6 major in international makro ekonomic

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This PDF is a selection from an out-of-print volume from the NationalBureau of Economic Research

Volume Title: NBER Macroeconomics Annual 2000, Volume 15

Volume Author/Editor: Ben S. Bernanke and Kenneth Rogoff, editors

Volume Publisher: MIT PRess

Volume ISBN: 0-262-02503-5

Volume URL: http://www.nber.org/books/bern01-1

Publication Date: January 2001

Chapter Title: The Six Major Puzzles in International Macroeconomics:

Is There a Common Cause?

Chapter Author: Maurice Obstfeld, Kenneth Rogoff

Chapter URL: http://www.nber.org/chapters/c11059

Chapter pages in book: (p. 339 - 412)


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MauriceObstfeldndKennethRogoffUNIVERSITY FCALIFORNIA,BERKELEYND NBER;AND HARVARDUNIVERSITY ND NBER

T h e S i x M a j o r P u z z l e s i nInternational Macroeconomics:I s T h e r e C o m m o n C a u s e ?

1. IntroductionInternational macroeconomics is a field replete with truly perplexing puz-zles, and we generally have five to ten (or more) alternative answers toeach of them. These answers are typically very clever but far from thor-oughly convincing, and so the puzzles remain. Why do people seem tohave such a strong preference for consumption of their home goods (thehome-bias-in-trade puzzle)? Why do observed OECD current-accountimbalances tend to be so small relative to saving and investment whenmeasured over any sustained period (the Feldstein-Horioka puzzle)?Why do home investors overwhelmingly prefer to hold home equity as-sets (the home-bias portfolio puzzle)? Why isn't consumption morehighly correlated across OECD countries (the consumption correlationspuzzle)? How is it possible that the half-life of real exchange-rate innova-tions can be three to four years (the purchasing-power-parity puzzle)?Why are exchange rates so volatile and so apparently disconnected fromfundamentals [the exchange-rate disconnect puzzle, of which the Meese-Rogoff (1983) forecasting puzzle and the Baxter-Stockman (1989) neutral-ity-of-exchange-rate-regime puzzle are manifestations]?What we attempt to do in this paper is to offer a unified basis forWethankJayShambaughandJuanCarlosHallak or excellentresearchassistance,andtheNational Science Foundation for support. We gratefullyacknowledgeCharlesEngel forsharingdata andRobertFeenstra orhelpfuladvice. We have benefited fromcommentsbyOwen Kosling, MichaelKremer,RichardPortes, Assaf Razin, Helene Rey, Alan Taylor,JeffreyWilliamson,and our discussants, CharlesEngel and OlivierJeanne,on an earlierconferencedraftversion.


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340 *OBSTFELD& ROGOFFunderstanding all of these puzzles, in which the key friction is a (signifi-cant but plausible) level of international trade costs in goods markets.These trade costs may include transport costs but also tariffs, nontariffbarriers, and possibly other broader factors that impede trade.We do not pretend to be the first to make this connection. In a funda-mental contribution to the literature on international trade and finance,Samuelson (1954) argued that the existence of an international transferproblem depends critically on whether there is a home bias in consump-tion, and he showed explicitly how a home bias could be derived fromtransport costs.1 In subsequent research, however, Samuelson's straight-forward approach has generally been abandoned in favor of a morestylized paradigm based on breaking up a country's products into twodichotomous categories, traded and nontraded goods.2 The analysis ofthe present paper suggests that for many purposes, this dichotomousgrouping is far less helpful than the natural alternative of simply intro-ducing trade costs.Especially in our treatment of capital-market anomalies, the approachin this paper differs from the one that is conventionally taken in theliterature. Typically, an author chooses from a menu of plausible capital-market imperfections the one best suited to explain a particular puzzle.We do not deny the importance of a variety of imperfections peculiar tointernational asset markets. Our goal here, however, is to show how farone can go in elucidating major empirical riddles without appealing tointrinsically international capital-market imperfections. Remarkably, wefind that once one allows for trade costs in goods markets, many of themain empirical objections to the canonical models of international macro-economics disappear. Our approach, which is based on a very simplestylized model, seems to be particularly successful in resolving the real-side quantity puzzles. To explain adequately the various pricing puzzles,we would need to develop a much richer framework featuring imperfect1. Obstfeld and Rogoff (1996, Chapter 4) embed trade costs in a version of the Dornbusch-Fischer-Samuelson (1977) Ricardian model and show that Samuelson's transfer-problemanalysis can be extended to a modern dynamic setting. See Krugman (1991) on therelevance of the transfer problem to contemporary debates in international macro-economics.2. A notable exception is Backus, Kehoe, and Kydland (1992), who find that their approxi-mate method for incorporating small trade costs does not resolve the consumptioncorrelations puzzle in a calibrated one-good global real-business-cycle model. Another isDumas (1992), who looks at a dynamic, stochastic, one-good open economy model withtransport costs and explores a number of issues, including the forward exchange-ratepremium. His work is theoretical and qualitative, however, and he does not calibrate hismodel's empirical implications for the various puzzles we look at here. Also, our mainpoints in this paper really require an extension to the multigood case. In a more recentcontribution, Ravn and Mazzenga (1999) examine further the business-cycle implica-tions of transport costs in a variant of the Backus-Kehoe-Kydland model.


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TheSixMajorPuzzles n International acroeconomics341competition plus sticky prices and/or wages, as in the extensive recentliterature on the "new open-economy macroeconomics." Although wedo not present such a model here, we do demonstrate why trade costsmust constitute an essential element, implicitly if not explicitly.The first puzzle we address is the home-bias-in-trade puzzle (Mc-Callum, 1995), which, as we have already noted, is closely related to theclassic transfer problem. Following Wei (1998) and Evans (1999), wediscuss how empirically plausible trade costs, combined with fairly stan-dard estimates of elasticities of substitution across imports and exports,can explain much of the puzzle.

Having established the trade friction at the core of our analysis, we nextturn to one of the most robust and intractable puzzles in internationalfinance, the Feldstein-Horioka puzzle. We show that trade costs cancreate a wedge between the effective real interest rates faced by borrowersand lenders. In our model, the effect is highly nonlinear, manifesting itselfstrongly only when current-account imbalances become very large. Weargue that it is precisely such incipient real-interest-rate effects that keepobserved current-account imbalances within a modest range. Though werely primarily on the theoretical force of the argument, we do demonstrateempirically that current-account-deficit countries tend to have higher realinterest rates, as our model predicts.Next, we show that the same approach can simply and elegantly ex-plain the widely discussed home bias in equity holdings (or, more gener-ally, in overall asset positions). The following section covers the con-sumption correlations puzzle, which is closely related to the precedingthree, so it is not surprising our same approach again applies. We alsobriefly address other related puzzles.

We largely ignore nominal rigidities in our discussion of the first fourpuzzles, because our main argument does not depend upon havingthem. But as we turn to our last two puzzles-the purchasing-power-parity puzzle and the exchange-rate disconnect puzzle-we obviouslymust think about adding other ingredients, in the form of imperfectcompetition and some degree of price or wage rigidity. We neverthelessargue that trade costs in output markets must be an essential ingredi-ent in resolving these puzzles as well. The final section concludes andalso evaluates our results in the light of long-term trends in worldtransport costs.2. ThePuzzleofHomeBias n TradePuzzle1)The starting point for all the puzzles we examine is the growing evidencethat international goods markets appear to be far more segmented than is


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342 *OBSTFELD& ROGOFFcommonly supposed. Perhaps the most dramatic suggestion of segmenta-tion stems from the work of McCallum (1995). Using a simple Tinbergen(1962) gravity model of trade that controls for distance, trading-partnersizes, and a small number of other factors, McCallum found that tradeamong individual Canadian provinces was twenty times greater thantrade between individual Canadian provinces and individual U.S. states,a surprisingly high differential. It is true that the subsequent literature hasboth tempered McCallum's estimates and challenged their interpretation.McCallum's calculations were based on the year 1988, still at the dawn ofthe U.S.-Canada free-trade agreement, and before trade patterns hadtime to adjust fully. Using data for 1993-1996, Helliwell (1998) found thatthe unexplained home bias had fallen to a factor of 12, which remains asurprisingly large number. Though intracountry trade data are availableonly for Canada and the United States, Wei (1998) and Evans (1999) useindirect methods to test home bias for other OECD country pairs. Weisuggests that the average bias may be as low as 2.5, while Evans findsvalues intermediate between Wei's and Helliwell's.3 Van Wincoop (2000)argues that even though McCallum controls for state and province size inhis gravity equation, his trade-diversion measure gives an exaggeratedimpression of home bias in global trade because it calculates the bias fromthe perspective of the small country, Canada, rather than from the per-spective of the large country, the United States.4 Overall, a balanced inter-pretation of the literature is that countries do exhibit a considerable degreeof home bias in trade, but the bias is not as extreme as McCallum's originalestimates suggested.But if there is still a significant degree of home bias in internationaltrade, how can we explain it? Clearly, international trade does involveadded border costs such as tariffs, nontariff barriers, and exchange-raterisk (and it is also possible that domestic transportation costs are lowerdue to greater coordination problems in constructing international trans-portation networks). Do these border costs need to be implausibly largeto generate observed home bias, even in the more modest range of Wei's3. Wei (1998) tries to estimate home bias indirectly by assuming that the amount a countryimports from itself is the difference between total production and total exports. How-ever, Wei's 2.5 home bias estimate could be downward biased due to his exclusion of theservice sector. Evans (1999) uses data on selected industries for a number of OECDcountries.4. Van Wincoop (2000) shows that McCallum's measure of trade bias must be carefullyinterpreted to ascertain the negative border effect on U.S.-Canada trade. Because Can-ada's economy is so small relative to that of the United States, a moderate percentagediversion of U.S.-Canada trade into intra-Canada trade amounts to a spectacular per-centage increase in intra-Canada trade. Using U.S. interstate trade data, van Wincoopestimates that the U.S.-Canada border reduces trade between the two countries by atmost 30%.


