Prospects for Inflation in a High Pressure Economy: Is the Phillips Curve Dead or is It Just Hibernating? (Working Paper 25792, May 2019)
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NBER Working Paper No. 25792, Prospects for Inflation in a High Pressure Economy: Is the Phillips Curve Dead or is It Just Hibernating?, by Peter Hooper, Frederic S. Mishkin and Amir Sufi, dated May 2019 and prepared for the 2019 US Monetary Policy Forum. The abstract states that the paper reviews a substantial range of empirical evidence on whether the Phillips curve is dead, meaning that its slope has flattened to zero. It states that national data going back to the 1950s and 60s yield strong evidence of negative slopes and significant nonlinearity, that this evidence weakens dramatically based on macro data since the 1980s for the price Phillips curve but not the wage Phillips curve, and that state level and MSA level data since the 1980s yield significant evidence of both.
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NBER WORKING PAPER SERIES
PROSPECTS FOR INFLATION IN A HIGH PRESSURE ECONOMY:
IS THE PHILLIPS CURVE DEAD OR IS IT JUST HIBERNATING?
Peter Hooper
Frederic S. Mishkin
Amir Sufi
Working Paper 25792
http://www.nber.org/papers/w25792
NATIONAL BUREAU OF ECONOMIC RESEARCH
1050 Massachusetts Avenue
Cambridge, MA 02138
May 2019
This paper was prepared for the 2019 US Monetary Policy Forum. This paper is not a product of
the Research Department of Deutsche Bank Securities Inc,. The views expressed here reflect
those of the authors only and may not be representative of others at Deutsche Bank Securities
Inc., Columbia University, University of Chicago or the National Bureau of Economic Research.
For disclosures related to Deutsche Bank Securities Inc. please see https://
ger.gm.cib.intranet.db.com/ger/disclosure/DisclosureDirectory.eqsr. Mishkin and Sufi thank the
Initiative on Global Markets at Chicago Booth for financial support. We want to thank especially
Justin Weidner for his many substantive contributions to this paper. We also thank Sebastian
Hanson and Suvir-Kumar Ranjan for their excellent research assistance. We have benefitted from
comments on earlier drafts of this paper by.Steve Cecchetti, Michael Feroli, David Greenlaw,
Ethan Harris, Jim Hamilton, Anil Kashyap, Oren Klachkin, Catherine Mann, John Roberts, Kim
Schoenholz, and Ken West. The views expressed herein are those of the authors and do not
necessarily reflect the views of the National Bureau of Economic Research.
At least one co-author has disclosed a financial relationship of potential relevance for this
research. Further information is available online at http://www.nber.org/papers/w25792.ack
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.
© 2019 by Peter Hooper, Frederic S. Mishkin, and Amir Sufi. 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.
Prospects for Inflation in a High Pressure Economy: Is the Phillips Curve Dead or is It Just
Hibernating?
Peter Hooper, Frederic S. Mishkin, and Amir Sufi
NBER Working Paper No. 25792
May 2019
JEL No. E31,E52,E65
ABSTRACT
This paper reviews a substantial range of empirical evidence on whether the Phillips curve is
dead, i.e. that its slope has flattened to zero. National data going back to the 1950s and 60s yield
strong evidence of negative slopes and significant nonlinearity in those slopes, with slopes much
steeper in tight labor markets than in easy labor markets. This evidence of both slope and
nonlinearity weakens dramatically based on macro data since the 1980s for the price Phillips
curve, but not the wage Phillips curve. However, the endogeneity of monetary policy and the
lack of variation of the unemployment gap, which has few episodes of being substantially below
zero in tis sample period, makes the price Phillips curve estimates from this period less reliable.
At the same time, state level and MSA level data since the 1980s yield significant evidence of
both negative slope and nonlinearity in the Phillips curve. The difference between national and
city/state results in recent decades can be explained by the success that monetary policy has had
in quelling inflation and anchoring inflation expectations since the 1980s. We also review the
experience of the 1960s, the last time inflation expectations became unanchored, and observe
both parallels and differences with today. Our analysis suggests that reports of the death of the
Phillips curve may be greatly exaggerated.
Peter Hooper Amir Sufi
Deutsche Bank University of Chicago
NYC Booth School of Business
60 Wall Street 5807 South Woodlawn Avenue
New York, NY 10005 Chicago, IL 60637
peter.hooper@db.com and NBER
amir.sufi@chicagobooth.edu
Frederic S. Mishkin
Columbia University
Graduate School of Business
Uris Hall 817
3022 Broadway
New York, NY 10027
and NBER
fsm3@columbia.edu
Section 1: Introduction
Starting in March of 2017, the unemployment rate has fallen below both the
Congressional Budget Office’s and the FOMC participants’ current estimates of the natural rate
of unemployment (4.6% and 4.4%, respectively). Since March of 2018, the unemployment rate
has fallen below 4%, levels that were last seen in the late 1960s. The most recent median
projections of FOMC participants for the unemployment rate are 3.5% in 2019, 3.6% for 2020
and 3.8% for 2021. FOMC projections indicate that the economy for the next several years will
be operating in a high-pressure environment, where labor markets are tight and the
unemployment rate remains below the natural rate of unemployment.
Monetary policy is also currently accommodative, despite the rising path of the federal
funds rate since December of 2015. The federal funds rate target is currently 2 ½%, which is a
real interest rate around 0.5%, given that inflation expectations for the PCE deflator are close to
the Federal Reserve’s inflation target of 2%. This real federal funds rate is very low by historical
standards. The current federal funds rate target is also below current FOMC participants’
median estimate of the “neutral” or long-run federal funds rate of 2.8%.
Important to the Federal Reserve’s decisions about the future path of the federal funds
rate is whether the Committee’s projection of a high-pressure economy for some time to come
will lead to inflationary pressures that would require significant further increases in the federal
funds rate. Phillips curves estimated with data prior to 1990 suggest that a high-pressure
economy in which the unemployment rate remains below the natural rate for long periods of time
can lead to an acceleration of inflation. Indeed, this is what happened in the 1960s, when a high-
pressure economy led to inflation accelerating to above 5% by the end of the decade. The Great
Inflation period then ensued, which was only terminated by very high federal funds rates under
the Volcker Fed.
Despite the projection of a high-pressure economy, at its most recent meeting, the FOMC
pivoted essentially to a neutral policy stance. Fed chair, Jerome Powell, made it clear that the
FOMC will be “patient” in making any further adjustments to the federal fund rate. Market
participants, including many economists have moved to expecting zero or at most one further
rate hike, leaving policy in an accommodative stance. The Fed’s shift reflects a combination of
concerns about global risks and an absence of worries about an inflation overshoot. Inflation
expectations, gleaned from market measures, various surveys, and the FOMC’s own projections,
remain subdued.
So far an unemployment rate below the natural rate of unemployment rate for the last two
years been associated with only a modest increase in inflation, which has continued to fall short
of the Fed’s 2% inflation objective. This result is consistent with a Phillips curve that is very
flat: in other words, the responsiveness of inflation to the unemployment gap—the difference
between the unemployment rate and the natural rate of unemployment—is very weak. Figure 1.1
provides estimates of the slope of the Phillips curve, that is, the coefficient on the unemployment
gap, from rolling regressions for core PCE. (The rolling regressions use 20-year windows, with
the date in the figure indicating the end of the window. Details of this Phillips curve analysis is
provided in section 2.)
2
Figure 1.1 Core PCE Phillips curve coefficient from 20-year rolling regressions
Source: Authors’ calculations
We see that starting with 20-year sample periods that would have begun by the early
1980s, the slope of the Phillips curve began to recede precipitously, and since the early 2000s it
has been much closer to zero. This finding has often been characterized by saying that the
Phillips curve is dead, or close to it, i.e., the unemployment gap tells us very little about what
will happen to inflation. Thus running a high-pressure economy presents very little risk of
accelerating inflation, and this provides an important rationale for patience in raising the federal
funds rate.
In this paper, we examine whether this sanguine view about the prospects for inflation
when there is a high-pressure economy is justified. We look at why the Phillips curve has been
so flat and whether there is a danger that it may not continue to be flat in the future, suggesting
that there is a risk that the current high-pressure economy could lead to accelerating inflation. In
other words we explore whether the Phillips curve is truly dead, or is just hibernating.
We conduct empirical analysis in the next four sections to examine whether the Phillips
curve is alive and if there is inflation risk should we turn back toward a high-pressure economy.
Section 2 examines the macro, time-series data for both price and wage inflation going
back as far as the early 1950s, with a particular focus on the finding that the Phillips curve has
flattened since the late 1980s. It also examines in some detail the question of whether the
Phillips curve is nonlinear with a slope that steepens appreciably when the unemployment rate is
well below the natural rate of unemployment. The analysis yields significant evidence that such
nonlinearity does exist, though less so in more recent years in the price Phillips curve. The
analysis also reveals a significant difference that has emerged between the price-Phillips curve
and the wage-Phillips curve in recent decades, with the wage-Phillips curve having flattened
significantly less and retained greater nonlinearity.
3
The time-series data since the 1980s have very few episodes of the unemployment rate
being well below the natural rate of unemployment. It is therefore possible that the inability to
find much slope, at least in the price-Phillips curve, in the more recent sample using macro, time-
series data occurs because there is insufficient variation in the data. We thus turn in Section 3 to
estimate Phillips curves using data from states and Metropolitan Statistical Areas (MSAs), which
have much greater variation. We do find that steeper and non-linear Phillips curves do appear in
more recent years in the state and MSA data.
One of the prominent explanations for a flattening of the Phillips curve is the anchoring
of inflation expectations in recent decades. However, there is a possibility that a high-pressure
economy could lead to a shift from a regime of low inflation with stable expectations to one of
significantly rising inflation. The last time this happened, with the Phillips curve coming out of
hibernation at the national level, was in the 1960s. In Section 4, we take a closer look at the
1960s and consider some of the key parallels and differences with the current economic and
policy environment.
Section 5 then turns to a more forward-looking assessment of what the various linear and
nonlinear models of price and wage inflation have to say about the prospects for inflation over
the next several years, under alternative scenarios, including both the FOMC’s projections for
unemployment and an even tighter labor market.
Finally Section 6 presents our conclusions.
4
Section 2. Evidence from Macro Time-Series Data
This section reviews the empirical evidence on both the slope of the Phillips curve—the
responsiveness of inflation to economic slack--and the existence of nonlinearities in that slope—
i.e., how it may change under different degrees of economic slack using macro (national) time
series data. Much has been written on the slope and its demise over recent decades, somewhat
less on the existence of nonlinearities. Our central interest is in determining just what macro data
have to say about how flat the slope is currently and what risks we can find that the slope could
steepen ahead (and when and how much) if the labor market should continue to tighten.
Following a brief review of the empirical literature, we outline a conventional Phillips
curve model—including both price and wage variants--and describe the data that is used to test
it. Next we put both linear and nonlinear versions of the model through their paces over the
entire sample period from the early 1950s through 2018. We then review the stability of these
models over time and document the extent to which both linear and nonlinear variants have held
up or changed in recent decades. In the final part of this section, we discuss questions raised by
the empirical results presented and set the stage for the analysis presented in the following
sections of this paper.
2.1 Review of Literature on Phillips Curve Slope and Nonlinearties
2.1.1 Flattening of the Phillips curve and Persistence of Inflation
There is a strong consensus view in the literature that US inflation dynamics have changed
dramatically over the past several decades. What was once seen as a robust relationship between
economic slack (or lack thereof) and inflation driven by the experience of the 1960s and 70s has
become much weaker over time, as documented in a substantial body of empirical literature. This
view has been bolstered in the past decade by the failure of price and wage inflation to fall as much
as earlier models predicted they would in response to the huge run-up in unemployment during the
great recession. The view that the Phillips curve is dead, dying, or at least has flattened
tremendously over the decades since the 1970s appears to have held up generally in the literature
for both price and wage inflation. Powell (2018a) summarized this development via rolling
regressions with a conventional Phillips curve, showing both a sharp decline in the slope of the
curve (the coefficient on the unemployment gap) after the 1980s, and a sharp drop in the
persistence of inflation more recently.
The decline in the persistence of inflation has been just as important as the flattening of the
Phillips curve slope in the short run because it implies that any cyclical shocks to inflation will be
transitory, not passed on to higher inflation and inflation expectations as they were in the past.
That is, reduced inflation persistence effectively reduces the longer-term slope of the Phillips curve
for any value that slope takes in the short run.
These developments have been reviewed and surveyed in more detail by Kiley (2015) who
focused in particular on the upside surprise in inflation following the great recession and Blanchard
(2016) who noted that the flattening of the Philips curve has been occurring since the 1980s.
5
Indeed, Bernanke (2007) and Mishkin (2007) among many others had made much the same
observation before the global financial crisis hit. Leduc and Wilson (2017) have recently
documented the flattening of the wage Phillips curve with rolling regressions, and Murphy (2018)
has observed that over the past decade, “The evidence for the U.S. suggests that the slopes of the
price and wage Phillips Curves…are low and have gotten a little flatter.”
The perceived flattening of the Phillips curve has also generated a good deal of research
into the question of why this has happened. The most prevalent explanation is that inflation
expectations have both become more important (than lagged inflation) as a determinant of
current inflation and have become more firmly anchored as the Fed has more clearly committed
to achieving a now stated inflation objective of 2%. This view has been analyzed and expressed
in a wide range of research and Fed communications, including among others, Roberts (2006),
Bernanke (2007), Mishkin (2007 and 2011), Kiley (2008 and 2015), Yellen (2015), Ng, Wessel,
and Sheiner (2018), Powell (2018a), and Pfajfar and Roberts (2018).
Other explanations of the flattening, especially of the wage Phillips curve, have focused
more on reasons for the failure of wage (and price) inflation to fall more during the Great
Recession. These reasons include the existence of menu costs that lead to downward rigidities in
wages and prices as assessed by Ball and Mazumder (2011), and other factors leading to
downward wage rigidities analyzed by Daly and Hobjin (2014). More recently, Daly, Hobijn,
and Pyle (2016) have turned to asking why wage inflation has not risen more as the labor market
has tightened. Their explanation is that the shifting composition of the labor force is imparting a
downward bias to aggregate wage inflation, with high-wage baby-boomers retiring in unusually
large number and lower-wage entrants and reentrants coming back into the labor force.
