Pith. sign in

REVIEW 3 major objections 4 minor 67 references

Heterogeneous Agents in the Data Economy

T0 review · 3 major / 4 minor · reviewed 2026-08-04 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read This paper claims that differences in firms' data investment ability alone create divergent output, data scale, productivity, and financing outcomes in the data economy.

desk verdict A novel threshold fixed point in a data-economy model, but the headline financial-friction result is a tautology once the paper's own definitions are substituted. read the letter →

arxiv 2509.09656 v1 pith:VZU73XLE submitted 2025-09-11 econ.TH

Yongheng Hu This is my paper · ORCID
classification econ.TH
keywords DataEconomyHeterogeneousAgentsInvestmentAbilityCostFinancialFrictionBorrowingConstraintThresholdModelTotalFactorProductivity
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper tries to establish that firms differ in their ability to invest in data, and that these ability differences alone generate divergent economic outcomes: higher-ability firms buy more data, pay higher data costs, produce more output, achieve higher productivity, and face weaker financial frictions. It builds a two-type heterogeneous-agent model with data users and data providers, where the data user's ability μ_i is normally distributed and determines who crosses a threshold to become a high-type user. The motivation is to move the data-economy literature beyond representative-agent models, which assume identical data utilization abilities and therefore miss ability-driven inequality. A sympathetic reader would care because if true, data policy, cost structures, and financial-market development affect different firms in systematically different ways.

What carries the argument

The threshold equation μ_k = F(τ_k, μ_k), where F includes the log-odds of the data cost rate, the truncated log-normal expectation of ability, and a risk-adjustment term from CRRA utility. It determines the cutoff ability that separates data users from providers and yields dμ_k/dτ_k > 0, so higher-cost data regimes select higher-ability users. The second piece of machinery is the borrowing-constraint coefficient λ in the wealth dynamics dW_t = W_t[(r_f + αμ̂ − λ)dt + ασ dZ − αL dN], with K_t = λ W_t, which connects ability to financial friction through a fixed-point equation f(λ, t*) = f(μ_i, t*).

What would settle it

Substitute W_0 = e^{μ_i+ε_0+ε_{i,0}}D_0(1−τ_0) and E K_t = λW_0 exp{(r_f + αμ̂ − λ + w(E(1−αL)−1))t} into f(λ,t*) = f(μ_i,t*). Both sides reduce to e^{λt*}/λ, so the two curves do not cross as distinct functions; hence λ_H > λ_L does not follow from the stated equations. A direct check of whether ∂f/∂λ > 0 holds at t* with λt* > 1 would settle the claim.

Watch

Extended reading notes

Core claim

The central claim is that a firm's data investment ability μ_i maps through a threshold rule to a full set of economic outcomes: higher μ_i leads to a higher data cost rate τ, a larger data input scale d, higher technology z (via z = d^η with η ∈ (0,1)), higher output y, and a higher borrowing-constraint coefficient λ (meaning lower financial friction). The paper formalizes this as Theorem 1, which classifies firms into High-type (μ_H > μ_k) and Low-type (μ_L < μ_k) and states y_H > y_L, z_H > z_L, d_H > d_L, λ_H > λ_L. The threshold μ_k is defined implicitly by an equation involving the data cost rate, the distribution of abilities, and the risk-adjusted utility difference between data user

Load-bearing premise

The financial-friction conclusion rests on the fixed-point equation f(λ, t*) = f(μ_i, t*) having a solution where ∂f/∂λ > 0, which the paper does not establish and which its own substitution may render trivial.

Editorial extensions

If this is right

  • If high-ability data users systematically face lower financial frictions, then financial market development disproportionately benefits firms that are already data-productive, potentially widening cross-firm dispersion.
  • Data cost policies (e.g., taxes or subsidies on data purchase) shift the ability threshold, changing which firms become data users and thereby changing aggregate output and productivity.
  • A representative-agent data model understates the dispersion produced by ability heterogeneity; accounting for ability differences is a prerequisite for analyzing data-economy inequality.
  • The mapping from ability to output implies that the distribution of μ_i in the population matters for aggregate data-economy growth, not just the average level.
  • Because higher data investment ability is tied to lower financial frictions, the model predicts a positive correlation between data intensity and financial leverage across firms.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • One testable extension: measure data investment ability using firm-level data-management practices or data-worker intensity, then check whether firms with higher measured ability indeed show higher data expenditure and lower borrowing constraints.
  • A dynamic extension could allow low-type firms to switch to being data providers over time; the current model fixes the choice as imperfect, so the persistence of ability-based outcomes is not yet explored.
  • The threshold mechanism suggests that data cost subsidies lower the cutoff μ_k and bring more firms into the data-user group, but the model implies this would also reduce the average ability of data users, which might offset aggregate output gains.
  • The financial-friction result hinges on the fixed-point crossing; an editor's inference is that the paper's own substitution may make both sides of f(λ,t*) = f(μ_i,t*) identical, so the comparative static needs a separate existence argument.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 4 minor

