Intergenerational Topological Inheritance

Introduction

Intergenerational mobility has been central to British sociology since the Oxford Mobility Study. A generation of research has established that parental socioeconomic position predicts children’s educational attainment, class position, and income. Most of this literature treats mobility as a status comparison: where did your parent end up, and where did you end up?

This paper asks a different question: does the structure of a career — its topological shape over time — transmit from parent to offspring? If career topology is heritable, this suggests that the mechanisms of intergenerational disadvantage extend beyond status transmission to encompass the transmission of career-path instability patterns themselves.

Background

Intergenerational Mobility Research

Classic British mobility studies (Goldthorpe 1980; Marshall, Swift, and Roberts 1997) focus on class positions at career peak. Life-course sociology has enriched this with attention to trajectories, but trajectory comparison has been limited to sequence distance methods that do not produce topologically meaningful representations.

Topological Similarity Measures

To measure topological similarity between parent and offspring trajectories, this paper uses the Wasserstein distance between persistence diagrams — a metric that is interpretable, satisfies stability theorems, and is robust to small perturbations in the data.

Methods

Matched parent–offspring pairs are constructed from the BHPS/Understanding Society linked panel using household identifier linkages. BHPS (1991–2009) and Understanding Society (2009–present) are combined into a single harmonised panel to provide sufficient observation windows; the linkage uses the BHPS–USoc sample members who were recontacted at the 2009 transition, as documented in the Understanding Society user guide. Parents’ trajectories are observed from labour market entry through age 50; offspring trajectories are observed equivalently. Both will be standardised to 30-year sequences using the combined panel, with individuals observed for fewer than 20 years excluded and shorter series padded using state-last-observed forward-fill rules documented in the analysis protocol. Persistent homology is computed for each individual, and the Wasserstein distance between parent and offspring persistence diagrams is compared to a bootstrap permutation null.

Mediation analysis uses the mediation R package with bootstrapped standard errors.

Data

BHPS household panel data (1991–2009) linked to Understanding Society (2009–present), providing a combined observation window of sufficient length for 30-year trajectory construction. Household identifier linkages and the harmonised BHPS–USoc activity variables are used to construct matched parent–offspring pairs. The datasets field in the frontmatter lists both sources. Final matched sample will comprise parent–offspring dyads with at least 20 years of observed trajectories for both members.

Results

Intergenerational Topology Transmission

The analysis will use bootstrap permutation testing to assess whether the mean Wasserstein distance between matched parent–offspring pairs is smaller than expected under a null model of random pairing. Results will be reported separately for H₀ (connected components, capturing overall employment level structure) and H₁ (one-cycles, capturing cyclical employment instability), with intergenerational correlations and standardised effect sizes compared to conventional earnings elasticity estimates. The analysis will also test whether the H₁ correlation is significantly larger than the H₀ correlation, and whether effects differ across parent–offspring gender combinations.

Mediation by Education

Mediation analysis will decompose the topological transmission effect into education-mediated and direct pathways, testing whether the direct pathway remains significant after conditioning on highest educational qualification.

Discussion

If career topology proves heritable, this would extend the concept of intergenerational transmission from status to structure. A finding that cyclical employment instability (H₁ topology) is more heritable than overall employment level (H₀) would be theoretically significant: it would suggest that the specific pattern of career precariousness — the rhythm of in-and-out of work — is transmitted between generations, not only the average level of disadvantage.

Conclusion

This paper will test whether employment trajectory topology transmits intergenerationally in UK panel data. If effect sizes prove comparable to earnings elasticity estimates, this would motivate the network-based analyses in Paper 8 and validate topology as a medium through which career disadvantage is inherited.