Download This PDF is a selection from a published volume from the... Economic Research Volume Title: NBER International Seminar on Macroeconomics 2007

This PDF is a selection from a published volume from the National Bureau of
Economic Research
Volume Title: NBER International Seminar on Macroeconomics 2007
Volume Author/Editor: Richard Clarida and Francesco Giavazzi, organizers
Volume Publisher: University of Chicago Press
ISSN: 1932-8796
Volume URL: http://www.nber.org/books/clar07-1
Conference Date: June 15-16, 2007
Publication Date: January 2009
Chapter Title: The Simple Geometry of Transmission and Stabilization in Closed
and Open Economies
Chapter Author: Giancarlo Corsetti, Paolo Pesenti
Chapter URL: http://www.nber.org/chapters/c3000
Chapter pages in book: (65 - 116)
2
The Simple Geometry of Transmission and
Stabilization in Closed and Open Economies
GiancarloCorsetti, EuropeanUniversityInstitute,UniversityofRomeIII
andCEPR
Paolo Pesenti, FederalReserveBankofNew York,NBERandCEPR
2.1 Introduction
How do shocks in a country transmitto the rest of the world? What is
the appropriateresponse of monetarypolicy? Do optimal policy strategies change when an economy becomes more globalized? Do they requirecoordinationamong centralbanks?
In the attemptto answerthese and similarqueries,the past decadehas
witnessed rapid and substantial developments in the literature on
macroeconomicstabilization in closed and open economies. Despite
importantdifferencesin emphasis and style, a numberof tightly related
research agendas- from the new neoclassical synthesis to the neoWicksellian monetary economics to the new open economy macroeconomics (NOEM),and so on- have shed light on the mechanism
of transmissionand propagationof supply and demand shocks in the
presenceof imperfectlycompetitivemarketsand price/ wage rigidities.
Buildingon these premises,a new generationof multicountrydynamic
stochasticgeneralequilibrium(DSGE)models for scenarioanalysisand
policy evaluation have recently found fertile grounds among central
banks and policy institutions.
The objectiveof this paperis to introducean intuitive graphicalapparatus to help understandand communicatesome of the key results of
these researchstrands.We make no attempt to provide an exhaustive
overview of the literature(a task well beyond the scope of a simple
geometry).Rather,based on our directexperiencein classrooms,conferences, and policy presentationsover the years, we are confident that a
broadaudienceof scholarsand policy analystswould welcome a graphical tool set to inspectthe mechanismand convey importantresultsfrom
more complexmodels in a direct,transparent,and immediatefashion.
This may be especially relevant for the study of internationalspill-
66
Corsettiand Pesenti
overs and cross-countryinterdependencies,a researchfield in which analyticalcomplexitiescan reachformidablepeaks and hinderaccesstoand communicationof- its basic results beyond a restrictedniche of
acolytes. Not surprisingly,graphicaltools have underlaidthe popularity of more traditionalteachingand researchmaterialin open economy
macroeconomicsfor decades. While the textbooktreatmentof the augmented IS-LMapproachto visualize the Mundell-Fleming-Dornbusch
model is unlikely to be superseded soon, alternativeapproachesthat
bridgefrontierresearchand pedagogicalobjectivesaredefinitelyviable.
This is a firstpass in that direction.
Transparencyand immediacy are achieved in what follows by focusing on a highly stylized model with very specificproperties.In fact,we
choose to parameterizehouseholds' preferencesand firms'technology
in such a way to maintainanalyticaltractabilityand concentrateon the
substance of the argument without sacrificing theoretical coherence.
Also, in characterizingmacroeconomicuncertainties,we restrict our
attentionto a very limited set of shocks. Needless to say, restrictionson
the model's specificationmay well hamperthe degree of realismof our
framework.But to a very large extent the general principlesconveyed
by our analysis are quite robust,and go through- mutatis mutandisin more articulatedmodels.
By the same token, intertemporalconsiderationsare kept at a minimum in our analysis:whenever possible, we choose to make our points
in terms of static concepts (say,prices and output) ratherthan dynamic
ones (inflationand growth),confidentthat our analyticalresultswill be
easily reinterpretedin termsof deviationsfromnominaland realtrends.
Veryfew equations- and only extremelyintuitive ones- appearin the
main text. Readersinterestedin analyticaldetails are referredto the appendices of the paper (availableonline or in Corsettiand Pesenti2005b),
where full-fledgedversions of the models describedin the main text are
available.
This paper is organized as follows. Section 2.2 describes the basic
macroeconomicmodel in closed economy,with flexiblepricesand nominal rigidities. Section 2.3 extends the model to interdependentopen
economies, discussing cross-bordermarketsegmentationand nominal
rigidities in export markets. Section 2.4 analyzes the macroeconomic
transmission mechanism, revisiting the traditional view of the role
played by exchange rate movements. Section 2.5 considers optimal
monetarypolicy under discretionand its implicationsfor the relationship between openness and inflation.Section2.6 characterizesoptimal
67
andStabilization
TheSimpleGeometryof Transmission
monetarypolicy undercommitmentand discusses the desirabilityof internationalpolicy coordination.Section2.7 concludes.
2.2 A Basic Model of Output and Prices
2.2.1 Preferences,Technology,and MarketStructure
We start by developing a stylized macroeconomicmodel for a closed
economy without externaltradein goods or assets. The population size
is normalizedto one, so thatwe can use the same notationfor aggregate
and per capita variables.The economy consists of households, firms,
and the government.
Households have identicalpreferences.They derive utility from consuming the productssupplied by the firms,and disutility from supplying labor to the firms in exchange for wage incomes. At any point in
time, utility U is equal to:
U = lnC-K€
(1)
where C is consumptionand € is hours worked. The consumptiongood
C is a basketof many productvarieties(orbrands),and households consume all availablevarietiessupplied by the firms.Theparameterk measures the discomfortassociated with labor effort, so that the marginal
rateof substitutionbetween consumptionand leisure is:
§1
=kC
Ol \dU=0
(2)
Firmshave identicaltechnologies.Theyproducetheirgoods by using
labor supplied by the households as the only input in production.
Households own the firms,and receivetheirprofitsas dividend income.
Productivity(outputper unit labor)is subjectto economy-wide shocks.
The labormarketis assumed to be perfectlycompetitive:real wages are
equal to productivity.
Eachfirmproduces a single variety of the consumptiongood, and no
otherfirmproduces the same variety:each firmhas thereforesome monopoly power over its product. However, each firm competes with all
the remainingfirms, since consumers consider each firm'sbrand as a
substitute- however imperfect- to all other availablebrands.
As firms have marketpower over the supply of their products, they
set pricesto maximizetheirprofits,keeping into accountthe elasticityof
demand for their varieties.We consider two cases, one in which prices
68
Corsettiand Pesenti
are fully flexible (a meaningful assumption over a long-termhorizon),
and anotherin which we allow fornominalpricerigidities(a realisticassumptionin the shortrun,say over the time horizonof a business cycle).
In the lattercase, for simplicitywe assume that firmspreset the price of
their own productsbefore the shocks are observed, and stand ready to
meet currentdemand at this price for any realizationof the shocks.
The governmentincludesboth the centralbankin chargeof monetary
policy and the fiscal authorities.Throughoutour analysis we abstract
from public consumption so that fiscal policymakersonly redistribute
revenue acrossagents.
2.2.2 Consumptionand Employment
Our model can be synthesized by means of three schedules, as illustrated in figure 2.1: Aggregate Demand [AD], Aggregate Supply [AS],
and the Natural Rate [NR].1Figure 2.1 plots labor effort € on the horizontal axis and consumptionC on the verticalaxis.
Let P denote the consumerprice index associatedwith the consumption basket C; that is, an average of the prices of all consumptionvarieties. Withoutinvestmentor governmentspending,Ccoincideswith aggregatedemand in real terms,while PCis aggregatenominalspending.
Figure 2.1
Equilibrium in closed economy
The SimpleGeometryof Transmissionand Stabilization
69
Let |x denote a variablethat synthesizes the effect of currentand expected futuremonetarypolicy (whateverthe specificpolicy instruments
used) on aggregatenominal spending PC. We can refer to |x as the aggregate monetarystance of the country.2The Aggregate Demand (AD)
equationcan then be written as:
C=
J.
0)
In terms of figure 2.1, the AD schedule is a horizontalline. A monetary
ease (higher |jl)provides nominal stimulus to the economy. Given the
pricelevel P, a highermonetarystance |x translatesinto higher realconsumption C. By the same token, given the monetarystance |x,consumption is high when agents'purchasingpower is strong;that is, when the
price level is low.
Next, let Z denote labor productivity.The Aggregate Supply (AS)
equationrelatesoutput (thatin closed economy is equal to realdomestic
expenditure)to totalemploymentmeasuredin termsof hours worked:
C = Z(.
(4)
Holding employment i constant,shocks to productivityZ lead to fluctuations in aggregate output C. In figure 2.1, the AS schedule is a ray
fromthe originwith slope determinedby the productivityparameterZ:
higher productivitytranslatesinto a steeper line.
At any point in time, the intersectionbetween AD and AS determines
the equilibriumallocationof consumption C and labor £ for given values of the exogenous variables|jland Z, as well as for a given price level
P. Of course,the pricelevel is an endogenous variablein our system. We
thereforeneed to analyzehow firmsoptimallyset theirprices.Note that
all firmsare symmetricand face similartechnologies,so that in equilibrium they all chargethe same price for theirproducts.
2.2.3 Flexible Prices
Considerfirstthe case in which pricesareperfectlyflexibleand adjustin
response to supply and demand interactionsin the product market(as
indexed by the superscript flex). Imperfectly competitive firms set
pricesby chargingan optimal markupover their marginalcosts. Labor
is the only input in production,so thatmarginalcosts are laborcosts per
unit of product;thatis, the wage rate(heredenoted by W) divided by labor productivityZ.
Corsettiand Pesenti
70
The markupchargedby a firmis a functionof its monopoly power in
the product market.Let 6 denote the elasticity of substitutionbetween
differentvarietiesof the consumptiongood. It is assumed that 6 is sufficiently large- to capturethe idea that consumptionvarieties are good
substitutes for each other- but not too large (otherwise all varieties
would substantiallybe similar in the eye of the consumers,and a firm
would have no monopoly power at all in settingthe priceof its product).
Specifically,we assume 1 < 6 < <*>.
The optimalprice chargedby the representativefirmwill then be:
markup marg.costs
0
W
pta-FT Y-
(5)
Interpretingthe expressionabove, if the elasticityof substitution6 were
very high, prices would be equal to marginalcosts W/Z. But if 6 were
relatively small (close to one), firms would face very inelastic demand
curves for their products, and would be able to exploit their significant
marketpower by chargingextremelyhigh prices relativeto the production costs.
Moreover,with a perfectlycompetitivelabormarket,the equilibrium
wage ratein units of consumption(W/P) must be equal to the marginal
rateof substitutionbetween consumptionand leisure of the representative agent accordingto (2):3
W
- = kC.
(6)
Combining (5) and (6), in equilibriumthe profit-maximizingproduct
is determinedas follows:
price Pflex
1Dflex=
°
0-1
™
Z
L*
(7\
(7)
Now, replacing C with Z€ according to (4) in the previous expression
and rearranging,we obtain:
<~-*
(8)
Equation(8) defines the naturalor potentialrateof employment,€, as
the level of employment that would prevail in an economy without
nominal rigidities. The natural rate depends on agents' preferences
about leisure, as capturedby the parameterk:the lower is k, the higher
is households' supply of laborinputs to firmsin equilibrium.It also de-
The SimpleGeometryof Transmissionand Stabilization
71
pends on the monopolistic distortions in the economy: the higher is 0,
the lower is the equilibrium markup, and the higher is the equilibrium
level of employment.4 Observe that, while the natural rate of employment is constant, the natural rate of output Zt, (defined as output in an
economy without nominal rigidities) will fluctuate as a function of productivity shocks Z.
