In a new NBER working paper Schmitt-Grohé and Uribe (2022) estimate to what extent the recent spike in U.S. inflation is driven by a change in its permanent component (the “trend”). We review the paper and compare its results to our updated set of trend inflation models.
Keep in mind
Schmitt-Grohé and Uribe (2022) broadly confirm the evidence of our set of models: research suggests that trend inflation is around 3 percent. This evidence represents a sizeable upside risk around the Fed staff (and SEP) medium-term forecast.
What the paper does
Using a semi-structural unobserved component model of output, inflation, and short-term interest rates, Schmitt-Grohé and Uribe (2022) estimate the persistent component of inflation (a.k.a. the “trend”). The annual sample starts in 1900 and ends in 2021. Identification relies on classical assumptions: (i) the level of real output and the level of the nominal interest rate are assumed to be cointegrated with a nonstationary natural rate shock, and (ii) the price level and the level of the nominal interest rate are cointegrated with a nonstationary inflation-target shock. Estimation is done using Kalman filter techniques. The inflation trend is defined as the first difference of the nonstationary inflation-target shock.
Results
When the model is estimated over the period 1900 to 2021 it predicts a modest increase in the permanent component of inflation of 51 basis points between 2019 and 2021. By contrast, when the model is run on postwar data (1955 to 2021), the permanent component of inflation is predicted to have increased by 238 basis points between 2019 and 2021.
Figure 1 and 2 of the paper, reported below, show the results of the models on the 1990-2021 and 1955-2021 samples.
What explains the difference between the two estimates?
Seen from the perspective of a model estimated on postwar data, the 2021 inflation spur is interpreted to be caused by a large increase in the permanent component of inflation. The reason is that the model is given little chance to conclude otherwise; indeed, the only other major prior inflation increase during this sample period (the 60-70s episode) turned out to be a protracted one, which naturally is ascribed to the permanent component. However, once the sample is expanded to include the sudden, large, and short-lived swings in inflation observed in the first half of the 20th century, the same model attributes a major fraction of the post COVID-19 inflation to its transitory component.
Note: the figures show Schmitt-Grohé and Uribe (2022) results over the 1900-2021 sample (left panel) and over the 1955-2021 sample (right sample). The red dashed line shows headline CPI inflation at annual frequency. The blue line shows the estimated permanent component of inflation (the “trend”).
How does Schmitt-Grohé and Uribe (2022) compare to our set of 11 trend models?
We have updated our 11 trend-inflation models through 2022:Q3 to reflect our nowcast for core PCE price inflation, as well as incoming data on long-term inflation expectations, the unemployment rate and other supply-side relevant variables. (for the record: our set of models mimics the Fed staff models of trend inflation as described in Rudd (2020)).
The inclusion of Q3 in the sample resulted in a marginally higher average across models (see figure and table below). According to our set of models, trend inflation is estimated at 2¾ percent in Q3. Most models are unrevised in Q3 as both long-term inflation expectations and actual observed inflation have remained broadly stable in the current quarter.
Figure 1
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) is inferred from Laubach et al. (2014) “Long-term Inflation Expectations and Risks to the Inflation Outlook“.
Table 1
Note: the 70% confidence intervals refer to 2022:Q3. The “Average” line is calculated as a simple mean across all models.
Comment
Schmitt-Grohé and Uribe (2022) is an interesting statistical exercise. Nonetheless, in our view the paper suffers from some limitations, including the use of annual data (2022 is not included in the sample) and the fact that the model suffers from well -known end-of-sample issues. In our experience, the inclusion of additional data (years) in the model of Schmitt-Grohé and Uribe (2022) might result in large revisions of the trend not only in 2021 but in the entire recent history. Therefore, the results of Schmitt-Grohé and Uribe (2022) should be interpreted with caution. Having said so, the interesting part is that the average of the two estimates in Schmitt-Grohé and Uribe (2022) is roughly in line with our own estimate. As presented above, our set of models (which is less prone to the end-of-sample issue) indicates that trend inflation has risen significantly since 2019 (by about 1 percentage point, from 1.8 percent to 2.7 percent).
(Note: a separate but complementary analysis by Dallas Fed economists Xiaoqing Zhou and Jim Dolmas released yesterday has shown that CPI rents and OER inflation is expected to remain elevated for at least one other year. This evidence broadly confirms the results of the trend inflation models).
Implications for the Fed staff
The average across models is one of the three ways the Fed staff uses to estimate pi* (the other two are long-term inflation expectations and the general equilibrium approach which considers the interaction between pi* and U*). As a reminder: the level and evolution of pi* is the crucial assumption in the Fed staff framework/forecast and it is possibly the single most important variable for monetary policy. According to the FOMC minutes, in our view the Fed staff is currently assuming pi* just above 2%. As such, the evidence from the trend models continues to signal significant upside risks to the medium-term Fed staff forecast.