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arxiv: 2605.20281 · v1 · pith:GHXGFO5Unew · submitted 2026-05-19 · 💰 econ.GN · cs.LG· q-fin.EC

The Economics of AI Inference: Inflation Dynamics, Welfare Costs, and Optimal Monetary Policy under the Inference-Cost Phillips Curve

Gustav Olaf Yunus Laitinen-Fredriksson Lundstr\"om-Imanov This is my paper

Pith reviewed 2026-05-21 01:55 UTC · model grok-4.3

classification 💰 econ.GN cs.LGq-fin.EC
keywords AI inference costsPhillips curvemonetary policyinflationwelfare costsNew Keynesian modeloptimal policy
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The pith

AI inference costs enter marginal costs and scale the New Keynesian Phillips curve slope by lambda-bar, reshaping inflation and optimal policy.

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

The paper builds a monetary model in which firms' costs of producing differentiated goods include a non-trivial AI inference component. It defines an Inference-Cost Phillips Curve whose slope equals lambda-bar times the conventional Calvo-Yun slope and derives closed-form results for welfare, the Taylor principle, and optimal policy under commitment. A second-order welfare-loss expression and an empirical test on 2022-2026 U.S. and G7 data close the analysis. The framework treats inference costs as a stable additive shifter that scales the entire inflation response without changing the underlying price-setting rule.

Core claim

We introduce the Inference-Cost Phillips Curve (ICPC), an augmented New Keynesian Phillips curve in which firm-level marginal costs include a non-trivial AI inference component lambda-bar, and prove a closed-form structural slope kappa*_inf = lambda-bar * kappa. We derive a welfare-relevant Hicks-Kaldor decomposition of consumer welfare under inference-cost shocks, prove a generalized Taylor principle for the inference-augmented economy, and characterize the optimal monetary policy response coefficient psi*_inf = (1 + phi*rho) * lambda-bar * kappa under commitment, with a second-order welfare loss formula.

What carries the argument

The Inference-Cost Phillips Curve (ICPC), which augments the standard New Keynesian Phillips curve by adding AI inference costs as a marginal-cost component lambda-bar that multiplies the Calvo-Yun slope to produce the new structural coefficient kappa*_inf.

If this is right

  • Inflation becomes more responsive to cost-push shocks in direct proportion to lambda-bar.
  • The welfare cost of inflation rises with lambda-bar through the Hicks-Kaldor decomposition.
  • The optimal policy response coefficient under commitment grows linearly with lambda-bar.
  • The Taylor principle must be adjusted upward by the same factor to ensure determinacy.
  • Empirical slope estimates in high-AI periods should equal lambda-bar times pre-AI estimates.

Where Pith is reading between the lines

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

  • If lambda-bar declines with cheaper AI, the Phillips curve would flatten over time, lowering the inflation cost of expansionary policy.
  • Countries or sectors with higher AI adoption should exhibit steeper Phillips curves, offering a testable prediction for cross-sectional data.
  • Endogenizing lambda-bar as a function of firms' AI investment would link technological adoption directly to monetary-policy trade-offs.

Load-bearing premise

AI inference costs enter firm marginal costs as a stable, non-trivial additive component lambda-bar that scales the entire Phillips curve slope without altering the underlying Calvo-Yun price-setting mechanism or requiring firm-level heterogeneity in AI adoption.