2.1.2 Nonlinearities
Interest in the existence of nonlinearities in the slope of the Phillips curve have existed
for as long as the curve itself, with the original Phillips (1958) curve estimated nonlinearly. A
decade and a half after Phillips introduced the concept, Tobin (1972) argued that it would be
kinked inasmuch as inflation would rise sharply once unemployment fell to a very low level. In
more recent empirical work, several approaches to capturing nonlinearities have been
considered; we focus on those employing national data here; approaches using panel data at the
state and local level are considered in the next section. Barnes and Olivei (2003) tested a
piecewise linear or “threshold” specification of the Phillips relationship, allowing the slope to
differ at different levels of the unemployment gap. They found using data from 1961 to 2002
that the slope of the core PCE Phillips curve was -0.3 when the unemployment gap was more
than 1.3% points above or 1.4% points below zero, and much flatter at -0.06 when it was within
that range around zero. Peach, Rich, and Cororaton (2011) used a similar approach and found
that the threshold--i.e., the distance from zero the unemployment gap has to move (plus or
minus) before the Phillips curve steepens--had increased to about to 1.5% points. This is also the
figure that Stock and Watson (2009) identified as the threshold beyond which the Phillips curve
model outperformed univariate models of inflation (i.e., models in which inflation is driven by
its own history) in forecasting tests.
6
The failure of inflation to fall as much as expected in a very weak labor market during the Great
Recession called the symmetric threshold model into question and led researchers to ask whether
wages and prices respond differently in weak versus tight labor markets. Doser, Nunes, and
Sheremirov (2017) used an approach similar to that of Barnes and Olivei with more recent data
and found evidence to support a single kink in the Phillips curve slope. When the unemployment
gap is above about 2.0, the slope is essentially zero and when it is below that level, the slope is
around -0.6.
2.1.3: Modeling Regime shifts with Markov Switching
As we have discussed, the most prevalent explanation for the flattening of the Phillips
curve and less persistence of inflation is that inflation expectations have both become more
firmly anchored in recent decades. This suggests that there might be two different Markov-
switching regimes, one in which inflation expectations are anchored as has occurred in recent
decades other periods prior to this in which inflation expectations are unanchored. One way to
model such a regime shift is with a Markov-switching model as in Nalewaik (2016).
Nalewaik’s approach was to allow the Phillips curve model to switch from a stationary
state (where the mean of inflation and inflation expectations are relatively stable over time), to a
nonstationary state, where the mean of inflation and inflation expectations can change
significantly over time. In the stationary regime, shocks to inflation generally have only
transitory effects as inflation is generally drawn back to its mean and there is a relatively flat
linear slope of the Phillips curve when the unemployment gap is above zero. In the nonstationary
regime, shocks to inflation have persistent effects as expectations follow an adaptive process. In
the terms we discussed above, this is a state where inflation is highly persistent and the
accelerationist version of the Phillips curve model prevails. When in the stationary regime, a
shock to inflation that is large and persistent enough can cause a shift to the nonstationary
regime. In both regimes, the slope of the Phillips curve has a quadratic form with steepening of
the slope the further the unemployment gap drops below zero. This nonlinearity allows the
model to capture the heightened inflationary effect of a tight labor market and the shift to a
nonstationary regime. In his empirical analysis, Nalewaik found, when estimating a model for
core PCE inflation, that the 1960s and the period since the mid-1990s conformed to the
stationary regime, and that the intervening years during the 1970s through the early 1990s
conformed more to the stationary regime. He also found that the probability of a switch from the
stationary to nonstationary regime was boosted substantially by the rise in actual inflation
induced by the large and persistent unemployment gap that emerged during the 1960s.
2.2 Estimating the Phillips Curve Model
To simplify our analysis, we adhere to what we term the current “consensus” or plain
vanilla version of the expectations augmented Phillips curve model—one that has been espoused
7
by the current and recent past Fed Chairs. 1 We employ one that is very close to the version
presented in Yellen (2017) and described in more general terms by Powell (2018a). The model
expresses current price or wage inflation as a function of (1) a constant term 𝛼, (2) the
unemployment gap (unemployment, 𝑢 , minus the natural rate or NAIRU, 𝑢∗ ) to capture the
effects of economic slack or lack thereof, (3) a measure of longer-run inflation expectations 𝜋 ,
(4) lagged values of actual inflation 𝜋 , and (4) other factors, X:
𝜋 = 𝛼 + 𝛽(𝑢 − 𝑢∗ ) + 𝛿𝜋 + 𝛾𝜋 + 𝜆𝑋
Lagged inflation may play more than one role in this model. First it may augment the
inflation expectations term to the extent that actual expectations are more backward looking than
the survey based measure included in the model. Second, it may capture inflation dynamics by
factoring in the lagged effects of changes in the other determinants of inflation. 2 In order to
preserve homogeneity in prices (i.e., to avoid having actual inflation diverge persistently from
expected inflation over time), the sum of the coefficients on expected inflation and the lagged
inflation terms (𝛿 + ∑ 𝛾 ) is constrained to 1.0. We included seven lags on the inflation term,
but generally only the first two or three lags were significant, and the results did not change
noticeably when either longer or shorter lags were tried. 3 The persistence of inflation is gauged
by the sum of the lagged inflation coefficients, ∑ 𝛾 ). The closer this sum is to 1.0, the more
persistent inflation is, and the greater is the longer-term slope of the Phillips curve for any given
short run slope. In the limit, when 𝛿 = 0 and ∑ 𝛾 = 1.0, the model effectively reverts fully to
the accelerationist version of the Phillips curve, where the change in inflation is a function of the
level of the unemployment gap. That is, a negative unemployment gap has a continuing positive
effect on inflation until the gap is closed. The closer this sum of lagged inflation coefficients is to
zero, the less persistent inflation is, the smaller the longer-term Phillips curve slope for any given
short run slope is, and the more closely inflation is anchored to the inflation expectations term. 4
For the wage Phillips curve, shown below, wage inflation is a function of labor market
slack, inflation expectations, lagged price inflation, and other control variables. As with the price
Phillips curve, the coefficients on inflation expectations and lagged price inflation are also
constrained to sum to 1.0, which gives this equation the interpretation of a real-wage Phillips
1
We do not estimate a New Keynesian Phillips curve, with the real marginal cost as an explanatory variable,
because of our focus on the direct relationship between economic slack and inflation.
2
Lagged influences are captured by the lagged dependent variable as follows: if the unemployment gap changes
today, it will change inflation today by an amount 𝛽 times the change in the gap. This will also affect inflation
tomorrow by an amount 𝛾 times today’s change in inflation. The eventual full change in price after all lags are
factored is will be equal to the change in the unemployment gap times the longer-term Phillips curve slope, which
is calculated as the short-run slope 𝛽 divided by one minus the sum of the lagged inflation coefficients, or 𝛽/(1 −
∑ 𝛾 ). With the constraint that the coefficients on inflation expectations and lagged inflation sum to 1.0, the
longer term Phillips curve slope is equal to 𝛽/𝛿 .
3
Yellen (2017) includes two lags; other Federal Reserve Board and Reserve Bank staff studies have used longer
lags. Brayton, Roberts and Williams (1999) have specifications with up to 24 lags.
4
See footnote 1.
8
curve where nominal wages are deflated by a combination of past inflation and inflation
expectations.
𝜋 = 𝛼 + 𝛽(𝑢 − 𝑢∗ ) + 𝛿𝜋 + 𝛾𝜋 + 𝜆𝑋
The other variables (𝑋 ) included in the wage and price models differ between the two models.
In the price Phillips-curve equation we add the change in the relative price of imported goods,
expressed as the ratio of import goods prices to domestic goods prices to capture the influence of
changes in both exchanges rates and foreign prices on the domestic prices of goods and services
that are imported or that compete with imports. In the wage equation, to account for the
independent influence of productivity trends on wages, we included HP-filtered growth in real
output per hour for the nonfarm business sector. Yellen (2017) included a similar measure of
trend productivity growth, though her measure was significantly more smoothed than ours. We
also included in both models a variable to control for Nixon era price and wage controls as in
Brayton, Roberts, and Williams (1999).
To test for nonlinearities, we ran several other r egressions replacing the linear specification of
slack, represented by the unemployment gap (u-u*) term, with several alternative nonlinear
functions of slack, each of which allowed inflation to have different sensitivities to slack
depending on the level of slack in the economy. The different specifications we tested include a
“spline” function that restricts the Phillips curve to be linear, but allows for different slopes when
the unemployment gap is negative versus positive. 5 It does this by not only including the normal
unemployment gap term (denoted by ugap) but also adding a dummied unemployment gap,
ugappos that is ugap 𝐼 ∗ , an indicator variable that takes the value 1.0 when 𝑢 > 𝑢∗ and
zero otherwise. While this is a simple and parsimonious way to incorporate nonlinearites which
has been utilized in many papers, it does omit the possibility of any curvature in the Phillips
curve.
To allow for such curvature, we also tried a “Cubic” specification includes a cubic
polynomial in the unemployment gap, using the terms ugap, ugap2, and ugap3.6 The drawback to
this specification is that depending on the estimated 𝛽’s, the Phillips curve slopes can differ
wildly with slight perturbations of the parameters, particularly at levels of the unemployment gap
that are well away from typical levels.
We also included specifications that are explicitly convex. The first convex specification,
“Convex1”, uses the unemployment gap divided by the unemployment, ugap/u as the variable
representing slack. The second convex specification, “Convex2”, uses the log of the ratio of the
unemployment rate to NAIRU, ln(ugap/u*) and finally a “piecewise quadratic” (Piece. quad.)
5
The spline specification does not include a separate intercept term for when the unemployment gap is positive.
This restricts the Phillips curve, though not its slope, to be continuous. Results do not change much if such an
intercept were included.
6
The cubic specification has an advantage over a straight quadratic because it allows for an asymmetric response
above and below a zero output gap. We also considered a one-sided quadratic specification as discussed further
below.
9
specification that uses a linear slack term, plus the squared value of that slack term, the
unemployment gap, only when the gap is negative. This allows for one-sided nonlinearity in
tight labor markets only, following the approach used by Nalewaik (2016). 7 The additional
2
variable in this case is ugapneg , that is ugap2 𝐼 ∗ , the indicator variable that takes the value
1.0 when 𝑢 > 𝑢∗ and zero otherwise. Murphy (2018) compares results from a similar set of
nonlinear specifications.
2.3 Data
2.3.1 Inflation
For the dependent variable in the price Phillips curve, we focus on core (ex food and energy)
PCE inflation, expressed as quarterly changes in seasonally adjusted price levels at annual rates.
Our results are robust to using core CPI instead. Core inflation is preferred over headline because
the occasional high volatility of food and energy prices due to idiosyncratic factors in those
markets can bias/affect estimation results for reasons not represented in the standard Phillips-
curve model. However, these data begin in the late 1950s (1957 for the core CPI and 1959 core
PCE). Given that we are also interested in the behavior of inflation in the 1950s, for which there
were periods with an extraordinarily tight labor market, we also examine headline PCE inflation
which goes back to the late 1940s.
For the wage Phillips curve, we look at several measures of wage inflation. One is the
quarterly annualized (log) change in average hourly earnings for production and nonsupervisory
workers, which begins in 1962 and covers about 80% of total private workers. For a more
comprehensive measure that goes back further we also utilize compensation per hour for the
nonfarm business sector; this series starts in 1947 but is more volatile than the other wage
inflation measures. We also tested the employment cost index, including both the wages and
salaries component and total compensation, which includes benefits. These series are more
comprehensive than average hourly earnings and less volatile than compensation per hour, but
they do not begin until 1982. Finally, we ran tests with unit labor cost inflation, or compensation
per hour growth minus productivity growth in the nonfarm business sector (also back to the late
1940s); the productivity trend variable was dropped from the right hand side of these equations.
In estimation, all price and wage inflation variables are expressed as (log) quarter to quarter
changes in prices or wages at annual rates.
2.3.2 Slack
Our preferred measure of slack is the U-3 unemployment rate minus the Congressional
Budget Office’s published estimate of the natural rate of unemployment or NAIRU. As is
evident from Figure 2.1, the labor market tightened tremendously during the 1950s and 1960s,
7
This specification is does not allow the linear term to differ when the unemployment gap is above or below zero.
This restriction forces the slope of the Phillips curve to be continuous and change smoothly as the unemployment
rate passes through NAIRU unlike the spline specification where the slope is discretely different above and below
NAIRU.
10
with unemployment falling more than 2 percentage points below NAIRU for extended periods.
As we will see later, it is important to note that since the 1970s there have been far fewer
instances of significantly tight labor markets. Only during 1999-2000 for a total of six quarters
has the unemployment gap exceeded -1 percentage point, and then only modestly so (with a peak
gap of -1.29% in late 2000). We also tested the output gap, or the log difference between real
GDP and the Congressional Budget Office’s published estimate of potential GDP; the
unemployment gap generally yielded a better statistical fit and the Phillips curve slopes were
generally about twice as large as those on the output gap, consistent with Okun’s law.
Figure 2.1: Civilian Unemployment Rate (U-3) and Natural Rate of Unemployment, 1948-
2018
% Civilian unemployment rate: 16 yr+ %
Natural rate of unemployment
12 12
10 10
8 8
6 6
4 4
2 2
48 53 58 63 68 73 78 83 88 93 98 03 08 13 18
Source: BLS, CBO, Haver Analytics
2.3.3: Inflation Expectations.
Our measure of inflation expectations is the series employed in the Fed’s FRBUS model
of the US economy (Figure 2.2). This series is a combination of survey based measures of long-
run (ten-year) inflation expectations from the Philadelphia Fed Survey of Professional
Forecasters going back to 1981. From 1967 to 1981, inflation expectations are based on bond
market expectations of long-run inflation expectations extracted from a term structure model
similar to that of Kozicki and Tinsley (2001). We extend this series back to 1961 by splicing in
the 10-year moving average of headline inflation. As can be seen in Figure 2.2, this measure of
inflation expectations was remarkably stable at less than 2% during the 1960s and again at
around 2% since the latter 1990s.8
8
Cecchetti et al (2017) found that inflation expectations did not have any explanatory power over and above
lagged inflation using data back to the mid-1980s. We take a more agnostic view in wanting to test the consensus
Phillips curve specification, in particular to see how the structure has shifted over time since the 1950s.
