Pricing to Market and the Real Exchange Rate Author(s): Hamid Faruqee Reviewed work(s): Source: Staff Papers - International Monetary Fund, Vol. 42, No. 4 (Dec., 1995), pp. 855-881 Published by: Palgrave Macmillan Journals on behalf of the International Monetary Fund Stable URL: http://www.jstor.org/stable/3867601 . Accessed: 22/02/2013 10:54
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IMFStaffPapers Vol. 42, No. 4 (December1995) © 1995International Fund Monetary

Pricing to Market and the Real Exchange Rate
HAMID FARUQEE*

Thispaper investigates the consequences of pricing to marketfor exchange ratepass-through and real exchange rate dynamics across differentpatterns of trade. Under two-way, intraindustrytrade-where home prices display greater linkage with those of foreign competitors-domestic and export prices exhibit lower pass-through and greater destination-specific adjustment compared to intersectoraltrade. Withboth tradepatterns, pricing-tomarket behavior intensifies the degree of persistence in the real exchange rate under nominal rigidities, and allows monetary shocks to have permanent effects on relativeprices so long as goods markets remain segmented. [JEL E12, F12, F41]

ANY

PLAUSIBLE THEORY of real exchange rate determination

must be

able to resolve two prominent stylized facts regarding international relative prices. First, at an aggregate level, real exchange rate movements tend to be very persistent. Second, at the micro level, individual prices tend to be sticky in terms of local currency.1 Of course, open-economy models in the Keynesian tradition have long since emphasized sticky

* HamidFaruqeeis an Economistin the ResearchDepartment.He received his Ph.D. fromPrinceton University.Workon thispaperbeganwhilethe author Afwas a lecturerin the WoodrowWilsonSchool of Public and International fairs.He wouldlike to thankWilliamBranson,LarryBall, Rex Ghosh, Michael Knetter, and IMF Research Department Seminar participantsfor helpful commentsand discussions. 1 the versus goodswithinthe samecountry Comparing relativepriceof different the relativepriceof the samegood acrossdifferentcountries,Engel (1993)finds the formermeasureto be less variablein all but a few cases suchas energyprices andprimary commodities. Moreover,the secondrelativepricetendsto be several times more variableon average,confirming that the local pricesprevailing a in given marketdestinationremaincomparatively quite stable. 855

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prices in goods and labor markets.Perhapsthe best-knownexampleis the Dornbusch(1976) overshootingmodel, whereinstickygoods prices in conjunctionwith flexible, forward-looking exchangerateslead to real rate overshootingand transitorydeviationsfrom purchasing exchange power parity(PPP). However,by invokingthe lawof one price,this literature incorporates price stickinessat the point of originratherthan at the marketdestination. In other words, the standardKeynesianapproachgeneratespricelevel inertiain termsof nationalcurrency(seller'scurrency)ratherthan local currency(buyer'scurrency).Furthermore, relyingon the law of by one price, these models typicallycannot generatethe degree of persistence that is observedin actualreal exchangerate time series. Not only do real and nominalexchangerates move togetherover the short term, they often movetogetherover muchlongerhorizonsas well-sometimes over many years. The law of one price has of course had a long-standing traditionin international economics.Interpreted a conditionfor spatialarbitrage, as the law of one price requiresthat the price of a good be the same in all locationswhen measuredin a commoncurrency.Extendingthis condition to all tradedgoods, PPP theory posits an aggregateversion of the lawof one price, appliedat the level of nationalpriceindices.The theory maintainsthat the price of entire basketsof goods should be equal (or proportional)acrosscountries.Together,PPP and the law of one price have served as the basis for some of the most widely-heldtheories in international economics, greatlyinfluencingthe discourseon exchange rate determination. Meanwhile, empiricalevidence supportingthe law of one price has remainedelusive. Numerousempiricalstudies have consistentlydocumented the absence of "one price" in practice, net of transportcosts, tariffs, and other trade impediments.2In combinationwith the very mixed evidence on PPP,3some have begun to call into question those theoriesthat rely upon the conceptof spatialarbitrage goods.4Given in
2See Engel (1993) for a study on the G-7 countries.Giovannini(1988) and Marston(1990) documentevidenceof pricingto marketpracticeswithinparticularJapaneseindustries.Otherstudieson the failureof one priceincludeIsard (1977), Mann (1986), and Knetter(1989 and 1993). 3 See Breuer (1994) for a recent surveyof the PPP literature. this 4Krugman (1989, p. 43) summarizes dissatisfaction: [W]e must now admit that internationalKeynesianism,while more like itself turnsout to have a problem:It monetarism, realitythaninternational does not go far enough in rejectinginternational arbitrage.Not only does the Law of One Price fail to hold at the level of aggregatenationalprice indices... it doesn't even hold at the level of individualgoods.

