Consumption and Real Exchange Rates: ACorrelation PuzzleDaniel VolbergyNew York UniversityDecember 2005Job Market PaperAbstractThis paper links real exchange rate movements to fundamental variables. Standard international business cycle models predict a perfect correlation between ratios of domestic to foreign aggregate consumption andbilateral real exchange rates. However, this prediction is inconsistent withthe empirical evidence. I use a dynamic exchange economy to show thatallowing for default in securities markets in conjunction with trade frictions can account for this phenomenon.I would like to thank David Backus, Gian Luca Clementi, Nouriel Roubini, Kate Kisselev,Fabrizio Perri, Stijn Van Nieuwerburgh, Frederic Lambert, Cristian Dezso, Paul Wachtel andLawrence White for helpful comments. All errors are my own.y Department of Economics, Stern School of Business, New York University, 44 West 4thStreet, Suite 7-176, New York, NY 10012. Tel: (212) 998-0879, Fax: (212) 995-4218, E-mail:firstname.lastname@example.org
1IntroductionUnravelling of the Bretton-Woods system of xed exchange rates in 1972 generated demand for a structural model of exchange rate determination. Onechallenge to building such a structural model has been the exchange rate disconnect puzzle. Many studies have shown that exchange rate movements areunrelated to ‡uctuations in virtually any kind of fundamental variable, including GDP, money supply, interest rate or consumption. In particular, Backusand Smith (1993) show that a feature of international business cycle modelswith complete markets is a perfect correlation between the ratio of domesticto foreign aggregate consumption and the bilateral real exchange rate. Backusand Smith further show that this prediction is in sharp contrast to the empiricalevidence. They nd that the cross correlation between growth rates of bilateralconsumption ratios and real exchange rates has a mean of 0.045 and a range of[-0.08,0.17]. In this paper I address the real exchange rate disconnect puzzle asa rst step in the direction of building an empirically sound structural model.I argue that trade and asset market frictions are some of the key ingredientsnecessary for resolving this puzzle.To break the tight theoretical relation between consumption and exchangerate, frictions need to be introduced. Trade frictions, nominal rigidities andasset market frictions are the three types of frictions most relevant for the exchange rate disconnect problem. Previous attempts at resolving the discrepancybetween theory and empirical evidence using structural models have focused ontwo of these frictions. However, nominal rigidities and trade frictions have beenunsuccessful in reconciling theory with the empirical evidence.1 In this paperI argue that it is the interaction of goods trade and asset market frictions thatholds the most promise in resolving the exchange rate disconnect puzzle. I introduce limited commitment in asset markets and obtain theoretical predictionsfor the correlation of real exchange rate and relative consumption on the orderof -0.4, a signi cant improvement on the body of work currently available. Limited commitment in asset markets, discussed later in greater detail, augmentsa complete markets framework with an option to default on assets. In orderto keep trade in assets going an agent with a low income shock needs to beborrowing constrained in the present and future periods in order to eliminateunsustainable debt levels. This introduces an extra, time varying, componentinto the relation between the consumption ratio and real exchange rate thatbreaks the perfect correlation of the complete markets model.Existing models of exchange rate behavior fall into two broad classes. Oneclass of models uses Arbitrage Pricing Theory (APT) to derive parity conditionsthat determine exchange rates. This class of models postulate exchange ratesas functions of ’fundamental variables’, such as relative money supplies, interestrates and outputs across countries, in an ad hoc manner. The ad hoc nature ofthe functional forms would have been less relevant if it generated serious gainsin predictive capacity, but this class of models is generally outperformed by a1 For example Chari, Kehoe and McGrattan (2002), Betts and Devereaux (2000) and Dumas(1992)2
naive random walk, limiting their e ectiveness2 . Another class of models takesa more structural approach to the problem by relating real exchange rates toratios of marginal utilities of representative consumers across countries. A standard reference is Backus and Smith (1993). However, an empirical assessmentof stripped down versions of this class of structural models yields much roomfor improvement3 . Even richer versions, such as Betts and Devereux (2000) orChari, Kehoe and McGrattan (2002), (CKM hereafter), that incorporate nominal rigidities and monetary shocks remain limited in their e ectiveness. CKM isparticularly enlightening since they rigorously examine monetary models with‡exible and sticky prices under the various hypotheses popular in the literature. CKM further shows that the Backus and Smith result of a structurallink