John Roberts (Former Fed Board officer) posted a blog post on labor market conditions and the implications for the Phillips curve. Roberts’ analysis is particular relevant after Powell’s words of yesterday.
In this note we summarize Roberts’ post and, based on his analysis, we use our Phillips curve models to forecast core PCE price inflation consistent with Roberts’ results.
To keep in mind
Recent literature (Roberts (2022) and Domash and Summers (2022)) has shown that some measures of slack underestimates current labor market tightness. After correcting the unemployment gap as suggested by the literature, our models show that the forecast for core PCE price inflation is not materially different neither using a higher U* nor using job openings (per unemployed) as a measure of slack. The reason is either because the Phillips curve is quite flat or because it is hard to forecast additional upper pressure from the labor market when using openings because the initial (current) level is very elevated. Rather, assuming either a non-linear effect of slack (possibly coming from high wage growth) or adaptive expectations results in a significantly higher forecast. Therefore, this environment seems to require a touch more judgment than usual when forecasting consumers inflation and a close monitor of wage growth and agents’ expectations.
What Roberts does
Roberts’ analysis uses labor-market search theory to map the high level of job openings into more-familiar unemployment rate terms (indeed, in a standard search model labor-market slack is best measured by the ratio of job openings to unemployment). Roberts uses this idea to estimate of how much extra pressure on inflation may be coming from the unusually high level of job openings and shows how that translates into unemployment terms.
Without entering into the details of the algebra behind Roberts’ approach, the intuition is the following: regress vacancies on the unemployment gap and a time trend. Then, use the estimated elasticity to back out the level of unemployment gap (or alternatively the level of U* given the current unemployment rate) consistent with the current level of vacancies.
Another way of explaining what Roberts does is to look at the figure below which plots the job openings per unemployed vs the unemployment gap (a quasi-Beveridge curve). The yellow squares show the period January 2010 – March 2020, while the blue triangles show the period April 2020 to present. The red dotted line is the quadratic fit of the pre-Covid period. The intuition behind Roberts’ analysis is that because openings are now higher for any given level of the unemployment gap, using the latter as a measure of slack is at risk of underestimating the current state of the labor market. Therefore, conditional on the job openings being a more realistic measure of slack, the unemployment gap needs to be corrected downwardly to reflect the “true” state of the economy.
Figure 1. Job openings per unemployed vs Unemployment gap (%)
Note: the scatter plot shows job openings per unemployed (x-axis) vs the unemployment gap (y-axis). Yellow squares show the Jan 2010 – Mar 2020 period. Blue triangles show Apr 2020 to present period. The dashed red line shows the quadratic fit of the yellow squares. The green dot shows the unemployment gap level consistent with the current level of job openings, net of time fixed effects.
Results
According to Roberts’ estimates, the extra tightness from high openings is equivalent of about 1¼ percentage points on the unemployment gap. Given the current estimate of the unemployment gap (-0.65% using CBO natural rate of unemployment), Roberts’ results imply that the unemployment gap consistent with the current job openings is about -2% (the green dot in the chart above) or alternatively that U* is about 5½ percent. Roberts conclude that the implied difference is substantial and can help explain the high wage and price inflation in recent months.
Note: Roberts’ results are roughly in line with a recent NBER paper by Domash and Summers (How Tight are U.S. Labor Markets?). According to Domash and Summers, the current vacancy and quit rates correspond to a degree of labor market tightness previously associated with sub-2 percent unemployment rates (that is, keeping U* fixed, it implies that the “consistent” unemployment rate is about 1¾ percent lower than the current level – or alternatively that U* is about 5¾ percent). VoxEu has published a column on Domash and Summers (2022) here.
Our own exercise based on Roberts’ estimates
Based on Roberts (2022) and Domash and Summers (2022) results, we have run our main Phillips curve model (which mimics Detmeister et al. (2014)) to generate alternative forecasts scenarios. Specifically, we have run one baseline scenario (which is identical to our latest update), and four alternative scenarios. As a reminder, our “main” Phillips curve model assumes the unemployment gap as a measure of labor market slack (using CBO estimates of U*), it is linear in slack, and it assumes that long-term term inflation expectations are anchored and stable (flat). For comparative purposes, in the four alternative scenarios we change one assumption at the time. Specifically, the four scenarios assume: (A) a 1.5 percent higher natural rate of unemployment from 2020:Q1, (B) job openings per unemployed as a measure of slack, (C) a non-linear (cubic) slack, and (D) a model with adaptive expectations in which long-term inflation expectations evolve according to recent realized inflation. Our results are reported in the table below.