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TheSixMajorPuzzles n International acroeconomics343and Evans' estimates? Not necessarily, since what really matters is theinteraction between border costs and the elasticity of substitution be-tween home and foreign goods. As this is a recurring theme in ourdiscussion of the various quantity puzzles, it is helpful to take up asimple illustrative example.2.1 A MODELOFTHEINTERACTION ETWEEN RADECOSTSAND THEPRICEELASTICITY F DEMANDHere, we show how costs of international trade can dramatically skewdomestic consumption in favor of home-produced goods.Consider an extremely simple two-country endowment economy, inwhich the utility function of the representative home consumer is givenby

\ 0/(-1)C= (C(H10+cr 1)1) , (1)where CH s home consumption of the home-produced good and CF ishome consumption of the foreign-produced good. Foreign agents areassumed to have identical utility functions inC1 and CF.Home agentsare endowed with YHper capita of the home good, and foreign agentsare endowed with YF.We assume icebergshipping costs T, so that forevery unit of home (foreign) good shipped abroad, only a fraction 1 - Tarrives at the foreign (home) shore. Let PH(PF) be the home price of thehome (foreign) good, and PH(PFj)he corresponding foreign prices, withall prices measured in terms of a common world monetary unit. (Sincewe are in a flexible-price world here, it is not important whether the twocountries share a common currency.) Then, if markets are competitive,arbitrage implies thatPF = P/(l - r), (2)PH= (1 - T)P*. (3)Thus, if p - PF/PH, and p* PF/PH,p* = p(l - T)2. (4)(We will maintain the assumption of competitive markets through thefirst four sections, though our main points would still apply in an imper-fectly competitive setting, as in our discussion of puzzles 5 and 6.)From the first-order conditions for utility maximization by home andforeign agents, we have


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344 *OBSTFELD& ROGOFFCH C(-P (p. (5)Cr C?FCombining (4) and (5) impliesCH 29C!CH(1 - 7) 2C(6)CF CF

For illustrative purposes, consider the easy symmetric case in whichYH= YF.Under that assumption, CH/CF= CF*/CHnd equation (6) reducestoCH CFH= -=(1 - 7)- = p .CF CHThis equation shows that the ratio of home (foreign) expenditure onimports relative to home (foreign) goods isC- - (1 -p)1-pCF CHThus, for example, if there were no trade costs (7 = 0), then pCF/CH = 1.If r = 0.25 (a large number just for goods actually traded but conserva-tive when applied to all of GNP) and 0 = 6, then CH/pCF= 4.2. This ratiois consistent with those we observe for many OECD countries, and thedegree of home bias can easily be made larger by raising 7, raising 0, orassuming that the home country is a small one trading with many like-sized foreign partners.2.2 THENONLINEARRELATIONSHIPETWEEN RADECOSTSAND HOMEBIASIN TRADEThe higher trade costs (the closer 7 is to 1), the greater the impact of a 1%reduction in r on home bias:d log(CH/pCF) =

d log 7 1 - TFor our baseline case of r = 0.25 and 0 = 6, the elasticity of home biaswith respect to trade costs is 7(0 - 1)/(1 - r) = 1.67.


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TheSixMajorPuzzles n International acroeconomics345Obviously, this example is wildly oversimplified. It implicitly assumesa common substitution elasticity across any individual pair of home and

foreign goods, and similarly lumps all goods together as having commontrade costs. It ignores the potential importance of substitution betweendomestic and foreign inputs in production. Nevertheless, it neatly illus-trates how a high elasticity of substitution can explain a large observedhome trade bias even with low trade costs. What then are plausiblevalues for the parameters r and 0?2.3 EMPIRICAL STIMATES F 0Though there is a range of estimates for 0, recent trade studies typicallyfind values for the elasticity of import demand with respect to price(relative to the overall domestic consumption basket) in the neighbor-hood of 5 to 6. Examples include Trefler and Lai (1999), who presentpanel estimates over 1972-1992 for a panel of 28 industries in 36 coun-tries; their preferred estimate is 5.3. That average number reflects esti-mated disaggregated substitution elasticities as high as 21.4 (for indus-trial chemicals) and 18.9 (for electrical machinery and electronics) but aslow as 1.2 (for printing and publishing). Harrigan (1993) looks at three-digit 1983 SITC data for 13 OECD countries representing 90% of OECDoutput and finds elasticities in the range of 5 to 12.Recognizing that much of trade involves imperfectly competitive in-dustries, one can attempt to infer the value of 0by looking at markups ofprice over marginal cost. Using that approach, Cheung, Chinn, and Fujii(1999) look at two-digit industry level data for a range of OECD coun-tries, and impute elasticities typically in the range of 3.5 to 4. Hummels(1999a) tries to disentangle the effects of trade elasticities from those ofsubstitution elasticities within a cross-section framework. Using linearleast squares, he comes up with an average markup of 22%, translatinginto a 0 of 5.6, although other of his estimates of 0 are higher. Finally, intheir classic article on the demand for automobiles-including both do-mestic and foreign makes-Berry, Levinsohn, and Pakes (1995) findprice elasticities of demand between 3.1 and 6.4.5Of course, these studies refer to goods actually traded. As Hummelsemphasizes, one would expect that elasticities of substitution would behigher on average for goods that are not traded. In this case, an estimate5. Studies of monopoly markups in domestic sales, while not necessarily directly applica-ble here, also yield similar estimates for 0. For example, Rotemberg and Woodford (1992)find a markup for the United States of around 20%, corresponding to 0 = 6. In subse-quent discussion, Rotemberg and Woodford (1995) argue that there is great uncertaintyabout actual markups in U.S. industry, but favor estimates in the range of 20% to 40%,that is, 0 between about 3.5 and 6.


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346 *OBSTFELD&ROGOFFof 0 = 20, as Wei proposes, does not seem so wild-eyed. Brown andStern (1989) use 6 = 15 for their policy experiments.2.4 EMPIRICAL STIMATES F TRADECOSTSTThere is far less consensus about the size of trade costs, which include(among other things), tariffs, nontariff barriers, and transport costs. For1993, average tariffs, on a domestic-production-weighted basis, were4.9% for the United States, 7.7% for the European Union, 3.5% for Ja-pan, and 8.9% for Canada.6 As for nontariff barriers, official statisticsonly give information on their existence, not their effectiveness, whichmust be estimated using an economic model. Anderson and Neary(1998) use a simple computable general equilibrium model to estimateuniform tariff equivalents for nontariff barriers for a broad range ofcountries, and typically find estimates on the same order of magnitudeas for tariffs, larger of course for some countries (such as Japan) than forothers (such as the United States). This result is also consistent with thetrade-equation estimates of Lee and Swagel (1997).7Differential international transportation costs are also an importantpotential element of 7.8 If one looks across all commodities on a value-weighted basis, freight and insurance charges for U.S. imports averaged3.6% in 1995, and 3.3% in 1996 and 1997.9 But these numbers consider-ably understate average costs in international shipping. First, As Hum-mels (1999a) shows, average costs are much higher for many other coun-tries (the United States has a vast coastline, and sea shipping tends to bemuch cheaper than shipping by land). Second, these numbers do notinclude other considerable costs of international shipping, including pre-paring the paperwork (bills of lading) needed to clear international cus-toms, and the costs of delays either in transit or at port of entry.Just as empirical measures of the elasticity of substitution betweenhome and foreign goods may be biased downwards, it is also likely thatsimple estimates of average transport costs grossly understate average racross all goods in the economy (due to substitution effects). Table 1 isdrawn from Hummels (1999a), who based his estimates on highly disag-6. See OECD (1996, Table 1.1, row 9).7. Harrigan (1993), however, finds nontariff barriers insignificant compared to tariffs andtransportation costs.8. Recall that Helliwell's and McCallum's estimates use distance in an attempt to controlfor transport costs. Geographical distance is an imperfect measure of these, however.9. The authors are grateful to Robert Feenstra for compiling these numbers based on U.S.Imports of Merchandise,U.S. Census Bureau. The estimates give shipping and freightcharges as a percentage of total value of imports excluding these charges. Importantly,these numbers do not include any inland shipping at point of departure or port ofarrival.