Summary. The paper proposes a heterogeneous-agent model of the data economy in which data users differ in an exogenous 'data investment ability' µ_i. It derives a threshold µ_k that classifies agents into high- and low-ability data users, and then claims (Theorem 1) that high-ability firms have larger data scale, higher output, higher productivity, and lower financial frictions than low-ability firms. The financial-friction part follows Moll (2014) and attempts to link µ_i to a borrowing-constraint coefficient λ through a fixed-point equation f(λ,t*)=f(µ_i,t*). The paper's contribution is intended as a first analytical step from representative-agent to heterogeneous-agent modeling of the data economy.

Significance. If the claims held, the paper would provide a simple and transparent analytical framework connecting data-ability heterogeneity to differences in output, technology, and financial frictions. The utility-comparison algebra in §2.2 is mostly correct after accounting for the γ>1 sign flips, and the lognormal aggregation is standard. The threshold equation is a genuine fixed-point construction rather than an immediate tautology. However, the paper's most distinctive result — the financial-friction comparison λ_H>λ_L — is vacuous as written, because the defining equation reduces to an identity once the paper's own substitutions are made. This is a load-bearing error, not a local presentation issue, and it undermines the abstract's central claim.

major comments (3)
  1. [§2.2, definition of f(µ_i,t) and Figure 1] The financial-friction mapping is an identity, not a fixed-point link. The paper defines W0 = e^{µ_i+ε0+ε_i,0}D0(1-τ0) and derives EK_t = λW0 exp{(r_f+αµ̂-λ+w[E(1-αL)-1])t}. Substituting these into f(µ_i,t*) = W0(EK_t*)^(-1)exp{(r_f+αµ̂+w[E(1-αL)-1])t*} gives f(µ_i,t*) = e^{λt*}/λ = f(λ,t*) identically, for every µ_i and every λ. Hence the crossing equation f(λ,t*)=f(µ_i,t*) carries no information about how µ_i maps to λ, and Figure 1's depiction of two distinct curves crossing is not valid. The asserted monotonicity ∂f(µ_i,t*)/∂µ_i > 0 is zero after substitution, and ∂f(λ,t*)/∂λ > 0 requires λt* > 1, a condition never stated. Consequently λ_H > λ_L in Theorem 1 does not follow from the model.
  2. [§2.2, fixed point µ_k = F(τ_k, µ_k)] The threshold classification is not rigorously established. The paper writes dµ_k/dτ_k = (∂F/∂τ_k)/(1-∂F/∂µ_k) > 0, but it never proves that a solution to µ_k = F(τ_k, µ_k) exists or that 1 - ∂F/∂µ_k > 0. The displayed expression for F also appears to contain a typo: the denominator in the log term is Φ(µ_k;0,σ²µ), whereas the survival function 1-Φ(µ_k;0,σ²µ) is needed for consistency with the earlier expression for m_k and E[e^{µ_j}|j∈L_k]. The high/low split then assumes τ_H > τ_k > τ_L and that high-ability agents choose τ_H, low-ability choose τ_L, rather than deriving this from any optimization or equilibrium condition. Since d_H > d_L and z_H > z_L are consequences of this assumed τ-ordering, the only non-obvious part of Theorem 1 is the financial-friction claim, which fails as shown above.
  3. [Theorem 1 and its proof] The proof of y_H > y_L is not well posed. It defines y_t(µ_k) as aggregate output as a function of the threshold, not as the output of a high- or low-type firm; the inequality y_H > y_L follows more directly from y_{i,t+1} = e^{µ_i}D_t... after conditioning on shocks, since µ_H > µ_L. Moreover, the statement 'µ_H = F(τ_H, µ_H) > µ_k' uses F in a way that is not defined by the fixed-point equation (F was defined as a map from (τ_k, µ_k) to the threshold, not as a map from ability to ability), and no existence proof is supplied. These issues make Theorem 1's logical structure unclear even apart from the financial-friction failure.
minor comments (4)
  1. [Throughout] There are many typographical and notational errors: missing spaces in displayed equations, inconsistent use of N_t for both the Poisson process and the risk-free-asset quantity, and 'dZ_t' appears where Z_t is intended in the SDE solution. The paper's own footnote states it is incomplete; this is consistent with the presentation.
  2. [Figure 1] The text refers to Figure 1 as 'Possible Solution for f(λ,t*)=f(µ_i,t*)', but no actual figure appears in the manuscript. This makes it impossible to verify the claimed crossing and slopes.
  3. [§2.1, Law of Large Numbers] The continuum aggregation uses E[e^{µ_j+ε_j}|j∈L_k] and the Law of Large Numbers without stating integrability/regularity conditions. This is standard in the heterogeneous-agent macro literature, but should be stated for completeness.
  4. [§2.2, threshold monotonicity] The claim that ∂f(µ_k)/∂µ_k > 0 relies on the hazard-rate monotonicity of the normal distribution; this is true, but the argument is compressed and the notation (µ_k;σ²µ,σ²µ) is confusing. The typo in the denominator should be corrected before the argument can be evaluated.