Table 1. Core PCE price inflation forecast (YoY, %) under different scenarios
Note: the table shows core PCE price inflation forecasts (YoY at quarterly frequency, %) generated by our “main” Phillips curve model. “Baseline” refers to the latest update. In Scenario A we assume a higher U* (1.5 percent higher from 2020:Q1). In Scenario B we use job openings per unemployed as a measure of slack. In Scenario C we assume that slack is non-linear (cubic). Finally, in Scenario D, we assume that long-term inflation expectations evolve according to recent (5 year average) realized inflation.
As previously communicated, our main model currently delivers a forecast of 4.1 percent (Q4/Q4) in 2022, 3.2 percent in 2023, and 3.0 percent in 2024. The model forecast for 2022 is identical to the March SEP projection. The forecasts under scenarios A and B are similar to the baseline, while the forecast under scenarios C and D are significantly higher.
What explains the difference across scenarios?
Scenario A: The forecast assuming a higher U* is only marginally higher than the baseline because the Phillips curve is rather flat. The model estimates that a 1 percentage point increase in the unemployment gap translates into about 12-13bps in core PCE price inflation after 4 quarters. Therefore, assuming a 1.5 percent larger unemployment gap translates into a 2 tenth (to rounding) higher forecast at the end of the medium-term.
Scenario B: The forecast using job openings (per unemployed) as a measure of slack is very similar to the baseline because openings are already very elevated and we do not forecast an additional acceleration going forward. Therefore, compared to the baseline, in scenario B there is less acceleration on consumers’ prices going forward, although the projection is higher in 2022 and 2023 because of the initial (elevated) level of openings.
Scenario C: The forecast under scenario C is higher than the baseline because of the non-linear (cubic) term in slack (that can be interpreted as a way to account for the elevated wage growth oterwise not captured by the model). The model estimates that a 1 percent of unemployment gap results in about 30bps of additional upward pressure on core prices compared to the linear case (the baseline). Therefore, because in the baseline the unemployment gap is about -1.5% at the end of the forecast horizon, under scenario C the forecast is ½ percentage point higher compared to the baseline in 2024.
Scenario D: The forecast under scenario D is constructed assuming adaptive expectations as opposed to a flat underlying trend. Under scenario D, the model remains “anchored” but the anchor (that is long-term inflation expectations) evolves over time following realized inflation. The idea is that it takes time for agents to realize that the inflation regime has changed and to reset their expectations. Under scenario D, we assume that long-term inflation expectations reflect actual inflation of the last 5 years; therefore, at the end of the projection horizon underlying inflation ends up well above the Fed target. Under scenario D, core PCE price inflation is forecasted at 4.3 percent in 2022, 3.7 percent in 2023, and 3.6 percent in 2024.
Needless to say, combining more scenarios in a single scenario result in a higher forecast. For instance, a model that features a higher U* with adaptive expectations (scenario A + scenario D) produces a forecast of about 4 percent by the end of the medium-term.
Finally, while under all scenario inflation remains elevated throughout the entire medium-term, the model predictions should be probably seen as an upper bound estimate because the information set of the econometrician is larger than the model (that is, the model does not know anything about the narrative of the incoming data and does not expect any moderation from durable goods while in fact it might happen, at least at some point).
Conclusion
Recent literature (Roberts (2022) and Domash and Summers (2022)) has shown that some measures of slack underestimates current labor market tightness. After correcting the unemployment gap as suggested by the literature, our models show that the forecast for core PCE price inflation is not materially different neither using a higher U* nor using job openings (per unemployed) as a measure of slack. The reason is either because the Phillips curve is quite flat or because it is hard to forecast additional upper pressure from the labor market when using openings precisely because the initial point is already very elevated. Rather, assuming either a non-linear effect of slack or adaptive expectations results in a significantly higher forecast.
We conclude by saying that while labor market dynamics are always crucial, the models suggest that price inflation can remain above 3 percent either if the Phillips curve is steeper than in the baseline (possible in the current environment) or if agents will reset their long-term expectations in the next 2-3 years (also possible given the elevated readings). Therefore, this environment seems to require a touch more judgment than usual when forecasting consumers inflation and a close monitor of wage growth and agents’ expectations.