Understanding U.S. Inflation During the COVID Era (BPEA Conference Drafts, September 8-9, 2022)

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A BPEA conference draft, Understanding U.S. Inflation During the COVID Era, by Laurence Ball, Daniel Leigh and Prachi Mishra, dated August 2022 for the conference of September 8-9, 2022. The abstract states that the paper analyzes the rise in U.S. inflation since 2020, decomposing it into a rise in core inflation and deviations of headline inflation from core, and explains core with the ratio of job vacancies to unemployment and pass-through from past headline shocks. It states that CPI inflation over the previous 12 months was 8.5 percent as of July 2022. It also states that the authors simulate future inflation paths, focusing on Federal Reserve policymakers' projection that unemployment rises only slightly to 4.1 percent.

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BPEA Conference Drafts, September 8-9, 2022



Understanding U.S. Inflation During the COVID Era
Laurence Ball, Johns Hopkins University
Daniel Leigh, International Monetary Fund
Prachi Mishra, International Monetary Fund
Conflict of Interest Disclosure: Daniel Leigh and Prachi Mishra are employees of the International Monetary Fund,
which conducts a review of all externally published pieces. The authors did not receive financial support from any firm
or person for this article or from any firm or person with a financial or political interest in this article. The authors are
not currently an officer, director, or board member of any organization with a financial or political interest in this article.
                        Understanding U.S. Inflation During the COVID Era


                            Laurence Ball, Daniel Leigh, and Prachi Mishra *

                                       Conference Draft, August 2022


This paper analyzes the dramatic rise in U.S. inflation since 2020, which we decompose into a rise
in core inflation as measured by the weighted median inflation rate and deviations of headline
inflation from core. We explain the rise in core with two factors, the tightening of the labor market
as captured by the ratio of job vacancies to unemployment, and the pass-through into core from
past shocks to headline inflation. The headline shocks themselves are explained by large increases
in energy and automobile prices and by supply chain problems as captured by backlogs of orders
for goods and services. Looking forward, we simulate the future path of inflation for alternative
paths of the unemployment rate, focusing on the projections of Federal Reserve policymakers in
which unemployment rises only slightly to 4.1 percent. We find that this unemployment path
returns inflation to near the Fed’s target only under optimistic assumptions about both inflation
expectations and the Beveridge curve relating the unemployment and vacancy rates. Under less
benign assumptions about these factors, the inflation rate remains well above target unless
unemployment rises by more than the Fed projects.




*
  Email: lball@jhu.edu; dleigh@imf.org; pmishra@imf.org. Ball is at Johns Hopkins University. Leigh and Mishra
are at the Research Department of the IMF. We are grateful to Philip Barrett, Nigel Chalk, Jason Furman, Pierre-
Olivier Gourinchas, N. Gregory Mankiw, Aysegul Sahin, Antonio Spilimbergo, and James Stock for comments on
an earlier draft. We thank Regis Barnichon for providing us with data; Mattia Coppo, Yiyang Han, Nino Kodua, and
Kyung Woong Koh for excellent research support; and Eduard Laurito and Gabi Ionescu for administrative support.
All errors remaining are our own. The views expressed here are those of the authors and do not necessarily represent
those of the IMF, its Management and Executive Board, or IMF policy.
   After four decades of low U.S. inflation, high inflation has emerged as a central economic
problem of the COVID era. As of July 2022, the rate of CPI inflation over the previous 12 months
was 8.5 percent. This experience has produced an outpouring of analyses of why inflation has risen
and where it might be heading in the future. This paper seeks to contribute to this debate.
   A central feature of our analysis is that we decompose the headline inflation rate into two
components that are determined by different factors: core inflation, and deviations of headline
from core. We seek to explain core inflation with long-term expected inflation and the level of
slack or tightness in the labor market, and to explain the non-core component of headline inflation
with large price changes in particular industries. We also study the pass-through over time from
these industry price shocks to core inflation, which can occur through the effects of headline
inflation on wages and other costs of production.
   Section 1 of this paper describes how we measure core inflation. Our primary measure is the
weighted median inflation rate published by the Federal Reserve of Cleveland, which strips out
the effects of unusually large price changes in certain industries. This variable isolates the core
component of inflation more effectively than the traditional core measure of inflation excluding
food and energy prices, especially during the COVID era, when much volatility in headline
inflation has come from price changes in industries other than food and energy. In July 2022,
weighted median inflation accounted for 6.3 percentage points of the 8.5 headline inflation rate.
   Section 2 studies the behavior of core inflation. A key feature of the analysis is that, following
recent studies such as Furman and Powell (2021) and Barnichon, Oliveira, and Shapiro (2021), we
measure the tightness of the labor market with the ratio of job vacancies (V) to unemployment (U).
We find that the very high levels of V/U over 2021-2022 can explain much of the rise in monthly
core inflation, especially during 2022. The rest of the rise is explained by a substantial pass-through
of headline-inflation shocks into core inflation.
   These results help us understand why persistently high inflation has been a surprise to the many
economists—including us (Ball and others, 2021a)—who dismissed the run-up in inflation in mid-
2021 as transitory. These economists typically measured labor market tightness with the
unemployment rate, which has so far only fallen to but not below pre-pandemic levels, and they
ignored the pass-through effect that can propagate the effects of headline-inflation shocks.
   Section 3 studies the pandemic-era shocks to headline inflation—the deviations of headline
from core—that have contributed to inflation both directly and through the pass-through to core.


                                                    1
We find that three factors have been most important in explaining this component of inflation:
changes in energy prices; changes in prices in auto-related industries; and a measure of backlogs
of goods and services orders from the information services firm IHS Markit Economics, which we
believe captures the widely-reported problems with supply chains.
   Section 3 also performs a decomposition of the 7.2 percentage point rise in headline inflation
between end-2020 and July 2022 (from 1.3 percent to 8.5 percent). It concludes that the
combination of direct and pass-through effects from headline-inflation shocks accounts for about
5.5 percentage points of the rise in 12-month inflation. A rise in expected inflation accounts for
0.5 percentage point, and the rise in labor market tightness (measured by the ratio of vacancies to
unemployment) accounts for 1.0 percentage point.
   After analyzing the inflation experience to date, we turn to what might happen in the future.
We focus on the question of what costs must be incurred for the Federal Reserve to meet its goal
of reining in inflation. Fed officials have predicted a soft landing in which inflation returns to their
target with only a small increase in unemployment, while pessimists such as Summers (2022b)
believe that disinflation will require a painful recession with high unemployment. Which outcome
is more likely?
   In our view, the answer depends largely on two factors, which we discuss in Section 4. One is
the relationship between unemployment and vacancies—the Beveridge curve. This relationship
has shifted unfavorably during the pandemic: a given level of vacancies implies a higher level of
unemployment. The unemployment costs of reducing inflation will be substantial if this
relationship now remains unchanged, but the costs will be lower if a normalization of the labor
market moves the Beveridge curve back toward its pre-pandemic position.
   The second factor concerns long-term inflation expectations. By various measures, these
expectations have been well-anchored through most of the pandemic period, but they have shown
hints of increasing during 2022. The costs of containing inflation will be greater if these hints turn
into a significant upward trend in expected inflation. It is difficult to predict how expectations will
evolve, but we try to shed light on the possibilities by estimating the response of survey measures
of expectations to movements in actual inflation.
   Section 5 presents simulations of future inflation under alternative assumptions about these
issues and about the path that the unemployment rate will follow. One unemployment path that
we consider is the one forecast by Fed policymakers in their June 2022 Summary of Economic


                                                   2
Projections (SEP), which peaks at 4.1 percent in 2024. In this case, if we make quite optimistic
assumptions about both the Beveridge curve and inflation expectations, the inflation rate falls to a
level near the Fed’s target by the end of 2024. For a range of other assumptions, however, inflation
stays well above the target. All in all, it seems likely that policymakers will need to push
unemployment higher than these SEP projections if they are determined to meet their inflation
goal.
      Research over the last two years has yielded many insights into the factors behind inflation, and
we borrow a number of these ideas, as we discuss throughout the paper. We seek to synthesize
much of the recent thinking about inflation in a way that allows a transparent analysis of the data,
a quantification of the impact of different factors, and an informed analysis of where inflation may
head in the future.


1. HEADLINE AND CORE INFLATION


      Our framework for studying inflation is based on a common decomposition:
(1)       headline inflation = core inflation + headline shocks .
Core inflation is also known as underlying inflation. We interpret this variable as a relatively slow-
moving component of inflation that depends on inflation expectations and slack in the aggregate
labor market, as in the textbook Phillips curve. Headline shocks—the deviations from core—are
high-frequency movements arising from large price changes in particular sectors of the economy.
Fluctuations in energy prices are a perennial source of headline shocks. During the pandemic, large
price changes have also occurred in industries affected by shutdowns and supply disruptions, such
as travel-related industries and used cars.
      Here we describe how we measure core inflation and then examine the paths of headline and
core inflation since 2020.


A. Measuring Core Inflation
      The traditional measure of core inflation, the one that the Federal Reserve focuses on, is the
inflation rate excluding food and energy prices (XFE inflation). This measure is so common that
some economists use the term “core inflation” as a synonym for XFE inflation. However, a
growing body of research argues that XFE inflation is a flawed measure of the economic concept


                                                    3
of core. The XFE measure was developed in the 1970s, when changes in food and energy prices
caused large fluctuations in headline inflation (Gordon, 1975). Since that time, volatility in
headline has also arisen from large price swings in industries besides food and energy, which are
not filtered out of XFE inflation, and this phenomenon has been especially pronounced during the
pandemic (Dolmas, 2005; Ball and others, 2021b).
    The shortcomings of the XFE core measure have led researchers to develop a class of
alternatives: “outlier exclusion” measures that systematically filter out large price changes in any
industry. These measures are weighted medians or trimmed means of the distribution of industry
price changes. A number of studies find that these core measures are less volatile and more closely
related to economic slack than XFE inflation (for example, Dolmas and Koenig, 2019; Verbrugge,
2021; and Ball and others, 2021b). 1
    This paper focuses on one specific outlier-exclusion measure of core, the weighted median CPI
inflation rate published by the Federal Reserve Bank of Cleveland. It is the oldest such measure,
published since the 1990s, and arguably the simplest. The Appendix to this paper considers other
outlier-exclusion core measures, such as the trimmed mean PCE deflator inflation rate published
by the Federal Reserve Bank of Dallas, and the weighted median PCE deflator published by the
Federal Reserve Bank of Cleveland.
    With core inflation measured by weighted median inflation, we define “headline-inflation
shocks” as deviations of headline from median. By construction, our measures of core inflation
and headline shocks sum to headline inflation.
    Bryan and Cecchetti (1994) discuss the rationale for outlier-exclusion measures of core. In their
framework, a large change in a sector’s relative price affects the aggregate price level because,
with costs of nominal price adjustment, large shocks to optimal prices have disproportionately
large effects on actual price changes. Removing outliers from the price distribution filters out the
effects of relative price changes, thereby isolating the part of inflation determined by
macroeconomic forces. See Ball and Mazumder (2011) for more on these ideas.
    The theory of core inflation has not been perfected, and more research is warranted. That said,
in judging core inflation measures for present purposes, we believe that the proof of the pudding
is in the eating. Throughout this paper, we find that our decomposition of headline inflation into


1
 Similar evidence led the Bank of Canada to adopt a weighted median and trimmed mean as official measures of
core inflation in 2016, replacing its CPIX measure, which is similar to XFE.

                                                       4
median and deviations from median is a fruitful framework for understanding COVID-era
inflation. We also show that much of our analysis would be infeasible if we measured core with
XFE inflation. 2


B. Headline and Core Inflation Since 2020
    We focus here on inflation in the consumer price index (CPI); the Appendix considers the
personal consumption expenditure (PCE) deflator. Figure 1 shows the paths of headline and
median CPI inflation from January 2020 through July 2022 (the latest data available as this paper
is written). The graph on the left shows monthly inflation at seasonally adjusted annualized rates,
and the graph on the right shows inflation over the past 12 months, a statistic that is widely reported
in the media.
    We can see from the Figure that monthly headline inflation has been highly volatile, plunging
close to -10 percent in April 2020, fluctuating up and down for the rest of that year, and coming in
at 10 percent or higher at a number of points in 2021 and 2022. Monthly headline inflation soared
to 17.1 percent in June 2022 and then fell to -0.2 percent in July. The preponderance of high
monthly readings since early 2021 pushed 12-month headline inflation up steadily to a peak (so
far) of 9.1 percent in June 2022, and it was 8.5 percent in July.
    Median inflation has been much less volatile, with the monthly series never changing by more
than 3 percentage points from one month to the next. Median inflation drifted down in the first
part of the pandemic, and as late as September 2021 the 12-month median was still below its level
in January 2020. This experience, and the common view that non-core inflation movements are
transitory, helps explain the insouciance about inflation among many economists when a handful
such as Blanchard (2021) and Summers (2021) were first sounding an alarm. Since the middle of
2021, however, high monthly rates have led the 12-month median to follow headline inflation
upward, although it was still well below headline at 6.3 percent in July 2022.
    The following sections of the paper seek to explain this experience.




2
  Some economists criticize the weighted median on the grounds that the median industry is often related to housing,
either rents or one of the four regional price indexes for owner-equivalent rent. In our sample, the fraction of months
with such an industry as median is about one quarter. It is not clear why it should matter which industry is the
median or how much that varies. Nonetheless, as a robustness check, we have constructed a series for median
inflation for all industries excluding housing, and its path is quite similar to that of the Cleveland Fed median.

                                                           5
2. EXPLAINING CORE INFLATION


    Our basic framework 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 captures the pass-through of headline inflation into core
that may occur through wages or other costs of producing output, channels emphasized by
economists such as Blanchard (2022) and di Giovanni and others (2022). In our 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)
over the current and previous eleven months; and past headline shocks by the average deviation of
headline from median inflation over the current and previous eleven months. 3
    Our findings include the following:
•   A 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.
•   There is some evidence of non-linearity in the effect of V/U on core inflation, with a large
    positive marginal effect when V/U is either above or below its usual range. There is also strong
    evidence of asymmetry in the pass-through effects of headline shocks, which we find are
    negligible for shocks that reduce headline inflation but strong for shocks that increase headline
    inflation.
•   We can estimate the contribution of the American Recovery Act (the “Biden stimulus”) to core
    inflation using estimates from Barnichon, Oliveira, and Shapiro (2021) of the ARP’s effects
    on V/U. For July 2022, we find an effect on annualized monthly inflation of 2.8 percentage
    points. The effect on 12-month inflation is 1.0 percentage point and rising.
•   We find that both V/U and past headline shocks have strong effects on nominal wage growth.
    These results confirm the common view that labor-market tightness and headline shocks
    transmit into core inflation through wage adjustment.


3
  The use of a 12-month moving average to measure labor market conditions is consistent with the approach of other
studies such as Hazell and others (2022). We report results based on contemporaneous rather than 12-month labor-
market conditions in the Appendix.

                                                        6
A. The Role of Expected Inflation
    A central tenet of mainstream macroeconomics is that the inflation rate depends strongly on
expected inflation. Following studies such as Hazell and others (2022) and our own past work, we
measure expected inflation with the median ten-year-ahead CPI inflation forecast from the Survey
of Professional Forecasters (SPF). The Appendix considers another common measure, the five-
year forecast from the Michigan survey of consumers.
     For the period since 2000, Figure 2 shows the path of the SPF expected inflation measure
along with median inflation at the quarterly frequency. 4 We see that expected inflation has been
stable. During 2000-2019 expected inflation averaged 2.36 percent, never deviating by more than
0.3 percentage points from this level. Economists have interpreted this level of CPI inflation as
consistent with the Fed’s 2 percent target for PCE deflator inflation, given the systematic tendency
of CPI inflation to exceed PCE inflation by several tenths of a point (the average gap is 0.3
percentage points during 2009-2019 as reported on the Federal Reserve Bank of Atlanta
Underlying Inflation Dashboard). These data support the common view that expected inflation has
been well-anchored over the past two decades (Yellen, 2019).
    That said, there has been some increase in expected inflation during the pandemic, from 2.2
percent in 2019Q4 to 2.8 percent in 2022Q3 (released in August). This rise presumably reflects
the high realizations of actual inflation during this period. A vital question, which we discuss in
Section 4, is whether expected inflation will de-anchor to a larger degree in the future.
    In our econometric work, we assume that core inflation responds one-for-one to movements in
long-run expected inflation. 5 The dependent variable in our equations is the difference between
core inflation and expected inflation, which we call the “core inflation gap.” We seek to explain
this variable with labor market tightness and pass-through from headline inflation shocks.