Furthermore, we do find a significant coefficient on expected inflation in our regressions.
11
Figure 2.2: Inflation and Inflation Expectations, 1948-2018
Source: BEA, Haver Analytics, Author’s calculations
2.3.4 Relative Import Prices and Other Global Factors
Relative import prices are measured as the ratio of the price index for imported goods
relative to that of overall goods PCE (Figure 2.3). We use the quarterly annualized (log) change
in this series in our regressions. Import prices appear to have added to inflation especially
around the oil price spikes of the 1970s and early 1980s and subtracted from inflation during the
later 1980s and 90s. Another run up in the early 2000s was subsequently reversed. When oil
prices are removed from overall goods import prices over the more recent period for which these
data are available, the swings in relative import prices are slightly more muted.
Figure 2.3: Relative Import Prices, 1948-2018
Source: BEA, Haver Analytics
12
We also considered other global factors in our regression models. We put global output
gap measures into the Phillips curve, as well as a measure of trade intensity (US exports plus
imports divided by GDP) to represent global competitive pressures that may not be captured by
movements in import prices, especially as new production and new products have entered the
global markets. These variables were at best only marginally statistically significant with the
expected sign or significant but with the wrong sign relative to expected values. The addition of
these variables had little impact on the slope coefficient of the Phillips curve. In sum, our testing
in this area offered little support for global factors explaining the flattening of the Phillips curve.
2.3.5 Productivity
Our productivity measure is growth in output per hour in the nonfarm business sector. As
noted above, we use an HP-filtered trend to smooth this volatile series, much as is done in Yellen
(2017).
2.4 Estimation Results
2.4.1 Price Phillips Curve: Full Sample 1961-2018
We start with our results estimating how core PCE inflation responds to the various linear
and non-linear specifications of labor market slack over the time period 1961:Q1-2018:3, which
we label as “full sample” (for core PCE inflation). These results are displayed in Table 2.1. The
top panel shows the coefficients that correspond to the particular specification of slack in each
regression. Standard errors are in parentheses and one, two, or three asterisks denote significance
at the 90%, 95%, and 99% level, respectively. We also show the coefficients on relative import
prices, as well as inflation expectations and the sum of the coefficients on lagged inflation. The
bottom four rows in the table provide the estimated Phillips curve slope (defined as the derivate
of inflation with respect to the unemployment rate, evaluated at the implied unemployment rate
relative to the current value of NAIRU, 4.61%) at several different levels of the unemployment
gap: +1 (slack), 0 (at full employment), -1 (tight labor market), and -2 (extraordinarily tight labor
market).
Inflation models are not noted for their ability to track quarterly fluctuations with
precision, and the ones we present here are no exception. For the core PCE equation in Table
2.1, the in-sample root mean squared prediction error is about 0.7% relative to an average
inflation rate of a little over 3% over the full sample period. This is somewhat better than the
performance of the models for headline inflation as well as those for wage inflation, especially
compensation per hour, which tends to be substantially more volatile.
13
Table 2.1: Core PCE Phillips Curve, Full Sample: 1961-2018
Linear Spline Cubic Convex1 Convex2 Piece. quad.
ugap -0.141 *** -0.423 *** -0.210 *** -0.082 **
(0.036) (0.085) (0.057) (0.041)
ugap pos 0.374 ***
(0.110)
2
ugap 0.072 **
(0.028)
3
ugap -0.009
(0.008)
ugap/u -1.033 ***
(0.204)
ln(u/u*) -0.913 ***
(0.207)
2
ugapneg 0.150 ***
(0.049)
Rel. Imp. Goods Infl. 0.035 *** 0.037 *** 0.037 *** 0.036 *** 0.036 *** 0.038 ***
(0.009) (0.009) (0.009) (0.009) (0.009) (0.009)
Infl. Expectations 0.193 *** 0.231 *** 0.235 *** 0.218 *** 0.205 *** 0.239 ***
(0.058) (0.060) (0.062) (0.058) (0.058) (0.062)
Sum Lag Infl. Coeffs. 0.807 0.769 0.765 0.782 0.795 0.761
RMSE 0.727 0.710 0.713 0.718 0.724 0.715
Slope at Linear Spline Cubic Convex1 Convex2 Piece. quad.
ugap = +1 (u = 5.61) -0.141 -0.048 -0.092 -0.151 -0.163 -0.082
ugap = 0 (u = 4.61) -0.141 -0.210 -0.224 -0.198 -0.082
ugap = -1 (u = 3.61) -0.141 -0.423 -0.380 -0.365 -0.253 -0.382
ugap = -2 (u = 2.61) -0.141 -0.423 -0.602 -0.699 -0.350 -0.682
Standard errors in parentheses. ∗ p < 0.05, ∗∗ p < 0.01, ∗∗∗ p < 0.001
In the linear specification in Table 2.1, the full sample Phillips curve slope is relatively
flat at -0.14, implying that a drop in the unemployment gap from 0 to -1% will raise inflation by
0.14% on impact--a pretty small effect overall. In the spline specification, the slope is
considerably steeper at – 0.42 when the gap is below zero, but very close to zero at -0.05 when it
is above zero (this is derived as the sum of the coefficients on the ugap and the ugappos term).
This result suggests a substantial nonlinearity, which holds up to a considerable extent across the
other nonlinear specifications (Cubic, Convex1, Convex 2 and Piece quad). The slope when the
gap is at -1% (not too far from its recent level) ranges from -0.25 to -0.38. When the gap moves
to +1, the slopes are noticeably smaller, ranging from -.08 to -.16.
If the labor market tightens to more extraordinary levels at two percentage points below
NAIRU, the slope of the Phillips curve generally steepens even more. The persistence of
inflation, gauged by the sum of the coefficients on lagged inflation is generally fairly high across
14
all of the linear and nonlinear specifications. The coefficients on inflation expectations are
relatively small but consistently highly statistically significant.
Figure 2.4 plots the slope of the various linear and nonlinear Phillips curves over a larger
range of values for the unemployment gap—this shows on the vertical axis the change in
inflation induced by a 1% point increase in the unemployment gap at any given level of that gap
across the various models. All of the nonlinear specifications show the slope to be quite low and
linear over a wide range of unemployment gap values when the gap is positive. They also show
that the slope is considerably steeper when the gap falls below zero and steepens further as the
labor market tightens further.
Figure 2.4: Slope of estimated Phillips Curves (1961-2018)
Source: Authors’ calculations
2.4.2 Headline PCE Extended sample—Back to the 1950s
Empirical work on the Phillips curve in more recent decades has often included the 1960s
but generally has not looked back to the 1950s given that core measures of inflation do not go
back that far and the complications from the wage and price controls imposed around the Korean
War during that period.
To include this earlier time period which exhibited an extraordinary level of labor market
tightness, we have to turn to headline PCE. As mentioned earlier, our measure of inflation
expectations does not extend back that far, so in our headline PCE results, we do not include a
measure of inflation expectations and we do not restrict the coefficients on lagged inflation to
sum to one. We first estimated this model with headline inflation over the same sample period as
for core inflation in Table 2.1. These results are shown in Table A.1 in the Annex and they are
quite similar to the results in Table 2.1.
15
In Table 2.2, we show results for the sample period extended back to 1954. We see a
slightly steeper slope of the Phillips curve in the linear case and the majority of the nonlinear
cases, particularly around the levels of the unemployment gap seen in the latter 1950s. The
persistence of inflation rises, but this may be in part because we were not able to include an
inflation expectations variable in this case. 9 In brief the addition of the experience during the
tight labor market period of the mid-latter 1950s bolsters the results we found back to the early
1960s.
We also ran the equations over the full range of available data, back to 1949 (Annex
Table A.2), attempting to account for the price and wage controls implemented around the
Korean War much as Brayton, Roberts, and Williams (1999) did for the Nixon era controls. In
this case, the slope was estimated to be much flatter than the post-1954 and post-1961 samples.
The instability of the price Phillips curve equation over the early 1950s could well reflect a
failure of our effort to account for the effects of the Korean War price controls, but it could also
warrant further investigation.
9
With the absence of an inflation expectations tem, we also dropped the constraint on the lagged price
coefficients (having them plus the expectations coefficient sum to 1.0). The Lagged price coefficients may be
picking up more of the expectations effect in this case.
16
Table 2.2: Headline PCE Phillips Curve, extended sample: 1954-2018
Linear Spline Cubic Convex1 Convex2 Piece. quad.
ugap -0.146 *** -0.467 *** -0.412 *** -0.090
(0.049) (0.122) (0.112) (0.059)
ugap pos 0.440 ***
(0.156)
2
ugap 0.011
(0.039)
3
ugap 0.021
(0.013)
ugap/u -1.111 ***
(0.299)
ln(u/u*) -0.986 ***
(0.300)
ugapneg2 0.128 *
(0.065)
Rel. Imp. Goods Infl. 0.058 *** 0.062 *** 0.059 *** 0.061 *** 0.059 *** 0.061 ***
(0.015) (0.015) (0.015) (0.015) (0.015) (0.015)
Sum Lag Infl. Coeffs. 0.871 0.868 0.893 0.870 0.869 0.867
RMSE 1.313 1.302 1.290 1.305 1.309 1.310
Slope at Linear Spline Cubic Convex1 Convex2 Piece. quad.
ugap = +1 (u = 5.61) -0.146 -0.027 -0.329 -0.163 -0.176 -0.090
ugap = 0 (u = 4.61) -0.146 -0.412 -0.241 -0.214 -0.090
ugap = -1 (u = 3.61) -0.146 -0.467 -0.371 -0.393 -0.273 -0.345
ugap = -2 (u = 2.61) -0.146 -0.467 -0.207 -0.752 -0.378 -0.601
Standard errors in parentheses. ∗ p < 0.05, ∗∗ p < 0.01, ∗∗∗ p < 0.001
2.4.3 Wage Phillips Curve, Full Sample—Back to the Mid 1960s
When we run the wage Phillips curve beginning in the mid-1960s, the results differ noticeably
from those for the price Phillips curve. First, for both average hourly earnings (Table 2.3) and
compensation per hour (Annex Table A.3) the short run Phillips curve slope is noticeably steeper
than the price Phillips curve over roughly the same sample period. Nonlinearities in the slope
are pronounced and persistent, with the slope generally much steeper in tight labor markets than
in easy labor markets. These results held up for compensation per hour when the sample was
extended back to the mid-1950s (Table 2.4). Results with compensation per hour going back to
the mid-1950s, are very similar to results using average hourly earnings, with no flattening of
the Phillips curve even when including the early 1950s (Annex Table A.4). Longer-term inflation
expectations do not play a significant role in the wage Phillips curve over the dull sample, and
their contribution is generally dominated by the lagged inflation variables.
17
Table 2.3: Wage Phillips Curve (Average Hourly Earnings): 1964-2018
Linear Spline Cubic Convex1 Convex2 Piece. quad.
ugap -0.379 *** -0.611 *** -0.874 *** -0.365 ***
(0.081) (0.176) (0.125) (0.089)
ugap pos 0.294
(0.214)
2
ugap -0.092 *
(0.050)
3
ugap 0.056 ***
(0.014)
ugap/u -2.519 ***
(0.461)
ln(u/u*) -2.344 ***
(0.474)
2
ugapneg 0.041
(0.086)
Trend prod. growth. 0.471 *** 0.420 *** 0.272 ** 0.415 *** 0.440 *** 0.460 ***
(0.103) (0.109) (0.107) (0.106) (0.106) (0.106)
Infl. Expectations 0.043 0.077 -0.006 0.097 0.071 0.056
(0.109) (0.117) (0.113) (0.114) (0.112) (0.122)
Sum Lag Infl. Coeffs. 0.957 0.923 1.006 0.903 0.929 0.944
RMSE 1.295 1.293 1.218 1.294 1.299 1.298
Slope at Linear Spline Cubic Convex1 Convex2 Piece. quad.
ugap = +1 (u = 5.61) -0.379 -0.317 -0.889 -0.369 -0.418 -0.365
ugap = 0 (u = 4.61) -0.379 -0.874 -0.546 -0.509 -0.365
ugap = -1 (u = 3.61) -0.379 -0.611 -0.521 -0.891 -0.649 -0.448
ugap = -2 (u = 2.61) -0.379 -0.611 0.171 -1.705 -0.898 -0.530
Standard errors in parentheses. ∗ p < 0.05, ∗∗ p < 0.01, ∗∗∗ p < 0.001
18
Table 2.4: Wage Phillips Curve (Compensation per Hour): 1954-2018
Linear Spline Cubic Convex1 Convex2 Piece. quad.
ugap -0.403 *** -0.927 *** -0.646 ** -0.297 *
(0.144) (0.238) (0.254) (0.178)
ugap pos 0.714 **
(0.342)
2
ugap 0.062
(0.091)
3
ugap 0.008
(0.030)
ugap/u -2.747 ***
(0.761)
ln(u/u*) -2.587 ***
(0.837)
ugapneg2 -0.239 *
(0.137)
Trend prod. growth. 0.631 *** 0.608 ** 0.569 ** 0.601 ** 0.605 ** 0.627 ***
(0.238) (0.237) (0.235) (0.235) (0.235) (0.237)
RMSE 2.710 2.698 2.706 2.699 2.705 2.706
Slope at Linear Spline Cubic Convex1 Convex2 Piece. quad.
ugap = +1 (u = 5.61) -0.403 -0.213 -0.498 -0.402 -0.461 -0.297
ugap = 0 (u = 4.61) -0.403 -0.646 -0.596 -0.561 -0.297
ugap = -1 (u = 3.61) -0.403 -0.927 -0.748 -0.972 -0.717 0.182
ugap = -2 (u = 2.61) -0.403 -0.927 -0.802 -1.859 -0.991 0.661
Standard errors in parentheses. ∗ p < 0.05, ∗∗ p < 0.01, ∗∗∗ p < 0.001
Note: Inflation expectations are not included. The seven lags of core PCE inflation are constrained to
sum to 1.0.
2.4.4 Stability over Time: More Recent Sample 1988-2018
Ample recent empirical literature and the rolling regression results we included in the
introduction to this paper say that the slope of the Phillips curve has flattened significantly over
time. But they do not have much to say about the potential steepening of the Phillips curve due
to nonlinearities, if the labor market continues to tighten. That is the subject of our next set of
tests: even if the overall slope has flattened, could it still bounce back if the unemployment gap
falls persistently below -1%?
