Frank Schmid · 31 October 2026 · The flow of the paper, section by section

Inflation Forecasting When the Phillips Curve Is Flat

When the Phillips curve is flat, upstream cost pressure read from indicators that are never revised forecasts Core PCE inflation. In the U.S. inflation-targeting era the output gap carries no forecasting power, while the GSCPI and the Philadelphia Fed prices-paid index improve on an autoregressive benchmark out of sample, the margin widening with the horizon under a protocol a forecaster can implement. The real-time discipline is met by first releases as well as by never-revised series, and richer parameterizations are not identified on the sample.

Real-time supply-side signal

Indicators that are never revised, read as they stood at the forecast origin, forecast Core PCE inflation. The paper fixes its reference model to such regressors and evaluates it one quarter ahead, across horizons, by episode, and on a year its coefficients did not see.

Parsimony against the flat Phillips curve

The sample identifies one symmetric supply-side loading and little beyond it: the output gap does not forecast, the funds rate adds nothing, asymmetric terms move the error by a few hundredths in either direction, the GSCPI alone is not separated from the model that adds the prices-paid index, and two regimes are not identified.

The line of sight

Two rails run down each section’s left edge, the left the first theme’s and the right the second’s. A filled mark ( ) names a section that carries the theme; a hollow mark ( ) a theme that passes through it.

1

Introduction

Real-time signalParsimony
Establishes
The hypothesis: if slack carries little information about inflation, upstream cost pressure carries more, and a forecaster can read it from indicators that are never revised. Three disciplines fix what the evaluation can show: every regressor is read as it stood at the forecast origin; the reference model uses only never-revised series; and the multi-horizon protocol states what it assumes about the indicators’ future path. Section 8 is the principal section.
Leads to
Is the Phillips curve flat on this sample, and why?
2

The Flat Phillips Curve: Motivation

Parsimony
Establishes
On 54 quarters through 2025:Q4 the output gap’s coefficient in a backward-looking Phillips curve is 0.0098, while the two lags of inflation sum to 0.928: the fit is carried by inflation persistence. The literature’s explanations are anchored expectations, globalization, the identification effect of a stabilizing central bank, and an unusual sample.
Values
0.0098
Output-gap coefficient, percentage points of inflation per point of the gap
0.928
Sum of the two inflation lags
Exhibits
Equation (1)
Leads to
Which series could a forecaster have seen at the forecast origin, and how are the others handled?
3

Real-Time Data: Methodology and Classification

Real-time signal
Establishes
Every variable is classified by revision status: six series are never revised (the federal funds rate, the GSCPI, the Philadelphia Fed prices-paid index, WTI crude, the dollar index, and the FAO food index), import prices and the PPI are lightly revised, and Core PCE, unit labor costs, and the output gap are revised. The paper estimates on three data versions: the publishers’ current files, the first release of each quarter, and never-revised regressors alone, the reference because a forecaster can use only data that exists when the forecast is made.
Exhibits
Table 1
Leads to
Which supply-side indicators lead consumer prices, and by how much?
4

Supply-Side Leading Indicators

Real-time signal
Establishes
Eight indicators of upstream cost pressure pass through the pricing chain with a lag of one to four quarters, five of them never revised. The GSCPI peaks in 2021:Q4, one quarter before Core PCE inflation peaks in 2022:Q1.
Values
4.3
GSCPI at its peak, 2021:Q4, standard deviations from its mean
5.5
Core PCE inflation at its peak, 2022:Q1, percent
Leads to
How are the candidate models specified, estimated, and selected?
5

Forecasting Models and Estimation

Real-time signalParsimony
Establishes
One-quarter-ahead equations for year-over-year Core PCE inflation on regressors dated at the origin, from the AR(1) through the model with every indicator. A forward selection by the Akaike information criterion on revised data adds the GSCPI, then the prices-paid index, and stops: on revised data it selects the two never-revised indicators of Model R. Model F, the GSCPI with unit labor costs, is kept as the comparison that carries a heavily revised regressor.
Values
−98.7
Akaike criterion, AR(1)
−125.8
Akaike criterion, Model R
Exhibits
Table 2; Equations (2) through (4)
Leads to
How do the models fit in sample across the three data versions?
6

In-Sample Results: Three Data Versions Compared

Real-time signalParsimony
Establishes
The output gap leaves the fit of the AR(1) all but unchanged and worsens the Akaike criterion, while the supply-side indicators improve both the fit and the criterion, Model R doing so from never-revised regressors alone. The GSCPI’s coefficient is distinguishable from zero in every data version; the coefficient on unit labor costs is not, in revised data or as first released, and in draws of simulated revision noise it is distinguishable from zero in a small share.
Values
0.924
R², AR(1)
0.925
R², with the output gap
0.959
R², Model R
3.1
Draws of revision noise in which unit labor costs are distinguishable from zero, percent
Exhibits
Tables 3 and 4
Leads to
Does the in-sample fit carry over to out-of-sample accuracy?
7

Out-of-Sample Forecast Evaluation

Real-time signalParsimony
Establishes
Over the 24 one-quarter targets of 2020:Q1 through 2025:Q4, Model R lowers the root mean squared error of the AR(1), and the output gap raises it. The revised-data models with the producer price index or unit labor costs forecast better still, and they still do when the revised regressor is replaced by its first release: the real-time discipline is met by first releases, not only by never-revised series. Next to the GSCPI the producer price index’s coefficient is not distinguishable from zero, and the sample does not separate the GSCPI alone (Model G) from Model R.
Values
0.556
RMSE, AR(1), percentage points
0.506
RMSE, Model R, percentage points
9.1
Improvement of Model R on the AR(1), percent
0.557
RMSE with the output gap, percentage points
Exhibits
Table 5
Leads to
Does the advantage hold, grow, or fade as the horizon lengthens?
8