B. The Effects of Labor-Market Tightness, as Measured by V/U
    Economists have long sought to explain short-run movements in the inflation rate with the level
of tightness or slack in the labor market. Since Phillips (1958), the standard measure of labor-

4
  Quarterly median inflation is constructed by aggregating monthly medians as described in Ball and Mazumder
(2011).
5
  A Phillips curve specification where changes in long-run inflation expectations affect current inflation one-for-one
is derived by Hazell and others (2022) in a New Keynesian framework under the assumption that shocks to the
natural rate of unemployment and cost-push shocks are transitory. The authors show that under such conditions,
long-run inflation expectations enter the Phillips curve with a coefficient of one.

                                                          7
market tightness has been the unemployment rate. To be sure, economists have developed more
sophisticated measures that account for job vacancies and factors such as the search intensity of
job seekers and firms (Abraham, Haltiwanger, and Rendell, 2020) and hours of work of the
employed (Faberman and others, 2020). But up until the pandemic, the unemployment rate
remained the most common measure of labor market tightness, in part because of its simplicity.
   An important development in the last two years is that a number of inflation researchers,
including Furman and Powell (2021), Barnichon and Shapiro (2022), and Domash and Summers
(2022), have adopted the ratio of job vacancies to unemployment (V/U) rather than the
unemployment rate as a simple measure of labor market tightness. This has been possible because
of the data on vacancies collected since 2001 in the Bureau of Labor Statistics’ Job Openings and
Labor Turnover Survey (JOLTS), and Barnichon’s (2010) extension of this data back to the 1950s
using the help-wanted index from the Conference Board. We follow this approach.
   The V/U ratio has strong theoretical appeal as a measure of wage pressures that feed into price
inflation: V/U determines the threat points of the workers and firms that bargain over wages in
search models (Mortensen and Pissarides, 1999). In addition, there is some evidence from the pre-
pandemic era that V/U out-performs the unemployment rate in explaining both wage and price
inflation, although the difference is not crystal clear because the two series are highly correlated
(see the studies cited above and the Appendix).
   For the pandemic period, it is easier to distinguish the roles of unemployment and V/U because
the two tightness measures have behaved differently. Over the first half of 2022, the
unemployment rate averaged 3.7 percent, which is slightly above its January 2020 level (3.5) and
not far below the Congressional Budget Office’s estimate of the natural rate of unemployment
(4.4), so by that measure the labor market has not been especially tight. In contrast, the average
V/U ratio for the same period was 1.88, the highest it has been since 1951 when the Barnichon
data begin. The recent levels of V/U imply a very tight labor market and potentially help explain
the rise in inflation. (The divergence of the two tightness measures reflects a shift in the Beveridge
curve relating unemployment and vacancies, which we analyze in Section 4.)
   Comparing V/U and the Inflation Gap: We examine the relation between the inflation gap
(median inflation minus expected inflation) and V/U in data back to 1968, when the Cleveland Fed




                                                  8
median series begins. 6 We examine both quarterly and monthly data, and compare the current level
of the inflation gap to an average of V/U over the current and previous three quarters or the current
and previous 11 months. We use these averages as a parsimonious way of capturing the lags in the
effects of labor market tightness that previous research typically finds. (As a robustness check, the
Appendix considers the relation between the inflation gap and the current level of V/U alone).
    Figure 3 shows quarterly and monthly scatter plots of the inflation gap against the averages of
V/U. We use different colors for the observations in four parts of the sample: 1968-1972; 1973-
1984, the period of high inflation and then disinflation ushered in by the first oil shock; 1985-2019,
a long period of low inflation that includes both the Great Moderation of 1985-2007 and the
subsequent Great Recession and recovery; and the COVID era of 2020-2022 (through 2022 Q2 or
July). 7
    Notice first that the 1973-1984 period jumps out as one with unusually high inflation gaps and
a steep relation between the gap and V/U. This anomalous behavior likely reflects the pre-Volcker
monetary regime of large inflation shocks, accommodative policy, and unanchored expectations.
The fluctuations in inflation are also magnified by the treatment of housing in the CPI before 1982,
which distorts inflation measurement relative to current practice when interest rates are volatile
(Bolhuis, Cramer, and Summers, 2022). In any case, we do not analyze this period further in this
paper.
    Starting in 1985, the data appear consistent with an upward-sloping relation between the
inflation gap and V/U that is fairly stable. The observations for late 2021 and 2022 appear in the
upper right of the graphs, with significantly higher gaps and a tighter labor market than at any
previous time since 1985. The recent levels of the inflation gap appear roughly consistent with the
unusually high levels of V/U and the pre-pandemic relation between the two variables.
    The recent observations are also fairly consistent with those from the late 1960s, a period of
overheating represented by the grey squares in the far right of the graphs. That was the last period


6
  Some data details: We splice the Cleveland Fed’s old and new series for the median following Ball and Mazumder
(2011). For expected inflation, we extend the SPF series back to 1982 by using data from Consensus Forecasts, as
suggested in the Philadelphia Fed’s documentation of the SPF data. For expected inflation before 1982, we use a
series on long-term expectations for PCE deflator inflation from the FRB/US data base. Following a rule of thumb
suggested in the documentation for that series, we add 0.4 points to convert to expectations of CPI inflation. When
we examine monthly data, we use expected inflation for a quarter to measure expectations in the middle month of
the quarter, when SPF forecasts are released, and linearly interpolate between those months.
7
  The observation for V in July 2022 is not available as this is written. For now, we estimate it by assuming that the
vacancy rate (defined as vacancies / labor force) is the same in July as in June.

                                                          9
with levels of V/U comparable to 2021-2022, and the inflation gap reached similar levels. We
believe this fact is noteworthy, although the econometric work in this paper will use only data
starting in 1985 to address concerns that the structure of the economy was very different in the
1960s.
   To aid in interpreting the scatter plots, Figure 4 shows the results of fitting flexible curves to
the data for 1985-2022. We consider a cubic function of V/U and a Lowess estimator with a
bandwith of 0.8, which produce similar results. The data suggest a fairly flat relation for mid-range
levels of V/U and a steeper relation on either side: V/U has a larger marginal effect on core inflation
when its level is unusually high or unusually low. The levels of the inflation gap are somewhat
above the fitted curves in late 2021, but the most recent observations are close to the curves.
   The Importance of Core Measurement: One thing that distinguishes this paper from most
inflation research is that we measure core inflation with the weighted median inflation rate. We
can now see some evidence that this choice is important. Figure 5 repeats Figure 2, the scatterplots
of the inflation gap against V/U, but with core inflation measured in the traditional way with
inflation excluding food and energy prices (XFE inflation). We see that the relation becomes
noisier before the pandemic, and that during the pandemic XFE inflation fluctuates erratically with
no clear relation to movements in V/U. These patterns reflect the noise in XFE inflation arising
from large price changes in industries other than food and energy.


C. Pass-Through from Headline-Inflation Shocks
   Many studies of core inflation, whether measured by the weighted median or by XFE inflation,
seek to explain its behavior with expected inflation and slack and assume implicitly that the
evolution of core is unrelated to the deviations of headline from core (for example, Ball and others,
2021a). Policymakers sometimes suggest that headline shocks can be ignored in analyzing and
forecasting core inflation. However, some strands of the literature call this view into question,
arguing that shocks to headline inflation can eventually be passed through into core.
   One possible mechanism, stressed by researchers such as Blanchard (2022), is wage
adjustment: increases in the cost of living as measured by headline inflation influence wage
demands throughout the economy and thereby contribute to core inflation. Blanchard suggests that
this effect may be especially strong for large movements in inflation, which are salient to wage
setters. Another pass-through channel arises because the goods and services whose price changes


                                                  10
contribute to headline shocks are inputs into the production of other goods, so the price changes
affect costs of production. Research at the European Central Bank, such as ECB (2014), stresses
this effect in analyzing the transmission of oil-price shocks into inflation.
   We explore the effects of headline shocks as captured by the average of headline minus core
inflation over the same four-quarter or 12-month period over which we measure V/U in the
analysis above. This approach is consistent with ECB work on oil shocks, which finds that they
transmit into inflation slowly. In the Appendix we experiment with headline shocks averaged over
shorter periods and find that they do not explain core inflation as well.
   Pass-through effects are potentially important in the pandemic era because headline shocks
have been large. The 12-month average of these shocks has risen as high as 3.7 percentage points,
far higher than at any point since the 1970s, and it was 2.3 percentage points in July 2022.


D. An Equation for Core Inflation
   For the rest of this paper, we seek to explain the core inflation gap (median minus expected
inflation) with four-quarter or 12-month averages of V/U and headline shocks. We denote the
headline-shock variable by H. There are reasons to think that the effects of V/U and H may be
non-linear. For example, Blanchard (2022) emphasizes the salience of large shocks; Ball and
Mankiw (1994) find that shocks have asymmetric effects in the presence of menu costs and trend
inflation; and Owyang and Vermann (2014) find asymmetric passthrough effects from crude oil
to retail fuel prices (“rockets and feathers”). Therefore, we allow for nonlinearities in a flexible
way, by including cubic functions of V/U and H in the core inflation equation. Despite our non-
traditional measure of labor-market tightness, we call this relation the Phillips curve.
   Estimates Table 1 presents estimates of our Phillips curve. We report results for both quarterly
and monthly data, which are similar. The data start in 1985, which is approximately the beginning
of the “Great Moderation” period of low macroeconomic volatility (Bernanke, 2004). We present
estimates for the pre-pandemic period of 1985-2019 and also for that period extended to the present
(2022 Q2 or July). We do not present results for the pandemic period alone, which would mean
estimating seven parameters with ten quarters of data.




                                                  11
    For both samples, the squared and cubic terms are statistically significant for both V/U and H:
the data indicate non-linearity in the effects of these variables. 8 To aid in interpreting the results,
Figure 6 shows the shapes of the estimated cubic functions for monthly data from 1985 to the
present, with 95 percent confidence intervals. We show the functions over the ranges of V/U and
H in the data. Panel A shows the fitted values of the inflation gap as a function of V/U with the
headline-shock variable set to zero, which reveals a shape similar to that of the bivariate relation
between the inflation gap and V/U in Figure 4. Panel B shows the effect of H for a given V/U,
which proves to be strikingly asymmetric: Negative values of H, that is, headline inflation rates
below median inflation, have negligible effects on core inflation, but positive values of H raise
core inflation. At H = 2.3 percent, the level in July 2022, the contribution of H to core inflation is
1.0 percentage points (s.e. = 0.13).
    Explaining Core Inflation During the Pandemic Do the variables in our inflation equation
explain core inflation during the pandemic? To address this question, we compare actual and fitted
values of the monthly core inflation gap from 2020 to the present in Figure 7. Panel A presents
results based on the full sample from 1985 to the present and Panel B based on the pre-pandemic
period from 1985 through 2019. In both cases, the fitted and actual values are close to each other.
Note that Panel B is an out-of-sample forecast; the good fit in this case means that we can explain
the pandemic experience based on the paths of V/U and H and the estimated effects of these
variables in the pre-pandemic period.
    Figure 7 also shows the fitted values for the core inflation gap with the actual path of V/U but
with the headline-shock variable H set to zero. We interpret these paths as showing the contribution
of labor market tightness to the rise in the inflation gap during the pandemic. In both panels, this
contribution is small until late 2021, but then it rises and accounts most of the inflation gap at the
end of the sample. The rest is explained by the pass-through effect, which is captured by the
difference between the fitted values with the actual path of H and with H = 0.
    Core Inflation Measurement, Again Once again, our choice of a core inflation measure is
critical for our results. The Appendix reports a version of the regressions in Table 1 with core
inflation measured by XFE inflation. In this case, headline shocks are the deviations of headline



8
 In one case, monthly data for 1985-2019, the joint significance of the (V/U) squared and (V/U) cubed terms is
borderline (p = 0.053). These terms are strongly significant in quarterly data for the same period (p = 0.012) and in
both quarterly and monthly data through 2022 (p < 0.01).

                                                          12
inflation from XFE inflation, which are determined by changes in the relative price of food and
energy. In this case, we find almost no evidence of a pass-through from past headline shocks into
core inflation, a result that we attribute to the flawed measure of core.


E. The Role of the American Rescue Plan
   Many economists and politicians blame the American Rescue Plan passed in March 2021—the
$1.9 trillion Biden stimulus plan with enhanced unemployment benefits and stimulus checks—for
the overheating of the economy and rise in inflation. Our framework suggests there was some such
effect: to the extent the policy stimulated demand, it presumably reduced unemployment and
increased vacancies, and the higher V/U ratio raised inflation. Here we seek to quantify this effect.
   We do not estimate the effects of the ARP on the labor market; rather, we take estimates from
a previous study by Barnichon, Oliveira, and Shapiro (2021) and then derive the implied effects
on inflation. The Barnichon study is useful for our purpose because it directly estimates the effects
of the ARP on the V/U ratio. It uses the Ramey and Zubairy (2018) methodology for estimating
the effects of fiscal policy based on identifying changes in government spending related to wars
or geopolitical events. A caveat is that the effects on V/U are uncertain because pandemic-era
lockdowns could have reduced the response of consumption to changes in government spending
(Congressional Budget Office, 2020). Barnichon, Oliveira, and Shapiro conclude that the ARP
increased V/U by approximately 0.6 at the end of 2021 and 0.5 at the end of 2022. We obtain a
monthly path for the effects by linearly interpolating between these values. Figure 8 shows the
actual path of V/U over 2020-2022 and the path when we subtract the effects of the stimulus.
   Using these results, we compare the actual path of core inflation to the path in the counterfactual
without the ARP. The counterfactual path is computed by subtracting the effect of the V/U
difference in the two cases, which we compute from the relation between V/U and the inflation
gap shown in Figure 6; we assume that expected inflation is unaffected so the effect on core
inflation equals the effect on the gap. We find that the difference between the two inflation paths
was small in 2021 but has risen in 2022. In July 2022, monthly core (median CPI) inflation is 2.8
percentage points lower in the counterfactual (3.7 percent rather than 6.5 percent) and 12-month
core inflation is 1.0 percentage point lower (5.3 percent rather than 6.3 percent). This difference
amounts to about one-quarter of the rise in 12-month core inflation from end-2020 to July 2022



                                                  13
and about one-seventh of the rise in 12-month headline inflation. The effect on 12-month inflation
has grown over time with sizable effects on monthly inflation.
    A caveat: we have assumed that labor-market tightness is the only channel through which the
ARP has affected inflation. Summers (2022a) suggests that the overheating of the economy arising
from the ARP has helped cause supply chain problems, which in our framework can contribute to
the headline-shock component of inflation. To the extent that such effects are present, our estimate
of the ARP’s effects on inflation should be interpreted as a lower bound.


F. Wage Inflation
    In arguing that labor market tightness and past headline shocks affect price inflation, many
researchers suggest that the channels are through wages: wage inflation responds to V/U and H,
and wage inflation increases firms’ costs and therefore passes into price inflation. We examine
these ideas with data on wage inflation as measured by the growth rate of the employment cost
index (ECI), a quarterly measure commonly used in previous work.
    Figure 9 shows a scatter plot of the wage-inflation gap—wage inflation minus expected
inflation—against the four-quarter average of V/U for the period 1968-2022Q2. We see an
upward-sloping relationship, albeit one that is somewhat noisy. The relationship appears consistent
across time (here, the 1970s do not jump out as unusual). 9
    To examine wage behavior more carefully, we estimate versions of the Phillips curves in Table
1 with the wage inflation gap rather than median price inflation on the left side. We again include
cubic functions of V/U and H, and following previous work on wage inflation we add a measure
of trend productivity growth (output per hour in the non-farm business sector smoothed with the
Hodrick-Prescott filter with λ = 16,000). We present the estimated equations in the Appendix and
focus here on the effects of V/U and H as captured in graphs.
    For 1985-2022, Figure 10 shows the wage inflation gap as a function of V/U (with H set to zero
and trend productivity set to its sample mean), and the effect of H, with 95 percent confidence
intervals. For reference, we super-impose the relations between median price inflation and the two
variables (estimated here with quarterly data). We find that the effects of V/U and H on wage




9
  We leave out one big outlier: 1972Q1, with an annualized wage increase of 13.2 percent. This increase may reflect
the end of the Nixon wage and price freeze.

                                                        14
inflation are broadly similar to their effects on price inflation, consistent with the common view
of transmission from wages to prices.
   In contrast to our results for price inflation, the estimated effect of V/U on wage inflation is
approximately linear. We are not sure whether this result reflects a meaningful difference between
price and wage behavior, or simply the difficulty of detecting non-linearities with noisy wage data.


3. EXPLAINING HEADLINE INFLATION


   We now examine the behavior of headline inflation, the variable that the public cares about.
We first examine the causes of headline-inflation shocks during the pandemic, and find important
roles for three variables: changes in energy prices; changes in auto-related prices; and backlogs of
orders for goods and services. We then combine these results with those of the previous section to
decompose the pandemic-era rise in inflation into the various factors that have influenced core
inflation and headline shocks. Finally, we ask why many economists have been so surprised by
the rise in inflation. Unanticipated shocks to the economy have played a role, but so have flaws in
our pre-pandemic understanding of inflation drivers.