Circularity Check

1 steps flagged · score 8.0 of 10

Financial-friction result is tautological: substituting the paper's W_0 and EK_t into f(μ_i,t) gives f(μ_i,t)=e^{λt}/λ=f(λ,t) identically, so the 'crossing' in Figure 1 imposes no relation between μ_i and λ; λ_H>λ_L is forced by definition, not derived.

  1. self definitional [Section 2.2, financial-friction block, equations for EK_t, f(λ,t), f(μ_i,t), and Figure 1]
    "EK_t =λW_0 exp{(r_f+αμ̂−λ+w[E(1−αL)−1])t} ... e^{λt}/λ = W_0(EK_t)^{-1}e^{(r_f+αbμ+w[E(1−αL)−1])t} e^{λt}/λ = e^{µ_i+ε_0+ε_i,0}D_0(1−τ_0)(EK_t)^{-1}e^{(r_f+αbμ+w[E(1−αL)−1])t} We denote: f(λ,t)=e^{λt}/λ; f(µ_i,t)=e^{µ_i+ε_0+ε_i,0}D_0(1−τ_0)(EK_t)^{-1}e^{(r_f+αbμ+w[E(1−αL)−1])t}"

    Using the paper's own definitions W_0=y_{i,0}(1−τ_0)=e^{µ_i+ε_0+ε_i,0}D_0(1−τ_0) and EK_t=λW_0 exp{(r_f+αμ̂−λ+w[E(1−αL)−1])t}, the quantity f(µ_i,t) collapses algebraically to e^{λt}/λ, which is exactly f(λ,t). Hence the equation f(λ,t*)=f(µ_i,t*) invoked for Figure 1 is an identity, satisfied for every µ_i and λ; it cannot select a value of λ as a function of µ_i. The stated monotonicity ∂f(µ_i,t*)/∂µ_i>0 also disappears after substitution because the µ_i dependence cancels with W_0. Therefore λ_H>λ_L in Theorem 1 is not derived from µ_H>µ_L; it is embedded in the construction of f(µ_i,t) via the same EK_t formula and is thus circular by definition.

full rationale

The paper's two-type classification in §2.1–2.2 is a genuine (if possibly flawed) fixed-point/threshold argument: µ_k is defined by a self-consistency condition F(τ_k,µ_k)=µ_k, and the inequalities y_H>y_L, z_H>z_L, d_H>d_L rest on explicit assumptions about τ_H>τ_L and z_i=d_i^η. Those parts are not circular. I also found no load-bearing self-citation: Hu (2025a,b) are cited for background and for the representative-agent assumption, but the financial-friction result relies on the paper's own equations and on Moll (2014), not on an unverified self-citation chain. However, the headline claim that higher data investment ability reduces financial frictions—'experience lower financial frictions'—is vacuous by construction. The paper defines EK_t with λ multiplied by W_0, then defines f(µ_i,t) using that same EK_t; when substituted, f(µ_i,t) becomes e^{λt}/λ, identical to f(λ,t). The 'possible solution' f(λ,t*)=f(µ_i,t*) is therefore not a fixed-point equation linking µ_i to λ. The conclusion λ_H>λ_L is forced by the construction, not by equilibrium or an independent mechanism. This is one central prediction reducing by definition, warranting a high score, while the rest of the model retains independent content beyond that circular block.

