Monetary Policy with Sectoral Trade‐Offs

• DOI: http://doi.org/10.1111/sjoe.12266
• Date: 01 January 2019
• Published date: 01 January 2019

Scand. J. of Economics 121(1), 55–88, 2019

DOI: 10.1111/sjoe.12266

Monetary Policy with Sectoral Trade-Offs*

Ivan Petrella†

University of Warwick, Coventry CV4 7AL, UK

ivan.petrella@wbs.ac.uk

Raffaele Rossi

University of Manchester, Manchester M13 9PL, UK

raffaele.rossi@manchester.ac.uk

Emiliano Santoro

University of Copenhagen, DK-1353 Copenhagen, Denmark

emiliano.santoro@econ.ku.dk

Abstract

Weformulate a two-sector New Keynesian economy featuring sectoral heterogeneity along three

dimensions: price stickiness, consumption goods durability, and the usage of input materials in

production. These factors affect both inter-sectoral and intra-sectoral stabilization. We examine

the welfare properties of simple rules that react to alternative measures of final goods price

inflation. Due to factor demand linkages, the cost of production in one sector is influenced by

price-setting in the other sector. Therefore, measures of aggregate inflation weighting sectoral

prices based on their relative stickiness do not allow one to keep track of the effective speeds of

sectoral price adjustment.

Keywords: Input–output interactions; interest-rate rules; sectoral heterogeneity

JEL classification:E23; E32; E52

I. Introduction

Along with major differences in the time span over which they

yield consumer utility, durable and non-durable consumption goods

are characterized by deep peculiarities in their production and price-

setting. Such structural traits are paramount to the monetary transmission

mechanism (Barsky et al.,2007) and need to be accounted for when

†Also affiliated with CEPR.

*Forhelpful comments and suggestions, we would liketo thank – without implicating –Alessandro

Cantelmo, Tiago Cavalcanti, Federico Di Pace, Sean Holly, Karl Whelan, three anonymous

referees, and seminar participants at the University of Trento, the Catholic Universityof Milan,

the 2010 Money Macro and Finance Research Group Conference in Cyprus, and the 2012

Computing in Economics and Finance Conference in Prague.

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The editors of The Scandinavian Journal of Economics 2017.

56 Monetary policy with sectoral trade-offs

designing realistic multi-sector economies.1From a normative point of view,

the literature to date has extensively reported that sectoral heterogeneity

presents the central bank with a non-trivial trade-off. With a single

instrument, the policy-maker cannot replicate the frictionless equilibrium

allocation in each sector of the economy. This principle applies whenever

sectoral discrepancies concern at least one of the following characteristics:

price rigidity (Aoki, 2001), durability of different consumption goods

(Erceg and Levin, 2006), and inter-sectoral trade of input materials (Huang

and Liu, 2005; Petrella and Santoro, 2011).2All these factors are widely

recognized to be major determinants of the relative prices of goods

produced by different sectors, which in turn exert a strong influence on

aggregate inflation (Reis and Watson, 2010). Therefore, making predictions

based on single-sector models fails to reflect the underlying sources of

aggregate inflation dynamics.3The present study addresses these issues

from a normative perspective, integrating the main sources of sectoral

heterogeneity into a two-sector New Keynesian economy.

In the economy being examined, the monetary authority cannot attain

the Pareto optimal allocation consistent with the full stabilization of

sectoral productions and inflation rates, even when distortions in the

labor market (i.e., imperfect labor mobility) and the goods market (i.e.,

monopolistic competition) are removed. Thus, we turn our attention to

policy strategies capable of attaining second-best outcomes. To this end,

we derive an appropriate welfare metric through a quadratic approximation

of households’ utility and assume that the central bank pursues its policy

under a “timeless perspective” commitment (Woodford, 1999,2003). In

doing so, the policy-maker needs to account for some distinctive features

that affect both inter-sectoral and intra-sectoral stabilization. As concerns

the first aspect, Erceg and Levin (2006) showed that durables are much

more interest-rate-sensitive than non-durables, even though they constitute a

relatively small share of households’ consumption in terms of expenditure.4

1Bouakez et al. (2009,2014) have shown that heterogeneity in price rigidity is a crucial factor

in understanding why sectoral inflation rates do not feature analogous responses to monetary

policy shocks (see also Galesi and Rachedi, 2016), while the degree of durability has important

implications for explaining sectoral output responses.

2Although other forms of sectoral heterogeneity could be envisaged, we focus on the most

pervasive ones that have been exploredin the cur rently available literature.

3Petrella and Santoro (2012) report substantial heterogeneity in sectoral inflation dynamics, with

variations in the income share of input materials traded among sectors representing a key driver.

4The pronounced magnitude of the durables’ response depends on two inherent features of this

type of good: first, the demand for durables is for a stock, so changes in the stock demand

translate into much larger fluctuations in the flowdemand for newly produced goods; and second,

the presence of sectoral price rigidities mitigates the role played by changes in the relativeprice

of durables in insulating the durables sector from shocks.

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The editors of The Scandinavian Journal of Economics 2017.

I. Petrella, R. Rossi, and E. Santoro 57

This property exacerbates the trade-off entailed in stabilizing real activity

in the two sectors, as compared with models featuring two non-durable

goods. In the present work, we show that factor demand linkages also

play a major role in shaping the behavior of the relative price. In fact,

the cross-industry flow of input materials is responsible for magnifying

negative sectoral co-movement in the face of monetary policy innovations.

With regard to intra-sectoral stabilization, it is important to recall that

intermediate goods reduce the slope of the sectoral production schedules,

as compared with models that neglect the presence of input materials

(Petrella etal.,2014). This property limits the pass-through from the sectoral

marginal costs to the respective rates of inflation. As a result, the central

bank might attach greater importance to limiting fluctuations in the sectoral

production gaps, as compared with models that disregard the role of input

materials.

We assess the capability of simple interest-rate feedback rules to

mimic the optimal policy benchmark. One obvious advantage of these

policy functions is the ability to abstract from the stringent informational

requirements of the rule under the timeless perspective. Moreover, while

the model-consistent welfare criterion involves sector-specific variables, we

assume that the policy rate is adjusted in response to broad measures of real

activity and prices. A major problem we are confronted with when designing

optimal interest-rate rules for multi-sector economies is that of finding the

most appropriate inflation rate to target (e.g., Huang and Liu, 2005). To this

end, the model lends itself to accounting for three options: (i) aggregate

inflation, according to which the sectoral inflation rates are aggregated

depending on the relative size of each sector; (ii) sticky-price inflation,

which weights sectoral price dynamics depending on both the relative size

and the relative degree of rigidity in price-setting of each sector; and (iii)

a measure of aggregate inflation that removes fluctuations in the price

of oil from changes in the general price level. It is important to stress

that sticky-price inflation is typically believed to be the most appropriate

variable to monitor relative price changes in multi-sector environments

that feature heterogeneous speeds of sectoral price adjustment (Woodford,

2003, pp. 435–443). Also, policy-makers are displaying increased interest

in these types of measures. For instance, the Atlanta Federal Reserve Bank

regularly publishes its Sticky Price Index, which sorts the components of the

consumer price index (CPI) into either flexible or sticky (slow to change)

categories, based on the frequency of their price adjustment. In addition,

Eusepi et al. (2011) have recently constructed a cost-of-nominal-distortions

index (CONDI), whose weights depend on sectoral price stickiness.

The analysis of the interest-rate feedback rules delivers one key finding:

targeting sticky-price inflation produces a higher loss of social welfare,

as compared with reacting to aggregate inflation or to a measure of price

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The editors of The Scandinavian Journal of Economics 2017.