A. Explaining Headline Shocks
   Here we seek to explain the monthly deviations of headline from core inflation, which affect
inflation both directly and through their pass-through to core. These deviations arise from shocks
that cause large price changes in certain sectors of the economy and thereby push the mean of the
price change distribution (headline inflation) away from the median. These shocks can be shifts in
either industry supply (such as disruptions in the supply of oil) or industry demand (such as the
fall in demand for many services at the onset of the pandemic). Unlike many studies of inflation,
we do not try to estimate the relative importance of supply and demand shocks.
   Large shocks occur in different sectors of the economy at different times. (That is why our core
inflation measure filters out all large price changes rather than excluding a fixed set of industries.)
We seek to identify the sources of headline-inflation shocks during the pandemic era—the red part
of the inflation decomposition in the first Figure of this paper.
   We explore the possible roles of many variables that are cited in discussions of pandemic-era
inflation. These variables include price changes in certain sectors of the economy, such as food


                                                  15
and energy. They also include variables that have affected multiple sectors, such as measures of
the severity of COVID lockdowns and disruptions in production and distribution in the economy.
Table 2 presents simple regressions of headline-inflation shocks on each of these variables and
multiple regressions on the variables that seem most important.
     In the simple regressions, the variables with the most explanatory power are (with adjusted R-
squared statistics in parentheses): energy-price shocks, measured as energy price inflation minus
median inflation (0.619); the IHS Markit Economics index of firms’ backlogs of goods and
services orders, which we interpret as a measure of supply chain disruptions (0.421); the share of
goods in aggregate consumption, which captures the shift away from services during lockdowns
(0.206); and auto-price shocks, measured as a weighted average of auto-related inflation rates (new
and used cars, car rentals, and car insurance) minus median inflation (0.178).
     In multiple regressions, we find high explanatory power from a combination of three variables:
energy-price shocks, backlogs of work, and auto-price shocks. A regression of headline shocks on
these variables has an adjusted R-squared of 0.911. When all three are included, the goods share
is not significant.
     Figure 10 shows the actual and fitted values of headline shocks with the three key variables in
the regression, along with the paths of the three variables. All three help explain the downward
spike in headline inflation at the start of the pandemic, and they explain different parts of the
subsequent high-inflation experience. For example, auto-related prices are important for the
inflation run-up in summer 2021, the height of the chip shortage that impeded auto production.
Both energy prices and backlogs help explain the ten-percentage-point headline shock in March
2022. Energy prices explain the positive headline shock in June 2022 and the negative shock in
July.
     In sum, we find that headline-inflation shocks during the pandemic are well-explained by some
of the factors stressed in popular discussions of inflation. 10


B. Accounting for the Rise in Inflation
     Having analyzed both core inflation and deviations from core, we can do an accounting of the
sources of the overall rise in inflation. We compare the 12-month headline inflation rate in July


10
   The energy-price and auto-price variables also help explain headline shocks before the pandemic, but backlogs do
not. Food-price inflation is significant before the pandemic but not during the pandemic (see Appendix).

                                                        16
2022, 8.5 percent, to the rate of 1.3 percent in December 2020, when the early-pandemic slump
had pushed inflation down. We account for the 7.2 point difference between these two inflation
rates. Over the same period, 12-month core (median) inflation has increased 3.9 percentage points
(from 2.3 percent to 6.3 percent, with rounding).
     In this exercise, we use the core inflation equation (column (4) of Table 1) to determine the
contributions to the rise in inflation of higher expected inflation, higher levels of V/U, and the
pass-through variable H. We then use our preferred equation for headline shocks (column (3) of
Table 2B) to determine the shares of H to attribute to energy-price shocks, backlogs, and auto-
price shocks. We use the same equation to account for the rise in the headline-shock part of
headline inflation. For each of the three contributors to headline shocks, we derive a total effect on
the rise in headline inflation by summing the direct effect and the contribution to pass-through. 11
     Figure 12 shows the results. The combination of direct and pass-through effects of headline-
inflation shocks accounts for about 5.5 percentage points of the 7.2 point rise in 12-month inflation.
Most of this 5.5 total reflects energy-price shocks and backlogs of work, with total contributions
of 3.3 and 2.0 percentage points, respectively. For each of these factors, roughly two thirds of the
contribution is the effect on current headline inflation and one third is the pass-through into core.
There is also a significant pass-through from past auto-price shocks, reflecting the run-up in auto
prices in Summer 2021, but the direct effect on headline inflation has turned negative as these
price increases have been partly reversed. A rise in expected inflation accounts for 0.5 percentage
point.
     The contribution of V/U to the rise in 12-month inflation is relatively small at 1.0 percentage
point. However, as discussed above, the effect of V/U is rising over time. If we decompose the
change in annualized one-month core inflation from December 2020 to July 2022 (a rise of 4.5
percentage points, from 1.9 percent to 6.5 percent), the contribution of V/U is [3.5] percentage
points.

11
  The details of our calculations are the following: 1. For a given month, we decompose core inflation into expected
inflation, the effect of labor market tightness, the effect of past headline shocks (“pass-through effect”), and a
residual (based on Table 1 column 4). 2. Next, we decompose the “pass-through effect” into effects of energy
shocks, backlogs, auto-price shocks, and another residual by using their coefficients in our headline-shock equation
(Table 2B, Column 3) and the 12-month averages of the three variables. 3. Finally, we divide the current headline-
inflation shock into components due to the three variables, and another residual, using the same headline-shock
equation (“direct effects” of the variables). Having decomposed inflation in a given month, we subtract the average
of each component over January – December 2020 from the average over August 2021 – July 2022 to derive the
decomposition of the 12-month inflation change shown in Figure 12. We report a single residual that combines the
residuals from the different steps in our calculations.

                                                         17
C. Why Has High Inflation Been Such a Surprise?
     As inflation began to rise in March 2021, Fed Chair Powell predicted that the increase would
be “neither particularly large nor persistent.” (Powell, 2021a). At the Jackson Hole conference that
August, Powell remained sanguine, noting “the absence so far of broad-based inflation pressures.”
(Powell, 2021b). Powell’s view was supported by the many economists on Krugman’s (2021)
“Team Transitory,” including the authors of this paper (Ball and others, 2021a). Today, it is clear
that inflation was much higher than we expected.
     What accounts for these forecasting errors? One factor is unexpected, adverse shocks to
headline inflation. These shocks include the unusual and persistent disruption of supply chains,
and the rise in energy prices associated with the war in Ukraine. On the other hand, part of the
problem was flaws in our pre-pandemic understanding of inflation that recent experience has made
apparent. There were three intertwined problems with conventional thinking. 12
     First, economists measured labor market tightness with the deviation of unemployment from
its natural rate, typically as estimated by the Congressional Budget Office. As a result, they
neglected the tightening of the labor market captured by the dramatic increase in the job vacancies-
to-unemployed ratio, although this was unexpected and did not occur until late 2021. 13
     Second, many (although not all) economists assumed that the effect of unemployment on slack
was linear and fairly small, based on estimates from the pre-pandemic era of stable inflation. As a
result, even when they considered the possibility of an extreme tightening of the labor market, they
expected the inflationary effects to be modest. Ball and others (2021a), for example, predicted that
if the unemployment rate fell to 1.5 percent, core inflation would rise only to 2.9 percent.
     Finally, economists typically assumed explicitly or implicitly that deviations of headline
inflation from core would not feed into core—they ignored the pass-through effect. If that effect
had been accounted for, there would have been greater concern about core inflation in mid-2021,
because at that point there had already been large headline-inflation shocks, and prudent
forecasters would have considered the risk of additional shocks as the economy reopened.




12
  The analysis here overlaps with Furman (2022).
13
  In March 2021, the V/U ratio was 0.9, well below its pre-pandemic (January 2020) level of 1.2, with little
indication that it would rise to above 2.0 by March 2022.

                                                         18
     To illustrate these points, we consider an equation for core inflation from our previous work,
which is linear in the 12-month deviation of unemployment from the natural rate estimated by the
Congressional Budget Office (CBO) and ignores the pass-through effect. Figure 13 shows the path
of the inflation gap predicted by this equation estimated over 1985-2019, given the evolution of
unemployment during the pandemic. 14 The equation predicts a decrease in inflation in 2020 and
almost no increase since then, reflecting the fact that the 12-month average of the unemployment
rate has only recently (in May 2022) fallen below the CBO’s natural rate estimate (currently 4.4
percent). These results contrast sharply with the good (out of sample) forecasting performance of
this paper’s preferred inflation equation, which Figure 13 illustrates.
     Today we can see that, even before the pandemic, inflation equations fit the data better with
tightness measured by a non-linear function of V/U than with a linear function of U, and with a
pass-through effect (see Appendix). Before 2020, however, the evidence on these points was not
striking enough to influence the inflation models of most economists. Movements in V/U were
strongly correlated with movements in unemployment, and we did not observe the extreme labor-
market tightness that has made non-linearity obvious. Headline inflation shocks were smaller and
less persistent than they have been since 2020, making the pass-through effect easy to miss. 15


4. TWO BIG QUESTIONS


     We now move from explaining past inflation to considering the future. Like most economists,
we presume that the Federal Reserve has the ability to rein in inflation if it raises interest rates by
enough. What is less clear is the costs of doing so: will containing inflation require a substantial
slowing of the economy and increase in unemployment? Here we consider two factors that will
help determine the answer: the behavior of the Beveridge curve, and the behavior of inflation
expectations. There is considerable uncertainty about both issues.


     A. The Beveridge Curve



14
   The estimated equation is: core inflation gap = 0.122 - (0.249)(U – U*), where U* is the natural rate as
estimated by the CBO and U and U* are averaged over 12 months.
15
   Ball and Mazumder (2021) find a pass-through effect for the euro area but fail to find one for the U.S. We can
now see that the negative U.S. result reflects an assumption that the effect is linear, which the data reject.

                                                         19
     The Beveridge curve is the relation between the unemployment rate and the vacancy rate. It is
downward-sloping, reflecting the fact that a tightening of the labor market increases vacancies and
reduces unemployment. As stressed by Blanchard, Domash, and Summers (2022), the Beveridge
curve determines the relation between the unemployment rate and V/U, and therefore affects the
level of unemployment needed to reduce inflation.
     The Shift in the Curve Figure 14 plots the unemployment and vacancy rates from 2001 through
May 2022. A stable Beveridge curve appears in different periods, but the curve has shifted at
discrete points in time. The curve was stable from 2001 to 2009, then shifted outward and was
stable again until March 2020. With the pandemic shutdown of April 2020, the curve abruptly
shifted outward by a larger amount. Initially, the shift was a jump in the unemployment rate to
14.7 percent with little change in the vacancy rate; since then, the tightening of the labor market
has moved the economy up the new Beveridge curve, and today the unemployment rate is close to
its pre-pandemic level and the vacancy rate is very high. 16
     Within a regime with a stable Beveridge curve, the curve is well approximated by a log-linear
relationship between the unemployment and vacancy rates. The Figure shows log-linear curves
that we estimate for the three periods since 2001.
     The outward shift in the Beveridge curve means that the labor market has become less efficient
at matching unemployed workers with vacant jobs. It is not clear why that has happened, although
recent work has suggested possible factors. Blanchard, Domash, and Summers cite increased
reallocation of workers across firms, as captured by the gross level of hiring. Briggs (2022) cites
decreased search intensity of unemployed workers, as indicated by a decline in the fraction who
actively submit job applications.
     Since we are not sure why the Beveridge curve has shifted, it is difficult to say whether
temporary factors are responsible, so we should expect it to shift back at some point, or whether
the shift is permanent. There was a small decline in V without a rise in U from March to June of
this year but it is too soon to tell if this is the start of a significant shift in the Beveridge curve. This
issue is closely related to the debate between Blanchard, Domash and Summers and the Federal
Reserve’s Figura and Waller (2022) about prospects for the labor market. Figura and Waller



16
  The unemployment rate is U / (labor force) and we define the vacancy rate as V / (labor force), so the ratio of the
two rates equals the V/U in our Phillips curve. Many researchers define the vacancy rate as V / (employment + V),
but that distinction does not make a material difference for our analysis.

                                                          20
suggest that a cooling of demand can reduce the vacancy rate with little increase in unemployment,
which will indeed be possible if the Beveridge curve shifts favorably. Blanchard, Domash and
Summers argue that this outcome is unlikely based on historical evidence. We will see that this
issue is critical for the costs of reducing inflation.
      The Relation Between Unemployment and Core Inflation A log-linear Beveridge curve defines
the vacancy rate v is a function of the unemployment rate u:
(2)       v = aub ,       a>0, b<0 ,
which implies a relation between the ratio V/U and the unemployment rate:
(3)       V/U = v/u = aub-1 .
If we substitute this expression for V/U into the Phillips curve, we obtain a relation between the
core inflation gap (median inflation minus expected inflation) and the unemployment rate. This
relation captures the unemployment-inflation tradeoff facing policymakers as they stimulate or
restrain demand and thereby move the economy along a stable Beveridge curve. In addition, this
relation implies that there are now two possible shocks to the Phillips curve relationship: the
Beveridge curve shock in addition to the more traditional cost-push shock. 17
      We derive this tradeoff for two versions of the Beveridge curve: the ones estimated for the pre-
pandemic period (dark blue in Figure 14) and the pandemic period (red). In both cases, we use the
monthly Phillips curve estimated for 1985-2022 (column 4 of Table 1). In this exercise we set the
headline-shock variable H to zero. 18
      Figure 15 shows the results for the two Beveridge curves. A feature that jumps out in both cases
is a striking non-linearity: there is a sharp bend in the curve. At high unemployment rates, the
relation is close to linear, and flat. For example, for the pre-pandemic period, the slope is -0.28 at
8 percent unemployment and -0.31 at 6 percent, numbers that are roughly comparable to pre-
pandemic estimates of the Phillips-curve slope (for example, Hazell and others, 2022). However,
the slope is -0.67 at 4 percent unemployment and rises dramatically to -2.8 at 3.5 percent
unemployment.



17
   These two shocks are not structural or independent. For instance, some shocks could increase production costs and
simultaneously increase mismatch in the labor market. But they are also not identical: shocks to the Beveridge curve
could be unrelated to cost-push shocks.
18
   The estimated parameters in the Beveridge curves are a = 13.9 and b = –0.85 for the pre-pandemic (July 2009 –
March 2020) sample and a = 16.2 and b = –0.62 for the pandemic (April 2020 – June 2022) sample. The latter
period ends in June 2022 because the vacancy rate for July is not yet available.

                                                        21
   The shape of the curves in Figure 15 supports Gagnon and Collins’s (2019) view that the
unemployment-inflation tradeoff is steeper when unemployment is low. In our framework, this
non-linearity has two sources corresponding to the two relations from which the curves are derived.
First, as seen in Figure 6, V/U has a non-linear effect on inflation, with a large marginal effect
when V/U is high. Second, V/U is strongly non-linear in U, with a large marginal effect when U
is low. This second non-linearity reflects the facts that both 1/U and V are convex in U, the latter
because of the shape of the Beveridge curve.
   The other message from Figure 15 is that the unemployment-inflation tradeoff has worsened
during the pandemic: the inflation rate is now higher for any given unemployment rate, especially
when unemployment is low. At an unemployment rate of 4 percent, the core inflation gap is 0.5
percentage point with the old Beveridge curve and 3.9 percentage points with the pandemic
Beveridge curve. This difference reflects the fact that 4 percent unemployment implies a much
higher V/U with the pandemic curve. Our finding of an adverse shift in the Phillips-curve tradeoff
is consistent with Crump and others (2022).


B. Will Inflation Expectations Remain Anchored?
   In the two decades before the pandemic, long-term inflation expectations were well-anchored
at the Federal Reserve’s inflation target, and this anchoring made it easier to return actual inflation
to target when it was pushed away temporarily. Looking forward, if expectations remain anchored,
then inflation will again return to target once the labor market normalizes and the economy moves
beyond the unusual shocks of the pandemic.
   However, the anchoring of inflation expectations is not immutable. Anchoring has occurred
because the Fed has built a track record of reversing short-run movements in inflation and returning
inflation to target. Presumably a large enough and persistent enough rise in inflation would
eventually lead people to revise their expectations upward, which in turn would push actual
inflation even higher. That outcome would worsen the unemployment-inflation tradeoff and
increase the costs of reining in inflation.
   There are hints that a de-anchoring of expectations may already have begun. As shown in Figure
2 above, ten-year expected inflation in the Survey of Professional Forecasters has risen from 2.2
percent in 2019Q4 to 2.8 percent in 2022Q3. Five-year expectations in the Michigan survey of
consumers have risen from 2.2 percent in December 2019 to 3.0 percent in August 2022.


