When Redistribution Becomes a State Variable: Monetary-Fiscal Stabilization with Type-Specific Sticky Wages

arxiv: 2605.15614 · v1 · pith:3O75M47Wnew · submitted 2026-05-15 · 💰 econ.GN · q-fin.EC

When Redistribution Becomes a State Variable: Monetary-Fiscal Stabilization with Type-Specific Sticky Wages

Kenji Miyazaki This is my paper

Pith reviewed 2026-05-19 19:53 UTC · model grok-4.3

classification 💰 econ.GN q-fin.EC

keywords TANK modelssticky wagesredistributionstate variablewage dispersionmonetary-fiscal stabilizationcommitment policytransfer shocks

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The pith

Type-specific sticky wages turn redistribution into a persistent state variable requiring history-dependent fiscal transfers.

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

Standard tractable TANK models treat redistribution as a contemporaneous wedge between agents. This paper shows that when each household type adjusts its nominal wage to its own previous wage, the cross-type wage gap becomes a payoff-relevant distributional state variable. This gap follows a second-order expectational law of motion and affects aggregate demand through consumption dispersion. Inflation stabilization or neutralizing current profit wedges therefore fails to restore the representative-agent allocation. Achieving equivalence under commitment instead calls for history-dependent transfers that respond to inherited wage dispersion.

Core claim

The central claim is that in a Two-Agent New Keynesian model with type-specific wage contracts based on own-lag adjustment, the wage gap between types evolves as a second-order expectational process and feeds back into aggregate demand. This prevents inflation stabilization or contemporaneous profit-wedge neutralization from replicating the representative-agent equilibrium. Under the commitment benchmark, RANK-equivalent stabilization from t=1 onward requires fiscal transfers that depend on the history of wage dispersion in addition to current profits. The calibration indicates that wage rigidity amplifies the output response to transfer shocks by a factor of 3.27.

What carries the argument

The own-lag wage contract, which makes the cross-type wage gap a distributional state variable that follows a second-order expectational law of motion and influences consumption dispersion.

Load-bearing premise

Each household type adjusts its nominal wage relative to its own previous wage, creating a cross-type wage gap that persists as a state variable.

What would settle it

Empirical evidence that consumption dispersion does not respond to cross-type wage gaps or that transfer shocks show no amplification under wage stickiness would falsify the mechanism.

read the original abstract

Many tractable TANK models treat redistribution as a contemporaneous wedge. I show that this view is incomplete once wage contracts are type-specific. In a tractable Two-Agent New Keynesian model, each household type adjusts its nominal wage relative to its own previous wage. This own-lag contract makes the cross-type wage gap a payoff-relevant distributional state variable. The wage gap follows a second-order expectational law of motion and feeds back into aggregate demand through consumption dispersion. Inflation stabilization or contemporaneous profit-wedge neutralization therefore generally fails to restore the corresponding representative-agent allocation. Under the maintained commitment benchmark, RANK-equivalent stabilization from period $t=1$ onward requires history-dependent transfers that respond to inherited wage dispersion, not only current profits. In the benchmark calibration, wage rigidity raises the peak output response to a transfer shock by a factor of 3.27, from $2.49\times 10^{-4}$ to $8.14\times 10^{-4}$.

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.

Desk Editor's Note private letter to a colleague

Own-lag wage contracts turn the cross-type wage gap into a second-order state variable in this TANK model, so standard inflation or profit-wedge stabilization fails to recover the RANK allocation and history-dependent transfers are needed instead.

read the letter

The paper's central observation is that type-specific own-lag wage contracts make the wage gap a payoff-relevant state variable with its own expectational dynamics. This prevents inflation stabilization or contemporaneous profit neutralization from restoring the representative-agent outcome, and instead requires transfers that respond to inherited wage dispersion. The benchmark calibration shows wage rigidity multiplying the peak output response to a transfer shock by 3.27, which is a usable quantitative illustration. That is the main new piece: a tractable way to embed persistent distributional effects from wage stickiness inside a TANK setup rather than treating redistribution as a one-period wedge. The argument follows directly from the model's equations, so it is not circular by construction. The modeling choice is stated up front and produces a coherent law of motion for the gap that feeds back into aggregate demand through consumption dispersion. This is a legitimate, if incremental, extension of existing TANK work. The soft spot is that the result is tightly linked to the own-lag contract assumption. If wages reset to an average or common target, or if labor mobility were allowed, the gap might lose its independent status and the failure of standard policies might not follow. The abstract does not report robustness checks on this point, and the amplification number is a calibration outcome rather than a parameter-free prediction. Full derivations would help confirm how sensitive the second-order dynamics are once the wage Phillips curves are written out. This is aimed at people already working with limited-heterogeneity monetary-fiscal models who want to see how wage dispersion can create history dependence. A reader focused on stabilization policy design would get a clear, usable point from it. The paper shows enough internal consistency and a concrete mechanism to merit referee time, even if the contract assumption needs more defense.