In figure 2.1, we plot equation (8) as the third schedule NR or Natural
Rate: a vertical line above the constant €. In the flex-price equilibrium,
the AD and AS schedules cross each other corresponding to the natural
rate of employment. Once C and € are determined at the intersection of
AS and NR, the price level P adjusts for any level of the current monetary stance jjlto make sure that AD intersects the other two schedules at
the equilibrium point.
2.2 A Nominal Rigidities
Macroeconomic adjustment is quite different with nominal price rigidities. Consider the case in which firms preset their prices and are unable
to modify them once they observe the actual realizations of W and Z.
Under these conditions, the optimally chosen price level5 depends on
expectedmarginal costs.6
Of course, when prices are preset, unanticipated changes in marginal
costs can reduce or raise the ex-post profits of the firm.7
We now show that, in a sticky-price environment, employment is
equal to the natural rate only in expectedterms. To see this, recall that
W = kPC and PC = |x from (6) and (3). Combine these expressions with
(9) to rewrite the optimal product price as follows:
Next, multiply both sides by C and use (4) and (3) to write:
Rearranging and taking expectations, we obtain:
/e-1
[l/Z \ = -9-1- = €.
E(€) = £ - - ,z^6k
y 6k E(|x/Z)y
(12)
72
Corsettiand Pesenti
An intuitive interpretationof (12) is that firms choose prices so as to
insure that, on average, they will operate on their flex-price supply
curve.If P is set at a level below (10),marketdemand for the firms'goods
turns out to be excessively high, and they need to hire laborabove € to
meet demand at unchangedprices, sacrificingtheirprofits.If P is set at
an excessively high level, firms' sales revenue turns out to be too low
and t falls below €. In equilibrium,expected employmentis equal to its
naturalrate.We will returnto this point laterin figure 2.11.8
To sum up: the Aggregate Demand equation (3) relates nominal
spending to the monetary policy stance. The Aggregate Supply equation (4) relatesaggregatesupply to employment.Pricesin the short run
areset such that,in expectation,the economy operatesalong the Natural
Rate equation (12). In the long run, when prices are flexible, the 'NR'
equation determineslabor €, the AS equation determinesconsumption
C given € and Z, and the AD equation (3) determinesthe price level P
given C and |x.
2.2.5 WelfareConsiderations
Withthe help of our graphicalapparatus,we can analyzethe welfareimplications of macroeconomicshocks and changes in structuralparameters that shift the three schedules in figure 2.1. Having specified the
utility function as in (1), the indifferencecurves in the space (€, C) are
convex and upward sloping, with slope proportionalto consumption
accordingto (2). In figure 2.1 the dashed curve is the indifferencecurve
associatedwith the equilibriumO. Utility is increasingas we move upwards or westwards, correspondingto higher consumption levels for
any given laboreffort,or lower laboreffort for any given consumption
level.
In the presence of monopolisticdistortionsin the productmarket,an
economy operatingat the naturalrate £ will not be Paretoefficient:9the
equilibriumlevel of employment and output will be suboptimallylow,
as firmscontracttheirsupply of goods to exploit theirmonopoly power
and maximize theirprofits.
We can provide a simple graphicalrepresentationof this point. In figure 2.1, the indifferencecurve that goes through the equilibriumpoint
crosses the AS locus from above. Thatis, at the equilibriumC = Z€, the
marginalrateof substitution(measuredby the slope of the indifference
curve of the representativehousehold) is smallerthan the marginalrate
of transformation(the slope of the aggregatesupply schedule):
73
TheSimpleGeometryof Transmissionand Stabilization
-dc\
-e-i -e-i_ = kC|,.7= kZ t)K = Z b < Z.
at \du=o,e=e
(13)
Intuitively,in equilibriumagentswork and consumetoo little,so thatthe
additionaldisutilityfroma smallincreasein laboreffortis lower thanthe
additionalutilityfromhigherrevenue.Thisillustratesa generaland crucial featureof economieswith monopolisticpower in production.
In the absence of monopolistic distortions, the equilibrium in the
model would correspondto a point in which the indifferencecurve is
tangent to the AS locus. To see this, assume that product varieties are
highly substitutable(i.e., let 6 become infinitely large, so that the monopoly power of firmsis arbitrarilysmall and the economy approaches
perfect competition). Expression (13) shows that in equilibrium the
slope of the indifferencecurve will be identicalto the slope of the AS locus, and equal to Z. Indeed, the competitive (and Pareto-efficient)level
of employmentis 1/ k > €. In section2.5 we reconsiderthe differencebetween natural(point O in figure2.10)and competitive(pointX in figure
2.10) output, and its implicationsfor the choice of monetarypolicy under discretion.
2.2.6 TheEffectsof Nominal and Real ShocksunderFlexiblePrices
We can now use our apparatusto analyze the macroeconomiceffects of
monetaryand productivityshocks (Christiano,Eichenbaum,and Evans
1999,2005;Clarida,Gali, and Gertler2000;Gali 2003;Goodfriendand
King2001;Walsh2003;Woodford2003).Throughoutthe analysis,we focus on positiveshocks,defined as unexpectedincreasesin |x and Z (with
the understandingthat the analysis of negative shocks would be perfectly symmetric).
Whenpricesare fully flexible,as in (7), the effectsof monetaryshocks
(exogenouschangesin jlx)are straightforward:nothing changesin terms
of realequilibriumallocation.In fact,to the extentthat |x and P move instantaneouslyin the sameproportion,consumptionremainsunchanged.
Considernow a productivityboom under flexibleprices.In this case,
an increase in Z does not affect the equilibriumlevel of employment,
which remainsconstantat €. Instead,a shock to Z raises proportionally
the equilibriumlevel of output for a given €, generatingexcess supply in
the economy. If nominal spending |x (and the wage rate W) does not
change, marginal costs fall, reflecting higher productivity. The price
level P then falls enough to boost consumptiondemand to the new level
of output.
74
Corsettiand Pesenti
Figure 2.2
Productivity shocks with and without price rigidities
Figure2.2 illustratesgraphicallythe effect of the positive productivity shock just described.Let O be the initial equilibriumallocation.An
increasein Z tilts the AS locus upwards:higher productivityraises the
level of consumption that is sustainable for any given employment
level. With employment at € and no change in the monetarystance |x,
prices fall in response to the excess supply, shifting the AD locus upward. The new equilibrium,A in the figure,correspondsto an increase
in consumption(measuredby the segment OA)and lower prices,while
employment remainsunchangedat its naturalrate €.
2.2.7 Sticky Prices and the Effectivenessof MonetaryPolicy
What do the data say about the equilibriumresponse to productivity
shocks?While the issue has not been controversy-freefrom a methodologicalviewpoint, the empiricalconsensus is that technologyimprovements are to some extent contractionaryon impact. This evidence can
hardly be reconciledwith the adjustmentprocess implied by flex-price
models and synthesized in the previous paragraph(Basu,Fernald,and
Kimball2006). Instead, models in which prices are sticky in the short
run provide a simple analytical framework consistent with the stylized facts.
If P cannot adjust, aggregate demand is pinned down by monetary
The SimpleGeometryof Transmissionand Stabilization
75
policy (x;without a change in nominal spending, consumption is constant in real termsin the short term.Hence, fluctuationsin productivity
thatarenot matchedby changesin aggregatedemand necessarilytranslate into changes in short-runemployment and output. Relativeto the
naturalrate of employment and output, a positive productivity shock
opens both an employment gap and an output gap.
Figure2.2 illustratesthese points. Withoutprice flexibility,a productivity shock that rotatesthe AS locus upwards does not translateinto a
fall in prices, and thereforeis not matched by a proportionalupward
movement of the AD locus. Unless |x is raisedby the monetaryauthorities, the new short-runequilibriumwill correspond to the point B in
which the new AS locus crosses the (unchanged)AD locus. Comparing
the short-runequilibriumB with the initialequilibriumO, employment
falls below € while output and spending remain unchanged, both in
nominaland in real terms.Agents are able to maintainthe same level of
consumptionin spite of a loss of wage incomes, thanks to higher dividend incomes accruingfrom the firmsthey own.
As shown in figure 2.3, a productivity shock opens an employment
gap OB,which in our economy is proportionalto the output gap OA10
Note that the appropriatemeasure of output gap in our context is the
differencebetween the amount of resourcesthat couldbe produced and
consumed under flexibleprices (at point A), and the actualamountproduced in the presenceof nominal rigidities (at point B).
Figure 2.3
Optimalmonetarypolicy responseto shocksunderpricerigidities
76
Corsettiand Pesenti
Monetarypolicy can be effective in this framework.Provided monetary authoritiesare able to observe or predict Z with accuracy,and can
use appropriatepolicy instrumentsto control nominal spending, they
can engineera monetaryexpansion to raise |x and bring the economy to
operateas //"priceswere flexible.Figure2.3 shows what happens when
policymakersuse monetaryinstrumentsto raise |jlin proportionwith Z:
the AD curve shifts up by the amount OA and closes the employment
and the output gaps. As a result,the short-runinflexibilityof pricesdoes
not prevent the economy from operatingat the naturalrate.
Note that the monetarystancethatbringsemploymentand output to
theirnaturalratesis expansionarywhen the economy experiencesa productivity shock that opens negative employment and output gaps (by
symmetry,it will be contractionarywhen an adverseproductivityshock
leads to overheatingof the economy at unchangeddemand conditions).
Intuitively,thanksto the productivityboom firmsarepotentiallyable to
supply an increasedamountof consumptiongoods. Butif prices do not
fall, consumers whose nominal incomes are unchanged are unable to
purchase these additional products. Hence the need for a monetary
stimulus, which generatesadditionalaggregatedemand and brings the
economy back to potential. By moving in tandem with productivity
shocks, monetarypolicy stabilizesthe markupsof domestic firms.
Needless to say, once we move beyond the boundariesof our stylized
frameworkand accountfor additionalrealisticelements,thereare other
possible policy trade-offsthat make monetarypolicy less effective than
suggested by the previous analysis. Namely, monetarypolicy will not
targetexactly the flex-priceallocationin the presence of cost-push and
sectoral shocks, dual wage and price rigidities, investment dynamics,
and so forth.Yetthe main principlesestablished in this section remain
largely valid: for instance, in response to positive supply shocks that
generatedeflationarypressure,it is generallymeaningfulfor the policy
authoritiesto provide nominal stimulus to the economy by easing the
monetarystance.We returnto these points in section 2.6.
2.3 ExchangeRates and Prices in Open Economies
Wenow extend our analysis to the study of interdependent,open economies. Relativeto the closed-economymodel analyzedpreviously,there
are at least two new importantfeaturesto consider.
First,firmssell now in two markets,both domesticallyand abroad.As
the NOEMliteraturehas emphasized,modeling nominal rigiditiesthus
The SimpleGeometryof Transmissionand Stabilization
77
raisesimportantissues aboutfirms'pricingbehavior.Are productprices
preset in the domestic currencyonly? Or rather,do firms fix two sets of
prices,one for the domestic marketand the other for the export market
(provided that product markets are sufficiently segmented so that
agents cannotarbitrageprice differentials)?
A second differenceis that, in addition to the macroeconomicdistortions associated with nominal rigidities and monopoly power in production, there is now a new distortionrelated to a country'smonopoly
power on its terms of trade;that is, the relativeprice of foreign (traded)
goods in terms of domestic (traded)goods. In fact, firms ignore the impact of their pricing and productiondecisions on the country'soverall
terms of trade. A decentralized equilibrium reflects this inefficiency,
adding a furtherdimension to the policy problem.