                                                  22
      Will these modest increases in expected inflation be reversed as the Fed takes action to control
inflation? Or are we seeing the beginning of a substantial de-anchoring? It is hard to know, but we
seek to inform discussions of the issue by carefully examining the response of expectations to
inflation movements, both in the pandemic period and earlier. (See also Reis (2021) and Hilscher,
Raviv, and Reis (2022), who examine the distribution of expectations across individual survey
respondents to assess the risk of de-anchoring.)
      A Simple Model of Inflation Expectations We posit a simple equation in which expectations
evolve in response to movements in headline inflation:
                      𝑒𝑒
(4)      𝜋𝜋𝑡𝑡𝑒𝑒 = 𝛾𝛾𝜋𝜋𝑡𝑡−1 + (1 − 𝛾𝛾)𝜋𝜋𝑡𝑡 ,
where πe is expected inflation and π is actual headline inflation. The parameter γ captures the
degree of anchoring. For γ=1, expected inflation is constant regardless of actual inflation behavior.
For γ=0, expected inflation adjusts one-for-one with current inflation.
      We consider the evolution of expected inflation over some period starting at t = τ. By
repeatedly substituting the equation for πe into itself, we obtain
                             𝑡𝑡−𝜏𝜏−1 𝑖𝑖
(5)       𝜋𝜋𝑡𝑡𝑒𝑒 = (1 − 𝛾𝛾) ∑𝑖𝑖=0   𝛾𝛾 𝜋𝜋𝑡𝑡−𝑖𝑖 + 𝛾𝛾 𝑡𝑡−𝜏𝜏 𝜋𝜋𝜏𝜏𝑒𝑒 ,   t>τ.
We estimate γ with the SPF’s quarterly series for ten-year expected inflation. We account for the
fact that the current quarter’s inflation rate is not known when a ten-year forecast is made by
replacing πt (the first term in the summation) with the current-period (SPF) expectation of πt, a
now-cast that is reported at the same time. We denote this expectation by tπt. We also add an error
term to the equation to capture other influences on expectations, yielding:
                                              𝑡𝑡−𝜏𝜏−1 𝑖𝑖
(6)      𝜋𝜋𝑡𝑡𝑒𝑒 = (1 − 𝛾𝛾)𝑡𝑡 𝜋𝜋𝑡𝑡 + (1 − 𝛾𝛾) ∑𝑖𝑖=1   𝛾𝛾 𝜋𝜋𝑡𝑡−𝑖𝑖 + 𝛾𝛾 𝑡𝑡−𝜏𝜏 𝜋𝜋𝜏𝜏𝑒𝑒 + 𝜖𝜖𝑡𝑡 ,   𝑡𝑡 > 𝜏𝜏.
We estimate γ, the single parameter in this equation, with non-linear least squares.
      Anchoring in Several Eras We examine the behavior of expectations in several time periods.
Specifically, we divide the data from 1985 to the present into four periods for which we have
reason to believe that expectations behaved differently. Figure 16 shows the path of expected
inflation since 1985, the estimated γ for each period, and the associated fitted values for expected
inflation. Our results and interpretation for the four periods are the following:
•     1985Q1-1998Q1: This is the period before anchoring, when the actual CPI inflation rate drifted
      down from about 4 percent to 2.5 percent and expectations followed. The estimated γ is 0.944,
      the lowest for the four periods.



                                                                     23
•   1998Q2-2008Q2: The start of this period is the beginning of the anchoring regime identified
    by Ball and Mazumder (2019). Actual inflation fluctuated but expected inflation was almost
    constant at 2.5 percent, and the estimated γ is 1.003.
•   2008Q3-2019Q4: This is the period following the Great Recession, when inflation repeatedly
    fell short of the Fed’s target, albeit by small amounts. It appears that this experience produced
    some de-anchoring, with expected inflation falling. The estimated γ is 0.991.
•   2020Q1-2022Q2. The pandemic period in which expected inflation has risen somewhat. The
    estimated γ is 0.980, suggesting that anchoring has become weaker than it was before the
    pandemic.
In what follows, we use these historical experiences as guides to what might happen in the future.


5. SCENARIOS FOR FUTURE INFLATION


    Where is inflation heading? We will not offer unconditional forecasts. The path of inflation will
depend on how quickly the Federal Reserve raises interest rates and how those actions and other
factors affect the labor market. We will leave forecasts concerning those issues to others, and
forecast inflation paths conditional on paths for unemployment. This exercise will help us see how
much the Fed needs to raise unemployment to return inflation to an acceptable level.
    One unemployment path we consider is the one projected by members of the Federal Open
Market Committee in their most recent (June 2022) Summary of Economic Projections (SEP). In
this scenario, the unemployment rate rises only a little from its current level, peaking at 4.1 percent
in 2024. We also consider a more pessimistic forecast from the IMF 2022 Article IV Consultation
Staff Report for the United States in which unemployment peaks at 5.3 percent, and a much more
pessimistic scenario suggested by Summers (2022b) in which unemployment rises to 7.5 percent
for two years. Summers suggests that unemployment must rise that much to return inflation to the
Fed’s target.
    Once we assume a path for the unemployment rate, there is still uncertainty about the path of
inflation because it will depend on the behavior of the Beveridge curve and of expectations. We
construct forecasts for both optimistic and pessimistic assumptions about these factors.
    In all our simulations, we set headline-inflation shocks to zero starting in August 2022. This is
a natural benchmark because historically headline shocks have been unpredictable and not


                                                  24
persistent. 19 However, it is important to keep in mind that the future could bring either positive or
negative headline shocks. We might see inflationary shocks resulting from a worsening of the war
in Ukraine or new disruptions of production as the pandemic waxes and wanes. We might see
disinflationary shocks if energy prices fall or other supply factors improve. (Currently, oil futures
curves suggest that crude oil prices are expected to peak in 2022 and decrease in coming years.)
Either way, there could be major movements in inflation that are unrelated to monetary policy.


A. Alternative Assumptions About the Beveridge Curve and Expectations
     We consider the following scenarios:
     The Beveridge Curve Our pessimistic case for the Beveridge curve is that it remains in its
position during the pandemic to date, as captured by the log-linear relation we have estimated (the
red curve in Figure 14). This means that the factors that have worsened the ability of the labor
market to match workers to jobs, whatever they are, persist.
     Our other scenario is that the Beveridge curve shifts back quickly to its pre-pandemic position
(the blue curve in Figure 14). Specifically, starting from the pandemic-era curve in July, the curve
shifts one quarter of the way toward its pre-pandemic position every month, which means the
outward shift during the pandemic is almost entirely reversed after about six months. 20
     Expectations We specify paths for expected inflation at the monthly frequency. In all cases we
set expected inflation in August 2022 at 2.8 percent, the level reported in the SPF for 2022Q3
(released in mid-August). We consider three scenarios for the evolution of expectations starting in
September.
     In our most optimistic scenario, confidence in the Fed’s commitment to low inflation ensures
that expected inflation quickly reverts to its pre-pandemic level of 2.2 percent. Specifically, it
moves one quarter of the way each month.
     A second scenario is that expected inflation continues to respond to actual inflation as our
estimates suggest it has so far during the pandemic. That is, expected inflation follows the
pandemic-era process: 𝜋𝜋𝑡𝑡𝑒𝑒 = 𝛾𝛾𝜋𝜋𝑡𝑡−1
                                   𝑒𝑒
                                        + (1 − 𝛾𝛾)𝜋𝜋𝑡𝑡 with 𝛾𝛾 = 0.980 at the quarterly frequency. We set
𝛾𝛾 equal to the cube root of 0.980 in our monthly simulations.


19
   The serial correlation of headline-inflation shocks is low: an AR(1) specification for the monthly headline-
inflation shock yields an estimated coefficient of 0.4 for both 1985-2019 and 2020-2022.
20
   If v*(u) and v**(u) are the pre-pandemic and pandemic Beveridge curves, then the curve in August 2022 is
(0.75)v**(u) + (0.25)v*(u). After August 2022, the curve in month t is vt(u) = (0.75)vt-1(u) + (0.25)v*(u).

                                                          25
     Finally, we consider a variation on the second scenario with 𝛾𝛾 = 0.944 at the quarterly
frequency, which is the estimated anchoring parameter for the 1985-1998 period. We view this
case as quite pessimistic: Expectations behave as they did before 1998, which means that all of the
progress in anchoring expectations since then is lost.


B. Deriving Inflation Paths
     For given assumptions about the Beveridge curve and inflation expectations and a given path
of the unemployment rate, and starting from actual data through July 2022, we construct a monthly
simulation of the economy. For each month, the steps are:
•    Use the Beveridge curve to derive V/U given the assumed U, and compute the 12-month
     average of V/U.
•    Compute the 12-month headline shock H given zero monthly shocks starting in August 2022
     and the actual shocks before that. The 12-month average declines to zero in July 2023.
•    Given the 12-month V/U and H, compute the core inflation gap from the monthly Phillips
     curve (column (4) of Table 1).
•    Given the core inflation gap and the level of expected inflation in the previous month, derive
     the current levels of core inflation and expected inflation from the equation for expected
     inflation (except in the most optimistic expectations scenario, in which expected inflation
     moves one quarter of the way toward 2.2). 21
These steps yield a monthly series for core inflation starting in August 2022. By the assumption
that future headline shocks are zero, the monthly path of headline inflation is the same. We
aggregate over time to derive a 12-month path of core inflation. The 12-month path of headline
inflation converges to core in July 2023.


     C. Inflation Paths for the FOMC’s Unemployment Forecasts
     In considering possible paths for unemployment, a natural starting point is the forecasts of Fed
policymakers, which are reported in the Summary of Economic Projections released after every
other FOMC meeting. The most recent SEP as this paper is written is the one for June 15, 2022.


21
    In August 2022, we set 𝜋𝜋𝑡𝑡𝑒𝑒 = 2.8 and add the core gap to get core. For later months, we use the equations 𝜋𝜋𝑡𝑡 = 𝜋𝜋𝑡𝑡𝑒𝑒
+ core gap and 𝜋𝜋𝑡𝑡𝑒𝑒 = 𝛾𝛾𝜋𝜋𝑡𝑡−1
                            𝑒𝑒                                             𝑒𝑒
                                 + (1 − 𝛾𝛾)𝜋𝜋𝑡𝑡 . Given the core gap and 𝜋𝜋𝑡𝑡−1 , we can solve the two equations for 𝜋𝜋𝑡𝑡 and
  𝑒𝑒
𝜋𝜋𝑡𝑡 .

                                                              26
In these forecasts, the unemployment rate rises only slightly over time and peaks in 2024 at 4.1
percent, a low level by historical standards (and below the CBO estimate of the natural rate of
unemployment). According to the SEP, the economy will experience low unemployment rates at
the same time as inflation falls back to the Fed’s target.
   The SEP forecasts the unemployment rate in the fourth quarters of 2022, 2023, and 2024. We
construct a monthly unemployment path by assigning each fourth quarter forecast to November
and then interpolating, starting with the actual unemployment rate of 3.5 percent in July 2022.
   Figure 17 shows simulated paths of 12-month core (median CPI) inflation for the SEP
unemployment path and our different Beveridge curve and expectations scenarios. Red lines are
cases with the pessimistic Beveridge curve and blue lines indicate the optimistic Beveridge curve.
The optimistic, middle, and pessimistic cases for expectations are shown in solid lines, dashes, and
short dashes, respectively. Appendix Figure 17A repeats this exercise for median PCE inflation,
yielding similar results. To illustrate the mechanisms behind the results, Figure 18 shows the paths
of all simulated variables for one case, the pessimistic Beveridge curve and intermediate
expectations assumption.
   The different core inflation paths in Figure 17 have some common features. They all rise from
the current level of 6.3 percent and peak at some point between December 2022 and November
2023, reflecting the fact that the 12-month average of V/U continues to rise even as slightly higher
unemployment reduces the current V/U. Eventually core inflation starts to decline as V/U
continues to fall and the pass-through effects of past headline shocks die out.
   The levels of inflation, however, vary greatly across the different scenarios. With the most
optimistic assumptions about both the Beveridge curve and expected inflation, core inflation peaks
at 7.2 percent and falls to 2.7 percent in December 2024. With the most pessimistic assumptions,
core inflation peaks at 9.5 percent and its December 2024 level is 8.8 percent, far higher than the
level today.
   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.


                                                  27
    In interpreting these results, one nuance is that we forecast core inflation as measured by the
weighted median CPI, whereas the Fed targets a two percent inflation rate in the personal
consumption expenditure (PCE) deflator. According to the Federal Reserve Bank of Atlanta
Underlying Inflation Dashboard, the Fed’s target is equivalent to a 2.5 percent target for median
CPI inflation, given the historical difference between the average levels of median CPI and
headline PCE inflation. The upshot is that our most optimistic forecast for December 2024, a core
inflation rate of 2.7 percent, is fairly close to the Fed’s target. In all the other scenarios, however,
inflation stays well above the target.


D. Inflation Paths with Higher Unemployment
   If the SEP’s unemployment path risks leaving inflation at a high level, how much higher must
unemployment rise to more reliably meet the Fed’s inflation goal? To shed light on this question,
we consider two other unemployment paths. One is based on forecasts in the IMF’s Article IV
Consultation Staff Report for the United States, published in July 2022. These forecasts are more
pessimistic than the Fed’s: the unemployment rate peaks at 5.3 percent in 2024. We construct a
monthly unemployment scenario by assigning the quarterly forecasts underlying the Staff Report
to the middle month of each quarter and interpolating. The other path is based on Summers’s
(2022b) highly pessimistic suggestion that reversing the rise in inflation will require two years of
7.5 percent unemployment. In this scenario, we assume that the unemployment rate rises linearly
from its July 2022 level to 7.5 percent in January 2023 and then stays at 7.5 percent through
December 2024.
   Figure 19A shows the inflation paths conditional on the IMF staff projected unemployment
path and our alternative Beveridge curve and expectations assumptions. As one would expect,
higher unemployment lowers inflation: the December 2024 inflation level ranges from 2.3 to 4.9
percent, compared to 2.7 to 8.8 percent for the SEP unemployment path. Yet inflation still levels
off well above the Fed’s target in many cases. Here, the behavior of inflation expectations is
critical. Even with the more pessimistic Beveridge curve, median CPI inflation falls to below 3.0,
only a bit above the implicit 2.5 percent target, if expected inflation reverts to its pre-pandemic
level.
   Figure 19B shows the inflation paths for the scenario with two years of 7.5 percent
unemployment. In this case, the differences across Beveridge-curve and expectations assumptions


                                                  28
are relatively small. The December 2024 inflation rates are clustered around 2.5 percent, with each
less than one percentage point away from that level. Our analysis suggests, therefore, that this
scenario’s unemployment path robustly brings inflation close to the Fed’s goal. Unfortunately, the
cost is a painful and prolonged increase in unemployment.


6. CONCLUSION


   Yogi Berra observed that “it’s tough to make predictions, especially about the future.” This
aphorism applies to the study of U.S. inflation.
   Looking backward, we can account fairly well for inflation behavior during the pandemic. A
tight labor market has pushed up core inflation; headline inflation has deviated from core because
of sharp rises in energy and auto prices, and supply chain problems; and pass-through from these
headline shocks has magnified the rise in core. All of these factors have been prominent in recent
discussions of inflation. We contribute a simple framework in which we quantify their roles. We
find that the combination of direct and pass-through effects from headline-inflation shocks
accounts for about 5.5 percentage points of the 7.2 percentage point rise in 12-month inflation
between end-2020 and July 2022. A rise in expected inflation accounts for 0.5 percentage point,
and the rise in labor market tightness (measured by the ratio of vacancies to unemployment)
accounts for 1.0 percentage point. The role of labor market tightness is rising over time.
   Looking forward, we can forecast inflation if we specify the path of unemployment and the
future behavior of the Beveridge curve and inflation expectations. There is much uncertainty about
these factors, so it is difficult to make unconditional predictions. Yet we have one broad finding:
The forecasts of Fed policymakers—inflation will return to target while unemployment barely
rises above four percent—are reasonable only under quite optimistic assumptions about both the
Beveridge curve and expectations. If the behavior of either proves less benign, then reducing
inflation is likely to require higher unemployment than the Fed anticipates.
   While our simple framework explains recent inflation fairly well, future research might
improve it along many dimensions. For example, researchers should continue to refine the
measurement of core inflation, of labor-market tightness, and of inflation expectations. We should
try to better understand the non-linear effects of tightness and past headline shocks on core



                                                   29
inflation. We also need more work on why the Beveridge curve shifts and why inflation
expectations become anchored or de-anchored.