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TheSixMajorPuzzles n International acroeconomics?347Table1 COMMODITY ISTRIBUTION FFREIGHTRATES UNITEDSTATES,1994)a

AveragefreightateCommodity Trade-weighted unweightedAll goods 3.8Food and live animals 8.2 14.1Beveragesand tobacco 6.9 14.4Crudematerials 8.2 15.1Mineralfuels, lubricants 6.6 15.7Animaland veg. oils, fats 7.1 10.6Chemicalsand relatedproducts 4.5 9.0Manuf.goods (bymaterial) 5.3 10.3Machineryand transp. equip. 2.0 5.7Misc.manufactures 4.7 8.3All othergoods, NES 1.0 2.5aSource:Hummels (1999a),compiledfrom U.S. Census Bureau,U.S. Imports f Merchandise.reightcosts includeshippingand insuranceas a percentageof total FASvalue. Calculations re based on 10-digit HarmonizedSystemlevel data(over15,000categoriesof goods). Unweightedshippingcosts arebasedon all individualgoods imported.

gregated 10-digit data. We see from the table that shipping costs formany categories of goods are quite a bit larger than the average (trade-weighted) shipping costs-and this table excludes goods that are nottraded at all.What other factors might be included in r? In a provocative paper, Rose(2000) uses a gravity model to argue that countries with currency unionstrade two to three times as much with each other as countries withseparate currencies. Certainly, currency conversion costs and exchange-rate uncertainty can add to trade costs. While exchange-rate variabilitycan have direct negative effects on capital flows, any direct negative effecton trade flows will result in an additional, indirect source of capital-market imperfection according to our analysis. A similar point can bemade for various informational costs of international trade; see Rauch(1999) and Portes and Rey (1999) for discussion and some empirical evi-dence.10 Differences in legal and payments systems may also add to r.Last, but not least, it is important to emphasize that our analysis hasassumed no home bias in preferences. Suppose we replace the represen-tative home agent's utility function (1) with10. Anderson and Marcouiller (1999) argue that corruption and imperfect contract enforce-ment are major factors in disrupting trade, especially in developing countries. Sinceour main focus is on industrialized countries, we will not consider these categories oftrade cost further here.


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348 *OBSTFELD&ROGOFFU = (C(H )/ + wC 1)/)?/0-1) (7)and the representativeforeign agent's utility function withU* = (wC*(-1)/S + CF-'/1)/0)-1)One can easily show that the effects of home bias in preferences(w< 1)can be isomorphicto the effects of tradecosts r. Helpman (1999)arguesthat once one controls for income, there is no clear evidence of homebias in preferences.Indeed, it is more illuminatingto derive trade biasesfrom other frictions. Nevertheless, it is important to recognize that ahome bias in demand forgoods canwork similarlyto tradecosts, at leastfor the trade and portfolio-biaspuzzles.2.5 OTHERREAL-TRADE U7ZI7.SThough international-financepuzzles are our main focus, we note thattrade costs can explaina numberof real-tradepuzzles as well. For exam-ple, Trefler's(1995)favored explanation of the "missing trade"puzzlecombines Hicks-neutralproductivitydifferencesacross countrieswith ahome bias in consumption (which, per our discussion above, may beinducedby transportcosts).ll Deardorff 1998)points out thatwith trans-port costs, the standard conditions for factor-priceequalization in aHeckscher-Ohlin world break down, also implying greaterspecializa-tion. Since factor-priceequalizationfails miserablyempirically,this im-plies anotherimportant puzzle that can be at least partiallyresolved bytransport costs. Anderson (1979), Deardorff (1998), and others haveshown that transport costs can help explain the surprising empiricalrobustness of the gravity equationof tradeflows. Not only do tradecostshelp to resolve a number of puzzles in the data, they also seem to beimportant in determining economic performance. Radelet and Sachs(1998)arguethat countriesthathave high shipping costs due to adversegeography (for example, high mountains or limited port access) growmuch more slowly than countries with natural transport advantages.Finally,we note that evidence on internationalprice differentialsseemsquiteconsistentwith the high degree of marketsegmentationevinced onthe quantitiesside;we shall refer to this work laterin discussingpuzzles5 and 6.Armed with a simple understandingof how plausible trade costs to-gether with high elasticities of substitution in consumption can explain11. "Missing trade" is how Trefler describes the puzzle that the imputed factor content oftrade does not seem to reflect comparative advantage.


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TheSixMajorPuzzles n International acroeconomics349substantial home biases in trade, we are ready to explore the linkages toother macro puzzles.3. TheFeldstein-Horiokauzzle Puzzle2)There has been no shortage of explanations for the famous saving-investment puzzle of Feldstein and Horioka (1980), with numerous arti-cles on the topic having been published in most of the leading journals.The problem is that none of the explanations advanced to date (includ-ing our own attempts) has been terribly convincing. Most explanationstend to be clever but empirically inadequate and, more troublesome still,tend to fix one puzzle at the expense of creating others. The fact that theFeldstein-Horioka regularity does not seem to characterize intranationalregional data suggests that factors intrinsic to trade between differentnations are at work.123.1 STILLA PUZZLEWhat Feldstein and Horioka actually demonstrated, of course, is thatacross OECD countries, long-period averages of national saving ratesare highly correlated with similar averages of domestic investment rates.Indeed, in the original data sample examined by Feldstein and Horioka,covering 1960 through the mid-1970s, cross-section regressions of invest-ment on saving yielded slope coefficients near unity. True, thisFeldstein-Horioka coefficient-which the original work interpreted asmeasuring the effect of the saving rate on the investment rate, or a"savings retention" measure-has fallen over time. As Table 2 illus-trates, however, it still remains large and significant. The table givessimple cross-country regressions of investment (relative to GDP) againstnational saving (relative to GDP), taking eight-year averages for themost recent period, 1990-1997. For the OECD countries, the coefficient(0.60) is a good deal smaller than the 0.89 found in Feldstein andHorioka's original work, but it is still larger than one might expect in aworld of fully integrated capital markets where global savings shouldflow to the regions with the highest rates of return. The coefficient fallsfurther once one includes countries outside the OECD (particularly poorcountries), although the extended results must be viewed with extremecaution given the poor quality of national income and product data formost non-OECD countries. (The data underlying the regressions in Ta-ble 2 are reported in Table 7 in the appendix, which also describes howthe countries in the sample were chosen.)12. See Obstfeld(1995),Obstfeldand Rogoff(1996),andCoakley,Kulasi,and Smith(1998)forrecentsurveys.


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350 *OBSTFELD& ROGOFFTable 2 FELDSTEIN-HORIOKA REGRESSIONS, I/Y = a + 13NS/Y + E,1990-1997a

No. of obs. a 13 R2All countriesb 56 0.15 0.41 0.33

(0.02) (0.08)Countries with GNP/cap. > 1000 48 0.13 0.48 0.39(0.02) (0.09)Countries with GNP/cap. > 2000 41 0.07 0.70 0.62(0.02) (0.09)OECD countriesc 24 0.08 0.60 0.68

(0.02) (0.09)aOLSregressions. Standard errors in parentheses.bIsraelis excluded from all regressions in this table. If Israel is added to the samples of size (56, 48, 41),the estimates of / are (0.39, 0.45, 0.63).If one adds Korea to the OECD sample, the estimate for 3rises to 0.76. Korea is included in the largersamples.

