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arxiv: 2606.10127 · v1 · pith:YPKDTCEDnew · submitted 2026-06-08 · 💰 econ.TH

Data-Driven Automation

Maryam Farboodi , Andrew Koh , Anchi Xia This is my paper

Pith reviewed 2026-06-27 13:56 UTC · model grok-4.3

classification 💰 econ.TH
keywords data-driven automationendogenous dataspilloversautomation frontierinefficiencycapital accumulationwage stagnationpower law dynamics
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The pith

Data-driven automation with endogenous capital accumulation generates explosive growth but stagnant long-run wages.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The authors develop a dynamic model where data is heterogeneous and task-specific, builds up endogenously from economic activity, and generates spillovers across tasks. Along the transition, data augments productivity in automated tasks while expanding the set of automatable tasks. The economy reaches full automation under certain spillover conditions, with the labor task share then declining as a power law. Including endogenous capital leads to explosive output growth alongside flat long-run wages. The market equilibrium is generically inefficient, and a planner would direct data accumulation differently.

Core claim

With endogenous capital accumulation, data-driven automation generates explosive growth but stagnant long-run wages. The economy is generically inefficient.

What carries the argument

Dynamic model of endogenous data accumulation with task-specific heterogeneity and cross-task spillovers that simultaneously raises productivity and expands the automation frontier.

If this is right

  • Tight conditions determine whether the economy is partially or fully automated in the long run.
  • Full automation features slow long-run dynamics with labor share decaying as a power law in time.
  • The decentralized economy fails to achieve the efficient direction of data accumulation.
  • Data plays a dual role in augmenting existing automated tasks and pushing the frontier.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Regulations on data sharing could alter the rate at which the automation frontier expands.
  • The combination of rapid growth and wage stagnation points to potential distributional conflicts not addressed by market forces.
  • Extensions might incorporate heterogeneity in firm data access to study concentration effects.

Load-bearing premise

Data is heterogeneous and task-specific, accumulates endogenously as a byproduct of economic activity, and exhibits spillovers such that data generated by one task can augment the productivity of another.

What would settle it

Tracking the time path of labor's share of tasks in highly automated sectors to check for asymptotic power-law decay, or measuring whether output growth accelerates while wages stagnate under widespread data-driven automation.

Figures

Figures reproduced from arXiv: 2606.10127 by Anchi Xia, Andrew Koh, Maryam Farboodi.