                                               30
References
Abraham, Katharine, John Haltiwanger, and Lea Rendell. 2020. “How Tight is the U.S. Labor
      Market?” Brookings Papers on Economic Activity, Spring, 97-165.
Ball, Laurence, and N. Gregory Mankiw. 1994. “Asymmetric Price Adjustment and Economic
       Fluctuations.” The Eonomic Journal, 104 (March). 247–261.
Ball, Laurence, Gita Gopinath, Daniel Leigh, Prachi Mishra, Antonio Spilimbergo. 2021a. “US
        Inflation: Set for Take-Off?”, VoxEU. 07 May 2021.
Ball, Laurence, Daniel Leigh, Prachi Mishra and Antonio Spilimbergo. 2021b. “Measuring U.S.
       Core Inflation: The Stress Test of COVID-19", NBER Working Paper, 29609.
Ball, Laurence, and Sandeep Mazumder, 2021. "A Phillips Curve for the Euro Area,"
        International Finance, Wiley Blackwell, vol. 24(1), pages 2-17, April.
Ball, Laurence, and Sandeep Mazumder. 2019. A Phillips Curve with Anchored Expectations
        and Short-Term Unemployment. Journal of Money, Credit and Banking, Vol. 51, No. 1.
Ball, Laurence, and Sandeep Mazumder. 2011. “Inflation Dynamics and the Great Recession.”
        Brookings Papers on Economic Activity 41 (1): 337–405.
Barnichon, Regis, Luiz E. Oliveira, and Adam H. Shapiro. 2021. “Is the American Rescue Plan
       Taking Us Back to the ’60s?”, FRBSF Economic Letter, 2021-27, October 18, 2021.
Barnichon, Regis. 2010. “Building a Composite Help-Wanted Index.” Economics Letters 109(3),
       pp. 175–178.
Barnichon, Regis and Adam Hale Shapiro. 2022. “What’s the Best Measure of Economic
       Slack?”, FRBSF Economic Letter, 2022-04 | February 22, 2022.
Bernanke, Ben S. 2004. “The Great Moderation.” Remarks by Governor Ben S. Bernanke at the
      Meetings of the Eastern Economic Association, Washington, DC. February 20, 2004
Blanchard, Olivier. 2021. “In Defense of Concerns over the $1.9 Trillion Relief Plan.” Real
      Time Economic Issues Watch, Peterson Institute for International Economics,
      Washington, DC.
Blanchard, Olivier. 2022. “Why I Worry about Inflation, Interest rates, and Unemployment”,
      Peterson Institute for International Economics, March 14, 2022.
Blanchard, Olivier, Alex Domash, and Lawrence H. Summers. 2022. “Bad News for the Fed
      from the Beveridge Space”, Peterson Institute for International Economics Policy Brief
      22-7.
Bolhuis, Marijn A., Judd N. L. Cramer & Lawrence H. Summers, 2022, “Comparing Past and
       Present Inflation”, NBER Working Paper No. 30116, June 2022.
Briggs, Joseph, 2022, “The Beveridge Curve Debate: Has Match Efficiency Really Declined?”,
       US Economics Analyst, Goldman Sachs Economics Research, August 7, 2022.
Bryan, Michael F., and Stephen G. Cecchetti. 1994. “Measuring Core Inflation.” In Monetary
       Policy, edited by N. Gregory Mankiw. University of Chicago Press.

Congressional Budget Office. 2020. “Key Methods That CBO Used to Estimate the Effects of
      Pandemic-Related Legislation on Output.”

Crump, Richard K., Stefano Eusepi, Marc Giannoni, and Ayşegül Şahin, 2022, “The
      Unemployment-Inflation Trade-off Revisited: The Phillips Curve in COVID Times”,
      NBER Working Paper No. 29785, February 2022.
di Giovanni, Julian, Ṣebnem Kalemli-Özcan, Alvaro Silva, and Muhammed A. Yildirim, 2022.
       “Global Supply Chain Pressures, International Trade, and Inflation.” NBER Working
       Paper No. 30240.
Dolmas, Jim, and Evan F. Koenig, 2019, “Two Measures of Core Inflation: A Comparison,”
      Federal Reserve Bank of St. Louis Review, Fourth Quarter 2019, 101(4), pp. 245-58.
Dolmas, Jim, 2005, “Trimmed Mean PCE Inflation,” Federal Reserve Bank of Dallas Research
      Department Working Paper No. 0506.
Domash, Alex and Lawrence H. Summers (2022), “How Tight are U.S. Labor Markets?”, NBER
     Working Paper 29739, February 2022.
European Central Bank, 2014, “Indirect Effects of Oil Price Developments on Euro Area
      Inflation”, Box 3, Page 54. Monthly Bulletin, December.
Faberman, R. Jason, Andreas I. Mueller, Ayşegül Şahin and Giorgio Topa, 2020. “The Shadow
      Margins of Labor Market Slack,” Journal of Money, Credit, and Banking, 52(S2), 355-
      391.
Figura, Andrew and Chris Waller, 2022, “What does the Beveridge Curve Tell Us About the
        Likelihood of a Soft Landing?”, FEDS Notes, July 29, 2022.
Furman, Jason 2022, “America’s Wage-Price Persistence Must Be Stopped”, Project Syndicate,
      August 2, 2022.
Furman, Jason, and Wilson Powell III, 2021, “What is the Best Measure of Labor Market
      Tightness?”, Peterson Institute for International Economics, November 22, 2021
Gagnon, Joseph E. and Christopher G. Collins, 2019, “Low Inflation Bends the Phillips Curve”,
      Peterson Institute for International Economics Working Paper No. 19-6, April 2019.
Gordon, Robert J., 1975, “Alternative Responses of Policy to External Supply Shocks,”
      Brookings Papers on Economic Activity, 1975, No. 1, pp. 183-206
Hazell, Jonathon, Juan Herreño, Emi Nakamura and Jón Steinsson, 2022. "The Slope of the
        Phillips Curve: Evidence from U.S. States," The Quarterly Journal of Economics, vol
        137(3), pages 1299-1344.
Hilscher, Jens and Raviv, Alon and Reis, Ricardo A.M.R., How Likely Is an Inflation Disaster?,
       2022. (April 26, 2022). Available at SSRN: https://ssrn.com/abstract=4083404 or
       http://dx.doi.org/10.2139/ssrn.4083404


                                                                                                 2
Krugman, Paul, 2021, “Wonking Out: I'm Still on Team Transitory,” New York Times,
     September 10.
Mortensen, Dale T. and Pissarides, Christopher. 1999. “Job Reallocation, Employment
      Fluctuations and Unemployment.” In: Taylor, John B. and Woodford, Michael, (eds.)
      Handbook of Macroeconomics. North-Holland. ISBN 9780444825285
Owyang, Michael T. & E. Katarina Vermann, 2014. "Rockets and Feathers: Why Don't Gasoline
     Prices Always Move in Sync with Oil Prices?," The Regional Economist, Federal
     Reserve Bank of St. Louis, October.
Phillips, A.W. 1958. “The Relation Between Unemployment and the Rate of Change of Money
        Wage Rates in the United Kingdom, 1861–1957.” (PDF). Economica, November 1958,
        Vol. 25, Issue 100, pp. 283-99.
Powell, Jerome. 2021a, “House Committee Hearing about the Coronavirus Aid, Relief, and
       Economic Security Act”.
Powell, Jerome. 2021b. “Monetary Policy in the Time of COVID”, At the "Macroeconomic
       Policy in an Uneven Economy," Economic policy symposium sponsored by the Federal
       Reserve Bank of Kansas City, Jackson Hole, Wyoming, August 27, 2021.
Ramey, Valerie A., and Sarah Zubairy. 2018. “Government Spending Multipliers in Good Times
      and in Bad: Evidence from U.S. Historical Data.” Journal of Political Economy 126(2),
      pp. 850–901.
Reis, Ricardo. 2021. “Losing the Inflation Anchor”, Brooking Papers on Economic Activity,
       September 9, 2021.
Summers, Lawrence H. 2022a. CNN of the interview of Summers by Fareed Zakaria on CNN,
     Aired July 24, 2022 - 10:00 ET, https://transcripts.cnn.com/show/fzgps/date/2022-07-
       24/segment/01

Summers, Lawrence H. 2022b. “Larry Summers Calls for High Unemployment to Curb
     Inflation”, Fortune Magazine, June 21, 2022
Summers, Lawrence H. 2021. “Opinion: The Biden Stimulus Is Admirably Ambitious. But It
     Brings Some Big Risks, Too.” Washington Post, February 4.
Verbrugge, Randal. 2021. “Is It Time to Reassess the Focal Role of Core PCE Inflation?”
      Federal Reserve Bank of Cleveland Working Paper No. 21–10.
Yellen, Janet. 2019. “Former Fed Chair Janet Yellen on why the answer to the inflation puzzle
       matters.” Remark delivered at “What's (not) up with inflation?" event hosted by the
       Hutchins Center on Fiscal and Monetary Policy at the Brookings Institution on October
       3, 2019.




                                                                                                3
Figure 1. CPI Inflation: Headline, Core, and Headline-inflation Shocks, 2020-2022

             Monthly Annualized Inflation                          12-month Inflation
   20       Headline                              10       Headline
            Core inflation                                 Core inflation
            Headline-inflation shocks                      Headline-inflation shocks




   10                                             5




   0
                                                  0




   -10
                                                  -5
     2020               2021            2022        2020               2021             2022


Note: Core inflation is median CPI inflation from the Federal Reserve Bank of Cleveland.
Figure 2. Long-term CPI Inflation Expectations and Median CPI Inflation, 2000-2022
  8         Long-term inflation expectations
            Weighted-median inflation



  6




  4




  2




  0
     2000            2005           2010           2015           2020

Note: Figure reports 10-year-ahead CPI inflation forecasts from the Survey of Professional Forecasters
(SPF).




                                                                                                         2
Figure 3. Inflation Gap vs. Ratio of Vacancies to Unemployed (V/U), 1968-2022


                            Quaterly Data                                                     Monthly Data
            10                                      1968-72             15
                                                    1973-84
                                                    1985-2019
                                                    2020-22
                                                                        10


            5                                                                                                       2022m6
                                                    2022q2
                                               2022q1
                                                                                                            2022m1 2022m5


                                                                   Inflation gap
                                      2021q4                                                        2021m10 2022m22022m4
                                                                                                                      2022m7



  Inflation gap
                                                                                                      2021m11 2022m3
                                                                                                   2021m92021m12
                                                                                                 2020m7 2020m1
                                                                                             2021m6
                                                                                                 2021m8

                                                                  0             5
                                2021q3                                                      2021m5
                                      2020q1                                              2021m4          2020m2
                                                                                                     2020m5
                                                                                                         2020m3
                            2020q3
                           2021q2                                                       2021m2 2021m7
                                                                                                2020m8
                                2020q2                                                      2020m10
                                                                                        2021m3
                                                                                          2020m12      2020m4
                                                                                                   2020m6
                                                                                         2021m1
                                                                                              2020m9
            0         2021q1
                        2020q4                                                             2020m11




                                                                        -5
                                                                                                                    1968-72
                                                                                                                    1973-84
            -5                                                                                                      1985-2019

                                                                        -10                                         2020-22

                  0    .5          1             1.5          2                     0    .5          1           1.5           2
                                  V/U                                                               V/U


Note: Figure reports quarterly and monthly scatter plots of the inflation gap against the averages of V/U.
Inflation gap is the difference between median and long-term expected inflation. Long-term expected
inflation is the ten-year-ahead CPI inflation forecast from the Survey of Professional Forecasters (SPF).
“V/U” denotes ratio of vacancies to unemployed (4-quarter or 12-month average).




                                                                                                                                   3
Figure 4. Fitted Relationship: Inflation Gap vs. V/U, 1985-2022

                            Quarterly Data                                                      Monthly Data
                                                                                                                        2022m6
       6
                                                                           6


                                                                                                             2022m1
                                                                                                                      2022m5
                                                        2022q2
                                                   2022q1                                                     2022m2
       4                                                                                              2021m10     2022m4
                                                                           4                                          2022m7
                                                                                                       2021m11 2022m3
                                          2021q4
                                                                                                        2021m12
                                                                                                   2021m9

  Inflation gap                                                       Inflation gap               2020m7
                                                                                                 2021m8 2020m1
                                                                                              2021m6

         2                                                                    2
                                                                                             2021m5
                                 2021q3
                                       2020q1                                                              2020m2
                                                                                                      2020m5
                                                                                            2021m4        2020m3
                             2020q3
                            2021q2                                                        2021m22021m7
                                                                                                 2020m8
                                 2020q2                                                       2020m10
                                                                                          2021m3
                                                                                            2020m12
                                                                           0                            2020m4
                                                                                                    2020m6
       0
                      2021q1                                                               2021m1
                                                                                                2020m9
                        2020q4
                                                        1985-2019                           2020m11                     1985-2019
                                                        2020-22                                                         2020-22
                                                        Lowess             -2                                           Lowess
       -2                                               Cubic                                                           Cubic

                  0    .5           1                1.5          2                   0    .5           1             1.5         2
                                   V/U                                                                 V/U


Note: Figure 4 shows the results of fitting flexible curves to the data for 1985-2022. “Lowess” denotes
locally weighted scatterplot smoothing strategy for fitting a smooth curve to data points. Inflation gap is
the difference between median and long-term expected inflation. Long-term expected inflation is the ten-
year-ahead CPI inflation forecast from the Survey of Professional Forecasters. “V/U” denotes ratio of
vacancies to unemployed (4-quarter or 12-month average).




                                                                                                                                      4
Figure 5. CPI Inflation Excluding Food and Energy vs. V/U, 1968-2022

                            Quaterly Data                                                       Monthly Data
            10                                        1968-72             15
                                                      1973-84
                                                      1985-2019
                                                      2020-22
                                                                          10
                                                                                           2021m4
                                                                                              2021m6
                            2021q2                                                           2021m5
            5                                                                                                       2022m6
                                                 2022q12022q2                                       2021m102022m1 2022m5
                                                                                                 2020m7 2021m12 2022m4

                                                                    Inflation gap
                                                                                                      2021m112022m2



  Inflation gap
                                 2021q3 2021q4                                                  2020m8



                                                                    0             5
                            2020q3                                                        2021m32021m7           2022m3 2022m7
                                                                                                     2021m92020m1
                                                                                                            2020m2
                                                                                                2020m9
                                                                                             2020m11 2020m6
                                                                                          2021m2   2021m8
                                                                                              2020m10
                                                                                            2020m12
                                                                                           2021m1
                        2020q4         2020q1
            0                                                                                          2020m5
                                                                                                           2020m3
                      2021q1


                                                                          -5
                                                                                                        2020m4        1968-72
                                 2020q2                                                                               1973-84
                                                                                                                      1985-2019
                                                                          -10                                         2020-22
            -5
                  0    .5             1            1.5          2                     0    .5            1          1.5          2
                                     V/U                                                                V/U


Note. Figure 5 repeats Figure 2, the scatterplots of the inflation gap against V/U, but with core inflation
measured in the traditional way with inflation excluding food and energy prices (XFE). Inflation gap is the
difference between XFE inflation and long-term expected inflation. Long-term expected inflation is the is
the ten-year-ahead CPI inflation forecast from the Survey of Professional Forecasters (SPF). “V/U”
denotes ratio of vacancies to unemployed (4-quarter or 12-month average).




