions: scaffolding capabilities ascend most readily, whereas structurally embedded physical requirements are most tightly confined. Identification leverages within-occupation variation in propagation direction, and results are robust to origin- and destination-side specifications. Together, these findings reveal a directional architecture of occupational change that can reproduce hierarchy through ongoing reconfiguration, even absent assortative preferences or coordinated action.

Structurally Conditioned Diffusion Reproduces Skills-Based Stratification

Abstract

Occupational hierarchies remain strikingly stable even as job content changes rapidly. We ask whether skill requirements propagate directionally along the wage hierarchy or follow symmetric diffusion. Using O*NET 2015-2024, we analyze 17.3 million directed diffusion opportunities linking 873 occupations and 161 skills. We show that propagation obeys an Asymmetric Trajectory Channeling (ATC) rule: the same requirement spreads differently upward and downward, and the asymmetry depends on skill domain and on the architecture of skill dependencies. Two mechanisms generate ATC. Directional incorporation asymmetry implies that wage gradients create distinct receiving environments: upward-moving socio-cognitive requirements encounter complementary infrastructure, whereas upward-moving sensory/physical requirements face structural indifference. Structural portability constraints imply that dependency position governs portability: requirements anchoring long prerequisite chains carry co-adoption burdens that restrict diffusion regardless of destination. Consistent with these mechanisms, socio-cognitive requirements propagate upward more often than downward (20.7% vs 14.9%), while sensory/physical requirements exhibit the mirror pattern (19.5% downward vs 10.3% upward). Nestedness amplifies these asymmetries in opposite directions: scaffolding capabilities ascend most readily, whereas structurally embedded physical requirements are most tightly confined. Identification leverages within-occupation variation in propagation direction, and results are robust to origin- and destination-side specifications. Together, these findings reveal a directional architecture of occupational change that can reproduce hierarchy through ongoing reconfiguration, even absent assortative preferences or coordinated action.
Paper Structure (21 sections, 6 equations, 4 figures, 1 table)

This paper contains 21 sections, 6 equations, 4 figures, 1 table.

Table of Contents

  1. INTRODUCTION
  2. Theory
  3. RESULTS
  4. DISCUSSION
  5. METHODS
  6. Data availability
  7. Code availability

Figures (4)

  • Figure 1: Raw adoption rates by structural distance and directional wage gap. Panel A shows adoption rates as a function of occupational relatedness (structural distance) for socio-cognitive (turquoise) and sensory/physical (black) requirements. Panel B plots adoption rates against the signed wage gap between source and destination occupations; the dashed vertical line separates downward (left) from upward (right) diffusion. Lines are LOWESS smooths; points are binned means across approximately 17.3 million dyadic opportunities (O*NET, 2015--2024).
  • Figure 2: Directional skill flows between wage quintiles by domain. Each arc represents the empirical adoption rate from a source quintile to a destination quintile, averaged across all skills within each domain (O*NET, 2015--2024; $n \approx 17.3$M dyadic opportunities). Blue arcs indicate upward diffusion; red arcs indicate downward diffusion. Arc thickness is proportional to adoption rate. Socio-cognitive requirements (left panel) diffuse upward at 20.7% versus 14.9% downward; sensory/physical requirements (right panel) diffuse downward at 19.5% versus 10.3% upward. Adoption is defined as the transition where skill $k$ reaches $\mathrm{RCA} \geq 1$ in occupation $j$ at $t_1$, conditional on $j$ not being specialized at $t_0$ and source $i$ being specialized at $t_0$.
  • Figure 3: Asymmetric trajectory channeling by skill domain. Estimated upward ($\beta^{\uparrow}$) and downward ($\beta^{\downarrow}$) friction parameters from the interval-censored gravity model, shown separately for socio-cognitive and sensory/physical requirements. Panel A absorbs source occupation and skill fixed effects; Panel B absorbs target occupation and skill fixed effects. In both specifications, the downward facilitation parameter for sensory/physical requirements ($\beta_{\downarrow} \approx -0.82$ and $-0.67$, respectively; more negative values indicate stronger downward facilitation) substantially exceeds the upward component, which is statistically indistinguishable from zero, while socio-cognitive requirements show comparable friction in both directions. The x-axis plots the signed wage gap (target minus source log-wage); slopes represent directional friction parameters. Points denote point estimates; bars denote 95% confidence intervals constructed via node-level bootstrap ($B = 1000$ replications).
  • Figure 4: Nestedness amplifies asymmetric trajectory channeling. Estimated directional friction parameters by domain--nestedness cell, from the interval-censored gravity model. Columns correspond to three empirically distinct trajectory types: SC_Specialized (low-nestedness socio-cognitive), SC_Scaffolding (high-nestedness socio-cognitive), and Physical_Terminal (sensory/physical). Panel A absorbs source occupation and skill fixed effects; Panel B absorbs target occupation and skill fixed effects. For socio-cognitive requirements, upward facilitation increases monotonically with nestedness ($\beta^{\uparrow}$ from 0.19 to 0.58 in Panel A). For sensory/physical requirements, the upward penalty intensifies with nestedness position ($\beta^{\uparrow} = -0.82$ in Panel A), while the high-nestedness physical cell is empirically rare, consistent with the theoretical prediction that foundational physical scaffolds do not accumulate in high-status destinations. The x-axis plots the signed wage gap (target minus source log-wage). Points denote point estimates; bars denote 95% confidence intervals constructed via node-level bootstrap ($B = 1000$ replications).