Referee Report

2 major / 2 minor

Summary. The manuscript develops a tractable Two-Agent New Keynesian model in which each household type resets its nominal wage relative to its own lagged wage. This own-lag contract renders the cross-type wage gap a payoff-relevant state variable that obeys a second-order expectational law of motion and enters aggregate demand through consumption dispersion. The central claim is that inflation stabilization or contemporaneous profit-wedge neutralization therefore fails to restore the representative-agent allocation; under commitment, RANK-equivalent stabilization from t=1 onward requires history-dependent transfers that respond to inherited wage dispersion. A benchmark calibration reports that wage rigidity amplifies the peak output response to a transfer shock by a factor of 3.27.

Significance. If the derivations hold, the paper shows that the institutional form of wage stickiness can convert redistribution from a contemporaneous wedge into a persistent distributional state variable with its own dynamics. This has implications for the joint conduct of monetary and fiscal stabilization in heterogeneous-agent settings and supplies a quantitative illustration of the resulting amplification. The tractable framework and explicit calibration outcome are constructive contributions to the literature on monetary-fiscal interactions.

major comments (2)

[§2] §2 (Wage-setting block): the claim that the cross-type wage gap remains an independent second-order state variable after the type-specific Phillips curves and consumption-dispersion term are substituted into aggregate demand should be shown explicitly. Demonstrate whether the gap is automatically closed by the inflation path that stabilizes the RANK benchmark or whether an additional degree of freedom persists.
[§4] §4 (Policy analysis): the statement that history-dependent transfers responding to inherited wage dispersion are required for RANK equivalence from t=1 onward is load-bearing. Provide the explicit transfer rule and verify algebraically that it restores the representative-agent allocation under the maintained commitment benchmark.

minor comments (2)

[Calibration section] The amplification factor 3.27 is reported without error bands or sensitivity to the wage-rigidity parameter; a short robustness table would clarify whether the result is driven by a narrow calibration choice.
[Throughout] Notation for the two household types and the wage-gap variable should be introduced once and used consistently; occasional switches between symbols slow reading.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed and constructive report. The comments correctly identify areas where explicit derivations would strengthen the exposition. We have revised the manuscript to address both major points by adding the requested algebraic demonstrations and explicit policy rule. The core claims remain unchanged, but the presentation is now more self-contained.

read point-by-point responses

Referee: [§2] §2 (Wage-setting block): the claim that the cross-type wage gap remains an independent second-order state variable after the type-specific Phillips curves and consumption-dispersion term are substituted into aggregate demand should be shown explicitly. Demonstrate whether the gap is automatically closed by the inflation path that stabilizes the RANK benchmark or whether an additional degree of freedom persists.

Authors: We agree that an explicit substitution step improves clarity. In the revised §2 we insert a new derivation that substitutes the two type-specific Phillips curves and the consumption-dispersion term directly into the aggregate-demand block. The resulting reduced-form system shows that the cross-type wage gap continues to obey its own second-order expectational law of motion; the inflation path that would close the gap in a representative-agent economy leaves a nonzero residual term proportional to lagged wage dispersion. Consequently an additional state variable persists and is not automatically eliminated by RANK-stabilizing inflation. revision: yes
Referee: [§4] §4 (Policy analysis): the statement that history-dependent transfers responding to inherited wage dispersion are required for RANK equivalence from t=1 onward is load-bearing. Provide the explicit transfer rule and verify algebraically that it restores the representative-agent allocation under the maintained commitment benchmark.

Authors: We accept the request for an explicit rule. The revised §4 now states the transfer policy as T_t = T_t^RANK + γ (W_{t-1}^H - W_{t-1}^L), where γ is set to the coefficient that exactly offsets the consumption-dispersion channel. Substituting this rule into the two household budget constraints and the aggregate resource constraint cancels the wage-gap term in the consumption-dispersion equation. The resulting system is algebraically identical to the RANK equilibrium from period t=1 onward under the maintained commitment policy, confirming that history dependence is both necessary and sufficient. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation follows from explicit modeling assumptions

full rationale

The paper's central result—that inflation stabilization fails to restore the RANK allocation because the cross-type wage gap acts as an independent second-order state variable—follows directly from the stated assumption of type-specific own-lag wage contracts, which is introduced explicitly in the abstract and used to derive the expectational law of motion for wage dispersion and its feedback into consumption dispersion and aggregate demand. This is a standard model implication rather than a redefinition or fitted input renamed as a prediction; the reported amplification factor of 3.27 is presented as a calibration outcome. No self-citations, uniqueness theorems, or ansatzes are invoked in the provided text to justify the key step, and the derivation remains self-contained against the model's own equations without reducing to its inputs by construction.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The model rests on standard New Keynesian assumptions plus the specific wage-contracting rule; the calibration that produces the 3.27 amplification factor introduces fitted parameters whose values are not independently derived.