                                                                                                                                     5
Table 1. Phillips Curve Estimates: Median CPI Inflation

                       (1)           (2)          (3)           (4)
                    Quarterly     Quarterly     Monthly       Monthly
                    1985-2019     1985-2022    1985-2019     1985-2022

V/U                 11.060***      8.232***      9.595**      8.288***
                      (3.651)       (2.386)       (4.302)       (2.429)
(V/U)-squared       -13.295**     -8.815***      -10.949*     -8.947***
                      (5.496)       (2.820)       (6.445)       (2.857)
(V/U)-cubed           5.558**      3.417***        4.475      3.568***
                      (2.536)       (1.013)       (2.963)       (1.014)
H                      0.021         0.013         0.011         0.041
                      (0.068)       (0.075)       (0.073)       (0.074)
H-squared            0.155***      0.087***     0.128***      0.094***
                      (0.041)       (0.018)       (0.035)       (0.020)
H-cubed              0.054***      0.031***     0.053***      0.035***
                      (0.019)       (0.010)       (0.017)       (0.012)
Constant            -3.030***     -2.477***     -2.766***     -2.506***
                      (0.747)       (0.603)       (0.879)       (0.620)

Observations           140           150           420           451
R-squared             0.512         0.701         0.284         0.521
Rbar-squared          0.491         0.689         0.274         0.514

Notes: V/U denotes ratio of vacancies to unemployed (4-quarter or 12-month average). H denotes
headline-inflation shock (4-quarter or 12-month average). Newey-West standard errors with 4 lags
(quarterly data) and 12 lags (monthly data) in parentheses. ***, **, and * denote statistical significance at
the 1,5, and 10 percent level, respectively.
Figure 6. Estimated Inflation Gap as a Function of Slack and Headline-inflation Shocks,
1985-2022
(Percentage points; monthly data)

                     A. Median Inflation Gap vs. V/U
   4




   2




   0




   -2
        0               .5              1               1.5              2
                              V/U (12-month average)


        B. Median Inflation Gap vs. Headline-inflation Shock
   4


   3


   2


   1


   0


   -1

        -4              -2              0                2               4
                               H (12-month average)


Note: Panel A reports fitted values for constant term and V/U terms from equation estimates reported in
Table 1 (column 4). Panel B reports fitted values for headline-inflation shock (H) terms. Bands report 95
percent confidence interval. Inflation gap denotes monthly annualized median CPI inflation minus long-
term Survey of Professional Forecasters inflation expectations.
Figure 7. Predictions for Median Inflation Gap During, 2020-2022
(Percentage points)

                           A. Sample: 1985-2022
   10        Actual
             Fitted values
   8
             Fitted values assuming no headline inflation shocks

   6


   4


   2


   0


   -2
      2020                      2021                      2022


                           B. Sample: 1985-2019
   10        Actual
             Fitted values
   8
             Fitted values assuming no headline inflation shocks

   6


   4


   2


   0


   -2
      2020                      2021                      2022


Note: Figure reports fitted values from Phillips Curve model estimated for the full sample (Table 1 column
4) and for the pre-pandemic sample (Table 1 column 3). Inflation gap denotes monthly annualized median
CPI inflation minus long-term Survey of Professional Forecasters inflation expectations.




                                                                                                        8
Figure 8. Counterfactual Scenario Without American Rescue Plan

                       V/U (monthly)                           V/U (12-month average)
       2            Actual                         2             Actual
                    Counterfactual                               Counterfactual

     1.5                                        1.5


       1                                           1


      .5                                           .5

            2021                     2022               2021                      2022


           Core Inflation (monthly; percent)       Core Inflation (12-month; percent)
     10            Actual                                      Actual
                                               6
                   Counterfactual                              Counterfactual
      8
                                               5
      6
                                               4
      4
                                               3
      2                                        2

           2021                      2022          2021                           2022


Note: Impact of American Rescue Plan on V/U comes from Barnichon, Oliveira, and Shapiro (2021). Core
inflation denotes median CPI inflation. Monthly inflation is annualized. Impact on core inflation derived
from Phillips Curve relation estimated for 1985-2022.




                                                                                                        9
Figure 9. Wage Inflation Gap vs. Ratio of Vacancies to Unemployed

         6


                                    2021q3
         4                                                 2022q2

                          2021q1                      2022q1



 Wage inflation gap
                                             2021q4
                                             2020q1
                              2021q2
                           2020q4




   0           2
                                2020q3

                                    2020q2



         -2                                                    1968-72
                                                               1973-84
                                                               1985-2019
         -4                                                    2020-22

                      0    .5             1             1.5            2
                                         V/U

Note: Wage inflation gap denotes the difference between quarterly wage inflation and long-term expected
inflation. Long-term expected inflation is the ten-year-ahead CPI inflation forecast from the Survey of
Professional Forecasters (SPF). “V/U” denotes ratio of vacancies to unemployed (4-quarter average).




                                                                                                     10
Figure 10. Estimated Wage and Price Inflation Gaps as Functions of Slack and Headline-
inflation Shocks, 1985-2022
(Percentage points; quarterly data)

                             A. Inflation Gap vs. V/U
                    Wage inflation gap            Price inflation gap
   4




   2




   0




   -2
        0               .5                 1              1.5            2
                                V/U (4-quarter average)


             B. Inflation Gap vs. Headline-inflation Shock
                    Wage inflation gap            Price inflation gap
   6



   4



   2



   0



   -2


        -4              -2                 0               2             4
                                 H (4-quarter average)


Note: For price inflation, figure reports fitted values for constant and ratio of vacancies to unemployed
(V/U) terms based on specification reported in Table 1 (column 2) in top panel and fitted values for
headline-inflation shock (H) terms in bottom panel. For wage inflation, figure reports fitted values for
constant, V/U and productivity growth terms based on specification reported in Annex Table 10 (column
2) with productivity growth set at its sample mean. Inflation gap denotes quarterly median CPI inflation or
wage inflation minus long-term Survey of Professional Forecasters inflation expectations. Bands report 95
percent confidence interval.




                                                                                                        11
Table 2. Explaining Headline Inflation Shocks, 2020-2022
(Dependent variable: Headline – Median CPI monthly annualized inflation)

A. Bivariate Regressions
                    (1)          (2)          (3)              (4)        (5)          (6)          (7)             (8)      (9)           (10)
                                                                                                                         Weighted
                                                                       Supplier       FRBNY                 Goods share average of      COVID-19
               Energy price   Food price   Harper                      delivery    Supply Chain Backlogs of    of real  car inflation intervention
                 inflation     inflation Charter Rate    Baltic Dry     times          Index       work     consumption     rates      stringency

Coefficient     0.060***        -0.285       0.001        0.002**      -0.142**       0.487       0.544***        1.746***   0.073***     0.009
                 (0.013)       (0.269)      (0.001)       (0.001)       (0.054)      (0.447)       (0.115)         (0.544)    (0.022)    (0.045)

Observations         31          31           31             31           31            31          31              31         31          31
R-squared          0.632        0.072       0.078          0.208         0.105        0.015        0.440           0.232      0.205      0.002
Rbar-squared       0.619        0.040       0.046          0.180         0.074        -0.020       0.421           0.206      0.178      -0.033

B. Selected Multivariate Regressions

                                                         (1)             (2)              (3)              (4)

Energy price inflation                                0.048***        0.045***        0.054***        0.053***
                                                       (0.011)         (0.010)         (0.008)         (0.008)
Backlogs of work                                      0.336***        0.289***        0.204***        0.200***
                                                       (0.084)         (0.068)         (0.063)         (0.062)
Durable goods share of real consumption                                0.797**                          0.192
                                                                       (0.345)                         (0.228)
Weighted average of car inflation rates                                               0.067***        0.063***
                                                                                       (0.007)         (0.008)
Constant                                              -17.088***      -46.081***     -11.145***       -18.476*
                                                        (4.183)         (14.076)       (3.314)         (9.028)

Observations                                              31              31              31                31
R-squared                                               0.773           0.816           0.920             0.922
Rbar-squared                                            0.757           0.796           0.911             0.910
Note: Relative energy, food, and auto-related price inflation variables are created by subtracting median
inflation from energy, food, and auto-related price inflation respectively, and these are in monthly
annualized terms. Backlogs of work variable is taken from IHS Markit Economics. Robust standard errors
in parentheses. ***, **, and * denote statistical significance at the 1,5, and 10 percent level, respectively.
Figure 11. Explaining Headline-inflation Shocks

A. Actual vs. Fitted Values
 15                                    Actual       Fitted


 10



 5



 0



 -5



 -10

       2020                         2021                           2022


Note: Headline-inflation shocks denote the difference between headline and median CPI inflation. “Fitted”
denotes fitted values of headline-inflation shocks from the regression in Column 3, Table 2.
Figure 11. Explaining Headline-inflation Shocks (Continued)

B. Headline-inflation Shocks vs. Selected Variables

                                                  Energy Prices



                                                                                  100 200 300
    10              Headline-inflation shocks

    5               Energy-price shocks (right)

    0



    -10 -5
                                                                                  -100 0
             2020                               2021                 2022


                                                Backlogs of Work




                                                                                  35 40 45 50 55 60
    10              Headline-inflation shocks

    5               Backlogs of work (right)

    0



    -10 -5

             2020                               2021                 2022


                                               Auto-related Prices
    10              Headline-inflation shocks                                     100
    5               Auto-related price shocks (right)
                                                                                  50
    0
                                                                                  0

    -10 -5
                                                                                  -50
             2020                               2021                 2022



Note: Headline-inflation shocks denote the difference between monthly annualized headline and median
CPI inflation. Energy and auto-related price shocks variables are created by subtracting median inflation
from energy and auto-related price inflation, respectively. These variables are in monthly annualized
terms. Backlogs of work variable is taken from IHS Markit Economics.




                                                                                                        14
Figure 12. Accounting for the Rise in Headline Inflation
(Decomposition of change in 12-month headline CPI inflation from December 2020 to July 2022;
percentage points)


  3.5                                                                                    Headline inflati on shock
                                               2.29
                                                                                         Passthrou gh
  3


  2.5

                                                                1.3 7
  2


  1.5
                              1.04
                                               0.97
  1
                                                                0.6 3             0.58
                0.48
  .5
                                                                                                       0.15
  0


  -.5                                                                            -0.30


        Expected inflatio n   V/U         Energy prices   B acklogs of work   Auto pri ces           Residual

Note: Total rise in 12-month headline inflation is 7.20 percentage points (from 1.28 percent to 8.48
percent). The total rise in 12-month core (median) CPI inflation over this period is 3.92 percentage points
(from 2.34 percent to 6.27 percent). “Expected inflation” denotes change in long-term (SPF) inflation
expectation from December 2020 to July 2022. V/U denotes contribution of change in ratio of vacancies
to unemployed to change in headline CPI inflation. “Energy prices” denotes contribution of relative energy
prices. “Backlogs of work” denotes contribution of change in index from IHS Markit Economics. “Auto
prices” denotes contribution of weighted average of auto-related prices. Based on estimates in Table 1
(column 4) and Table 2B (column 3).




                                                                                                                15
Figure 13. Predictions for Median CPI Inflation Gap During the Pandemic: Comparison
Across Models
  10      Actual
          Fitted values: nonlinear model with V/U
  8       Fitted values: linear model with unemployment rate


  6


  4


  2



  0



  -2
       2020                        2021                          2022

Note: Figure reports predicted values based on monthly equations estimated for 1985-2019 (Table 1,
column 3 and traditional Phillip Curve reported in footnote 14). V/U denotes ratio of vacancies to
unemployed. Inflation gap denotes monthly annualized median CPI inflation minus long-term Survey of
Professional Forecasters inflation expectations.




                                                                                                      16
Figure 14. The Behavior of the Beveridge Curve, 2001-2022

       8                                            April 2020 - June 2022
                                                    July 2009 - March 2020
                                                    December 2001 - June 2009

                 2022m6
       6




  Vacancy rate            2020m12


       4
                                                                       2020m4


       2




       0
                 4           6         8      10              12             14
                                    Unemployment rate

Note: December 2001 – June 2009 covers Great Recession and the preceding expansion, based on
NBER business cycle dates. July 2009 – March 2020 covers the pre-COVID expansion and the first
month of COVID era. Figure reports log-linear curves fitted to each period.




                                                                                                 17
Figure 15. Median CPI Inflation Gap vs. Unemployment Rate for Different Beveridge
Curves

                                          Based on pandemic Beveridge curve
        10                                Based on pre-pandemic Beveridge curve


        8




  Inflation gap

       4       6

        2


        0


        -2
                   3   4        5      6      7       8                  9         10
                                    Unemployment rate

Note: Inflation gap denotes monthly annualized median CPI inflation minus long-term SPF inflation
expectations. Curves are derived from the estimates of the Phillips curve (Table 1 column 4) and the
Beveridge curves reported in footnote 18.




                                                                                                       18
Figure 16. Actual and Fitted Inflation Expectations
 5                                 Actual           Fitted

 4.5

 4

 3.5

 3

 2.5

 2

 1.5     γ = 0.944               γ = 1.003             γ = 0.991          γ = 0.980

 1
       1985    1990     1995     2000        2005      2010        2015    2020

Note: Figure reports actual values of long-term CPI inflation expectations from the Survey of Professional
Forecasters (SPF) and fitted values for several periods from the partial-adjustment model described in the
text. The parameter γ indicates the degree of anchoring of inflation expectations in each period.




                                                                                                       19
Figure 17. Scenarios for Core CPI Inflation Conditional on June 2022 FOMC Unemployment
Forecasts
(12-month; percent)
    11          Pessim. BC, expectations revert

   10           Pessim. BC, expectations drift (γ=0.98)
                Pessim. BC, expectations drift (γ=0.94)
     9          Optim. BC, expectations revert
                                                                        8.82
                Optim. BC, expectations drift (γ=0.98)
     8
                Optim. BC, expectations drift (γ=0.94)
     7
     6
     5
     4
     3
                                                                        2.75
     2
     1

         2020          2021            2022               2023   2024     2025

Note: Unemployment forecast from the Summary of Economic Projections of the Federal Open Market
Committee (FOMC) published in June 2022 which provides numbers for the fourth quarters of 2022,
2023, and 2024. We assign those forecasts to November of each year and interpolate a monthly
unemployment series starting from the actual value of 3.5 percent in July 2022. Vertical line indicates July
2022. Core inflation denotes CPI median inflation. Horizontal dashes show 2.5 percent target for median
CPI based on 2 percent PCE target as reported on Federal Reserve Bank of Atlanta Underlying Inflation
Dashboard.




                                                                                                         20
Figure 18. Scenario Conditional on June 2022 FOMC Unemployment Forecasts with Pessimistic
Beveridge Curve and Drifting Expectations (γ = 0.98)

                  Unemployment                                                       Beveridge Curve
                                                                8
    14                                                                            2022m8
                                                                                    2024m12
    12

                                                           Vacancy rate
    10


                                                          2     4      6
     8
     6
     4
                                                                0

          2020   2021   2022      2023      2024   2025                        4       6   8    10 12                 14
                                                                                       Unemployment rate


                              V/U                                          Headline Inflation Shocks
      2                                                         10

    1.5                                                             5

      1                                                             0

     .5                                                          -5
                                         Monthly                                                            Monthly
                                                              -10
      0                                  12-month avg.                                                      12-month avg.


          2020   2021      2022   2023      2024   2025                    2020      2021     2022   2023      2024   2025


                    Core Inflation                                                  Expected Inflation
    12           Monthly
                                                               12
    10           12-month                                      10
     8                                                            8
     6                                                            6
     4                                                            4
     2                                                            2
     0                                                            0

          2020   2021   2022      2023      2024   2025                 2020        2021      2022   2023      2024    2025



Note: Figure reports scenario with COVID-era Beveridge Curve and drifting expectations (γ = 0.98).
Observations up to July 2022 in blue; projections thereafter in red. Core inflation denotes CPI median
inflation.




                                                                                                                              21
Figure 19. Scenarios for Core CPI Inflation Conditional on Alternative Unemployment Paths
(12-month; percent)

                    A. Conditional on IMF Staff Unemployment Path
     11          Pessim. BC, expectations revert
     10          Pessim. BC, expectations drift (γ=0.98)

      9          Pessim. BC, expectations drift (γ=0.94)
                 Optim. BC, expectations revert
      8
                 Optim. BC, expectations drift (γ=0.98)
      7
                 Optim. BC, expectations drift (γ=0.94)
      6
      5
                                                                         4.92
      4
      3
      2                                                                  2.34

      1

          2020          2021              2022             2023   2024     2025


                      B. Conditional on Higher Unemployment Path
     11          Pessim. BC, expectations revert
     10          Pessim. BC, expectations drift (γ=0.98)

      9          Pessim. BC, expectations drift (γ=0.94)
                 Optim. BC, expectations revert
      8
                 Optim. BC, expectations drift (γ=0.98)
      7
                 Optim. BC, expectations drift (γ=0.94)
      6
      5
      4
                                                                         3.24
      3
      2
      1                                                                  1.60



          2020          2021              2022             2023   2024     2025


Note: Vertical line indicates July 2022. Core inflation denotes CPI median inflation. IMF staff forecast for
the quarterly path of unemployment underlying the 2022 IMF Article IV Staff Report. Quarterly forecasts
are allocated to the second month of each quarter and a monthly path is obtained via interpolation.
“Higher unemployment” path assumes 7.5 percent unemployment during 2023 and 2024 as suggested by
Summers (2022b). In this scenario, the unemployment rate rises linearly from its July 2022 level to 7.5
percent in January 2023 and remains at that level through December 2024. Horizontal dashes show 2.5
percent target for median CPI based on 2 percent PCE target reported on Federal Reserve Bank of
Atlanta Underlying Inflation Dashboard.




                                                                                                         22
                ONLINE APPENDIX

“Understanding U.S. Inflation During the COVID Era”

    Laurence Ball, Daniel Leigh, and Prachi Mishra

                  August 25, 2022
Alternative Measures of Core Inflation

Here we examine the robustness of our results to two alternative measures of core inflation,
median PCE Inflation (from the Federal Reserve Bank of Cleveland) and trimmed mean PCE
inflation (from the Federal Reserve Bank of Dallas). We find that the results are similar to those
obtained with median CPI inflation.