The Feldstein-Horioka puzzle is durable because the core regressionsimply summarizes in a compact way the fact that OECD current ac-counts tend to be surprisingly small relative to total saving and invest-ment, especially when one averages over any sustained period. Fordeveloping countries, notably the many that have repeatedly had trou-ble servicing debts, it is perhaps not so surprising that creditors preventthem from running up large sustained deficits. But it is hard to appeal tosovereign-default risk for OECD countries, especially when one consid-ers that gross international flows of financial assets are much bigger thannet international flows. Indeed, for OECD countries, asset price compari-sons suggest a high degree of integration; arbitrage in similar nominallyrisk-free assets appears to be nearly perfect. We leave it to the reader tolook at other sources (for example, Obstfeld and Rogoff, 1996, Chapter 3)for assessments of previous attempts to explain the Feldstein-Horiokaconundrum.A fair summary of the literature is that there are at least five or sixleading explanations (and ten or so close seconds). All are unconvincingempirically-some because they are based on very special assumptionsabout the nature of the exogenous shocks (e.g., Obstfeld, 1986, or Men-doza, 1991), others because they raise collateral empirical contradictions.For example, in the asymmetric information model of Gordon andBovenberg (1996), a "lemons" problem is invoked to explain why foreign-ers finance so little domestic investment, yet departures from covered


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TheSixMajorPuzzles n International acroeconomics351interest parity must also be assumed if there is to be any foreign equityinflow at all. Explanations that try to maintain the assumption of perfectcapital mobility often have the strong implication that one should alsoobserve high saving-investment correlations across states or regionswithin a given country. But the partial evidence available on saving andinvestment by subnational regions simply does not produce the Feld-stein-Horioka regularity; see, for example, Helliwell (1998, Chapter 4).We are going to propose here an entirely new explanation, based ontransaction costs for international trade in goods. An especially attrac-tive feature of our approach is that it seems to help resolve other puzzlesrather than exacerbating them.It is important to emphasize that whereas our model includes tradecosts for goods, it is consistent with free and costless trade in securities.Thus, it is perfectly consistent with the observation that gross interna-tional flows of securities are substantial even though net flows are small.Our account is also notable both for endogenizing the price and interesteffects of trade impediments, and for showing how moderate transportcosts could generate empirically significant international differences inreal interest rates despite full asset-market integration.3.2 TRANSPORTCOSTSCAN INDUCEA NONLINEARRELATIONSHIPETWEEN HECURRENTACCOUNTAND THEREAL NTEREST ATEThe basic intuition of why transport costs can temper current-accountimbalances can be illustrated in a standard two-period, two-good, small-country endowment model. It would not be difficult to endogenize theworld real interest rate, or to incorporate uncertainty (as in the nextsection), but neither generalization is essential here. We will later discussinvestment to confirm that the basic argument we make still goesthrough.The model below is entirely standard except that we will again allowfor Samuelsonian "iceberg" costs in trade, so that Tpercent of any goodis lost in transit. The utility function of a representative home resident isu(C) + 8u(C2),where total real consumption C depends on consumption of the homeand foreign goods, CHand CF,with constant elasticity of substitution 0 asin equation (1). The small country is endowed only with good H, withYH,1 in period 1, and YH,2n period 2. Good F must always be imported.(Endowing the country with both goods would not overturn our argu-ment.) The home country is small in the sense that its actions have no


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352 *OBSTFELD&ROGOFFeffect on the world prices PHand PF,which are constant across the twoperiods in terms of a world unit of account (money). Nor can it affect theforeign real interest rate r* (which equals the foreign nominal interestrate assuming there is zero foreign inflation). Because of iceberg transitcosts Tin shipping either good, however, home consumption patternscan affect home relative prices and the home real interest rate.Though we shall give a formal analysis below, the basic argument issimple. Suppose, for example, that the country's endowment pattern andrate of time preference 8 are such that in the first period, net exports ofgood H are negative (in which case intertemporal solvency dictates theymust be positive in period 2). Then, as we shall shortly confirm, therelative price of good H will be higher in period 1 than in period 2. Therewill be expected deflation, and the home real interest rate will be above r*.The situation is reversed when the country is initially running a suffi-ciently large current-account surplus, so that its real consumption-basedlending rate must lie below r*. As we demonstrate formally below, thiseffect can be quite dramatic, assuming realistic values for trade costs andthe elasticity of substitution 0 (values similar to those needed to resolvethe home-bias-in-trade puzzle).133.3 BUDGETCONSTRAINTSAND TRANSPORTCOSTSA formal analysis requires one to think carefully about the budget con-straints facing the representative agent. In general, the first-period bud-get constraint can be written asPH1H,1 + D PH,1CH,l + PF,1CF,1l PlClwhere PH(PF) s the home-soil price of good H (F) in terms of the worldcurrency unit, and D is borrowing from abroad in world currency units.The overall home price level, in terms of world currency units, isP = (Pj-0 + p-)/l- . (8)Therefore, given a total real consumption level C in any period, theconsumptions of the two individual home and foreign goods are

PH - C- (9FCH= ) C, CF= P C. (9)13. Dumas(1992) ikewiseshows how international eal interest-ratedifferentials anarisein a modelwith transport osts, though, as we have alreadynoted, his one-goodmodelis very differentand he does not explore the implicationsfor the Feldstein-Horiokapuzzle.


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TheSixMajorPuzzles n International acroeconomics353Similarly, the second-period budget constraint, measured in worldcurrency units, is

PH,2H,2 - (1 + r*)D = PH,2CH,2 PF,2CF,2 P2C2.Combining the period budget constraints gives the consolidated inter-temporal budget constraint as

P2C2 PH,2YH,2PC11 + =PH, YH,11 + r* 1 + r*or, in terms of the domestic real interest rate 1 + r = (1 + r*)PI/P2, as

C2 PHlyHl 1 PH,2H,2C, + + )PYH (10)1 + r Pi + r P23.4 INFLATIONSince good F is always imported, its home price, PF=PF/(1 - r), must behigher than the foreign price in both periods, per equation (2). By thesame logic, when good H is exported- as it must be in at least one ofthe two periods-its home price PH= PH(1- T)must be lower than theforeign price, per equation (3). However, if total domestic spending ishigh enough relative to income in any given period, it is possible thatgood H is importedrather than exported (CH> YH), in which case itshome price PH= PH/(1- T)must be higherthan the foreign price. As weshall see, there are also important intermediate cases where CH= YH none period, in which case PHwill turn out to lie between P*(1 - r) andP*/(1 - T),despite the fact that no goods roundtrip.3.5 A GRAPHICALANALYSISOFTHELINKBETWEEN EALINTEREST ATESAND CURRENTACCOUNTSThe link between the effective real interest rate faced by the home coun-try and its first-period borrowing decision is illustrated in Figure 1,which plots total real consumption in period 1, C1,against the domesticreal interest rate, 1 + r. (Note that the period 1 current account deficit issimply Y1 - C1). The resulting graph is a step function that can bedivided up into five segments; it shows the schedule of effective realinterest rates faced by the country as a function of its borrowing-lendingdecision.In the first segment C1 is so low, and the period 1 current-accountsurplus so high, that in period 2 the country will consume an amount


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354 *OBSTFELD & ROGOFFFigure 1 DOMESTIC SPENDING AND THE DOMESTIC REAL INTERESTRATE IN A TWO-GOOD MODEL WITH TRADE COSTS

Domestic eal nterest ate,1 + r

V

World eal l /interest -------- --rate,1 +r

First-periodotalrealspending,ClCH,2> YH,2 Since in period 2 the home good must be imported, while inperiod 1 it is exported, we have

(1 + r*) (P,-19 + P- 9)11(1-9)1 + H F(Pk2 ? P:/9)(1 + r*) {[PH(1 - 7)11-0 + Pl-}1/(1- )F= < 1 + r*

{[P/(1 - T)]1- +p/-F 1/-(0)

in segment I. If the country contemplates being a big lender, it will facean effective real interest rate significantly below the world real interestrate.Segment II starts when period 1 consumption first reaches the level Clnsuch that CH,2 = YH,2-In this region, PH,2is determined by equation (8) andthe first relation in equation (9), with CH,2= YH,2 (so there is no round-


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TheSixMajorPuzzles n International acroeconomics355tripping). Period 2 consumption of the home good remains constant atYH,2 s long as PH2remains strictly between P((1 - T)and P*/(1 - T),butequation (9) implies that PH,2alls as C1rises and C2 alls, until PH,2eachesP*(1 - T).Accordingly, the real interest rate rises over segment II.14At thepoint C1= Cm,Segment IIIbegins as the home country becomes a period2 exporter of its endowment good. On this stretch, 1 + r = 1 + r*.Because here, CH< YHn both periods, the overall price level is constantover time. In region III, the country is running a sufficiently smallcurrent-account surplus or deficit that there is never any reversal of thepattern of trade in either good. It is precisely in this region that tradecosts have no effect on the real interest rate.At C1= Cv, however, CH,reaches YH,, and the real interest rate beginsto rise once more. In segment IV, CH, remains stuck at YH,1 as C1rises,pushing PH,1up with it until PH, reaches PH/(1 - 7). As P,H rises alongsegment IV,with PH2constant at PH(1 - T),the real interest rate rises. AtCv, however, where PH, first reaches PH/(1- T), the country becomes aperiod 1 importer of its own endowment good, and the real interest ratestabilizes (along segment V) at the level

+ r(1 + r*) {[PH/(1 - T)]1-o + P1-J}1/(1-) +l+r = >1 + r*{[P4(1 - T)]1'- + Pl-U1/(1-9)The range of possible real interest rates produced by this simple exam-ple can encompass a wide distribution. For example, with r* = 0.05, r =0.1, 0 = 6, and PH= PF= 1, we find that the highest possible real interestrate is 20% (15% above the world level) while the lowest is -8% (13%

below the world level). The interplay between the commodity transportcosts T and the substitution elasticity 0 is similar to what we saw in thepreceding section. As 0 rises, the maximum and minimum real domesticinterest rates move apart-with higher substitutability, the price-levelimpacts of changes in P, are more pronounced. In the limiting case as 0-oo the two goods are asymptotically perfect substitutes, in which casethe country's effective real borrowing rate will be 30%, and its lendingrate, -15%!Of course, the range of real domestic interest rates encompassed byFigure 1 is far greater than what we usually observe in practice, espe-cially for OECD countries. But this simply reflects the fact that incipient