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its dubious validity, the law of one price has been subject to various modifications,5 including the allowance of systematic violations to one price as manifested by the phenomenon of pricing to market. With pricing to market, forces that would normally assure spatial arbitrage are absent, allowing corresponding prices to diverge across markets. This view-which is adopted in this paper-essentially breaks from standard models by favoring market segmentation rather than integration, and thereby acknowledging the presence of economic barriers and structural rigidities that restrict convergence in intermarket prices. Pricing to market may thus provide an alternative to the traditional view that differential rates of adjustment in goods prices versus asset prices alone underlie persistence in the real exchange rate. Much of the empirical evidence on market segmentation has drawn from the experience of United States in the 1980s. In particular, several studies have focused on the behavior of U.S. import prices during the period of massive appreciation6 and subsequent depreciation7 of the dollar. For example, Krugman (1987) examines U.S. import prices during the period of the dollar's rise. Constructing dollar price indices for U.S. import bundles and comparing them with the dollar price of the same bundle exported to third-country markets, he concludes that more than 30 percent of the real appreciation of the dollar was reflected in a divergence between these prices. In light of the empirical support for the proposition that certain markets may be segmented, the theoretical avenues regarding the issue of pricing to market have not yet been fully developed. Typically, models or 5Aizenman(1984), for example, illustratesthat when transport informaover the very shortterm, PPP holds up to constant tion costs impede arbitrage movements plus white noise. However, it is the persistenceof relative-price that dominate the time series of the real exchangerate that requiresfurther explanation. (1987, p. 104) 6Duringthe dollarupswingbetween1980and 1985,Dornbusch U.S. importprices: observesthe followingfact regarding of [T]heorderof magnitude the decline[in importprices]remainsrelatively smallcomparedto the changein relativeunit laborcosts. Witha changein relativeunit laborcosts of more than40 percent,the declinein the relative priceis in most cases less than20 percent.Thatis not at all out of line with to the theoryonce some degree of "pricing the Americanmarket"is taken into account.... 7 Forthe period1985-87, whenthe dollarfell precipitously, HooperandMann increases,in percentageterms, were well short of (1987) find that import-price the nominaldepreciation. findingin the specific (1989)reportsa similar Krugman case of Japaneseexportsin manufactures, findingthat exportprices(in dollars) were relativelystable in the destinationmarketdespitesharplyrisingunit labor costs (in dollars)at the point of origin.

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of pricing to market present static, partial equilibrium results from the perspective of an exporting industry or firm.8Hence, these models cannot address the dynamic price interactions and adjustment underlying the evolution of relative prices and the real exchange rate at the macroeconomic level. Using a general equilibrium model of monopolistic competition and market segmentation, this paper investigates the macroeconomic consequences of pricing to market for real exchange rate behavior across different patterns of trade. Allowing producers to price discriminate between local and foreign markets, the monetary model examines exchange rate pass-through and pricing-to-market behavior under segmented markets, and relative-price dynamics under nominal rigidities. By also incorporating the structure of trade, the paper examines the cross-sectional implications of intersectoral versus intraindustrytrade for macroeconomic adjustment.9 The central result can be summarized as follows. The pattern of industry specialization and trade largely determines the degree of strategic complementarity or price linkage between producers from different countries. In particular, under intraindustry trade-wherein home and foreign products are close substitutes-there exists a higher degree of linkage between domestic and foreign prices prevailing in the same market than under intersectoral (cross-industry) trade. Consequently, domestic and export prices exhibit greater responsiveness to exchange rate fluctuation, a lower degree of pass-through, and a greater degree of pricing to market under two-way trade. In a setting of imperfect integration,"' a greater degree of price linkage across borders translates into stronger mean reversion in the real exchange rate. The intuition is as follows. With menu costs and price staggering, prices display inertia in terms of national currency (unit of account) through a lack of coordination among decentralized price setters. In an open economy, however, producers are concerned with relative prices both at home and abroad. With the law of one price, the added concern with the foreign currency price of output compels price setters to partly overcome the coordination failure underlying domestic price
8A partialexceptionis Delgado (1991),whichdevelopsa dynamic menu cost model of pricingto market,albeit in a partialequilibrium setting. 9See also Faruqee(1994). in for "'Under imperfectintegration worldmarkets goods and services,countries differin their nationalconsumption patternsand in the unitsof accountin which they set prices-favoring both their own goods and their own currency. However, the law of one price still equates currency-adjusted prices across markets.Fora generaldiscussion imperfectintegration, Krugman of see (1989).

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inertia. Pricesbecome less stickyin termsof nationalcurrencyin order to reduce variationin terms of foreign currency.Hence, the stronger international tradereduces variability the linkagein pricesundertwo-way and persistenceof real exchange rate fluctuationcomparedwith intersectoral trade.1'However, once the assumptionof spatial arbitrageis removed, this comparativeresult no longer holds true. Once exportpricesdetachfrom domesticpriceswith segmentedmarratherthannational kets, pricesarein effect set in termsof localcurrency and price linkages predominantlyexist within a particular currency, marketratherthanacrossmarkets.If home andforeignpricesare inertial in the same unit of account, the patternof trade no longer affects the comparativedegree of variabilityand persistence in relative prices. Instead, the level of persistencebecomes solely a function of the frequency and timing of price adjustment.As a result, market segmentation allows internationalrelative prices to exhibit equally persistent deviationsacrossdiversepatternsof trade, despite inherentdifferences between home and foreign goods. in the substitutability issues aside, pricingto marketensuresgreaterprice staComparative bility in terms of local currencythan otherwise,regardlessof the trade pattern. Consequently,segmentedmarketsallow greaterinertiain the and in pricelevel domestically sloweradjustment relativepricesinternationallythanunderthe lawof one price.Thus,pricingto marketprovides an importantpropagationmechanismfor explainingthe large and proof tractedswingsin real exchangerates characteristic the post-Bretton Woods era. Moreover,in the presenceof marketsegmentation,monetary shocks have lastingeffects on relativeprices. Withoutgoods arbithe trage,absentarethe economicforcesthatwouldotherwiseguarantee priceof a basketof goods acrosscountries.Insteadof long-run equivalent disturbances havepermanent effectson the realexchange PPP,monetary rate in the absence of one price. Persistenceand permanencein relativeprices have importanttimefor series implications exchangerates. Whenmonetaryshockshavepersistenteffects on relativepricesas a resultof pricelevel inertia,nominal and real exchange rates move together in the short run, as has been models. When monetaryshocks have emphasizedin earliersticky-price effects on relativeprices, nominaland real exchangerates "permanent" move together over the longer run as well-so long as marketsremain fails. segmentedand the law of one price systematically The paper is organizedas follows. Section I develops a two-country model of monopolisticcompetitionand marketsegmentationunderinSee Faruqee(1994).

