Slack and Cyclically Sensitive Inflation

• DOI: http://doi.org/10.1111/jmcb.12757
• Published date: 01 December 2020
• Date: 01 December 2020

DOI: 10.1111/jmcb.12757

JAM ES H . STO CK

MARK W. WATSON

Slack and Cyclically Sensitive Ination

Weinvestigate the attening Phillips relation by making two departures from

standard specications. First, we measure slack using real activity variables

that are bandpass ltered or year-over-year changes in activity (these are

similar), instead of gaps. Second, we study the components of ination in-

stead of the standard aggregates. We nd that some ination components

havestrong and stable correlations with the cyclical component of real activ-

ity; these components tend to be relatively well-measured and domestically

determined. Other components, typically prices that are poorly measured

or internationally determined, have weak and/or unstable correlations with

cyclical activity.We construct a new ination index, cyclically sensitive in-

ation, that weights the components by their joint cyclical covariation with

real activity. The index has strong and stable correlations with cyclical ac-

tivity and provides a real-time measure of cyclical movements in ination.

F 1    of the attening Phillips

curve in the United States. From 1960 to 1983, a one percentage point increase in the

annual average unemployment gap, as measured by the unemployment rate minus the

Congressional Budget Ofce’s (CBO) estimate of the natural rate of unemployment,

was associated with a –0.48 (standard error of 0.10) percentage point change in the

year-over-year change in the rate of core PCE (personal consumption expenditures)

ination. In 1984–99, this slope attened to –0.26 (SE =0.08). From 2000 through

the rst quarter of 2019, by this measure, the Phillips curve was essentially at, with

a slope of –0.03 (SE =0.03). As discussed in Section 3, this attening is also found

The authors thank Brian Barnier, Alan Detmeister, Jim Dolmas, Karen Dynan, Sylvester Eijfnger,

Martin Feldstein, Benjamin Friedman, David Friedman, Jason Furman, Jordi Galí, Justine Guillochon,

Michael Kiley,Kyle Hood, Peter Ireland, Chiara Osbat, Jennifer Ribarsky, Lucrezia Reichlin, Robert Rich,

Argia Sbordone, Ellis Tallman, KenWest, John Williams, two referees and participants at the 2018 ECB

Economic Forum, the XXII Annual Conference of the Central Bank of Chile, and the 2019 FRBNY-JMCB

conference for helpful comments and/or discussions. An earlier version of this paper, under the same title,

was presented at the ECB Forum on Central Banking, June 2018, Sintra Portugal. Replication les are

posted on Watson’sWeb site.

J H. S is with Harvard University and the NBER.MW.Wis with Princeton

University and the NBER (E-mail: mwatson@princeton.edu)

Journal of Money, Credit and Banking, Supplement to Vol. 52, No. S2 (December 2020)

© 2021 The Ohio State University

394 :MONEY,CREDIT AND BANKING

Fig 1. The attening U.S. Phillips curve: Year-over-yearchange in the rate of ination vs. the four-quarter average of the

CBO unemployment gap. Numerical values are slopes. Left: Headline PCE (total); right: core PCE.

N: 1960–83 (circles); 1984–99 (diamonds); 2000–2019q1 (squares). Data are quarterly. The year-over-yearchange

in ination plotted on the vertical axis is the four-quarter change of the (backwards-looking) four-quarter moving av-

erage of the ination rate. The horizontal axis plots the (backwards-looking) four-quarter moving average of the CBO

unemployment gap.

JAMES H. STOCKAND MARK W. WATSON :395

using other gap measures of slack, in Phillips curve forecasting regressions, and in

New Keynesian Phillips curves.

This apparent disconnect between the rate of ination and labor market slack raises

new questions for monetary policy. Is this attening of the Phillips curve a new and

permanent feature of modern economies with credible monetary authorities? Is it the

consequence of structural changes, such as the increasing importance of international

markets in setting prices? Or is it in some sense a measurement artifact, so that tight

economic conditions are building inationary pressures that simply have not yet been

observed?

The ination puzzle is typically expressed, as it is in Figure 1, as a relation be-

tween ination aggregates, typically headline or core, and an activity gap, such as

the unemployment gap. In this paper, we make two departures from this standard

approach.

First, we go beyond the aggregates and consider the Phillips curve properties of

the components of PCE ination. There are multiple reasons why the sensitivity of

ination to real activity might differ from one component to the next. For example,

the extent to which the price of a given good or service responds to domestic cyclical

pressures depends in part on the extent to which that price is set based on international

or domestic market conditions. At one extreme, the prices of commodities such as oil

are set in world markets, so the link between economic activity in any one country and

the change in the oil price will be attenuated. In contrast, many services, such as recre-

ational services or food served at restaurants, are largely nontradable and have prices

that are set in local markets, so should be more subject to local and national cyclical

pressures. More generally, price-setting dynamics and thus cyclical variation would

be expected to vary across sectors based on market structure, wage-setting practices,

and so forth. In addition, the quality of price measurement varies considerably across

components: for some components, measurement problems are sufciently severe

that measurement error could overwhelm cyclical movements.

Second, we take a nonstandard approach to ltering that leads us to consider al-

ternative activity measures. Instead of focusing on gaps, which can be thought as the

output of passing a real activity variable through a high-pass lters with a very low

frequency cutoff, we consider real activity variables that have been ltered using l-

ters that concentrate their gain at business cycle frequencies. Concretely,we consider

two lters, a business cycle bandpass lter with pass-band of 6 to 32 quarters and the

year-over-year lter (the four-quarter difference of the four-quarter average), which

is the lter applied to the ination rate in Figure 1. As we show in Section 2, these two

lters have similar low-frequencyproperties, although the year-over-year lter passes

more high-frequency variation (noise) than the bandpass lter. We apply these lters

to both ination and real activity.Using these lters allows us to sidestep the problem

of estimating low-frequency trends, such as aggregate trend ination, sectoral trend

ination, potential output, or the natural rate of unemployment.

It turns out that the 17 components of the PCE price index do, in fact, exhibit a wide

range of cyclicality. When we compare sectoral ination to a bandpass-ltered index

of real activity, some components, such as health care, transportation services, and