What Caused the US Pandemic-Era Inflation? (Blanchard and Bernanke, NBER Working Paper 31417)
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NBER Working Paper No. 31417, What Caused the US Pandemic-Era Inflation?, by Olivier J. Blanchard and Ben S. Bernanke, dated June 2023. The abstract states that the authors specify and estimate a simple dynamic model of prices, wages, and short-run and long-run inflation expectations to quantify the sources of U.S. pandemic-era inflation and wage growth. It states that most of the inflation surge that began in 2021 was the result of shocks to prices given wages, including sharp increases in commodity prices and sectoral price spikes. It also states that the effects of overheated labor markets on nominal wage growth and inflation are more persistent than the effects of product-market shocks. The introduction discusses the CARES Act, a December 2020 bill that included $900 billion for covid relief, and the $1.9 trillion American Rescue Plan.
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About this paper. Blanchard and Bernanke find that, contrary to early concerns that overheated labor markets would drive inflation, "most of the inflation surge that began in 2021 was the result of shocks to prices given wages." The paper describes several sources of pandemic-era inflation; it does not support a single-cause account, including one that blames relief spending alone.
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NBER WORKING PAPER SERIES
WHAT CAUSED THE US PANDEMIC-ERA INFLATION?
Olivier J. Blanchard
Ben S. Bernanke
Working Paper 31417
http://www.nber.org/papers/w31417
NATIONAL BUREAU OF ECONOMIC RESEARCH
1050 Massachusetts Avenue
Cambridge, MA 02138
June 2023
This research was funded by the Hutchins Center on Fiscal and Monetary Policy at Brookings
and the Peterson Institute for International Economics. Neither institution has a financial,
ideological, or political stake in its findings. The views expressed herein are those of the authors
and do not necessarily reflect the views of the National Bureau of Economic Research.
NBER working papers are circulated for discussion and comment purposes. They have not been
peer-reviewed or been subject to the review by the NBER Board of Directors that accompanies
official NBER publications.
© 2023 by Olivier J. Blanchard and Ben S. Bernanke. All rights reserved. Short sections of text,
not to exceed two paragraphs, may be quoted without explicit permission provided that full
credit, including © notice, is given to the source.
What Caused the US Pandemic-Era Inflation?
Olivier J. Blanchard and Ben S. Bernanke
NBER Working Paper No. 31417
June 2023
JEL No. E31
ABSTRACT
We answer the question posed by the title by specifying and estimating a simple dynamic model
of prices, wages, and short-run and long-run inflation expectations. The estimated model allows
us to analyze the direct and indirect effects of product-market and labor-market shocks on prices
and nominal wages and to quantify the sources of U.S. pandemic-era inflation and wage growth.
We find that, contrary to early concerns that inflation would be spurred by overheated labor
markets, most of the inflation surge that began in 2021 was the result of shocks to prices given
wages. These shocks included sharp increases in commodity prices, reflecting strong aggregate
demand, and sectoral price spikes, resulting from changes in the level and sectoral composition of
demand together with constraints on sectoral supply. However, although tight labor markets have
thus far not been the primary driver of inflation, we find that the effects of overheated labor
markets on nominal wage growth and inflation are more persistent than the effects of product-
market shocks. Controlling inflation will thus ultimately require achieving a better balance
between labor demand and labor supply.
Olivier J. Blanchard
Peterson Institute for International Economics
1750 Massachusetts Avenue, NW
Washington, DC 20036
and NBER
oblanchard@piie.com
Ben S. Bernanke
The Brookings Institution
1775 Massachusetts Avenue, NW
Washington, DC 20036-2103
bensbernanke75@brookings.edu
Replication files are available at http://www.nber.org/data-appendix/w31417
Introduction
Central bankers and most outside economists failed to predict the sharp rise in inflation that
began in 2021, and policymakers, both in the United States and in other advanced economies, were
accordingly slow to react. Action was further delayed by the view that the inflation burst would be
temporary.
Misjudgments of the economic effects of covid-era fiscal programs are one potential
explanation of the failure to forecast the subsequent inflation. Federal Open Market Committee (FOMC)
forecasts of inflation changed little between the September 2020 and June 2021 iterations of the Survey
of Economic Projections, and the Committee continued to expect that inflation would return close to the
Fed’s 2 percent target by 2023, despite congressional passage of a bill in December 2020 that included
$900 billion for covid relief and the $1.9 trillion American Rescue Plan signed by President Biden in
March 2021. These two programs came on top of the $2.2 trillion CARES Act, passed in March 2020 and
signed by President Trump, which had already strengthened firms’ and households’ balance sheets and
increased future ability to spend. Overall, as a share of GDP, the headline costs of these three covid-era
fiscal packages were about 4-1/2 times the size of the American Recovery and Reinvestment Act (ARRA),
enacted in response to the 2008 financial crisis and the ensuing recession. 1
According to conventional economic theory, expansionary fiscal policies can stoke inflation if
they cause labor markets to become overheated and output to exceed the economy’s potential.
Indeed, some early analyses of the American Rescue Plan using standard fiscal multipliers concluded
that the additional federal spending would indeed overheat the economy, possibly leading to higher
inflation (Blanchard, 2021; Edelberg and Sheiner, 2021). These studies acknowledged uncertainty about
magnitudes, as the fiscal impacts on employment, output, and inflation would depend on many factors,
including the effects of the pandemic on potential output, the size of the initial output gap, households’
propensities to consume out of the one-time checks authorized by the bill, and the relation between
labor market tightness and inflation.
Inflation optimists (Reifschneider and Wilcox 2022) argued that, even if the new fiscal spending
were to drive down unemployment by more than expected, a large burst of inflation was still unlikely, as
many studies had concluded that the Phillips curve is quite flat (that is, inflation is relatively insensitive
1
The headline cost of the CARES Act and the December supplemental appropriations package together totaled
about 15 percent of gross domestic product (GDP) in 2020, and the American Rescue Plan was roughly 8 percent of
2021 GDP. By comparison, the ARRA of 2009 was slightly more than 5 percent of that year’s GDP.
2
to labor market tightness), and—in light of more than three decades of low inflation in the United
States—inflation expectations were likely to remain well anchored.
In contrast, some economists (including one of the authors) argued that wage inflation, and
consequently price inflation, could rise much more than predicted by conventional calculations
predicated on a flat Phillips curve (Summers, 2021; Blanchard, 2021). Their concerns were that the
increase in aggregate demand likely to result from the unprecedentedly large fiscal transfers, together
with the cumulative effects of the easing of monetary policy begun in March 2020, could cause more
overheating of an already-tight labor market than the optimists expected. An extremely low
unemployment rate might in turn cause the Phillips curve to steepen. Moreover, higher and,
consequently, more psychologically salient levels of inflation might lead inflation expectations to de-
anchor, raising the potential for a wage-price spiral.
The critics’ forecasts of higher inflation would prove to be correct—indeed, even too
optimistic—but, in substantial part, the sources of the inflation, at least in its early stages, would prove
to be different from those they warned about. The labor market did tighten significantly in 2021 and
2022, as reflected in several indicators, including unsustainably high rates of job creation, an increasing
ratio of job openings to unemployed workers, and low levels of quits. 2 But, as this paper will show, the
behavior of nominal wages in 2021 and 2022 was broadly consistent with the relations the Fed had
relied on, and medium-term inflation expectations rose modestly by some measures but did not de-
anchor. Labor market overheating would indeed ultimately prove to be a source of persistent inflation,
as the critics had expected, but the traditional wage Phillips curve mechanism was not the main event,
at least not until recently.
In retrospect, the failure to forecast the inflation burst reflected in large part the fact that, in
focusing on the labor market, both the Fed and its critics underestimated the inflationary potential of
developments in goods markets, that is, from increases in prices given wages. The shocks to prices came
from several sources. First, like other forecasters (including participants in commodity futures markets),
most economists did not anticipate either the magnitude or the duration of the rise in commodity prices
that began in 2021. Beyond the more-familiar (but unexpectedly large and sustained) shocks to food and
energy prices, the pandemic itself led to unusual distortions in key product markets, such as those for
new and used vehicles. Strong aggregate demand and shifts in the composition of consumer spending
(e.g., from services to durable goods) during the pandemic combined with constraints on supply in some
2
By contrast, the unemployment rate, which remained close to FOMC projections, showed fewer signs of labor
market tightening.
3
sectors to create shortages and sectoral price increases not offset by decreases in other sectors
(Guerrieri et al., 2022; di Giovanni et al., 2023). These sectoral mismatches between demand and supply
proved more intractable and longer-lasting than many had expected. Together, these shocks to prices
given wages would prove to be the critical triggers of the rise in inflation.
This is the story we develop in this paper.
We start with a simple analytical model, focusing on the behavior of wages, prices, and short
and long-run inflation expectations, taking labor market slack and shocks to prices as given. We show
the very different dynamic effects on wage and price inflation of overheating in the labor market and
price shocks in goods markets. Appreciating these differences is essential for understanding the
changing relative importance of the two sources of inflation, and by implication, the evolution of
inflation over time.
We then estimate an empirical version of the model, allowing for a generous lag structure to
accommodate flexible dynamics and estimating it on the pre-covid period. We examine the stability of
the wage, price, and short and long-run inflation expectations relations betweem the pre-covid and
covid periods, taking into account the roles of labor market tightness, energy and food price shocks, and
sectoral shortages. We use the estimated model to decompose the sources of the pandemic-era
inflation into the effects of the various shocks. Our decomposition captures general equilibrium effects,
lags, and linkages among alternative sources of inflation operating through inflation expectations and
other channels. We conclude that labor market tightness made at most a modest contribution to
inflation early on, resolving the puzzle of how inflation could rise so much despite a flat wage Phillips
curve. Instead, most of the early action in inflation came from the goods market, in the form of sharp
increases in some relative prices, including commodity prices and prices in sectors in which strong
demand confronted limits on supply. To the extent that commodity prices stabilize and sectoral
shortages moderate—processes that both seem well advanced as of this writing (June 2023)—the goods
market component of inflation is likely to decrease in importance, and the labor market component to
become more dominant. Looking forward, with labor market slack still below sustainable levels and
inflation expectations modestly higher, we conclude that the Fed has to slow the economy to return
inflation to target. The extent of that slowing will depend however on the evolution of certain structural
features of the labor market, notably the efficiency of the process of matching workers with jobs.
4
I. A Brief Literature Review
Much recent work has provided empirical analyses of the pandemic-era inflation. Ball et al
(2022) is the closest to ours, and we learned from it. They propose a decomposition of inflation into
weighted median inflation (instead of the conventional core measure of inflation) and a residual, equal
to headline inflation less median inflation. Their use of median inflation rather the more conventional
measure of core inflation is intended to remove large price spikes, due not only to the prices of energy
and food, which core inflation does, but also those due to sectoral shortages, which have made this
inflation episode different from earlier ones. They find that the increase in overall inflation resulted
primarily from shocks to the residual (headline less median inflation) but that labor market tightness has
been an important and increasing contributor to median inflation. These conclusions are broadly
consistent with ours, but differences in sample period and model specification (e.g., their specification
implies that the effects of labor market tightness are felt only gradually) lead them to be generally more
pessimistic than we are about the costs of reversing the inflation surge.
Cecchetti et al (2023) study the recent inflation and the prospects for disinflation in a historical
context. As we do, they provide a stripped-down model of the inflation process. However, in contrast to
the largely unconstrained dynamics that we allow in the empirical model presented below, they impose
a tight New Keynesian structure. They argue that nonlinearities in the Phillips curve are important for
explaining inflation (see also Benigno and Eggertsson 2023, Gagnon and Sarsenbayev 2022). In contrast,
we find that a linear relation between labor market tightness and wages, estimated on pre-covid data,
fits the covid-era data reasonably well and is adequate to explain the recent behavior of wages.
Cecchetti et al also conclude that, based on the historical record, disinflation is likely to be costly, and
they fault the Fed for failing to tighten policy pre-emptively.