Assumptions & free parameters 4 free parameters · 9 assumptions · 2 invented entities

The model carries one latent distribution (ability), three uncalibrated shock/friction parameters, and an imported technology elasticity; it imports its financial-friction structure from Moll (2014) and its z = d^η technology from Jones and Tonetti (2020). Two ad hoc constructs do real work: the assumption that low-ability firms stay data users despite preferring to be providers, and the type-specific cost rates τ_H/τ_L needed to obtain d_H > d_L. The single most fragile input is the fixed-point regularity for the threshold equation, which is asserted without proof.

free parameters (4)
  • σ²_µ (dispersion of data investment ability)
    Ability µ_i ~ N(0, σ²_µ) (later written N(µ̄, σ²_µ), with µ̄ undefined; the two statements are inconsistent). σ²_µ drives the truncated-lognormal terms in the threshold equation and the sign of dµ_k/dτ_k; it is not calibrated to any data.
  • ϑ (minimum retained asset share)
    Market-incompleteness parameter ϑ ∈ (0,1) that survives in the participation threshold through log E[(ϑe^{ε_i}+(1-ϑ))^{1-γ}]; chosen by hand, no calibration.
  • σ²_1 (idiosyncratic shock variance)
    Variance of the lognormal idiosyncratic shock ε_{i,t+1} (mean-adjusted so E[e^{ε_i}]=1); enters the threshold through the same term as ϑ.
  • α, L, w, r_f, µ̂ (financial-block parameters)
    Portfolio share, jump loss ratio, Poisson intensity, risk-free rate and excess return in the wealth-dynamics block. Exogenous and uncalibrated; the λ comparative static is supposed to hold for all values, but ∂f(λ,t*)/∂λ > 0 only holds if λt* > 1.
assumptions (9)
  • standard math Continuum Law of Large Numbers: ∫_j e^{µ_j+ε_j} dj = m_t E[e^{µ_j}|L] (idiosyncratic shocks wash out)
    Used to aggregate total output y_{t+1} and to reduce the risky-asset payoff ∫ N^ij y_j dj to (1-ϑ)D e^{µ_i} e^{ε_{t+1}} in §2.1.
  • domain assumption Output technology: y_{i,t+1} = e^{µ_i+ε_{t+1}+ε_{i,t+1}} D_t
    The production function IS the heterogeneity channel: high µ_i means high output by definition. This makes y_H > y_L in Theorem 1 true but definitional.
  • domain assumption CRRA terminal utility with SDF pricing: M^i_t = E_t[π_{t,t+1} y_{i,t+1}(1-τ_t)]
    Standard asset-pricing setup inherited from Pástor and Veronesi (2020); the market price of risk and the SDF are otherwise unspecified.
  • domain assumption Portfolio rule: market clearing forces δ(γ)=1 and N^i0_t=0
    The optimal weight δ(γ) is asserted, not derived from the CRRA optimization; the market-clearing identity then sets δ=1 and zeroes the risk-free position in §2.1.
  • ad hoc to paper Technology: z_i = d_i^η, η ∈ (0,1), and data scale d_i linear in the paid cost rate
    Taken from Jones and Tonetti (2020) for z = d^η, but the 'linear relationship between data input costs and data input scale' and the type-specific rates τ_H > τ_L are asserted in the Theorem 1 proof with no mechanism.
  • domain assumption Financial friction: K_t = λ W_t with λ ≥ 1 (Moll 2014)
    The borrowing-constraint structure is imported from Moll (2014); the paper adds the Poisson-jump wealth dynamics on top.
  • ad hoc to paper Imperfect switching: low-ability firms remain data users even though V^i_t < V^s_t
    Stated in §2.2: 'the choice of agents with low data investment ability is imperfect'. This contradicts the participation rule that defines the threshold µ_k, which selects agents into the user group precisely when V^i_t > V^s_t.
  • ad hoc to paper Fixed-point regularity: ∂F(τ_k, µ_k)/∂µ_k < 1 and existence of a unique solution to µ_k = F(τ_k, µ_k)
    Needed for dµ_k/dτ_k = F_τ/(1-F_µ) > 0; ∂F/∂µ_k is a difference of normal hazard rates and can exceed 1, and neither existence nor uniqueness is shown in §2.2.
  • standard math Normal hazard-rate monotonicity: φ/S is increasing
    Used to sign ∂f(µ_k)/∂µ_k ('the inequality above holds for all cases') in the y_H > y_L step; this part of the math is correct.
invented entities (2)
  • Data investment ability µ_i
    purpose: Latent heterogeneity driver appended multiplicatively to output; all comparative statics (y, d, z, λ, utility) run through µ_i.
    No measurement, calibration, or falsifiable prediction is attached to its distribution N(0, σ²_µ). The paper's own results are monotone in µ_i essentially because µ_i was written into the production function.
  • Type-specific data cost rates τ_H and τ_L
    purpose: Deliver d_H > d_L and hence z_H > z_L in Theorem 1 by assuming higher-ability firms pay higher cost rates.
    The model's τ is a single economy-wide share of output paid to providers (all users face the same τ in the utility and consumption equations). The existence of individual rates τ_H > τ_k > τ_L is asserted in the Theorem 1 proof with no market or contract that would produce them.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Heterogeneous Agents in the Data Economy." pith.science (2026). https://pith.science/paper/VZU73XLE