Multi-Horizon Iterated Forecasts

Real-time signal
Establishes
The principal section. On a common window of 21 targets, with the GSCPI and the prices-paid index held at their values at the origin, the rule a forecaster can implement, Model R’s improvement on the AR(1) rises from one quarter to four; with the realized path of the indicators, which no forecaster has, it is larger still from two quarters on. The GSCPI alone improves by a nearly constant margin across horizons, so in the point estimates the widening is the prices-paid index’s, and at no horizon does the sample separate the two models. The AR(1) over-predicts by more as the horizon lengthens, and Model R under-predicts, the GSCPI normalizing ahead of consumer prices.
Values
13.3
Improvement at one quarter, percent
33.5
Improvement at four quarters, percent
43.0
At four quarters with the realized indicator path, percent
27.0
GSCPI alone at four quarters, percent
Exhibits
Figure 1; Table 6
Leads to
Is the horizon profile a property of the indicators or of the iteration?
9

Four-Quarter-Ahead Direct Forecasts

Real-time signal
Establishes
Estimated directly four quarters ahead, Model R lowers the in-sample error of the direct AR(1) by a margin in line with the out-of-sample improvement of the iterated protocol at four quarters: the profile belongs to the indicators.
Values
33.3
Reduction of the direct AR(1)’s error, percent
Exhibits
Table 7
Leads to
Where in the pandemic era does the advantage come from, and would richer indicator terms have helped?
10

The Pandemic and Its Aftermath: A Sub-Period Decomposition

Real-time signalParsimony
Establishes
Model R is more accurate than the AR(1) in 2022–2023, 2024, and 2025, and less accurate in 2020, a demand collapse, and in the surge of 2021, when both models under-predicted and the AR(1) by less. Asymmetric GSCPI terms move the out-of-sample error by a few hundredths in either direction, and the symmetric loading is kept.
Values
−11.3
Improvement in 2021, percent
52.7
Improvement in 2022–2023, percent
30.4
Improvement in 2025, percent
Exhibits
Figure 2; Tables 8 and 9
Leads to
What happens when the models are frozen before a year of a supply shock of a different kind?
11

2025 Genuine Out-of-Sample Validation

Real-time signal
Establishes
Estimated through 2024:Q4 and forecasting the four quarters of 2025, the year of the tariff increases, Model R records the lowest error of the models compared; the AR(1) places the year above the outcome and the revised-data models below it, and Model L, which adds the policy stance, stands between them.
Values
0.068
RMSE, Model R, 2025
0.100
RMSE, AR(1), 2025
0.111
RMSE, Model L, 2025
Exhibits
Table 10
Leads to
Can a two-regime model carry a logistics channel and an import-price channel at once?
12

Regime-Switching Models

Parsimony
Establishes
A two-regime Markov-switching model, a GSCPI regime and an import-price regime, searched from 600 random starts: the maximum of its likelihood stands on the floor set for a regime’s residual standard deviation, and the best interior optimum reverses the regime reading of the optimum an earlier version of the paper reported. The sample does not identify the regimes, and the paper reports no regime parameters. Out of sample, the model’s error moves with the convention by which its refits restart, from below the AR(1)’s to twice it.
Values
342
Distinct basins found
0.500
Lowest out-of-sample RMSE across restart conventions
1.111
Highest out-of-sample RMSE across restart conventions
Exhibits
Equations (5) and (6); Tables 11 and 12
Leads to
Do the supply-side models lose anything by omitting the federal funds rate?
13

Does the Fed’s Reaction Function Matter?

Real-time signalParsimony
Establishes
The federal funds rate does not Granger-cause Core PCE inflation, while the GSCPI and the prices-paid index do: the funds rate’s apparent content is the Federal Reserve reacting to inflation, consistent with Model L in Section 11.
Exhibits
Table 13
Leads to
What follows for policy from a model that forecasts inflation the Federal Reserve cannot control through demand?
14

Implications for Monetary Policy

Real-time signalParsimony
Establishes
Forecasting inflation and controlling it are different capabilities: under a flat Phillips curve a policymaker who sees supply-driven inflation coming holds no additional instrument for preventing it through demand. Never-revised supply-side indicators, monitored by the FOMC alongside its structural models, would let it tell supply shocks from demand shocks in real time, communications can draw on the distinction while an episode is under way, and a forecasting suite that gives Phillips-curve models less weight in supply-driven periods moves toward the accuracy documented here.
Leads to
Which findings does the paper carry forward?
15

Conclusions

Real-time signalParsimony
Establishes
Seven contributions: the Phillips curve provides no forecasting power in the inflation-targeting era; never-revised supply-side indicators forecast, at one quarter and with a margin that widens across horizons; the real-time discipline is met by first releases, not only by never-revised series; the Federal Reserve’s reaction function is not needed for forecasting; the advantage is episode-specific in an interpretable way; structure beyond a single symmetric supply-side loading is not identified on the sample; and every series is read from its publisher’s file under a stated rule.
Leads to
Appendix A: Data Sources and Provenance