In what follows we build a two-countrygeneral-equilibriumtheoretical framework.Thisis the analyticalskeletonof the medium- and largescale multi-countryDSGEmodels for policy evaluationcurrentlyunder
developmentat policy institutionsworldwide, such as GlobalEconomy
Model (GEM)at the InternationalMonetaryFund, SIGMAat the Federal ReserveBoardof Governors,and New Area-wideModel (NAWM)
at the EuropeanCentralBank,among others. Our graphicalapparatus
in the two-countrycase is to a large extent similarto the one developed
for closed-economyanalysis.However,because of a numberof features
specific to open economies, the derivation and interpretationof the
equilibriumschedules need to be modified appropriately.
2.3.1 Extendingthe Basic Model to the WorldEconomy
The world economy consists of two countriesof equal size, Home and
Foreign,each producing a country-specifictype of good that is traded
worldwide. Countriesand types of goods are denoted by the letters H
and F, respectively.Similarto the closed-economycase, in each country
monopolisticcompetitorsproduceimperfectlysubstitutablevarietiesof
the same nationalgood, employing a lineartechnologywith laboras the
only input in production.
Households consume both nationaland foreign goods. In both countriesthe elasticityof substitutionbetween differentvarietiesof the same
type of goods (6) is higherthan the elasticityof substitutionbetween the
two types of goods H and F, that we posit equal to one.11
In terms of notation, we adopt the convention that prices denominated in Foreigncurrency,as well as quantitieschosen by Foreignfirms
78
Corsettiand Pesenti
and households, are denoted with a star.So, the Home and Foreignconsumerprice indexes are denoted by P and P* respectively,employment
levels by € and €*, aggregate consumption levels by C and C*. Home
consumptionC is a symmetricbasketof the two country-specificgoods:
CHis Home consumptionof the Home good, and CFis Home consumpis Foreignconsumption
tion of the Foreigngood. By the same token, C%
and
C*
of local varieties
denotes Foreignimportsfrom the Home country.Similarly,P is an index of the pricesof the two goods PHand PFin the
Home countries,and P* is an index of the prices P£ and PJ in the Foreign country.
Thereare threeinternationalprices.First,the nominalexchangerateis
denoted e, defined as Home currencyper unit of Foreigncurrency.Second, the realexchangerateis defined as the relativeprice of the Foreign
consumption basket in terms of Home consumption baskets, and is
thereforeeP*/P. Third,the termsoftradeare defined as the relativeprice
of Home imports in terms of Home exports, or PF/eP%Each international price is defined in such a way that its increaserepresentsa depreciationor deteriorationfrom the viewpoint of the Home country.
We denote the country-specificmonetary stances with |x and |x*,respectively. In each country output is subjectto a country-specificproductivity shock, denoted by Z and Z*.
Our stylized model has no room for capital accumulationand internationalinvestment,thus it has intrinsicallylittle to say about the main
driving forces of currentaccountadjustment.Also, given our emphasis
on the mechanismof price adjustmentin response to world shocks, it is
meaningful to opt for simplicity and to minimize analyticaldifferences
with respect to the closed-economycase. For these reasonswe proceed
by positing from the startthat there is balancedtrade,so that aggregate
net exports are zero in each country:
PFCF= eP*C*.
(14)
A synthesis of the model (exceptthe equationsdeterminingprices)is
given in table2.1. It is also illustratedin figure2.4, with the Home country on the left and the Foreigncountry on the right. As for the closedeconomy case, the monetarystance in each country synthesizes the effect of monetarypolicy on nominal spending. Hence, the AD schedule
(firstrow of table2.1) is formallyidenticalto the AD in the previous sections. However, private spending on consumption now falls on both
Home and Foreign goods. As shown by the second and third rows in
table2.1,nominalspending on consumptionis equallydivided between
TheSimpleGeometryof Transmissionand Stabilization
79
Table2.1
Theopen-economymodel
Home country
TheAD block
TheAS block
PHCH=±PC
PfCf=IpC
p*c*H= Lp*c*
p*c* = -p*c*
p = 2P]{2py2
p* = 2P*i/2p*i/2
C = Z€t
C* = Z*€*t*
|_2\PH
L 2 Vf*
eP*JJ
Pf)\
e= -
Exchangerate
NaturalRate
Foreigncountry
C* = \x*/P*
C = [l/P
JJL*
I = -^
6k
€*= -^
0k
domesticallyproducedgoods and imports,consistentwith the assumption of symmetric consumption baskets. Hence, relative to the closed
economy case, the domestic price level is an equally-weightedindex of
domestic and importprices (fourthrow of table 2.1).12
The AS schedule (fifth row of table 2.1) is also different from the
closed-economy case, since it now translates the supply of domestic
goods into the consumptionof bothdomestic and imported goods. The
Home (Foreign)AS schedule includes the new termt (t*), defined in the
sixth row of table 2.1. To understandthis term, observe that at current
prices it takes 1/t units of Home output to buy one unit of the Home
consumption basket C (a symmetric definition applies to the Foreign
economy).
Intuitively,t must then be a functionof the degree of openness of the
Home economy.In fact,in a symmetricequilibriumt is equal to 1/2, the
size of imports in the Home consumption basket. Graphically,the importantimplicationis that the AS locus is flatterrelative to the closedeconomy case (ort = 1).Recall(fromfig. 2.1) thatin the closed-economy
equilibriumthereis a wedge between the (low) slope of the indifference
80
Corsetti and Pesenti
Figure2.4
Worldeconomy model
curve and the (high) slope of the AS locus, as monopolisticcompetition
creates a distortionbetween marginalrate of transformationand marginal rate of substitution.Now, in an open economy (fig. 2.4) the slope
of the AS locus is lower, and consequently the differencebetween the
two slopes at the equilibriumpoint O is smaller.This is because in equilibriumthere are now twodistortions- the monopolisticdistortionand
the termsof tradedistortion- thatto some extent offset each other.This
point has importantimplicationsfor the relationbetween openness and
inflationarybias. We returnto this issue in section 2.5.
As we discuss in detail in the following, the price of consumptionin
terms of output is also a functionof the terms of tradebetween the two
countries,definedpreviously as the priceof importsin termsof the price
of exports, or PF/(eP*).For instance,a lower internationalprice for the
Home good worsens the Home terms of trade and reduces t, causing a
downward rotation of the AS schedule. For any level of Home consumption, Home output and employment must now rise. So, in an
open-economycontextthe AS can tilt downward eitherbecause of negative productivityshocks (which are exogenous), or because of relative
pricemovementsworsening the termsof trade(whichareendogenous).
Finally,in our economy the nominal exchangeratee depends on cur-
The SimpleGeometryof Transmissionand Stabilization
81
rent and expected futuremonetarydevelopments in the Home country
relativeto the rest of the world (last row of table 2.1). This result is a direct consequenceof the balancedtrade assumption (14) which, in light
of the previous spending equations,can be rewrittenas:
PC = zP*C*.
(15)
13
Accountingfor the AD equations,we obtain e = |x/|x* in table 2.1. A
Home monetaryexpansion and/or a Foreignmonetary tightening depreciatethe Home nominalexchangerate.Similarly,e appreciateswhen
the monetarystance of the Home country is contractionaryrelative to
the Foreignstance.
As in the closed-economymodel, in the absenceof nominal rigidities
firms chargean optimal fixed markupover marginalcosts. With linear
technologies and constant-elasticitydemand functions, there is no incentive for a firmto price-discriminateacrossmarkets:this implies that
prices are equalized across countries when expressed in terms of the
same currency(i.e., the law of one priceholds). Thus,the four equations
P*flex
are:
determiningthe four (flexible)prices P£ex,P£ex,P*flex,
Dflex= pp*flex _
H
H
p*flex = £f_
=
!^_ J^.
e- 1 z
UK
»L-
{(\fr\}
(17)
Once again, the naturalemployment rates NR in both countriescan be
easily calculatedusing these expressions togetherwith the AD and AS
equations.
Tosum up: the AS is a line throughthe origin.Its slope includes a term
reflectingopenness and the level of the terms of trade.The naturalrate
locus NR remainsidenticalin both the closed- and open-economy versions of our model- a propertythat will be very useful in carryingout
comparativeanalysis of our results. The AD is similar to the closedeconomy case: it draws a horizontalline in the (€, C) or (€*, C*) spaces
depicted in figure2.4. However, in a closed economy PHand P coincide,
so that nominal rigiditiesaffectingthe producerprice PHimply that the
consumerprice index P is also fixed in the short run. This need not be
the case in an economy open to internationaltrade:in the Home country,
the consumer price level P may now adjust in the short run- despite
nominalrigiditiesaffectingthe producerpricePH- per effectof fluctuations in importprices PFdriven by the exchangerate8.
Corsettiand Pesenti
82
2.3.2 Nominal Rigidities and the Pricing of Exports
The recentliteraturehas revived an importantdebate about the empirical evidence on the responseof pricesto exchangeratemovements,providing differentpossible approachesto model nominal rigidities in an
open economy. Empiricalevidence on the elasticity of exchange rate
pass-throughonto import (export)prices supports few certainties:this
elasticity is smaller over the short-termthan in the long run, it varies
across sectors and countries, and is different for consumer goods and
wholesale prices (Goldberg and Knetter 1997; Campa and Goldberg
2005).
Consideredas a decision variableof the exporter,the determinantsof
exchange rate pass-throughmay clearly include some of the variables
considered in our model, such as the volatility of monetary and real
shocks (Taylor2000; Corsetti and Pesenti 2002; Devereux, Engel, and
Storgaard2004). But it may reasonablydepend on many other factors
outside the scope of our contribution- such as the exporter-importer
working relationshipstressed in the relationship-marketingliterature,
the presenceof distributioncosts (Corsettiand Dedola 2005;Laxtonand
Pesenti 2003), the market share of exporters in the local market (Bacchettaand VanWincoop2005),or the availabilityof financialstrategies
to limit exposure of exporters' profits to exchange rate fluctuations
(Friberg1998).
Given the scope of our contribution,we take the degree of passthrough as an exogenous factor linked to the invoice currencyin the
presenceof nominalrigidities.In what follows we discuss threepossible
specificationsof exportprices consistentwith such an approach.
ProducerCurrencyPricing (PCP) In a firstclass of models, firmspreset prices in their own currencyand let prices abroadmove one-to-one
with the exchange rate (Obstfeld and Rogoff 1995, 1996 ch.10, 2000;
Corsettiand Pesenti 2001).In other words, PHand P£ are sticky but PF
and P£ arenot. Sinceexportpricesare set in the producer'scurrency,the
literatureoften refersto this case as ProducerCurrencyPricing,or PCP.
WithPCP,firmsoptimally set:
0k
/ix\
'«=*•«=
en e(£)
(18)
p*= El = J^e(^\
(19)
TheSimpleGeometryof Transmissionand Stabilization
83
Observe that in this case there is one-to-one pass-throughof exchange
rate movements onto the price of imports, at both the border and the
consumer-pricelevel. As demand elasticities are identical in the two
countries,the law of one price holds: once measured in the same currency,goods prices are the same in all markets.
Under PCP,the terms of trade Pf/eP%are equal to P*e/PH.Since PH
and P* in (18)and (19)are preset, the Home termsof tradeworsen with
a nominaldepreciationof the Home currency(i.e.,a highere). The same
nominal depreciationof the Home currencywill instead appreciatethe
Foreigntermsof trade.Thus,when the Home currencyweakens, Home
goods are cheaperrelative to Foreigngoods in both the Home and the
Foreigncountry.As demand shifts in favor of the goods with the lowest
relativeprice, world consumptionof Home goods increasesrelative to
consumption of Foreign goods. These are referred to as expenditure
switching effects of exchangeratemovements.