Figure 2
Figure 2. Figure 2: Illustration of ψK i vs ψL literature in computer science (see, e.g., Hoffmann et al. (2022) and a large body of subsequent work) demonstrating that the loss—a measure of imperfection for a task—diminishes polynomially with the amount of data used for training large lan￾guage models. Heuristically, they find that the loss approximately takes the func￾tional form: LOSS ≃ 1 Nα + 1 Dβ for α,β > 0 where D is d… view at source ↗
Figure 3
Figure 3. Figure 3: Dynamics of equilibrium outcomes when the degree of substitutability [PITH_FULL_IMAGE:figures/full_fig_p019_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Balanced data growth Note: We set ψL = L = K = 1, D0 := 1, f (i) = 1−i, η = 0.2, g = δ{0}, σ = 0.5. Details of procedure in Section C. Figure 3b illustrates the evolution of automation boundary in this case. Red lines represent the relative factor price of capital and blue curves reflect the cross-sectional distribution of task productivities. The important observation is that the automation boundary γt mo… view at source ↗
Figure 5
Figure 5. Figure 5: Imbalanced data growth Note: parameters same as [PITH_FULL_IMAGE:figures/full_fig_p022_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Dynamics of equilibrium outcomes when tasks are highly substitutable [PITH_FULL_IMAGE:figures/full_fig_p023_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Comparative dynamics over time for different values of [PITH_FULL_IMAGE:figures/full_fig_p024_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Bounds on the speed of data-driven automation [PITH_FULL_IMAGE:figures/full_fig_p027_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Overlapping neighbors ports are non-overlapping—task k but not i could value the data of some other task ℓ ∈ X. Then, if Dℓt grows quickly, the limit ratio of effective data Ri k could, in princi￾ple, be 0. Nonetheless in Section A.2 we show via a chaining argument that, because the space of tasks X is bounded, this cannot happen in equilibrium—connectedness implies that along the equilibrium path full aut… view at source ↗
Figure 10
Figure 10. Figure 10: Evolution of γ under alternative spillover geometries Note: m denotes the measure of the g (·) kernel that induces W (·,·), which captures the depth of spillovers. The remaining parameters are as in [PITH_FULL_IMAGE:figures/full_fig_p031_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: A two-block core-periphery graphon. Rows index the beneficiary task [PITH_FULL_IMAGE:figures/full_fig_p032_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Automation paths and the time τ at which the wider economy begins to be automated can be analytically characterized via a pair of coupled ODEs. We emphasize here that the automation can have a non-monotonic relationship with link strength: by intensifying the degree of within-core spillovers wCC , this can delay the time at which peripheral tasks begin to be automated. This is because ψC now grows more qu… view at source ↗
Figure 13
Figure 13. Figure 13: Numerical illustration of the planner’s solution [PITH_FULL_IMAGE:figures/full_fig_p035_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: Illustration of proof ideas for 1 < σ < 1/η the planner speeds up the rate at which block ℓ’s data is accumulated—at the cost of static misallocation—in order to loosen the bottleneck more quickly. Conversely, when tasks are highly substitutable σ > 1/η, the right hand side of Equa￾tion (13) will be larger, so the planner is incentivized to lean into tasks that are al￾ready data-rich—even though the equil… view at source ↗
Figure 15
Figure 15. Figure 15: Comparison of capital allocated to the data-rich sector. [PITH_FULL_IMAGE:figures/full_fig_p067_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: The time-path of wages and output. In the complements case, wages rise [PITH_FULL_IMAGE:figures/full_fig_p080_16.png] view at source ↗
Figure 18
Figure 18. Figure 18: σ = 0.5 with Solow-style capital accumulation. (a) (b) (c) (d) (e) (f) (g) (h) (i) 81 [PITH_FULL_IMAGE:figures/full_fig_p082_18.png] view at source ↗
Figure 19
Figure 19. Figure 19: σ = 5.5 with Solow-style capital accumulation. (a) (b) (c) (d) (e) (f) (g) (h) (i) 82 [PITH_FULL_IMAGE:figures/full_fig_p083_19.png] view at source ↗
Figure 20
Figure 20. Figure 20: Planner’s allocation at σ = 0.5 [PITH_FULL_IMAGE:figures/full_fig_p084_20.png] view at source ↗
Figure 21
Figure 21. Figure 21: Planner’s allocation at σ = 5.5 83 [PITH_FULL_IMAGE:figures/full_fig_p084_21.png] view at source ↗
Figure 22
Figure 22. Figure 22: Planner’s allocation at σ = 0.5 with labor included 84 [PITH_FULL_IMAGE:figures/full_fig_p085_22.png] view at source ↗
read the original abstract

We build a dynamic model of data-driven automation in which data (i) is heterogeneous and task-specific; (ii) accumulates endogenously as a byproduct of economic activity; and (iii) exhibits spillovers such that data generated by one task can augment the productivity of another. Along the transition path of automation, data plays a dual role in simultaneously augmenting the productivity of already-automated tasks and expanding the automation frontier. We derive tight conditions for the economy to be partially versus fully automated in the long-run. In the latter case, automation exhibits rich short-run dynamics that depend on the pattern of data spillovers but is always slow in the long-run: the share of tasks produced by labor decays asymptotically as a power law in time. We show that the economy is generically inefficient and analyze how a planner optimally tilts the direction of data accumulation. With endogenous capital accumulation, data-driven automation generates explosive growth but stagnant long-run wages.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 0 minor

Summary. The paper develops a dynamic model of data-driven automation in which data is heterogeneous and task-specific, accumulates endogenously as a byproduct of production, and features spillovers across tasks. Data augments productivity of automated tasks while expanding the automation frontier. The model derives conditions distinguishing partial from full long-run automation; under full automation, labor's task share decays as a power law asymptotically (with short-run dynamics depending on spillover patterns). The decentralized equilibrium is generically inefficient, and a planner can improve outcomes by tilting data accumulation. With endogenous capital accumulation, the economy exhibits explosive growth but stagnant long-run wages.

