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Interdependence and Exchange Rates

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Interdependence and Exchange Rates Doireann FitzgeraldyUC-Santa CruzDecember 2003AbstractI use a multi-country general equilibrium trade model to illustrate how asymmetricrelations between countries induce dependence of bilateral exchange rates on third-country fundamentals. I discuss the implications of asymmetry for standard empiricaltests of bilateral models of equilibrium exchange rate determination. I demonstratethat third-country e¤ects are present in real exchange rates from a sample of 25 OECDcountries. I show that controlling for third-country fu ndam entals substantially im-proves the in-sample …t of a fundamentals-based empirical model of real exchange ratesfor these countries. At short horizons, it reduces the bias of out-of-sample forecasts ofreal exchange rates and also reduces the variance of out-of-sample forecast error.JEL codes F12, F31Keywords: Exchange rates, trade1 IntroductionThe empirical literature on testing equilibrium models of real and nominal exchange ratedetermination is vast. The conclusions of this literature have not materially changed sinceFrankel and Rose wrote in 1995: “We, like much of the profession, are doubtful of thevalue of further time-series mo delling of exchange rates at high or medium frequencies usingmacroecomomic models.”This paper takes the view that progress can still be made in the I would like to thank my advisors, Ken Rogo¤, Elhanan Helpman and Greg Mankiw. I would also like tothank Manuel Amador, Juan Carlos Hallak, Philip Lane, Marc Melitz, David Papell, James Stock, SilvanaTenreyro and seminar participants at Chicago GSB, Harvard, the New York Fed, the San Francisco Fed,Stanford and UC-Santa Cruz for helpful comments and suggestions. All remaining errors are my own.yDepartment of Economics, UC-Santa Cruz, Santa Cruz, CA 95064, d…[email protected] modelling of exchange rate behavior by moving beyond the equilibrium models ofthe 1970s.The …rst part of the paper uses a multi-country general equilibrium trade model to illus-trate how asymmetric relations between countries induce dependence of bilateral exchangerates on third-country fundamentals. In this model, when trade in goo ds is costless, bilateralexchange rates (both real and nominal) depend on bilateral fundamentals alone, even whenthere is asymmetry in country size and bilateral distance. However when trade is costly,asymmetric trade relations and consumption patterns are induced, and bilateral real andnominal exchange rates depend on fundamentals in all countries. Simulations of a three-country version of the model indicate that the importance of third-country e¤ects dependson the degree of asymmetry across countries. I discuss the implications of asymmetry forempirical tests of exchange rate determination, and argue that the standard bilateral ap-proach may lead to inappropriate testing procedures. I argue further that third-countrye¤ects could potentially explain a number of features of previous empirical results, such assensitivity to the choice of numeraire country that have not so far been well understood.The second part of the paper uses annual data on 25 OECD countries to examine theextent to which third-country e¤ects matter in the data. There are 300 bilateral exchangerates in the sample. In a clear majority of these cases, the productivity of third countrieswithin the sample can explain a signi…cant proportion of the residual variance in real ex-change rates after bilateral productivity has been controlled for. This is true both in levelsand in di¤erences. This is clear evidence that the interdependence issue should be takenseriously in testing fundamentals-based models of equilibrium exchange rate determination.The third part of the paper investigates whether taking interdependence into accountcan mitigate the puzzle referred to by Frankel and Rose: that fundamentals cannot explainor predict the medium-frequency behavior of exchange rates. I focus on real exchange rates.I do not …nd strong statistical evidence of an equilibrium long-run relationship between realexchange rates and productivity (as predicted by the model), whether or not third-countrye¤ects are controlled for. However, for certain pairs of countries where there is a good dealof asymmetry present, there is strong evidence that third-country fundamentals belong inany fundamentals-based model of real exchange rates. Additionally, adding third-countryfundamentals to the standard bilateral model can improve forecasts of real exchange ratesboth in-sample and out of sample. In-sample, while the bilateral model is b eaten by a2random walk in 91% of the 300 cases investigated, in 51% of cases the model augmented toinclude third-country fundamentals can beat a random walk. At short horizons, controllingfor third-country fundamentals systematically reduces the bias and forecast error varianceof out-of-sample forecasts.I conclude that asymmetric interdependence does not explain the many outstandingexchange rate puzzles. But there is strong evidence that it matters for exchange rate deter-mination, and that it should be taken into account in estimating long-run relationships andin forecasting.2 A trade model of exchange rate determinationThis section presents a multi-country model, where production of goods is specialized dueto a desire for variety and increasing returns in production. Equilibrium exchange rates aretied down by trade in goods. First, the case with costless trade is analyzed. In this case,irrespective of asymmetry in size, productivity and bilateral distance, trade and consumptionare perfectly symmetric: the share of country i’s trade accounted for by country j is the sameas the share of country k’s trade accounted for by country j for all i, j and k. This modelis similar to that used by Anderson and van Wincoop (2003a) to investigate trade betweenmultiple countries in general equilibrium. It is also related to the model presented by Eatonand Kortum (2002).2.1 Costless tradeThere are N countries, indexed i = 1; : : : ; N. No restrictions are placed on the distributionof country size or bilateral distances b etween countries. World labor supply is normalized toone, and country i has share siof the world labor force. Each country produces a number ofvarieties of a traded aggregate consumption good.1There is a potentially in…nite number ofvarieties. Because of …xed costs of production of individual varieties, each country specializesin the production of


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