WP-003 The Valley at the Frontier: Who Gains from Generative AI

Abstract

Does generative AI widen or compress productivity differences between workers? This paper develops a microeconomic model in which an AI tool has two separate margins: a frontier, the problems it can solve for anyone, and leverage, the extra work it lets a person get through. The gain from adoption is V-shaped in ability, with its minimum at the worker whose knowledge equals the AI’s frontier. Frontier advances are equalising and leverage is skill-biased. The average AI×skill complementarity therefore changes sign as the frontier moves through the ability distribution, and the conflicting experimental findings describe different points on the same curve. Relative inequality never rises with ability-neutral leverage, but inequality in levels can. When the frontier is jagged, the ability to judge AI output becomes the skill-biased margin, and over-trusting workers can lose. Adoption is two-tailed, so the sign of selection bias depends on the vintage of the technology. Workers capture a share of the gain that rises with diffusion across employers. The return to ability falls to zero below the frontier, which removes the incentive for juniors to climb rungs the AI already occupies. The paper closes with seven testable predictions and the designs needed to test them.

Keywords generative AI, technology adoption, skill complementarity, knowledge hierarchies, wage inequality, human capital, rent sharing

01The question

Whether AI makes workers more productive is largely settled. The open question is who becomes more productive, and whether the gain reaches wages.

Does generative AI increase, reduce or redistribute productivity differences between workers?

The evidence seems to conflict. In customer support and professional writing, the least experienced gained most. Among entrepreneurs given an AI adviser, the best gained and the weakest lost. The paper argues that these results describe different regions of the same gain profile.

02Frontier and leverage

A worker's ability \(a\) is the hardest problem they can solve unaided. An AI tool has two separate properties. Its frontier \(k\) is the range of problems it can solve for anyone who asks. Its leverage \(\lambda\) is the additional work it lets a person get through:

\[Y_1(a) = (1+\lambda)\,V\big(\max\{a,k\}\big)\]

The frontier sets a floor under everyone's output. Leverage multiplies output, so it is worth more to those who already produce more. A model release mostly moves \(k\). Integration into workflows mostly moves \(\lambda\).

Exposure and intensity are different objects. Exposure, \(H(k)\), is the same for everyone in a job. Intensity, the share of a worker's problems that are solved only because of the AI, is highest for the least able.

03The valley at the frontier

The gain from AI is V-shaped in ability, with its minimum at the worker whose knowledge equals the AI's frontier. The cross-derivative \(\partial^2 Y/\partial AI\,\partial a\) is negative below the frontier and positive above it.

The average AI × skill interaction is strictly decreasing in the frontier and changes sign once at \(\hat k(\lambda)\). Early tools are skill-biased and later ones equalising. The sign estimated in any study therefore reflects the technology vintage and the job as much as the technology.

Uniform benchmark\[S(k,\lambda)=(1+\lambda)(1-k)^2(1+2k)-1\]

04Relative and absolute dispersion

With leverage that is the same for every worker, AI never raises relative inequality: the Lorenz curve shifts inward, and the Gini, the variance of logs and every 90/10-type ratio fall. Inequality in levels can still rise, because leverage scales absolute gaps. Over an intermediate range of frontiers, a study in logs finds compression and one in levels finds widening, using the same data.

05The jagged frontier: judgment

Beyond its frontier, the AI still produces answers, and its wrong ones look right. Using it there requires the ability to detect errors, \(\pi(a)\). Reaching beyond one's own competence pays only above a threshold of ability:

\[r(a)=q-(1-q)\big(1-\pi(a)\big)d\]

Judgment is the skill-biased margin of AI. Workers who over-trust the tool can lose, and those losses are concentrated at the bottom. Verification such as review layers, tests and checklists can be bought, so firms can raise \(\pi\) for their weaker workers.

06Adoption and selection

With a cost of learning the tool, adoption is two-tailed. The able adopt for leverage, the less able for the floor, and the competent middle last. As the frontier advances, adopters go from being the able to being the less able, so the bias in comparing users with non-users changes sign:

\[\mathbb{E}[Y\mid D=1]-\mathbb{E}[Y\mid D=0]=\mathbb{E}[\Delta\mid D=1]+\underbrace{\mathbb{E}[Y_0\mid D=1]-\mathbb{E}[Y_0\mid D=0]}_{\text{sign depends on }k}\]

In experiments that randomise access but leave use voluntary, the valley appears as a flat trough. Heterogeneity by baseline performance then mixes take-up with gains.

07Who keeps the gain

With Nash bargaining and an outside option that depends on how many employers use the tool, the worker keeps a share \(\varphi+\beta(1-\varphi)\) of the net gain. Early in diffusion the employer captures most of it, and wages catch up as the tool becomes standard. In the long run the return to ability falls to zero below the frontier and rises above it: the skill premium develops a kink at the AI frontier.

08The missing rungs

Because ability below the frontier is not paid, a junior has no reason to climb rungs the AI already occupies unless they can get past the frontier within the horizon. Learning becomes all-or-nothing, and the threshold rises one-for-one with the frontier:

\[a_1^\ast = k-(1+\tau)\gamma+\frac{\kappa}{\delta(1+\lambda)}\]

AI used as a tutor (\(\tau\)) works against this. An employer that does not capture the return to general skills has no reason to pay for practice when the tool can do the work.

09Results and predictions

The two hypotheses, skill-biased and knowledge-diffusing, are two sides of one valley.

Prediction	Design that tests it
Gains V-shaped in baseline ability, minimum near the frontier	Staggered rollout with mandated use, effects by ability decile
AI × skill interaction falls after each frontier advance	Model upgrade within an unchanged interface
Losses outside the frontier fall when verification rises	Randomised review layers
Adoption moves from the top to the bottom, the middle last	Usage logs linked to baseline performance
Wage pass-through rises with employer-side diffusion	Matched employer–employee data
Juniors below the frontier practise and learn less	Hiring cohorts before and after access, unaided tests

CaveatTheory paper. Propositions are proved and verified symbolically, and figures use stylised parameters. The paper reads existing experiments against the model but does not estimate it.

10Status

Level	Where it stands
Model	Seven propositions, proved and verified symbolically and numerically.
Numerics	Uniform benchmark; robustness on random ability and difficulty distributions.
Evidence	Research design and reading of published experiments; no own estimation. Working paper v1.

Together with WP-002, the paper forms a pair. One studies how AI changes what firms sell, and the other how it changes what workers produce. Verification links them: it decides whether software can be sold by outcome, and whether weaker workers gain from AI.

Abstract

01The question

02Frontier and leverage

03The valley at the frontier

04Relative and absolute dispersion

05The jagged frontier: judgment

06Adoption and selection

07Who keeps the gain

08The missing rungs

09Results and predictions

10Status

Citation