The Signed Error: The Direction of AI Adoption and Its Correction

Abstract

AI is a double-edged sword for the labor share, and through the labor share for the public finances. Along its substitution branch, adoption erodes the payroll base that finances social insurance just as sovereign debt service absorbs a rising share of revenue; along its productivity branch, it is the only realistic source of the growth that stabilizes debt ratios without default, inflation, or austerity. Which branch dominates is not a property of the technology; it is the aggregate of millions of adoption decisions taken at distorted prices. This paper models the choice. In a task framework with endogenous direction of technical change, a welfare- and growth-optimal degree of complementarity between AI and labor exists and is interior: full substitution scraps human capital, demand, and reallocation capacity for thin "so-so automation" gains, while full complementarity is protection dressed as humanism and sacrifices growth. The optimum is not computable ex ante, because it depends on labor's comparative advantage over tasks that do not yet exist. The central result is that no one needs to compute it: the market's deviation from the optimum is signed. Four wedges, the tax asymmetry between payroll and automation inputs, the gap between the private wage and the social opportunity cost of displaced labor, the demand externality of retained payroll, and an appropriability asymmetry that pays automation R&D in full while new-task R&D creates labor demand its inventor barely captures, all point the same way: over-substitution and under-creation. Three of the wedges are unconditional facts of the tax code and the labor market; the fourth requires a wage-led demand regime, and the sign of the total survives its removal. A signed error means Pigouvian correction works without locating the target, and the correction belongs on the deployment margin, not the development margin: adopters consume metered inference and book no AI capital, the producing sector is small and demand-led, and a corrected adopter price propagates into laboratory R&D allocation with no instrument touching the producer, once that sector prices to adopter demand rather than financing a capability race, which is the pass-through's one live vulnerability. The instrument is a labor-share screen: exemption of above-trend margin increments from an excess-margin tax, conditioned on the firm's own labor share against a ratcheted baseline. The screen taxes so-so automation regardless of how adoption is booked, exempts output expansion whose gains are shared into compensation, survives price-led masking and outsourcing, and deliberately taxes hoarded productivity gains. The fiscal result completes the macro argument: under the substitution branch the payroll base erodes as above-trend margins swell, so the paired instrument's legs move opposite and revenue adequacy migrates with the income, holding in the fiscal-dominance state that motivates the paper, subject to an incidence of the increment tax that the fiscal companion finds does not pass through on the pricing margin, leaving a general-equilibrium residual.

Keywords: automation, directed technical change, labor share, task framework, Pigouvian taxation, fiscal dominance, AI adoption. JEL codes: E25, E63, H23, J23, O33

JEL Classification: E25, E63, H23, J23, O33