Gagliardone and Gertler (2023) focus on the monetary-policy origins of the inflation. Using a
calibrated DSGE model to structure their analysis, they argue that the Fed’s commitment to high
employment in the face of inflationary oil price shocks explains the sharp rise in the pace of price
increases. Gagliardone and Gertler’s attention to oil price shocks parallels our own focus on factors
directly affecting prices given wages. Their main contributions concern the role of the Fed’s reaction
function and policy framework in the over-expansion of aggregate demand during the recovery from the
pandemic—an important topic but not the focus of our own paper.
Koch and Noureldin (2023) of the International Monetary Fund conduct a post-mortem of their
institution’s failure to forecast the (global) inflation. Like other papers in the literature, their work finds
5
an important role for increased aggregate demand and, especially, pandemic-induced supply constraints
in setting off the inflation. They also point to over-estimation of output gaps as a factor leading to
excessive stimulus. However, they pay limited attention to dynamics, and in particular they place less
weight than we would on commodity price shocks and their effects on other prices and inflation
expectations over time.
II. A Simple Model of Wage-Price Determination
To help interpret recent inflation developments without imposing too much a priori structure,
we use a bare-bones but flexible model of aggregate wage-price determination. Our approach to
inflation is aggregative, or “top down”; with a partial exception discussed in the next section, we do not
consider the microeconomic determinants of sectoral price changes, e.g., factors affecting the behavior
of rents or the differential impact of the pandemic on different industries. Our model reduces to four
equations, which jointly determine nominal wages, prices, and short-run and long-run inflation
expectations. As already noted, when we take the bare-bones model to the data in the next section we
incorporate a more flexible lag structure, to allow for richer dynamics, and include measures of key
shocks to product and labor markets to account more explicitly for the forces affecting inflation.
The wage equation
We start with an aggregate wage equation. We make the standard assumptions that nominal
wages depend on the expected price level and the degree of labor market slack. In a departure from the
standard specification, we pursue the question of whether workers accept losses in purchasing power
resulting from unanticipated price shocks, or whether instead, in their wage bargaining, they try to
“catch up” with prior inflation. 3
Specifically, we assume that the nominal wage w in each quarter depends on the expected price
for that quarter 𝑝𝑝𝑒𝑒 , an aspiration real wage 𝜔𝜔 𝐴𝐴 (see below), and an indicator of the tightness of the
labor market 𝑥𝑥:
(Eq 1) 𝑤𝑤 = 𝑝𝑝𝑒𝑒 + 𝜔𝜔 𝐴𝐴 + 𝛽𝛽𝛽𝛽
3
Kamin and Roberts (2023) analyze how alternative forms of real-wage catch-up might affect the course of the
economy.
6
Wages, prices, and expected prices are in log-levels, so differences should be interpreted as growth
rates. We use 𝜔𝜔 to designate the real aspiration wage as a reminder that that variable is in real terms, in
distinction to the nominal wage w. We discuss empirical measures of labor market tightness 𝑥𝑥 in the
next section, only noting here the sign convention that we interpret higher values of 𝑥𝑥 as corresponding
to a tighter labor market. We suppress the time subscript for current-quarter variables.
We include the aspiration real wage 𝜔𝜔 𝐴𝐴 in the model as a device for modeling a possible catch-
up effect, in which workers seek to make up for past losses of purchasing power, implying a degree of
real-wage rigidity. The aspiration wage may be thought of as the real wage that workers believe is
achievable—a focal point in wage bargaining, perhaps—given recent developments in wages, prices, and
other factors. Alternatively, the aspiration real wage might be thought of as representing the long-run
equilibrium real wage, toward which the actual real wage gradually adjusts. Adopting the notation
𝑞𝑞(−𝑛𝑛) to stand for the variable 𝑞𝑞 lagged 𝑛𝑛 quarters, we assume that the aspiration real wage in each
quarter is a weighted average of the previous quarter’s aspiration wage and realized real wage, plus a
shock term 𝑧𝑧𝜔𝜔 , standing for all the other factors that affect wage determination:
(Eq 2) 𝜔𝜔 𝐴𝐴 = 𝛼𝛼𝜔𝜔 𝐴𝐴 (−1) + (1 − 𝛼𝛼)𝑤𝑤(−1) − 𝑝𝑝(−1) + 𝑧𝑧𝜔𝜔
When estimating the model, we also allow wage growth to depend on an exogenous trend in
productivity growth. For simplicity of exposition, we ignore that term here.
Putting the two equations above together to eliminate 𝜔𝜔 𝐴𝐴 yields:
(Eq 3) 𝑤𝑤 − 𝑤𝑤(−1) = 𝑝𝑝𝑒𝑒 − 𝑝𝑝(−1) + 𝛼𝛼𝑝𝑝(−1) − 𝑝𝑝𝑒𝑒 (−1) + 𝛽𝛽𝑥𝑥 − 𝛼𝛼𝛼𝛼(−1) + 𝑧𝑧𝑤𝑤
Examination of these equations suggests two cases of interest, depending on the value of the
“catch-up” parameter 𝛼𝛼. If 𝛼𝛼 = 0 then, from (Eq 2), the aspiration real wage in each quarter is just the
real wage in the previous quarter (adjusted for trend productivity growth, in the empirical version of the
model later) plus an error term. Further, from (Eq 3), in the special case of 𝛼𝛼 = 0, the change in the
nominal wage equals the expected rate of inflation in the previous quarter, 𝑝𝑝𝑒𝑒 − 𝑝𝑝(−1), plus a term
that depends on the degree of labor-market tightness 𝑥𝑥—in short, a standard expectations-augmented
wage Phillips curve.
If 𝑎𝑎 ≠ 0, on the other hand, then (Eq 3) implies that among the factors determining nominal
wage growth is the difference in the previous period’s price level and the price level that had been
7
expected for that period, 𝑝𝑝(−1) − 𝑝𝑝𝑒𝑒 (−1). We call this term the catch-up term. The existence of a
catch-up term implies that, in their bargaining with employers, workers seek to be compensated for last
period’s unexpected inflation. In other words, to the extent that workers’ expectations or focal points
(or those of their institutional representatives) influence the wage bargaining process, the economy
exhibits a degree of real-wage rigidity. Note also from (Eq 3) that, if 𝑎𝑎 ≠ 0, the term relating to labor-
market tightness can be rewritten as (1 − 𝑎𝑎)𝑥𝑥 + 𝑎𝑎(𝑥𝑥 − 𝑥𝑥(−1)), implying that wages potentially depend
on both the level and change of labor-market tightness.
The price equation
Given wages, we assume that the price level 𝑝𝑝 depends on the level of nominal wages plus a
shock term 𝑧𝑧𝑝𝑝 that captures the relative costs of nonlabor inputs, variations in markups, and other
factors affecting price-setting:
𝑝𝑝 = 𝑤𝑤 + 𝑧𝑧𝑝𝑝
Or, in first differences:
(Eq 4) 𝑝𝑝 − 𝑝𝑝(−1) = (𝑤𝑤 − 𝑤𝑤(−1)) + (𝑧𝑧𝑝𝑝 − 𝑧𝑧𝑝𝑝 (−1))
In the empirical model, we will flesh out the shock term by including variables such as commodity price
shocks and supply-chain problems that increase prices given wages. Since prices should depend on unit
labor costs rather than wages per se, in the estimation we also include the productivity trend in the
price equation. We will not treat producer markups as an independent variable but note that markups
will endogenously increase in our model when strong sectoral demand confronts limited supply (see
below).
Inflation expectations equations
The model is closed by equations that describe the behavior of the public’s short-run and long-
run inflation expectations. Short-run inflation expectations are a weighted average of long-run inflation
expectations, 𝜋𝜋 ∗ , and last period’s inflation:
(Eq 5) 𝑝𝑝𝑒𝑒 − 𝑝𝑝(−1) = 𝛿𝛿𝜋𝜋 ∗ + (1 − 𝛿𝛿)(𝑝𝑝(−1) − 𝑝𝑝(−2))
8
Long-run inflation expectations in turn evolve as a weighted average of last period’s long-run inflation
expectations and actual inflation:
(Eq 6) 𝜋𝜋 ∗ = 𝛾𝛾𝜋𝜋 ∗ (−1) + (1 − 𝛾𝛾)(𝑝𝑝(−1) − 𝑝𝑝(−2))
The parameters 𝛿𝛿 and 𝛾𝛾 capture the degree of anchoring of short and long-run inflation expectations.
If both 𝛿𝛿 and 𝛾𝛾 are close to 1, expectations are well anchored. Both 𝛿𝛿 and 𝛾𝛾 play important though
different roles in determining the dynamic effects of shocks on inflation. The parameter 𝛿𝛿 affects short
run dynamics, and the degree to which price inflation affects wage inflation: the lower 𝛿𝛿, the more
persistent the dynamic effects of a price shock. The parameter 𝛾𝛾 affects long run dynamics, and in
particular the effect of transitory shocks on long run inflation.
Inspection of the equations above shows that, in the long-run steady state, both inflation
expectations and the inflation rate consistent with full employment are indeterminate. For any value of
long-run expected inflation 𝜋𝜋 ∗ , assuming that 𝑥𝑥 = 0, the model solution implies that short-run inflation
expectations, wage inflation, and price inflation all equal the arbitrarily chosen value of 𝜋𝜋 ∗ . Put another
way, the value of 𝜋𝜋 ∗ at any point in time is determined by the history of inflation. An episode of higher
inflation leads to higher steady-state inflation; the longer the episode, or the lower 𝛾𝛾, the stronger the
effect on steady-state inflation. One can think of the “de-anchoring” that pessimists worried about at
the start of the inflation episode as decreases in either 𝛿𝛿 or 𝛾𝛾. Other things equal, such de-anchoring
would lead to stronger and more persistent inflation following an inflationary shock.
When the aspiration wage is substituted out, as above, the model determines the evolution of
four endogenous variables: 𝜋𝜋 ∗ , 𝑝𝑝𝑒𝑒 , 𝑤𝑤 , and 𝑝𝑝. Despite its simplicity, the basic model displays interesting
dynamic properties.
To illustrate, Figure 1 below shows, for alternative parameter assumptions, the model-implied
dynamic responses of inflation to a one-time shock to the price equation. Specifically, we simulate the
full model under the assumption that the price shock 𝑧𝑧𝑝𝑝 rises permanently by one unit in period 1.
(Note that a permanent shock to the price level is a one-period shock to price inflation). We consider
two cases: In the first, we assume a limited catch-up effect and stable inflation expectations (𝛼𝛼 =
0.2, 𝛿𝛿 = 0.9, 𝛾𝛾 = 0.95). 4 In this case, as Figure 1 shows, the shock to the price level leads to a sharp
increase in inflation that is almost completely reversed after a few periods (see the curve marked “weak
4
We do not need to assign a value to 𝛽𝛽 as doing so would not affect these simulations.
9
feedback”). The low persistence of inflation in this case reflects the weak catch-up effect (workers are
unable to recoup the effects of unexpected inflation on their real wages) and well-anchored inflation
expectations. Because of the (small) effect of the inflation shock on long-run expectations, however,
inflation ends up permanently slightly higher, by 0.06 percent in this example. With a limited catch-up
effect and well-anchored expectations, the conventional wisdom that monetary policymakers can “look
through” temporary supply shocks is justified.
The response of inflation to a one-time price shock is quite different when the catch-up effect is
stronger and inflation expectations are less well anchored (say, 𝛼𝛼 = 0.6, 𝛿𝛿 = 0.7, 𝛾𝛾 = 0.9). In this
second case the inflation response to a one-time price shock dies down only slowly (see the curve
marked “strong feedback” in Figure 1). A stronger catch-up effect implies that a “price-wage spiral” is
operating, with inflation triggering higher nominal wage demands, which in turn imply higher prices and
greater inflation persistence. In this case, the simulated long-run effect on inflation of a temporary
inflation shock, 0.34 percent, is no longer negligible. Again, the simulation is consistent with
conventional wisdom at central banks, which holds that poorly-anchored inflation expectations lead to
more extended episodes of inflation and to higher inflation in the long run, thereby requiring a strong
policy response.