Significance. If the derivations hold, the framework supplies a microfounded mechanism for the decoupling of productivity growth from wage growth via endogenous data and spillovers, while delivering falsifiable predictions such as power-law labor-share decay and generic inefficiency. The dual role of data and the explicit treatment of directionality under a planner are strengths that could inform policy analysis of data-driven automation.

major comments (2)
  1. [Abstract] Abstract: the claim that 'tight conditions' for partial versus full automation are derived cannot be verified because the model equations, state variables, and functional forms governing data accumulation and spillovers are not provided; without these it is impossible to confirm whether the partial/full distinction follows from the three posited data properties or requires additional restrictions.
  2. [Abstract] Abstract: the statement that 'the share of tasks produced by labor decays asymptotically as a power law in time' under full automation is presented as following directly from the spillover structure, but no derivation, functional-form assumptions, or limiting argument is visible to assess whether the exponent is pinned down by primitives or depends on normalization choices.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their comments. We address the two major comments on the abstract below. The abstract provides a summary of results that are fully derived in the manuscript.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the claim that 'tight conditions' for partial versus full automation cannot be verified because the model equations, state variables, and functional forms governing data accumulation and spillovers are not provided; without these it is impossible to confirm whether the partial/full distinction follows from the three posited data properties or requires additional restrictions.

    Authors: The abstract is a concise summary and does not include technical details such as equations. The model is fully specified in the main text, with data accumulation governed by an endogenous law of motion that incorporates task-specific heterogeneity and spillovers. The tight conditions for partial versus full automation are derived directly from these three properties in Section 2 without additional restrictions, as formalized in the propositions there. The referee's observation is correct that the abstract alone does not allow verification, but the manuscript does. revision: no

  2. Referee: [Abstract] Abstract: the statement that 'the share of tasks produced by labor decays asymptotically as a power law in time' under full automation is presented as following directly from the spillover structure, but no derivation, functional-form assumptions, or limiting argument is visible to assess whether the exponent is pinned down by primitives or depends on normalization choices.

    Authors: The asymptotic power-law decay is established in Section 3 through analysis of the dynamic system under full automation. The functional form of spillovers is specified as a general spillover function, and the limiting behavior is derived using standard techniques for asymptotic analysis of the resulting ODE system. The exponent is determined by the spectral properties of the spillover structure, which are primitives of the model, and is independent of normalization choices. Short-run dynamics vary with the specific spillover pattern as stated. revision: no

Circularity Check

0 steps flagged

No significant circularity; derivations self-contained from model assumptions

full rationale

The paper constructs a dynamic model from explicit assumptions on data (heterogeneous/task-specific, endogenous accumulation as byproduct, spillovers across tasks) plus endogenous capital accumulation, then derives long-run automation conditions, power-law labor share decay, generic inefficiency, planner's optimal data direction, and explosive growth with stagnant wages. These follow from the posited primitives and transition dynamics without any quoted reduction of a 'prediction' or 'result' to a fitted parameter, self-citation chain, or definitional equivalence. No load-bearing step is shown to collapse by construction to its inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 3 axioms · 0 invented entities

The central claims rest on three core domain assumptions about data properties that are stated directly in the abstract; no explicit free parameters or invented entities are mentioned.

axioms (3)
  • domain assumption Data is heterogeneous and task-specific.
    Explicitly listed as model feature (i) in the abstract.
  • domain assumption Data accumulates endogenously as a byproduct of economic activity.
    Explicitly listed as model feature (ii) in the abstract.
  • domain assumption Data exhibits spillovers such that data generated by one task can augment the productivity of another.
    Explicitly listed as model feature (iii) in the abstract.

pith-pipeline@v0.9.1-grok · 5682 in / 1376 out tokens · 23499 ms · 2026-06-27T13:56:39.828484+00:00 · methodology

discussion (0)

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