Inflation’s Last Half Mile: Higher for Longer?

where ${\pi }_t$ stands for inflation at time t, a is a constant, c is a parameter value, there are n parameter values denoted by b_j, there are m parameter values denoted by d_k, ${\pi }_{t+s}^{expect}$ stands for the expectation of inflation s periods in the future, there are m driving forces of inflation, denoted by X_k,t, and there is a random shock e_t. If the sum of the b_j coefficients is large, or c is both large and ${\pi }_{t+s}^{expect}$ is typically close to last period’s inflation reading, then inflation will have a lot of intrinsic persistence. Inflation will have a lot of extrinsic persistence over a given period if one or more of the X_k,t is then experiencing a very persistent fluctuation and its corresponding coefficient d_k is large. In like manner, inflation can appear to be nonpersistent over a period of time if it is being driven during that period by a powerful nonpersistent driving force X_k,t.

This brings us to today. Many economists believe that the recent sharp increase and decrease in inflation was caused by X factors: the recent runup being caused by a sharp increase in supply constraints combined with a demand shock (Sheremirov, 2022; di Giovanni et al., 2023) and perhaps abetted by an overheated labor market, and the recent decrease largely driven by sharp improvements in supply conditions (possibly abetted by the labor market cooling that has happened so far). It is tempting to think that inflation will keep moving downward at its recent pace, but given that both the Federal Reserve Bank of New York’s global supply chain pressure index and the PPI for core intermediate goods have moved from deeply negative readings to near zero or positive readings of late, it seems likely that the downward pressure from these aforementioned sources is nearly over. Absent such exogenous favorable downward forces, inflation’s movements in the near future will be largely driven by its intrinsic persistence.

To understand inflation dynamics, it helps to use a good measure of inflation. Measuring inflation is not easy, and official measures are noisy. For the rest of this Economic Commentary, I will generally focus on trimmed-mean PCE inflation, which removes noise from headline PCE inflation (to better focus on the signal) in a statistically sound manner. Historically, it has been a more accurate indicator of the medium-term trend in inflation than has core PCE inflation (Mertens, 2016; Dolmas and Koenig, 2019; Verbrugge, 2022). For instance, when core PCE inflation and trimmed-mean PCE inflation diverge, it is core PCE inflation that adjusts to eliminate the gap (Verbrugge, 2022).

I first look at economic theory for guidance as to whether intrinsic persistence of inflation is high or low at the present moment. This theory is divided. There are two sorts of theoretical arguments suggesting that right now inflation may have low persistence. First, some theories suggest that the responsiveness of inflation to changes in labor market tightness (in other words, the Phillips curve) may be particularly strong right now; if so, continued small reductions in labor market tightness may result in large inflation decreases. Higher inflation seems to strengthen the Phillips curve (Hadjini, 2023; Dedola et al., 2023), and the Phillips curve has been found to be nonlinear in labor market tightness: inflation responds more to overheating than to slack (Filardo, 1998; Ashley and Verbrugge, 2023; Gitti, 2024), and the labor market may still be overheated today. Second, deviations of inflation expectations from the FOMC’s 2 percent target may not be persistent today or even strongly anchored at that target. Why? In many imperfect information models, inattention leads inflation expectations to be more persistent (Afrouzi, 2023; Hubert and Ricco, 2018). Further, there is more attention to inflation when inflation is high (Weber et al., 2023; Korenok et al., 2023; Braitsch and Mitchell, 2023). As such, recently higher inflation may be increasing attention to inflation, hence reducing its persistence. Relatedly, when inflation is high, more households are exposed to information on monetary policy (Knotek et al., 2024), a situation which could lead them to expect a rapid return of inflation to target.

But there are also some theoretical reasons to think that today inflation may have high intrinsic persistence. Since inflation has come down so much, attention to inflation may have already waned (Weber et al., 2023; Korenok, Munro, and Chen, 2023), and the Phillips curve may have already weakened.⁶ On the flip side of this argument, increased attention to inflation has a wide range of effects. One pertinent theoretical mechanism is that high inflation makes workers more likely to realize that their wage growth has not kept pace with inflation, and thus they are more likely to demand wage increases in response to recent inflation; this series of realization and demand can ignite wage-price spirals (Borio et al., 2023). The nonlinearity in the Phillips curve cuts both ways: since labor market tightness (measured, for instance, by the vacancy–unemployment ratio) has eased so much already, there may be little remaining benefit to further easing in the labor market. Other imperfect information models of inflation suggest that inflation is likely to be more persistent today (Pfauti, 2023).⁷ Finally, downward rigidity in prices or wages can reduce the speed at which inflation subsides. That there are competing theories indicates that theory alone does not give us a clear answer to our question.