Local CurrencyPricing (LCP) Accordingto a second class of models,
firmspreset a price in domestic currencyfor the domestic market,and a
pricein foreigncurrencyfor the exportmarkets(Bacchettaand van Wincoop 2000;Bettsand Devereux2000;Chari,Kehoe,and McGrattan2002;
Duarte and Stockman2005).Since export prices are preset in the consumers'currency,the literatureoften dubs this case as Local Currency
Pricing,or LCP.WithLCPfirmsoptimally set:
0K
/V\
0K
/ |X \
6k
/ix*\
6k
/ix*e\
Exchange rate pass-through onto import prices is zero both at the
border-and the consumer-pricelevel. The law of one price is violated
with any unanticipatedfluctuationof the exchange rate:unless the exchange rate is fixed or perfectlyforecastable,the consumerprice of the
Home good in domestic currencyPHwill be different from its export
price in Home currencyeP£. Analogously, the consumer price of the
Foreign good in Foreign currencyP£ will be different from its export
price in ForeigncurrencyPF/e.14
Observethat,with P* and PFpredeterminedin the short run, a nominal depreciationof the Home currency improves the Home terms of
tradePF/zP%Correspondingly,the Foreignterms of tradeworsen. The
effects of currencymovements on the terms of trade go in the opposite
84
Corsettiand Pesenti
direction relative to the PCP case. Since prices are preset in local currency,exchangeratefluctuationsdo not affectthe relativepricefacedby
importersand consumers.There is no expenditure switching effect of
exchangeratemovements.
Dollar Pricing (DP) While the literaturehas mainly focused on the
previous two polar cases, there is also a third possibility (probablythe
most relevantone froman empiricalviewpoint):the world exportprices
are set in one vehicle currencyonly, for example,in the Home country's
currency.Home firms preset all prices in their own currency;Foreign
firms preset export prices in the Home currency(Corsettiand Pesenti
2005a;Devereux, Engel, and Tille2003;Devereux,Shi, and Xu 2007).In
this case- that we dub dollarpricingor DP- we have:
p«= eP«=
0k
(22)
i^TE(z)
/u*\
8k
/ix*e\
In the DP case the law of one price only holds for the Home country
products. Exchange rate pass-through is asymmetric:it is zero in the
Home country,but complete in the Foreigncountry.Thus, a Home depreciationdoes not affect the price of importsin the Home country,but
lowers the price of imports in the Foreigncountry.Interestingly,however, the benefits of lower prices and higher purchasingpower for the
Foreign country consumers are offset by the profit losses of Foreign
firms and shareholders.In fact, Foreignfirms that export to the Home
country sell their products at the price PF- which is fixed in the short
run- but repatriatetheir export sales revenue at the rate 1/e - which
falls with the Home currencydepreciation.
ExportPricing and the Natural Rate We conclude this sectionby noting an importantpropertyof the model. Independentof which pricing
specificationis selected among the three possibilities described previously, expected employmentis always equal to its naturalrate- exactly
as in the closed economy.As a straightforwardimplicationof the equations presentedpreviously,we have in fact:
E(i) = £(€*) = ^-
(24)
for anycharacterizationof the nominal rigiditiesin the exportmarkets.
The SimpleGeometryof Transmissionand Stabilization
85
2.4 InternationalMacroeconomicTransmission
In this section we study the international transmission of countryspecific productivity shocks. Similar to the closed-economy case, we
startby consideringthe allocationwith flexibleprices,which provides a
benchmarkto guide our policy analysis.Next, we study the equilibrium
allocationand internationalspilloverswhen policymakersreactto shocks
by pursuing policies that stabilizeoutput and employment at theirnatural rate- the policy conduct that,as we saw before,is able to replicate
the flex-priceallocationin a closed economy.
2.4.1 Domestic and ForeignEffectsof Productivity Shocksunder
Flexible Prices
Figure2.5 illustratesthe macroeconomicresponse to a positive productivity shockin the Home country,assumingthatpricesareperfectlyflexible. On impact,a positive shock to Z rotatesthe AS schedule upward.
We have seen that the natural rate of employment is independent of
productivityshocks. Hence, in an equilibriumwithout price rigidities,
higher productivity raises consumption along the NR locus. Different
from the closed economy case, however, the higher supply of Home
Figure 2.5
Internationaltransmissionof productivityshocksunderflexibleprices
86
Corsettiand Pesenti
goods lowers their internationalprice:the terms of trade move against
the Home country.15
The fall in t, that reflectsworsening termsof trade,tilts the AS schedule downward, partiallyoffsettingthe upward rotationof the AS due to
a positive Z shock. In otherwords, relativeto the closed-economycase,
a shock to Z makes the AS rotateby less. Forany given Home monetary
stance, |x the domestic marginalcost and the price of Home goods PH
both fall one-to-one with the productivity increase. The Home CPI P
also falls, althoughby less thanPHas partof Home consumptionfalls on
importedForeigngoods. Hence the AD shifts upwards,but not as faras
it would in a closed economy. The equilibriummoves from point O to
point H.
Partof the gains fromhigherproductivityin the Home countryaccrue
to consumersabroad.The fall in the internationalprice of Home goods
raisesForeignincomes in realterms.Becauseof lower importprices,the
Foreignterms of trade are stronger,raisingt*: the AS* rotatesupward.
Lowerimportpricesalso lower the ForeignCPIP*, raisingconsumption
demand along with the AD* schedule. The equilibriumin the Foreign
country moves from point O* to point H*. Overall,Foreignconsumption increaseswhile employment remainsat its naturallevel. This is an
unambiguous welfare gain for the Foreigneconomy.The international
transmissionof productivityshocks is clearlypositive.
2.4.2 Productivity Shocksin OpenEconomieswith Nominal
Rigidities
In the presence of nominal rigidities, the macroeconomicimpact of
country-specific productivity shocks is sharply different. An unexpected increase in Home productivity does not move the nominal exchange rate,which only responds to monetaryfactors.Hence the shock
has no impact on import prices, which are either sticky (as in the LCP
case) or move with the exchange rate (as in the PCP case). With no
changes in prices and the CPI, aggregate demand is constant in real
terms in both countries.Higher domestic productivity at Home therefore translatesinto a lower level of domesticemployment- preciselyas
in the closed-economycase. Withoutchangesin the exchangerate,there
are no consequencesfor the Foreigneconomy.
The previous point can be restatedin graphicalterms,as in figure2.6:
otherthings equal, a positive shock to Home productivityrotatesthe AS
upwardand opens an employment/output gap. Theequilibriummoves
The SimpleGeometryof Transmissionand Stabilization
87
Figure 2.6
Internationalnontransmissionof productivityshocksunderpricerigidities
frompoint O to point B. Consumptionis not affected,economicactivity
is too low - exactly as in the sticky-priceequilibriumof figure 2.2. The
Foreigneconomy remainscompletely unchangedat point O*.
Note that this result holds regardlessof the specificationof nominal
rigiditiesin the exportmarkets(i.e.,PCPor LCPor DP). In all cases,productivityshockshave no directeffectson pricesand exchangerates.But
as for the closed economy, shocks that translateinto undesirable employment fluctuations,and open employmentand output gaps, invite a
monetarypolicy response.Thus,productivityshocks may have an indirecteffectson prices,via changes in the monetarystanceaimed at stabilizing the macroeconomy.
2.4.3 Stabilization Propertiesof the ExchangeRate (the PCP Model)
In our analysis of the closed economy we have seen that, when monetary authoritiesreact to productivity shocks by closing the output gap
completely,the marketequilibriumcoincideswith the flex-priceallocation. Is monetarypolicy equally effective in our open-economysetting?
To answer this question we need to focus on the role of exchange rate
movements in the internationaltransmissionmechanism.
88
Corsettiand Pesenti
The conventionalwisdom exemplifiedby the enduringcontributions
of Friedman1953and Mundell 1963suggests that,in a world with nominal price rigidities,exchangeratemovements facilitatethe efficientadjustmentof internationalrelativeprices.Withflexibleprices,the relative
price of Home goods falls in response to a positive productivityshock.
Withsticky prices, adjustmentcan be achieved via an exchangeratedepreciation(correspondingto Home monetaryexpansionrelativeto Foreign), which lowers the internationalprice of the Home goods relative
to Foreigngoods.
Torevisit the theoreticalfoundationsof the conventionalwisdom, we
can reconsider our open-economy model under PCP (the first of the
three export-pricingspecificationsdiscussed previously). We focus on
the following scenario.Thereis an unexpected,positive increasein productivity in the Home country.Home monetary policymakersare assumed to adopt an inward-lookingpolicy rule, and set the monetary
stance to close the domestic output gap opened by productivityfluctuations. Foreign monetary policymakersmaintain a constant monetary
stance.Thisscenarioprovides a useful baselinefor our analysisof the internationaltransmissionmechanism. Note that we have said nothing
about the optimality of the policy responses described previously:we
take these monetary conducts as given and analyze their macroeconomic properties.Later,we discuss whether or not these policies can be
rationalizedas welfare-maximizing.
The experimentis illustratedin figure 2.7. The positive productivity
shock at Home rotatesthe AS upward,but when the monetaryauthorities respond to the shock by loosening the monetary stance, the exchange ratedepreciatesand the termsof tradefall, lowering t: a drop in
t offsets in part the rotationof the AS due to Z. At the same time, looser
monetary conditions (a higher |x) shift the AD upward, but less than
one-to-one.This is because,to the extent that importprices rise with exchange rate depreciation,the country experiences some CPI inflation.
The Home economy moves from O to H along the NR schedule.
The exchange rate depreciationin the Home country improves the
terms of trade abroad:a higher t* tilts the AS* upward. Note that the
AS* rotationdoes not reflectany improvementin Foreignproductivity
(Z* remains constant).Lower import prices translateinto a fall of the
ForeignCPI.Fora given Foreignmonetarystance |x*,a fall in the price
level raises demand, shifting the AD curve upwards. The Foreigneconomy moves from point O* to point H* along the NR* schedule, mirroring the adjustmentof the Home economy.In the new equilibrium,For-
The SimpleGeometryof Transmissionand Stabilization
89
Figure 2.7
Stabilization policy under high pass-through (PCP)
eign households enjoy a higher level of consumptionfor an unchanged
level of labor effort. The internationaltransmissionof Home shocks is
unambiguouslypositive.
Threepoints are worth emphasizing. First,in a PCP world it is possible to undo the effectsof nominal rigiditiesand replicatethe flex-price
allocationby following exactly the same policy prescriptionconsidered
in the closed-economycase (|x moves one-to-onewith Z). A policy that
targetsdomestic price stability,and closes the Home employment gap,
raises consumptionat Home and abroadin proportionto productivity.
Given that employment remainsconstantin equilibrium,higher Home
productivityZ means a higher world supply of Home goods. In an efficient allocation,theirworld prices must drop.
Second,observethatwith nominalprices sticky in domesticcurrency,
it is the exchange rate that induces the efficient adjustmentin relative
prices,redirectingworld demand towards the more abundantproduct.
Thus, under PCP exchange rate movements are stabilizing and exchange rateflexibilityis desirable.16
Third,we should note, however, that since the exchangerate is equal
to the relativemonetarystance, the right price adjustmentthrough the
exchangeratedepends on the rightconductof monetarypolicy.17While
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Corsettiand Pesenti
the equilibriumof figure 2.5 is exactly similarto the equilibriumof figure 2.7 (pointsH and H* are the same in the two figures),the adjustment
mechanismsare different.In the flex-pricecase of figure2.5 adjustment
is automatic.Under price stickinessas in figure2.7, efficientadjustment
requires a specific and deliberate course of action by the monetary
policymakers.