14. The increasing portions of the schedule have the shapes we show for 0-values that areplausibly high.


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356 *OBSTFELD&ROGOFFreal interest differentials put a sharp check on a country's incentives torun large current-account deficits or surpluses.153.6 EXTENSIONSAND ALTERNATIVEORMULATIONSThe preceding account of the effect of domestic spending on real interestrates is overly stylized, but a number of obvious extensions can add torealism without diluting the main message.3.6.1 A Continuum of Goods and TransportCosts Assume, for example,that countries are endowed with multiple goods in various proportionsand that these goods display a distribution of transport costs. Then, asdomestic spending rises, progressively more types of goods are im-ported from abroad, leading to a steadily rising real domestic interestrate. In this more realistic setup, the relationship between expenditureand the home real interest rate will still resemble a version of Figure 1,but with very many small steps-to the naked eye, a smoothly upward-sloping curve. With a rich enough range of goods, transport costs, andelasticities of substitution, even small current-account deficits may pro-duce trade reversals in a small number of goods, thereby resulting in aninterest-rate effect. We conjecture, though it remains to be proved, thatone would obtain a similar nonlinearity to that depicted in Figure 1, withsmall current-account imbalances having relatively little effect on inter-est differentials.3.6.2 Long-TermBorrowingand Lending An obvious question is how theresults here might be tempered in a model with many periods so thatthere are opportunities for long-term borrowing and lending. For exam-ple, if a country ran a big current-account deficit in the initial periods, itcould repay slowly over many periods. Though a more careful analysisis required than we can provide here, it seems unlikely that this consider-ation would overturn our basic point; there would still be a big priceswing between the big deficit periods and surplus periods-which isprecisely why a country would seek to avoid such swings. We note alsothat in a richer model with a continuum of goods, the current accountwould not necessarily have to swing between deficit and surplus toinduce real-interest-rate effects. In general, the range and type of goods15. The suggestion that idiosyncratic real-interest-rate developments might help explainthe Feldstein-Horioka puzzle can be found in earlier work, for example, Frankel(1986). However, to the extent that real-interest-rate effects have been touched upon inthe literature, no one has taken the idea very seriously, since earlier models could notgive any reason why the real interest rate might be so important quantitatively. Norcould they really explain the durability of the Feldstein-Horioka relationship acrossdifferent time periods and regimes.


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TheSixMajorPuzzles n International acroeconomics357being imported and/or exported will vary more or less continuously inthe level of trade-balance deficit (or surplus). Thus, the real-interest-rateeffect will arise along any path where there are big trade-balance swings,either over any short period, or cumulatively over any long period. Thiswould be true even in a setting with growth in which countries could, inprinciple, run perpetual deficits and surpluses.3.6.3 Investment How is the preceding analysis affected by introducinginvestment? In the case where the country desires to be a large netborrower (segments IV and V), the real-interest-rate effect will be tem-pered to the extent the country can cut back on investment instead ofborrowing from abroad. But that very mechanism dictates that reduc-tions in national saving will be accompanied by reductions in domesticinvestment. In segments I and II, the country could channel some of itshigher savings into higher investment, again tempering the fall in theeffective real interest rate but creating the positive Feldstein-Horiokacorrelation between increases in saving and increases in investment.163.6.4 Deriving SimilarResults in a More ConventionalSetupwith TradedandNontradedGoods The reader may well ask whether we needed such anextravagant formulation to make the basic point that the consumption-based real interest rate can be linked to the current account. Couldn't wehave made the same point in the context of a standard Salter-Swanmodel having two classes of goods, one with infinite trade costs and theother with zero trade costs (as discussed, for example, in Chapter 4 ofObstfeld and Rogoff, 1996)? Indeed, for a pure endowment case, thestandard traded-nontraded model does produce a graph very much likeFigure 1. Holding endowments of both goods flat, if the country choosesto run a large deficit in period 1, the price of nontraded goods will behigh in that period, and low in the following period. This implies aconsumption-based real interest rate above the world interest rate, justas in segments IV and V of Figure 1, and the effect can similarly be non-linear. We prefer our formulation largely because it is much easier tothink concretely about trade costs than about the arbitrary dividing linebetween traded and nontraded goods. Perhaps the ideal model wouldbe a richer one incorporating a range of transport costs in which thedegree of tradability is endogenous and some goods are consistentlyproduced exclusively for the home market.16. Though their focus is on the short-run time-series properties of the data rather than onthe Feldstein-Horioka regularity, Backus, Kehoe, and Kydland (1992) do note that asmall trade cost can sharply reduce the variability of net exports in their simulations.


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358 *OBSTFELD&ROGOFF3.6.5 Monopoly Pricing and Sticky Prices Our analysis assumes thatprices are flexible and set in competitive markets. Introducing realisticfeatures such as price rigidity and monopoly pricing, as in our discus-sion of puzzles 5 and 6, would enrich the model without overturning themain points. Also, the most troubling manifestations of the Feldstein-Horioka puzzle are at medium-term horizons of five to fifteen years,when price flexibility is much greater and firms' ability to preserve mo-nopoly power is less.3.7 EMPIRICSThe model does contain one simple prediction that can easily bechecked. Countries running current-account surpluses should havelower real interest rates than countries running deficits.This connection is illustrated in the panel regression results reportedin Table 3. Specification 1 regresses the domestic real interest rate, de-fined as the average three-month nominal interest rate in a given yearless lagged annual inflation, on the ratio of the current-account surplusto GDP. Specification 2 forms real interest rates by using December aver-age nominal interest rates in year t less year t inflation, in an attempt to

Table 3 REAL NTEREST ATESAND THECURRENTACCOUNT,1975-1998CoefficientonCA/GDP Significance p R2

SpecificationOLS -36.9 0.00 0.65 0.05Countryfixed effects -46.3 0.00 0.65 0.08Countryfixed effects, time dummies -32.3 0.00 0.55 0.50SpecificationOLS -17.9 0.00 0.58 0.02Countryfixed effects -19.4 0.00 0.58 0.05Countryfixed effects, time dummies -18.9 0.01 0.54 0.32Thedependentvariable s theannualized hree-monthnominal nterestrate ess laggedannual nflationCPIrate(specification1) or less the contemporaneousnflationrate(specification2). Thesampleusesannualdata and coversthe years1975-1998andallOECDcountriesexceptIceland,Korea,Mexico,andTurkey.Currentaccounts(as a percentageof GDP)are reportedby the OECD. We use three-monthinterestrates,usuallyaTreasury illrate,but an interbank ate fno governmentrate s available.Thesedatacome fromInternationalinancial tatistics nd the OECD.CPI nflationrates are basedon IFSdata.For the specification2 regressions,four countriesdid not report monthlyinterest-ratedatauntil afterthe startof oursample.Thecountries,with theirstartingdatesin parentheses,areSpain(1977),Greece(1980),Portugal 1985),and Finland 1987).


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TheSixMajorPuzzles n International acroeconomics359capture that agents can incorporate contemporaneous information intoforming inflation expectations. In both specifications we employ anautoregressive correction. We report estimates for simple ordinary leastsquares (OLS), a model with country fixed effects, and a model withfixed effects and time dummies (the latter to capture global influences onnational real interest rates).The results show highly significant negative correlations between thecurrent-account surplus and the real domestic interest rate, as our modelsuggests. However, the two specifications differ somewhat in their nu-merical predictions, with specification 1 giving an effect that is substan-tially larger than that given by specification 2. Taking the regressionswith country fixed effects and time dummies as likely to be most reliable,we see that a 1% of GDP rise in an OECD country's current-accountsurplus is associated with roughly a 20- to 30-basis-point decline in itsreal interest rate.174. ThePuzzleofHomeBias in EquityPortfoliosPuzzle3)Despite the rapid growth of international capital markets toward theclose of the twentieth century and a much expanded world market forequities, stock-market investors maintain a puzzling preference forhome assets. When they first highlighted the extent of the home-biasportfolio puzzle at the end of the 1980s, French and Poterba (1991) ob-served that Americans held roughly 94% of their equity wealth in theU.S. stock market whereas the Japanese held roughly 98% of their equitywealth at home.18 Figure 2, drawn from Tesar and Werner (1998), sug-gests that the home equity bias is muted for smaller countries and hasshown some tendency to decline over time-by the mid-1990s about10% of U.S. equity wealth was invested abroad. Standard models ofoptimal international portfolio diversification imply, however, that eq-uity investors still have not diversified internationally nearly as much asthey should, and so the puzzle remains.1917. Weexperimentedwith anumberof otherspecifications, xpectedinflationproxies,andtimeperiods, almostalways findingresults similar o those reported n Table3. Gordonand Bovenberg(1996)also establish a relationshipbetween currentaccounts and realinterestrates forOECDcountries,but theirtestandtheirspecificationaremotivatedbya model that is very different hanours.18. See also Golub(1990),who comparedgrossinternational sset flows with grossdomes-tic asset creation or OECDcountries.19. Universityof California nvestment policies illustratethe extent and persistence ofhome bias even for large, sophisticatedinvestors. On April20, 2000,the U.C. regentsannounced a revision in investment guidelines for the university's retirementandendowment funds. The overall target portfolio share for equities remained at 65%,but the recommendedtargetshare for non-U.S. equities, previouslyzero,was raised


