A Hazard Model for AI-Induced Compression in Knowledge Professions

Existing forecasts of AI-induced labor displacement collapse a multi-dimensional phenomenon
onto a single occupation-level probability and, with rare exceptions, condition on capability
alone. We argue that compression is properly decomposed into four nested but distinct
quantitiestask replacement, billable-hour reduction, role consolidation, and headcount dis-
placement each governed by a dierent combination of capability, adoption, retention, and
demand-elasticity dynamics. We develop a continuous-time hazard framework in which each
component is modeled separately with profession-specic priors and combined into a stochas-
tic dierential system for log-headcount with a Jevons demand-expansion term. Inference
proceeds via Approximate Bayesian Computation, anchored where possible on documented
empirical 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]. We
apply the framework to four professions spanning an order of magnitude in AI exposure: data
scientists, statisticians, probability theorists, and theoretical mathematicians. The posterior
at 5-, 10-, and 20-year horizons reveals systematic structure: the gap between billable-hour
compression and headcount compression the Jevons wedge is the dominant feature for
high-exposure professions, while retention-oor and role-consolidation rates dominate the
long-run tail for mathematical professions. We provide credible intervals for each (profes-
sion, dimension, horizon) cell and discuss why the conventional probability of automation
framing produces both overstated and understated forecasts depending on which dimension
implicitly anchors the question.