                                                                                                     2
Table 1A. Phillips Curve Estimates: Median PCE Inflation
                       (1)          (2)           (3)           (4)
                    Quarterly    Quarterly      Monthly       Monthly
                    1985-2019    1985-2022     1985-2019     1985-2022

V/U                   6.821*       6.639***       5.344        8.684***
                      (3.472)       (1.871)      (3.925)        (2.206)
(V/U)-squared          -7.555     -7.510***      -5.335      -10.942***
                      (5.410)       (2.317)      (6.011)        (2.907)
(V/U)-cubed            2.953       3.053***       1.954        4.838***
                      (2.527)       (0.840)      (2.785)        (1.141)
H                      0.129         0.119        0.091          0.189
                      (0.113)       (0.096)      (0.128)        (0.124)
H-squared              0.144       0.169***      0.146*        0.133***
                      (0.099)       (0.029)      (0.084)        (0.040)
H-cubed                0.035        0.046**       0.049          0.026
                      (0.034)       (0.020)      (0.033)        (0.032)
Constant            -1.837***     -1.797***     -1.564**      -2.128***
                      (0.618)       (0.418)      (0.718)        (0.467)

Observations           140           150           420          450
R-squared             0.308         0.575         0.157        0.389
Rbar-squared          0.277         0.557         0.145        0.381

Notes: V/U denotes ratio of vacancies to unemployed (4-quarter or 12-month average). H denotes
headline-inflation shock (4-quarter or 12-month average). Newey-West standard errors with 4 lags
(quarterly data) and 12 lags (monthly data) in parentheses. ***, **, and * denote statistical significance at
the 1,5, and 10 percent level, respectively.




                                                                                                                3
Figure 6A. Estimated PCE Inflation Gap as a Function of Slack and Headline-inflation
Shocks, 1985-2022
(Percentage points; monthly data)

                A. PCE Median Inflation Gap vs. V/U
   6



   4



   2



   0



   -2
        0             .5                  1              1.5        2
                                V/U (12-month average)


    B. PCE Median Inflation Gap vs. Headline-inflation Shock
  3



  2



  1



  0



  -1

        -4                 -2                    0             2
                                H (12-month average)


Note: Panel A reports fitted values for constant term and V/U terms from equation estimates reported in
Table 1A (column 4). Panel B reports fitted values for headline-inflation shock (H) terms. Bands report 95
percent confidence interval. Inflation gap denotes monthly annualized median PCE inflation minus long-
term Survey of Professional Forecasters inflation expectations.




                                                                                                         4
Figure 7A. Predictions for PCE Median Inflation Gap During 2020-2022
(Percentage points)

                             A. Sample: 1985-2022
   10          Actual
               Fitted values
   8           Fitted values assuming no headline inflation shocks

   6


   4


   2


   0


   -2
        2020                      2021                      2022


                             B. Sample: 1985-2019
   10          Actual
               Fitted values
   8           Fitted values assuming no headline inflation shocks

   6


   4


   2


   0


   -2
        2020                      2021                      2022



Note: Figure reports fitted values from Phillips Curve model with PCE Median estimated for the full
sample (Table 1A column 4) and for the pre-pandemic sample (Table 1A column 3).




                                                                                                      5
Table 1B. Phillips Curve Estimates: Trimmed Mean PCE Inflation

                       (1)          (2)           (3)           (4)
                    Quarterly    Quarterly      Monthly       Monthly
                    1985-2019    1985-2022     1985-2019     1985-2022

V/U                  6.854**        4.080*         5.804       5.432**
                      (3.404)       (2.179)       (3.742)      (2.232)
(V/U)-squared          -8.068       -3.672         -6.508     -5.857**
                      (5.187)       (2.724)       (5.616)      (2.866)
(V/U)-cubed            3.317         1.236         2.632       2.335**
                      (2.384)       (1.026)       (2.559)      (1.110)
H                    0.333***      0.259***      0.307***     0.316***
                      (0.098)       (0.098)       (0.109)      (0.102)
H-squared              0.091       0.117***        0.098      0.110***
                      (0.102)       (0.022)       (0.095)      (0.022)
H-cubed                -0.020        0.006        -0.005        -0.003
                      (0.037)       (0.019)       (0.036)      (0.019)
Constant            -2.141***     -1.647***     -1.947***    -1.898***
                      (0.647)       (0.501)       (0.732)      (0.504)

Observations           140           150           420          450
R-squared             0.307         0.526         0.156        0.347
Rbar-squared          0.276         0.506         0.144        0.338

Notes: “V/U” denotes ratio of vacancies to unemployed (4-quarter or 12-month average). “H” denotes
headline-inflation shock (4-quarter or 12-month average). Newey-West standard errors with 4 lags
(quarterly data) and 12 lags (monthly data) in parentheses. ***, **, and * denote statistical significance at
the 1,5, and 10 percent level, respectively.




                                                                                                                6
Figure 6B. Estimated Trimmed mean PCE Inflation Gap as a Function of Slack and
Headline-inflation Shocks, 1985-2022
(Percentage points; monthly data)

             A. Trimmed Mean PCE Inflation Gap vs. V/U
   3


   2


   1


   0


   -1


   -2
        0             .5              1              1.5            2
                            V/U (12-month average)


             B. Trimmed Mean PCE Inflation Gap vs. H
   3



   2



   1



   0



   -1
        -4            -2              0              2              4
                             H (12-month average)



Note: Panel A reports fitted values for constant term and V/U terms from equation estimates reported in
Table 1B (column 4). Panel B reports fitted values for headline-inflation shock (H) terms. Bands report 95
percent confidence interval. Inflation gap denotes monthly annualized trimmed mean PCE inflation minus
long-term Survey of Professional Forecasters inflation expectations.




                                                                                                         7
Figure 7B. Predictions for Trimmed Mean PCE Inflation Gap During 2020-2022
(Percentage points)


                             A. Sample: 1985-2022
   10          Actual
               Fitted values
   8           Fitted values assuming no headline inflation shocks

   6


   4


   2


   0


   -2
        2020                      2021                      2022


                             B. Sample: 1985-2019
   10          Actual
               Fitted values
   8           Fitted values assuming no headline inflation shocks

   6


   4


   2


   0


   -2
        2020                      2021                      2022


Note: Figure reports fitted values from Phillips Curve model with trimmed mean PCE estimated for the full
sample (Table 1B column 4) and for the pre-pandemic sample (Table 1B column 3).




                                                                                                        8
Measuring Inflation Expectations with University of Michigan Five-year-ahead CPI
Inflation Expectations

Here we examine another common measure of inflation expectations, the five-year-ahead
forecast from the Michigan Survey of Consumers. We find that the results are similar to those
for the 10-year-ahead expectations from the Survey of Professional Forecasters.




                                                                                                9
Figure 2c. 5-year-ahead CPI Inflation Expectations and Median CPI Inflation, 2000-2022
  8         Weighted-median inflation
            Michigan five-year-ahead expectations



  6




  4




  2




  0
     2000            2005           2010            2015            2020

Note: Figure reports five-year-ahead CPI inflation forecasts from the University of Michigan Survey of
Consumers.




                                                                                                         10
Table 1C. Phillips Curve Estimates: Median CPI Inflation. Michigan 5-year-ahead Instead
of SPF 10-year-ahead Inflation Expectations

                       (1)          (2)           (3)           (4)
                    Quarterly    Quarterly      Monthly       Monthly
                    1985-2019    1985-2022     1985-2019     1985-2022

V/U                  14.107***     9.674***    12.405***     10.176***
                       (3.288)      (2.236)      (4.058)        (2.287)
(V/U)-squared       -17.868***   -10.780***    -14.869**     -11.405***
                       (5.088)      (2.787)      (6.168)        (2.781)
(V/U)-cubed           7.624***     4.237***     6.133**        4.548***
                       (2.376)      (1.051)      (2.853)        (1.017)
H                        0.018       -0.028       0.038          0.020
                       (0.055)      (0.061)      (0.064)        (0.060)
H-squared              0.075**     0.057***      0.054*        0.064***
                       (0.038)      (0.015)      (0.033)        (0.019)
H-cubed                 0.030*     0.032***       0.027        0.035***
                       (0.016)      (0.010)      (0.018)        (0.010)
Constant             -3.824***    -3.027***    -3.561***      -3.173***
                       (0.649)      (0.540)      (0.813)        (0.566)

Observations           140           150           420          451
R-squared             0.603         0.741         0.315        0.528
Rbar-squared          0.585         0.730         0.305        0.522

Notes: “V/U” denotes ratio of vacancies to unemployed (4-quarter or 12-month average). “H” denotes
headline-inflation shock (4-quarter or 12-month average). Newey-West standard errors with 4 lags
(quarterly data) and 12 lags (monthly data) in parentheses. ***, **, and * denote statistical significance at
the 1,5, and 10 percent level, respectively.




                                                                                                            11
Figure 6C. Estimated Inflation Gap as a Function of Slack and Headline-inflation Shocks,
1985-2022. Michigan 5-year-ahead expectations (instead of SPF 10-year)
(Percentage points; monthly data)

                   A. Median Inflation Gap vs. V/U
   6



   4



   2



   0



   -2

        0             .5              1              1.5            2
                            V/U (12-month average)


        B. Median Inflation Gap vs. Headline Inflation Shock
   3


   2


   1


   0


   -1


   -2
        -4            -2              0              2              4
                             H (12-month average)



Note: Panel A reports fitted values for constant term and V/U terms from equation estimates reported in
Table 1C (column 4). Panel B reports fitted values for headline-inflation shock (H) terms. Bands report 95
percent confidence interval. Inflation gap denotes monthly annualized median CPI inflation minus 5-year
ahead inflation expectations from the Michigan Survey of Consumers.




                                                                                                        12
Figure 7C. Predictions for Median Inflation Gap During 2020-2022. Michigan 5-year-ahead
(instead of SPF 10-year)
(Percentage points)

                             A. Sample: 1985-2022
   10          Actual
               Fitted values
   8           Fitted values assuming no headline inflation shocks

   6


   4


   2


   0


   -2
        2020                      2021                      2022


                             B. Sample: 1985-2019
   10          Actual
               Fitted values
   8           Fitted values assuming no headline inflation shocks

   6


   4


   2


   0


   -2
        2020                      2021                      2022



Note: Figure reports fitted values from Phillips Curve model with five-year-ahead inflation expectations
from the Michigan Survey of Consumers estimated for the full sample (Table 1C column 4) and for the
pre-pandemic sample (Table 1C column 3).




                                                                                                           13
Measuring Labor Markets Conditions with the Unemployment Gap

Here we measure labor market conditions with the difference between the unemployment rate
and its natural rate from the CBO. With the unemployment gap, the fit of our Phillips curve is
somewhat worse. For example, with monthly pre-pandemic data, the Rbar-squared is 0.27 and
0.25 for V/U and ugap respectively. For the full sample through 2022, the corresponding
numbers are 0.51 and 0,46 respectively. In a horse race with both measures of labor market
conditions, both are statistically significant. However, once V/U is included, the increase in
Rbar-squared from including ugap is small. For example, for monthly data, for the full sample,
the increase is only 0.005. In contrast, when the ugap is included, adding V/U increases Rbar-
squared by 0.055.




                                                                                             14
Table 1D. Phillips Curve Estimates with Quarterly Data: U-U* vs. V/U
                          (1)         (2)         (3)         (4)                (5)           (6)
                       1985-2019 1985-2022 1985-2019 1985-2022                1985-2019     1985-2022

    U-U*                 -0.381***    -0.407***                                  -0.379*     -0.308*
                           (0.103)      (0.102)                                  (0.213)      (0.159)
    (U-U*)-squared          0.154*      0.145*                                 0.279***       0.158*
                           (0.083)      (0.079)                                  (0.097)      (0.095)
    (U-U*)-cubed            -0.027       -0.023                                 -0.031**       -0.022
                           (0.017)      (0.016)                                  (0.014)      (0.016)
    H                      -0.130*      -0.150*        0.021        0.013         0.021        -0.059
                           (0.075)      (0.077)       (0.068)      (0.075)       (0.075)      (0.083)
    H-squared             0.192***     0.141***      0.155***     0.087***      0.132***    0.113***
                           (0.033)      (0.022)       (0.041)      (0.018)       (0.038)      (0.021)
    H-cubed               0.091***     0.072***      0.054***     0.031***       0.041**    0.047***
                           (0.018)      (0.010)       (0.019)      (0.010)       (0.020)      (0.014)
    V/U                                             11.060***     8.232***     28.219***    8.980***
                                                      (3.651)      (2.386)       (7.470)      (2.925)
    (V/U)-squared                                   -13.295**    -8.815***    -38.100***   -10.907***
                                                      (5.496)      (2.820)      (11.050)      (3.465)
    (V/U)-cubed                                      5.558**      3.417***     16.136***    4.267***
                                                      (2.536)      (1.013)       (4.890)      (1.212)
    Constant               -0.074       -0.035      -3.030***    -2.477***     -6.597***    -2.359***
                          (0.081)       (0.074)       (0.747)      (0.603)       (1.560)      (0.777)

    Observations            140           150          140          150           140          150
    R-squared              0.489         0.672        0.512        0.701         0.586        0.721
    Rbar-squared           0.466         0.659        0.491        0.689         0.558        0.703


Notes: “U-U*” denotes gap between unemployment rate and Congressional Budget Office estimate of
natural rate (4-quarter or 12-month average). “V/U” denotes ratio of vacancies to unemployed (4-quarter
or 12-month average). “H” denotes headline-inflation shock (4-quarter or 12-month average). Newey-
West standard errors with 4 lags (quarterly data) and 12 lags (monthly data) in parentheses. ***, **, and *
denote statistical significance at the 1,5, and 10 percent level, respectively.




                                                                                                         15
Table 1D (Continued). Phillips Curve Estimates with Monthly Data: U-U* vs. V/U
                      (1)         (2)         (3)        (4)         (5)       (6)
                  1985-2019 1985-2022 1985-2019 1985-2022 1985-2019 1985-2022

U-U*                 -0.402***    -0.423***                                   -0.320      -0.225
                       (0.095)      (0.096)                                  (0.195)      (0.139)
(U-U*)-squared        0.145**       0.139*                                 0.279***         0.128
                       (0.073)      (0.071)                                  (0.090)      (0.089)
(U-U*)-cubed            -0.023      -0.021                                  -0.030**       -0.017
                       (0.015)      (0.015)                                  (0.013)      (0.015)
H                       -0.131      -0.111         0.011        0.041          0.041       -0.008
                       (0.080)      (0.074)       (0.075)      (0.068)       (0.076)      (0.073)
H-squared             0.142***     0.148***      0.128***     0.094***      0.107***     0.108***
                       (0.031)      (0.029)       (0.033)      (0.019)       (0.030)      (0.022)
H-cubed               0.079***     0.074***      0.053***     0.035***       0.036**     0.045***
                       (0.019)      (0.013)       (0.019)      (0.011)       (0.018)      (0.012)
V/U                                               9.595**     8.288***    29.995***    10.166***
                                                  (3.796)      (1.993)       (7.320)      (3.184)
(V/U)-squared                                    -10.949*    -8.947***    -39.678***   -12.009***
                                                  (5.751)      (2.399)      (10.639)      (3.727)
(V/U)-cubed                                       4.475*     3.568***     16.642***     4.753***
                                                  (2.670)      (0.877)       (4.701)      (1.300)
Constant               -0.047       -0.025      -2.766***    -2.506***     -7.204***    -2.789***
                      (0.072)       (0.068)       (0.761)      (0.499)       (1.593)      (0.855)

Observations            420          451           420          451           420          451
R-squared              0.259        0.472         0.284        0.521         0.329        0.528
Rbar-squared           0.248        0.464         0.274        0.514         0.315        0.519


Notes: “U-U*” denotes gap between unemployment rate and Congressional Budget Office estimate of
natural rate (4-quarter or 12-month average). “V/U” denotes ratio of vacancies to unemployed (4-quarter
or 12-month average). “H” denotes headline-inflation shock (4-quarter or 12-month average). Newey-
West standard errors with 4 lags (quarterly data) and 12 lags (monthly data) in parentheses. ***, **, and *
denote statistical significance at the 1,5, and 10 percent level, respectively.




                                                                                                         16
Contemporaneous V/U Instead of 4-quarter or 12-month Average

Here we consider the relation between the median CPI inflation gap and the current level of V/U
instead of the 4-quarter or 12-month average reported in the text. In the scatter plot, we see a
strong positive relationship with the inflation gap, but the recent observations are more of an
outlier compared to the past. For the Phillips curve equations, the coefficient estimates are
similar but the R-bar-squared statistic is lower. For monthly data with the full sample, the R-bar-
squared is 0.473, compared with 0.514 reported in Table 1 Column 4 of the text.