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360 *OBSTFELD&ROGOFFFigure2 HOMEBIASIN EQUITYPORTFOLIOS:987-1996

262422 , ,

. 16 |;~~~~~~~ 16-\----- -l- - -I. K.S 14 (-Germany

| f10^ y^^"^^"*- - -Canadal 12l f ~----- Japan

X. 4

1987 1988 1989 990 1991 2 13 1994 15 19961987 1988 1989 1990 1991 1992 1993 1994 1995 1996

From Tesar and Werner (1998)Potential explanations range from nontraded factors such as humancapital (which may worsen or reduce the puzzle; see Baxter and Jermann,1997) to nontraded consumption goods to asymmetries of information todata inadequacy. Yet it is fair to say that none of the available stories alonehas provided a quantitatively satisfactory account of the observed homebias; see Lewis (1999) for an up-to-date and thorough survey.To set the stage for our discussion of trade costs, it is worthwhilebriefly reviewing what is perhaps the leading explanation, which isbased on the classic Salter-Swan traded-nontraded-goods dichotomywe have already mentioned. While these two types of goods lie at polarextremes in terms of their tradability, equity claims on either type ofindustry can be frictionlessly traded. Thus, even though cement isprohibitively costly to transport, there is nothing to stop foreign inves-tors from buying shares in the domestic cement industry. Earnings, ofcourse, must be redeemed in traded goods, since nontradables cannot

be shipped to foreign equity holders by assumption. The key result onegets out of this framework is that, for the baseline case of separableto 7%. The positive target position in foreign equities, meant to "reduce risk andbroaden portfolio diversification while maintaining or improving investment perfor-mance," represents a substantial advance. It still falls far short, however, of the optimalforeign equity share that simple models of international diversification would predict.


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TheSix MajorPuzzles in InternationalMacroeconomics?361preferences (across the two types of good), investors hold a globallydiversified portfolio of traded-goods industries. But nontraded-goodsindustries are held entirely domestically. The intuition is that, sincepayments can only be made in traded goods and utility is separable,there is no way to enhance risk sharing in tradables by linking theallocation of tradables consumption to returns in nontraded-goods in-dustries. (That intuition has to be modified for the case of nonseparablepreferences, but it is still a useful reference point.20) Thus, if nontradedgoods constitute, say, 50% of total output (a popular rule of thumbbased on the fact that for many OECD countries, services, construction,and transport constitute roughly 50% of GDP; see Stockman and Tesar,1995), then agents will (loosely speaking) hold more than half theirequity in home assets.While elegant, this explanation still is not entirely satisfactory. First,although it goes some way toward explaining home bias, it falls short ofexplaining the 80% to 90% domestic equity shares we actually observe(Figure 2). Second, the sharp dichotomy between traded and nontradedgoods is a contrived one, since in reality transport costs differ acrossgoods, and a particular good may or may not enter trade under differentmarket conditions. For most goods, tradability is not absolute andtradedness is endogenous.21Here we will take an approach based on intuition similar to that in thepreceding discussion. We explore just how far can one get in explainingthe home portfolio bias by explicitly introducing trade costs, rather thansplitting goods into two arbitrary and dichotomous categories. What wewill show is that, with a plausible elasticity of substitution across goodsand reasonable-sized costs for trading them, our model can produce avery high and realistic level of home portfolio bias.4.1 A SIMPLEMODELWe now add uncertainty to the two-country general equilibrium versionof our model, with each country having a random endowment of itsdistinct perishable consumption good, along the lines of Lucas (1982) orCole and Obstfeld (1991). To keep notation simple, we again abstractfrom dynamics and consider a one-period portfolio problem. We as-sume a completely symmetric joint distribution for the national outputs(YH YF).A home or foreign individual chooses state-contingent consumptionsCHand CFof the home and foreign goods in order to maximize20. Baxter,Jermann,and King (1998)develop some results for the case of nonseparablepreferences.21. Fora morethoroughdiscussion, see Obstfeldand Rogoff(1996,Chapter5).


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362 *OBSTFELD&ROGOFF1 -/ \0/(f-1)~ -p cl-pEU = E C8-1)/.+ C(0-1)/ =E . (11)1-p H F / _ J1)- p

Above, C is the index of total real consumption [per equation (1)], 0 isconsumers' elasticity of substitution between the two goods, and p isthe coefficient of relative risk aversion.There is free and costless international trade in a complete set of state-contingent Arrow-Debreu securities. (Imagine again that the securities'payoffs are made in a costlessly tradable international monetary unit ofaccount.) We continue to assume that there are iceberg costs of trade,such that only a fraction 1 - r of a unit of good shipped abroad reachesits destination, so that under competitive markets PF = PF/(1- r)and PH= (1 - r)PH,per equations (2) and (3).22Because, in addition, the countries are symmetric, free trade inArrow-Debreu securities yields an allocation in which1 aU 1 aU

PHaCH PHaCHand1 au 1 aU*

PF aCF PF aCFfor every state of nature, orCHV1C1/8-P= (1 - r)CZ-V0C*1/-P (12)and(1 - r)C^F~/Cv'-p = CF-1/0 C*l/-P. (13)Together these conditions imply the ex post consumption efficiencycondition

PH CF CF PHThe model is closed by the output-market clearing conditions:

22. Just as in our discussion of the trade-bias puzzle, one could obtain similar results onhome bias in equity holdings if trade costs were zero but there existed a home bias inpreferences along the lines of equation (7).


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TheSix MajorPuzzles in InternationalMacroeconomics?363H = (1 - T)(YH- CH),

CF = (1 - r)(YF - CF)Four of the preceding five equations are independent and yield solutionsfor the consumption levels CH,CF,CH,and CF.4.2 INTERPRETINGHEMODELIt may puzzle some readers that we focus on the Arrow-Debreu alloca-tion when in fact we are interested in relating our analysis to observedtrade in the narrower class of equity-type assets that one observes in thereal world. One rationale, perhaps, is that we do not want our theoreti-cal home bias results to be driven by ad hoc assumptions about the kindsof securities that can be traded, especially since many assets like debtand direct foreign investment have complex optionlike qualities thatmay be difficult to summarize in a simple model. A second, more prag-matic, rationale is that the equilibrium for the complete-markets case isrelatively simple to compute. A final rationale, as we shall see, is that forrealistic parameters, trade in equities alone can come quite close to attain-ing the complete-markets consumption allocation, so that the home biasevident under complete markets is a good guide to the home bias in anequities-only model.4.3 EVALUATING HEHOMEBIASIt is helpful to begin by analyzing the special case p = 1/0, in which theArrow-Debreu conditions (12) and (13) simplify enormously. One canalso show that the Arrow-Debreu allocation is then identical to the onein which people can trade only straight equity shares. Given our assump-tion of symmetry, the equilibrium portfolio shares are