Empirical Evidence

As noted above, inflation in 2024:Q1 picked up. Looking at the components of core PCE, over the past three months, the deceleration in housing services prices has stalled near 6 percent; core services excluding housing inflation has picked up, averaging over 5 percent; and core goods inflation, which had previously been strongly negative, has averaged +1.3 percent. Trimmed-mean PCE inflation in 2024:Q1 was 3.6 percent. What about other inflation indicators? Wage inflation has also remained well above prepandemic levels, and above levels that some economists view as consistent with 2 percent inflation. So far in 2024, according to the May 2024 report of the National Federation of Independent Businesses survey, the proportion of respondents who reported raising prices, at 24, is nearly double the rate in 2019; likewise, the proportion of respondents planning to raise prices, at 31, is 9 percentage points higher than its average in 2019.

Persistence in inflation may be time-varying, and there is some evidence suggesting that inflation may be quite persistent today. Estimated persistence in inflation has risen of late (Almazura and Sbordone, 2023; Kiley, 2023).⁸ Quantile regressions indicate that higher inflation implies higher persistence (Ghysels et al., 2018; Mitchell and Zaman, 2023). In general, higher inflation kicks off persistent effects: Blanco et al. (2022) document that, worldwide, inflation tends to stay persistently high after inflation initially surges (see also Borio et al., 2023, and Pfauti, 2023).

I turn to the VZ model to study the historical evidence. Doing so highlights episodes during which inflation’s dynamics were dominated by its intrinsic persistence, which seems to be rather high. Then, in a simple exercise, I compare the intrinsic persistence of the VZ model to that of two other models. This comparison suggests that the VZ model’s intrinsic persistence, which lies between that of the other two models, seems to be appropriate. Finally, I provide forecasts from the three models going forward.

The VZ model is a four-equation model with a nonlinear Phillips curve. Its inflation variable is trimmed-mean PCE inflation, modeled in gap form as deviations from the Survey of Professional Forecasters 10-year PCE inflation forecast. Such inflation-gap modeling follows good practice in the inflation forecasting literature (Verbrugge and Zaman, 2024) and also serves to impose anchored long-run inflation expectations (in the sense that if the model is stationary, inflation must return to its expectation). The inflation equation has three extrinsic (X) drivers: an overheated labor market driver, a recessionary labor market driver, and a supply shocks driver.⁹

The model is estimated on data from 1985–2019. Estimating the inflation equation allows me to determine the amount of “force,” by quarter, that has been exerted on trimmed-mean PCE inflation by these X drivers over the entire sample. If $X_{OLM,t-1}$ represents the overheated labor market term, and ${\hat{\beta }}_{OLM}$ is the estimated coefficient, then ${\hat{\beta }}_{OLM}{X}_{OLM,t-1}$ represents the force exerted by the overheated labor market on inflation at time t. I add up this force to the forces associated with the other two X variables, rescale the resulting time series to provide visual clarity, and then plot this series in orange in Figure 1. This represents extrinsic force on inflation.

When extrinsic force is weak or small, then inflation is mostly determined by its intrinsic dynamics. I use an ad hoc rule of thumb to classify when extrinsic force is weak: when this force is less than one standard deviation in magnitude. In yellow dashed lines, I depict the one-standard-deviation bounds of the extrinsic force series. When the orange line lies between the yellow lines, extrinsic force is weak; and when it is outside the yellow lines, extrinsic force is strong. Thus, for example, between 1987:Q4 and 1990:Q3, extrinsic drivers were applying more than a one-standard-deviation amount of upward force on inflation; similarly, between 2008:Q4 and 2010:Q3, extrinsic drivers exerted strong downward force on inflation. Notice that over the recent period (2020:Q3–2023:Q3), extrinsic force was quite strong, but also notice that in 2023:Q4, extrinsic force returned to its normal, weak levels, suggesting that going forward, inflation will be governed by its intrinsic dynamics.

Figure 1 also plots, in light gray, the four-quarter trimmed-mean PCE inflation gap. I argue above that when extrinsic force is weak, inflation’s dynamics are governed by intrinsic persistence. There are five periods during which extrinsic force was weak for more than two quarters; inflation realizations corresponding to such periods are depicted in blue. If intrinsic persistence is generally low, then we should expect the inflation gap to move quickly to zero during these periods.