@misc{pith2026250909656,
  author       = {Pith},
  title        = {Pith review of: Heterogeneous Agents in the Data Economy},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/VZU73XLE}},
  note         = {Machine review of arXiv:2509.09656}
}
read the original abstract

In this short paper, we define the investment ability of data investors in the data economy and its heterogeneity. We further construct an analytical heterogeneous agent model to demonstrate that differences in data investment ability lead to divergent economic results for data investors. The analytical results prove that: Investors with higher data investment ability can obtain greater utility through data investment, and thus have stronger incentives to invest in a larger scale of data to achieve higher productivity, technological progress, and experience lower financial frictions. We aim to propose a prerequisite theory that extends the analytical framework of the data economy from the currently prevalent representative agent model to a heterogeneous agent model.

Figures

Figures reproduced from arXiv: 2509.09656 by the authors.

Figure 1
Figure 1. Possible Solution for f(λ, t∗ ) = f(µi , t∗ ) We constructed a special case to derive the analytical solution. As shown in [PITH_FULL_IMAGE:figures/full_fig_p011_1.png] view at source ↗

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

67 extracted references · 5 linked inside Pith

  1. [1]

    The changing economics of knowledge production

    Simona Abis and Laura Veldkamp. The changing economics of knowledge production. The Review of Financial Studies, 37 0 (1): 0 89--118, 2024

    2024

  2. [2]

    The simple macroeconomics of ai

    Daron Acemoglu. The simple macroeconomics of ai. Economic Policy, 40 0 (121): 0 13--58, 2025

    2025

  3. [3]

    The race between man and machine: Implications of technology for growth, factor shares, and employment

    Daron Acemoglu and Pascual Restrepo. The race between man and machine: Implications of technology for growth, factor shares, and employment. American Economic Review, 108 0 (6): 0 1488--1542, 2018

    2018

  4. [4]

    A model of online misinformation

    Daron Acemoglu, Asuman Ozdaglar, and James Siderius. A model of online misinformation. Review of Economic Studies, 91 0 (6): 0 3117--3150, 2024

    2024

  5. [5]

    When big data enables behavioral manipulation

    Daron Acemoglu, Ali Makhdoumi, Azarakhsh Malekian, and Asuman Ozdaglar. When big data enables behavioral manipulation. American Economic Review: Insights, 7 0 (1): 0 19--38, 2025

    2025

  6. [6]

    Mean field games and applications: numerical aspects

    Yves Achdou and Mathieu Lauri \`e re. Mean field games and applications: numerical aspects. arXiv preprint arXiv:2003.04444, 2020

    arXiv 2003

  7. [7]

    Income and wealth distribution in macroeconomics: A continuous-time approach

    Yves Achdou, Jiequn Han, Jean-Michel Lasry, Pierre-Louis Lions, and Benjamin Moll. Income and wealth distribution in macroeconomics: A continuous-time approach. The Review of Economic Studies, 89 0 (1): 0 45--86, 2022

    2022

  8. [8]

    Liquidity and leverage

    Tobias Adrian and Hyun Song Shin. Liquidity and leverage. Journal of Financial Intermediation, 19 0 (3): 0 418--437, 2010

    2010

Show all 67 references
  1. [9]

    When inequality matters for macro and macro matters for inequality

    SeHyoun Ahn, Greg Kaplan, Benjamin Moll, Thomas Winberry, and Christian Wolf. When inequality matters for macro and macro matters for inequality. NBER Macroeconomics Annual, 32 0 (1): 0 1--75, 2018

    2018

  2. [10]

    Uninsured idiosyncratic risk and aggregate saving

    S Rao Aiyagari. Uninsured idiosyncratic risk and aggregate saving. The Quarterly Journal of Economics, 109 0 (3): 0 659--684, 1994

    1994

  3. [11]

    Inattentive economies

    George-Marios Angeletos and Karthik A Sastry. Inattentive economies. Journal of Political Economy, 133 0 (7): 0 2265--2319, 2025

    2025

  4. [12]