FIGURE 1. RESPONSES OF INFLATION TO A PRICE SHOCK FOR ALTERNATIVE PARAMETER CHOICES
Note: The figure shows inflation in alternative simulations of the model, starting from steady state and
assuming a permanent shock to the price level in period 1. Parameter choices that imply less wage
catch-up and well-anchored inflation expectations lead to less persistent inflation (weak feedback).
Parameters implying greater catch-up and less well-anchored expectations lead to more persistent
inflation (strong feedback).
10
Inflation can also originate in the labor market in our model. For the same two parameter
configurations as in Figure 1, Figure 2 shows the simulated behavior of inflation following a one-time,
permanent one-unit increase in labor market tightness x. After an initial increase, inflation continues to
increase over time as the labor market remains tight. The rate at which inflation increases depends on
the degree of anchoring of expectations, and to a lesser degree, the strength of the catch-up effect.
With well-anchored expectations and little catch-up effect (case 1), a tight labor market results in a
relatively slow increase in price inflation (see the curve labeled “weak feedback” in Figure 2.) However,
real-wage rigidity and loosely-anchored inflation expectations (case 2) magnify the effects of labor
market tightness on wages and, in turn, on prices (the curve marked “strong feedback” in Figure 2).
Thus, the longer the overheating episode, the stronger the catch-up effect, and the weaker the
anchoring of expectations, the larger is the effect of labor market tightness on inflation, and, implicitly,
the stronger the eventual monetary contraction needed to return inflation to target, all else equal.
FIGURE 2. RESPONSES OF INFLATION TO A PERMANENT INCREASE IN LABOR MARKET TIGHTNESS FOR
ALTERNATIVE PARAMETER CHOICES
Note: The figure shows inflation in alternative simulations of the model, starting from steady state and
assuming a permanent one-unit shock to labor market tightness in period 1. Parameter choices that
imply less catch-up and well-anchored inflation expectations lead to a weaker effect of labor market
tightness on inflation, while parameters consistent with stronger catch-up effects and less well-
anchored inflation expectations lead to a stonger effect.
Figures 1 and 2 yield important conclusions. If, in our model, an economy experiences a large,
positive, permanent price shock, it will experience a strong but mostly temporary increase in (headline)
inflation. The persistence of that increase depends on the anchoring of expectations and the degree of
real-wage rigidity. If, on the other hand, the economy experiences sustained overheating in the labor
11
market, it will see a slow but steady increase in inflation, with the rate of increase reflecting not only the
sensitivity of wages to labor market tightness, but, as in the case of a price shock, on the degree to
which inflation expectations are anchored and the extent of real wage rigidity. If the two types of shocks
hit the economy simultaneously, the shock to prices will dominate inflation initially. However, as those
effects fade, higher underlying inflation emanating from the labor market will become increasingly
important.
III. Empirical Implementation of the Model
In this section we discuss the empirical implementation of the model, including our choices of
exogenous driving variables, and we summarize the estimation results for each of the four equations.
More complete estimation results and results for alternative specifications are presented in the
Appendix. The model is estimated using quarterly data. For data availability reasons, and because there
is evidence of a break in inflation dynamics around 1990 (e.g., Blanchard, 2016), we begin our
estimation in 1990Q1, using a data set that, to accommodate four quarterly lags, begins in 1989Q1.
For our baseline results, in order to see whether pre-covid relations can explain what has
happened since covid struck, we end the sample in 2019Q4, thus excluding the covid period (2020Q1-
2023Q1), with one exception: In order to include meaningful variation in the effects of sectoral
shortages, we estimate the baseline price equation over the full sample, including the covid period.
Generally, the results obtained for the wage and inflation expectations equations (as well as for the
price equation, excluding the sectoral shortage term) are very similar whether we use the pre-covid
period or the whole sample. This similarity suggests that, given the shocks, the conditional process
generating prices, wages, and expectations during the pre-covid period remained largely stable during
the covid era.
Our estimation strategy is a hybrid approach that approximates a structural vector
autoregression (SVAR) with added exogenous variables. In the spirit of SVAR analysis, we imposed
restrictions on the contemporaneous relationships among the variables based on our simple model but
left the coefficients on lagged variables largely unrestricted. 5 Specifically, in each estimated equation we
5
In the reported results, we imposed a homogeneity restriction on the estimates that implies that, in the long run,
a given change in inflation implies an equal change in short-run and long-run inflation expectations. Alternatively,
the restriction can be interpreted as requiring that the long-run Phillips curve be vertical. Under either
interpretation, the restriction seems economically justified. The restriction is not rejected at the 5 percent level for
12
included four lags of each of the endogenous and exogenous variables included in that equation. (We
included only one lag of the productivity trend, which is already constructed as an eight-quarter moving
average, in the price and wage equations.) Identification of the wage equation is achieved by assuming
that wages respond to other variables with a lag of one quarter. Wage inflation then affects inflation,
and by implication, inflation expectations contemporaneously.
We turn now to estimation of the model equations. With the estimated parameters in hand, we
will be able to evaluate the drivers and dynamics of any of the endogenous variables, including wage
and price inflation. For reference, Table 1 below lists the mnemonics and data sources of the
endogenous and exogenous variables in the empirical model.
Table 1. Variables and mnemonics used in estimation of the model
Endogenous variables
• gp Price inflation, as measured by quarterly annualized rates of change in the
Consumer Price Index (CPI), Bureau of Labor Statistics (BLS)
• gw Rate of growth of nominal wages, quarterly and annualized, as measure by the rate
of change in the Employment Cost Index (ECI), BLS
• cf1 Short-term inflation expectations, measured by one-year inflation expectations as
constructed by the Federal Reserve Bank of Cleveland
• cf10 Long-term inflation expectations, measured by the Cleveland Fed’s ten-year inflation
expectations series
• catch-up Losses to workers’ purchasing power due to inflation, measured by the four-
quarter average of CPI inflation minus the one-year inflation expectation four quarters
earlier. Catch-up is a linear combination of past gp and cf1.
Exogenous variables
• grpe Rate of growth of the relative price of energy, quarterly and annualized, measured
as the rate of change of the ratio of CPI energy prices to the ECI
• grpf Rate of growth of the relative price of food, quarterly and annualized, measured as
the rate of change of the ratio of CPI food prices to the ECI
the wage and price equations but is rejected at the 2 percent level for the two expectations equations. However,
even in the latter case, the estimates under the restriction are very close to the unrestricted estimates.
Consequently, the restriction has no material effect on the main results of the paper.
13
• v/u Ratio of job vacancies to unemployment, from the BLS job openings and labor
turnover survey (JOLTS) and the BLS Employment Report. Pre-2001 data from Barnichon
(2010)
• shortage An index of supply chain problems based on Google searches; described below
• gpty Trend productivity growth, measured by the eight-quarter moving average of log
changes of nonfarm business value added divided by nonfarm employee hours, from the BLS
The wage equation
Following our simple model, we posit that nominal wage growth depends on labor market
tightness, short-run inflation expectations, the catch-up effect (the tendency of wages to rise to
compensate for past unexpected inflation), and trend productivity growth.
We choose the Employment Cost Index (ECI), wages and salaries component, as our measure of
the nominal wage. The ECI is generally thought to be a better measure of wages than the main
alternative, average hourly earnings as collected by a monthly BLS survey of employers, because it
corrects for changes in average earnings due to changes in the composition of employment. The ECI is
available only quarterly, but that is not a problem here since we are using only quarterly data in
estimation. Official ECI data begin in 2001Q1. To allow our estimation to start in 1990, we extended the
series backward using an older ECI series based on a different BLS survey. 6
We need a measure of the tightness of the labor market, denoted 𝑥𝑥 in the previous section.
Traditionally, the state of the labor market has been measured by the unemployment rate 𝑢𝑢, or
sometimes by the difference between the unemployment rate and the “natural” or sustainable
unemployment rate, 𝑢𝑢∗ . The perceived importance of unemployment as a labor-market indicator is
reflected in the fact that it is one of only four macroeconomic variables forecast by the FOMC in its
Summary of Economic Projections.
A conceptual weakness of the unemployment rate as an indicator is that it is based solely on
information about the status of households and does not directly incorporate information on the hiring
needs of employers. But the labor market involves costly search by employers for workers as well as by
workers for jobs. In principle at least, a given unemployment rate could be consistent with either a
6
The older survey was discontinued in 2005. That series is an index for total compensation for all civilian workers,
that is including benefits, seasonally adjusted. The BLS mnemonic is ECS10001I. We thank David Reifschneider for
calling this series to our attention. We used a dummy variable to correct for a level shift between the pre-2001 ECI
data and the currently official post-2001 series.
14
strong labor market, with upward pressure on wages, or a weak labor market and low wage pressure,
depending on whether job openings are plentiful or scarce.
An alternative indicator of labor market slack that uses information from both workers and
employers is the ratio of the vacancy rate (job listings reported by employers divided by the labor force)
to the civilian unemployment rate, 𝑣𝑣/𝑢𝑢. Normally 𝑢𝑢 and 𝑣𝑣/𝑢𝑢 usually move closely (inversely) together—
their correlation in our pre-covid sample is -0.88—and they perform similarly in wage Phillips curves
estimated over the pre-covid period (Ball et al., 2022; Cecchetti et al., 2023). However, as has been
widely noted, including in Federal Reserve communications, during the covid era these two indicators
diverged dramatically. Following a spike during the pandemic lockdowns, the unemployment rate
declined gradually. By the end of 2021 it appeared to stabilize at a level modestly below 4 percent,
implying—under the FOMC’s maintained assumption of a 4 percent natural unemployment rate—that
labor market conditions, though moderately tight, were not becoming significantly tighter. Moreover,
the unemployment rate in late 2021 was comparable to or slightly higher than that just prior to the
pandemic, a period without evident inflation pressures. The signal from the unemployment rate was
consequently that labor market overheating was not an imminent threat to price stability.
The picture portrayed by the vacancy-to-unemployment ratio during the covid era was quite
different. That ratio rose from less than 1.0 in April 2021 (that is, less than one open job per
unemployed worker) to a historically high level of about 1.9 (nearly two job openings per unemployed
worker) a year later. This increase implied an exceptionally rapid pace of labor-market tightening, to a
level considerably greater than during the immediate pre-covid period and, indeed, any period since
these data have been collected. As of this writing, 𝑣𝑣/𝑢𝑢 has declined only moderately from its peak,
consistent with a labor market that remains overheated.
Which indicator of labor market tightness is better? As their high correlation and comparable
performance in Phillips curves suggests, in normal times the two indicators give very similar assessments
of labor market conditions. However, the relationship between vacancies and unemployment changed
materially during the covid period, with more vacancies (more search effort by employers) needed to
achieve a given rate of hiring, holding constant the number of unemployed (Blanchard, Domash, and
Summers 2022). Equivalently, the Beveridge curve, the downward relation between vacancies and
unemployment, has shifted upward since 2020. 7 If labor market tightness, as reflected in workers’
7
Many factors no doubt contributed to this shift. A high rate of firm closures implied that many laid-off employees
had to find new jobs rather than return to their old ones. Shifts in consumer demand patterns and worker
preferences induced a reallocation of jobs among firms and sectors, slowing the matching process. Changes in
15
bargaining power, depends on the number of jobs available relative to the number of people looking for
work, then the ratio of vacancies to unemployment remains a good measure of tightness even when
employers must search more intensively to find potential hires. In contrast, given the number of
unemployed, workers’ bargaining power and labor market tightness is much greater when there are
many vacancies to be filled than when vacancies are scarce. We conclude that 𝑣𝑣/𝑢𝑢 is a more reliable
indicator of labor market conditions in times, as during the pandemic and its aftermath, in which the
efficiency of the employer-worker matching process has changed materially. 8 For this reason, and
following the direction taken in much recent research and in Federal Reserve policy communications, we
use 𝑣𝑣/𝑢𝑢 as our empirical measure of labor market pressure. 9
To capture short-term inflation expectations, we use one-year inflation expectations as
constructed by the Federal Reserve Bank of Cleveland. This expectations series is partly retrospective
and model-based, which is a drawback, but it has the advantage of combining several types of real-time
information, including data from financial markets and from surveys. We have also estimated our model
using forecasts of the Survey of Professional Forecasters (SPF) as proxies for inflation expectations (see
the Appendix for the results). 10 When we use this alternative measure, the differences for both the
wage equation and the other equations are minor, and the conclusions we draw in the text do not
change. We comment on some results for alternative data choices and sample periods below.
