The Inflation of Resetting Workers

Abstract: The standard wage Phillips curve aggregates away from which workers reset wages when. I show this aggregation omits a first-order term: the covariance between workers' cost-push exposure and their reset frequency. I introduce two sufficient statistics and embed them in a multi-country HANK model calibrated to six euro-area economies. The omitted term generates 7 percent more cumulative core inflation in the baseline and 10--26 percent more when monetary policy is delayed. Two economies with identical openness can differ by 6.6 percentage-point-quarters solely from within-country composition. Targeted essentials subsidies reduce welfare loss by 32 percent relative to aggressive tightening. Out of sample, the model correctly predicts the persistence ranking across the UK, the US, and Japan.

• The paper introduces a reset-heterogeneity wedge, a key factor amplifying inflation during cost-push shocks and disproportionately affecting low-income workers.
• It employs a heterogeneous-agent New Keynesian model calibrated to euro-area data to capture cross-sectional differences in wage-setting behavior and policy delays.
• The study indicates that targeted fiscal policies and moderated monetary tightening significantly reduce inflation persistence compared to standard CPI indexation.

The Inflation of Resetting Workers: Revisiting the Wage Phillips Curve under Heterogeneity

Introduction and Conceptual Advances

This paper analyzes a fundamental aggregation error in the canonical wage Phillips curve, particularly in the context of multi-country monetary unions and large cost-push shocks concentrated on essentials. The standard wage Phillips curve, building on Erceg, Henderson, and Levin (2000), aggregates the wage-setting process and implicitly assumes either uniform consumption baskets, identical wage-reset frequencies across workers, or uniform price shocks. In practice, especially in Europe, the distribution of wage-reset frequency and cost-push exposure is highly heterogeneous. Workers most exposed to sharp inflation in essentials (e.g., food, energy) are also the ones resetting nominal wages most frequently, primarily low-income workers with short contract durations in retail, hospitality, and services.

The paper derives a heterogeneous wage Phillips curve in which each worker type targets its own experienced inflation when resetting wages. This micro-founded approach yields an additional aggregate term: the within-country covariance between a worker’s reset frequency and the inflation they experience, termed the reset-heterogeneity wedge ($\Omega_{c,t}$). This wedge is strictly positive except in knife-edge cases and becomes large during supply shocks concentrated on essentials, amplifying aggregate wage and core inflation in ways the standard representative-agent model systematically misses.

Theoretical Framework and Sufficient Statistics

The paper formalizes the new aggregation by introducing two sufficient statistics:

• Reset-Weighted Experienced Inflation (RWEI): Measures the average experienced inflation among workers actually resetting wages in a period. RWEI exceeds CPI when cost-push shocks hit items over-represented in the consumption baskets of frequent resetters.
• Marginal Wage Setter Inflation (MWSI): Builds on RWEI by incorporating sectoral propagation through the input-output structure, linking wage changes concentrated in high-propagation sectors to broader core inflation.

Significantly, both statistics are computable using only micro data: household expenditure surveys, wage-setting calendars, and input-output tables. The wedge remains shock-dependent—it is negligible for broad-based demand shocks but first-order for large cost-push shocks concentrated on necessity items.

Quantitative Model and Empirical Calibration

To quantify these transmission mechanisms, the author embeds the heterogeneous Phillips curve in a multi-country Heterogeneous-Agent New Keynesian (HANK) model, calibrated to six euro-area economies. The model captures five income quintiles to align with Eurostat Household Budget Survey data and uses detailed contract duration data to map reset frequencies. The model captures two pivotal real-world features observed during 2021–2023:

1. Asymmetric Wage Catch-up: Real-wage losses from inflation produce aggressive wage catch-up in subsequent resets, but real-wage gains do not induce symmetric pay cuts, yielding nonlinear, self-reinforcing inflation persistence.
2. Policy Inertia: Delays in monetary policy response, as experienced by the ECB, permit the wedge to accumulate, further amplifying inflation above model-predicted levels.

The quantitative results are robust. In baseline scenarios, the standard model underestimates cumulative core inflation by 7% (3.1 percentage-point-quarters), but this gap rises as high as 26% with policy delay or in economies where cross-sectional heterogeneity is steeper. Calibration checks confirm that the model, using only pre-shock observables, accurately predicts the cross-country persistence ranking of core inflation (UK > Euro Area > US > Japan) observed in the 2021–2023 shock.

Policy Implications

The presence of the wedge has three central policy implications:

1. Interest Rate Insufficiency: The cross-sectional composition of wage resetting and price exposure implies that the interest rate cannot directly offset the wedge. Divine coincidence fails: output-gap closure does not stabilize inflation when the wedge is present.
2. New OCA Criterion: The wedge creates a new optimal currency area (OCA) cost—countries with identical aggregate characteristics can differ substantially in inflation persistence solely due to within-country distributional composition. The common policy rate will over-tighten in high-wedge countries and under-tighten in low-wedge countries.
3. Policy Instruments: Targeted fiscal policies, especially essentials subsidies directed to frequent resetters, are substantially more effective at reducing welfare loss than aggressive tightening. These can directly erode the wedge and are net disinflationary at the medium-term horizon. CPI indexation, however, only covers the average and leaves the composition (wedge) channel entirely intact.

The sufficient statistic MWSI offers an operational tool: policymakers can compute it for any country and any shock composition using only pre-existing micro data, enabling direct forecasting of wedge-driven inflation persistence.

Analytical and Numerical Results

Strong numerical results underline the paper's main claims:

• The wedge accounts for 7–26% of cumulative core inflation in recent euro-area episodes, and cross-country differences in cumulative overshoots of 6.6 percentage-point-quarters exist among economies with identical aggregate openness and average wage-setting institutions.
• Aggressive monetary tightening is welfare-inferior to moderate tightening combined with targeted subsidies, with union-wide welfare loss reduced by 32% using the latter.
• Out-of-sample prediction of inflation persistence rankings is accurate, relying solely on pre-shock data for RWEI and wage-setting intervals.

Tables and policy exercises reveal that attempts to recalibrate the representative-agent model cannot address the qualitative state- and shock-dependence of the aggregation error. The wedge vanishes for uniform shocks or homogeneous baskets and frequencies; it is most prominent for large, essentials-like supply shocks.

Implications and Future Directions

The findings directly challenge the calibration and inference strategies used in macroeconomic models of inflation, as well as the current best practices in monetary union stabilization. The presence of the wedge introduces a shock-dependent amplification mechanism that is both empirically relevant and theoretically robust, especially under the nonlinear bargaining dynamics captured by the HANK model.

Practical implications include a reorientation of fiscal responses toward targeted transfer or subsidy regimes informed by the sufficient statistics outlined. The inability of CPI indexation to neutralize the wedge suggests that the most common institutional response to recent inflation episodes will be ineffective in addressing composition-driven persistence.

Theoretically, this research establishes a new empirically-grounded micro-foundation for optimal monetary and fiscal policy design in monetary unions and underlines the need for models of occupational sorting, contract evolution, and housing cost inclusion for future work.

Conclusion

By introducing and quantifying the reset-heterogeneity wedge, this paper demonstrates a critical omission in standard wage Phillips curve aggregation, with first-order quantitative and policy implications for large, compositionally-concentrated supply shocks. The paper's sufficient statistic approach offers a portable and operational tool for inflation forecasting and policy design, especially for central banks, and highlights the urgent need to integrate cross-sectional heterogeneity in both wage-setting and policy analysis for monetary unions.