between relative consumptions and bilateral real exchange rates applies inmonetary models as well and generates theoretical predictions that are the mostat odds with the data.The nding that limited commitment in asset markets breaks the tight linkbetween consumption and real exchange rate is in line with a nascent literaturepointing to asset market frictions as a promising tool in modeling exchange ratebehavior. Cochrane, Brandt and Santa-Clara (2005) identify asset markets asthe primary drivers of the disconnect between consumption and real exchangerates. Sarkissian (2003) shows that incomplete consumption risk sharing cangenerate realistic time-varying risk premiums in the foreign exchange market.Choi (2005) identi es an empirical relationship linking exchange rates and consumption ratios by introducing relative trade ‡ows into the analysis. Furthermore, her results clearly point to a model with either taste shocks or limitedcommitment as potentially giving rise to that empirically consistent relationship.The rest of the paper is arranged as follows: Section 2 describes the problemin detail and presents the empirical evidence, section 3 presents the benchmarkcomplete markets and the limited commitment models, section 4 discusses themechanics of the models, section 5 outlines a calibration of the model and section6 concludes.2EvidenceHere I will set out the problem that the paper addresses by reviewing the relatedliterature and documenting the empirical evidence on bilateral real exchangerates and fundamentals. In addition I present empirical evidence for a largerset of international macroeconomic data that helps evaluate model performancealong several other important dimensions. The analysis uses annual data fromthe Organization for Economic Cooperation and Development (OECD) andWorld Bank databases covering the period 1980-2000 for Australia, Austria,Belgium, Canada, Denmark, Finland, France, Germany, Greece, Iceland, Italy,2 See3 ForFrankel and Rose (1996) for a thorough surveyexample Kollman (1995) or Head, Mattina and Smith (2003)3
Japan, Korea, the Netherlands, New Zealand, Norway, Portugal, Spain, Sweden,the United Kingdom and the United States.42.1DataThe real exchange rate is based on the purchasing power parity and is a keymeasure of competitiveness for an open economy. It is de ned asRER ePPwhere e is the direct quote nominal exchange rate, P is the price level in theforeign country and P is the domestic price level. Common measures of pricelevels are the consumer price index, the wholesale price index or the consumption price de‡ator. The consumption price de‡ator lends itself naturally as ameasure of price level when examining the relationship between real exchangerates and relative consumptions.The empirical evidence on real exchange rate ‡uctuations is quite stark.Figure 1 shows the rst di erence of natural logarithms of bilateral real exchangerate and the ratio of consumptions for the United States and Japan. Whilenot a statistical measure it illustrates the apparent lack of any relationshipbetween relative real consumption and real exchange rate, with brief periods ofco-movement followed by equally brief periods of counter-movement. Table 1documents the correlation between level and log-linear ltered U.S. bilateral realexchange rate and relative consumptions for the twenty industrialized countriesin the sample. These two transformations are commonly used in the literatureand they show similar results. The numbers for the correlation between realexchange rate and relative real consumption are consistent with various previousstudies, including Backus and Smith (1993) and Corsetti, Dedola and Leduc(2004). The correlation is weak, with a mean of -0.09 and 0.05 and standarddeviations of 0.4 and 0.3 for level and linear lter, respectively. These lowcorrelations illustrate the central issue of an apparently weak connection betweenfundamentals and real exchange rates.Real exchange rate movements are characterized by large and persistent deviations from purchasing power parity (PPP). Under standard theory, wherePPP holds, nominal exchange rate movements should directly o set relativeprice movements, resulting in unitary real exchange rates. However in practice nominal exchange rate movements and relative price movements are notsynchronized in the short run leading to large deviations from unity in the realexchange rate. In low in‡ation, industrialized countries, that are the focus ofthis study, most of the volatility in real exchange rates comes from nominalexchange rate movements. In emerging market countries, where two- and threedigit in‡ation rates are common, nominal exchange rate movements would makeup only a modest fraction of real exchange rate ‡uctuations. Formally the deviations from PPP are summarized by examining the half life of innovations to4 The sample of countries is chosen based on the availability of sectoral consumption andGDP data. For a detailed description of the series see the data appendix4