                                                                                                 17
      Figure 3A. Inflation Gap vs. Ratio of Contemporaneous Vacancies to Unemployed (V/U)

                                        Quaterly Data                                                           Monthly Data
                10                                            1968-72             15
                                                              1973-84
                                                              1985-2019
                                                              2020-22
                                                                                  10


                5                                                                                                                           2022m6
                                                                   2022q2
                                                                  2022q1
                                                                                                                                       2022m1
                                                                                                                                            2022m5

                                                                             Inflation gap
                                                             2021q4                                                              2021m10 2022m2
                                                                                                                                              2022m4
                                                                                                                                           2022m7



      Inflation gap
                                                                                                                                    2021m11 2022m3
                                                                                                                               2021m9    2021m12
                                                                                                       2020m7               2020m1
                                                                                                                       2021m6
                                                                                                                       2021m52021m8
                                                                            0             5
                                                   2021q3
                               2020q3
                                              2020q1
                                            2021q2
                                                                                                   2020m5
                                                                                                         2020m8      2021m42020m2
                                                                                                                  2020m3
                                                                                                                 2021m2     2021m7
                          2020q2                                                                     2020m62020m10
                                                                                                  2020m4           2021m3
                                                                                                             2020m12
                                                                                                               2021m1
                                                                                                          2020m9
                0                      2021q1
                                   2020q4                                                                    2020m11




                                                                                  -5
                                                                                                                                        1968-72
                                                                                                                                        1973-84
                -5                                                                                                                      1985-2019

                                                                                  -10                                                   2020-22

                      0          .5              1          1.5         2                     0            .5           1             1.5            2
                                                V/U                                                                    V/U


Note: Figure reports quarterly and monthly scatter plots of the inflation gap against the current level of
V/U. Inflation gap is the difference between median and long-term expected inflation. Long-term expected
inflation 10-year-ahead CPI inflation forecasts from the Survey of Professional Forecasters (SPF). “V/U”
denotes contemporaneous (instead of 4-quarter or 12-month average) ratio of vacancies to unemployed.




                                                                                                                                                         18
Table 1E. Phillips Curve Estimates: Median CPI Inflation. Contemporaneous V/U

                         (1)            (2)             (3)            (4)
                      Quarterly      Quarterly        Monthly        Monthly
                      1985-2019      1985-2022       1985-2019      1985-2022

V/U                   13.381***        7.845***      13.028***       6.720***
                         (3.254)        (2.090)        (3.354)        (2.085)
(V/U)-squared         -17.072***      -8.073***     -16.335***      -6.328***
                         (4.896)        (2.341)        (5.010)        (2.340)
(V/U)-cubed             7.266***       2.830***       6.870***       2.146***
                         (2.230)        (0.746)        (2.271)        (0.755)
H                         0.044          0.019          0.048          0.063
                         (0.070)        (0.084)        (0.077)        (0.088)
H-squared               0.177***       0.087***       0.158***       0.105***
                         (0.044)        (0.025)        (0.034)        (0.023)
H-cubed                 0.042**          0.015        0.038**          0.016
                         (0.020)        (0.013)        (0.018)        (0.015)
Constant               -3.433***      -2.373***      -3.397***      -2.215***
                         (0.651)        (0.540)        (0.682)        (0.543)

Observations              140            150            420             451
R-squared                0.482          0.657          0.278           0.480
Rbar-squared             0.458          0.642          0.267           0.473


Notes: “V/U” denotes contemporaneous ratios of vacancies to unemployed. “H” denotes headline-inflation
shock (4-quarter or 12-month average). Newey-West standard errors with 4 lags (quarterly data) and 12
lags (monthly data) in parentheses. ***, **, and * denote statistical significance at the 1,5, and 10 percent
level, respectively.




                                                                                                          19
Headline Shocks Averaged over Shorter Periods

Here we experiment with headline inflation shocks averaged over shorter periods (one, three,
and six months) instead of 12 months as in Text Table 1. We find that these shorter averages
explain core (median) inflation less well.




                                                                                               20
Table 1F. Phillips Curve Estimates: Median CPI Inflation. Headline-inflation Shocks Over Different Horizons


                       (1)          (2)          (3)          (4)          (5)           (6)           (7)          (8)
                   1985-2019    1985-2022     1985-2019    1985-2022    1985-2019     1985-2022    1985-2019    1985-2022
                    1 month      1 month      3 months     3 months     6 months      6 months     12 months    12 months

V/U                  7.998*       7.773**      8.135*       7.683**       9.303**      7.612**      9.595**     8.288***
                     (4.680)       (3.277)     (4.626)       (3.280)       (4.469)      (3.194)      (4.302)      (2.429)
(V/U)-squared         -8.640      -8.886**      -8.887      -8.749**      -10.620      -8.395**     -10.949*    -8.947***
                     (6.867)       (4.169)     (6.786)       (4.190)       (6.577)      (4.015)      (6.445)      (2.857)
(V/U)-cubed            3.438      4.052***       3.567      3.981***        4.376      3.684**        4.475     3.568***
                     (3.111)       (1.515)     (3.074)       (1.531)       (2.989)      (1.476)      (2.963)      (1.014)
H                      0.013       0.038*        0.027        0.164         0.070        0.124        0.011        0.041
                     (0.016)       (0.020)     (0.105)       (0.121)       (0.080)      (0.093)      (0.073)      (0.074)
H-squared            0.005**       0.004**    0.236***     0.248***      0.215***     0.187***     0.128***      0.094***
                     (0.002)       (0.002)     (0.066)       (0.061)       (0.070)      (0.045)      (0.035)      (0.020)
H-cubed              0.000**        0.000     0.099***     0.088***      0.059***     0.046***     0.053***      0.035***
                     (0.000)       (0.000)     (0.021)       (0.023)       (0.021)      (0.017)      (0.017)      (0.012)
Constant            -2.382**     -2.309***    -2.409**     -2.304***     -2.680***    -2.350***    -2.766***    -2.506***
                     (0.985)       (0.771)     (0.976)       (0.770)       (0.941)      (0.766)      (0.879)      (0.620)

Observations          420           451          420          451           420          451          420          451
R-squared            0.255         0.437        0.271        0.449         0.269        0.465        0.284        0.521
Rbar-squared         0.244         0.430        0.260        0.442         0.259        0.458        0.274        0.514

Notes: “V/U” denotes ratio of vacancies to unemployed (12-month average). “H” denotes headline-inflation shock (12-month average). Newey-
West standard errors with 12 lags in parentheses. ***, **, and * denote statistical significance at the 1,5, and 10 percent level, respectively.
Core Inflation Measured by CPI Inflation Excluding Food and Energy
Here we report a version of the regressions in Table 1 in the text with core inflation measured by
CPI inflation excluding food and energy (XFE). Headline shocks are the deviations of headline
inflation from XFE inflation, which are determined by changes in the relative price of food and
energy. We find no evidence of a pass-through from past headline-inflation shocks into core
inflation—a result that we attribute to the flawed measure of core— we find headline-inflation
shocks to be jointly insignificant in all specifications in contrast to the strong joint significance
when we use median CPI inflation.
Table 1G. Phillips Curve Estimates: CPI Inflation Excluding Food and Energy

                       (1)          (2)           (3)           (4)
                    Quarterly    Quarterly      Monthly       Monthly
VARIABLES           1985-2019    1985-2022     1985-2019     1985-2022

V/U                     3.867      8.894**         2.550      8.735**
                      (4.098)       (3.473)      (4.522)       (4.166)
(V/U)-squared          -2.705     -10.836**       -0.461      -10.241*
                      (6.359)       (4.893)      (6.994)       (5.687)
(V/U)-cubed             0.472      4.659**        -0.643      4.250**
                      (2.988)       (1.903)      (3.295)       (2.160)
H                      -0.063         0.218       -0.073         0.244
                      (0.090)       (0.201)      (0.100)       (0.221)
H-squared               0.026         0.053        0.009         0.054
                      (0.030)       (0.046)      (0.026)       (0.047)
H-cubed                 0.026        -0.015        0.025        -0.014
                      (0.018)       (0.033)      (0.016)       (0.034)
Constant             -1.603**     -2.546***       -1.377     -2.552***
                      (0.779)       (0.683)      (0.880)       (0.834)

Observations           140           150           420          451
R-squared             0.216         0.315         0.077        0.149
Rbar-squared          0.181         0.286        0.0632        0.137


Notes: “V/U” denotes ratio of vacancies to unemployed (4-quarter or 12-month average). “H” denotes
headline-inflation shock (4-quarter or 12-month average). Newey-West standard errors with 4 lags
(quarterly data) and 12 lags (monthly data) in parentheses. ***, **, and * denote statistical significance at
the 1,5, and 10 percent level, respectively.




                                                                                                            23
Wage Phillips Curve
Here we show estimates of the wage Phillips curve equation which are used to generate Figure
10 reported in the text. Given the lack of evidence of non-linearity in V/U in this case, we also
consider a specification in which the effect of V/U is assumed to be linear.




                                                                                               24
Table 10. Wage Phillips Curve Estimates

                                                 (1)          (2)          (3)           (4)
                                              1985-2019    1985-2022    1985-2019     1985-2022

V/U                                             -4.334        1.640      2.017***     2.070***
                                               (3.201)       (2.736)      (0.241)      (0.224)
(V/U)-squared                                  9.845*         0.784
                                               (5.062)       (3.371)
(V/U)-cubed                                    -4.572*        -0.400
                                               (2.408)       (1.220)
H                                               -0.148        -0.084       -0.082       -0.080
                                               (0.125)       (0.130)       (0.120)      (0.119)
H-squared                                       -0.030         0.031        -0.031       0.027
                                               (0.059)       (0.032)       (0.061)      (0.028)
H-cubed                                          0.037     0.056***         0.026     0.053***
                                               (0.027)       (0.020)       (0.027)      (0.018)
Trend pty growth, 4-quarter avg.              0.527***      0.366**      0.507***     0.367***
                                               (0.115)       (0.162)       (0.101)      (0.136)
Constant                                       -0.912*     -1.736***     -2.055***    -1.797***
                                               (0.511)       (0.442)       (0.288)      (0.357)

Observations                                     140          150           140          150
R-squared                                       0.403        0.442         0.394        0.441
Rbar-squared                                    0.372        0.414         0.371        0.422

Notes: “V/U” denotes ratio of vacancies to unemployed (4-quarter average). “H” denotes headline-inflation
shock (4-quarter average). Trend productivity growth measured using output per hour in the non-farm
business sector smoothed with the Hodrick-Prescott filter with λ = 16,000. Newey-West standard errors
with 4 lags in parentheses. ***, **, and * denote statistical significance at the 1,5, and 10 percent level,
respectively.




                                                                                                         25
Table 2A.

Here we estimate the drivers of headline-inflation shocks in the pre-pandemic period, with the
start date of the sample in each column depending on availability of data. The energy-price and
auto-price variables also help explain headline shocks before the pandemic, but backlogs do
not. Food-price inflation is significant before the pandemic but not during the pandemic




                                                                                             26
Table 2A. Explaining Headline-inflation Shocks Before 2020
(Dependent variable: Headline – Median CPI monthly annualized inflation)

A. Bivariate Regressions
                           (1)          (2)               (3)               (4)         (5)          (6)           (7)          (8)         (9)
                                                                                                                             Durable    Weighted
                                                                                      Supplier      FRBNY                  goods share average of
                   Energy price     Food price   Harper                               delivery   Supply Chain Backlogs of     of real  car inflation
                     inflation       inflation Charter Rate              Baltic Dry    times         Index       work     consumption      rates

                      0.068***      0.189***           0.001**           0.000***     -0.151*     1.603***        0.061      0.159***     0.104**
                       (0.007)       (0.011)           (0.001)            (0.000)     (0.091)      (0.510)       (0.121)      (0.041)     (0.042)

Observations            720            720                228              410          152          264          123          720          263
Start of sample       1960m1         1960m1            2001m1            1985m1       2007m5       1998m1      2009m10       1960m1       1998m2
R-squared              0.503          0.170              0.026            0.041        0.020        0.061        0.001        0.014        0.021
Rbar-squared           0.502          0.169             0.0221           0.0391       0.0134       0.0571      -0.00694      0.0131       0.0171

B. Selected Multivariate Regressions
                                                 (1)               (2)

    Food price inflation                      0.186***           0.131***
                                               (0.009)            (0.027)
    Energy price inflation                    0.068***           0.069***
                                               (0.007)            (0.009)
    Weighted average of car inflation rates                      0.089***
                                                                  (0.020)
    Constant                                   -0.151**         -0.807***
                                                (0.063)           (0.123)

    Observations                                 720              263
    Start of sample                            1960m1           1998m2
    R-squared                                   0.667            0.794
    Rbar-squared                                0.666            0.792

Note: Relative energy, food, and auto-related price inflation variables are created by subtracting median inflation from energy, food, and auto-
related price inflation respectively, and these are in monthly annualized terms. Backlogs of work variable is taken from IHS Markit Economics.
Robust standard errors in parentheses. ***, **, and * denote statistical significance at the 1,5, and 10 percent level, respectively.
Simulations of Core (Median) PCE Inflation
Here we report simulations of future core inflation as measured by median PCE inflation as the
measure of core inflation, instead of median CPI inflation. These simulations use the Phillips
curve for median PCE inflation in Table 1A column 4 and the same equations for the Beveridge
curve and inflation expectations as in the text. The results are similar to those obtained for
median CPI inflation.
Figure 17A. Scenarios for Core (Median) PCE Inflation Conditional on June 2022 FOMC
Unemployment Forecasts
(12-month; percent)

    13           Pessim. BC, expectations revert
    12           Pessim. BC, expectations drift (γ=0.98)
                                                                                   11.39
    11           Pessim. BC, expectations drift (γ=0.94)
                 Optim. BC, expectations revert
    10
                 Optim. BC, expectations drift (γ=0.98)
      9          Optim. BC, expectations drift (γ=0.94)

      8
      7
      6
      5
      4
      3
                                                                                    2.84
      2
      1

          2020          2021            2022               2023        2024            2025

Note: Unemployment forecast from the Summary of Economic Projections of the Federal Open Market
Committee (FOMC) published in June 2022 which provides numbers for the fourth quarters of 2022,
2023, and 2024. We assign those forecasts to November of each year and interpolate a monthly
unemployment series starting from the actual value of 3.5 percent in July 2022. Vertical line indicates
June 2022. Core inflation denotes PCE median inflation. Horizontal dashes indicate assumed 2.4 percent
target for median PCE inflation based on 2 percent PCE target and 0.4 percentage point gap between the
median PCE inflation and PCE inflation excluding food and energy following approach on Federal
Reserve Bank of Atlanta Underlying Inflation Dashboard.




                                                                                                    29
Figure 18A. Scenarios for Core (Median) PCE Inflation Conditional on Alternative Unemployment
Paths
(12-month; percent)

                    A. Conditional on IMF Staff Unemployment Path
     13          Pessim. BC, expectations revert
     12          Pessim. BC, expectations drift (γ=0.98)
     11          Pessim. BC, expectations drift (γ=0.94)
     10          Optim. BC, expectations revert
      9          Optim. BC, expectations drift (γ=0.98)
      8          Optim. BC, expectations drift (γ=0.94)
      7
      6                                                                  5.43
      5
      4
      3
      2                                                                  2.45
      1

          2020          2021              2022             2023   2024     2025


                      B. Conditional on Higher Unemployment Path
     13          Pessim. BC, expectations revert
     12          Pessim. BC, expectations drift (γ=0.98)
     11          Pessim. BC, expectations drift (γ=0.94)
     10          Optim. BC, expectations revert
      9          Optim. BC, expectations drift (γ=0.98)
      8          Optim. BC, expectations drift (γ=0.94)
      7
      6
      5
      4
                                                                         3.28
      3
      2
                                                                         1.93
      1

          2020          2021              2022             2023   2024     2025


Note: Vertical line indicates June 2022. IMF staff forecast for the quarterly path of unemployment
underlying the 2022 IMF Article IV Staff Report. Quarterly forecasts are allocated to the second month of
each quarter and a monthly path is obtained via interpolation. “Higher unemployment” path assumes 7.5
percent unemployment during 2023 and 2024 as suggested by Summers (2022). In this scenario, the
unemployment rate rises linearly from its July 2022 level to 7.5 percent in January 2023 and remains at
that level through December 2024. Horizontal dashes indicate assumed 2.4 percent target for median
PCE inflation based on 2 percent PCE target and 0.4 percentage point gap between the median PCE
inflation and PCE inflation excluding food and energy following approach on Federal Reserve Bank of
Atlanta Underlying Inflation Dashboard.


                                                                                                        30


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