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Section and trade. Using this staticframework, traindustry intersectoral II addresses the issues of exchange rate pass-throughand pricing to market. A dynamicversion of the model is developed in Section III. nominalrigiditiesinto the analysis,this section examines Incorporating of the dynamicadjustment relativepricesandthe time-seriesbehaviorof the real exchangerate. Section IV offers some concludingremarks. I. Model of Pricing to Market Considera worldeconomyconsistingof a home anda foreigncountry, witheach countrycomposedof N producer-consumers. These individual and sell a differentiatedgood in order to purchaseand agents produce consumethe varietyof goods made by all agents, takingothers' prices as given. Meanwhile, each agent acts as a monopolisticcompetitor, setting a price and choosing a level of productiondepending on the demand that the individualproducerfaces. Building on the constant of elasticityof substitution(CES) approach Dixit and Stiglitz(1977),the model focuses on two basicvariantsof this centralframework: cases the trade.12 of intersectoraland intraindustry Underintersectoral trade,countries specializeandtradeat the industry level accordingto internationaldifferencesin comparativeadvantage. Thispatternof trade-often associatedwiththe exchangebetweennorth in differences relativefactor andsouth-emerges as a resultof underlying trade. Thus, this framework proportionsand gains from cross-industry view of internaessentiallyembodies the traditionalHeckscher-Ohlin tional trade, although, in this context, each sector is characterized by ratherthan by perfect competition. monopolisticcompetition are Underintraindustry trade,the premiseis quitedifferent.Countries now essentiallyidenticalwith respectto factorcomposition,yet they still gain from specializationand trade at the varietylevel because of scale of economies and productdifferentiation.This modern interpretation for tradeoffersan explanation the two-way,intraindustry often exchange for observedbetween OECD countries,but left unaccounted underthe standardfactor proportionstheory. Thus, the second case drawsfrom in some recentdevelopments the noncompetitive theoryof international trade.13 Under both trade patterns, the local and export demandsfacing an individualhome produceri are given in Table 1.14 Note that monetary
12

See Appendixfor details and the basicsetup of the model. 3See, for example, Helpmanand Krugman (1985). 4See Appendixfor details.

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Table 1. Domesticand ExportDemandFunctions UnderMonopolisticCompetition
Pattern of trade Home market Foreign market

Intersectoral trade

(-i)
Yi)'^)" )( )

(

(

-

I)

(

) EM*

Intraindustry trade.& Intraindustry trade

)

)

*i=Ej

( )-((1 1-

P)EQ*) )

variables with asterisks are expressed in units of foreign currency, and E is the nominal exchange rate expressing the domestic price of foreign currency. Also in Table 1, E> 1 represents the constant elasticity of substitution between any two varieties from the same industry, while a and 13are taste parameters, measuring the extent to which countries symmetrically favor their own goods in consumption. These latter two measures roughly capture the nominal expenditure shares allocated to locally produced goods from each country.15Assuming that countries predominantly consume the goods that they produce themselves, the model assumes that 0.5 < a,(3 < 1 under local goods preference. From Table 1, demand for output Yiin each market under interindustry trade is a function of two components: relative price and aggregate demand. Demand for a particular variety is a decreasing function of its price Pi relative to other prices in the industry, where P is the relevant index of producer prices set by producer i and his (n - 1) compatriots. Second, product demand for each variety depends on aggregate demand facing the industry in each country, where real money balances measure real aggregate demand in each market through a simple quantity equation relationship (see Appendix). More precisely,with interindustry trade, the domesticCPI is a functionof home and foreignproducerpricesgiven by prevailing Q = (P)Y(EP*)- , wherea is the exactexpenditure shareon homegoods.Underintraindustry trade, the home CPI and expenditureshare on home goods are Q = [PP'- + (1 - P)EP*'- ]and &=
15

+

P

Givenrelativeproducerpricesin generalequilibrium, is chosenso that a = ( )a, keepingexpenditurepatternsidenticalacrosstradepatterns.

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In the case of intraindustry trade, variety demand is once again a functionof relativepriceand aggregatedemand.However,since foreign goods now compete in the same industry,the relative-price component is a functionof the individualprice relativeto other home and foreign in industryprices.This modification demandis seen by the ratioof Pi to domesticCPI Q at home andthe foreignCPIEQ* abroad,wherethe the consumerprice indices and producerprice indices naturallycoincide undertradein one industry.Moreover,real moneybalancesalso reflect the appropriate deflatorto capturerealaggregate demandin the relevant market. Note that the demandsunder two-waytrade assumefrom the outset that countrysize is not an issue (n = n*). Otherwise,a measure of relativecountrysize wouldalso enter the demandunderintraindustry it trade.'6 trade, furtherdistinguishing from the case of intersectoral market segmentationinto the analysis, the model also Introducing assumesthateachproducer pricediscriminate can acrossmarkets,setting a differentpricein each locationif the agentso chooses.Thisassumption the fromFaruqee(1994),wherethe represents criticalpointof departure law of one price applied. Now, with segmented markets,the implicit arbitragemechanismsthat assured the law of one price are absent. each home andforeignproducer priceto each market can Consequently, on the market conditions that prevail in each separately, depending location. In standardmodels of marketsegmentation,firmsprice to marketby making destination-specificadjustmentsto price-cost margins in response to exchange rate changes. However, in this CES framework, markupsare constant, closing the usual channel throughwhich prices differ.Hence, to ensurethatproducers havean incenmaysystematically tive to price discriminate given their abilityto do so, it is also assumed that costs are separable(and convex) in the productionof domesticand export goods.17Otherwise, producerswould always choose the same price for each marketunder either patternof trade.18
Helpmanand Krugman(1985). for costs. If there '7Thereare manyjustifications the premiseof differential existmarketspecificcostsin transportation, distribution, production, advertising and/orservicing,then costs can differat the marginfor the home and exported good. Forexample,foreignmarketsmayrequiredifferentproductspecifications and/orhavedifferentgovernmental that costsof producregulations differentiate the tion; producing exportgood may even take place in the destinationcountry itself, involvinga completely separate plant and productionrun. These and similarexplanations may also help explainwhy marketsare actuallysegmented in the first place. 18 Constantdifferential couldbe introduced this CESframework into markups differential elasticities substitution of acrossmarkets 4 e*). In that (e by assuming case, there would exist a constantdegree of pricingto market.
16See