real exchange rates which are obtained from the following regression equationlog (RERt ) 0 1t 2log (RERt1) twhere RER is the real exchange rate de ned using the consumption price de‡ator as price level and is white noise. Constructing the twenty possible bilateralU.S. real exchange rates in the sample the values of 2 range from 0.607 for theNetherlands implying a half life of 17 months to 0.882 for Canada implying ahalf life of 66 months. The full set of results is presented in table 2.A model of real exchange rate and fundamental ‡uctuations will also generate theoretical predictions for a larger set of economic variables. These modelpredictions can be compared with the empirical evidence for a larger set ofinternational data in assessing the quality of the model. An economy is summarized by its national income and product accounts (NIPA). The NIPA breakdown gross domestic product into private and government consumption, investment and the trade balance. In the model presented in section 3 there is nogovernment or investment, thus data on these items in the NIPA are omitted.Correlations with the U.S. variable for linearly detrended aggregate and disaggregated consumption and gross domestic product are presented in table 3. Theaverage correlation of aggregate output for the twenty countries is 0.837. Theaverage correlation of aggregate consumption is 0.176. At the disaggregatedlevel the average correlation with the United States is 0.768 for tradeable grossdomestic product and 0.796 for nontradeable gdp. Disaggregated consumption correlations are 0.128 for the traded and 0.078 for the nontraded sectors.Output correlation across countries that is higher than the correlation of consumption at both aggregate and disaggregated levels is a feature of the datathat presents a signi cant challenge for structural models with risk sharing.2.2LiteratureThe relatively large literature linking fundamentals to exchange rates has by andlarge produced negative empirical results, rejecting existing theoretical models.At the same time a number of studies point to preference shocks as a device forreconciling theory with empirical evidence.5 However, preference shocks arean unsatisfactory device for a structural theory of exchange rate ‡uctuation.One of the contributions of this paper is to show that introducing default inasset markets is observationally equivalent to preference shocks in a two sectoreconomy. This is an important result because asset market frictions, unlikepreference shocks, can be measurable and predictable. The related literatureis surveyed in order to place the current study in a broader context.Meese and Rogo (1983) challenged the validity of the class of models mostused to forecast exchange rates in their empirical analysis. This class of models,working under the assumption that the exchange rate is the relative price offoreign and domestic money, attempt to tie the exchange rate to money suppliesusing arbitrage pricing theory. Starting with a money market equilibrium5 Forexample Stockman and Tesar (1995) or Kollman (1995)5
equation, mt pt yt it t , for home and foreign countries these modelsderive the expression for the exchange rateptpt (mtmt )(ytyt ) (itit )(tt)This equation assumes that the uncovered interest parity (UIP) holds eventhough numerous studies have documented large departures from UIP in international nancial data. Further identi cation of the exchange rate relieseither on the PPP or a price friction adjusted version of it that attempts to capture the observed large departures from PPP in price and exchange rate data.This class of exchange rate models are based on the assumption of full arbitragein nancial markets. One of the drawbacks of such models is that they onlyimplicitly incorporate individual behavior that ultimately drives all the results.Distortions, such as asset market or information frictions, or transaction costs,to name a few, could signi cantly alter underlying individual behavior but wouldnot be re‡ected in this class of models. The main results obtained by Meeseand Rogo (1983) and con rmed ten years later by Frankel and Rose (1996)show that a naive random walk predicts exchange rates as well as this class ofmodels. The ad hoc nature of the theoretical relationships is one of the keyweaknesses of this class of models, making them in‡exible to di erent aspectsof individual behavior.A more structural approach to exchange rate determination was taken byBackus and Smith (1993), (B&S hereafter). In their model, used as the benchmark in this paper, key aspects of individual behavior lead to a straightforwardrelationship between real exchange rate and relative consumption. B&S modeleach country as a utility maximizing agent with preferences over consumption ofmultiple goods. In equilibrium marginal utilities are equalized across countriesleading to a direct theoretical link between the cross country ratio of consumptions and their bilateral real exchange rate. B&S further show that undercomplete markets the real exchange rate is related to relative consumption viaCtCtRERt (1)where RER is the real exchange rate, is a constant, Ct is the home country aggregate consumption at time t and * denotes the foreign variable. Thisrelationship holds in a number of environments, including trade frictions andnontraded goods if markets are complete and there are no preference shocks6 .The relationship between consumption and real exchange rate is intuitively appealing since choices between traded and nontraded goods or foreign and domestic consumptions should depend on the relative price – the real exchange rate.Clearly equation (1) predicts a perfect correlation between relative consumptionand the real exchange rate in contrast to empirical evidence. The strength ofthe B&S model is that various complications and frictions can be introducedwith clear implications for individual behavior a ecting the link between thereal exchange rate and relative consumption.6 SeeBetts and Devereaux (2000), Chari, Kehoe and McGrattan (2002), Dumas (1992)6