2.4.4 MarketSegmentationand ImperfectPass-through(the
LCPModel)
Accordingto the conventionalview, exchange rate movements modify
the relativeprice of domestic and importedgoods. However, empirical
studies and casual observation suggest that, in practice,the prices of
most imported goods at the consumer level are ratherinelastic to exchange rate movements (Engel 1999;Engel and Rogers 1996;Goldberg
and Knetter1997;Parsley and Wei 2001;Rogoff 1996).Then, exchange
rate movements may not induce the expenditure-switchingeffects that
the conventionalview places at the heartof the transmissionmechanism
(Engel2002).
Considerour model under the assumptionthat firmspreset prices in
domestic currencyfor the national market,and in foreign currencyfor
the export market (the LCPcase discussed previously). With nominal
rigidities,all prices in the world economy are now fixed in the shortrun
regardless of currency fluctuations. In contrast to the PCP case, exchange rate movements neither affect the price of the Home goods
abroad,nor redirectworld demand towards them. The crucialeffect of
exchange rate movements in this economy is on firms' markups and
profits.Since the Foreign-currencyprice of the Home goods is preset, a
depreciationof the Home exchange rate raises the revenue in domestic
currencyof each unit of product sold abroad:hence the markup over
marginalcosts increaseswith depreciation.Butthis means thatnominal
depreciation improves- instead of worsening- the Home terms of
trade PF/eP*H.
Letus reconsiderthe equilibriumeffectsof a productivityshockwhen
Home monetaryauthoritiesstabilize the output gap in the new framework (fig. 2.8). As in the PCPcase, a positive productivityshock rotates
the AS upward, and a Home monetaryexpansion raisesHome nominal
spending. However, its macroeconomiceffectsdifferfrom the PCPcase
in two importantrespects.First,raising |x now has a much strongerimpact on the aggregatedemand,since all consumerpricesarestickyin the
The SimpleGeometryof Transmissionand Stabilization
91
Figure 2.8
Stabilizationpolicy underlow pass-through(LCP)
shortrun.Evenif the exchangeratedepreciates,thereis no importedinflation.TheAD shifts one-to-onewith |x (as in the closed economy case).
Second,the Home depreciationimprovesthe termsof trade:t rises with
the exchangerateand the AS rotatesupwards even further,reinforcing
the initialimpactof the productivityshock.
The Home economy moves from point O to point L. In the new equilibrium,employment is at its naturalrate (this is by construction,given
our assumption about Home monetary policy), but stronger terms of
trade allow domestic households to increase their consumption much
more than in the PCPcase. Forany given shock to Z, the segment O L in
figure 2.8 is largerthan the segment O H in figure 2.7. The economy operates away from its flex-pricebenchmarkallocation,delivering higher
utility to domestic households.
Theextragains for the Home economy come at the expense of the Foreign country.Home expansionshave no effecton Foreignconsumption.
Foreignconsumerprices are preset in Foreigncurrencyand are therefore inelasticto exchange rate movements in the short run:the Foreign
AD* schedule does not move. Conversely,the Foreign terms of trade
now worsen with the Home currency depreciation. The AS* rotates
downward and hours worked increase:Foreigncountryresidentsneed
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Corsettiand Pesenti
to work more to sustain the same level of consumption. A higher level
of effort at an unchanged level of consumption unambiguously worsens
Foreign households' welfare. The international transmission of policy
shock is clearly negative, that is, "beggar thy neighbor."
To sum up, the main predictions of the LCP model are quite distant
from the PCP case. The sign of policy transmission is different: positive
in the PCP case, negative in the LCP case. Also far apart are the responses of international prices: in a world with PCP, monetary expansions worsen the terms of trade; they improve it in the LCP case. In the
PCP case, exchange rate movements affect relative prices for a given
consumption level, switching demand across different categories of
goods. In the LCP case, there is no expenditure-switching effect from exchange rate movements. If anything, what is switched is the labor burden to sustain world consumption.
2A.5 A Case of Asymmetric Transmission (the DP Model)
Transmission in an economy where all export prices are set in one currency (the DP case) somewhat combines the two cases discussed previously. The crucial feature of such an economy is that different mechanisms mute the responses of t and t* to shocks. In the Home country,
consumer prices do not respond to the exchange rate, while dollar pricing insulate exporters' markups from exchange rate movements. In the
Foreign country, the positive effects of lower import prices are offset by
a fall in profits from exports: the local-currency value of export sales fall
with the Home depreciation.
We can visualize these effects in figure 2.9. Once again, the shock to Z
tilts the AS upward and prompts an increase in |jlto close the output gap.
In the Home country, where all prices are preset in Home currency, the
monetary expansion raises domestic demand one-to-one. The ensuing
Home depreciation has no implications for the profits of domestic firms,
since pass-through of exchange rate movements onto Home export
prices is complete. Consumption rises above the natural rate, while employment remains at the natural rate. The Home economy moves from
O to D, where the length of the segment O D lies somewhere between O
H in figure 2.7 and O L in figure 2.8.
In the Foreign country, Home depreciation translates into lower import prices, hence into a lower CPI. For a given domestic monetary
stance, the AD* shifts upward. But since there is no effect on the relative
price of consumption in terms of output, t*, the AS* does not rotate. The
The SimpleGeometryof Transmissionand Stabilization
93
Figure 2.9
Stabilization policy under asymmetric pass-through (LCP)
Foreigneconomy moves frompoint O*to point D* along the unchanged
AS* schedule. Thus, in the new equilibriumForeignhouseholds enjoy
higherconsumption(actually,as high as in the PCPcase:the gain in Foreign consumption O*H*in figure 2.9 is equal to the segment O*H*in
figure 2.7),but also work more. In other words, the internationaltransmission is positive as regardsconsumption,negative as regardslaboreffort.However, to the extent that monopolisticdistortionsin production
aremore relevantthanthe termsof tradedistortion,the firstcomponent
dominatesand the internationaltransmissionis overall positive. In this
case, in fact, the indifferencecurve in the preshockequilibriumcuts the
AS*fromabove.Hence,a small movementalong the AS*raiseswelfare.
Note that,fromthe point of view of Foreignconsumers,the exchange
rate plays a stabilizing role in the product market:Home currencydepreciationslower the price of Home goods. The sign of the adjustment
is consistent with the flex-pricebenchmark.But the negative implications of exchange rate movements on Foreignfirms'profits are clearly
destabilizing.Vis-a-visthe received wisdom on internationaltransmission (correspondingto the PCPcase) and its strongestcritique(the LCP
case), the case of dollar pricing stresses the realisticpossibility of counteractingeffects from exchangeratemovements within an economy.
To conclude our analysis of transmissionin the DP case, it is worth
94
Corsetti and Pesenti
noticingthatthe Home economy is fully insulatedfromexternalshocks:
for any given |xand Z, exchangerateshocks or cyclicaldevelopmentsin
the Foreign country have no macroeconomiceffects on output, consumption, and terms of trade in the Home country. In other words,
when Home policymakersrespond to local productivity shocks there
arerepercussionsin the restof the world (as illustratedin figure2.9),but
when Foreignpolicymakersreactto local shocks thereare no spillovers
to the Home country economy. This asymmetry stems from the predominant role in global trade of the vehicle currency issued by the
Home country.
2.5 Globalization and InflationaryBias
2.5.1 MonetaryDiscretion in the Closed-EconomyCase
In the previous sections, monetary policy has been characterizedin
termsof ad hoc, arbitraryrules (such as the Home countrytargetingfull
employmentand the Foreigncountrymaintaininga passive stance).The
remainderof the paper is devoted to an intuitiveexplanationof optimal
policies in closed and open economies.
As a startingpoint, an importantresult of our section on monetary
policy in a closed economy is that policymakers informed about the
state of the economy Z could use monetaryinstrumentsto move aggregate demand C towardits flex-pricelevel for a given pricelevel P. Would
such a policy conductbe optimal?
To performsuch an exercise,we need to specify a welfare metric:in
our model, it is naturalto assume that the objectivefunctionof the policymakerscoincideswith the utility of the nationalrepresentativeagent,
visualized graphicallyin termsof our map of indifferencecurves.In figure 2.10we returnto the closed-economymodel we introducedin figure
2.1.Theeconomy is in equilibriumat point O, where actualemployment
is at its naturalrate.The problemwith such allocationis that monopoly
distortions result in a socially suboptimal level of welfare: in equilibrium the indifferencecurve cuts the AS curve from above. Once prices
are set, ex-post utility could be increasedthrougha monetaryexpansion
that moves the equilibriumto the right of €, up to the point X at which
the indifferencecurve is tangentto the AS locus.
To shed light on this point, consider what policymakerswould do if
they optimized their monetary stance in a discretionarymanner once
the monetarystance that maximizes
prices have been set. Define as \y,dis
The SimpleGeometryof Transmissionand Stabilization
95
Figure 2.10
Inflationary bias
the utility of the representativehousehold (i.e., solves the following
problem):
max U = In C - k€ = In £ - k€.
P
n
(25)
The monetaryauthoritiestake prices as given,independent of their decisions. Accountingfor (3) and (4), the firstorderconditionof the above
problemis:
£-7
(26)
according to whether the optimal monetary policy under discretion
pushes labor effort (. (the left-hand side of 26) towards its competitive
level (the right-handside of 26) equal to 1/k.
In our setting there is, however, a crucial problem in solving for an
equilibriumwith discretionarymonetarypolicy. Using (26) to solve for
P in (10),we obtain:
This condition cannotbe part of a rational-expectationsequilibrium.In
fact,takeexpectationson both sides of (27):the two sides are equal only
Corsettiand Pesenti
96
when 6/(6 - 1) = 1 (i.e., for 6 -> °°).Otherwise,whatever the price level
chosen by the firms,thereis always an incentivefor the policymakersto
expand the monetarystanceabove privateexpectationsand, in termsof
figure 2.10,manipulateprivateagents'real incomes to increaseemployment and consumptionat X.
To derive a model where a rational-expectationsequilibriumexists,
one could modify our specification above by accounting for welfare
costs from realized inflation in (25).18This approach leads to models
in the traditionof the Kydland-Prescott1977and Barro-Gordon1983a,
1983b analysis of inflationarybias. Alternatively,some contributions
to the literatureanalyze monetary policy in economies where distortionary (Pigouvian) tax and subsidies can eliminate the distortions
caused by monopoly power, hence making the optimal policy timeconsistent.
Suppose in fact that the governmentcan subsidize firms'production
at the rate(1- Q"1,with C,= 1/6, raisingtax revenue in a lump-sumfashion. Then,firms'optimalitywill ensure thatprices areequal to expected
marginalcosts:
6
fw\
/kll\
"-F-r<i-?)E(y)-£(T)
<*>
Under these conditions, a monetary stance |x that moves one-to-one
with shocksZ is the optimalmonetarypolicy under discretion\kdis
as derived in (26).In equilibriumthere is no longer any incentivefor the policymakersto deviate from the optimal policy:
^
A
«-«#)=#)
(29)
The economy operatesat an efficient(first-best)naturalrateof employment,equal to the competitivelevel 1/ k, such thatthe indifferencecurve
in our graph is tangentto the AS curve in equilibrium.
The intuitionunderlying this result is straightforward.Thereare two
distortionsin our closed economy:nominal price rigiditiesand monopoly power in production. The government needs at least two instruments to achieve efficiency:on the demand side of the economy,monetary policy eliminates the negative consequencesof fixed prices;on the
supply side of the economy, fiscal policy eliminates distortionsdue to
monopolistic competition.The appropriatemonetaryand fiscal stance
allows the policymakersto bring the economy to a first-bestallocation.
