Endogenous data makes automation self-reinforcing but slow: data both improves existing automation and widens the automation frontier, yet the share of tasks performed by labor falls only asymptotically as a power law. The model predicts explosive aggregate growth when capital is endogenous but persistent wage stagnation and a generic role for policy to reorient data accumulation toward socially valuable directions.

Main Finding

Data-driven automation—where task-specific data accumulates endogenously and spills across tasks—creates rich dynamics in which (i) the long-run extent of automation is determined jointly by cross-task substitutability (σ) and diminishing returns to data (η); (ii) local data spillovers (graphon connectivity) can produce contagious, core-periphery patterns but ultimately guarantee full automation; (iii) automation is generically inefficient from a planner’s perspective; and (iv) with endogenous capital accumulation the data-automation feedback can generate explosive (finite-time) growth while long-run wages may stagnate when the economy fully automates.

Key Points

• Model ingredients
  • Task space X = [0,1], final good is a CES aggregator over continuum of tasks (elasticity parameter σ).
  • Two factors: capital and labor (perfect substitutes at task level). A task is “automated” if produced by capital.
  • Data is task-specific, non-depreciating, accumulates endogenously as the time integral of task output Dit = Di0 + ∫0^t yi(s) ds, and can spill across tasks via a graphon-like structure.
  • Capital productivity for task i is fi · (Ai(D))^η with η ∈ (0,1) (diminishing returns to data); fi captures task-specific scalars (e.g., ease of data accumulation).
• Long-run automation threshold (no capital accumulation baseline)
  • Two key parameters: σ (elasticity / substitutability across tasks) and η (returns-to-data exponent).
  • If σ ≤ 1/η (tasks relatively complementary / data has sufficiently weak diminishing returns), the economy is fully automated in the long run: the automation frontier expands to cover all tasks (Proposition 1). The economy approaches a balanced data path.
  • If σ > 1/η (tasks sufficiently substitutable or data has strong diminishing returns), the economy can remain partially automated in the limit, with capital concentrated on a small set of data-rich tasks and persistent labor for a fat tail of tasks (Proposition 2).
• Dynamics and speed of automation
  • Short-run automation can be rapid and imbalanced depending on the network of spillovers; automation can spread contagiously through chains of spillovers.
  • However, absent capital accumulation, the share of tasks performed by labor decays only as a power law in time (long tail): automation is ultimately slow asymptotically (Proposition 4).
  • Core-periphery structure: dense core sectors may automate quickly and generate reinforcing data, while periphery sectors automate much later depending on within-core linkage strength and core→periphery bottlenecks.
• Spillovers and connectivity
  • If the task-spillover graphon is connected (there exists a positive-measure path connecting any two tasks), full automation occurs in the long run regardless of σ, η, and initial data distribution (Proposition 5). Local spillovers substitute for global complementarities.
• Wages and distributional effects
  • “Labor trains its own replacement”: when the economy fully automates (σ ≤ 1/η, or via connected spillovers), long-run wages stagnate even as capital productivity rises (Proposition 3).
  • When automation is partial (σ > 1/η), long-run wages can grow unboundedly.
  • Paradoxically, greater cross-task complementarities can reduce long-run wages once dynamic data accumulation and equilibrium allocation are accounted for.
• Efficiency and policy-relevant distortions
  • Equilibrium data accumulation is generically inefficient (Proposition 6). The planner would optimally tilt data accumulation directions relative to equilibrium:
    • If σ ≤ 1/η (complements), planner favors boosting data for data-poor/bottlenecked tasks.
    • If σ > 1/η (substitutes), planner favors away from data-poor tasks relative to market allocation.
  • The inefficiency arises because private producers do not internalize how their task production affects aggregate future data and thus future automation paths.
• Endogenous capital accumulation
  • Introducing capital accumulation can convert the data-automation feedback into explosive (finite-time) growth because data (i) augments already-automated tasks, (ii) expands the automation frontier, and (iii) does not depreciate. This can produce a growth singularity even under conservative assumptions on diminishing returns and depreciation (Proposition 7).
  • Despite explosive aggregate growth, long-run wages can remain stagnant in the fully-automated regime.

Data & Methods

• Purely theoretical / analytical approach: the paper builds and analyzes a continuous-time dynamic general-equilibrium model with a continuum of tasks.
• Production structure
  • CES aggregator for the final good over tasks; linear task-level production in the chosen factor (capital or labor).
  • Task-level capital productivity is a power function of an effective data aggregator Ai(D) with exponent η ∈ (0,1).
• Data accumulation and spillovers
  • Data stock for each task evolves as the time integral of the task’s output (non-depreciating).
  • Cross-task spillovers modeled via a graphon (dense continuous-limit network), so local transfer-learning / spillovers are captured by an integral operator mapping the task data vector into effective data for each task.
• Analytical techniques
  • Characterization of equilibrium automation boundary γt and capital allocations.
  • Asymptotic and non-asymptotic bounds on automation speed; proofs of power-law decay of labor-task share.
  • Comparative statics in (σ, η) to classify long-run regimes and wages.
  • Planner’s problem to derive welfare-optimal tilts in data accumulation.
  • Extension with endogenous capital accumulation to analyze growth dynamics and possible finite-time singularities.
• Key assumptions
  • Data does not depreciate and is nonrival for training (can be reused).
  • Capital and labor are perfect substitutes at the task level; factor prices determine which factor supplies each task.
  • Diminishing returns to data through exponent η < 1.
  • Initial data distribution is bounded, continuous, and decreasing in task index in baseline; graphon connectivity formalizes spillovers.

Implications for AI Economics

• Data is a central economic input for automation: its task-specific accumulation and spillovers shape both the direction and speed of automation, not merely model size or compute.
• Spillovers matter: localized transfer learning can make automation contagious and overcome complementarities that would otherwise slow broad automation. Policy or investments that strengthen cross-task data links (or open data sharing) can accelerate economy-wide automation.
• Long tails and labor persistence: even powerful data-driven learning generates a slow, power-law decay in the share of tasks done by labor. Expect persistent pockets of labor-intensive tasks for long horizons unless complemented by other forces (e.g., capital accumulation or stronger spillovers).
• Distributional and wage outcomes are nontrivial: more automation does not mechanically raise wages; in many plausible parameterizations wages stagnate because labor generates the very data that enables its replacement. This complicates standard narratives that automation simply boosts productivity and wages.
• Market failure and policy levers: because firms do not internalize the future value of data spillovers, decentralized data production is generically misdirected. Policy tools (subsidies for data collection in bottleneck sectors, regulations on data sharing, or public data goods) could improve social outcomes and re-orient the automation frontier.
• Core-periphery risks: rapid automation in a small “core” of sectors could produce concentrated value creation and data accumulation, delaying broader-based automation and potentially exacerbating inequality and sectoral dislocation. Policies should consider the network structure of tasks when targeting interventions.
• Macro growth considerations: with capital accumulation, data-driven automation can induce explosive growth even under conservative assumptions. This raises questions about transitional dynamics, capital allocation, and stabilization policies in fast-automating economies.
• Empirical agenda: the framework suggests testing for (i) the elasticity threshold interaction (σ vs 1/η) in observed sectoral automation patterns; (ii) measures of task similarity/graphon structure predicting contagion; and (iii) the predicted power-law decay in labor-task shares over long horizons.

Concluding remark: This paper formalizes how endogenous, task-specific data and its networked spillovers fundamentally reshape automation dynamics, wages, efficiency, and growth—highlighting data policy and the network structure of tasks as crucial elements for economists and policymakers to consider in the age of AI.