We construct our measure of the wage catch-up term as the difference between realized CPI
inflation over the current and past three quarters and the one-year expectation of inflation as of four
quarters earlier. The catch-up variable thus equals unexpected inflation, which we hypothesize may
affect subsequent wage bargains if workers are focused on maintaining the real buying power of their
wages. As has been noted, our measure of labor productivity is an eight-quarter moving average of
nonfarm productivity growth.
family arrangements, illness, and other effects of the pandemic lockdowns may have reduced the (unobserved)
intensity of search effort of some unemployed workers. And employers may have failed to appreciate the extent to
which, because of concerns about returning to jobs involving personal contact or perhaps because of
reassessments of work-life balance, workers had increased their reservation wages.
8
Like the vacancy-to-unemployment ratio, the quit rate also reflects both labor demand and labor supply, in that
the willingness of workers to quit their current jobs depends on their perceptions of labor-market conditions. We
found however that the quit rate does not perform as well as 𝑣𝑣/𝑢𝑢 in our wage equation.
9
For more on the Beveridge curve, and a formalization of the argument that the vacancy-to-unemployment ratio
should be used as a measure of labor market tightness, see Blanchard and Diamond (1989).
10
The SPF forecasts are made in real time, an advantage. However, they raise some issues of timing, e.g., ten-year
forecasts in each quarter are for the subsequent decade including the current year, rather than for the ten years
beginning in the forecast quarter. This feature leads to discontinuities between fourth-quarter and first-quarter
ten-year forecasts.
16
As also discussed above, we want to be guided by our formal model while maintaining flexible
lag structures. We make the identifying assumption that wages respond only to lagged values of the
independent variables, and we regress wage growth gw on a constant, four (quarterly) lags of itself, four
lags of short-run inflation expectations cf1, four lags of the unexpected inflation term catch-up, four lags
of our proxy for labor market tightness 𝑣𝑣/𝑢𝑢, and one lag of trend productivity growth gpty.
Table 2 below reports, for each right-side variable in the wage equation, the included lags, the
sum of the estimated coefficients for each variable and two p-values. The first p-value, denoted p-stat
(sum), is the probability of rejection of the null hypothesis that the sum of current (if applicable) and lag
coefficients for a given variable is zero. The second p-value, p-stat (joint), tests the joint hypothesis that
each of the current and lag coefficients is separately zero. To ensure that the long-run wage Phillips
curve is vertical, we impose a homogeneity assumption (see footnote 5 for more discussion), which here
implies that the sum of coefficients on lagged nominal wage growth and lagged short expectations is
equal to one.
Table 2. Wage growth regression: Dependent variable = gw
Independent variable gw v/u catch-up cf1 gpty
Lags -1 to -4 -1 to -4 -1 to -4 -1 to -4 -1
Sum of coefficients 0.460 0.693 -0.024 0.540 0.031
p-stat (sum) 0.008 0.030 0.765 0.002 0.608
p-stat (joint) 0.071 0.023 0.994 0.022 0.608
R-squared 0.578
No. observations 120
Notes: Sample is 1990Q1 to 2019Q4. p-stat (sum) is the p-value for the null hypothesis that the sum of
coefficients is zero, p-stat (joint) is the p-value for the joint hypothesis that each of the lag coefficients
separately equals zero.
Table 2 suggests that, when 𝑣𝑣/𝑢𝑢 is used as the measure of slack, the wage Phillips curve remains
alive and well, in that the estimated effect of labor market conditions on wage growth is significant,
both statistically and economically. Based on the sum of estimated coefficients for the four quarterly
lags of the vacancy-to-unemployment ratio, and the sum of the coefficients on lagged nominal wage
growth, an increase in 𝑣𝑣/𝑢𝑢 from, say, 1.0 to 1.5, holding constant other factors, has a long-term effect
on nominal wage growth of 0.5 x 0.693/(1-.460), or 0.64 percentage points. 11 When we use the SPF 1-
11
Note the importance of “holding constant other factors”. As we saw in the simple model, and as is the case in
the empirical model as well, in general equilibrium, letting other factors adjust leads to steadily increasing
inflation.
17
year forecast as a proxy for short-run inflation expectations, the effect of 𝑣𝑣/𝑢𝑢 is marginally larger, 0.75,
and highly statistically significant.
The sum of the coefficients on short-run inflation expectations is high relative to the sum of
coefficients on lagged nominal wage growth (under the homogeneity assumption, the sums of the
coefficients on the two variables add to one). This estimate suggests that short-run inflation
expectations feed fairly quickly into wages, although, as we shall see below, short-run inflation
expectations react slowly to actual price inflation.
There is no evidence of a catch-up effect in Table 2, a result that appears robust. For example,
when we use SPF 1-year forecast to measure short-run inflation expectations, the catch-up effect is
estimated to be small and positive, though not statistically significant, with sum of coefficients equal to
0.1. When we estimate the equation over the full sample, for either measure of short-term
expectations, the estimated catch-up effect remains small, and is again statistically insignificant.
The moving-average trend in productivity growth has no statistically significant effect on wage
growth, suggesting that some of the effect of productivity growth may be captured by the constant term
of the equation.
As a check on our specification, we can see how the wage equation estimated on the pre-covid
sample fits wage data during the covid period (2020Q1-2023Q1). As Figure 3 shows, the estimated wage
equation predicts wage behavior after 2019 reasonably well, including the upward trend in wage growth
over the period. The fitted wage equation’s largest miss is for 2020Q3, when the equation predicts a
larger decline in wage growth than actually occurred. Given the tremendous deterioration in labor
market conditions in the early stages of the pandemic, it is not surprising that the equation predicts a
commensurate decline in wages in that quarter. Downward nominal rigidity in wages and pervasive
measurement issues likely explain most of the miss.
18
FIGURE 3. WAGE GROWTH, 2020Q1-2023Q1, COMPARED TO PREDICTIONS OF WAGE EQUATION
Note: The figure shows actual and predicted nominal wage growth, 2020Q1-2023Q1, based on the wage
equation estimated on the pre-covid sample.
The price equation
We turn now to the determinants of price inflation. In our model, price inflation depends on
nominal wage growth and on other factors that affect prices given wages, such as growth in other input
costs. Our estimated equation includes four lags of inflation and the current value and four lags of wage
growth. We use the more familiar and timelier Consumer Price Index (CPI) as our measure of the price
level. The Appendix shows that measuring prices using the personal consumption expenditures (PCE)
deflator leads to very similar results. We continue to use the ECI as our measure of nominal wages.
A substantial part of the pandemic-era inflation surprise reflected rapid, largely unanticipated
increases in food and energy prices. We consequently included in our specification contemporaneous
values and four lags each of the growth rates in food (grpf) and energy prices (grpe), as defined by the
CPI, with both measured relative to the contemporaneous growth rate in nominal wages. Shocks to
these variables should thus be interpreted as shocks to relative rather than absolute prices. Since lags of
nominal wage growth are included in the estimated equation, however, the fit of the equation would be
the same independent of whether the growth of input prices enters in relative or absolute terms.
Simply treating relative food and energy prices as exogenous in the price equation, per
conventional practice, is unsatisfying, as it leaves unanswered the question of why these prices moved
up so sharply and, apparently, in a roughly synchronized way. To gain some insight into this question, we
performed the following experiment.
We hypothesized that common movements in the prices of a range of disparate commodities
were more likely to reflect the influence of global demand changes (the result of global macroeconomic
19
policies, reopening from the pandemic, and large geopolitical events like the Ukraine war) rather than
changes in supply, as conditions affecting the supplies of diverse commodities, such as local weather
conditions or the opening of new mines, are likely to be largely idiosyncratic. To find the common trend
in commodity prices, we used a principal components approach.
Specifically, we collected monthly prices for 1990 to the present of the 19 commodities included
in the familiar Commodity Research Bureau (CRB) commodity price index. 12 We standardized each
commodity price series to have mean zero and a standard deviation of one. We calculated the first
principal component of these price series, finding that it explained 66.0 percent of the overall variance.
The two figures below show the estimated principal component (converted to a quarterly frequency),
together with the CPI energy (Figure 4) and food price (Figure 5) components since 2020Q1. 13
FIGURE 4. CRB PRICES PRINCIPAL COMPONENT AND ENERGY PRICES, 2020Q1-2023Q1
Note: The figure shows the first principal component (common trend) of the prices of 19 commodities
currently included in the CRB commodity price index, together with the CPI price of energy, in levels
(1982-84 = 100).
12
The CRB index currently comprises prices of 19 commodities, including energy, metals, and agricultural
commodities. We gathered prices of commodities currently included in the index, ignoring changes since 1990 in
the composition of the index. Commodity prices were weighted equally in our principal components exercise. 𝑅𝑅2 s
of regressions of each commodity price on the principal component, using monthly data from 2020M1, were high
for energy, food, and metals, with a few exceptions, notably gold (𝑅𝑅2 = 0.08), cocoa (𝑅𝑅2 = 0.0), and orange juice
(𝑅𝑅2 = 0.41).
13
As noted in the text, Figures 4 and 5 show the principal component of all the commodity prices in the CRB index,
including energy and food prices. To avoid the possibility of a spurious correlation between CPI energy and food
prices and the principal component, we repeated the exercise excluding from the principal components analysis, in
sequence, (i) all energy and food commodities (ii) all energy commodities, and (iii) all food commodities. The first
principal components extracted from these reduced lists of commodity prices looked quite similar to that shown in
Figures 4 and 5.
20
FIGURE 5. CRB PRICES PRINCIPAL COMPONENT AND FOOD PRICES, 2020Q1-2023Q1
Note: The figure shows the first principal component (common trend) of the prices of 19 commodities
currently included in the CRB commodity price index, together with the CPI price of food, in levels (1982-
84 = 100).
Figures 4 and 5 present a mixed picture. Energy prices generally moved in line with the common
component, rising for a period, spiking in early 2022, and then declining. Food prices followed the
common component upward as well but continued to rise after the common component peaked and
began to decline. Our interpretation is that in the earlier part of the pandemic, energy and food prices
were indeed driven primarily by demand factors, including stimulative U.S. fiscal and monetary policies
and the reopening of many economies from covid lockdowns. The Russian invasion of Ukraine that
began on February 24, 2022, caused a further spike in commodity prices, which waned as the perceived
threat to global commodity supplies moderated. That story is consistent with the behavior of energy
prices. However, the continued increase in food prices following the sharp decline in the prices of raw
commodities, a phenomenon not confined to the United States, bears further investigation. Since retail
food prices reflect many inputs beyond raw commodities, including labor, changes in non-commodity
input prices and wages could be one reason for this divergence. Non-competitive behavior is another
possibility, as the food price index includes distribution margins, and the retail food industry has become
more concentrated in recent decades (Zeballos, Dong, and Islamaj, 2023).
Besides commodity prices, pervasive shortages of certain goods have often been cited as a
source of inflation during the pandemic period (Comin, Jones, and Johnson 2023). These shortages and
disruptions have reflected developments in both demand and supply. On the demand side, lockdowns
and fears of infection led to a shift in consumer spending from in-person services to goods, especially
durable goods. The share of nominal consumer spending devoted to durable goods rose from about 10
21
percent in the years before the pandemic to about 13 percent once the pandemic began, an increase of
nearly a third, and it remained high. This sectoral demand shift was augmented by increases in overall
consumer spending driven by supportive monetary and fiscal policies. On the supply side, global supply
chains and transportation networks were disrupted by pandemic-induced shutdowns, constraining
production in key sectors, and even those industries not affected by such problems were in many
instances pushed to the limits of their capacity. The combination of an increased demand for goods and
limited supply resulted, not surprisingly, in sharp rises in prices in a number of sectors.
