Overview

Core PCE inflation and the two never-revised indicators

Quarterly, 2012:Q1 through 2025:Q4. Core PCE inflation is year over year in percent; the GSCPI is in standard deviations from its mean; the Philadelphia Fed prices-paid index is a diffusion index (50 is neutral). Each series on its own panel and scale.

The model and its reading

One-quarter-ahead accuracy by model

Rolling pseudo-out-of-sample forecasts over the pandemic-era window, expanding estimation window; each bar is the root mean squared error in percentage points.

Multi-horizon forecasts on a common target window

Model R against the AR(1) at one through four quarters ahead. Under the real-time feasible treatment the indicators are held at their origin-date values; under the conditional treatment their realized path enters, a diagnostic a forecaster cannot implement.

Five episodes

The one-quarter record of the rolling evaluation, re-estimated at each origin, decomposed by target quarter. Its 2025 RMSE differs from that of the section below, whose model is estimated once, through 2024:Q4; both are the paper's.

2025 out of sample, estimated through 2024:Q4

Root mean squared error over the four quarters of 2025, percentage points; coefficients estimated on data through 2024:Q4 and not updated.

Coefficients across data versions

One-quarter-ahead equations for year-over-year Core PCE inflation; t-statistics in parentheses.

The real-time discipline

Granger causality

F-statistics for adding two lags of each variable to a regression of inflation on two of its own lags; a p-value below 0.05 marks a variable that Granger-causes inflation at the 5 percent level.

Asymmetric GSCPI specifications

The regimes are not identified

Out of sample, by restart convention

The quarter in progress

Forecasts with the paper's coefficients, logged as the quarters complete

Sources and method

Core PCE inflation is the year-over-year change of the Bureau of Economic Analysis Core PCE price index; the Global Supply Chain Pressure Index is the Federal Reserve Bank of New York's; the prices-paid index is the Federal Reserve Bank of Philadelphia Manufacturing Business Outlook Survey's diffusion index; the effective federal funds rate is the Federal Reserve Board's; each as published by its provider and, where the paper says so, via FRED; first releases are from the Federal Reserve Bank of Philadelphia real-time data set.

The equations forecast Core PCE inflation one quarter ahead from regressors dated at the origin, estimated by ordinary least squares on 2012:Q1 through 2025:Q4; the out-of-sample record re-estimates on an expanding window at each origin. Every number on the Overview, Estimates, Out of sample, and Regime search tabs is printed by the paper, and the Overview's chart plots the paper's data series; the paper's sections give the derivations.

The Real-time log, from each completed quarter, forecasts the following quarter with the paper's coefficients, not re-estimated, from the values of the three series as published on the run date; the target is the following quarter, and its realized value enters when the quarter completes.