Price-Phillips curve has flattened.
Table 2.5 and Figure 2.5 presents results parallel to those in Table 2.1 and Figure 2.4, for
the price Phillips curve, but with estimation starting in 1988. This starting point was selected as
being both near the midpoint of our core full sample, and at a point where our rolling regression
19
tests said that the flattening of the Phillips curve slope had about been completed. What we find
is that not only has the linear slope moved even closer to zero, but that evidence of significant
non-linearities has all but disappeared. None of the non-linear slope coefficients are significantly
different from zero. Moreover, the linear specification yields a lower root mean squared
prediction error than almost all of the nonlinear ones. The most we can say is that all of the
nonlinear specifications do yield steeper slopes when the unemployment gap is negative than
when it is positive, but the statistical significance of this observation is low. We also find that
the persistence of inflation has declined, as the sum of the coefficients on lagged inflation has
been reduced almost by half, and the coefficient on inflation expectations has risen
commensurately. On the whole these results are consistent with observations made by Kiley
(2015) and Powell (2018a).
Table 2.5: Core PCE Phillips Curve: 1988-2018
Linear Spline Cubic Convex1 Convex2 Piece. quad.
ugap -0.037 -0.116 -0.107 * -0.031
(0.032) (0.128) (0.062) (0.039)
ugap pos 0.091
(0.152)
2
ugap 0.066
(0.055)
3
ugap -0.010
(0.011)
ugap/u -0.318
(0.229)
ln(u/u*) -0.251
(0.201)
2
ugapneg 0.052
(0.135)
Rel. Imp. Goods Infl. 0.015 ** 0.015 ** 0.016 ** 0.015 ** 0.015 ** 0.015 **
(0.008) (0.008) (0.007) (0.008) (0.008) (0.008)
Infl. Expectations 0.526 *** 0.512 *** 0.498 *** 0.519 *** 0.524 *** 0.514 ***
(0.145) (0.151) (0.157) (0.144) (0.145) (0.154)
Sum Lag Infl. Coeffs. 0.474 0.488 0.502 0.481 0.476 0.486
RMSE 0.501 0.503 0.502 0.500 0.501 0.503
Slope at Linear Spline Cubic Convex1 Convex2 Piece. quad.
ugap = +1 (u = 5.61) -0.037 -0.024 -0.006 -0.047 -0.045 -0.031
ugap = 0 (u = 4.61) -0.037 -0.107 -0.069 -0.055 -0.031
ugap = -1 (u = 3.61) -0.037 -0.116 -0.270 -0.113 -0.070 -0.134
ugap = -2 (u = 2.61) -0.037 -0.116 -0.495 -0.215 -0.096 -0.237
Standard errors in parentheses. ∗ p < 0.05, ∗∗ p < 0.01, ∗∗∗ p < 0.001
20
Figure 2.5: Slope of estimated Phillips Curves (1988-2018)
Source: Authors’ calculations
Wage-Phillips curve is much more stable.
When we turn to the wage Phillips curve, this picture of instability changes considerably..
Table 2.6 describes the results where we run the wage Phillips curves with lagged price inflation,
partly as a proxy for inflation expectations that might not be captured by our expectations
variable. For average hourly earnings, while the linear slope has flattened some, it remains
close to -0.2 and statistically significant. More strikingly, evidence of nonlinearity remains
highly significant, and the Phillips-curve slope appears to have steepened substantially (to -0.9 or
more) when the labor market is tight. The slope remains much closer to zero when
unemployment is running above NAIRU. One significant change from the full sample results is
that longer-term inflation expectations have become much more important as a determinant of
wage inflation over the more recent period. At the same time, the contribution of lagged
inflation has dropped noticeably.
21
Table 2.6: Wage Phillips Curve (Average Hourly Earnings): 1988-2018
Linear Spline Cubic Convex1 Convex2 Piece. quad.
ugap -0.180 *** -0.929 *** -0.656 *** -0.123 **
(0.055) (0.248) (0.123) (0.060)
ugap pos 0.840 ***
(0.279)
2
ugap 0.123 *
(0.073)
3
ugap 0.003
(0.014)
ugap/u -1.809 ***
(0.404)
ln(u/u*) -1.318 ***
(0.349)
ugapneg2 0.694 ***
(0.245)
Trend prod. growth 0.439 *** 0.328 *** 0.280 *** 0.358 *** 0.403 *** 0.320 ***
(0.097) (0.098) (0.100) (0.097) (0.097) (0.097)
Infl. Expectations 0.627 * 0.546 0.430 0.639 * 0.639 * 0.515
(0.380) (0.372) (0.365) (0.366) (0.375) (0.383)
Sum Lag Infl. Coeffs. 0.373 0.454 0.570 0.361 0.361 0.485
RMSE 0.895 0.872 0.838 0.872 0.886 0.877
Slope at Linear Spline Cubic Convex1 Convex2 Piece. quad.
ugap = +1 (u = 5.61) -0.180 -0.089 -0.400 -0.265 -0.235 -0.123
ugap = 0 (u = 4.61) -0.180 -0.656 -0.392 -0.286 -0.123
ugap = -1 (u = 3.61) -0.180 -0.929 -0.893 -0.640 -0.365 -1.511
ugap = -2 (u = 2.61) -0.180 -0.929 -1.111 -1.224 -0.505 -2.898
Standard errors in parentheses. ∗ p < 0.05, ∗∗ p < 0.01, ∗∗∗ p < 0.001
Broadly similar results are found across the other measures of wage inflation that we
tested, as seen in Table 2.7. Here we report a subset of the models, including the linear version
and the spline specification to represent the nonlinear, across the different wage measures,
including compensation per hour, ECI total compensation, ECI wages and salaries, and unit labor
costs. In general, these results show short run Phillips curve slopes in the vicinity of -0.2 to -0.3,
considerably steeper than for the price Phillips curves over this period. They also show
substantial nonlinearities, with the slope much steeper in tight labor markets than easy labor
markets. Productivity growth is a significant contributor throughout. Inflation expectations have
become much more important and lagged inflation much less important than over the full sample
period.
22
Table 2.7: Wage Phillips Curve using four different wage measures: 1988-2018
CPH ECI TC ECI WS ULC
Linear Spline Linear Spline Linear Spline Linear Spline
ugap -0.321 -1.750 -0.156 *** -0.748 *** -0.274 *** -0.925 *** -0.337 -1.127
(0.223) (1.105) (0.050) (0.289) (0.051) (0.278) (0.312) (1.650)
ugap pos 1.603 0.665 0.731 ** 0.919
(1.218) (0.301) (0.288) (1.805)
Trend prod. growth 0.804 ** 0.592 0.612 *** 0.523 *** 0.341 *** 0.244 **
(0.371) (0.383) (0.116) (0.129) (0.109) (0.119)
Infl. Expectations 1.423 * 1.268 * 0.674 *** 0.610 *** 0.962 *** 0.891 *** 0.740 0.602
(0.744) (0.742) (0.222) (0.212) (0.282) (0.262) (0.887) (0.847)
Sum Lag Infl. Coeffs. -0.423 -0.268 0.326 0.390 0.038 0.109 0.260 0.398
RMSE 3.3725 3.3614 0.7888 0.7729 0.8092 0.7899 4.1446 4.155
CPH ECI TC ECI WS ULC
Slope at Linear Spline Linear Spline Linear Spline Linear Spline
ugap > 0 -0.321 -0.147 -0.156 -0.083 -0.274 -0.195 -0.337 -0.207
ugap < 0 -0.321 -1.750 -0.156 -0.748 -0.274 -0.925 -0.337 -1.127
Note: CPH is compensation per hour, ECI TC is the Employment Cost Index: Total Compensation for
private workers, ECI WS is the Employment Cost Index: Wages and Salaries for private workers, and
ULC is unit labor costs. Lagged inflation terms are core PCE inflation.
Rolling regressions
As a final check on some of the relative wage and price stability results discussed above,
we ran the linear versions of the core PCE and average hourly earnings Phillips curves using
rolling regressions with 20 year windows. The results are shown in the following two figures.
Figure 2.6 shows the rolling short run slope estimates and persistence estimates (sum of lagged
inflation coefficients) for core PCE. Figure 2.7 shows the same for average hourly earnings, in
this case using lagged wage inflation rather lagged price inflation. This is done to allow for
some dynamics in the adjustment of wage inflation to changes in its determinants and thereby to
test for “persistence” in wage inflation. Figure 2.6 is very similar to the picture reported by
Powell (2018a), showing a sharp drop over time in the absolute value of the slope, and a more
recent plunge in persistence. The picture for wages differs: both the absolute value of the slope
and persistence decline over time, but much less, and to significantly more elevated levels than
their price Phillips curve counterparts.
23
Figure 2.6: Rolling Regression Slope and Persistence Coefficients for Price Phillips Curve
Source: Authors’ calculations
Figure 2.7: Rolling Regression Slope and Persistence Coefficients for Wage Phillips Curve
Source: Authors’ calculations
2.4.6 Questions raised
Our results so far raise some key questions. First, why in recent decades has the price
Phillips curve flattened and evidence of nonlinearities weakened so much? This result is made
even more puzzling by evidence that the wage Phillips curve has been more stable. Second, has
the price Phillips curve really died or is it just hibernating, and if the latter, what could bring it
back to life? Third, what are the reasons for and implications of the different paths the price and
wage Phillips curves have travelled over this period? In what follows we address the first two
questions, the third, we leave for future research.
24
One possible explanation of why we don’t find a steep Phillips curve with nonlinearities
in the more recent data is that economic up-cycles have become more muted over time, so there
has been too little variability in the data to pick up a more normal Phillips curve in the national
data. As we observed in Figure 2.1, substantial labor market tightening was much more
prevalent in earlier decades than it has been in more recent decades. This is shown more clearly
in Figure 2.8. In the past three decades the unemployment gap was wider than -1 about 4% of
the time. Over the full sample back to 1962, this occurred more than three times as frequently.
Because there are so few observations in the macro, time-series where the unemployment rate is
more than 1 percentage point below the natural rate of unemployment, it would be very difficult
to estimate a nonlinearity in the Phillips curve slope in the more recent sample period. 10 In other
words, the power of tests for the slope of the Phillips curve and nonlinearities would be very low.
Figure 2.8: Histograms of the unemployment gap
Source: BLS, CBO, Haver Analytics
A second reason why the estimated Phillips curve for the recent period might not display
a steep slope is that, since the 1980s, the Fed focused much more on avoiding labor market
overheating in order to stabilize inflation.11 As pointed out by Fitzgerald and Nicolini (2014) and
McLeay and Tenreyro (2018), the resulting endogeneity of monetary policy can obscure the
relationship between unemployment and inflation in macro time-series data. These papers show
10
Cecchetti et al (2017) made this point in their failure to find statistical support for the Phillips curve in
data since the mid-1980s : “A potentially important caveat to our entire analysis is that, since we have not
experienced extremely tight labor markets since the 1960s, data with those properties are not in our
sample. If the Phillips curve is nonlinear, so that inflation is more sensitive to a very tight labor market
than to a very loose one, our empirical analysis could not detect this.” (page 6)
11
The endogeneity of monetary policy could also help explain why there is less variation in the data in the more
recent sample period. Following the 1970s, the Fed focused much more on avoiding labor market overheating in
order to stabilize inflation. Its success in doing so has likely resulted in the significant reduction in the incidence of
very tight labor markets in recent decades.
25
that when monetary policy pursues a goal of minimizing welfare losses, measured as a sum of
deviations of inflation from its target and deviations of output from potential (which is inversely
related to the unemployment gap), monetary policy seeks to decrease inflation when the
unemployment gap is negative. Endogenous monetary policy then induces a positive correlation
between inflation and the unemployment gap that biases the slope coefficient of the Phillips
curve toward zero. Indeed, in the Fitzgerald and Nicolini (2014) and McLeay and Tenroyo
(2018) models, optimal monetary policy completely eliminates any correlation between inflation
and the output gap (or equivalently the unemployment gap). This reasoning suggests that the
Phillips curve slope in the regression estimates for the recent period likely understates the true
steepness of the Phillips curve.
The models by Fitzgerald and Nicolini (2014) and McLeay and Tenroyo (2018) imply
that empirical estimates of a flattening Phillips reflect a monetary policy that is more responsive
to deviations in the unemployment gap. As a result, it would be a mistake to conclude that the
flattening of the Phillips curve in the data implies that inflation would remain subdued with a
significantly negative unemployment gap if the Fed responded more passively. The flattening
reflects a responsive monetary policy, but we should expect a steepening if monetary policy were
too accommodative.”
The argument above suggests that we might seek out data that not only has more
variation than the macro, time-series data, but is also not subject to the possible bias created by
endogenous monetary policy. A natural place to look is data for U.S. states and Metropolitan
Statistical Areas (MSAs), because there are many more observations of very tight labor markets.
Furthermore, monetary policy can be treated as exogenous in state and MSA data because
monetary policy is national and so is the same for all states and MSAs. In Section 3, we provide
evidence on the slope and nonlinearity in this data.
The third explanation for the flattening of the Phillips curve, and the one that has
attracted by far the most attention in the literature, is the anchoring of inflation expectations. As
we saw in Figure 2.2, for at least the past two decades, longer-term inflation expectations as
gauged by the Survey of Professional Forecasters has been remarkably stable in the vicinity of
2%. This anchoring may have been bolstered by the Fed’s adoption of a specific 2% inflation
objective in 2012, which was preceded by a decade during which that objective was widely seen
as implicit, and a longer period during which the Fed had striven, successfully, to reduce
inflation to that neighborhood from much higher levels. Inflation may have appeared
reasonably well anchored during the 1960s, following a period (since the Korean War) during
which it had averaged 2% or less. But that episode ended badly, in a great inflation. This leads
to the question of could history repeat itself, or what might cause the Phillips curve to come out
of hibernation again? We address this issue in Section 4, by taking a closer look at the
experience of the 1960s and what led to the great inflation.
26
Section 3: Evidence from State and City Level Data
3.1 State and City Level Estimates
This section explores regional data in the United States to provide more insight into the
relationship between the unemployment rate and inflation. One of the main advantages of
regional data sets is that the typically contain a wider distribution of employment conditions than
national level data.