The SimpleGeometryof Transmissionand Stabilization
97
2.5.2 Inflationaryversus DeflationaryBias in OpenEconomies
How does economic globalizationaffect the previous analysis?A large
literaturehas focused on the relationshipbetween openness and inflation,providingevidence thatmore open economiesarecharacterizedby
lower averageinflationratesin a largecross-sectionof countries(Romer
1993;Lane1997).Wecan revisit this point in terms of our apparatus.As
for the closed-economycase, the optimal policy in an open economy is
not, in general, time-consistent.However, each country faces now the
additional distortion related to its monopoly power on the terms of
trade.Termsof tradeconsiderationsmay actuallymitigateand possibly
offset the inflationarybias describedpreviously.
Under discretionHome policymakersmaximize agents' currentutility with respect to |x afterobserving the shocks Z and Z*, taking firms'
prices as well as Foreignpolicy as given. Foreignpolicymakerssolve a
similarproblem. In the PCP model, the welfare-maximizingmonetary
stancesunder discretionare:
z"2e-iV/
z*
2 e-i
\z*/
The above conditions cannotbe part of a rationalexpectationsequilibrium,except in the special case in which 1/0 = 2.19Wehave seen that in
a closed economy,monopolistic distortionsin production create an incentive for the policymakersto expand demand and bring output to its
competitive level 1/k. This need not be true in an open economy. The
above expressions make clear that policymakershave an incentive to
either expand or contractaggregate demand (given prices) depending
on whether the importsharein consumption(equalto 1/2 in our specification)is above or below the reciprocalof the markup(6 - 1)/9.
In termsof figure2.10,openness reduces(otherthings equal)the slope
of the AS locus. Thus, the slope of the indifferencecurve at the equilibrium point O can be lower (as in the closed economy case), equal to, or
possibly higher than the slope of the equilibriumAS.
Intuitively,recallthatin an open economy monopolisticdistortionsin
production coexist with terms of trade distortions, whose magnitude
depends- among otherthings- on the degree of openness of the economy. Under discretion,welfare-maximizingpolicymakersexpand aggregatedemand if the formerdistortionsare sufficientlyimportantrelative to the latter.When monopoly power in production is sufficiently
Corsettiand Pesenti
98
high (6 < 2 in our specification),policymakersare less concernedwith
adverse import price movements due to an exchange rate depreciation
than with the inefficientlevel of domestic output. By the same token,in
economies that are relatively closed to trade, the exchange rate affects
the price of a relativelysmall share of consumptiongoods. Also in this
case, benevolent policymakershave an incentive to raise output above
marketequilibrium.
The reverse is true when monopolistic distortionsin productionare
relatively low (6 > 2), or the economy is sufficientlyopen. In the latter
case, while raising output and employment, a monetary expansion
would also increasethe priceof a substantialproportionof consumption
goods. When terms of trade movements become the dominantconcern
in discretionarypolicy making, monetaryauthoritiesactuallypreferto
engineersurpriserevaluationsas a way to improvethe relativepricesof
theircountry'soutput.20
Weclose this sectionwith an importantcaveat:openness in itselfneed
not guarantee a lower inflationarybias. Exchange rate pass-through
considerationsalso matter.In fact, moving away from the PCP model
and reducingthe degree of pass-throughwould clearlyblunt the terms
of trade effects of monetarypolicy. Toshow this, consider the LCPcase
previously introduced.Whenpass-throughis low worldwide, the solutions to the policy problemsunder discretionare:
z "e-ih\ z f
z* "e-i^z*/
(31)
In this case, discretionarypolicy is unambiguouslybiased towards surprisemonetaryexpansions,even moreso thanin the closed-economycase!
2.6 Optimal MonetaryPolicy under Commitment
2.6.1 TheClosed-EconomyCaseRevisited
In section 2.5 policymakerswere unable to commit to a crediblemonetarypolicy.In this sectionwe areinterestedinsteadin the optimaldesign
of monetaryrules, accountingfor the factthatforward-lookingfirmsset
the prices of theirproductson the basis of theirexpectationsaboutboth
economicfundamentalsand policy variables.Is it still true thatthe optimal policy stance does stabilize producers'markups?And what happens when both domestic and foreign firms supply products to local
consumers?
andStabilization
TheSimpleGeometryof Transmission
99
To address these questions, we startby respecifyingthe appropriate
welfare metric.In our model, it is naturalto assume that the objective
functionof the policymakers,here denoted by °W,coincideswith the expectedutility of the nationalrepresentativeagent:
W = E(U) = E(]nC-Ke).
(32)
As before,the welfare-maximizingstanceis contingentto the realization
of the shocks.Differentfrombefore,it is determinedtakinginto account
that private expectations (and prices) are affected by the specific features of the policy rule itself.
Letus reconsiderthe closed-economycase, and recallthatin a market
equilibriumexpected employment is constant and equal to its natural
rate,accordingto (12).Thus, using the equilibriumexpressionfor optimal preset prices (10),the welfare criterionsimplifies to:
+ constant.
W = £(ln £) - k€ = £(ln \l) - In e(
^ )
(33)
Maximizingthe above expressionwith respectto |x yields:
I-
!£--
0
(34)
|x E(\l/Z)
solved by a policy (xthat moves one-to-one with productivity shocks
Z, say:
jjl
= olZ
(35)
where a is an arbitrarypositive parameterthat firms know when they
set theirprices.21
The previous condition characterizesthe optimal monetary policy
stanceup to the scale of nominal variablesin the economy.The optimal
policy consists of a commitment to provide a nominal anchor for the
economy, a, and to deviate from such stance only when productivity
shocks in the economy threatento destabilizemarginalcosts and move
employmentand output away from theirpotentiallevels. In our framework, by responding fully and systematically to Z, such policy completely eliminates uncertainty in marginal costs, and thus in profits.
Pricesare stabilizedat the level P = aK0/(0 - 1).22
If monetary authorities deliver the optimal monetary stance (35),
nominal rigidities are inconsequential,in the sense that policymakers
can stimulate aggregate demand to close the output gap and push the
economy toward potential regardlessof stickinessin price adjustment.
100
Corsettiand Pesenti
In termsof figure 2.3, any stochasticrotationof the AS locus is perfectly
matched by a correspondingshift in the AD locus, so that in the short
run the equilibriumalways lies along the NR verticalline above the natural rate. Note that, under optimal monetarypolicy, consumptionwill
not be constantbut ratherfluctuatewith productivity,perfectlymatching the flexible-priceallocation.
2.6.2 High Markupsand Low PurchasingPower as the Outcomesof
InsufficientStabilization
Having establishedwhat optimalpolicy means in the frameworkof our
model, we can now turn our attentionto a differentissue: what are the
consequences of adopting a suboptimal monetarypolicy not aimed at
full stabilization?We will show that insufficientstabilizationtranslates
into suboptimally high markups and price levels- making a case for
price stabilityin the design of optimal stabilizationpolicies.
Toprovide a graphicaltreatment,without loss of generalityconsider
an economy where Z is a random variable that can rise or fall by the
same amount with equal probability1/2, with E(Z) = 1. Figure2.11depicts the two possible AS lines, correspondingto a high and a low level
of Z. They intersectthe NR locus at points A and A', respectively.Observe that,were the optimalpolicy (35)in place, employmentwould be
Figure 2.11
Effects of suboptimal policy
The SimpleGeometryof Transmissionand Stabilization
101
constant at its naturallevel (,, and consumption would be high or low
depending on the realization of the productivity shock. For convenience, we draw the AS line correspondingto the average productivity
level, £(Z) = 1, which intersectsthe NR locus at point O,with AO = O'A.
The BOB'AD line that goes through O correspondsto the average consumption level in the flex-priceallocation.In the graph,we also draw a
second AD locus below the firstone, the FQF'line whose interpretation
will be made clearshortly.
Weare interestedin studying the equilibriumallocationwhen policymaking deviates from the optimal monetarystance. For instance,suppose thatmonetaryauthoritiesset the currentstanceaccordingto a passive rule:
|x = a.
(36)
In otherwords, |ljldoes not respond at all to the output gap. Withsticky
prices,consumptionwill then be constantbut employmentwill be fluctuatingwith Z: it will be below the naturalrate when the shock is positive, above the naturalratewhen the shock is negative.
Thesepoints areillustratedin figure2.11.Considerthe upper AD line,
drawn for the price level PBat a level of consumptionequal to average
consumption in a flex price equilibrium.If prices are predetermined,
and monetarypolicy is passive, the economy will operateeither at B or
at B'. Thesame is true for the lower AD locus, correspondingto a higher
price level PF> PB,thus intersectingthe NR locus at the point Q below
the point O:when P = PFthe economy operateseither at F or at F\
Now, it is easy to see thataverageconsumptionunder a passive monetary policy must be lower than the level that would prevail in a fully
stabilized economy. In other words, the preset price PBcannot be an
equilibrium.To see why, recallthat firms optimally preset prices to ensure that,onaverage,they operateon theirsupply schedule.As discussed
previously,an importantimplicationof such behavior is that expected
employment is equal to its naturalrate.But figure 2.11 clearlysuggests
that this conditionis violated when P = PB.
In fact, consider the two possible equilibria on the upper AD line.
When the productivityshock is positive, employment falls by the segment BO. But when the shock is negative, employment increasesby a
'
largeramount,equal to the segment OB >BO. Takingthe averageof the
two employment levels with equal probability,it follows that at PBthe
expected employment gap is positive; that is, expected employment is
above the naturalrate:
102
Corsettiand Pesenti
E(€)|p=Pa>€.
(37)
In other words, at PBeach firm is supplying too much relative to the level
of output that maximizes its expected discounted profits. Each firm has
therefore an incentive to cut back on its production plans, raising its
price: hence, PBcannot be the equilibrium price level.23
Given the distribution of Z, equilibrium pricing always equates the
average gap between employment and its natural rate to zero. In our example this principle has a simple geometrical interpretation: given the
two AS curves corresponding to the two different realizations of the
productivity process, and holding |x constant, prices (and the AD schedule) must be set such that the low and high employment allocations are
perfectly symmetric around €. In figure 2.11, this happens in correspondence to the lower AD curve, based on the higher price index PF.In this
case, when the productivity shock is positive employment falls by the
segment FQ, and when the shock is negative employment increases by
the segment QF', where FQ = QF'.
Figure 2.11 sheds light on one of the key reasons why insufficient stabilization can reduce national welfare. Facing uncertainty in marginal
costs, firms raise their average markups and charge higher prices for
their products. As a result, households' purchasing power is suboptimally low: failure to stabilize the economy does not affect expected disutility from labor effort (which is kept constant by firms' optimal pricing),
but does reduce utility from consumption.
Observe that, for any given suboptimal monetary policy, the higher
the variance of the shock (the further away are the two AS lines from
each other in figure 2.11), the higher the equilibrium price level (thus, the
lower the equilibrium AD). It follows that, for a given monetary stance,
changes in the variance of the shocks from one period to another lead to
adjustment in prices, creating temporary fluctuations of inflation.24
2.6.3 Optimal Policy in Open Economies and the Gains from
International Coordination
Do optimal stabilization rules in an open economy deviate from their
counterparts in closed economy? How do openness and trade affect the
design and conduct of monetary policy? In this section we take a first
pass at these issues by studying optimal policies for each of the three
specifications of export pricing (i.e., PCP,LCP,and DP). We discuss both
the case in which national policymakers design their policies indepen-
andStabilization
TheSimpleGeometryof Transmission
103
dently of each other,and the case in which they do so in a cooperative
way (Ball1999;Benigno 2002;Canzoneri,Cumby,and Diba 2005;Clarida, Gali, and Gertler2002;Corsettiand Pesenti 2005a;Gali and Monacelli 2005; Lombardoand Sutherland 2004; Monacelli 2005; Obstfeld
2002;Sutherland2005;Svensson 2000).