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is Qualitatively, pricingbehaviorundercost separability similarto the pricing-to-market responsesunder differentialmarkups.Usually, firms reduce markupsin marketswhere the currencyhas weakenedin order In to stabilizepricein termsof the localcurrency.19 thiscontext,exchange rate movementselicit a very similarresponse.For example, a depreciation of the foreigncurrency lowersdemandfor home exports,whichare now more expensiveabroad.Consequently, facedwith reduceddemand and cost, home producersrespondby loweringexportpricesin units of home currencyin order to offset the price increasein terms of foreign currency.Producersstill desire local price stability,but now througha marginalcost channelratherthan the markupchannel. of Note that this simple representation price discrimination places no boundarieson the degree of divergencebetween prices for the same good. Clearly,this is an extreme assumption.More likely, there would exist some neutralband-based upon the level of transportor adjustwouldpersist.Beyond that ment costs-within whichprice differentials markets"would emerge as agents found it profitableto range, "gray circumventthe producer's own distributionchannels. However, for smallenoughdemanddiscrepancies (largeenoughadjustment costs) this is representation certainlya reasonableassumption. As for notation, the home and foreigndestinationsare designatedas market 1 and 2, respectively.So, for example, the prices set by home produceri and foreign producerj for the home marketare denoted by Pi'andPj' expressedin unitsof nationalcurrency. Solvingthe producer's problem, by maximizingreal revenuesfrom domestic and export sales minusthe utilitycosts of production(see Appendix),yields the optimal price for each agent for each marketdestination. Table2 presentsthe optimalprice-setting rule (ignoringconstants)for each marketand underboth trade patternsfrom the perspectiveof the home producer.Note that lowercaselettersdenote logarepresentative rithmsof variables(q In Q). FromTable2, note that in everycase the is optimal(log) pricepi in units of home currency2" a weightedaverage of local money, consumerpricesat home, and local producerpricesfor the industry,with all weightsbeing strictlypositive.2'
9 withdifferential demandis less convexthanthe constant markups, Typically, elasticitycase. See Marston(1990). 20 Krugman (1984)findsthatmostcountriesinvoiceexportsin termsof domestic currency whenrelativecountry-size differences not significant. excepare The tion is developingcountryexports, which are predominantly invoiced in U.S. dollars. 21Based on taste parameters, the coefficients in Table 2 are given by
Y-1

e(Y- 1) + 1 where both coefficientsand their sum are between (0,1).

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Table 2. OptimalPrice-Setting Rules
Destination Pattern Home market of trade Foreignmarket Intersectoral + trade pi2 = (e + m*)+ Oq+ (1 - iTr )p2 pl = qrm 0q + (1-Tr- 0)p' Intraindustry trade p,2= ,(e + m*) + 0q + (1 - ,r- 0)(e + q*) pi = Irm +(1- rr)q

Under intersectoral trade, the price rule for the home market places a weight, rI, on domestic money, which represents nominal aggregate demand in that market. An increase in aggregate demand raises demand for each individual variety, effecting an increase in price. The weight placed on domestic consumer prices captures a real-income effect. Since each producer is also a consumer-ultimately concerned with utility-an increase in domestic consumer prices translates into a loss of real purchasing power in general and a desire to raise nominal price in response. The weight placed on industry prices, 1 - Tr 0, captures a relative-price effect. An increase in industry prices lowers producer i's relative price, raising the agent's product demand and price. Under intraindustry trade, the price rule for domestic prices has the same general form. Once again, producers are concerned about domestic consumer prices to the extent reflected by 0. Now, however, the relativeprice coefficient 1 - T - 0, capturing the positive interaction between industry prices, is also placed on the home CPI under two-way trade. Together with the real-income effect, the weight placed on q sums to 1 - rr in Table 2. So whereas price setters place a weight 1 - rt - 0 on p1 under cross-industry trade, that weight now falls on pl, p'*, and e (subsumed in q). Hence, there exists a greater degree of linkage between home and foreign producer prices prevailing in the domestic market. In the terminology of Cooper and John (1988), there is a greater degree of strategic complementarity between home and foreign pricing decisions under intraindustry trade.22 The intuition behind this result is relatively straightforward. Home and foreign varieties are closer substitutes under two-way trade, so that movements in international relative prices have larger consequences for individual demands. Hence, home price setters are more concerned with foreign prices set for the home market when choosing their own price. The same conclusion holds true for export prices as well. Home export prices under two-way trade display greater influence and interaction with
22See Faruqee (1994) for further discussion.