    Quantifying confidence

    George-Marios Angeletos, Fabrice Collard, and Harris Dellas. Quantifying confidence. Econometrica, 86 0 (5): 0 1689--1726, 2018

    2018

  5. [13]

    Presidential address: The economist as designer in the innovation process for socially impactful digital products

    Susan Athey. Presidential address: The economist as designer in the innovation process for socially impactful digital products. American Economic Review, 115 0 (4): 0 1059--1099, 2025

    2025

  6. [14]

    The labor market impact of digital technologies

    Sangmin Aum and Yongseok Shin. The labor market impact of digital technologies. Working Paper 33469, NBER, 2025

    2025

  7. [15]

    Inefficient automation

    Martin Beraja and Nathan Zorzi. Inefficient automation. Review of Economic Studies, 92 0 (1): 0 69--96, 2025

    2025

  8. [16]

    Automation and jobs: When technology boosts employment

    James Bessen. Automation and jobs: When technology boosts employment. Economic Policy, 34 0 (100): 0 589--626, 2019

    2019

  9. [17]

    Survey data and subjective beliefs in business cycle models

    Anmol Bhandari, Jaroslav Borovi c ka, and Paul Ho. Survey data and subjective beliefs in business cycle models. Review of Economic Studies, 92 0 (3): 0 1375--1437, 2025

    2025

  10. [18]

    Solving heterogeneous agent models with the master equation

    Adrien Bilal. Solving heterogeneous agent models with the master equation. Working Paper 31103, NBER, 2023

    2023

  11. [19]

    A macroeconomic model with a financial sector

    Markus K Brunnermeier and Yuliy Sannikov. A macroeconomic model with a financial sector. American Economic Review, 104 0 (2): 0 379--421, 2014

    2014

  12. [20]

    Generative ai at work

    Erik Brynjolfsson, Danielle Li, and Lindsey Raymond. Generative ai at work. The Quarterly Journal of Economics, 140 0 (2): 0 889--942, 2025

    2025

  13. [21]

    Data engineering for cognitive economics

    Andrew Caplin. Data engineering for cognitive economics. Journal of Economic Literature, 63 0 (1): 0 164--196, 2025

    2025

  14. [22]

    Rationally inattentive behavior: Characterizing and generalizing shannon entropy

    Andrew Caplin, Mark Dean, and John Leahy. Rationally inattentive behavior: Characterizing and generalizing shannon entropy. Journal of Political Economy, 130 0 (6): 0 1676--1715, 2022

    2022

  15. [23]

    Data union and regulation in a data economy

    Lin William Cong and Simon Mayer. Data union and regulation in a data economy. Working Paper 30881, NBER, 2023

    2023

  16. [24]

    Knowledge accumulation, privacy, and growth in a data economy

    Lin William Cong, Danxia Xie, and Longtian Zhang. Knowledge accumulation, privacy, and growth in a data economy. Management Science, 67 0 (10): 0 6480--6492, 2021

    2021

  17. [25]

    Data, intangible capital, and productivity

    Carol Corrado, Jonathan Haskel, Massimiliano Iommi, Cecilia Jona-Lasinio, and Filippo Bontadini. Data, intangible capital, and productivity. NBER Chapters, 2024

    2024

  18. [26]

    Exploring the societal and economic impacts of artificial intelligence: A scenario generation methodology

    Carlos J Costa and Joao Tiago Aparicio. Exploring the societal and economic impacts of artificial intelligence: A scenario generation methodology. arXiv preprint arXiv:2504.01992, 2025

    2025 arXiv

  19. [27]

    Socio-economic consequences of generative ai: A review of methodological approaches

    Carlos J Costa, Joao Tiago Aparicio, and Manuela Aparicio. Socio-economic consequences of generative ai: A review of methodological approaches. arXiv preprint arXiv:2411.09313, 2024

    2024 arXiv

  20. [28]

    Consumer-financed fiscal stimulus: Evidence from digital coupons in china

    Jing Ding, Lei Jiang, Lucy Msall, and Matthew J Notowidigdo. Consumer-financed fiscal stimulus: Evidence from digital coupons in china. American Economic Review: Insights, 7 0 (3): 0 411--427, 2025

    2025

  21. [29]

    Economics in the age of big data

    Liran Einav and Jonathan Levin. Economics in the age of big data. Science, 346 0 (6210), 2014

    2014

  22. [30]

    A model of the data economy

    Maryam Farboodi and Laura Veldkamp. A model of the data economy. Working Paper 28427, NBER, 2021

    2021

  23. [31]

