Pi* edged higher in Q1. Our models estimate “underlying inflation”in PCE space at 2.6% for the quarter, marking an upward revision from recent periods. A decline to 2% will take time due to the persistence of Pi*, making it unlikely to occur in 2025. Risks remain tilted to the upside unless a recession hits the economy.
We remind readers that Pi* is a key variable in the Tealbook and plays a crucial role in shaping the medium-term forecast (see details below).
The definition and why it is important
We defer the reader to Rudd (2020) for the definition and why it is important for the Fed staff.
Results
Trend inflation models
Trend inflation was revised upward in Q1. We have updated our set of 11 trend inflation models, which follow the approach of Rudd (2020).
Figure 1 illustrates the estimated trends (gray lines) along with their average (black line).
In our latest run—Q1 in-sample, assuming core PCE price inflation at 2.9% QoQ SAAR—the model indicates that trend inflation edged up to 2.55%, compared to 2.49% in the previous quarter. This upward revision reflects both new incoming data and higher inflation expectations.
An Excel contaning all numbers of Figure 1 can be downloaded here.
Figure 1. Trend inflation models
Note: the chart shows the estimated trend inflation from 11 econometric models. The models are split into three groups. The first group is a collection of Phillips-curve (PC) type of trend inflation models in which a measure of long-term inflation expectations is used as a proxy of trend inflation. The second group is a collection of state-space unobserved component models in which we have modelled trend inflation either as a smooth trend or as an augmented local level. Finally, the third group of models is a collection of Time Varying Parameters Vector AutoRegressive models (TVP-VAR) with different endogenous variables. This set of models follows the FEDS Note by Rudd (2020) “Underlying Inflation: Its Measurement and Significance”. The Fed staff assumption about the level of underlying inflation (set at 1.8 percent pre-Covid) is inferred from Laubach et al. (2014) “Long-term Inflation Expectations and Risks to the Inflation Outlook“.
Measures of Inflation Expectations
Inflation expectations in Q1 align with trend inflation at approximately 2.5%. Figure 2 presents the Fed’s published Common Inflation Expectations (CIE) index alongside our updated model-based nowcast (see this note for Q&As on the CIE).
The key takeaway is that current expectations are broadly in line with past periods when core PCE price inflation averaged around 2.5%.
Figure 2. Fed CIE: published and our nowcast
Note: the Figure shows the published Fed Common Inflation Expectations (CIE) index (the thick blue bar), and our Dynamic Factor Model (DFM) nowcasts (the black circles). Both series are displayed at quarterly frequency. The latest published quarter of the Fed-CIE is 2024:Q4. The latest circle in the Figure shows our nowcast for 2025:Q1. The dashed-blue lines are estimated confidence intervals. The Fed-CIE model is a DFM that includes 21 measures of inflation expectations. The estimated common factor is projected on a chosen measure of long-term inflation expectations (the SPF PCE 10 years). By construction, the level of the common factor cannot be interpreted because the underlying series are demeaned (in fact, normalized) at the beginning of estimation. Instead, the level of the common factor can be compared to its own history.
The general equilibrium
Models that account for the joint behavior of wages and prices suggest that Pi* is slightly below 3%. Figure 3 displays core PCE price inflation (QoQ, annualized) alongside the estimated Pi* from our general equilibrium model, “OUI.” This model incorporates the interactions between Output, Unemployment, and Inflation (both price and wage inflation).
For those interested in the details, model documentation can be found here. According to the model, Pi* remained at 2.9% in Q1, unchanged from the previous quarter.
Figure 3. Estimated pi* in “OUI” model
Note: the figure shows published core PCE price inflation (black line, QoQ ar) and the estimated pi* of our “OUI” model. “pi*” refers to “underlying inflation”.
Putting the three pieces together
Pi* at 2.6%. Figure 4 presents a slide from our Pre-FOMC meeting package, updated with the latest results. The three estimation approaches converge around a Pi* value of 2.6%.
Figure 4. The three ways of estimating pi*
Conclusion
We use Pi* to inform our medium-term forecast. Simply put, Pi* represents the expected average level of inflation over the medium term, excluding economic fluctuations and temporary shocks. Pi* is extremely persistent by nature, typically little changed from one quarter to the next (2 tenths to rounding is the maximum change we have seen quarter-to-quarter in our career).
Currently, our models suggest that core PCE price inflation could average around 2.5% going forward, while core CPI may trend closer to 3%.