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effect also includesforeign foreign local prices, since the relative-price and the nominalexchangerate. industryprices II. Pass-Through and Pricing to Market Using the static frameworkof the previous section, the effects of on variousdisturbances nominalpricescan be measuredgiven a particular calibrationof the model. These comparativestatic exercises are carriedout in thissection. In particular, responsiveness the optimal the of in priceto an exchangeratedisturbance all fourcases, giventhatall other variablesremainunchanged,is calculated. The first measure of interest is the degree of exchange rate passthrough. Pass-throughis defined as the percentage change in home prices-measured in termsof foreigncurrency-resultingfroma change in the nominal exchange rate. If the foreign-currency price of a good one for one with the exchangerate, the degree of pass-through changes is one. In other words, the exchangerate changeis fully reflectedin the price remainsunaffected.At the price changewhile the home-currency other extreme, if a price responds fully to offset the change in the exchangerate, leavingthe foreign-currency priceunaffected,the degree is this of pass-through zero. Mathematically, sensitivitymeasureis calculated (in absolutevalue) by I{dp/dae 11e(0,1), for m = 1,2. in 1 displaysthe degree of pass-through home prices, holding Figure shares fixed and allowing the elasticity of substitutionto expenditure and intersectoral vary; dashed and solid lines representintraindustry trade, respectively.Note that the pass-throughresponses shown also as Whenthe elasticapplyto foreignproducers well throughsymmetry.23 is ity of substitution exactlyone, the two typesof tradeareidentical.This of resultfollowsfrom the characterization international tradesubsumed in consumerpreferences. Explicitly,preferencesare Cobb-Douglasacrossgoods fromdifferent industries,while CES preferencesapply to goods within an industry. Hence, when countries engage in one-way trade across sectors there betweenhome and foreigngoods. exists a low degree of substitutability Meanwhile, with two-way intraindustry trade, the CES specification thathome andforeigngoods areclosersubstitutes-unless Eequals posits unity, in whichcase the distinctionin utilityvanishes.24 Conversely,as E
1 23Pass-through abroadis defined as dp,/e-lae+ for m = 1,2.

rule to preferences describedin the Appendixverifies 24 ApplyingL'H6pital's this equivalenceresultin the limit as e--->1.

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Figure 1. Exchange-RatePass-Throughand the Patternof Trade
Pass-through 1.0 0.9 -Domestic prices

0.70.6
^l-_z

-^

Exportprices

0.4
1

i
2

!i
3 4

.

I .
5

6 7

betweenthe patternsof tradewidensin termsof increases,the disparity how agents perceive domesticgoods comparedto foreign goods. of This characterization preferencesembodies the basic idea behind The separabilityassumptionunder the Cobbthe Armingtonmodel.25 in utility makes the distinctionthat goods from Douglas specification different industries-appropriatelydefined-belong to separate comdistinctproducts.At the industry level, each modityclasses,representing into is then furtherdifferentiated manyvarietieswith a constant product elasticityof substitutionbetween them. Several results from this frameworkcan be inferredfrom Figure 1. is Naturally,the degreeof pass-through lowerin exportpricesregardless the trade structuresince export demandis alwaysmore sensitive to of thanis domesticdemand.In contrast,note that exchangeratefluctuation in in case of the lawof one price,pass-through domesticandexportprices must be identicalin each case, by definition. Also in Figure 1, as e increases,the degree of pass-through generally declines under two-waytrade, but increasesunder intersectoraltrade. The intuitionbehindthe latterresultfollowsfromthe previousdiscussion of preferences and trade. As the elasticity of substitutionincreases, with their industry producersdisplaygreaterstrategiccomplementarity
25 In Armington(1969), goods are imperfectsubstitutesaccording country to ratherthan industry.

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rivals.This strongerlinkagein pricestranslates into greatersensitivityto in relative prices. Under intersectoraltrade, as industry any changes varieties become closer substitutes, price setters become increasingly concernedwith keepingpricesin line with other residentproducers.At thatmargin,exchangeratefluctuations of no consequence relative are for prices as industryprices are set in the same currency(same unit of account).Hence, producersare more content to allow a greaterdegree of exchangerate pass-through. As for intraindustry trade, as the elasticityof substitutionincreases, price setters prefer to keep prices more closely in line with those of industrycompetitors,as before, but now the industryincludesforeign producersin each destination.Consequently,home producersdisplaya to by greaterresponsiveness exchangeratefluctuations makingoffsetting in in theirhome-currency pricesto minimizemovements relative changes under each 2 displaysthe degree of price discrimination prices. Figure This degree trade patternresultingfrom an exchangerate disturbance. of pricingto marketis measuredas the percentagedeviationbetween the domesticprice and export price for the same good as a percentage this of the changein exchangerate.26 Mathematically, measureis given absolutevalue) by lap/'lde_pj/ael. (in Once again, when e = 1, the two patternsof tradeare reallythe same and the degree of pricingto marketis also identical.As the elasticityof trade decide to substitutionincreases, producersunder intraindustry price discriminateacross markets to a greater extent. The reasoning follows as before. Strongerprice linkageswithin the industrymotivate home price setters to keep price more closely in line with competitors, includingforeignproducers,in each destination(see againdashedlines in Figure1). However,since demandabroadfor the domesticproductis more sensitiveto the rate of exchange, movementsin the value of currencyinducea greaterresponsein pricesset for the foreignmarketthan This for the home market,increasingthe extent of pricediscrimination. result is seen in Figure 2 by an increasingdegree of pricingto market undertwo-waytrade. As for intersectoraltrade, the total absence of an import-competing industryin each countrygreatlylimitsproducerconcernsabout international relativeprices. Furthermore,as e increases,closer ties between industryprice setters who happento be from the same countryfurther This is seen by a decreasing reduce the level of price discrimination.
26 An alternate but relateddefinitionof pricingto marketusedelsewherewhen is betweenvarious considering multiplemarkets the discrepancy exportpricesfor a given producer.See, for example, Krugman(1987) and Knetter(1993).