Figure 3.1 shows the distribution of the unemployment rate for the United States as a
whole (left panel) and for states within the United States (right panel) from 1980 to 2017. As the
left panel shows, there is little precedent for the country as a whole for an unemployment rate
below 4%. In contrast, as the right panel shows, there are several states that have experienced an
unemployment rate below 4% during the 1980 to 2017 period. In fact, just over 15% of the
observations of the state-year level panel have an unemployment rate below 4%. The mass of the
distribution in the state-year level data below 4% can help identify the slope of the Phillips curve
during low unemployment rate situations such as the United States is experiencing currently.
Figure 3.1: Distribution of the Unemployment Rate, 1980-2017
A. Aggregate
Source: BLS
27
B. States
Source: BLS
The data used in this section are detailed in two studies: Kumar and Orrenius (2016) for
the wage-Phillips curve estimation at the state level from 1981 to 2017, and Babb and Detmeister
(2017) for the price-Phillips curve estimation at the MSA-level from 1990 to 2017. For the wage-
Phillips estimation at the state level, the state unemployment rates are calculated from the
monthly Current Population Survey. The state-level wages are average hourly wage rates
calculated from the monthly CEPR uniform extracts of CPS outgoing rotation groups. State-level
price inflation rates are not available for this full time frame. As a result, the core inflation
measure for the state-level analysis is based on price inflation from the CPI-U data by Census
region. For the MSA level analysis, the unemployment rates at the city-year level come from the
BLS, and the price inflation data are derived from the consumer price index for All Urban
Consumers, and the specific measure is all items less food and energy.
Studies that rely on regional data to estimate the Phillips curve typically conduct
regression specifications with both year and geography fixed effects. Given that inclusion of year
fixed effects removes the aggregate time series variation that identifies national-level Phillips
curve estimation, such an inclusion ensures that the identifying variation in state-level or MSA-
level analysis is distinct from the identifying variation in national-level analysis. Put simply, the
estimations seek to use a new source of variation to identify Phillips curve slope.
The inclusion of geography level-fixed effects helps ensure that cross-sectional
differences in unobservable average differences across areas are not used to identify the Phillips
curve relationship. For example, the natural unemployment rate may differ across states, and
inclusion of state-fixed effects ensures that such a difference is not the identifying variation in a
state-level Phillips curve estimation. Instead, the curve is identified using deviations in the
unemployment rate from the average unemployment rate in a geographic area.
28
Figure 3.2 shows a scatterplot and regression line of nominal wage inflation against the
unemployment rate for the state-year level panel. The sample covers the 50 states and the District
of Columbia from 1981 to 2017. To ensure that the scatterplot matches the regression
specifications below, both the unemployment rate and nominal wage inflation are first regressed
on state and year fixed effects before being plotted. As a result, the scatterplot contains
deviations from the state and year mean for each state-year level observation. As the table below
shows, the estimated coefficient on the unemployment rate is -0.41.
Figure 3.2: Nominal Wage Phillips Curve, States, 1981-2017
Source: Authors’ calculations
Figure 3.2 shows a steep slope in the state-year level wage-Phillips curve. A state with a
negative deviation from its normal unemployment rate sees a larger than average increase in
nominal wage inflation. Column 1 of Table 3.1 shows the point estimate of the regression line,
which is -0.41. Column 2 of Table 3.1 includes a control variable for lagged core price inflation
at the regional level, following Kumar and Orrenius (2016). The inclusion of this control variable
is meant to capture inflation expectations or any other factor that may be determined by lagged
inflation in that region. The point estimate on the unemployment rate is almost identical. The
specification reported in Column 2 includes year fixed effects, which implies that the negative
slope coefficient is not driven by national inflation dynamics. The state-year wage-Phillips curve
shows a significant and steep negative slope. This is consistent with findings in Kumar and
Orrenius (2016).
29
Table 3.1: Wage Phillips Curve, State Level, 1981-2017
Log change in nominal wage
(1) (2) (3) (4)
Unemployment rate, annual -0.410∗∗∗ -0.407∗∗∗ -1.000∗∗∗ -0.987∗∗
(0.049) (0.049) (0.300) (0.300)
Unemployment*(4 < Unemp ≤ 5.5) 0.389 0.388
(0.356) (0.356)
Unemployment*(5.5 < Unemp ≤ 7.5) 0.291 0.278
(0.339) (0.340)
Unemployment*(7.5 < Unemp) 0.807∗∗ 0.793∗
(0.307) (0.308)
Core inflation, lagged 0.180 0.131
(0.138) (0.138)
(4 < Unemp ≤ 5.5) -1.698 -1.703
(1.422) (1.422)
(5.5 < Unemp ≤ 7.5) -0.898 -0.830
(1.503) (1.505)
(7.5 < Unemp) -4.778∗∗∗ -4.698∗∗∗
(1.293) (1.296)
Level State State State State
Source CEPR CEPR CEPR CEPR
State effects Y Y Y Y
Year effects Y Y Y Y
N 1887 1887 1887 1887
R-sq 0.336 0.337 0.346 0.347
Standard errors in parentheses
∗ p < 0.05, ∗∗ p < 0.01, ∗∗∗ p < 0.001
The specifications in columns 3 and 4 test for non-linearity in the wage-Phillips curve.
More specifically, the specification utilizes bins of state-year level data based on the
unemployment rate. Unlike the national specification, the state-level specification cannot focus
on the natural rate of unemployment because no such estimates are available at the state level.
Instead, we follow Leduc, Marti, and Wilson (2019) and form the bins for the unemployment
rate below 4%, between 4 and 5.5%, between 5.5 and 7.5%, and above 7.5%. For each bin, the
specification includes both an indicator variable for each bin, and the bin variable interacted with
the unemployment rate. The coefficient estimates on the interaction terms answer the following
question: does the slope of the wage-Phillips curve change significantly when the level of the
unemployment rate differs?
Columns 3 and 4 report the estimates, which are very similar. We focus on column 4,
which are our preferred estimates because it makes sense to have lagged core inflation in the
specification to reflect inflation expectations or any other factor that may be determined by
lagged inflation in that region. The omitted group is the bin with an unemployment rate below
30
4%. For this group, the wage-Phillips curve is especially steep: -0.99. The interaction term
coefficient estimates for the next two bins suggest a flatter wage-Phillips curve, but the point
estimates are not statistically distinct from zero at a reasonable confidence level. However, the
interaction term coefficient estimate for the bin of unemployment above 7.5% is 0.79 and
statistically distinct from zero at the 5% confidence level. We should note that the results
presented in Table 3.1 are qualitatively similar if the regression specifications are weighted by
the labor force for each state-year observation.
Figure 3.3 plots the slope coefficient for each unemployment bin implied by the
coefficient estimates in column 4 of Table 3.1. For the bin of observations with the
unemployment rate below 4%, this is simply the point estimate from the top row of column 4.
For the other bins, it is the point estimate from the top row of column 4 plus the estimated
coefficient on the interaction term for the bin in question. Figure 4.3 shows that the wage-
Phillips curve shows evidence of non-linearity, particularly when the unemployment rate exceeds
7.5%.
Figure 3.3: State-level Wage-Phillips Curve Coefficients by Unemployment Rate
Source: Authors’ calculations
The findings of Figure 3.3 are consistent with the analysis in Leduc et al (2019) of non-
linearity in the state-year level wage-Phillips curve at higher levels of unemployment. The
difference in the slope coefficient is statistically significant when the unemployment rate
increases from below 7.5% to above 7.5%. The point estimate implies a flatter slope when the
unemployment rate goes from below 4% to above 4%, but the difference is not statistically
significant at a reasonable confidence level.
We next examine price-Phillips curve estimation. For consumer prices, the analysis
follows Babb and Detmeister's (2017) analysis of 23 MSAs from 1990 to 2017. Figure 3.4 shows
the price-Phillips scatterplot at the MSA level, where once again the MSA fixed effects and year
fixed effects are removed.
31
Figure 3.4: Price-Phillips Curve, MSA, 1990-2017
Source: Authors’ calculations
The MSA-level price-Phillips curve reveals a negative slope, consistent with the evidence
in Babb and Detmeister (2017). The regression version is in the first column of Table 3.2. The
point estimate is -0.441. The specification reported in column 2 includes lagged core inflation of
the MSA, and the slope coefficient changes to -0.301.
32
Table 3.2: Price Phillips Curve, MSA Level, 1990-2017
Log change in core CPI
(1) (2) (3) (4)
Unemployment rate, annual -0.441∗∗∗ -0.301∗∗∗ -0.954∗∗∗ -0.698∗∗∗
(0.037) (0.036) (0.165) (0.154)
Unemployment*(4 < Unemp ≤ 5.5) 0.413∗ 0.328
(0.198) (0.183)
Unemployment*(5.5 < Unemp ≤ 7.5) 0.703∗∗∗ 0.560∗∗
(0.193) (0.178)
Unemployment*(7.5 < Unemp) 0.632∗∗∗ 0.491∗∗
(0.175) (0.161)
Core inflation, lagged 0.404∗∗∗ 0.368∗∗∗
(0.036) (0.037)
(4 < Unemp ≤ 5.5) -1.779∗ -1.346
(0.786) (0.726)
(5.5 < Unemp ≤ 7.5) -3.446∗∗∗ -2.792∗∗∗
(0.873) (0.807)
(7.5 < Unemp) -3.041∗∗∗ -2.444∗∗
(0.811) (0.749)
Level MSA MSA MSA MSA
Source BLS BLS BLS BLS
MSA effects Y Y Y Y
Year effects Y Y Y Y
N 593 591 593 591
R-sq 0.642 0.709 0.671 0.722
Standard errors in parentheses
∗ p < 0.05, ∗∗ p < 0.01, ∗∗∗ p < 0.001
Columns 3 and 4 test for non-linearity. Relative to the wage-Phillips curve estimations
above, there is more robust evidence of a non-linearity in the slope of the price-Phillips curve at
low levels of the unemployment rate. In particular, in column 4, the slope of the price-Phillips
curve is -0.70 for observations with an unemployment rate below 4%. It is half as large in
absolute value for observations with an unemployment rate between 4 and 5.5%, and this
difference is marginally significantly distinct from zero. The price-Phillips curve definitely
flattens for observations with an unemployment rate above 5.5%.
Figure 3.5 summarizes these results. As it shows, the slope of the price-Phillips curve is
substantially more negative when the unemployment rate is below 4%. It flattens considerably
when moving into the 4 to 5.5% bin, and then flattens further for unemployment rates above
5.5%.
33
Figure 3.5: MSA-level Price-Phillips Curve Coefficients by Unemployment Rate
Source: Authors’ calculations
3.2 Comparing National and Regional Level Estimates
From a statistical perspective, it is important to emphasize that the national level and
regional level estimates of the Phillips curve are exploiting different sources of variation. The
regional level estimates are produced with specifications that include year fixed effects, and so
the national level effect of unemployment on inflation is eliminated. As a result, from a purely
statistical perspective, there is no reason to expect similarity between the national and regional
level Phillips curve coefficients presented above.
That being said, the coefficient estimates for the wage-Phillips curve are similar for the
national- and state-level specifications, both in terms of the level and the evidence for non-
linearities. For example, in the national level data from 1988 to 2018 in Table 3.3, the slope of
the wage-Phillips curve is between -0.29 and -0.35 depending on the measure of wage inflation
used. In the state-level data, the slope is -0.41 for the sample from 1981 to 2017, and the estimate
is similar if we restrict the sample to 1988 to 2017.
34
Table 3.3: Comparison of National and City/State Phillips Curve Slopes
Linear Linear
National National National MSA National National National State
1954-2018 1961-2018 1988-2018 1990-2017 1954-2018 1964-2018 1988-2018 1981-2017
Price Phillips Curve Wage Phillips Curve
Headline PCE -0.15*** -0.13*** -0.01 AHE¹ -0.38*** -0.18*** -.41***
Core PCE -0.14*** -0.04 CPH -0.40*** -0.39*** -0.18
Core CPI -0.24*** -0.10*** -0.30*** ECI - TC -0.16***
ECI - WS -0.27***
ULC -0.34
Non-linear / Tight labor market² Non-linear / Tight labor market²
National National National MSA National National National State
1954-2018 1961-2018 1988-2018 1990-2017 1954-2018 1964-2018 1988-2018 1981-2017
Price Phillips Curve Wage Phillips Curve
Headline PCE -0.467*** -0.42** -0.44 AHE¹ -0.61*** -0.93*** -.99***
Core PCE -0.42*** -0.12 CPH -0.93** 0.85*** -1.58
Core CPI -0.52*** -0.21* -0.70*** ECI - TC -0.75***
ECI - WS -0.93***
ULC -1.13
Non-linear / Easy labor market² Non-linear / Easy labor market²
National National National MSA National National National State
1954-2018 1961-2018 1988-2018 1990-2017 1954-2018 1964-2018 1988-2018 1981-2017
Price Phillips Curve Wage Phillips Curve
Headline PCE -0.03 -0.03 0.06 AHE¹ -0.32*** -0.09 0.20*
Core PCE -0.05 -0.02 CPH -0.21 -0.24 -0.02
Core CPI -0.15** -0.08* 0.21*** ECI - TC -0.08*
ECI - WS -0.19***
ULC -0.21
Standard errors in parentheses. ∗ p < 0.05, ∗∗ p < 0.01, ∗∗∗ p < 0.001
¹National AHE is average hourly earnings for production and non-supervisory workers. At the state level, they are calculated from the CPS.
²Tight (easy) national labor market is unemployment rate below (above) CBO NAIRU. At state/M SA level, it is below (above) 7%.
The non-linearity estimates are a bit harder to compare, given that there is no state-level
estimate of the natural rate of unemployment. But the estimate in a tight labor market in the
national estimation (unemployment rate below NAIRU) is similar to the estimate in a tight labor
market in the state-level estimation (unemployment rate below 4%). In both cases, the slope is
about -1 on the unemployment rate in a tight labor market.
The price-Phillips curve estimates are significantly different at the national and the state
level when the specifications are run on a similar time period. More specifically, the slope on the
unemployment rate is -0.04 for the national level specification using core PCE from 1988 to
2018, and the estimate is -0.30 for the MSA level specification from 1990 to 2017 (when
controlling for lagged inflation). The difference is not driven by sample composition differences.
