Systems and tools Calibrated · every parameter sourced

Task-based labor market

A calibrated production function where every parameter is sourced and can be swapped out, so you can see which assumption drives which result.

Economics · machine learning. Engine built and outputs cached, with the companion paper in progress.
01

The problem

There are now seven major measures of AI exposure, and they disagree, to the point that the measures built before LLMs are negatively correlated with the ones built after. Meanwhile, claims about AI's effect on wages and employment have gotten ahead of the evidence. Another estimate would not settle this, whereas a framework where every parameter is disclosed, sourced and swappable does help, because when results differ you can see which assumption made them differ.

02

How it works

01The economy as tasks

The model has three nested levels: an industry combines tasks in stable expenditure shares, each task is produced from capital and labor with its own substitution elasticity, and the labor input is a bundle of skills. Tasks that resist automation differ from exposed ones in a single parameter.

Economics

02Calibrated from published sources

No elasticity is estimated from market data and no equilibrium is solved. Every parameter is calibrated to a published source, such as staffing matrices, task-importance profiles, output weights and skill proximities, and records where it came from.

Economics · data science

03Exposure as a pluggable adapter

The AI-exposure parameters come from interchangeable adapters that share one interface, with several published measures available, and results are reported for each measure as a standard output, so the disagreement between measures is out in the open.

Machine learning · engineering

04Validated against observed shifts

The headline test asks whether calibrated task-level exposure anticipates observed wage shifts better than flat per-occupation scores and a zero-information null. Validation runs on healthcare occupations, where within-industry variation in substitutability is largest.

Econometrics
Framework three levels, two outputs

The structure nests Cobb-Douglas over tasks, capital against labor within each task, and skills within labor, and the two engine outputs follow directly from it.

Industry combines tasks
Y = A · Πi Tiβi
Each industry produces output by combining tasks in stable expenditure shares βi.
Each task combines capital and labor
Ti = Bi · [ δi Kiρi + (1−δi) Liρi ]1/ρi
The substitution elasticity σi = 1/(1−ρi) is task-specific: near zero, capital and labor are complements and the task resists automation. Large, they substitute and the task is exposed.
Labor is a bundle of skills
Li = CES( S1 … SK . γi,k, σj,k )
Skill shares γi,k are task-specific. Pairwise elasticities σj,k say which skills substitute within a task and which cannot.
The outputs
θk = Σi βi (1−δi) γi,k     ∂θk/∂δi = −βi γi,k
θk is skill k's weight in aggregate output. Its derivative is skill k's exposure to a marginal increase in task i's capital intensity. Every surface and every figure reads from these two.
This is a measurement tool with disclosed parameters. It estimates no elasticities, solves no equilibrium and makes no causal claims about wages or employment.
Where every parameter comes from the provenance

None of the parameters are estimated structurally, and each one comes from a published source.

βi · industry task shares
National staffing matrices × task importance profiles, weighted by industry output.
δi, σi · capital share and substitutability
Pluggable AI-exposure adapters: several published task-level measures behind one contract, with a blended option.
γi,k · skill shares within a task
Task-to-skill importance matrices, with an embedding fallback where no direct mapping exists.
σj,k · skill-to-skill substitutability
Occupation-pair skill proximity, a monotone transform of cosine similarity over skills, knowledge, and work activities.
Every engine output carries its adapter and calibration vintage as columns.
03

Tools used

Python, numpy, scipyThe nested CES calibration, read top-down and bottom-up.
sentence-transformersSkill and occupation embeddings for skill-to-skill proximity.
O*NET task, skill, and work-activity matricesThe parameter sources behind every share.
Published AI-exposure measuresPluggable adapters behind one contract, with a blended option.
pandasThe task atlas of several hundred thousand calibrated rows.
04

Final state

The engine is built and its outputs are cached: skill exposure, role resilience, and a task atlas of several hundred thousand calibrated rows, each carrying its adapter and calibration vintage. I also use the framework for research, and a companion paper on measuring labor market resilience and AI exposure is in progress. The equations above are the ones the production system uses, though worked magnitudes are not shown here.

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