In this note, we show how to estimate “underlying inflation”, the steady-state rate of price changes. According to our models, “underlying inflation” is a bit below 3%. A fall to 2% requires time, given its persistency. We also discuss the importance of the idea of “underlying inflation” for the Fed staff and the FOMC.
The definition
“Underlying inflation” (or pi* in a New Keynesian Phillips curve) is the steady-state rate of inflation, that is the rate of inflation that would be expected to eventually prevail in the absence of economic slack, supply shocks, idiosyncratic relative price changes, or other disturbances (Rudd (2020)). “Underlying inflation” is a “deep” concept that depurates not only from noise in the data (like measures of “core inflation”) but also from the cycle and other cyclical disturbances. In other words, measures of “core inflation” answer the question “what would inflation be if the data were less noisy/volatile?”; while “underlying inflation” answers the question “what would inflation be without labor market (and other) temporary factors”?
(For the record: this is why of our name!)
Why it is important
The idea of “underlying inflation” is crucial for monetary policy because it suggests to policy makers whether the central bank can hit target -on average- once “slack” is around zero. In our experience, the fact that pi* was estimated below 2% before Covid was crucial for the Fed strategy review.
The estimation
Because underlying inflation is defined in terms of a state of the economy that is unlikely to ever be exactly realized, it cannot be directly observed; rather, it must be inferred from the behavior of actual inflation, either in a univariate context or with additional reference to the behavior of inflation’s other determinants. In theory, pi* can be estimated in three ways: (i) by the use of statistical models to extract the trend of inflation, (ii) by looking at measures of inflation expectations (indeed, in a NK Phillips curve what drives inflation in the long-run are expectations), and (iii) by the general equilibrium of the economy, given the joint behavior of prices and wages.
Models of trend inflation
Trend inflation close to 3%. We have updated our collection of 11 models of trend inflation which mimic Rudd (2020). Figure 1 shows the estimated trends (the gray lines) together with the average across them (the black line). In the latest run (our nowcast of Q3 in-sample), the models revised down a bit the estimate at 2.7%, which nevertheless remains close to 3%.
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 are consistent with core PCE price inflation around 2¼-2½ percent. We have updated our nowcast of the Fed CIE (Common Inflation Expectations index), which the Fed staff uses to gauge the evolution of a large set of measures of expectations. Figure 2 shows the published Fed CIE and our updated model-based nowcast. The main takeaway is that the level of expectations is roughly consistent with periods in the past when core PCE price inflation averaged 2¼-2½ percent.
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 2023:Q2. The latest circle in the Figure shows our nowcast for 2022:Q3. 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 consider the joint behavior of wages and prices also suggest pi* is close to 3%. Figure 3 shows core PCE price inflation (QoQ, ar) together with the estimated pi* from a general equilibrium model we maintain. The model is called “OUI” because it considers the joint dynamics of Output, Unemployment, and Inflation (both prices and wages). For the nerds, the model documentation is here. According to the model, pi* is at 2.7%, with some flattening in the last quarter or so. The estimated value is roughly in line with the estimate of pi* in FRB-US.
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* is a bit below 3%. Figure 4 shows slide 18 of our Pre-FOMC meeting package, updated with today’s results. The three ways of estimating pi* seem to agree on a value a bit below 3%.
Figure 4. The three ways of estimating pi*
How persistent is pi*?
By construction/estimate, pi* is very persistent. Lowering pi* from 3% to 2% will require some quarters. Figure 5 shows the evolution of the estimates of “trend inflation” from the January 2023 FOMC. Back in January, our set of models put trend inflation at 3%. Seven months later, the models continue to suggest a similar number, although in the last couple of runs the models have revised down their estimates for the first time since Covid. Similar evidence applies to the evolution of expectations and the general equilibrium of the US economy. The takeaway is simple: pi* is persistent by definition and its estimate changes only gradually overtime. Therefore, it can return to 2% only with time, that is at least some quarters.
Figure 5. Evolution of the estimates of “trend inflation”.
Implications for the Fed staff and the FOMC
We suspect that cutting the FF rate will require pi* close to 2%. The importance for the Fed staff of “underlying inflation” can be seen in Rudd (2020) and Detmeister et al. (2014). So far, we have been quite silent about the evolution of pi* because it has been roughly stable for a year. The suspect is that it will become progressively more important once closer to target. For now, we can safely say that the behavior of the US economy is consistent with a pi* close to 3%, with some initial signs of moderation. A full reversal back to 2% requires time, and some help from expectations, the incoming data, and the labor market.