If we take the MSA level data and collapse it to a single national level time series and then run
the estimation, we find a slope coefficient on the unemployment rate that is significantly lower (-
35
0.09). This is similar to estimates reported in Babb and Detmeister (2017), who find a coefficient
of -0.12 using national level data, but -0.23 using state level data. In other words, the steeper
slope of the Phillips curve is driven by within-MSA, within-year variation in the unemployment
rate, as opposed to sample composition changes.
The post 1987 MSA-level Phillips curve specification with MSA and year fixed effects
produces a significantly steeper slope than the single time series national estimates. This
difference appears to be quite robust. What could explain such a difference?
From the perspective of economic theory, a steeper price-Phillips curve in MSA level
data is surprising. Given that trade is quite open and robust across MSAs within the United
States, more of the price of goods in a given MSA should be determined by production costs of
firms that are not located in the MSA. As a result, we would expect that price inflation should
not be as strongly determined by the local unemployment rate. But we find the opposite pattern
in the data.
One potential reason for the steeper estimate in MSA-level data is more statistical power
for identification. If the price-Phillips curve is non-linear and especially steep at unemployment
rates below 4% (as suggested by Table 3.2), the national level specification after 1988 will have
a difficult time identifying this effect. In fact, from 1988 to 2017, there is only one year (2000) in
which the unemployment rate reached 4% or lower. The post 1987 national sample Phillips
curve estimate is produced with almost no data from the unemployment regime in which the
MSA-level data say the slope is steepest. In contrast, there are a large number of observations
(115) in the MSA-year level data with unemployment rates below 4%.
As we noted in Section 2, another possible reason for the steeper slope of the Phillips
curve using MSA-level data is that this slope is not affected by the endogeneity of monetary
policy. Monetary policy is the same for all MSAs and so is necessarily exogenous in this data.
Hence the MSA-level data would not be subject to the bias that flattens the estimated slope of the
Phillips curve and so could display steeper Phillips curve estimates.
While the regional level data may help better identify the slope of the Phillips curve
given more variation in the employment environment and the exogeneity of monetary policy, this
comes at a theoretical cost. Such state and MSA level specifications are less well grounded in
theory. While there is important work exploring how to interpret fiscal multiplier estimates at the
regional level (e.g., Guren, McKay, Nakamura, and Steinsson (2018), Chodorow-Reich (2018)),
there is less theoretical work trying to understand the relationship between regional-level
estimates of the Phillips curve and national level estimates.
36
Section 4. The 1960s Regime Shift
As we discussed in the literature review on nonlinearities in the Phillips curve, the economy
might shift from a stationary regime in which inflation and inflation expectations are relatively
stable over time to a second, nonstationary regime in which a persistent unemployment gap leads
to inflation and inflation expectations becoming unanchored. This is exactly what seemed to
happen in the 1960s. To better understand the possibility that history might repeat itself, with
inflation becoming unanchored, it is important to understand how and why this happened in the
1960s and 70s.
4.1 How inflation became unhinged in the latter 1960s
The last time the US labor market (on a national scale) was significantly tight (as defined
by various threshold analyses--including the seminal work by Stock and Watson (2009) which put
the threshold at a negative unemployment gap of 1.5%) was the latter half of the 1960s. We came
close for a brief period in the late 1990s, but the 1960s is the period that has attracted the most
attention as a case study for the steepening of the Phillips curve and an unhinging of inflation
expectations. Much has been written about this period. Orphanides and Williams (2013) covered
it in some detail. Lacker (2017) touched on it at some length in his critique of that year’s USMPF
paper by Cecchetti et al (2017), which found little evidence to support the existence of the Phillips
curve during the period of low inflation based on data since the 1980s. More recently, Powell
(2018a) discussed the 1960s as well.
In what follows, we draw on these and other observations, especially an analysis by
Luzzetti et al (2017).
To better understand what happened in the mid-1960s, it is helpful to review the setting
going back to the 1950s. Inflation had soared early during the Korean War as the labor market
tightened greatly (with the unemployment gap falling below -2%--see Figure 4.1). However,
inflation then plunged to below 2% despite further tightening of the labor market, as remarkably
effective wage and price controls were imposed. With the removal of the controls in 1953, inflation
nevertheless fell further to around zero as the economy moved into recession. Inflation rose
moderately during the subsequent recovery and then eased after the recession of 1958. For the
next seven years or so, through 1965, inflation remained in a narrow band around 1.5% even as
the labor market tightened sharply, with the unemployment gap declining to close to -2%. It is also
noteworthy that inflation did not fall much below this level when the unemployment gap spiked
during the recession of 1960.
37
Figure 4.1: Inflation and the Unemployment Gap, 1949-1971
% Unemployment gap (ls) % y/y
Headline PCE inflation (rs)
Core PCE inflation (rs)
2 10.0
1 7.5
0 5.0
-1 2.5
-2 0.0
-3 -2.5
49 54 59 64 69
Source: BEA, BLS, CBO, Haver Analytics
The behavior of inflation during the latter 1950s and early 1960s was remarkably similar
to what we have seen in recent years. It was as if well-anchored inflation expectations were in
the driver’s seat. Certainly inflation had been low for long enough by the mid-1960s to engender
such expectations. Available indicators of inflation expectations would seem to back this view.
The Livingston survey of year-ahead inflation forecasts remained flat until mid-1965; so did a
measure of the bond market 10-year term premium, which would have been heavily influenced
by market inflation expectations (see Figures 4.2 and 4.3). 12
12
The term premium measure we look at is that from Adrian, Crump, and Moench (2013). This measure is based
on nominal bonds and as such is interpreted as the additional compensation that a risk averse investor needs to
bear future volatility in either real rates or inflation. To the extent that expected inflation volatility is positively
correlated with expected inflation, the term premium will be a good proxy for inflation expectations. Note that
the term premium in the early-1960s was likely distorted by the introduction of Operation Twist in 1961, which
limits the inferences that can be made about inflation expectations during this period.
38
Figure 4.2: Inflation and Inflation Expectations, 1961-1970
Source: BLS, FRB Philadelphia, Haver Analytics
Figure 4.3: Term Premium and Core Inflation, 1961-1970
% %y/y
ACM term premium: 10 year (ls) Core CPI (rs)
1.8 8
1.6
7
1.4
1.2 6
1.0 5
0.8
4
0.6
0.4 3
0.2 2
0.0
1
-0.2
-0.4 0
61 62 63 64 65 66 67 68 69 70
Source: BLS, FRB New York, Haver Analytics
The inflation picture changed dramatically beginning in early 1966. As the
unemployment rate moved below 4% and the unemployment gap approached 2%, core inflation
started to take-off, surpassing 3.5% by the end of 1966 and 5% two years later. This jump was
the opening salvo of the great inflation of the 1970s. The unemployment gap would eventually
bottom at nearly 2.5% in the run up to the 1970 recession.
Measures of inflation expectations moved just ahead of the initial jump in core inflation,
evidently anticipating the higher inflation episode to come, and they tracked inflation higher for
the next several years. Nominal wage growth moved gradually higher during 1965-66, and then
accelerated sharply after mid-1967, more than a year after the jump in core inflation (Figure 4.4).
39
At the same time, productivity growth surged through 1965 as firms evidently found ways to
make their existing work force more productive in the face of a tight labor market. This caused
unit labor cost inflation to drop briefly into negative territory (Figure 4.5). This dynamic reversed
during 1966-67 as productivity growth slowed and unit labor costs accelerated above 4% and
eventually significantly higher, no doubt helping to push core inflation higher through the
remainder of the decade.
Figure 4.4: Average Hourly Earnings Growth and Inflation, 1965-1969
% %y/y
Average hourly earnings (ls) CPI (rs)
8 8
7 7
6 6
5 5
4 4
3 3
2 2
1 1
65 66 67 68 69 70
Source: BLS, Haver Analytics
Figure 4.5: Core Inflation, Unit Labor Cost Growth and Productivity Growth, 1965-1969
% %
Core CPI
10.0 Unit labor costs: non farm business (%y/y) 10.0
Real output per hour: nonfarm business (%y/y)
7.5 7.5
5.0 5.0
2.5 2.5
0.0 0.0
-2.5 -2.5
65 66 67 68 69 70
Source: BLS, Haver Analytics
40
What caused price and wage inflation and inflation expectations suddenly to shift upward
in 1966 after having averaged less than 2% for so many years? Was there really a threshold as
the unemployment gap neared 2%? An analysis of the jump in inflation as well as the drop in
unemployment may shed some light on this issue. The drop in unemployment reflected growth in
aggregate demand (real GDP) that had risen to well above the economy’s 4.5% potential rate of
growth at the time. Much of the above-trend GDP growth during this period was fueled by fiscal
expansion, including some ongoing effects from the Kennedy tax cuts, and a substantial pickup
in both defense spending related to the war in Vietnam and nondefense spending associated with
President Johnson’s Great Society programs. An important element of the latter was the
introduction of Medicare and Medicaid in the second half of 1965.
The initial surge in inflation in 1965 was broadly based across goods and services; prices
for food, shelter, and apparel all accelerated significantly. The single most impressive
contributor was health care, where inflation rates more than doubled from already elevated levels
over the latter half of the 1960s, led by an even stronger acceleration of physicians’ fees (see
Figure 4.6). The Great Society programs were having a substantial impact on the prices of the
new services it was providing for. It would take many years for supply in the health care sector
to catch up with the government-funded increase in demand. With households suddenly facing
surges in prices of such key goods and services, it is little surprise that inflation expectations
would finally have become unanchored.
Figure 4.6: PCE Inflation and Medical Care Inflation, 1961-1969
% y/y % y/y
CPI: medical care services
Personal consumption expenditures: health care price index
10 PCE exculding food & energy: chain price index 10
8 8
6 6
4 4
2 2
0 0
63 64 65 66 67 68 69
Source: BLS, BEA, Haver Analytics
Monetary policy also played an important part in the unanchoring of inflation
expectations and the ongoing rise in inflation in the latter 1960s. The Fed’s initial reaction to the
jump in inflation was to tighten policy modestly. Based on a reading of FOMC minutes and staff
Greenbook analyses at the time, the FOMC recognized that the economy had moved beyond full
employment and that inflation risks were rising. 13 The Committee agreed that its policy should
13
For example, the minutes from the January 11, 1966 FOMC meeting noted that: “Chairman Martin thought the
Committee was more or less in agreement on policy… the System now would be operating in an entirely new
41
resist increases in inflation, and they raised the nominal fed funds rate from around 4% in Q4
1965 to over 5-1/2% in Q4 1966. But these moves were largely in response to market pressures
on short term rates, and they turned out to be about in line with the rise in inflation, leaving real
rates little changed. The Committee then reversed this increase in the first four months of 1967
when growth slowed significantly, but temporarily, and headline and to a lesser extent core
inflation eased briefly. Inflation then took off again and the Fed was well behind the curve with
real interest rates having fallen significantly (Figure 4.7).14
Figure 4.7: Nominal and Real Federal Funds Rate, 1961-1969
% %
Nominal fed funds rate Real fed funds rate
10 10
8 8
6 6
4 4
2 2
0 0
63 64 65 66 67 68 69 70
Source: FRB, BEA, Haver Analytics
Inflation expectations were not monitored or assessed in the Fed’s analysis of current
economic developments at the time, and the FOMC may not have appreciated the extent to
which those expectations and their underlying implications for inflation may have shifted in a
fundamentally higher direction. Increases in expectations appeared to give some warning, but by
only a few months at most. There are several leading academic theories about the Fed's role in
the inflationary episode that began in the mid-1960s.
First, the Fed may have been susceptible to political pressure during this period to
coordinate with fiscal policy and finance the fiscal deficit. As Meltzer (2010) noted, the Fed
Chair's "acceptance of policy coordination with the administration prevented the Federal Reserve
from taking timely actions and contributed to more expansive policies than were consistent with
environment--one that had not been contemplated a year ago--of full employment generally and over-full
employment of skilled workers. He personally would favor a little inflation if he thought it would benefit the
unemployables, but he did not think it would; rather, it would do them harm.” The Greenbook analysis from that
meeting stated: ““…the magnitude of improvement in resource utilization – particularly for labor -- also
considerably exceeded expectations…” and that “…upward pressures on prices appear likely to be strong.”
14
The minutes from the January 1967 FOMC meeting show a change in the Fed’s tone: “The economic and
financial developments reviewed at this meeting indicate further moderation in various expansionary forces and
sharply increased inventory accumulation. The pace of advance of broad price measures has slowed… To
implement this policy, System open market operations…shall be conducted with a view to attaining somewhat
easier conditions in the money market.”
42
price stability." Or, as Lacker (2017) put it more colorfully, President Johnson could be very
convincing as he drove the Fed Chair around his Texas ranch at breakneck speeds in his white
Cadillac.
This was also a time shortly after the famous paper by Paul Samuelson and Robert Solow
(1960) was published, in which they argued that policy makers could achieve a
“nonperfectionist” goal of a 3% unemployment rate at what they considered to be a tolerable
inflation rate of 4 to 5%. This thinking was influential among academic economists, some of
whom were in the Kennedy and Johnson administrations, who promoted the adoption of
expansionary policies to stimulate the economy and bring inflation down to low levels.
Second, the Fed may have made analytical errors by both overestimating the degree of
slack in the economy and underestimating the sensitivity of inflation to slack. For example,
Romer and Romer (2002) argue that the implicit estimate of NAIRU that can be inferred from
the Fed's Greenbook forecasts during the time was around 2.5%. This compares with the CBO's
current estimate of about 5.5% during the mid-1960s. As Powell (2018a) put it,
“…policymakers misperceived the level of the natural rate of unemployment, which we now
believe had shifted up markedly in the 1960s. With the higher natural rate, the labor market was
much tighter and provided much greater upward pressure on inflation than policymakers realized
in real time. As a result, they were continually "behind the curve.”
On both counts, we may be better off today than we were a little over 50 years ago, with
an emphasis on “may.” With respect to the second issue, we suspect that much has been learned
over time on the data front, but uncertainty about concepts like the natural rates of
unemployment and interest may be just as high today as they were in the mid 1960s, as
suggested by Powell (2018b).