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Figure 2. Pricing to Market and the Pattern of Trade Pricingto market 0.5

0.4 Intraindustry 0.3 --

~~ ^~. 0.1. ~.._ ~Intersectoral

0
1

I
2

1
3

I
4

I
5

I
6 7

degree of pricing to market in Figure 2. As the relative-priceeffect receivesgreaterweightcomparedto the aggregatedemandand income effects, exchangerate changesare increasingly ignoredin both market destinationsunder intersectoraltrade. This finding is clearly at one extreme. Fromthe setup of the model, complete specialization the industry at level characterizes intersectoral tradebetweentwo nationsthatcouldnot be more different.In sharpcontrast,completeoverlapin industryproduction representsintraindustry trade between identical tradingpartners. In an intermediatestructurebetween these two boundarycases, each countrywould producepredominantly one sector or the other, in but would at least have some presence in both. In that instance, the typicaldegree of pricingto marketwouldlikely be increasingin E,lying somewherein between the limitingcases shown in Figure2. Interpretedas a boundaryrange, Figure 2 illustratesthe significant variationin pricing-to-market behaviorassociatedwith variouspatterns of international trade. In a multisectorsetting, the same general result wouldobtain. In those sectorswherethe degreeof intraindustry tradeis setterswoulddisplaya greaterdegreeof pricingto marketand high,price a lowerdegreeof pass-through. Recent empirical evidencedocumenting the degree of cross-industry variationin pricing-to-market behavioris Knetter (1993). Examiningvariousexport prices for Gerreportedby many, Japan, the United Kingdom, and the United States, Knetter

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is the (1993)findsthatindustry the criticaldimensionexplaining variation withinand acrosscountries. in the patternof pricing-to-market practices III. Relative Prices and Dynamics This section extends the model to incorporatedynamics.In the presence of nominalfrictionssuch as menu costs, producersdo not adjust prices continuously.Instead, price setters respondto changingmarket conditionsonly intermittently. Moreover,when decentralized producers adjust, they do so at differenttimes because of a lack of coordination. in This lack of synchronization pricingdecisions and revisionsinduces inertia in the overall price level. When price setters move at different times, agents who respondand change their prices do not adjust completely in an effort to maintainrelative prices with those who wait. of the Consequently, repercussion demandshocksmayextendlong after natureof price adjustment. the initialimpulsethroughthis overlapping To capturethis overlappingadjustmentprocess, a simple staggered timingstructurefor price setting is imposed. Specifically,it is assumed that half of all firms,home and foreign,revisetheirdomesticand export prices in even periodswhen necessary,while the remaininghalf adjust in odd periods.27 price Takingthe frequencyand timingof intermittent as given, the comparative dynamicsthat emergefromthis comchanges undercontrasting structure mon staggering patternsof tradeand market can then be examined. segmentation price setters by their time Droppingthe i subscriptand representing for rule(withoutdiscounting) locationinstead,the dynamic optimalprice both trade patternsis market-domestic or export-under a particular x, = 0.5p, + 0.5,pt+l, (1)

set wherex, is the actualprice28 for the periodst and t + 1 by home firms moving at time t.29 Also in equation (1), pt and tft+l represent the actual

and expected optimalprice at time t and t + 1, where expectationsare

27 See Ball and Cecchetti (1988),andBall andRomer(1989)for furtherdiscusand sion on the optimaltimingand frequencyof priceadjustment explanations for the existenceof price staggering. that 28 Agents are not riskneutral here, andequation(1) omitsa riskpremium

is a function of the conditional distribution of all nominal variables. For example, if money, prices, and the exchange rate are log-normal, the risk premium is a constant (comprised of variance and covariance terms) and can be ignored. Alternatively, the dynamics can be interpreted as deviations from a (stochastic) trend reflecting time-varying risk-which has very little impact on relative prices

throughsymmetryacrosshome and foreignprice setters. 29 In a generalsense, one can view equation(1) as the outcomeof minimizing

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HAMIDFARUQEE

formed rationally, based on all the information available at time t. Hence, time-dependent pricing leaves prices predetermined for two periods. Furthermore, the even-odd timing structure introduces asynchronized adjustment similar to that in Taylor (1980). Illustrating the overlapping nature of prices, the index of home producer prices prevailing in the domestic market takes the (approximate) form: pl = 0.5x' I + 0.5x. Substituting the static price rules from Table 2 and their corresponding foreign counterparts into the dynamic price-setting equation (1) defines a system of equations with four state variables, consisting of home and foreign local prices and export prices, where each price equation takes the form of a second-order stochastic difference equation as a result of the simple two-period overlapping structure of price adjustment. However, with the focus on real exchange rate dynamics, the four-variable system can be reduced to one difference equation in relative prices, given the behavior of the three forcing variables consisting of home and foreign money and the nominal exchange rate.3"See the Appendix for details. In the case where home and foreign money follow a random walk,31 the dynamic equation for the CPI-based (log) real exchange rate r under either trade pattern can be written compactly as rt = Xr,t-i+ ol(m, - m?*) + 02(m,-1 - m*-i). (2)

Note that the simple even-odd staggering structure in nominal price adjustment gives rise to a simple first-order autoregressive process in relative prices, where the coefficient X in equation (2) can be interpreted as a measure of persistence or inertia in the real exchange rate.32

a quadraticloss function defined by squareddeviationsin actual price from optimalprice over the period for whichprices are predetermined. 30Thebehaviorof the nominalexchangerate is identicalacrossboth trade patterns.Givenmoneymarketclearingand balancedtrade(see Appendix),the (log) nominalexchangerate is given by e,t= m - m*.

this to the Comparing expression equation(2), whichfollows,highlights factthat asset marketprices and goods marketspricesadjustat differentialrates.
3' That

is, it is assumed that

m, = m,_ + v, and m* = m* l + v*, in (wherev, v* are randomdisturbances), whichcase the nominalexchangerate will also follow a randomwalk.
32

One can show that A=

1 -\/,r + 20(l - oa)

+ )e(b,1). 1 + VIT + 20(1- a)

See Appendix.

