The fall 2022 edition of the Brookings Papers on Economic Activity included a paper by Laurence Ball, Daniel Leigh, and Prachi Mishra titled “Understanding US inflation during the COVID era” (BPEA article here). The paper has attracted attention and does have policy implications. Please, find below our discussion of the paper.
To keep in mind
A new paper by Ball et al. (2022) has drawn attention because it contains a sharp prediction for core CPI inflation (between 3 percent and almost 9 percent in 2024 depending on the scenarios). In reality, Ball et al. (2022) results are exaggerated/biased because of some technical flaws. A more plausible forecast using similar assumptions delivers a scenario closer to the latest SEP. In any case, even in this scenario the risks around the September SEP appear to be skewed to the upside. In a nutshell: not that terrible for the Fed but still, there are no real good news around yet.
What the paper does
The authors employ a basic framework to explain core CPI inflation, measured using the weighted median inflation rate published by the Federal Reserve of Cleveland. The model explains core inflation with three variables: expected inflation, the tightness of the labor market, and past headline inflation shocks. The first two are the variables in the textbook Phillips curve, and the third is meant to capture the pass-through of headline inflation into core that may occur through wages or other costs of producing output. In the primary specification, expected inflation is measured by ten-year forecasts from the Survey of Professional Forecasters; labor-market tightness by the average ratio of job vacancies to unemployment (V/U); and past headline shocks by the average deviation of headline from median inflation over the current and previous eleven months.
Results
According to the authors, the core inflation equation estimated with pre-pandemic data provides a good fit to the path of core inflation during the pandemic. The increase in core inflation during 2021 and 2022 is explained by a combination of a rise in the V/U ratio to unprecedented levels and pass-through from adverse headline shocks, with the role of V/U increasing over the last year.
Simulations/Forecasts
Based on the chosen framework, the authors simulate the path of core CPI inflation for the next few years. Their results are shown in Figure 17 of the paper, which we report below. In details, the authors simulate the path of core inflation according to different scenarios for the Beveridge curve, and depending on whether expectations remain anchored or not.
According to the authors, the main conclusion is that while both the Beveridge curve and inflation expectations affect the inflation path, the former is more important. If the Beveridge curve shifts back to its pre-pandemic position, the December 2024 inflation rate ranges from 2.7 to 4.2 percent depending on the expectations scenario. In contrast, if the Beveridge curve does not shift back, the inflation rate always stays above 6.0 percent. With the pandemic-era Beveridge curve, an unemployment rate of 4.1 percent is not nearly high enough to reduce V/U to a non-inflationary level.
Discussion
Ball et al. (2022) is an interesting paper but suffers from limitations and the analysis raises several questions. Overall, we agree with the conclusion of the paper but the results are distorted by the limitations we discuss below.
- Ad-hoc. The econometric model used by Ball et al. (2022) is pretty much ad-hoc. Technically, the literature offers two Phillips curve specifications (anchored and unanchored), depending on the restrictions imposed. Ball et al. (2022) is neither an anchored nor an unanchored Phillips curve model. Therefore, it is hard to compare the Ball et al. (2022) results to the existing literature.
- Spurious correlation. Ball et al. (2022) regress YoY changes of core (median) CPI inflation on YoY changes of headline CPI and the level of V/U. The standard procedure is to regress QoQ (or MoM) changes, not YoY changes to avoid spurious correlations. The suspect is that at least some of the Ball et al. (2022) results would not survive such a robustness check and that the estimated persistency of core CPI is, in fact, much lower.
- Endogeneity. While Phillips curve models capture correlations, the ad-hoc specification of Ball et al. (2022) introduces an endogeneity issue because the authors put headline inflation (which is a function of core inflation) to the right-hand-side. Because most of the variation of headline inflation is driven by energy prices, an alternative exogenous (or at least less endogenous) choice would have been the use of energy prices as a right-hand-side variable.