On the political front, the Administration has expressed displeasure with some of its
choices for the Board of Governors, and in the past month, the Wall Street Journal reported that
top White House economic adviser Lawrence Kudlow said President Trump will seek to fill two
Federal Reserve Board vacancies with nominees who don’t believe a rapidly expanding economy
has to fuel faster inflation. Kudlow was quoted as saying, “The White House wants highly
capable, competent people who understand that you can have strong economic growth without
higher inflation. Surges in the economy’s productive capacity mean that more people can work at
higher wages without causing inflation to pick up.” If political pressure leads the FOMC to
move to a belief that a rapidly expanding economy poses no inflationary dangers, there would be
a shift toward policy views that were present in the 1960s.
In sum, there are important parallels and important differences between the 1960s and
today.
Parallels:
In both periods the unemployment rate was approaching 3-1/2% from substantially
higher levels with little or no evidence of core price inflation rising significantly above
the relatively subdued levels they had been at for many years.
Fiscal stimulus was boosting aggregate demand
Consistent with low realized inflation, inflation expectations were stuck at low levels.
43
While Fed officials during both periods were/are aware of the effects of tight resource
utilization on inflation, the absence of inflation pressures despite steep declines in
unemployment led to beliefs that NAIRU was low, and could be falling, and that the
Phillips curve was flat
The Fed faced strong political pressure from the Administration not to raise rates
Uncertainty about NAIRU remains high
Differences:
The NAIRU was estimated to be considerably higher in the 1960s than it is now; we still
have a ways to go to get to an unemployment gap of negative 1.5-2.0%; various
technological advances may be reducing the NAIRU even further today.
The Fed’s policy performance since the great inflation and its adoption of a formal price
mandate and specific inflation objective in 2012 may have helped to anchor inflation
expectations more solidly than they were in the mid-1960s
Today’s Fed has had the benefit of having learned from past experience:
o At least until very recently, they have been tightening in a pre-emptive, though
gradual manner, and recognize that the fed funds rate has to rise by more than
one-for-one with inflation in order to tighten policy. They are also mindful of the
central importance of Fed independence in the conduct of policy.
o But the composition of FOMC membership can change over time.
44
Section 5: Prospects for Inflation in a High Pressure Economy
5.1 Inflation projections
Turning to a more forward-looking portion of the paper, in this section we investigate
what the macro Phillips curve models we estimated in Section 2 have to say about the prospects
for inflation. In doing so we begin by reviewing the in-sample prediction performance of the
models. We then simulate some forward-looking scenarios with the various linear and nonlinear
versions of the models for price and wage inflation. The results for some of the core PCE
inflation projections are shown here, and those for wage inflation projections are included in the
Annex.
The in-sample fits since 1988 for the various linear and nonlinear specifications of the
core PCE equation estimated over the full sample are shown in Figure 5.1, and that for the same
equations estimated over the period since 1988 are shown in Figure 5.2. Visually, the full sample
estimates appear to track the quarterly fluctuations in inflation more closely, whereas the partial
sample estimates track the underlying trend but appear to miss more of the quarterly variance.
The full sample results may benefit from hindsight inasmuch as lagged inflation is a more
important driver in those model estimations. In the partial sample results, inflation expectations
play a much more prominent role, and the relative stability of those expectations since the late
1980s helps to explain the smoother trajectory of those projections.
Figure 5.1: In sample fit (1961-2018 coefficients)
Source: BEA, Haver Analytics, Authors’ calculations
45
Figure 5.2: In sample fit (1988-2018 coefficients)
Source: BEA, Haver Analytics, Authors’ calculations
In Figure 5.3, we show a similar figure for the models estimated over the full sample,
except that the focus here is on the fit during the tight labor market period of the latter 1960s.
Whereas during other periods it was difficult to distinguish between the different nonlinear
versions, when the labor market tightened significantly, the differences across these models
began to show up significantly.
Figure 5.3: In-sample fit over the 1960s (1961-2018 coefficients)
Source: BEA, Haver Analytics, Authors’ calculations
Turning to the projections, we considered two scenarios. In the first scenario,
unemployment was assumed to follow the median path in the FOMC’s December 2018 summary
46
of economic projections (SEP). In the second scenario, the unemployment rate is assumed to
decline further to 3% by the end of 2020 and remain there through 2021. In both cases, the
natural rate or NAIRU was assumed to remain at the FOMC’s median longer run projection of
4.4%. The resulting unemployment gaps are shown in Figure 5.4. Under both scenarios the
unemployment gap is negative throughout, but diminishes in the SEP median scenario and
declines to and remains at nearly-1.4% in the tighter labor market scenario.
Figure 5.4: Unemployment Gap Scenarios
Source: BLS, CBO, FRB, Haver Analytics, Authors’ calculations
For the price-Phillips curves, inflation expectations were assumed to hold steady at 2%
(though this assumption was later relaxed), and relative import prices were held at their 2018Q3
values. Lagged inflation was projected dynamically by each model (i.e., next period’s lagged
inflation was the model’s prediction of inflation this period). For the wage equation projections
(which are reported in the Annex), inflation expectations and trend productivity growth were
held constant at their 2018Q3 values and lagged inflation was handled in two different ways. In
one case, lagged inflation was assumed to follow the December 2018 FOMC median projections.
In a second case, lagged inflation was assumed to follow the mean projection of the various core
PCE inflation models matched by sample period. (In this latter case, for example, lagged
inflation for the wage-Phillips curves estimated over the longer sample period from the 1960s to
2018 was assumed to follow the mean projection of the price Phillips curves estimated over the
same period.) Finally, in order to consider the possibility of a shift to a nonstationary or adaptive
expectations regime, we endogenized inflation expectations, having them move with lagged
inflation projections as discussed further below. 15
15
We elected not to use the model itself to predict lagged inflation in a rational expectations framework because
we wanted to see what would happen if the structure of the model reverted to more of an adaptive expectations
framework as existed prior to the 1980s. The projections reported here are partial-equilibrium scenarios designed
47
Figures 5.5 and 5.6 present projections with the core PCE models estimated over the full
sample and the more recent sample period respectively; in both cases FOMC median
unemployment projections were used. The forecasts of inflation generally dip in the near term
because of the lagged effects of the transitory drop in inflation in 2017. Models based on the full
sample period show a significant upward trajectory over the next three years, more so for the
nonlinear variants—especially the spline equation—than the linear version. This reflects the
steeper nonlinear Phillips curve slopes that apply when the unemployment gap is negative. The
more recent sample period yields forecasts that are much flatter and more in line with (though
still several tenths above) the median FOMC inflation projections.
Figure 5.5: Core PCE Scenario 1: FOMC Median Unemployment Path, 1961-2018
Coefficients
%, y/y %, y/y
Core PCE Linear Spline
5.0 Cubic Convex1 Convex2 5.0
Piece Quad Fed Dec Forecast
4.5 4.5
4.0 4.0
3.5 3.5
3.0 3.0
2.5 2.5
2.0 2.0
1.5 1.5
1.0 1.0
2016 2017 2018 2019 2020 2021
Source: BEA, FRB, Haver Analytics, Authors’ calculations
to show the properties of the different models rather than true forecasts. These projections do not factor in the
likely policy reactions that significant increases in inflation would induce.
48
Figure 5.6: Core PCE Scenario 1: FOMC Median Unemployment Path, 1988--2018
Coefficients
Source: BEA, FRB, Haver Analytics, Authors’ calculations
When these models are run with our alternative, tighter labor market scenario
(unemployment falling further to 3% and remaining there), the full sample coefficients yield a
further pickup of two to five tenths in core inflation over the next three years (Figure 5.7). The
shorter sample coefficients yield only a slight pickup in most cases, with the cubic variant being
a notable exception (Figure 5.8).
Figure 5.7: Scenario 2: Unemployment to 3%, 1961-2018 Coefficients
Source: BEA, FRB, Haver Analytics, Authors’ calculations
49
Figure 5.8 Scenario 2: Unemployment to 3%, 1988-2018 coefficients
Source: BEA, FRB, Haver Analytics, Authors’ calculations
Finally, we considered what would happen if in the event of a further tightening of the
labor market to 3% unemployment, inflation expectations shifted away from being anchored at
2% (as we have assumed in all of the projection scenarios so far) and instead became more
adaptive. To achieve this effect, we estimated an equation for inflation expectations as a
function of lagged inflation over the adaptive expectations period from the mid- 1960s to the
early 1980s. Our specific model, using three lags on inflation was:
𝜋 = 0.63 + 0.30𝜋 + 0.02𝜋 + 0.34𝜋
based on data for the period 1964Q1 – 1981Q4.
Allowing inflation expectations to adjust away from a 2% anchor, albeit slowly, moves
the inflation outcomes up noticeably further (Figure 5.9). The increase is considerably more
subdued under the more recent sample estimation (Figure 5.10). If unemployment were to
decline to 3% and remain there for a couple years, the full-sample results might be more
pertinent than the post-1988 sample results, because a period of such tight labor markets could be
enough to begin to shift the current very stationary Phillips curve into a more nonstationary
regime as in Nalewaik’s work and the experience of the 1960s suggested. That is, inflation
expectations would become more adaptive, inflation more persistent, and the Phillips curve
steeper, as captured in the full sample coefficients. Were such a shift to occur, the various
projections in Figure 5.15 say that inflation could rise to between 2.75% (linear model) and
4.25% (spline model) over the next three years in the event of the tighter labor market scenario.
Of course, it is unlikely that inflation would rise as much as some of these model projections
suggest over this time period, because the Fed would most likely step in with policy restraint if it
became evident that inflation expectations were becoming unmoored.
50
Figure 5.9: Scenario 2: Unemployment goes to 3%, 1961-2018 Coefficients
Source: BEA, FRB, Haver Analytics, Authors’ calculations
Figure 5.10: Scenario 2: Unemployment goes to 3%, 1988-2018 Coefficients
Source: BEA, FRB, Haver Analytics, Authors’ calculations
51
Section 6. Conclusions
As the USMPF gathers this year, belief that the Phillips curve is dead has never been
stronger, at least not for the past 50 years. Unemployment has been running noticeably below
most estimates of the natural rate for well over a year now, while core inflation has remained
persistently below the Fed’s objective.
The Fed has moved essentially to neutral recently despite unemployment continuing to
run noticeably below its estimate of NAIRU with ample momentum behind it, partly because of
growing risks to the outlook abroad, but partly also because of concern that inflation remains
slightly below 2% despite a seemingly tight labor market. Doubts about the Phillips curve
relationship may well be on the rise even within the Fed.
Evidence that the price Phillips curve has been dormant for the past several decades does
not necessarily mean that it is dead. As the empirical evidence in this paper indicates, the
Phillips curve could be hibernating, and there is a risk of the Phillips curve waking up, with
inflationary pressures rising in the face of an overheating labor market.
There are several arguments from the evidence in this paper that we can have concerns
about inflation if we continue to experience a high-pressure economy.
First, some of our empirical specifications in Section 2 of the paper, suggest that the
price-Phillips curve might have substantial nonlinearities. If these nonlinearities are present, the
simulations in Section 5 suggest that inflation could rise above the Fed’s target level if the
unemployment rate continues on the path projected in December by the FOMC participants, or
declines even further. However, the evidence from the post-1988 sample period is much less
supportive of these nonlinearities. We are not sure which Phillips curve sample periods provides
more reliable information about where the Phillips curve is now. However, the state and MSA
evidence suggests that the post-1988 Phillips curve may not be able to reveal these nonlinearities
because there are so few observations of very tight labor markets since 1988 and possibly
because of the endogoneity of monetary policy. The state and MSA data, which has many more
observations with very tight labor markets, suggests that the Phillips curve with nonlinearities
might be alive and well. Thus the reports of the death of the Phillips curve might be greatly
exaggerated. We should not discount the possibility that substantial nonlinearities are present in
today’s Phillips curve and so a high-pressure economy could lead to inflationary pressures.
Second, our evidence, both in the macro, time-series data and the state and MSA data in
Sections 4 and 5, suggests that the wage-Phillips curve is alive and well. This is consistent with
the observation that wage inflation has marched steadily, if slowly, upward in recent years as the
labor market has tightened, as shown in Figure 6.1. However, Chair Powell (2018b) has noted,
we did see something like this in the late 1990s-early 2000s without an inflation lift (Figure 6.2).
But that was also a period during with strong dollar helped keep a tight lid on inflation, and the
tight labor market was cut short by the recession of 2001, Could we see this play out again?
Wage inflation did rise significantly in the late 90s (both in nominal terms and in excess of
productivity trends), as it had in the mid 1960s. While the wage Phillips curve may have
flattened some over time, it remains much steeper and evidence of nonlinearities much more
robust than for the price Phillips curve in the post-1988 sample period. It is possible that the link
between wage and price inflation has become weak, but this is a puzzle that requires further
research.
52
Figure 6.1: Unemployment Gap and Wage Growth, 2008-2016
% Unemployment gap (ls) % y/y
Avg hourly earnings: prod & nonsupervisory: total pvt industries (rs)
Employment cost index: civilian workers (rs)
Core PCE (rs)
5 4.0
4 3.5
3.0
3
2.5
2
2.0
1
1.5
0 1.0
-1 0.5
08 09 10 11 12 13 14 15 16 17 18 19
Source: BLS, CBO, Haver Analytics
Figure 6.2: Unemployment Gap and Wage Growth, 1992-2002
% Unemployment gap (ls) % y/y
Avg hourly earnings: prod & nonsupervisory: total pvt industries (rs)
3 Employment cost index: civilian workers (rs) 5.0
Core PCE (rs)
4.5
2 4.0
3.5
1
3.0
2.5
0
2.0
-1 1.5
1.0
-2 0.5
92 93 94 95 96 97 98 99 00 01 02
Source: BLS, CBO, Haver Analytics
Third, Nalewaik’s (2016) evidence suggests that the economy can switch from a
stationary regime, in which shocks to inflation only have transitory effects on inflation and
inflation expectations are anchored, to a nonstationary regime, in which shocks to inflation have
persistent effects and inflation expectations become unanchored. Our case study of the 1960s in
Section 4 and the parallels between that period and the current one suggest that there is a
possibility that we could move to a nonstationary regime if the unemployment rate stays well
53
below the natural rate of unemployment for a long period of time, especially if political pressures
begin to influence market expectations. We do not think this is a likely scenario because starting
in 2012, the Federal Reserve has adopted the monetary policy strategy of inflation targeting
which has proved successful in anchoring inflation expectations in many countries. However,
changes in the composition of the FOMC could possibly weaken the Fed’s commitment to its
inflation target, which would make an unmooring of inflation expectations more likely. If
inflation expectations did become unanchored, our case study of the 1960s in Section 4 and the
simulations in Section.5 do raise concerns that inflation could become a problem.