In the absenceof internationalcoordination,Home policymakersdeterminetheirwelfare-optimizingmonetarystanceby maximizing°Was
defined in (32)with respectto |x,while takingthe monetarypolicy in the
other country |x* as given. Similarly,Foreignauthoritiesmaximize W*
with respect to |x* given jx.We denote the monetary stances indepenand |x^ashas shorthand
dently chosen by the two authoritieswith |xNash
forNash equilibrium.Instead,in a cooperativeequilibrium,nationalauthorities jointly maximize a weighted average of Home and Foreign
welfare 0.5°^ + 0.5°lf*, whereas the weights coincide with the share of
each countryin world consumption.The cooperativemonetarystances
and \x*c
are denoted ^Coop
oop.
The PCP Model Our model with PCP provides an example in which
the optimalpolicy in open economy is identicalto the optimal policy in
closed economy: domestic policymakersfocus exclusively on the domesticoutput gap, offsettingany fluctuationin employmentand output
aroundtheirnaturallevel.
In the contextof a noncooperativeequilibrium,using the pricingequilibriumexpressionswith PCP,the policy problemin the Home country
can be written as
(38)
maxE[lnC-K€]
= max Eln|jL+ -E In ^l*- -In £(-£ - -|lnE|-^-)
+ constant .
2 \Z 2)
2
i L
\Z*J
J
=
The optimalmonetarypolicy satisfies |x^h aZ, preciselythe same expression as in the closed economy (Clarida,Gali, and Gertler2001).The
optimal policy is completely inward looking, in the sense that it is only
concernedwith stabilizingdomesticmarkupsand prices.This is exactly
the policy behaviorfollowed by the Home countryin figure 2.7.
Symmetrically,in the Foreigncountrythe policy problemis:
max E[lnC*-K€*]
(39)
= max - E In |x + E In ji* - - In E f-^-) - - In E (-^t- ) + constant ,
2
2
*•
[2
\ZJ
\Z*J
J
104
Corsettiand Pesenti
= a*Z*. Note that a and a* may differ,reflectingnawhich yields |x*^hp
tional preferencesover the desired rate of inflation. If the two steadystate inflationratesaredifferent,therewill be a trendfor the nominalexchange rate equal to the inflation differential,without effects on the
steady-statereal exchangerate.
Are theregains frominternationalpolicy cooperation?Toanswer this
question note that,with PCP,the objectivefunctionof the Home policymakersin (38)is identicalto the Foreignobjectivefunction(39):in other
words, °W= W*. Maximizingan averageof W and W* yields exactlythe
same optimalpolicy prescriptionsp^p = <*Zand |i££^ = a*Z*.Thenoncooperative rules remain the best policy rules also under cooperation:
by keeping one's house in order,so to speak, policymakersare already
able to achieve economic efficiency(Obstfeldand Rogoff2002).This result provides an extremeversion of the case for flexible exchange rates
made by Friedman(1953):even without price flexibility,monetaryauthoritiescan engineer the rightadjustmentin relativeprices throughexchange ratemovements. In our model with PCP,expenditure-switching
effects make exchange rate and price movements perfectsubstitutes.25
The LCPModel The optimality of inward-lookingpolicy rules, however, is not a general result. Notably, with LCP,the optimal policy rule
still prescribessome degree of output gap stabilization,but complete
stabilizationis not desirable.Under LCP,the Home policy problemin a
noncooperativeequilibriumcan be written as:
max \E In |ji- - In E(-^ ] - - In E\-^-) + constant .
2
2
it [
\z/
\z /
J
The optimal policy satisfies:
(40)
•
( )
2 E(n[&/Z*)
Home policymakersstabilize a weighted averageof Home and Foreign
marginal costs, using the CPI weights for the Home and the Foreign
goods.
Why? Suppose that the Home monetary authoritiesfollowed an inward looking rule; that is, they completely stabilized Home marginal
costs, moving (xto offset productivityshocks as in figure2.8.Whilesuch
conduct would stabilize domestic producers'markups, Foreign firms
selling in the Home country would face exchange rate variability.This
would affect the expected discounted profits from the Home market,
2 E(^£h/Z)
TheSimpleGeometryof Transmissionand Stabilization
105
thus Foreignconsumers'dividend incomes (with referenceto figure2.8,
Foreignresidentswould suffer large fluctuationsof employment away
from the naturalrate).
Foreignfirmswould then reactto volatility of profitsby raising their
average markups in their export markets, charging higher prices for
theirproducts sold in the Home country.The intuition underlying this
result is exactlythe same as discussed in the closed-economycase, with
referenceto figure 2.11. In that graph, uncertainty stemmed directly
from domestic supply shocks Z. In the LCP case the source of uncertainty in the Foreign country is exchange rate fluctuations associated
with the response of Home policymakersto domestic shocks. In both
cases, the optimal response of the producers is to raise markups and
prices (on average),in orderto reach(on average)full employment.
Home policymakers thus face a trade-off between stabilizing the
markups of domestic producers (translatinginto lower Home good
prices) and stabilizing the markups of Foreignproducers'(translating
into lower importprices).At an optimum, they will pursue some average between the two, depending on the weight of imports in the consumption basket of Home households. This is precisely the interpretation of (41).
Graphically,the noncooperativeequilibriumunder LCPfinds the two
economiesat points S and S* in figure2.8. Heuristically,this point is determinedas follows. First,consider the AS locus in the Home country
afterthe realizationof the shock Z (but keeping t unchanged).Takethe
horizontal distance between the NR locus and the AS locus. This distanceis zero at point D (incidentally,this is the same point D as in figure
2.9)where the two loci intersect,and increasesmoving downward from
D to O, with Home labor( below the naturalrate€. Second,considerthe
AS* locus in the Foreign country and its horizontal distance from the
NR* locus. This distance is zero at point O* and increasesmoving upward, with €* above the natural rate €*. Startingfrom O and O* and
moving upward, therewill be a value of consumptionC = C* such that
the two employment gaps in the Home and Foreign countries offset
each other.This correspondsto the segment SR in the Home country,
equal to R*S*in the Foreigncountry.The monetary stances |x and |jl*
move in tandem to support consumption gains in both countries by
OR = O*R*.Theseconsumptiongains are not as high as in the PCPcase
(points R and R* in figure 2.8 are below points H and H* in figure 2.7).
World employment remains unchanged:the contractionin the Home
country is matchedby the expansion in the Foreigncountry.Exchange
Corsettiand Pesenti
106
ratesand termsof traderemainunchangedin all countries.Utility gains
are largerin the Home countrythan in the Foreigncountry.
The magnitude of the optimal deviation from inward looking rules
depends on a country'sdegree of tradeopenness. In our stylized model,
half of the domestic consumption expenditure falls on foreign goods.
In the case of small and very open economies, there is a strong incentive to pursue policy rules that are quite outward oriented.In large and
less open economies,these considerationsmay affectpolicy design only
marginally.
In more generalterms,the optimalpolicy prescriptioncould be stated
in terms of targetinga weighted average of markups,assigning higher
weights (otherthings equal) to the core sectorsin which nominal rigidities are more pronounced.In the PCPcase, import prices are fully flexible while domestic prices are sticky,so that the optimal monetarypolicy only stabilizes domestic markups. In the LCP case both domestic
and import prices are sticky, and the optimal policy targets the CPIweighted averageof the markups.
Becauseof the internationalspillovers of monetarypolicy on international pricing,one may expect thatwith LCPtherewill always be an incentive to cooperate.Surprisingly,however, this is not the case in our
model. To see why, note that the objectivefunction of Foreignpolicymakersis identical to (40),except that In jljlis replacedby In jx*.Hence,
the noncooperativeoptimal policy satisfies:
1 m.T£S/z 1 uSSS/z*=
2E(m*K/Z)
2E(m.TS/Z*)
*
l '
Comparing(41)with (42)shows thatboth policymakersstabilizeexactly
the same weighted averageof Home and Foreignmarginalcosts. Hence,
they pursue exactly the same monetarypolicy, |x^h = |x*!£hp,
implying
that the nominal exchangeratedoes not reactto shocks.Insteadof closing the domesticoutput gap completely,nationalpolicymakerstakeinto
accountthe effects of theirpolicies on exchangeratevariability.In equilibrium, an efficient monetary rule limits exchange rate fluctuations
(Devereuxand Engel 2003).
Solving the cooperativeproblemdoes not change this prescriptionat
all. There are no gains from cooperationnot because domestic policymaking is alreadyefficient(as in the PCPcase, where thereare no spillovers in equilibrium),but becausewhat can be achievedby cooperating
(thestabilityor predictabilityof the exchangerate)is alreadyachievedin
the absenceof cooperation.As the only spilloversin the world economy
The SimpleGeometryof Transmissionand Stabilization
107
stem from exchange rate movements, the world economy cannot gain
by pursuing asymmetricpolicies that imply exchangerate fluctuations.
Once again,keeping one's house in orderis the best rule of conduct.
The DP Model An interesting case of asymmetric deviation from
inward-lookingrules is provided by an economy with DollarPricing.In
this case, Home welfare is equal to (40),so thatHome optimalmonetary
policy must satisfy (41). Foreign welfare is (38). Correspondingly,the
Foreign optimal policy is completely inward-looking.So, the country
that issues the currencyused worldwide for export pricing (the Home
country)optimally responds to shocks hitting the global economy.The
othercountryonly needs to stabilizedomestic markups.
The interestin this case mainly concernsits implicationfor the desirability of internationalpolicy cooperation. World welfare indeed increaseswhen monetarypolicy rules are designed in a cooperativeway
(by maximizing an equally weighted average of the two national welfare functions).However, the cooperativeand noncooperativeoptimal
policy rules coincide for the Foreign country, but not for the Home
country.The contributionto cooperationis thereforeunilateral:only the
Home countryis expected to modify its rules. This raises an interesting
issue as to whether there is any incentive for this country to enter any
binding cooperativeagreementregardingstabilizationpolicy.
2.7 Conclusion
It is hard to deny that the new paradigmof choice-theoreticmodels has
been contributingmany empiricaland theoreticalelements to our understandingof the internationaltransmissionof productivity,monetary
and financialshocks,the sign and magnitudeof cross-borderspillovers,
as well as the determinantsand cyclicalpropertiesof interna-tionaltrade
in goods, services,and assets. Recentcontributionsexplore the implications of frictionsin the asset and credit markets,attemptto integratefinancialand real aspects of the internationaltransmission,and address
crucialstylized facts of the internationaleconomy,from the low degree
of internationalrisk-sharingdocumentedby Backusand Smith(1993)to
the excess volatility of real exchangerates to the dynamics of comparative advantages in the world economy (Chari,Kehoe, and McGrattan
2002;Ghironi and Melitz 2005;Corsetti,Dedola, and Leduc 2004). At
the same time, pressing policy issues are raising the hurdles for DSGE
models;examplesincludecurrentaccountdynamicsand the adjustment
108
Corsettiand Pesenti
to global imbalances (Erceg,Gust, and Guerrieri2005; Faruqeeet al.
2007).
This paper has presented a stylized but rigorous frameworkthat illustrates fundamental traits of the recent stabilization literature,and
sheds light on the architectureof fully-fledged quantitativemodels in
internationalmacroeconomics.As DSGEmodels are increasinglyused
as tools for policy evaluationby domesticand internationalinstitutions,
one of the goals of this paper is to provide an introductoryset of analytical instrumentsto convey the main ideas about internationaltransmission and stabilizationpolicies underlying these models, as well as to
provide a smorgasbordof basic questions and intuitionsthat are developed in quantitativework.
While for the sake of analytical tractabilitythroughout the text we
have abstractedfrom dynamic considerations,it is worth emphasizing
that our results would qualitativelygo throughin richermodel specifications;for instance,in models with staggeredpricesetting.Theoptimal
policy for the PCPmodel derived in section 2.6.3 would be identicalin
our economy if firms adjustedprices with constantprobabilityin each
period (i.e., accordingto the Calvo process).Sincemonetaryauthorities
stabilize domestic marginalcosts in nominal terms, there would be no
incentivefor any firmto change its productprice at any time:firmsable
to reoptimizewould post exactly the same price as firmsunableto reset
their price. The exchange rate would move with the relative stance of
monetarypolicy,keeping the termsof tradein line with the flex-priceallocation (Clarida,Gali, and Gertler2001).