One might argue that increases in relative demand in some sectors, and associated higher
prices, should have been largely offset by decreases in relative demand in other sectors, and associated
lower prices. Shortages however introduce a fundamental asymmetry. If we think for example of firms
facing a flat marginal cost up to some physical constraint where supply becomes vertical, then relative
demand increases, if large enough, will move prices along the vertical supply curve, but the
corresponding relative demand decreases will move prices along the horizontal portion of the supply
curve. The increase in prices in some sectors will not be offset by a decrease in prices in the others. This
effect will be stronger, the larger the variation in relative demand or in relative supply constraints. Both
factors seemed to have played a role in the past three years.
The automobile sector, an important contributor to the early surge in inflation, illustrates the
role of demand and of supply constraints (see Figure 6 below). U.S. vehicle production plunged during
the initial lockdowns then recovered as factories reopened. Assemblies ran at about an 11.7 million
annual rate in July 2020, comparable to or slightly higher than pre-pandemic production rates (top panel
of Figure 6). However, persistent shortages of critical chips and other key components subsequently
restrained vehicle production, which fell below an annual rate of 9 million units—a decline of about a
quarter—by the fall of 2021. The other panels of the figure show that the reduced production did not
reflect a lack of potential customers. Inventories of new cars for sale fell to record low levels as dealers
could not keep up with demand (second panel of Figure 6) and, consequently, new automobile prices
spiked (third panel). The bottom panel of Figure 6 shows an index of U.S.-based Google searches for
“chip shortage” and “car shortage,” both of which rose sharply in 2021. The vertical dashed line in the
figure at 2021Q3 illustrates the close relationship between these developments. That quarter saw the
trough in automobile production, the decline in inventories to record low levels, the spike in auto prices,
and (a quarter earlier) the peak in Google searches, consistent with a shortage-induced price jump.
22
FIGURE 6. PRODUCTION AND SHORTAGES IN THE U.S. AUTOMOBILE INDUSTRY, 2018Q1-2022Q4
Note: Motor vehicle assemblies data pertain to the United States, inventories represent inventories held
in the U.S. of vehicles assembled in North America. Google searches are measured by an index,
2021Q3=100. Sources include the Federal Reserve Board of Governors, Bureau of Economic Analysis,
Google Trends.
As the figure suggests, the Google search variables appear to be good proxies for the sectoral
demand shifts and supply constraints, at least in one very important industry. (Shortages of new cars
spilled over to the prices of used cars, which at times were also important drivers of inflation.) This led
us to use an index of the quarterly average of the number of U.S.-based Google searches for the term
23
“shortage” in our price equation (the underlying series is weekly, and is normalized by Google to equal
100 in the week when it reaches its highest value, May 2 to 9, 2021) as a proxy for the combined effects
of the shift in demand towards durable goods and the disruptions of and limits on supply. 14 We
experimented with several other measures of supply chain and transportation problems used in the
literature, including the Federal Reserve Bank of New York’s supply chain index, the Baltic Dry Index,
supplier delivery times as reported by the Institute for Supply Management, the ratio of durable goods
to services spending, and others, but found that the Google search variables provided, by far, the most
explanatory power.
The collision of high demand and limited supply in some sectors can account for at least some of
the increase in markups observed during the pandemic period. While other factors no doubt have
influenced markups, including for example the fiscal transfers that directly affected demand in product
markets, at least in this simple specification we do not find that including these factors is needed to
explain the behavior of pandemic-era inflation (see Figure 7 below).
A summary of estimation results for the price equation is given in Table 3. As before, the
Appendix provides more complete results, as well as estimation results using the PCE deflator rather
than the CPI as the measure of prices.
Table 3. Price inflation regression (dependent variable = gp)
Independent variable gp gw grpe grpf shortage gpty
Lags -1 to -4 0 to -4 0 to -4 0 to -4 0 to -4 -1
Sum of coefficients 0.335 0. 665 0.066 0.126 0.018 -0.143
p-stat (sum) 0.037 0.000 0.000 0.050 0.281 0.026
p-stat (joint) 0.066 0.000 0.000 0.050 0.000 0.026
R-squared 0.947
No. observations 133
Note: Sample is 1990Q1 to 2023Q1. p-stat (sum) is the p-value for the null hypothesis that the sum of
coefficients is zero, p-stat (joint) is the p-value for the joint hypothesis that each of the current and lag
coefficients separately equals zero.
14
The normalization based on weekly data is different from the quarterly normalization we use in Figure 6 (this
difference has no consequence for the estimation results). The Google data start in 2004Q1. For earlier
observations, to avoid an artificial discontinuity, we assume that shortage takes a constant index value of 5,
approximately its pre-pandemic average.
24
The table reports the results of a regression of price inflation on a constant, four lags of itself,
the current value and four lags of nominal wage growth, and the current values and four lags each of
inflation in the relative prices of energy and food. Also included as independent variables were the
current value and four lags of Google searches for shortage, and one lag of trend productivity growth,
which should affect unit labor costs and thus prices. Recall that, in order to include the shortage
variable, which is roughly constant and small pre-covid, the inflation equation, unlike the other
equations in our model, is estimated for a sample that includes the covid period. Estimation of the price
equation in the pre-covid sample, excluding shortage, produced similar estimates for the coefficients of
the other variables in the equation. The estimated equation reflects the imposed homogeneity
assumption that the sum of the coefficients on past price and on wage inflation sum to one.
In Table 3, the large sum of coefficients on nominal wage growth relative to the sum of
coefficients on lagged inflation implies a fairly rapid passthrough of wages to prices. The relative prices
of energy and food also affect inflation, as expected, though the sum of the coefficients on the relative
price of food is only marginally statistically significant. The estimated long-run effect of an energy price
shock on the price level, other things equal, is 0.066/(1-0.335) = 10 percent, so about a third larger than
energy’s share in the CPI basket (7.4 percent). The estimated long-run effect of a food price shock is
equal to 0.126/(1-0.335) = 19 percent, so about 30 percent larger than the share of food in the basket
(14.4 percent). Since wages are controlled for, these findings suggest the presence of some second-
round price-price effects of energy and food price shocks on the prices of other goods and services over
time.
The sum of the coefficients on the shortage variable is not statistically significant, though the
joint hypothesis that the lag coefficients are each zero is strongly rejected. We interpret these findings
as suggesting that shortages have a strong but temporary effect on the price level. Trend productivity
growth enters with the expected negative sign (higher productivity reduces unit labor costs, given
wages), with an estimated coefficient that is statistically significant at the 5 percent level.
As we did for wage growth above, we can use this estimated equation to predict the path
of inflation over the covid period. As Figure 7 shows, the predicted inflation series is quite close to the
actual covid-era data.
25
FIGURE 7. INFLATION, 2020Q1-2023Q1, COMPARED TO PREDICTION OF PRICE EQUATION
Note: The figure shows predicted and actual inflation, 2020Q1-2023Q1, based on the price equation
estimated over the full sample.
Inflation expectations equations
The final equations to be estimated are those determining short-run and long-run inflation
expectations. Inflation expectations can be measured in many ways, including through financial-market
indicators, consumer and business surveys, and the expectations of professional forecasters. For our
baseline results we use the one-year and ten-year inflation expectations series constructed by the
Cleveland Fed. The Appendix discusses results obtained when we use measures of inflation expectations
based on the Survey of Professional Forecasters.
Begin with the equation for short-term inflation expectations (cf1). Our model posits that short-
run inflation expectations in each period are a weighted average of long-term inflation expectations and
realized inflation. In the application we also include lags of short-term inflation expectations, which
allows for the possibility of gradual adjustment. We accordingly estimate an equation that has short-run
inflation expectations depending on four lags of itself, the current value and four lags of our measure of
long-run inflation expectations, cf10, and current and four lags of actual inflation. Table 4 below
summarizes the results.
26
Table 4. Short-run inflation expectations (dependent variable = cf1)
Independent variable cf1 cf10 gp
Lags -1 to -4 0 to -4 0 to -4
Sum of coefficients 0.369 0.506 0.124
p-stat (sum) 0.014 0.000 0.001
p-stat (joint) 0.001 0.000 0.000
R-squared 0.908
No. observations 120
Note: Sample is 1990Q1 to 2019Q4. p-stat (sum) is the p-value for the null hypothesis that the sum of
coefficients is zero, p-stat (joint) is the p-value for the joint hypothesis that each of the current and lag
coefficients separately equals zero.
We again impose homogeneity, which in this case implies that the sum of the coefficients of the
three variables equal one. (The restriction has little effect, as the unconstrained sum of coefficients is
0.99.) As noted, this homogeneity restriction, together with a similar restriction on the long-run inflation
expectations equation, ensures that, in the long run, a sustained increase in inflation will raise inflation
expectations by the same amount. In the short run, however, that relation need not hold, and the fact
that current and lagged inflation enter this equation with a small sum of estimated lag coefficients
suggests that short-term inflation expectations are relatively well-anchored—that is, all else equal, they
are only modestly affected by near-term changes in inflation. However, given the high autocorrelation of
short-run inflation expectations, the estimates also imply that sustained inflation gets increasingly
reflected in short-run expectations over time.
Like the previous equations, the estimated equation for short-run inflation expectations does a
good job of predicting pandemic-era inflation expectations out of sample, as shown by Figure 8. There is
no evidence of de-anchoring, defined here as an increase in the short-run effect of inflation on expected
inflation: If estimated over the whole sample, including the covid period, estimated coefficients are very
similar. For example, the sum of coefficients on inflation is 0.133 in the full sample, compared to 0.124
in the pre-covid sample alone.
27
FIGURE 8. SHORT-RUN INFLATION EXPECTATIONS, 2020Q1-2023Q1, COMPARED TO PREDICTION OF
SHORT-RUN EXPECTATIONS EQUATION
Note: The figure shows predicted and actual short-run inflation expectations, 2020Q1-2023Q1, with
predicted values based on the associated equation estimated on the pre-covid sample.
Finally, Table 5 shows our estimated equation for long-run inflation expectations (cf10).
Following our modeling assumption that long-run inflation expectations evolve as a weighted average of
the previous level of long-run expectations and actual inflation, in the estimated equation we allow
long-run inflation expectations to depend on four lags of itself and the current value and four lags of
realized inflation. The results echo those for short-run inflation expectations. We impose the
homogeneity restriction that the sum of coefficients is equal to one. The unconstrained sum of
coefficients is 0.99, so once again the homogeneity restriction makes no substantial difference to the
results.
The response of long-run inflation expectations to short-run movements in prices is small,
suggesting that long-run expectations are well anchored. In particular, there is no evidence that long-run
expectations became de-anchored during the covid period. The sum of coefficients on current and
lagged inflation were not much changed, being estimated as 0.031 in the whole sample, compared to
0.025 in the pre-covid sample. The high estimated autocorrelation of long-run inflation expectations
implies that a sustained increase in inflation will lead to slowly but steadily rising long-term inflation
expectations, which matches the pattern in the covid-era data. See Figure 9.
28
Table 5. Long-run inflation expectations (dependent variable = cf10)
Independent variable cf10 gp
Lags -1 to -4 0 to -4
Sum of coefficients 0.975 0.025
p-stat (sum) 0.000 0.208
p-stat (joint) 0.000 0.004
R-squared 0.931
No. observations 120
Note: Sample is 1990Q1 to 2019Q1. p-stat (sum) is the p-value for the null hypothesis that the sum of
coefficients is zero, p-stat (joint) is the p-value for the joint hypothesis that each of the current and lag
coefficients separately equals zero.
FIGURE 9. LONG-RUN INFLATION EXPECTATIONS, 2020Q1-2023Q1, COMPARED TO PREDICTION OF
LONG-RUN EXPECTATIONS EQUATION
Note: The figure shows predicted and actual long-run inflation expectations, 2020Q1-2023Q1, with the
prediction based on the associated equation estimated over the pre-covid sample.
Impulse Response Functions
The estimates of this section provide parameter values for the empirical version of our model.
The model determines four endogenous variables (price inflation, wage inflation, and short-run and
long-run inflation expectations) given initial conditions and five exogenous variables (the vacancy-to-
unemployment ratio, the relative prices of food and energy, the shortage indicator, and trend
productivity.)
