A Theory of Intrinsic Inflation Persistence

• Published date: 01 December 2023
• Author: TAKUSHI KUROZUMI,WILLEM VAN ZANDWEGHE
• Date: 01 December 2023
• DOI: http://doi.org/10.1111/jmcb.13066

DOI: 10.1111/jmcb.13066

TAKUSHI KUROZUMI

WILLEM VAN ZANDWEGHE

A Theory of Intrinsic Ination Persistence

We propose a novel theory of intrinsic ination persistence by introducing

trend ination and Kimball (1995)-type aggregators of individual differen-

tiated goods and labor in a model with staggered price- and wage-setting.

Under nonzero trend ination, the non-CES (constant elasticity of substitu-

tion) aggregator of goods and staggered price-setting give rise to a variable

real marginal cost of goods aggregation,which becomes a driver of ination.

This marginal cost consists of an aggregate of the goods’ relative prices,

which depends on past ination, thereby generating intrinsic inertia in ina-

tion. Likewise, the non-CES aggregator of labor and staggered wage-setting

lead to intrinsic inertia in wage ination, which enhances the persistence of

price ination. With the theory we show that ination exhibits a persistent,

hump-shaped response to monetary policy shocks. Wealso demonstrate that

lower trend ination reduces ination persistence and that a credible disin-

ation leads to a gradual decline in ination and a fall in output.

JEL codes:E31, E52

Keywords:trend ination, non-CES aggregator, credible disination

“Taken as a whole, accordingly, the results suggest that it is worth searching for ex-

planations of ination inertia beyond the traditional ones that rely heavily on arbitrary

lags.”—Galí and Gertler (1999, p. 219)

The authors are grateful to three anonymous referees, Pok-sang Lam (the editor), Argia Sbordone (dis-

cussant), Marco Bassetto, Susanto Basu, Toni Braun, Brent Bundick, Olivier Coibion, Ferre De Graeve,

Michael Dotsey, AndrewFoerster, Jeffrey Fuhrer, Mark Gertler, Kinda Hachem, Narayana Kocherlakota,

Michal Marencak, Kiminori Matsuyama, Emi Nakamura, Roberto Pinheiro, Juan Rubio-Ramírez, Slavik

Sheremirov, Lee Smith, Joe Vavra, Raf Wouters,and participants at 2017 NASMES, 2017 SNDE, Spring

2017 MMM, 2015 Federal Reserve System Meeting on Macroeconomics, SWET 2017, 2019 CEF, 6th

CIGS End of Year Macroeconomics Conference, 2020 Econometric Society World Congress, and semi-

nars at the Federal Reserve Banks of Boston, Cleveland, and Kansas City,the Federal Reserve Board, the

National Bank of Belgium, and the University of Kansas for comments and discussions. Martin DeLuca

provided excellent research assistance. The views expressed in this paper are those of the authors and do

not necessarily reect those of the Bank of Japan, the Federal Reserve Bank of Cleveland, or the Federal

Reserve System.

T K is the Head of Policy Studies Division, Monetary Affairs Department, Bank of

Japan (E-mail: takushi.kurozumi@boj.or.jp).W V Z is an Assistant Vice President,

Research Department, FederalReserve Bank of Cleveland (E-mail: willem.vanzandweghe@clev.frb.org).

Received February 4, 2020; and accepted in revised form March 1, 2023.

Journal of Money, Credit and Banking, Vol. 55, No. 8 (December 2023)

© 2023 The Ohio State University.

1962 :MONEY,CREDIT AND BANKING

T -   of ination to monetary policy shocks

has been documented by a large empirical literature. Christiano, Trabandt, and

Walentin (2011), for instance, use a structural vector autoregression (VAR) to show

that ination responds gradually to a shock to the monetary policy rate and that its

peak response is delayed until sometime after the shock. The source of ination per-

sistence is a long-standing question of interest to academic economists and monetary

policymakers. Many previous studies haveaccounted for ination persistence by em-

bedding price indexation to past ination (Christiano, Eichenbaum, and Evans 2005,

Smets and Wouters 2007) or backward-looking rule-of-thumb price-setters (Galí and

