A Hazard Model for AI-Induced Compression in Knowledge Professions

Abstract

Existing forecasts of AI-induced labor displacement collapse a multi-dimensional phenomenononto a single occupation-level probability and, with rare exceptions, condition on capabilityalone. We argue that compression is properly decomposed into four nested but distinctquantitiestask replacement, billable-hour reduction, role consolidation, and headcount dis-placement each governed by a dierent combination of capability, adoption, retention, anddemand-elasticity dynamics. We develop a continuous-time hazard framework in which eachcomponent is modeled separately with profession-specic priors and combined into a stochas-tic dierential system for log-headcount with a Jevons demand-expansion term. Inferenceproceeds via Approximate Bayesian Computation, anchored where possible on documentedempirical signals such as the Stanford ADP-payroll evidence on AI-exposed entry-level work-ers [BCC25] and capability trajectories on standardized benchmarks [Jim+24; Nov+25]. Weapply the framework to four professions spanning an order of magnitude in AI exposure: datascientists, statisticians, probability theorists, and theoretical mathematicians. The posteriorat 5-, 10-, and 20-year horizons reveals systematic structure: the gap between billable-hourcompression and headcount compression the Jevons wedge is the dominant feature forhigh-exposure professions, while retention-oor and role-consolidation rates dominate thelong-run tail for mathematical professions. We provide credible intervals for each (profes-sion, dimension, horizon) cell and discuss why the conventional probability of automationframing produces both overstated and understated forecasts depending on which dimensionimplicitly anchors the question.

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