The estimated model can be used to calculate impulse response functions (IRFs) that take into
account both the simultaneity and lagged relationships among wages, prices, and inflation expectations.
For example, we can estimate the dynamic effects of a shock to a particular equation or of a change in
any of the exogenous variables, taking a general equilibrium and dynamic perspective. Estimated
impulse responses using the full model capture not only the direct effects of a given shock (e.g., as
29
reflected in the estimated coefficients of the shocked variable in each of the equations) but also the
knock-on effects in all subsequent periods. For example, an increase in the relative price of energy
affects price inflation directly, but it may also motivate workers to try to maintain their real wages (the
catch-up effect) and lead to increases in both short-run and long-run inflation expectations, each of
which feeds into wage inflation and subsequently into price inflation over time.
In Section 2, using the simple model and starting from the steady state, we showed the
responses of price inflation to (i) a positive, permanent shock to the price equation (Figure 1) and (ii) a
positive, permanent shock to labor market tightness (Figure 2). We conducted these exercises using two
sets of hypothetical parameters, in the process confirming the intuition that the persistence of inflation
in the face of a shock is typically less when the catch-up effect is small (workers are unable to regain
much of the purchasing power lost to unexpected inflation) and inflation expectations are well
anchored. With the full model, now including estimated parameters and unrestricted lags, we can
repeat those exercises. As before, we start from a steady state and consider one-standard-deviation
positive shocks to each of three price shock variables—the relative price of energy, the relative price of
food, and the shortage index—and to the vacancy-to-unemployment ratio. The standard deviations used
for the shocks are calculated using data from 2020Q1 to 2023Q1. 15 The results are given in Figure 10
below for the three price shocks and in Figure 11 for the vacancy-to-unemployment ratio.
Figure 10 is striking, in that the effects of the three price shocks on inflation are quite short-
lived, even more so than in the simulation of the analytical model under weak feedback parameters
(Figure 1). The effects mostly disappear in the quarter following the shock, although the short burst of
inflation together with not fully anchored inflation expectations yields, in the case of an increase in the
price of energy, a small sustained increase in inflation of about 0.1 percent. This long-term effect reflects
the fact that, as discussed earlier, inflation is indeterminate in this model, and its steady-state level
depends on the behavior of inflation in the past.
15
The standard deviations are respectively 32 percent for the quartely rate of change of the relative price of
energy (which varied for 45 percent to -52 percent during the period) at an annual rate, 3.2 percent for the rate of
change of the relative price of food (which varied from 8.9 percent to -1.3 percent), 11.6 for the shortage index
(which varied from 10 to 48), and 0.5 for the vacancy-to-unemployment ratio (which varied from 0.26 to 1.91).
30
FIGURE 10. RESPONSES OF INFLATION TO SHOCKS TO THE RELATIVE PRICE OF ENERGY, THE RELATIVE
PRICE OF FOOD, AND THE SHORTAGE INDEX
Note: The figure shows the full-model, dynamic responses of inflation to a one-standard-deviation
positive shock to relative energy prices, relative food prices, and the shortage variable. It may be
compared to the hypothetical responses of inflation under alternative parameter assumptions in Figure
1.
The short-lived responses of inflation to various price shocks shown in Figure 10 reflect our
findings that real wage rigidity (the catch-up effect) is limited, and that short-run and long-run inflation
expectations appear to be reasonably well anchored, adjusting very slowly in response to actual
inflation. This anchoring likely reflects the credibility of the Fed’s commitment to return inflation to its
target level over time. These results are good news for policy makers, as they suggest that, as price
shocks fade, their effects on inflation quickly (although not fully) disappear. These results are also in
sharp contrast to what happened in the 1970s, a time when inflation expectations were much less
anchored, and because of automatic cost-of-living adjustments and other mechanisms, catch-up effects
were presumably much stronger. As a result, inflation due to price shocks (notably oil and food price
shocks, in the 1970s) was very persistent, despite the fact that on the whole the labor market was not
particularly tight during that decade.
Figure 11 shows a full-model simulation of how inflation responds over time to a persistently
tight labor market, modeled as a permanent one-standard deviation increase in the ratio of vacancies to
unemployment. The jagged initial response reflects the fact that, in the empirical wage equation, both
the level and the change in the vacancy-to-unemployment ratio affect inflation. Once these short-run
effects fade, inflation increases slowly but steadily, reflecting the effects of a tight labor market on
wages (which in turn affect prices) and the feedback of realized inflation to short-run and long-run
31
inflation expectations. In this simulation, inflation has risen about 0.7 percent after 6 quarters, 1.0
percent after 12 quarters, and keeps increasing at about 0.15 percent per year from then on. This
pattern is very similar, even quantitatively, to the weak feedback case we showed in Figure 2. In general,
the takeaway is that persistent labor market pressure leads to ever-increasing inflation. The rate of
increase in our estimated model is relatively low, reflecting a weak estimated catch-up effect and well-
anchored inflation .expectations. Yet, as inflation expectations are not fully anchored, extended labor
market tightness can lead to significant additional inflation.
FIGURE 11. RESPONSE OF INFLATION TO SHOCKS TO THE VACANCY TO UNEMPLOYMENT RATIO.
Note: The figure shows the full-model, dynamic responses of inflation to a one-standard-deviation
positive shock to vacancy-to-unemployment ratio. It may be compared to the hypothetical responses of
inflation under alternative parameter assumptions in Figure 2.
Quantifying the sources of the pandemic-era inflation
With the estimated model in hand, we can calculate the impulse response functions of any
endogenous variable to shocks to both (i) the residuals associated with the four structural equations and
(ii) the exogenous variables. As we have seen, these estimated impulse responses capture both the
direct and indirect (general equilibrium) effects on each endogenous variable, in both the current period
and in the future, of any exogenous shocks. Moreover, because the model is linear, the IRFs of each
endogenous variable, including the responses to the equation residuals, sum exactly to realized value of
the endogenous variable at each date. Consequently, the estimated model and the calculated IRFs for
historical shocks can be used to decompose the variation in any endogenous variable into its sources,
taking fully into account dynamic and general equilibrium effects.
32
FIGURE 12. THE SOURCES OF PRICE INFLATION, 2020Q1 to 2023Q1
Note: The figure shows a decomposition of the sources of inflation, 2020Q1 to 2023Q1, based on the
solution of the full model and the implied impulse response functions. The continuous line shows actual
inflation, and the total net heights of the bars are the model’s forecast of inflation in each period, given
initial conditions through 2019Q4 and excluding the effects of equation residuals. The grey portion of
each bar shows the contribution of pre-2020 data (and also include the contributions of productivity
shocks). Colored segments of each bar show the general equilibrium, fully dynamic contribution of each
exogenous variable to inflation in that period, as implied by the estimated model.
Using this approach, Figure 12 shows the estimated sources of inflation from 2020Q1 to
2023Q1. For comparison, the continuous line shows actual inflation. (The inflation data are quarterly, at
annualized rates, and thus more jagged than the annualized series often reported.) Figure 12 does not
show the contributions to inflation of shocks to the residuals of the model equations, both to avoid
clutter and because the residuals by definition do not have a clear structural interpretation.
Consequently, the sum of the estimated sources of inflation in each quarter (the net heights of the bars)
does not exactly equal realized inflation, the difference being the omitted effects of the equation
residuals.
The decomposition underlying Figure 12 takes as given data prior to 2020Q1. The implications of
the constants in the equation, plus the dynamic effects of pre-covid shocks, plus the actual behavior of
the productivity variable (whose dynamic effects we do not analyze) are put together in an “initial
conditions” category, shown in the figure by grey bars. The figure shows the contribution of initial
conditions to be roughly constant over time, suggesting that, absent the pandemic-era shocks
considered here, inflation would have likely remained stable at around 2 percent or a bit higher into
2023.
33
Initial conditions aside, the colored components of the vertical bars in Figure 12 show the full
dynamic contributions to inflation, in each quarter, of each of the four exogenous variables. Shocks to
the rate of change of the relative price of energy and food are constructed as deviations of the values of
those variables from zero. Shocks to the shortage and the vacancy-to-unemployment ratio variables are
constructed as the actual values of those variables minus their values in 2019Q4.
Figure 12 yields several conclusions. First, the contributions of food and (especially) energy price
shocks to the pandemic-era inflation were large. Energy price shocks in particular account for much of
the rise of overall inflation in late 2021 and the first half of 2022, and the for the decline in inflation in
the second half of 2022. The large and extended contributions of commodity price shocks to inflation
shown in Figure 12 are not inconsistent with our earlier finding that price shocks tend to have transitory
effects on inflation, as both energy and food prices rose continuously over much of the period (see
Figures 4 and 5), which our procedure interprets as a series of positive shocks. Second, sectoral
shortages were the dominant source of inflation in 2021Q2, and the effects of shortages on inflation,
both direct and indirect, remained significant through the end of our sample period. Third, and
importantly, the contribution to inflation of tight labor-market conditions—the leading concern of many
early critics of U.S. monetary and fiscal policies—was quite small early on, and indeed was negative in
2020 and early 2021 as labor markets suffered from the effects of the pandemic recession. However,
over time, as the labor market has remained tight, the traditional wage Phillips curve effect has begun to
assert itself, with the high vacancy-to-unemployment ratio becoming an increasingly important, though
by no means dominant, source of inflation.
To get a better understanding of the role of labor market tightness, we can use the same
approach to decompose wage inflation into its sources (Figure 13). Again, the contribution of “initial
conditions” is very stable, at around 3 percent per year, roughly the rate of nominal wage growth
consistent with 2 percent price inflation. Price shocks (energy, food, shortages) contribute less to wage
growth than to price inflation, but even at the beginning of 2023 the direct and indirect effects of shocks
to prices still explain a greater share than does the vacancy-to-unemployment ratio of the excess of
wage growth over that predicted by the initial conditions.
34
FIGURE 13. THE SOURCES OF WAGE INFLATION, 2020Q1 to 2023Q1
Note: The figure shows a decomposition of the sources of nominal wage growth, 2020Q1 to 2023Q1,
based on the solution of the full model and the implied impulse response functions. The continuous line
shows actual wage growth, and the total (net) heights of the bars are the model’s forecast of wage
growth in each period, given initial conditions through 2019Q4 and excluding the effects of equation
residuals. The grey bar shows the contribution of pre-2020 data (and also includes the contributions of
productivity shocks). Colored segments of each bar show the general equilibrium, fully dynamic
contribution of each exogenous variable to wage growth in that period, as implied by the estimated
model.
The retrospective evaluation of how policymakers assessed the economy in early 2021, around
the time of the passage of the American Rescue Plan, is thus more complicated than sometimes
portrayed. At least for the short run, policymakers were initially more right than wrong in arguing that
tight labor markets would not generate high inflation, although in focusing on unemployment rates and
total employment rather than the vacancy-to-unemployment ratio they did underestimate labor market
tightness. As we have seen, the initial sources of the inflation were primarily shocks to prices given
wages, including large energy price shocks and the surprisingly persistent shortages of cars and other
durable goods. By raising inflation expectations, and to a smaller extent by creating a catch-up effect,
these shocks ultimately affected wages as well as prices. However, over time a very tight labor market
has begun to exert increasing pressure on inflation, pressure which our model predicts will continue to
grow. Over the longer run, then, the critics who worried about an overheated economy leading to
inflation may be able to claim some vindication.
Model-based projections
Some insight into the future, as well as into the workings of the model, can be obtained by
projecting the model forward, under specified assumptions about the future paths of the four
35
exogenous variables. We briefly look at some projections in this section. However, we do so very
cautiously, for several reasons.
First, beyond the usual statistical uncertainty surrounding the parameter estimates and the
specification of the model itself, there is also a great deal of uncertainty about the future course of the
exogenous variables in the model. A full analysis would consider alternative scenarios with differing
assumptions about energy prices and other variables, which we do not attempt here. Instead, we
interpret the simulations described below as conditional projections, not unconditional forecasts.