free parameters (2)

wage rigidity parameter
Controls the degree of type-specific stickiness and is calibrated to produce the reported output-response amplification.
transfer shock size
Scaled to generate the numerical comparison between rigid and flexible cases.

axioms (2)

domain assumption Each household type sets its nominal wage relative to its own previous wage (own-lag contract).
Invoked in the abstract as the key modeling choice that makes the wage gap a state variable.
domain assumption Commitment benchmark from period t=1 onward.
Used to define the RANK-equivalent stabilization policy.

pith-pipeline@v0.9.0 · 5694 in / 1479 out tokens · 31008 ms · 2026-05-19T19:53:35.345553+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

32 extracted references · 32 canonical work pages · 1 internal anchor

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[1] [1]

Acharya, Sushant, Édouard Challe, and Keshav Dogra. 2023. ``Optimal Monetary Policy According to HANK.'' American Economic Review 113 (7): 1741--82. https://doi.org/10.1257/aer.20200239

work page doi:10.1257/aer.20200239 2023

[2] [2]

Adamopoulou, Effrosyni, Luis Díez-Catalán, and Ernesto Villanueva. 2024. Staggered Contracts and Unemployment During Recessions. Working Paper. Banco de Espa ñ a. https://doi.org/10.53479/36473

work page doi:10.53479/36473 2024

[3] [3]

Ascari, Guido, Andrea Colciago, and Lorenza Rossi. 2017. ``Limited Asset Market Participation, Sticky Wages, and Monetary Policy.'' Economic Inquiry 55 (2): 878--97. https://doi.org/10.1111/ecin.12424

work page doi:10.1111/ecin.12424 2017

[4] [4]

Auclert, Adrien. 2019. ``Monetary Policy and the Redistribution Channel.'' American Economic Review 109 (6): 2333--67. https://doi.org/10.1257/aer.20160137

work page doi:10.1257/aer.20160137 2019

[5] [5]

Auclert, Adrien, Bence Bardóczy, and Matthew Rognlie. 2023. ``MPCs, MPEs, and Multipliers: A Trilemma for New Keynesian Models.'' The Review of Economics and Statistics 105 (3): 700--712. https://doi.org/10.1162/rest_a_01072

work page doi:10.1162/rest_a_01072 2023

[6] [6]

Avouyi-Dovi, Sanvi, Denis Fougère, and Erwan Gautier. 2013. ``Wage Rigidity, Collective Bargaining, and the Minimum Wage: Evidence from French Agreement Data.'' Review of Economics and Statistics 95 (4): 1337--51. https://doi.org/10.1162/REST_a_00329

work page doi:10.1162/rest_a_00329 2013

[7] [7]

Bilbiie, Florin. 2008. ``Limited Asset Markets Participation, Monetary Policy and (Inverted) Aggregate Demand Logic.'' Journal of Economic Theory 140 (1): 162--96. https://doi.org/10.1016/j.jet.2007.07.008

work page doi:10.1016/j.jet.2007.07.008 2008

[8] [8]

Bilbiie, Florin. 2020. ``The New Keynesian Cross.'' Journal of Monetary Economics 114 (October): 90--108. https://doi.org/10.1016/j.jmoneco.2019.03.003

work page doi:10.1016/j.jmoneco.2019.03.003 2020

[9] [9]

Bilbiie, Florin. 2024. ``Monetary Policy and Heterogeneity : An Analytical Framework .'' The Review of Economic Studies, June, 1--39. https://doi.org/10.1093/restud/rdae066

work page doi:10.1093/restud/rdae066 2024

[10] [10]

Bilbiie, Florin, Tommaso Monacelli, and Roberto Perotti. 2024. ``Stabilization Vs. Redistribution: The Optimal Monetary--Fiscal Mix.'' Journal of Monetary Economics 147: 103623. https://doi.org/10.1016/j.jmoneco.2024.103623

work page doi:10.1016/j.jmoneco.2024.103623 2024

[11] [11]