1XH + (1 -)1H(1 - )0-1

XH= Y-11 + (1 - T)(1 - y)0-1XF= Y,1 + (1 - r)o- F

11= Y(1 + (-1 -)0-1F


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364 - OBSTFELD& ROGOFFwhere XH (XF)denotes the home agent's share of total equity in the home(foreign) industry, and XH(X*)denotes the foreigner's optimal equityshares. Note that if we were to translate these equity positions intoconsumptionshares, we would find cF and cH ower than XFand X*by afactor of 1 - r, reflecting the trade costs. Of course, in the absence oftrade costs all the portfolio (and consumption) shares would equal 0.5,reflecting full diversification (under symmetry).For 0 = 6 and trade costs of r = 0.25 (again, a seemingly reasonablenumber when applied to all of output, especially compared to the usualassumption that fully half of output is nontraded), one obtains XH= 0.81,XH = 0.19. Since share prices will be equal due to symmetry, this impliesa home equity share of 81%. If 0 = 10, then the home portfolio share ofhome equities is 72% even with trade costs of just 10%. (As in the caseof home bias in trade, there is significant nonlinearity: the elasticity offoreign shareholdings with respect to trade costs is very high when r isnear 1, but falls as trade costs fall.) The preceding calculations constrainthe value of p to equal 1/0, but, as we shall now demonstrate numeri-cally, the results turn out to be remarkably insensitive to this assump-tion, given realistic levels of output uncertainty.If we relax our restriction p = 1/0, the exact conditions needed toimplement the Arrow-Debreu allocation through equity trade alone arebroken. Trade costs create an international wedge between marginalrates of substitution such that standard stock-market spanning theoremsno longer apply.23Nevertheless, one can still gain a good deal of insightinto home bias by computing the state-contingentconsumptions of thetwo goods in the Arrow-Debreu efficient allocation.We can reduce the dimensionality of our numerical simulations bynoting that, in equilibrium, the ratios of consumption to output, H CH/YHJ F CF YF, c - CH/YH, and cF= C*/YF, depend only on the outputratio YH= YH/YF. Table 4 illustrates how the consumption ratios CHand CFdiffer both across states of nature and across a number of settings of theparameters r, 0, and p.24 (The values of cH and cFare apparent from theassumed symmetry of the model.) Notice that the home country's out-put shares decline across states of nature as its relative endowment rises.That pattern compensates the foreign country for the greater share oftransport costs it must pay in states of nature such that home output isrelatively high, and it is naturally more pronounced the higher the riskaversion parameter p.For the cases in which 0 = 6 and Tis 10% or 20%, the table documents23. See Obstfeld and Rogoff (1996, Section 5.3).24. In a "baseline" model with trade frictions in which individuals nonetheless consumethe proceeds from fully diversified portfolios, we would have CH= and F = (1 - r)/2.


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TheSixMajorPuzzles n International acroeconomics365Table4 PORTFOLIO OSITIONSN HOMEAND FOREIGNGOODSFORSTATEOFNATUREYH YH/YF

Parametersettings Portfolioshares H, CF

T p YH= 0.8 0.9 1.0 1.1 1.20.1 2 2 0.53, 0.43 0.53, 0.43 0.53, 0.43 0.53, 0.43 0.52, 0.420.1 3 2 0.56, 0.41 0.55, 0.40 0.55, 0.40 0.55, 0.40 0.55, 0.400.1 5 2 0.61, 0.37 0.61, 0.36 0.60, 0.36 0.60, 0.35 0.60, 0.350.1 6 1/0 0.63, 0.33 0.63, 0.33 0.63, 0.33 0.63, 0.33 0.63, 0.330.1 6 2 0.64, 0.35 0.63, 0.34 0.63, 0.33 0.62, 0.33 0.62, 0.320.1 6 5 0.64, 0.35 0.64, 0.34 0.63, 0.33 0.62, 0.33 0.62, 0.320.2 2 2 0.56, 0.36 0.56, 0.36 0.56, 0.36 0.55, 0.35 0.55, 0.350.2 6 1/0 0.75, 0.20 0.75, 0.20 0.75, 0.20 0.75, 0.20 0.75, 0.200.2 6 2 0.78, 0.22 0.76, 0.21 0.75, 0.20 0.74, 0.19 0.73, 0.180.2 6 5 0.78, 0.22 0.77, 0.21 0.75, 0.20 0.74, 0.18 0.73, 0.180.3 6 2 0.89, 0.13 0.87, 0.11 0.86, 0.10 0.84, 0.09 0.83, 0.080.3 8 2 0.95, 0.08 0.94, 0.07 0.92, 0.05 0.91, 0.04 0.89, 0.04

how insensitive the portfolio shares are even to large changes in p.Because the results turn out to be fairly insensitive to p, we find that ourearlier calculations are indeed little affected by relaxing the assumptionpO = 1. The low sensitivity to p over the range of relative output out-comes in Table 4 is consistent with the conjecture by Cole and Obstfeld(1991) that, for moderate uncertainty, the gains from global risk sharingmay be so low as to be mostly offset by costs of trade. Here, the equilib-rium with a rich variety of assets is not so different from the one in whichindividuals can hold only equity. Another conclusion we can draw fromthese numbers is that trade costs have to be quite large before there is asubstantial discrepancy between the Arrow-Debreu consumption alloca-tion and the one that trade in equities alone would produce. Even fortrade costs of 30%, an equity allocation that gave each country the sameconsumption share in every state of nature as it would have in theArrow-Debreu equilibrium only when the realization was YH= 1 wouldnot entail a large departure from efficiency. As a result, even when pO 1,the home bias evident in the complete-markets example is quite close towhat a model of pure equity trade would imply.2525. Backus,Kehoe, and Kydland(1992)reportsome relevantexperimentswith theircali-bratedtwo-country,complete-markets ersion of the Brock-Mirmantochasticgrowthmodel. It is true that they do not focus on the equityhome-biaspuzzle and that theyallow foronly a single consumptiongood, effectivelymakingthe elasticityof substitu-tion between nationaloutputs infinite.However,the fact thatthey find thatmoderatetransportation osts produce an allocation close to that with full autarkyis quite inaccordwith ourresultshere.


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366 *OBSTFELD&ROGOFF4.4 CAVEATSWe do not believe that trade costs in goods markets are necessarily thewhole story in explaining observed portfolio biases, and we certainlyexpect that the kinds of information asymmetries and legal restrictionsemphasized in earlier work also play a role. These frictions can be viewedas trade costs in a broader sense, as we have noted, and they can affectportfolios through the trade-cost channel that we have emphasized in thispaper. Nevertheless, it is remarkable that our simple model based on thetrade-cost channel alone matches up so well to the data. As we havenoted, our explanation not only has the merit of (extreme) simplicity, butis also more convincing because the same basic approach seems to helpexplain such a diverse range of puzzles. Finally, we note that our resultsare consistent with recent empirical work by Portes and Rey (1999). Theyfind that international trade in both equities and goods is surprisingly wellexplained by an enhanced gravity model in which informational distanceproxies supplement the standard set of geographical explanatory vari-ables.26These results are certainly in accord with our model's predictionthat equity biases in large measure reflect goods-market biases.27

A caveat to our findings is that transaction costs, and the resultinghome bias, would be reduced somewhat in a fully dynamic model. Inves-tors could then reinvest dividends abroad rather than repatriating themimmediately. As is true for a tax-deferred asset, they could earn divi-dends on wealth that would otherwise be burned up as shipping costs.The question deserves further research. Dumas and Uppal (2000) de-velop a dynamic two-country growth model with shipping costs, buttheir focus is on welfare rather than on the home-bias puzzle. (They alsoassume 0 = 0othroughout by positing a single consumption good.) Ourguess is that trade costs will remain an important determinant of homebias even in a realistic dynamic setting.We have used a complete-markets model to illustrate how trade costscan generate a home equity bias. By taking that modeling approach,however, we certainly do not intend to endorse an empirical view that26. Portes and Rey (1999)reportthat their informationvariablesare quite significantinexplaining goods-market rade,even aftercontrolling orgeographicaldistance.27. One consideration hat dovetailsnicelywith ourexplanation s illustrated n the modelof Martinand Rey (1999),which provides the closest antecedentto our approach.InMartin and Rey's (endogenously) incomplete-markets etup, the main driving forcebehind home bias is that owners of home firmsretaina disproportionate hare of theirequity in order to extracta higher monopoly price for remainingshares from otheragents. Martinand Rey focus on transactioncosts in asset rather than in goods mar-kets, in the traditionof Aiyagariand Gertler 1991).They posit an asymmetrybetweentransactioncosts for home andforeignagents, and this cost also affectssharevalues. Itdoes not interactwith 0, however, so the effectsare much smaller thanhere.


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TheSixMajorPuzzles n International acroeconomics367real-world asset markets are complete or nearly complete, either domesti-cally or internationally. The complete-markets assumption is not essen-tial, and our arguments would go through in a fully articulated in-complete-markets model, for example, one in which households haveunequal access to equity markets, so that only some hold equity (Mankiwand Zeldes, 1991). The home-equity-bias puzzle has a strong empiricalbasis that is independent of any narrow theoretical framework. The con-sumption correlations puzzle, which we turn to next, encompasses abroader notion of market completeness, but its exact formulation is alsomore model-specific.5. TheInternationalonsumptionorrelationsuzzle(Puzzle4)If one believes that both domestic and international capital markets arewell approximated by an Arrow-Debreu complete-markets framework,then it is a puzzle that international consumption growth correlations arenot much higher than they appear to be. In an Arrow-Debreu world,country-specific output risks should be significantly pooled, and there-fore domestic per capita consumption growth should not depend tooheavily on country-specific income shocks. Of course, in some sense, theconsumption correlations puzzle is almost a corollary of the Feldstein-Horioka and home-equity-bias puzzles. Given that the most transparentmarket means of consumption smoothing-debt and equity trade-arefar less operative across borders than within them, it should not come asany great surprise that international consumption correlations are low.However, there are many reasons for thinking about consumption cor-relations independently. One is that we have only very imperfect mea-sures of international trade in equity and debt, and another is that theremay be other market channels, such as direct investment, for pooling risk.The international consumption correlations puzzle has spawned a vari-ety of subpuzzles. Backus, Kehoe, and Kydland (1992) highlight the factthat international output growth rates are actually more highly corre-lated than consumption growth rates. Backus and Smith (1993) note thatin a world with traded and nontraded goods, efficient risk sharing callsfor giving higher rates of consumption growth to countries that experi-ence relative drops in the real price of consumption. (Very loosely speak-ing, the United States and Canada should write contracts that imply bigtransfers to Canada in states of nature where the Canadian dollar is veryweak so that Canadians can exploit bargain Canadian prices, and viceversa when the Canadian dollar is high.)As we shall see, most consumption correlations puzzles tend to be