Second, all else equal, our model is designed to project inflation and wage growth conditional
on the state of the labor market, as measured by the vacancy-to-unemployment ratio (𝑣𝑣/𝑢𝑢). Since we
know the past realizations of 𝑣𝑣/𝑢𝑢, we were able to use the model in the previous section to estimate
the portion of historical price and wage inflation stemming from tight labor markets. However, the
model takes 𝑣𝑣/𝑢𝑢 as given and provides no insight about the particular fiscal and monetary policies that
would be needed to achieve a given state of the labor market in the future. In addition, we know that
the Beveridge curve, the downward-sloping relation between job vacancies and unemployment, shifted
dramatically during the pandemic (Blanchard, Domash, and Summers 2022), obscuring the relationship
of the vacancy-to-unemployment ratio and other measures of labor market tightness, including
unemployment. We return to this point below.
Finally, for the purposes of projection the “natural” or steady-state value of the vacancy-to-
unemployment ratio, 𝑣𝑣/𝑢𝑢 ∗ , is important. Specifically, absent new shocks, in our model bringing down
wage inflation requires a period in which 𝑣𝑣/𝑢𝑢 is below its steady-state value. The steady state of 𝑣𝑣/𝑢𝑢
implied by our model depends on the parameters of the wage and price equations and is not tightly
estimated. For consistency with the decomposition exercises of the previous section, and following the
assumption made by Blanchard, Domash, and Summers, for these projections we assume that 𝑣𝑣/𝑢𝑢∗
equals 1.2, its value in 2019Q4, the last full quarter before the pandemic, a period when inflation
appeared stable. 16
With these substantial caveats, we can use the model to project the course of price inflation and
wage growth, starting in 2023Q2, with initial conditions determined by the actual data for the prior four
quarters. We assume that food and energy prices grow for the next few years at a rate equal to nominal
wage growth, so the growth rates of the relative prices grpe and grpf are both equal to zero; that
16
We adjust the constant in the estimated wage equation so that the model delivers a steady-state value of 𝑣𝑣/𝑢𝑢∗
equal to 1.2.
36
demand and supply at the sectoral level have largely normalized, so that the shortage variable takes an
index value of 10 (on a scale in which, recall, its highest weekly value is 100); 17 and that productivity
growth is 1 percent, close to its in-sample average. Equation residuals are set to zero. As in the rest of
the paper, we use the price equation estimated over the full sample, including the covid period, and
base the estimates for the other three equations on pre-covid data.
We consider three projections, corresponding to three assumed trajectories of the labor market.
Specifically, in our simulations we assume that macro policy brings down 𝑣𝑣/𝑢𝑢 over eight quarters,
beginning in 2023Q2, to one of three terminal values: 1.8 (approximately the current value of 𝑣𝑣/𝑢𝑢); 1.2
(the value that prevailed immediately before the pandemic, which we have assumed is the steady-state
or “natural” value of 𝑣𝑣/𝑢𝑢); and 0.8. Obviously, lower values of 𝑣𝑣/𝑢𝑢 require tighter monetary and fiscal
policies, all else equal. The value of 𝑣𝑣/𝑢𝑢 after eight quarters is not important for the points we want to
make, so we simply assume that it remains constant thereafter. The results of the projections are shown
in Figure 14. The three curves in the figure show the projected path of inflation under each of the
assumed terminal points for the vacancy-to-unemployment ratio (the first observation in each trajectory
is actual inflation in 2023Q1). As before, we use the CPI to measure inflation (not the PCE deflator,
which the Fed targets) and the ECI to measure the nominal wage.
FIGURE 14. INFLATION PROJECTIONS UNDER ALTERNATIVE PATHS FOR 𝑣𝑣/𝑢𝑢
Note: The figure shows projected inflation in the model if 𝑣𝑣/𝑢𝑢 is brought down linearly to the specified
terminal level over eight quarters. The value for 2023Q1 reflects actual data.
17
The realized values of shortage in the four quarters preceding the start of the simulation are 33, 18, 24, 22.
37
The qualitative lesson of Figure 14 is straightforward and would generalize for alternative
assumptions about the steady-state value of 𝑣𝑣/𝑢𝑢. All else equal, and not surprisingly, allowing 𝑣𝑣/𝑢𝑢 to
remain near current levels does not bring inflation down in our projections. Indeed, because an
extended period of inflation raises long-term inflation expectations, it leads to slowly increasing
inflation. In contrast, in our projections, reducing the vacancy-to-unemployment ratio to its assumed
steady-state level of 1.2 over the next eight quarters brings CPI inflation down to about 2.7 percent,
which, adjusting for historical differences between CPI and PCE inflation, is within striking distance of
the Fed’s target. A more aggressive policy, which brings 𝑣𝑣/𝑢𝑢 down to 0.8 in eight quarters, is projected
to reduce CPI inflation to close to 2 percent by the end of that period. In the latter case, the projections
show continuing declines in inflation for a constant level of 𝑣𝑣/𝑢𝑢; the implication is that this more
restrictive policy should ultimately be reversed.
One would like to know the unemployment rates associated with the three alternative paths.
Unfortunately, that depends on a factor outside the model, namely, the future evolution of the position
of the Beveridge curve (see the debate between Blanchard, Domash, and Summers 2022 and Figura and
Waller 2022). As we have discussed, during the pandemic the Beveridge curve shifted upward, implying
that, for reasons not fully understood, the job-worker matching process had become less efficient. If
that shift were to be fully reversed, then a decline in 𝑣𝑣/𝑢𝑢 to a level below its natural rate of 1.2,
together with an unemployment rate above the implied natural rate of 3.6 percent (the actual
unemployment rate in late 2019) could bring down inflation over time with a limited increase in
unemployment (not quite an “immaculate disinflation”, as unemployment must exceed the natural rate
for some time). If, in the other extreme case, the Beveridge curve were to remain at its position as of
early 2023, then the unemployment rate associated with 𝑣𝑣/𝑢𝑢 equal to 1.2—that is, the implied natural
rate of unemployment—would be about 4.3 percent. 18 As implied by the figure, reducing inflation to the
2 percent target in that case would require an unemployment rate above that level for a time.
IV. Conclusion
18
Blanchard, Domash, and Summers show that the unemployment rate associated with a given 𝑣𝑣/𝑢𝑢 is proportional
𝑣𝑣 −0.6
to . We calculate the natural rate by inferring the coefficient of proportionality from current data on
𝑢𝑢
unemployment and vacancy-to-unemployment rates and then multiplying by our estimated 𝑣𝑣/𝑢𝑢* of 1.2, raised to
a power of -0.6.
38
The pandemic-era inflation has been a complicated phenomenon that involved both multiple
sources and complex dynamic interactions. Ultimately, as many have recognized, the inflation largely
reflected strong aggregate demand, the product of easy fiscal and monetary policies, excess savings
accumulated during the pandemic, and the reopening of locked-down economies. The strength of
aggregate demand led to a (belatedly recognized) tightening of the labor market, as reflected in record
high ratios of job openings to unemployed workers. However, at least initially, the arguments that the
tighter labor market would not create much inflation, so long as the labor market tightness was
temporary, were in fact correct. Although the wage Phillips curve was operative, inflation expectations
did not de-anchor and there was little evidence of a wage-price spiral, in that workers did not achieve
nominal wage gains sufficient to compensate them for unexpected price increases (a weak catch-up
effect). Our decomposition of inflation shows that tight labor markets alone made only a modest
contribution to inflation early on.
Instead, initially, the inflation reflected primarily developments in product markets. Excessive
aggregate demand set off the inflation but did so primarily by raising prices given wages, through its
contribution to higher commodity prices (which reflected other forces as well, including, from 2022 on,
the war in Ukraine) and by increasing the demand for goods for which supply was inelastic.
The good news for policymakers from our analysis is that the indirect effects of the price shocks
on inflation were more short-lived than might have been expected. In particular, inflation expectations,
especially short-run expectations, rose enough to put upward pressure on wages and prices but
generally remained well anchored. Although shocks to prices given wages played a central role in the
pandemic-era inflation, in the absence of strong indirect effects or renewed shocks, the portion of
inflation accounted for by these shocks should largely (although not fully) dissipate over time, even
without policy action.
However, even as the effects of price shocks have waned, the effects of tight labor markets have
begun to cumulate. Our decomposition shows that, as of early 2023, tight labor market conditions still
accounted for a minority share of excess inflation. But according to our analysis, if current labor market
conditions persist, that share is likely to grow and will not subside on its own. The portion of inflation
which traces its origin to overheating of labor markets can only be reversed by policy actions that bring
labor demand and supply into better balance. The effects of such policies on unemployment depend on
the extent to which matching efficiency in the labor market normalizes (that is, on whether the
Beveridge curve shifts down to its pre-pandemic position).
39
What are the lessons of all this for macroeconomics? The pandemic was extraordinarily
disruptive, making forecasting and policymaking difficult. Nevertheless, we don’t think that the recent
experience justifies throwing out existing models of wage-price dynamics. We were able to simulate the
pandemic-era inflation using a simple and rather traditional model of the interactions of wages, prices,
and inflation expectations. That said, our results show that inflation can be a complicated phenomenon.
Policymakers must be alert to the possibility that inflationary pressures can come from product markets
as well as labor markets, for example, through unexpected changes in input costs or shifts in demand
that collide with inelastic sectoral supply curves. Moreover, through various mechanisms, inflationary
pressures from product and labor markets can interact and be mutually reinforcing. The good news is
that, empirically, we find the second-round and indirect effects of product-market shocks to be
relatively modest, implying that, as the early critics warned, labor-market balance should ultimately be
the primary concern for central banks attempting to maintain price stability.
40
Appendix. Model estimates and robustness checks
Estimates and selected statistics for the four equations of the model using alternative measures
of the endogenous variables are given immediately below (Tables A2 and A3). Table A4 provides full
estimation results, including estimated coefficients for all lagged values, for the base specification and
some specifications using alternative data. Price equations are estimated over the sample 1990Q1 to
2023Q1, which includes the covid period, while other equations are estimated on the pre-covid sample,
ending in 2019Q4. P-values are given for both (i) the hypothesis that the sum of a set of coefficients is
zero (p-stat (sum)) and (ii) the joint hypothesis that each of the coefficients applying to a given right-side
variable is zero (p-stat (joint)). Numbers in parentheses indicate included lags, e.g., (0 to -4) says that the
contemporaneous value and four lags of the variable are included in the regression. Variable mnemonics
used in the reporting of regression results are given in Table A1 below (see also Table 1 in the text).