So how high is intrinsic persistence? The above decomposition of history into periods when inflation is facing high extrinsic force versus low extrinsic force suggests that intrinsic persistence in inflation is rather high indeed, and, moreover, inflation seems somewhat prone to “head fakes,” times when inflation moves one way but then reverses itself. Looking at things episode by episode, from 1985:Q1 to 1987:Q3, inflation showed no signs of moving towards its long-run expectation. From 1990:Q4 to 1994:Q3, inflation moved away from its expectations, and then it moved sideways. From 1996:Q1 to 1997:Q2, there was a head fake: inflation was moving up, then dropped markedly, and then rebounded. From 2002:Q4 to 2004:Q1, inflation moved further away from its long-run expectation (this episode was part of a head fake). Finally, 2011:Q4 to 2017:Q3, inflation essentially moved sideways. And more generally, over the post-Global Financial Crisis episode, inflation experienced a head fake: inflation rose sharply between 2010:Q2 and 2012:Q1 but then fell back notably by 2013:Q2.¹⁰

All told, this exploration of the history of trimmed-mean PCE inflation suggests two things. First, historically, head fakes are not uncommon; second, again historically, intrinsic persistence appears to be very high.

Evidence from Comparing Forecasting Models

What do forecasting models tell us about the risks that inflation may remain higher for longer? Forecasting models differ on whether they condition upon or abstract from X factors. Each forecasting model has a different implied or inherent level of persistence of inflation that may be too high or too low. A model that abstracts from X factors will implicitly assume that the average historical persistence of the X-factor influence on inflation is actually part of inflation’s inherent persistence.

In this section, I look at some representative historical forecasts from three different models over recent history (2010–2019). The purpose of this comparison is not to provide a general test of these models’ forecasting ability, since standard forecast comparison tests of these models over various time periods are provided elsewhere (see, for example, Verbrugge and Zaman, 2023). Instead, these forecasts are intended to demonstrate visually each model’s implied level of intrinsic persistence in inflation, something which can help inform judgments about inflation prospects going forward.

The first two models are both univariate models that are considered in the forecast literature to be hard to beat: the Stock and Watson (2007) UCSV model and the Faust and Wright (2013) model (the FW model). The third model is the aforementioned VZ model.¹¹

I provide illustrative forecasts from each of the three models at two different points in this period: 2010:Q3 and 2013:Q1.¹² According to the VZ model decomposition above, at both points (and throughout their forecasts), X forces played little role, so at these points one can compare how each model matches the intrinsic persistence of inflation. As will be seen, using just two forecast points suffices to demonstrate the general behavior, and inherent persistence, of the three models. Figure 2 depicts the inflation realization in black. As can be seen, the UCSV forecasts, in gray, are flat, that is, close to simple random walk forecasts; this model features very high persistence that results in a very poor forecast in 2010:Q3 and a passable forecast in 2013:Q1. The FW model, in yellow, has much less persistence and projects very rapid returns to near 2 percent. In 2010:Q3, the FW forecast initially looks great—until inflation sinks back to 1.5 percent starting in early 2012. This forecast, in other words, completely misses the head fake. The 2013:Q1 FW forecast also returns to target too quickly. In short, the FW model seems to have too little persistence over this period. In contrast, the VZ model, in orange, does fairly well in capturing the dynamics of inflation at both forecast points, including not being fooled by the head fake. The tentative conclusion I draw from this exercise is that the UCSV model may have too much intrinsic persistence, the FW model seems to have too little intrinsic persistence, and the VZ model appears to have about the right amount of intrinsic persistence.

In Figure 3, I provide forecasts from these three models. Each model conditions on the 2024:Q1 inflation readings; for instance, four-quarter trimmed-mean PCE inflation was then at 3.1 percent. The VZ model conditions on the May Blue Chip Economic Indicators unemployment rate forecast, which projects that unemployment will converge to its long-run forecast by the end of 2024. In keeping with this, as noted above, the VZ model decomposition suggests that extrinsic force on inflation is fairly weak at present, so inflation may be governed by its intrinsic persistence. (As a reminder, neither the FW nor the UCSV model distinguishes between extrinsic and intrinsic persistence.)

As one would expect from Figure 2, the FW model predicts a fairly rapid decline in trimmed-mean PCE inflation, such that it sees inflation at 2.1 percent by 2025:Q2. This forecast is similar to the Blue Chip PCE inflation forecast; but recall that the FW model may have too little persistence. The UCSV model sees inflation picking up to a 3.6 percent pace, and then moving sideways; but recall that this model may have too much persistence. Finally, the VZ model predicts that inflation remains near its current level of 3.1 percent in 2024:Q2, followed by gradual deceleration in prices. In 2025:Q2, when the FW model sees inflation at 2.1 percent, the VZ model conversely sees inflation at 2.7 percent. And according to this model, inflation does not fall to near to 2 percent until mid-2027. Taken together, these model-based forecasts indicate notable upside risk to forecasts that see inflation back to 2 percent by spring of next year.

Conclusion

Inflation fell rapidly last year, and many forecasters expect it to return to the FOMC’s 2 percent longer run target by spring of next year. But, as explained above, the Verbrugge and Zaman (2023) model suggests that this conclusion may be premature. There are both theoretical and empirical reasons to think that, absent X factors such as continued favorable supply shocks or strong productivity gains, the last half-mile could well take several years.