We want to be very clear that the evidence in this paper does not say that inflation will
rise in the near future. First, our evidence is ambiguous about the degree to which the Phillips
curve may have a steeper slope and nonlinearities because we obtain different results for the pre-
1988 and post-1988 sample period. However, because of the lack of variation in the
unemployment gap data since 1988 and the endogeneity of monetary policy in this sample
period, we are more doubtful that the 1988-2018 estimated Phillips curve is reliable. Second,
there is currently substantial uncertainty about whether the economy will remain in a high-
pressure mode. Thus our analysis not about whether inflation will rise in the near future, but
rather that we cannot be complacent about inflationary pressures. As we have discussed, the
flattening of the Phillips curve in recent decades reflects some combination of the absence of
very tight labor markets, the endogeneity bias of monetary policy, and the anchoring of inflation
expectations. Monetary policy committed to stabilizing inflation has been central to all three of
these factors. A departure from this policy would likely lead to a steepening of the Phillips
curve.
54
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Annex
Annex to Section 2: Additional Phillips Curve model estimation results
Table A.1: Headline PCE Phillips Curve, full sample: 1961-2018
Linear Spline Cubic Convex1 Convex2 Piece. quad.
ugap -0.131 *** -0.421 *** -0.368 *** -0.076
(0.049) (0.125) (0.116) (0.059)
ugap pos 0.395 **
(0.159)
2
ugap 0.013
(0.039)
3
ugap 0.017
(0.013)
ugap/u -1.000 ***
(0.304)
ln(u/u*) -0.882 ***
(0.302)
2
ugapneg 0.123 *
(0.065)
Rel. Imp. Goods Infl. 0.061 *** 0.064 *** 0.061 *** 0.063 *** 0.062 *** 0.064 ***
(0.016) (0.016) (0.016) (0.016) (0.016) (0.016)
Sum Lag Infl. Coeffs. 0.864 0.862 0.882 0.862 0.862 0.861
RMSE 1.320 1.312 1.303 0.000 0.000 1.318
Slope at Linear Spline Cubic Convex1 Convex2 Piece. quad.
ugap = +1 (u = 5.61) -0.131 -0.026 -0.290 -0.146 -0.157 -0.076
ugap = 0 (u = 4.61) -0.131 -0.368 -0.217 -0.191 -0.076
ugap = -1 (u = 3.61) -0.131 -0.421 -0.344 -0.354 -0.244 -0.322
ugap = -2 (u = 2.61) -0.131 -0.421 -0.215 -0.677 -0.338 -0.567
Standard errors in parentheses. ∗ p < 0.05, ∗∗ p < 0.01, ∗∗∗ p < 0.001
58
Table A.2: Headline PCE Phillips Curve, extended sample: 1949-2018
Linear Spline Cubic Convex1 Convex2 Piece. quad.
ugap -0.057 -0.083 -0.192 -0.083
(0.051) (0.145) (0.125) (0.073)
ugap pos 0.039
(0.198)
2
ugap -0.042
(0.058)
3
ugap 0.020
(0.018)
ugap/u -0.245
(0.312)
ln(u/u*) -0.301
(0.310)
ugapneg2 -0.042
(0.087)
Rel. Imp. Goods Infl. 0.044 *** 0.044 *** 0.042 *** 0.044 *** 0.044 *** 0.043 ***
(0.016) (0.016) (0.016) (0.016) (0.016) (0.016)
Sum Lag Infl. Coeffs. 0.825 0.824 0.839 0.823 0.824 0.826
RMSE 1.552 1.555 1.552 1.553 0.000 1.554
Slope at Linear Spline Cubic Convex1 Convex2 Piece. quad.
ugap = +1 (u = 5.61) -0.057 -0.044 -0.217 -0.036 -0.054 -0.083
ugap = 0 (u = 4.61) -0.057 -0.192 -0.053 -0.065 -0.083
ugap = -1 (u = 3.61) -0.057 -0.083 -0.048 -0.087 -0.083 0.001
ugap = -2 (u = 2.61) -0.057 -0.083 0.212 -0.166 -0.115 0.086
Standard errors in parentheses. ∗ p < 0.05, ∗∗ p < 0.01, ∗∗∗ p < 0.001
59
Table A.3: Wage Phillips Curve (Compensation per Hour): 1964-2018
Linear Spline Cubic Convex1 Convex2 Piece. quad.
ugap -0.386 *** -0.847 *** -0.710 *** -0.300
(0.149) (0.247) (0.269) (0.182)
ugap pos 0.606 *
(0.356)
2
ugap 0.029
(0.094)
3
ugap 0.019
(0.030)
ugap/u -2.678 ***
(0.798)
ln(u/u*) -2.498 ***
(0.883)
ugapneg2 -0.206
(0.138)
Trend prod. growth. 0.671 ** 0.591 ** 0.525 * 0.603 ** 0.626 ** 0.641 **
(0.285) (0.287) (0.282) (0.283) (0.283) (0.286)
RMSE 2.767 2.761 2.763 2.758 2.763 2.766
Slope at Linear Spline Cubic Convex1 Convex2 Piece. quad.
ugap = +1 (u = 5.61) -0.386 -0.240 -0.595 -0.392 -0.445 -0.300
ugap = 0 (u = 4.61) -0.386 -0.710 -0.581 -0.542 -0.300
ugap = -1 (u = 3.61) -0.386 -0.847 -0.712 -0.947 -0.692 0.112
ugap = -2 (u = 2.61) -0.386 -0.847 -0.603 -1.812 -0.957 0.524
Standard errors in parentheses. ∗ p < 0.05, ∗∗ p < 0.01, ∗∗∗ p < 0.001
60
Table A.4: Wage Phillips Curve (Compensation per Hour): 1949-2018
Linear Spline Cubic Convex1 Convex2 Piece. quad.
ugap -0.303 ** -0.542 ** -0.288 -0.251
(0.134) (0.214) (0.256) (0.182)
ugap pos 0.353
(0.336)
2
ugap 0.051
(0.086)
3
ugap -0.010
(0.030)
ugap/u -1.597 **
(0.647)
ln(u/u*) -1.726 **
(0.757)
ugapneg2 -0.086
(0.131)
Trend prod. growth. 0.798 *** 0.785 *** 0.800 *** 0.812 *** 0.797 *** 0.794 ***
(0.250) (0.251) (0.255) (0.252) (0.252) (0.251)
RMSE 2.817 2.817 2.826 2.819 2.818 2.821
Slope at Linear Spline Cubic Convex1 Convex2 Piece. quad.
ugap = +1 (u = 5.61) -0.303 -0.189 -0.215 -0.234 -0.308 -0.251
ugap = 0 (u = 4.61) -0.303 -0.288 -0.346 -0.374 -0.251
ugap = -1 (u = 3.61) -0.303 -0.542 -0.419 -0.565 -0.478 -0.079
ugap = -2 (u = 2.61) -0.303 -0.542 -0.610 -1.081 -0.661 0.093
Standard errors in parentheses. ∗ p < 0.05, ∗∗ p < 0.01, ∗∗∗ p < 0.001
61
Table A.5: Wage Phillips Curve using lagged nominal wages instead of lagged prices:
1988-2018
AHE CPH ECI TC ECI WS ULC
Linear Spline Linear Spline Linear Spline Linear Spline Linear Spline
ugap -0.127 *** -0.192 -0.312 -2.087 * -0.144 *** -0.824 *** -0.175 *** -0.709 *** -0.530 -1.484
(0.042) (0.198) (0.225) (1.247) (0.049) (0.318) (0.047) (0.263) (0.327) (1.539)
ugap pos 0.072 1.946 0.744 0.573 ** 1.078
(0.209) (1.316) (0.337) (0.271) (1.640)
Trend prod. growth -0.104 -0.111 0.957 ** 0.828 * 0.435 *** 0.301 * -0.003 -0.072
(0.103) (0.109) (0.467) (0.453) (0.156) (0.164) (0.115) (0.124)
Infl. Expectations 0.120 0.126 1.138 *** 1.289 *** 0.755 *** 0.730 *** 0.386 *** 0.441 *** 1.444 *** 1.495 ***
(0.102) (0.104) (0.248) (0.275) (0.150) (0.149) (0.122) (0.125) (0.307) (0.324)
Sum Lag Infl. Coeffs. 0.880 0.874 -0.138 -0.289 0.245 0.270 0.614 0.559 -0.444 -0.495
RMSE 0.6081 0.6105 3.3233 3.3022 0.7982 0.7809 0.7382 0.727 3.8499 3.8552
AHE CPH ECI TC ECI WS ULC
Slope at Linear Spline Linear Spline Linear Spline Linear Spline Linear Spline
ugap > 0 -0.127 -0.120 -0.312 -0.141 -0.144 -0.081 -0.175 -0.137 -0.530 -0.406
ugap < 0 -0.127 -0.192 -0.312 -2.087 -0.144 -0.824 -0.175 -0.709 -0.530 -1.484
Note: AHE is average hourly earnings for production and nonsupervisory workers, CPH is compensation
per hour, ECI TC is the Employment Cost Index: Total Compensation for private workers, ECI WS is the
Employment Cost Index: Wages and Salaries for private workers, and ULC is unit labor costs.
Annex to Section 5: Wage inflation projections
Projections with the wage inflation models comparable to those reported for the price
inflation models in Section 5 are reported here. We use the model for average hourly earnings
inflation under the assumptions as described in Section 5. The simulation under the FOMC
median unemployment gap projection generally shows fairly similar (both relatively flat)
trajectories for the wage inflation projections with full sample and shorter sample coefficients
(Figures A.1 and A.2, respectively). Recall that the estimation results for the wage equations
were much closer between the two sample periods than they were for the price equations. What
is more surprising is that the wage equations, if anything show less upward tilt than the full
sample price equation results. The greater upward movement in the projections with the full
sample price models is because of the inclusion of lagged dependent variables (i.e., lagged
inflation) in those models with relatively high coefficients (i.e., relatively high inflation
persistence or longer-term Phillips curve slopes. This magnifies the effects of the decline in the
unemployment gap over time. These dynamics are excluded in the wage equations, which
include lagged price inflation rather than lagged wage inflation. This difference is more
dramatic for the tighter labor market scenario.
62
Figure A.1 Wage-Phillips curve, Scenario 1: FOMC Median Unemployment Path 1964-
2018 Coefficients
%, y/y %, y/y
AHE PNS y/y% Linear
5.0 Spline Cubic 5.0
Convex1 Convex2
4.5 Piece Quad 4.5
4.0 4.0
3.5 3.5
3.0 3.0
2.5 2.5
2.0 2.0
1.5 1.5
1.0 1.0
2016 2017 2018 2019 2020 2021
Source: BLS, Haver Analytics, Authors’ calculations
Figure A.2 Wage-Phillips curve, Scenario 1: FOMC Median Unemployment Path 1988-
2018 Coefficients
%, y/y %, y/y
AHE PNS Linear Spline
5.0 Cubic Convex1 Convex2 5.0
Piece Quad
4.5 4.5
4.0 4.0
3.5 3.5
3.0 3.0
2.5 2.5
2.0 2.0
1.5 1.5
1.0 1.0
2016 2017 2018 2019 2020 2021
Source: BLS, Haver Analytics, Authors’ calculations
When unemployment is assumed to decline further to 3% (Figures A.3 and A.4), the
wage models do begin to show some upward tilt, as was the case with the price models. But the
move still seems subdued relative to the full-sample price equation results shown in Figure 5.5.
Again, this result occurs because the tighter labor market was assumed to have no effect on
63
(lagged) price inflation in the wage equation. That is, price inflation was assumed to follow the
FOMC’s median projection of 2%, and this assumption effectively anchored wage inflation.
Figure A.3: Scenario 2: Unemployment to 3% and Core PCE Follows FOMC’s Median
Forecast, 1964-2018 coefficients
%, y/y %, y/y
AHE PNS Linear Spline
5.0 Cubic Convex1 Convex2 5.0
Piece Quad
4.5 4.5
4.0 4.0
3.5 3.5
3.0 3.0
2.5 2.5
2.0 2.0
1.5 1.5
1.0 1.0
2016 2017 2018 2019 2020 2021
Source: BLS, Haver Analytics, Authors’ calculations
Figure A.4: Scenario 2: Unemployment to 3% and Core PCE Follows FOMC’s Median
Forecast, 1988-2018 coefficients
%, y/y %, y/y
AHE PNS Linear Spline
5.0 5.0
Cubic Convex1 Convex2
4.5 Piece Quad 4.5
4.0 4.0
3.5 3.5
3.0 3.0
2.5 2.5
2.0 2.0
1.5 1.5
1.0 1.0
2016 2017 2018 2019 2020 2021
Source: BLS, Haver Analytics, Authors’ calculations
When we relax this assumed constraint on lagged inflation in the wage equations and
allow future lagged inflation to rise in line with the average of the corresponding price inflation
model forecasts, the upward tilt in the wage forecasts increases noticeably, at least in the full
64
sample model projections (Figure 5A.5). The impact in the full sample results is more
noticeably than in the post-1988 sample results (Figure A.6) because the corresponding price
inflation forecasts rise faster in this scenario (compare Figures 5.7 and 5.8).
Figure A.5: Core PCE Follows Average of Core PCE Forecasts in the 3% Unemployment
Scenarios Above, 1964-2018 Coefficients
%, y/y AHE PNS Linear Spline %, y/y
5.0 Cubic Convex1 Convex2 5.0
Piece Quad
4.5 4.5
4.0 4.0
3.5 3.5
3.0 3.0
2.5 2.5
2.0 2.0
1.5 1.5
1.0 1.0
2016 2017 2018 2019 2020 2021
Source: BLS, Haver Analytics, Authors’ calculations
Figure A.6: Core PCE Follows Average of Core PCE Forecasts in the 3% Unemployment
Scenarios Above, 1988-2018 Coefficients
%, y/y %, y/y
AHE PNS Linear Spline
5.0 5.0
Cubic Convex1 Convex2
4.5 Piece Quad 4.5
4.0 4.0
3.5 3.5
3.0 3.0
2.5 2.5
2.0 2.0
1.5 1.5
1.0 1.0
2016 2017 2018 2019 2020 2021
Source: BLS, Haver Analytics, Authors’ calculations
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