TABLE A1. VARIABLE MNEMONICS USED IN THIS APPENDIX
WAGE EQUATION
gw = change in the log nominal wage (ECI)
cf1 = one-year inflation expectations (Federal Reserve Bank of Cleveland)
spf1 = one-year inflation expectation (Survey of Professional Forecasters)
v/u = vacancy-to-unemployment ratio
catch-up = the excess of the actual log price level over the expected log price level
gpty = 8-quarter moving average productivity trend
PRICE EQUATION (additional variables)
gp = gcpi = change in the log nominal price level (CPI)
gpce = change in the log nominal price level (PCE)
grpe = change in the log of CPI energy prices relative to the aggregate wage
grpf = change in the log of CPI food prices relative to the aggregate wage
shortage = index of Google searches for “shortage”
INFLATION EXPECTATIONS EQUATIONS (additional variables)
cf10 = ten-year inflation expectations (Federal Reserve Bank of Cleveland)
spf10 = long-run inflation expectations (ten-year inflation forecast from Survey of Professional
Forecasters)
41
TABLE A2. ESTIMATION WITH PCE INFLATION RATHER THAN CPI INFLATION
Dependent variable: gw
Independent variable gw v/u catch-up cf1 gpty
Lags -1 to -4 -1 to -4 -1 to -4 -1 to -4 -1
Sum of coefficients 0.345 0.774 0.008 0.655 0.068
p-stat (sum) 0.050 0.016 0.092 0.000 0.258
p-stat (joint) 0.226 0.037 0.404 0.003 0.258
R-squared 0.579
No. observations 120
Dependent variable: gpce
Independent variable gpce gw grpe grpf shortage gpty
Lags -1 to -4 0 to -4 0 to -4 0 to -4 0 to -4 -1
Sum of coefficients 0.501 0.499 0.038 0.086 0.014 -0.104
p-stat (sum) 0.001 0.001 0.002 0.133 0.442 0.116
p-stat (joint) 0.001 0.004 0.000 0.237 0.018 0.116
R-squared 0.844
No. observations 133
Dependent variable: cf1
Independent variable cf1 cf10 gp
Lags -1 to -4 0 to -4 0 to -4
Sum of coefficients 0.375 0.527 0.098
p-stat (sum) 0.031 0.001 0.016
p-stat (joint) 0.001 0.000 0.000
R-squared 0.884
No. observations 120
Dependent variable: cf10
Independent variable cf10 gp
Lags -1 to -4 0 to -4
Sum of coefficients 0.971 0.029
p-stat (sum) 0.000 0.129
p-stat (joint) 0.000 0.006
R-squared 0.929
No. observations 120
42
TABLE A3. ESTIMATION WITH SURVEY OF PROFESSIONAL FORECASTERS INSTEAD OF CLEVELAND FED FORECASTS
Dependent variable: gw
Independent variable gw v/u catch-up spf1 gpty
Lags -1 to -4 -1 to -4 -1 to -4 -1 to -4 -1
Sum of coefficients 0.233 1.154 0.087 0.767 0.154
p-stat (sum) 0.205 0.002 0.285 0.000 0.024
p-stat (joint) 0.494 0.001 0.441 0.001 0.024
R-squared 0.599
No. observations 120
Dependent variable: gp
Independent variable gp gw grpe grpf shortage gpty
Lags -1 to -4 0 to -4 0 to -4 0 to -4 0 to -4 -1
Sum of coefficients 0.335 0.665 0.066 0.126 0.018 -0.143
p-stat (sum) 0.037 0.000 0.000 0.050 0.281 0.027
p-stat (joint) 0.066 0.000 0.000 0.050 0.000 0.027
R-squared 0.947
No. observations 133
Dependent variable: spf1
Independent variable spf1 spf10 gp
Lags -1 to -4 0 to -4 0 to -4
Sum of coefficients 0.854 0.113 0.033
p-stat (sum) 0.000 0.031 0.067
p-stat (joint) 0.000 0.000 0.000
R-squared 0.952
No. observations 120
Dependent variable: spf10
Independent variable spf10 gp
Lags -1 to -4 0 to -4
Sum of coefficients 0.969 0.031
p-stat (sum) 0.000 0.002
p-stat (joint) 0.000 0.029
R-squared 0.978
No. observations 120
43
TABLE A4. FULL ESTIMATION RESULTS FOR ALTERNATIVE MEASURES OF INFLATION AND INFLATION EXPECTATIONS
Dependent variable: gw
Using gcpi Using gpce Using spf
gw (-1) 0.16 gw (-1) 0.14 gw (-1) 0.08
(0.10) (0.10) (0.10)
gw (-2) 0.12 gw (-2) 0.08 gw (-2) 0.10
(0.10) (0.10) (0.10)
gw (-3) 0.17* gw (-3) 0.15 gw (-3) 0.12
(0.10) (0.10) (0.10)
gw (-4) 0.00 gw (-4) -0.03 gw (-4) -0.06
(0.10) (0.10) (0.10)
cf1 (-1) 0.34** cf1 (-1) 0.38*** spf1 (-1) -0.11
(0.14) (0.13) (0.40)
cf1 (-2) -0.03 cf1 (-2) 0.00 spf1 (-2) 0.22
(0.15) (0.14) (0.46)
cf1 (-3) 0.20 cf1 (-3) 0.27* spf1 (-3) 0.35
(0.16) (0.15) (0.45)
cf1(-4) 0.03 cf1(-4) -0.01 spf1(-4) 0.30
(0.16) (0.15) (0.39)
magpty (-1) 0.03 magpty (-1) 0.07 magpty (-1) 0.15**
(0.06) (0.06) (0.07)
vu(-1) 3.77* vu(-1) 3.31* vu(-1) 3.38*
(1.98) (1.94) (1.96)
vu (-2) -1.81 vu (-2) -1.69 vu (-2) -0.67
(3.63) (3.58) (3.57)
vu. (-3) -3.64 vu. (-3) -3.58 vu. (-3) -3.77
(3.66) (3.61) (3.60)
vu (-4) 2.38 vu (-4) 2.74 vu (-4) 2.21
(2.10) (2.07) (2.10)
catch-up (-1) -0.01 catch-up (-1) -0.11 catch-up (-1) 0.12
(0.08) (0.13) (0.08)
catch-up (-2) 0.01 catch-up (-2) 0.13 catch-up (-2) 0.04
(0.08) (0.15) (0.09)
catch-up (-3) -0.00 catch-up (-3) -0.05 catch-up (-3) -0.07
(0.08) (0.14) (0.09)
catch-up (-4) -0.02 catch-up (-4) 0.04 catch-up (-4) -0.00
(0.07) (0.11) (0.08)
constant -0.27 constant -0.93* constant -0.75***
(0.20) (0.50) (0.24)
R-squared 0.578 R-squared 0. 579 R-squared 0. 599
No. observations 120 No. observations 120 No. observations 120
44
Dependent variable: gp = (gcpi or gpce)
Using gcpi Using gpce Using spf
gcpi (-1) 0.04 gpce (-1) 0.03 gcpi (-1) 0.04
(0.11) (0.09) (0.11)
gcpi (-2) 0.18* gpce (-2) 0.23** gcpi (-2) 0.18*
(0.10) (0.09) (0.10)
gcpi (-3) 0.23** gpce (-3) 0.29*** gcpi (-3) 0.23**
(0.11) (0.09) (0.11)
gcpi (-4) -0.11 gpce (-4) -0.04 gcpi (-4) -0.11
(0.10) (0.08) (0.10)
gw 0.37*** gw 0.21** gw 0.37***
(0.09) (0.10) (0.09)
gw (-1) 0.18 gw (-1) 0.08 gw (-1) 0.18
(0.11) (0.11) (0.11)
gw (-2) 0.04 gw (-2) 0.24** gw (-2) 0.04
(0.11) (0.11) (0.11)
gw (-3) 0.04 gw (-3) -0.04 gw (-3) 0.04
(0.11) (0.11) (0.11)
gw (-4) 0.05 gw (-4) 0.00 gw (-4) 0.05
(0.10) (0.11) (0.10)
magpty -0.14** magpty -0.10 magpty -0.14**
(0.06) (0.07) (0.06)
grpe 0.09*** grpe 0.04*** grpe 0.09***
(0.00) (0.00) (0.00)
grpe (-1) 0.00 grpe (-1) 0.03*** grpe (-1) 0.00
(0.01) (0.00) (0.01)
grpe (-2) -0.01 grpe (-2) -0.01 grpe (-2) -0.01
(0.01) (0.01) (0.01)
grpe (-3) -0.02** grpe (-3) -0.02*** grpe (-3) -0.02**
(0.01) (0.01) (0.01)
grpe (-4) 0.01 grpe (-4) -0.01 grpe (-4) 0.01
(0.01) (0.00) (0.01)
grpf 0.11*** grpf 0.03 grpf 0.11***
(0.04) (0.03) (0.04)
grpf (-1) -0.02 grpf (-1) 0.03 grpf (-1) -0.02
(0.04) (0.03) (0.04)
grpf (-2) -0.00 grpf (-2) -0.04 grpf (-2) -0.00
(0.04) (0.03) (0.04)
grpf (-3) -0.00 grpf (-3) -0.01 grpf (-3) -0.00
45
(0.04) (0.03) (0.04)
grpf (-4) 0.04 grpf (-4) 0.07** grpf (-4) 0.04
(0.04) (0.03) (0.04)
shortage 0.11*** shortage 0.04* shortage 0.11***
(0.02) (0.02) (0.02)
shortage (-1) -0.03 shortage (-1) 0.04** shortage (-1) -0.03
(0.02) (0.02) (0.02)
shortage (-2) 0.00 shortage (-2) 0.01 shortage (-2) 0.00
(0.02) (0.02) (0.02)
shortage (-3) -0.03 shortage (-3) -0.04** shortage (-3) -0.03
(0.02) (0.02) (0.02)
shortage (-4) -0.02 shortage (-4) -0.04* shortage (-4) -0.02
(0.02) (0.02) (0.02)
constant -0.11 constant -0.27 constant -0.11
(0.16) (0.20) (0.16)
R-squared 0.947 R-squared 0.844 R-squared 0.947
No. observations 133 No. observations 133 No. observations 133
Dependent variable: cf1/spf1
Using gcpi Using gpce Using spf
cf1 (-1) 0.30*** cf1 (-1) 0.25*** spf1 (-1) 0.63***
(0.09) (0.10) (0.09)
cf1 (-2) -0.23** cf1 (-2) -0.21** spf1 (-2) 0.17
(0.10) (0.10) (0.11)
cf1 (-3) 0.18* cf1 (-3) 0.15 spf1 (-3) 0.21*
(0.10) (0.10) (0.11)
cf1 (-4) 0.12 cf1 (-4) 0.19** spf1 (-4) -0.15*
(0.07) (0.09) (0.09)
cf10 1.20*** cf10 1.23*** spf10 0.67***
(0.14) (0.16) (0.15)
cf10 (-1) -0.47** cf10 (-1) -0.40 spf10 (-1) -0.04
(0.23) (0.25) (0.18)
cf10 (-2) 0.02 cf10 (-2) -0.14 spf10 (-2) -0.58***
(0.23) (0.26) (0.19)
cf10 (-3) 0.14 cf10 (-3) 0.20 spf10 (-3) -0.11
(0.23) (0.25) (0.18)
cf10 (-4) -0.38** cf10 (-4) -0.36* spf10 (-4) 0.18
(0.17) (0.20) (0.15)
gcpi 0.04*** gpce 0.09*** gcpi 0.03***
(0.01) (0.02) (0.01)
gcpi (-1) 0.10*** gpce (-1) 0.08*** gcpi (-1) 0.02***
(0.01) (0.03) (0.01)
gcpi (-2) 0.00 gpce (-2) -0.01 gcpi (-2) -0.01
(0.02) (0.03) (0.01)
gcpi (-3) 0.01 gpce (-3) -0.01 gcpi (-3) -0.00
46
(0.02) (0.03) (0.01)
gcpi (-4) -0.02 gpce (-4) -0.05** gcpi (-4) -0.01
(0.02) (0.03) (0.01)
R-squared 0.908 R-squared 0.929 R-squared 0.952
No. observations 120 No. observations 120 No. observations 120
Dependent variable: cf10/spf10
Using gcpi Using gpce Using spf
cf10 (-1) 0.85*** cf10 (-1) 0.82*** spf10 (-1) 0.70***
(0.09) (0.09) (0.09)
cf10 (-2) -0.05 cf10 (-2) -0.06 spf10 (-2) 0.26**
(0.12) (0.12) (0.11)
cf10 (-3) 0.20 cf10 (-3) 0.25** spf10 (-3) 0.00
(0.12) (0.12) (0.11)
cf10 (-4) -0.03 cf10 (-4) -0.05 spf10 (-4) -0.00
(0.09) (0.09) (0.09)
gcpi 0.03*** gpce 0.05*** gcpi 0.01
(0.01) (0.01) (0.00)
gcpi (-1) 0.01 gpce (-1) -0.02 gcpi (-1) 0.01**
(0.01) (0.02) (0.00)
gcpi (-2) -0.01 gpce (-2) -0.00 gcpi (-2) 0.01*
(0.01) (0.01) (0.00)
gcpi (-3) -0.00 gpce (-3) -0.01 gcpi (-3) 0.00
(0.01) (0.01) (0.00)
gcpi (-4) -0.00 gpce (-4) 0.01 gcpi (-4) 0.01*
(0.01) (0.01) (0.00)
R-squared 0. 931 R-squared 0.932 R-squared 0.978
No. observations 120 No. observations 120 No. observations 120
47
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