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As alluded to, the dynamicsgoverningthe behaviorof the real exchange rate in equation (2) apply to both patterns of trade. At first glance, this equivalencyresultmay seem a bit surprising given the comparativedifferencesshown earlierin Section II. However, the findings are mutuallyconsistent.In fact, the differencesregarding response the of nominalprices describedearlierare what guaranteethe equivalence result regardingthe behaviorof relativeprices. Forillustration, comparethe optimalpricerulesfor the home exporter shownin Table2. The single differenceacrosstradepatternsis found in the relativeprice component.Under intraindustry trade, the home produceris concernedwithcompetingforeignprices,the exchangerate, and otherhome exportprices, whereasthat same agentundercross-industry trade is concernedonly with other home export prices. Under the law of one price, the added concern with the foreigncurrencyprice of outputwould compel price settersin the first instance to reducethe degree of domesticpriceinertiaresultingfrommenu costs and price staggering.Prices would be less sticky in terms of national in in leading currency orderto reducevariation termsof foreigncurrency, and persistentdeviationsin the real exchangerate under to less variable However,as indicatedby equation(2), once the assumptwo-waytrade.33 differenceregarding is tion of spatialarbitrage removed,thiscomparative holds true. the behaviorrelativeprices no longer Instead,once exportpricesdetachfromdomesticprices,goods prices are in effect set in termsof local currencyratherthan nationalcurrency since price linkages predominantlyexist within market destinations ratherthanacrossthem. As a result,undertwo-way trade,the destination set by industryrivalsfrom differentcountriesare inertialin the prices same unit of account,as if they were from the same country,whichjust happens to be the case of intersectoraltrade. Consequently,real exchange rate dynamicsare the same across differingpatternsof trade, ceteris paribus, and depend only upon the timing structureof price adjustment. behavior increases the degree of persisOverall, pricing-to-market tence in the real exchangerate comparedwith the settingof one price. Regardlessof the tradepattern,if pricesetterseffectivelystabilizeprice in terms of local currency,destinationprices become less responsiveto exchange rate disturbances.Pricing to market in effect allows price setters to keep export prices more stable in terms of foreign currency that domesticpricesbe more flexiblein termsof home withoutrequiring unlike the law of one price. Consequently,the real exchange currency,
3See

Faruqee(1994).

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872
Table 3.

HAMIDFARUQEE Real Exchange Rate Dynamics

PersistenceX
Openness a e= 2 e= 6 e= 10 Permanence

0.99 0.95 0.90 0.80 0.70 0.60

0.40 0.35 0.29 0.21 0.14 0.09

0.51 0.46 0.40 0.33 0.26 0.21

0.57 0.52 0.47 0.40 0.34 0.29

0.02 0.10 0.20 0.40 0.60 0.80

rate displays greater variability and persistence.34 For example, with an import share equal to one quarter, the degree of persistence under intersectoral trade would be twice that under the law of one price, and the corresponding increase under two-way trade would be even larger.35 Based on equation (2), Table 3 presents a sample of computed persistence values for the real exchange rate across different degrees of openness ot and substitutability e. Note that a decrease in a, representing an increase in expenditure on imports as a share of national income, reflects an increase in openness. The last column measures the long-run impact of a monetary shock on the real exchange rate. This permanence factor measures the change in the steady-state value of the real exchange as a percentage of the change in the equilibrium nominal exchange rate.36So, for example, if o = 0.9, a permanent 10 percent increase in the domestic

34 a closed-economycontext, Ball and Romer (1990) show that real rigidiIn ties-such as efficiencywages-reinforce the effectsof nominalrigidities,inducing a greater degree of persistencein domestic prices. In an open economy, pricingto marketprovidesthe sourceof realrigidity-allowingfirmsto stabilize relativepricesin each market-which increasesthe degreeof stickinessin nominal prices (in terms of local currency)and magnifiesthe degree of persistence in the real exchangerate. 35 equivalent tradeunderone priceforthe degree solutionfor intersectoral The In of inertiais (2a - 1) , comparedwith k undermarketsegmentation. a closed economy (t = 1), the dynamicsin the two instancesare identical,as one would expect. Meanwhile,when a = 0.75, inertiaunder one price is half that under is pricingto market,and the increasein persistence even largerfor intraindustry trade. See Faruqee(1994). 36 The steady-state value(denotedwitha bar)for the realexchangerateas seen from equation(2) is given by 2 _ (O1 + _ r= 1(m -m*), where the coefficient in this expression measures the long-run impact of a permanent monetary shock. See Appendix for details.

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money stock (and proportionalnominal depreciation)would induce a steady-statereal depreciationof 2 percent.37 In Table 3, note that persistencedeclines with increasingopenness. The basic reasoningis as follows. As the importshare rises, a nominal depreciationleads to greater CPI inflation, and real income is thus affectedmore by exchangerate changes. Since producersare also consumersconcernedwith theirpurchasing power,greaterconcernwith the value of revenue reduces price stickinessin terms of foreign-currency local currency, thereby reducing inertia in the real exchange rate
(0(1 - a)t >X ).