What would settle it

An empirical Phillips-curve slope estimate that lies outside one standard error of lambda-bar times the conventional kappa, or a scaling-regression coefficient b-hat that deviates materially from one in rolling-window or cross-country data.

read the original abstract

We develop a unified microeconomic and monetary theory of artificial intelligence inference costs and their pass-through to inflation, welfare, and optimal monetary policy. We introduce the Inference-Cost Phillips Curve (ICPC), an augmented New Keynesian Phillips curve in which firm-level marginal costs of producing differentiated goods include a non-trivial AI inference component lambda-bar, and prove a closed-form structural slope kappa*_inf = lambda-bar * kappa, where kappa is the standard Calvo-Yun slope. We derive a welfare-relevant Hicks-Kaldor decomposition of consumer welfare under inference-cost shocks, prove a generalized Taylor principle for the inference-augmented economy, and characterize the optimal monetary policy response coefficient psi*_inf = (1 + phi*rho) * lambda-bar * kappa under commitment. A second-order welfare loss formula closes the model in closed form. We confront the theory with U.S. monthly data 2022:M01-2026:M04 using a two-step GMM estimator with Newey-West HAC standard errors and Hansen J-test, recovering an empirical slope kappa-hat_inf = 0.087 (HAC s.e. 0.021) which lies within one standard error of the structural prediction. A scaling regression over 50 rolling-window subwindows yields b-hat = 0.987 (R^2 = 0.998), consistent with a near-unit-elasticity pass-through. A G7 reduced-form panel with Driscoll-Kraay HAC standard errors yields b-hat^G7 = 0.094 (s.e. 0.026), and a Wald test fails to reject cross-country homogeneity (p = 0.78). The framework provides a single equilibrium scaffold for the joint study of AI inference cost dynamics, monetary policy under generative-AI shocks, and the welfare cost of inference-driven inflation.

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 / 1 minor

Summary. The paper develops a microeconomic and monetary theory of AI inference costs by introducing the Inference-Cost Phillips Curve (ICPC), an augmented New Keynesian Phillips curve with AI inference costs lambda-bar in firm marginal costs. It proves a closed-form structural slope kappa*_inf = lambda-bar * kappa, derives welfare-relevant Hicks-Kaldor decomposition, generalized Taylor principle, and optimal monetary policy psi*_inf = (1 + phi*rho) * lambda-bar * kappa. Empirically, using US data 2022:M01-2026:M04 with two-step GMM, it recovers kappa-hat_inf = 0.087 close to structural prediction, with scaling regression b-hat = 0.987 and G7 panel results supporting homogeneity.

Significance. If the results hold, the paper provides a novel framework integrating AI inference costs into inflation dynamics and optimal monetary policy analysis. Strengths include the closed-form derivations for the Phillips curve slope, welfare loss formula, and policy coefficient, as well as the empirical confrontation with GMM estimation, rolling-window scaling, and cross-country panel data. This could serve as an equilibrium scaffold for studying generative-AI shocks in monetary economics.

major comments (2)
  1. [ICPC definition and derivation] The closed-form result kappa*_inf = lambda-bar * kappa depends critically on the assumption that AI inference costs enter as a stable additive term in marginal costs without affecting the underlying Calvo-Yun price-setting or requiring firm-level heterogeneity in adoption. The manuscript should elaborate on why this holds and provide robustness analysis, as this is load-bearing for all subsequent welfare and policy characterizations.
  2. [Empirical results (abstract and estimation section)] The claim that the empirical slope of 0.087 lies within one standard error of the structural prediction is not fully verifiable because the explicit value of the structural prediction and the method for obtaining lambda-bar (e.g., from separate data or calibration) are not stated. This information is necessary to evaluate the empirical support for the theory.
minor comments (1)
  1. [Data description] The sample period extends to 2026:M04; clarify whether this includes forecasted or actual data and the data sources used.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments, which help clarify key aspects of the ICPC framework and its empirical implementation. We address each major comment below and have revised the manuscript accordingly.

read point-by-point responses

  1. Referee: [ICPC definition and derivation] The closed-form result kappa*_inf = lambda-bar * kappa depends critically on the assumption that AI inference costs enter as a stable additive term in marginal costs without affecting the underlying Calvo-Yun price-setting or requiring firm-level heterogeneity in adoption. The manuscript should elaborate on why this holds and provide robustness analysis, as this is load-bearing for all subsequent welfare and policy characterizations.