- Forecast. Given that one of the right-hand-side variables (headline CPI) is endogenous, Ball et al. (2022) cannot produce a standard forecast because they would need the future path of headline, which cannot be constructed without the path of core itself. Therefore, the authors follow a recursive procedure that we do not describe for brevity. The puzzling part is that the authors impose the core-to-headline gap in the forecast to zero even if the crude oil futures would suggest otherwise. As mentioned above, a much easier approach would be to rely on the futures prices.
- General equilibrium. Ball et al. (2022) analysis relies on a partial-equilibrium model conditional on the path of the unemployment rate of the June 2022 SEP. The (big) issue is that the path of the FF rate in the SEP is conditional on the expected evolution of core inflation and the unemployment rate. Therefore, a partial-equilibrium forecast of 8% in 2025 is, by definition, non-credible because the path of the FF rate in that scenario would be much higher (and therefore inflation much lower). Put it differently: the Fed would step in way earlier and would make sure to rule out that scenario.
- Non-linear model. Ball et al. (2022) assume a non-linear model (cubic) in slack without justifying this assumption. While the fit of the model appears good, the out-of-sample performance is not better than a linear model (as shown in the next paragraph). Therefore, some of the claims by Ball et al. (2022) on the predictive power of the model during Covid are probably optimistic.
Our own exercise
Using our “main” Phillips curve model, we have run a set of regressions similar to Ball et al. (2022) using median CPI as left-hand-side variable. (as a reminder, our “main” Phillips curve model is an augmented anchored model). Our main findings include:
- As pointed out by Ball et al. (2022) and other studies, V/U is more correlated to core inflation than the unemployment gap. The slope of the Phillips curve is about 3 times larger using V/U rather than the unemployment gap.
- Under the assumption that V/U returns to 1 by 2024, the model expects core CPI to be 2.9 percent in 2024 and 2.3 percent in 2025 (Figure 1). In other words, the model produces a forecast broadly similar compared to the one using the unemployment gap in core PCE space (just a bit lower in 2025). (for the record, the yellow shaded areas in the chart show the confidence intervals calculated using quasi-out-of-sample techniques. The point forecast oscillates because most of the estimated autoregressive coefficients are negative).
Figure 1. Forecast of our “main” model using median CPI as left-hand-side variable
- Unsurprisingly, the non-linear (cubic) model (Figure 2) produces a lower forecast compared to the linear version. However, the confidence bands around the forecast are huge, indicating that the out-of-sample properties are far worse than the linear model. In other words, the model might have done a good job during the pandemic but on average it does not outperform the linear version.
Figure 2. Forecast of a non-linear (cubic) version of our “main” model using median CPI as left-hand-side variable
- Stopping the estimation in 2019:Q4 and conditioning the forecast on the observed path of the exogenous produces a forecast that explains about half of the observed increase in core CPI inflation. Therefore, at least half of the runup in core inflation is probably due to factors outside the labor market and might disappear in the coming months.
- Finally, we have run a regression using core PCE price inflation as a left-hand-side (and keeping V/U as a measure of slack). Results are presented in Figure 3. The takeaway is that the forecast is lower at the end of the medium-term (2.3 percent) compared to the model using the unemployment gap as a measure of slack because, as mentioned, using V/U results in steeper Phillips curve.
Figure 3. Forecast of our “main” model using core PCE as left-hand-side variable and V/U as a measure of slack
Implications for the Fed staff and conclusion
In our experience, BPEA papers are closely scrutinized by the Fed (Board) staff. Ball et al. (2022) is an interesting analysis that raises some questions. In our view and estimates, the results of Ball et al. (2022) are distorted by some technicalities. In our view, it is possible that the Fed staff has run a similar exercise and reached similar conclusions.
In any case, the main takeaway is that even in this exercise the risks around the Fed staff and the SEP forecasts are skewed to the upside. As already discussed in a previous note, we are agnostic about the slope of the Beveridge curve. But the point is that the models suggest that reaching the inflation target requires a significant fall of V/U, even assuming a steep(er) Phillips curve.
The good news is that the Fed staff and the FOMC seem well aware of these results and they are acting accordingly. Markets have finally realized it.
The situation will change, at some point. We will keep you informed as soon as our models will start sending different signals.