Table3 also showsthat persistenceincreaseswith the elasticityof substitutionbetween goods. The argumentfollows similarlyto that above, but via the relative-pricechannel rather than the income channel. A between varietiesimpliesthat demand higherdegree of substitutability is more sensitive to a change in relative price (see Table 1). As producersbecome more concernedwith theirpricerelativeto the industry, effortsto stabilizeprice in termsof local currency each marketintenin The resulting increasein localpricestickiness inducesgreateroverall sify. persistencein the real exchangerate. is functionof Lastly,Table3 illustratesthat permanence an increasing As importexpenditure sharesincrease,the asymmetric effects openness. of a lasting domestic monetaryexpansionon prices across segmented marketsbecomelarger.Moresimply,thisresultcanbe interpreted the in If contextof tradability. the productis essentiallynot traded(a-- 1), the effects of pricingto marketon the long-runreal exchangerate are small. Conversely,the degree of permanencerises with increasingopenness since the effects of pricingto marketare morepronounced with a higher of international trade. Finally,note thatthe permanent effects of degree monetaryshocks are a result of marketsegmentationand not nominal rigidityand would exist even if priceswere perfectlyflexible (h = 0; see Appendix). in Persistenceandpermanence relativepriceresponseshaveimportant for time-seriesimplications exchangerates. As with earliersticky-price ratesof adjustment goodspricesversusassetprices in models,differential allow nominaland real exchangerates to move closely together in the short term. Followingan initial impulse, the real exchange rate then

37Themodel thus includesa role for monetaryfactorsin determiningequiremainsegmented.See Krugman librium exchangerates,so long as markets real of on exchangerates. (1990)for a recentdiscussion realdeterminants equilibrium

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HAMID FARUQEE

eventuallyself-correctstowardequilibrium,reflectingthe persistentefon fects of monetarydisturbances relativeprices.The current framework also predictsthatthe nominaland realexchangeratemovetogetherover since monetaryshocks have permanenteffects the longer run as well,38 on the nominalrateof exchangeandon equilibrium relativepricesto the if extent thatgoods marketsremainsegmented.Alternatively, the lawof one price ultimatelyholds in the long run, the "permanence" factorcan be viewed as long-termpersistencein the real exchangerate, extending beyond the period requiredfor prices to adjust.

IV. ConcludingRemarks of With the collapse of Bretton Woods and the abandonment fixed rates in 1973, the two decadessince have seen a great deal of exchange in turbulence foreignexchangemarkets.Yet the largeswingsin exchange ratesunderthe era of floatingrateshave not broughtabout largemoveas mentsin inflationor disinflation one wouldexpectwithpass-through. into Instead,volatilenominalexchangerateshavetranslated volatilereal exchangeratesin the post-BrettonWoodsworld,while local priceshave stable. remainedremarkably In an attemptto understand these developments,this paperdevelops a model of marketsegmentationand pricingto market,with important macroeconomicconsequencesfor the behaviorof internationalprices of broadlyin line with the stylizedfacts. Motivatedby a preponderance evidencedisavowing lawof one price,the modeldetails the the empirical behavior.The some of the economic implicationsof pricing-to-market nominalprices resultsincludebothcross-sectional regarding implications and time-seriesimplicationsregardingrelativeprices. Across differentpatternsof trade, significantvariation, exists in the of pass-through pricingto marketdependinguponthe degree and degree betweenhome and foreign of intraindustry tradeandthe substitutability in Across time, dynamicadjustment pricessuggeststhat nominal goods. and real exchangeratesmove togetheroverthe shortrun, as well as over the longer run to the extent that marketsremainsegmented. Overall, pricingto marketprovidesa potentiallyimportantsource of local price stickinessand real exchangerate persistence.

38SeeAdams and Chadha(1991) for empiricalevidence.

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APPENDIX Two-Country Model The Consumer's Problem For the home country,agent i's utilityfunctionis given as follows:
Uci
MiQ /_l1

(y

2

_

F

< 1,y > 1, (Al) where Ci is a consumptionbasket of home and foreign goods, Mi represents Q substitution), is the domestic money holdingsof home currency(no currency consumerprice index, and Y1, Y/ are agent i's level of outputfor the domestic of and exportmarkets.Fi denotes fixed costs in the production a singlevariety, while z capturesthe "menucost" for changingprice. Also in equation(Al), D, is a decisiondummyvariable,equalingone if agenti changeshis or her own price and the shares andzerootherwise.Lastly,pL 1 - pL expenditure represent constant of with the of goodsandmoney,whiley - 1 measures elasticity marginal disutility respectto output. overhome and In the case of intersectoral trade, agentshave CES subutilities foreignvarietiesof goods, respectively.Explicitly,Ci is given as I =ci c) ) ; 1,

(A3)

basketof all foreigngoods: and where Cf representsi's consumption Cf n)1/1j= I

(Cf)

e-;

l.

(A4)

In these last two subutility representagenti's consumpexpressions,Ci and C{f tion levels of home good j and foreign good j, while e measuresthe constant elasticityof substitutionbetween any two home or any two foreign varieties, respectively. trade. Home and foreign goods no Considernow the case of intraindustry groupsas countriesexchangegoodswithin longerbelongto separatecommodity the same industry.To modifypreferencesaccordingly, equations(A2) through (A4) are replacedwith:
C= (nmul-

oe j=l god

e (j) Ejui

2l

-

;

1