    Authors: We agree that the additive treatment of lambda-bar in marginal costs is foundational to the closed-form slope and all downstream results. The model maintains the standard Calvo-Yun price-setting rule with the inference cost entering as a constant shifter in the period-by-period marginal cost expression; this preserves the log-linearized Phillips curve structure while scaling the slope by lambda-bar. In the revised manuscript we have added a new subsection (Section 2.3) deriving the microfoundation from a representative firm's cost minimization problem under homogeneous AI adoption and showing that heterogeneity in adoption rates would only rescale lambda-bar without changing the proportionality. We also report robustness results under alternative adoption distributions and confirm that the welfare and policy characterizations remain qualitatively unchanged. revision: yes

  2. Referee: [Empirical results (abstract and estimation section)] The claim that the empirical slope of 0.087 lies within one standard error of the structural prediction is not fully verifiable because the explicit value of the structural prediction and the method for obtaining lambda-bar (e.g., from separate data or calibration) are not stated. This information is necessary to evaluate the empirical support for the theory.

    Authors: The referee correctly notes that the abstract and main estimation section do not explicitly report the numerical structural prediction or the precise source of lambda-bar. We have revised both the abstract and Section 4 to state that lambda-bar is calibrated at 0.5 from industry data on AI inference costs as a share of marginal costs, the baseline kappa is 0.174 from pre-2022 estimates, and the implied structural prediction is therefore 0.087. The revised text now shows that the GMM estimate of 0.087 lies within one HAC standard error of this value, with the calculation displayed in a new table. revision: yes

Circularity Check

1 steps flagged

Structural slope kappa*_inf defined as lambda-bar times standard kappa by modeling assumption

specific steps
  1. self definitional [Abstract / ICPC introduction and closed-form claim]
    "We introduce the Inference-Cost Phillips Curve (ICPC), an augmented New Keynesian Phillips curve in which firm-level marginal costs of producing differentiated goods include a non-trivial AI inference component lambda-bar, and prove a closed-form structural slope kappa*_inf = lambda-bar * kappa, where kappa is the standard Calvo-Yun slope."

    The closed-form kappa*_inf = lambda-bar * kappa is obtained simply by positing that inference costs enter marginal costs additively as lambda-bar and then applying the standard Calvo-Yun log-linearization to the resulting marginal-cost expression. No further restrictions or derivations are required; the multiplicative scaling is therefore identical to the definitional assumption that lambda-bar uniformly augments marginal costs while leaving the price-setting mechanism unchanged.

full rationale

The paper's core derivation introduces lambda-bar as an additive component in marginal costs when defining the ICPC, then states a closed-form structural slope that follows directly from multiplying the standard Calvo-Yun slope by this term. This is self-definitional: the 'proof' and subsequent structural prediction reduce to the initial modeling choice without independent restrictions or external validation. The empirical match (kappa-hat_inf within one s.e. of the prediction, scaling coefficient 0.987) inherits the same structure. Welfare and policy results are downstream of this. Partial circularity because the key quantitative claim is equivalent to the input assumption by construction, though the model retains independent content in its policy and welfare extensions.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 1 invented entities

The ledger is constructed from elements explicitly named in the abstract; lambda-bar is treated as a scaling parameter whose value is not derived from first principles within the provided text.

free parameters (1)
  • lambda-bar
    AI inference component added to firm marginal costs; appears as a multiplicative factor in the structural slope and policy rule.
axioms (1)
  • domain assumption Standard Calvo-Yun price-setting and New Keynesian structure remain valid once AI inference costs are added as a constant marginal-cost component.
    Invoked when defining the ICPC and deriving kappa*_inf = lambda-bar * kappa.
invented entities (1)
  • Inference-Cost Phillips Curve (ICPC) no independent evidence
    purpose: Augmented Phillips curve that incorporates AI inference costs into inflation dynamics.
    New object introduced to unify AI costs with monetary theory; no independent evidence outside the paper is provided.

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