In the LCP case, we have seen in the text that the previously mentioned strategy (optimal for the PCP case) would translateinto inefficient average prices. With staggered price setting, however, it would
also produce welfare-reducingprice dispersion in the import sector,as
only some foreign firmswould be able to adjusttheirprices in response
to fluctuations in exchange rates (Smets and Wouters 2002, Corsetti,
Dedola, and Leduc,forthcoming).So, importedgoods thatare symmetric in productionand preferenceswould be sold, inefficiently,at different prices. Depending on the degree of openness of the economy,monetaryauthoritiescould improve welfareby tradingoff lower prices and
less price dispersion in the imports market,against some dispersion in
the marketfor domesticallyproduced goods. The design of optimalstabilization policies would therefore be concerned with minimizing a
weighted average of inefficientmisalignment of relative prices across
categoriesand within each category of goods, generalizingour results
TheSimpleGeometryof Transmissionand Stabilization
109
on the internationaldimensions of optimal monetarypolicy discussed
in the text.
Beforedrawing strong conclusionsfrom the LCPversus PCPdebate,
however, it is worth stressing that models where deviations from the
law of one price are an exclusive implicationof nominal rigidities (and
thereforea short-runphenomenon) may overlook persistentprice discrepanciesacross regions or over time, and overestimatethe degree of
nominal inertia required to explain the stability in local currency of
import prices. A promising way to address these issues appears in recent models that allow for distributionservicesintensive in local inputs
or local assembling of imported intermediateinputs (Ercegand Levin
1995;McCallumand Nelson 1999;MacDonaldand Ricci2001;Burstein,
Neves, and Rebelo2003;Corsetti,Dedola, and Leduc2004;Corsettiand
Dedola2005).Assessingthe relativeimportanceof optimalpricediscrimination and monetary frictionsin generatingincomplete pass-through
is clearlya relevantgoal for futureresearch.
Acknowledgments
We thank Pierpaolo and GianlucaBenigno, Rich Clarida,Jeff Frankel,
FabioGhironi,GalinaHale, MauriceObstfeld,Ken Rogoff,LarsSvensson, CedricTille,and MikeWoodfordfor useful commentsand suggestions.Wealso thankRaymondGuiteras,AlessandroMaravalle,and Natalie Levy for excellentresearchassistance.Corsetti'swork on this paper
is partof the PierreWernerChairProgrammeon MonetaryUnion at the
RobertSchumanCenterof the EuropeanUniversity Institute.Financial
support from the programme is gratefully acknowledged. Corsetti's
work on the projectis also part of the researchnetwork on "TheAnalysis of InternationalCapitalMarkets:UnderstandingEurope'sRole in
the GlobalEconomy,"funded by the EuropeanCommission under the
ResearchTrainingNetwork Programme(ContractNo. HPRN-CT-199900067).The views expressed here are those of the authors, and do not
necessarilyreflectthe position of the FederalReserveBankof New York,
the Federal Reserve System, or any other institution with which the
authorsare affiliated.
Notes
1. Throughoutthe paper we maintainthe AggregateDemand/Aggregate Supply conceptualapparatusof most macrotextbooks,althoughour graphicalapproachis closerin
110
Corsetti and Pesenti
spirit to the microeconomic treatment of input/output relations. Thus, readers used to
thinking about Aggregate Supply in reference to the relation between the price level and
output, or inflation and the output gap, may prefer to consider our AS schedule as the consumption-employment relation implied by the technology of production.
2. In Corsetti and Pesenti 2005b, appendix 1, we consider some examples of policy instruments corresponding to a given stance (x.
3. If the labor market were imperfectly competitive, there would be a wedge (labor market markup) between real wage and marginal rate of substitution, reflecting workers'
market power.
4. This result can be easily extended to the case of nonlinear disutility of labor effort. Suppose for instance that U = In C - k€1+7(1 + v). In this case the natural rate of employment
is a constant equal to [(6 - 1)/6k]1/1+v.For more general model specifications, the natural
rate need not be constant, and consequently the graphical representation of the equilibrium allocation turns out to be less straightforward. For a generalization of our graphical
apparatus to the case in which the natural rate depends on consumption see Corsetti and
Pesenti (1997).
5. Product prices are optimally preset to maximize the discounted value of the firm's profits. While in general this problem is quite complex, it greatly simplifies in our setting.
6. In what follows, £(X) will refer to the expected value of the variable X based on information available at the time expectations are taken. With one-period nominal rigidities,
the expression £(X) is shorthand for E^X,).
7. The ex-post gross markup is P/(W/Z), or 0/(6 - 1) X E(W/Z)/(W/Z). As long as 6 > 1
and the shocks are not too large, firms' ex-post markups will remain above one. Note that
in a model without monopolistic distortions any increase in marginal cost would lower the
ex-post markup below one, prompting firms to adjust their prices in response to the shock:
in that framework, nominal rigidities would be inconsistent with the rational behavior of
firms.
8. In more complex models, expected employment need not be at the natural rate in any
period. Nevertheless, optimal price setting is such that employment converges to the natural rate asymptotically.
9. An allocation is Pareto efficient if there is no other allocation in which some other individual is better off and no individual is worse off.
10. With P fixed during the period, there is no short-run inflation (deflation) in response
to positive (negative) output gaps. However, one could obtain some responsiveness of the
AD schedule to productivity shocks by allowing for an imperfect degree of short-run price
flexibility without changing the message from our results above. For instance, if prices
could partially respond to excess supply, a fall in the price level would somewhat raise the
AD schedule, moving the equilibrium allocation closer to the natural rate.
11. See Tille 2001 for a theoretical extension of this setup and Bergin 2003 for an empirical
assessment of similar models.
12. For this reason, nominal price rigidities do not necessarily rule out endogenous fluctuations in the consumer price indexes P and P*, which may reflect movements in import
prices in response to appreciation or depreciation of the currency. For instance, given |x, an
increase in e may raise the Foreign good price in domestic currency, thus reducing Home
aggregate demand. However, such imported inflation would affect not only the level, but
The SimpleGeometryof Transmissionand Stabilization
111
also the composition of consumer demand. In fact, Home consumption would switch in
favor of the now cheaper domestic good.
13. What would happen if we relaxed the balanced trade assumption? In principle, national residents in the two countries would benefit from having access to international
financial markets, trading securities whose payoffs move in tandem with the domestic
shocks, and reducing the exposure of their wealth and consumption to national sources
of risk. Consider the opposite extreme case of complete international asset markets. In
this case, the ratio of the marginal utilities of Home and Foreign consumption in any state
of nature must be proportional to the relative price of consumption (i.e., the real exchange
rate):
dU*/dC* = P*e
~P~'
dU/dC
Now, given the specification of utility in (1) and its Foreign analog, the risk-sharing expression above can be written exactly as (15)! Cole and Obstfeld 1991 show that under condition isomorphic to our parameterization, movements in the terms of trade are sufficient
to guarantee full consumption risk-sharing across countries exactly as if agents had access
to a system of transfers contingent to the realization of the shocks.
14. It is worth restating that, for these differences to be a feature of a market equilibrium,
one needs to assume that no agent in the economy can take advantage of arbitrage opportunities in the goods markets.
15. A new generation of models are revisiting the implications of productivity shocks on
the terms of trade when accounting for creation and trade of new product varieties. The
analysis of this section only focuses on the intensive margin of trade; that is, the international performance of sectors producing a given set of varieties, without studying the extensive margin associated with new traded products. See Bergin and Glick 2003; Ghironi
and Melitz 2005; and Corsetti, Martin, and Pesenti 2007.
16. This general principle is subject to a number of caveats, as optimal exchange rate
regimes depend in practice on the circumstances of the particular country and time
(Frankel 1999).
17. From a global perspective, the effect of the Home monetary expansion can be broken
down into two components. The first component is symmetric and affects the level of
world demand: a looser monetary stance at Home translates into a looser monetary stance
for the world economy as a whole, raising consumption worldwide. The second component is instead asymmetric and affects the composition of world demand. The monetary
stance is relatively more expansionary at Home, depreciating the exchange rate, and redirecting world demand towards Home goods.
18. For instance, in Albanesi, Chari, and Christiano (2003) inflation leads to a costly reduction in consumption purchases because of the operation of the cash in advance constraint.
19. Comparing (29) with (30), an increase in trade openness has effects similar to those of
the fiscal subsidy considered before. There is, however, an important difference. In closed
economy the socially optimal level of employment is higher than the natural rate and
equal to the competitive level 1/k; an appropriate subsidy allows the competitive level to
be supported in a time-consistent equilibrium. Openness instead reduces the gap between
socially optimal employment and natural rate €. This makes it easier but does not guarantee - for the socially optimal level to be supported in a time-consistent equilibrium.
112
Corsettiand Pesenti
Appropriatefiscalinstrumentsare still required,unless by chanceopennessand monopolisticdistortionshappento exactlyoffseteach other.
20. It is worth mentioninganotherdimension of the relationshipbetween globalization
and inflation.Ifglobalizationincreasesthe degreeof competitionin the economyand lowers averagemarkups(i.e., moves 6 upward),then it also reducesthe gap between competitive and naturaloutput. As the distancebetween O and X shrinksin figure 2.10, so
does the underlyinginflationarybias (Rogoff2007).
21. In expression(35),a need not be constantover time:it can representany deterministicprocessthatfirmsareableto predictat the time they taketheirexpectations.Adao,Correia,and Teles(2005)provide conditionsthat rule out indeterminacy,so that the equilibrium is unique. In our framework,this follows from perfectcommitmentby the central
bank,implyingthata providesa crediblenominalanchorto privatesectorexpectations.
22. It would be straightforwardto restate the results above in terms of inflationrates
ratherthan price levels. Suppose that the monetaryauthoritiesset the nominal anchor
accordingto a = P_,(l + it), where P1is the lagged pricelevel observedat the time expectationsaretaken,and iris the desiredrateof inflation- thatis, the (implicitor explicit)inflationtargetof the policymakers,which may be equal to zero. Given the above nominal
anchor,in the absenceof shocks (Z = 1) firmswould optimallyset theirprices equal to
a in each period and the economywould exhibita constantinflationrateequal to ttt;that
is, P/P_x= (1 + tt). Butthis is preciselythe outcomethatwould prevailin the presenceof
shocksto Z, provided thatthe monetaryauthoritiesimplement(35).
23. Our intuitivegraphicalanalysiscan be easily checkedusing the pricingequationdirectly.Holding (x= a, the equilibriumpricelevel is:
*=a e-i
\z)
e-i
since,with £(Z) = 1, £(1/Z) > 1. As a straightforwardimplicationof the Jensen'sinequality the optimalpriceis above our candidateexpressionon the right-handside:the preset
pricelevel is increasingin the varianceof the productivityshock.
24. Similarconsiderationsgo through in standardmodels with price rigidities.For instance,in the absenceof policy stabilizationlowerutilityand higherinflationvolatilityare
the resultsof inefficientdispersionof pricesand activitiesamong producersunderprice
staggering.In principle,one cannotrule out thatfor particularparameterizationsof preferences and technology,suboptimal stabilizationpolicies put downward pressure on
prices.However,the specificationscommonlyadoptedby the literatureyield resultsconsistentwith the one discussedin the text.
25. The equivalence between Nash equilibriumand flex-priceallocationneed not go
throughundermoregeneralconditions;forexample,with less restrictivepreferencespecificationsas shown by Benignoand Benigno2003.
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