Head, Mattina and Smith (2003), (HMS hereafter), use data for Canada,Denmark, Finland, France, Italy, Japan, New Zealand, Sweden, the U.K. andthe U.S. to empirically test the relation between real exchange rate and relative consumption in a wide range of permutations on the B&S model. HMSintroduce money, habit persistence, asset market frictions and alternative speci cations for aggregate consumption in testing structural models of real exchangerate ‡uctuations. The results they nd are negative, in the sense that the models do not perform well empirically. The speci cations that most improve theempirical performance are asset market frictions and preference shocks. WhenHMS introduce asset market frictions by restricting the set of available securitiesto a single, uncontingent bond the empirical performance of the model improvesbut is still weak. Habit persistence in agent preferences also improves performance but, once again, the model remains weak empirically. The results arein line with the literature pointing to taste shocks or asset market frictions as away of reconciling this class of structural models with the empirical evidence.7Two sophisticated analyses of the structural model are o ered in Stockmanand Tesar (1995) and Chari, Kehoe and McGrattan (2002). Stockman andTesar (1995), ST hereafter, calibrate a two country real business cycle modelwith traded and nontraded sectors and compare the model predictions with theempirical evidence. Complete asset markets in the ST model result in a perfectcorrelation of relative consumption and real exchange rate, a result consistentwith B&S. Signi cantly, the model is successful at matching second momentsfor most fundamental variables. ST further nd that introducing taste shockssigni cantly improves model performance in matching the correlation of real exchange rate and relative consumption without detracting from the performancein matching second moments in fundamental variables. Chari, Kehoe and McGrattan, (CKM hereafter), calibrate a two country general equilibrium modelwith production, nominal rigidities and monetary shocks. They model the setof commodities as two traded goods, each exclusively produced by one of thecountries. Sticky prices and monetary shocks generate deviations from PPPbut do not a ect the correlation of real exchange rate with relative consumption.CKM experiment with a number of environments but nd that the real exchangerate is perfectly correlated with relative consumption under both complete andincomplete markets. The asset market friction CKM introduce is to limit theset of traded securities to a single uncontingent bond. The only improvementin model performance in replicating the correlation of relative consumption andreal exchange rate is generated by making preferences non-separable in consumption and leisure. This speci cation generates e ects similar to preference shocksby changing marginal utility through variation in the labor input in responseto productivity and monetary shocks. The calibrated models ST and CKMexamine lead to the conclusion that demand shocks or asset market frictionsare necessary for reconciling empirical evidence and theory on the correlationof real exchange rate and relative consumption.Choi (2005) presents the rst empirical study with positive results for a7 SeeKollman(1995), Stockman and Tesar (1995)7
structural model of real exchange rate ‡uctuation. In parallel to this paper Choiexamines the relation between real exchange rates and relative consumptions byaugmenting the standard consumption speci cation with relative trade ‡ows andtraded sector consumptions. In the B&S model the real exchange rate is linkedto consumption by
tice nominal exchange rate movements and relative price movements are not synchronized in the short run leading to large deviations from unity in the real exchange rate. In low in ation, industrialized countries, that are the focus of this study, most of the volatility in real exchange rates comes from nominal exchange rate movements.
Exchange Rate Systems (continued) In a fixed-exchange-rate system exchange rates are set at officially determined levels. The official rates are maintained by the commitment of nations' central banks to buy and sell their own currencies at the fixed exchange rate. Real Exchange Rate The real exchange rate is the number of
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