Gertler 1999) in dynamic stochastic general equilibrium (DSGE) models.1These as-

sumptions generate intrinsic inertia in ination, but remain controversialbecause they

are ad hoc assumptions that rely on nonoptimizing price-setting behavior. Moreover,

the price indexation implies that all prices change in every period, which contradicts

the microevidence that many individual prices remain unchanged for severalmonths,

as argued by Woodford(2007). In addition, Benati (2008) questions the assumptions,

because they “hardwire” intrinsic inertia of ination in models and imply that the

degree of intrinsic ination persistence is policy-invariant, which contrasts with the

result of his historical empirical analysis that the degree of ination persistence varies

across monetary policy regimes.2

Our paper proposes a novel theory of intrinsic ination persistence by introduc-

ing trend ination and Kimball (1995)-type aggregators of individual differentiated

goods and labor—which relax the requirement of a constant elasticity of substitu-

tion (CES) between the goods or labor—in a DSGE model with Calvo (1983)-style

staggered price- and wage-setting.3Nonzero trend ination affects ination dynam-

ics in the model because in each period some prices remain unchanged in line with

microevidence.4Then, under staggered price-setting, the Kimball-type non-CES ag-

gregator of individual goods gives rise to a variablereal marginal cost of aggregating

the goods, which becomes a driver of ination. Moreover,the real marginal cost con-

sists of an aggregate of the goods’ relative prices, which depends on current and past

ination rates, thereby generating intrinsic inertia in ination. Likewise, under stag-

1.Woodford(2007) reviews different theories of intrinsic inertia in ination. Fuhrer (2011) discusses

the distinction between “intrinsic” vs. “inherited” persistence in ination.

2.Hofmann, Peersman, and Straub (2012) present empirical evidence of changes in wage dynamics

over time, and similarly argue that hardwiring the degree of intrinsic persistence in wage ination can

be misleading.

3.In the macroeconomic literature, Kimball (1995)-type non-CES aggregators havebeen widely used

as a source of strategic complementarity in price setting; see, for example, Eichenbaum and Fisher (2007),

Smets and Wouters (2007), and Levin et al. (2008). Dotsey and King (2005) introduce a Kimball-type

aggregator in a state-dependent price-setting model to show that it enhances the persistence of output

and ination.

4.For microevidence on price setting, see, for example, Klenowand Kryvtsov (2008), Nakamura and

Steinsson (2008), and Nakamura et al. (2018). Ascari and Sbordone (2014) survey the literature on the

role of trend ination in ination dynamics.

TAKUSHIKUROZUMI AND WILLEM VAN ZANDWEGHE:1963

gered wage-setting, the non-CES aggregator of labor leads to intrinsic inertia in wage

ination, which enhances the persistence of price ination. Therefore, our model

provides a theoretical justication for intrinsic ination persistence without relying

on ad hoc backward-looking price- and wage-setting behavior and hence responds

to the suggestion of Galí and Gertler (1999) in the opening quote. Consequently, a

plausibly calibrated version of the model shows that ination exhibits a persistent,

hump-shaped response to monetary policy shocks, as documented by the empirical

literature.

Why does the Kimball-type non-CES aggregator of individual differentiatedgoods

lead the real marginal cost of aggregating the goods to vary under nonzero trend ina-

tion and staggered price-setting? The real marginal cost equalizes each good’s ratio

of the relative price to marginal product for prot maximization, where the marginal

product depends inversely on the demand for the good. Suppose that an expansion-

ary monetary policy shock hits the economy. Then, the dispersion of relative prices

increases, since rms that can adjust their goods’ prices raise them, while other rms

keep prices unchanged and thus have their relative prices eroded by ination. The

increased price dispersion leads to a shift in demand away from goods with higher

relative prices toward those with lower ones, thus moving the marginal product of

each good in the same direction as its relative price. In the case of the CES aggregator,

the price elasticity of demand for goods is constant, allowing each good’s marginal

product to shift proportionally with its relative price and hence their ratio (the real

marginal cost) remains constant. By contrast, the non-CES aggregator can give rise

to a positive superelasticity of demand, which assigns a larger elasticity of demand to

goods with higher relative prices.5Accordingly, the marginal products of individual

goods with higher relative prices show muted increases, whereas those of individual

goods with lower relativeprices exhibit sharper decreases. The real marginal cost then

rises to equalize each good’s ratio of the relativeprice to marginal product. Therefore,

an increase in the dispersion of relative prices arising under nonzero trend ination

and staggered price-setting generates a rise in the real marginal cost of aggregating

individual goods.

Our model provides a microfoundation of intrinsic inertia in price and wage in-

ation by relating the degrees of intrinsic inertia to structural parameters of the

model. Consequently, the model is not subject to the criticism by Benati (2008)

of models in which intrinsic ination persistence is policy-invariant. In particu-

lar, the degrees of intrinsic inertia in price and wage ination are related to the

rate of trend ination, which represents the ination target of the monetary author-

ity in our model. We then show that lower trend ination reduces ination persis-

tence. A number of empirical studies, such as Cogley and Sargent (2002), Stock

and Watson (2007), Cogley, Primiceri, and Sargent (2010), and Fuhrer (2011), in-

dicate that ination persistence has decreased in the United States since the early

5.The term superelasticity of demand refers to the elasticity of the elasticity of demand.