    Big data and firm dynamics

    Maryam Farboodi, Roxana Mihet, Thomas Philippon, and Laura Veldkamp. Big data and firm dynamics. In AEA papers and proceedings, volume 109, pages 38--42, 2019

    2019

  24. [32]

    Financial frictions and the wealth distribution

    Jes \'u s Fern \'a ndez-Villaverde, Samuel Hurtado, and Galo Nuno. Financial frictions and the wealth distribution. Econometrica, 91 0 (3): 0 869--901, 2023

    2023

  25. [33]

    The dynamics of inequality

    Xavier Gabaix, Jean-Michel Lasry, Pierre-Louis Lions, and Benjamin Moll. The dynamics of inequality. Econometrica, 84 0 (6): 0 2071--2111, 2016

  26. [34]

    A quest for ai knowledge

    Joshua S Gans. A quest for ai knowledge. Working Paper 33566, NBER, 2025 a

    2025

  27. [35]

    Ai as strategist

    Joshua S Gans. Ai as strategist. Working Paper 33650, NBER, 2025 b

    2025

  28. [36]

    Big data and big cities: The promises and limitations of improved measures of urban life

    Edward L Glaeser, Scott Duke Kominers, Michael Luca, and Nikhil Naik. Big data and big cities: The promises and limitations of improved measures of urban life. Economic Inquiry, 56 0 (1): 0 114--137, 2018

    2018

  29. [37]

    Digital economics

    Avi Goldfarb and Catherine Tucker. Digital economics. Journal of Economic Literature, 57 0 (1): 0 3--43, 2019

    2019

  30. [38]

    Robots at work

    Georg Graetz and Guy Michaels. Robots at work. Review of Economics and Statistics, 100 0 (5): 0 753--768, 2018

    2018

  31. [39]

    Artificial intelligence and the labor market

    Menaka Hampole, Dimitris Papanikolaou, Lawrence DW Schmidt, and Bryan Seegmiller. Artificial intelligence and the labor market. Working Paper 33509, NBER, 2025

    2025

  32. [40]

    The use of knowledge in society fa hayek

    FA Hayek. The use of knowledge in society fa hayek. American Economic Review, 35 0 (4): 0 519--530, 1945

    1945

  33. [41]

    The rise of the machines: Automation, horizontal innovation, and income inequality

    David H \'e mous and Morten Olsen. The rise of the machines: Automation, horizontal innovation, and income inequality. American Economic Journal: Macroeconomics, 14 0 (1): 0 179--223, 2022

    2022

  34. [42]

    Analysis theory of data economy: Dataization, technological progress and dynamic general equilibrium

    Yongheng Hu. Analysis theory of data economy: Dataization, technological progress and dynamic general equilibrium. arXiv preprint arXiv:2507.13274, 2025 a

    2025 arXiv

  35. [43]

    How big data dilutes cognitive resources, interferes with rational decision-making and affects wealth distribution? arXiv preprint arXiv:2508.20435, 2025 b

    Yongheng Hu. How big data dilutes cognitive resources, interferes with rational decision-making and affects wealth distribution? arXiv preprint arXiv:2508.20435, 2025 b

    2025 arXiv

  36. [44]

    The risk-free rate in heterogeneous-agent incomplete-insurance economies

    Mark Huggett. The risk-free rate in heterogeneous-agent incomplete-insurance economies. Journal of economic Dynamics and Control, 17 0 (5-6): 0 953--969, 1993

    1993

  37. [45]

    Ai and the extended workday: Productivity, contracting efficiency, and distribution of rents

    Wei Jiang, Junyoung Park, Rachel Jiqiu Xiao, and Shen Zhang. Ai and the extended workday: Productivity, contracting efficiency, and distribution of rents. Working Paper 33536, NBER, 2025

    2025

  38. [46]

    The ai dilemma: Growth versus existential risk

    Charles I Jones. The ai dilemma: Growth versus existential risk. American Economic Review: Insights, 6 0 (4): 0 575--590, 2024

    2024

  39. [47]

    How much should we spend to reduce ai's existential risk? Working Paper 33602, NBER, 2025

    Charles I Jones. How much should we spend to reduce ai's existential risk? Working Paper 33602, NBER, 2025

    2025

  40. [48]

    Nonrivalry and the economics of data

    Charles I Jones and Christopher Tonetti. Nonrivalry and the economics of data. American Economic Review, 110 0 (9): 0 2819--2858, 2020

    2020

  41. [49]