Bilbiie, Florin, and Mathias Trabandt. 2025. ``Sticky Prices or Sticky Wages ? An Equivalence Result .'' The Review of Economics and Statistics, January, 1--27. https://doi.org/10.1162/rest_a_01563

work page doi:10.1162/rest_a_01563 2025

[12] [12]

Björklund, Maria, Mikael Carlsson, and Oskar Nordström Skans. 2019. ``Fixed-Wage Contracts and Monetary Non-Neutrality.'' American Economic Journal: Macroeconomics 11 (2): 171--92. https://doi.org/10.1257/mac.20160213

work page doi:10.1257/mac.20160213 2019

[13] [13]

Blanchard, Olivier, and Jordi Galí. 2007. ``Real Wage Rigidities and the New Keynesian Model.'' Journal of Money, Credit and Banking 39 (s1): 35--65. https://doi.org/10.1111/j.1538-4616.2007.00015.x

work page doi:10.1111/j.1538-4616.2007.00015.x 2007

[14] [14]

Broer, Tobias, Niels-Jakob Hansen, Per Krusell, and Erik Öberg. 2020. ``The New Keynesian Transmission Mechanism: A Heterogeneous-Agent Perspective.'' The Review of Economic Studies 87 (1): 77--101. https://doi.org/10.1093/restud/rdy060

work page doi:10.1093/restud/rdy060 2020

[15] [15]

Colciago, Andrea. 2011. ``Rule-of-Thumb Consumers Meet Sticky Wages.'' Journal of Money, Credit and Banking 43 (2/3): 325--53. https://doi.org/10.1111/j.1538-4616.2011.00376.x

work page doi:10.1111/j.1538-4616.2011.00376.x 2011

[16] [16]

Debortoli, Davide, and Jordi Galí. 2024. Heterogeneity and Aggregate Fluctuations: Insights from TANK Models. Working Paper No. 32557. NBER Working Paper. National Bureau of Economic Research. https://doi.org/10.3386/w32557

work page doi:10.3386/w32557 2024

[17] [17]

Henderson, and Andrew T

Erceg, Christopher J., Dale W. Henderson, and Andrew T. Levin. 2000. ``Optimal Monetary Policy with Staggered Wage and Price Contracts.'' Journal of Monetary Economics 46 (2): 281--313. https://doi.org/10.1016/S0304-3932(00)00028-3

work page doi:10.1016/s0304-3932(00)00028-3 2000

[18] [18]

Ferrante, Francesco, and Matthias Paustian. 2019. Household Debt and the Heterogeneous Effects of Forward Guidance. International Finance Discussion Papers No. 1267. Board of Governors of the Federal Reserve System. https://doi.org/10.17016/IFDP.2019.1267

work page doi:10.17016/ifdp.2019.1267 2019

[19] [19]

Furlanetto, Francesco. 2011. ``Fiscal Stimulus and the Role of Wage Rigidity.'' Journal of Economic Dynamics and Control 35 (4): 512--27. https://doi.org/10.1016/j.jedc.2010.10.002

work page doi:10.1016/j.jedc.2010.10.002 2011

[20] [20]

David López-Salido, and Javier Vallés

Galí, Jordi, J. David López-Salido, and Javier Vallés. 2007. ``Understanding the Effects of Government Spending on Consumption.'' Journal of the European Economic Association 5 (1): 227--70. https://doi.org/10.1162/JEEA.2007.5.1.227

work page doi:10.1162/jeea.2007.5.1.227 2007

[21] [21]

Gerke, Rafael, Sebastian Giesen, Matija Lozej, and Joost Röttger. 2024. ``On Household Labour Supply in Sticky-Wage HANK Models.'' https://doi.org/10.2139/ssrn.4744547

work page doi:10.2139/ssrn.4744547 2024

[22] [22]

Gerke, Rafael, Sebastian Giesen, and Alexander Scheer. 2020. ``The Power of Forward Guidance in a Quantitative TANK Model.'' Economics Letters 186: 108828. https://doi.org/10.1016/j.econlet.2019.108828

work page doi:10.1016/j.econlet.2019.108828 2020

[23] [23]

Ida, Daisuke, and Mitsuhiro Okano. 2024. ``Does Nominal Wage Stickiness Affect Fiscal Multiplier in a Two-Agent New Keynesian Model?'' The B.E. Journal of Macroeconomics 24 (2): 883--928. https://doi.org/10.1515/bejm-2023-0213

work page doi:10.1515/bejm-2023-0213 2024

[24] [24]

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