    Monetary policy according to hank

    Greg Kaplan, Benjamin Moll, and Giovanni L Violante. Monetary policy according to hank. American Economic Review, 108 0 (3): 0 697--743, 2018

    2018

  42. [50]

    Income and wealth heterogeneity in the macroeconomy

    Per Krusell and Anthony A Smith, Jr. Income and wealth heterogeneity in the macroeconomy. Journal of Political Economy, 106 0 (5): 0 867--896, 1998

    1998

  43. [51]

    The parable of google flu: traps in big data analysis

    David Lazer, Ryan Kennedy, Gary King, and Alessandro Vespignani. The parable of google flu: traps in big data analysis. Science, 343 0 (6176): 0 1203--1205, 2014

    2014

  44. [52]

    Optimal fiscal policy with heterogeneous agents and capital: Should we increase or decrease public debt and capital taxes? Journal of Political Economy, 133 0 (7), 2025

    Fran c ois Le Grand and Xavier Ragot. Optimal fiscal policy with heterogeneous agents and capital: Should we increase or decrease public debt and capital taxes? Journal of Political Economy, 133 0 (7), 2025

    2025

  45. [53]

    On the mechanics of economic development

    Robert E Lucas Jr. On the mechanics of economic development. Journal of Monetary Economics, 22 0 (1): 0 3--42, 1988

    1988

  46. [54]

    How do your data grow? Nature, 455 0 (7209): 0 28--29, 2008

    Clifford Lynch. How do your data grow? Nature, 455 0 (7209): 0 28--29, 2008

    2008

  47. [55]

    Insider imitation

    Erik Madsen and Nikhil Vellodi. Insider imitation. Journal of Political Economy, 133 0 (2): 0 652--709, 2025

    2025

  48. [56]

    Present bias amplifies the household balance-sheet channels of macroeconomic policy

    Peter Maxted, David Laibson, and Benjamin Moll. Present bias amplifies the household balance-sheet channels of macroeconomic policy. The Quarterly Journal of Economics, 140 0 (1): 0 691--743, 2025

    2025

  49. [57]

    Productivity losses from financial frictions: Can self-financing undo capital misallocation? American Economic Review, 104 0 (10): 0 3186--3221, 2014

    Benjamin Moll. Productivity losses from financial frictions: Can self-financing undo capital misallocation? American Economic Review, 104 0 (10): 0 3186--3221, 2014

    2014

  50. [58]

    Mean field games without rational expectations

    Benjamin Moll and Lenya Ryzhik. Mean field games without rational expectations. arXiv preprint arXiv:2506.11838, 2025

    2025

  51. [59]

    Inclusive GovTech: Enhancing efficiency and equity through public service digitalization

    Manabu Nose. Inclusive GovTech: Enhancing efficiency and equity through public service digitalization. International Monetary Fund, 2023

    2023

  52. [60]

    Political cycles and stock returns

    Lubo s P \'a stor and Pietro Veronesi. Political cycles and stock returns. Journal of Political Economy, 128 0 (11): 0 4011--4045, 2020

    2020

  53. [61]

    Increasing returns and long-run growth

    Paul M Romer. Increasing returns and long-run growth. Journal of Political Economy, 94 0 (5): 0 1002--1037, 1986

    1986

  54. [62]

    Endogenous technological change

    Paul M Romer. Endogenous technological change. Journal of Political Economy, 98 0 (5, Part 2): 0 S71--S102, 1990

    1990

  55. [63]

    Long-term growth driven by a sequence of general purpose technologies

    Andreas Schaefer, Daniel Schiess, and Roger Wehrli. Long-term growth driven by a sequence of general purpose technologies. Economic Modelling, 37: 0 23--31, 2014

    2014

  56. [64]

    Technical change and the aggregate production function

    Robert M Solow. Technical change and the aggregate production function. The Review of Economics and Statistics, 39 0 (3): 0 312--320, 1957

    1957

  57. [65]

    Economic growth and capital accumulation

    Trevor Winchester Swan. Economic growth and capital accumulation. Economic Record, 32 0 (2): 0 334--361, 1956

    1956

  58. [66]

    Measuring human leadership skills with artificially intelligent agents

    Ben Weidmann, Yixian Xu, and David J Deming. Measuring human leadership skills with artificially intelligent agents. Working Paper 33662, NBER, 2025

    2025

  59. [67]

    A survey on deep learning for big data

    Qingchen Zhang, Laurence T Yang, Zhikui Chen, and Peng Li. A survey on deep learning for big data. Information Fusion, 42: 0 146--157, 2018

    2018

Pith tools

Reviewed August 4, 2026 · model on record in the stance chip above.