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368 - OBSTFELD& ROGOFFquite model-specific (depending on factors like the completeness ofmarkets and the exact form of the utility function), so they are not quiteas obviously puzzles about the real world in the same way that, say,the equity-home-bias puzzle is. One does not have to believe that theworld is Arrow-Debreu to think it a puzzle that agents do not takemore advantage of international diversification opportunities. Neverthe-less, consumption correlation puzzles play a very important role inassessing alternative general equilibrium models, and, at a more funda-mental level, we can ask why consumption risk pooling tends to behigher across regions within a country's boundaries than across na-tional boundaries.5.1 THEPUZZLEOF LOWINTERNATIONALCONSUMPTIONCORRELATIONSConsider a single-good world with time-separable preferences in whichall agents have identical period utility functions of the form u(C) = C'-p/(1 - p). Then, if there are no trade costs, trade in a complete set ofArrow-Debreu securities would imply that home and foreign consump-tion growth rates are equalized:

Ct?1 C*1 (14)C, C?regardless of relative shocks to home and foreign outputs. (See Obstfeldand Rogoff, 1996, Chapter 5.) This is hardly what one observes in prac-tice, as Table 5, which gives consumption growth-rate correlations basedon Penn World Table data from the Group of Seven industrial countries,illustrates. The strong prediction of equation (14) is relaxed somewhat inmodels where utility depends nonseparably on both consumption andleisure. However, in this case, the benchmark frictionless world econ-omy model of Backus, Kehoe, and Kydland (1992) still predicts a cross-country consumption correlation of almost 0.9, far above the correlationswe see in the table.

Since, as we have already noted, the low-consumption-correlation puz-zle is virtually a corollary of the previous two puzzles we have studied,the reader will hardly be surprised when we note that introducing tradecosts works just as well in explaining it. Indeed, our model of the equity-home-bias puzzle can easily generate correlations of the sort seen inTable 5.2828. Lewis (1999) points out that when a significant share of output is absolutely non-tradable, international consumption correlations will be sharply reduced. However,


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TheSixMajorPuzzles n International acroeconomics369Table 5 CORRELATIONSN PERCAPITAPRIVATECONSUMPTIONGROWTH,1973-1992

France Germany Italy Japan U.K. U.S.Canada 0.25 0.31 0.44 0.05 0.40 0.64France 0.52 0.27 0.68 0.43 0.51Germany 0.27 0.40 0.33 0.51Italy 0.21 0.30 0.13Japan 0.59 0.50U.K. 0.65Source: enn WorldTable.Correlations f log differences n per capitarealconsumption.Simpleaver-age of correlation oefficients s 0.40.

5.2 THEBACKUS-SMITH UZZLEBackus and Smith (1993) derive a generalization of equation (14) thatholds when trade is costly and, as a consequence, national price levelsfor the consumption baskets entering u(C) generally differ. Let P denotethe home price level and P* the foreign price level, with both price levelsmeasured in the same numeraire currency. As in the last section, cur-rency and securities can be traded without transport costs even thoughgoods are costly to trade. Then complete markets in state contingentassets ensure that growth rates in the marginal utility of currency-themedium in which state-contingent insurance payments are made-areequalized across countries. If the utility-of-consumption function exhib-its constant relative risk aversion and is independent of leisure, as inequation (11), that equality impliesC-P / p I *Ct+l /t+l C t+-I Pt+1l= (15)CtP/Pt C / Pt(This generalizes equation (14) in that P = P* absent international tradefrictions.Given the high volatility of real exchange rates under floating togetherwith the low volatility of consumption, it is perhaps not surprising thatBackus and Smith's empirical work forcefully rejects the optimal risk-sharing condition (15). In fact, the empirical rejection of condition (15) is

Stockman and Tesar (1995) observe that, insofar as the data can be trusted, interna-tional consumption correlations for apparently tradable goods are not appreciablyhigher than those for goods generally classified as nontradable. Their finding supportsthe view that the dichotomous distinction between tradables and nontradables is over-drawn, and simultaneously suggests that there are substantial impediments to interna-tional risk sharing in traded goods.


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370 *OBSTFELD& ROGOFFeven more devastating, since even very high values of p cannot reconcilethat condition with the data. One possible explanation is that their as-sumption that preferences are separable in consumption and leisure istoo strong, so that one needs to look instead at a generalized version of(15). In our view, however, incompleteness of asset markets is the majorreason why condition (15) fails so miserably in practice. Indeed, giventhe volatility of exchange rates, the size of transfers required for (15) tohold would require a level of risk sharing even greater than we observein domestic markets.The alert reader will note that a version of the Backus-Smith conditionwill hold in a dynamic extension of our earlier model of the home-equity-bias puzzle. That model implicitly assumed flexible nominal prices, andwould not produce nearly the level of real-exchange-rate volatility onesees in the data. We do not take this as damning, since for us thecomplete-markets assumption was only a useful device for calibration,and not a conviction. Trade costs would play essentially the same role ina world with, say, trade in debt and equities but not a complete set ofArrow-Debreu securities. Indeed, in the context of this paper, the reallyinteresting issue is not why international consumption correlations aredifficult to replicate in a complete-markets model, but the extent towhich consumption risk sharing is less prevalent across distinct coun-tries than within countries.5.3 INCOMPLETENESSF DOMESTICVS.INTERNATIONALMARKETSCertainly, empirical studies based on domestic micro data reject resound-ingly the proposition that markets are complete. For example, Attanasioand Davis (1996) find that consumption risk sharing is strikingly incom-plete within the United States, and for reasons that apparently are unre-lated to asymmetric information. The question the present paper raisesis whether risk sharing is even more impaired internationally than do-mestically due to costs of specifically international trade. Our discussionof home equity bias, which does not rely fundamentally on a complete-markets assumption, suggests that this should be the case, since re-gional equity bias seems to be far less than the strong national home biasthat we see in international data. Backus and Smith's theoretical proposi-tion points in the same direction.A growing body of empirical evidence supports the prediction thatfinancial markets are less effective in promoting risk sharing among coun-tries than among regions within a country. A full review of this literaturewould take us too far afield, but we can mention briefly a few relevantpapers. Atkeson and Bayoumi (1993), in one of the first empirical studiesin this area, find that regional financial transfers within the United States


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TheSixMajorPuzzles n International acroeconomics371are much larger than those among the major industrial countries. A com-parison of the variance-decomposition results of Asdrubali, Sorensen,and Yosha (1996) on the United States with those of Sorensen and Yosha(1998) on the OECD suggests that financial markets play a much biggerrole in consumption smoothing among U.S. states than is the case amongindustrial countries. Crucini (1999), using an alternative method, con-cludes that Canadian provinces pool risks more effectively than U.S. re-gions, and that either country shows more internal risk pooling than doesthe sample of industrial countries. Bayoumi and Klein (1997) find thatCanadian provinces display more financial integration with each otherthan with the outside world.29

So there indeed is a puzzle as to why intranational consumption risksharing is more efficient than international risk sharing, but it can beresolved in the same manner as we have resolved the home-bias andFeldstein-Horioka puzzles.5.4 THERELATIVE ORRELATIONSF INTERNATIONALCONSUMPTIONAND OUTPUTGROWTHRATESBackus, Kehoe and Kydland (1992) emphasize the puzzle that empiricalconsumption correlations are actually lower than output correlations.That pattern holds in the Penn World Table data analyzed here: theaverage international correlation in per capita real GDP growth rates is0.53 over 1973-1992, while the corresponding average consumption cor-relation is only 0.40.Our model, on its own, does not offer a new rationalization of theirfinding. However, we do not consider this to be a fundamental problem,since the existence of international risk sharing need not generate highercorrelation among consumptions than outputs across countries. The rea-son is that only the output remaining after investment and governmentconsumption can be shared by private consumers. Thus, a more appro-priate comparison to assess the degree of global risk sharing is thatbetween international consumption correlations and correlations ingrowth rates of output net of investment and government consumption(Y - I - G). Table 6 reports these correlations for the same sample periodand data set used to construct Table 5. The average international correla-tion in the growth of Y - I - G is 0.17, far below the average correlation0.40 of international consumption growth rates. For six of the 21 countrypairs that ranking is reversed, but in most of these cases the discrepancyis not significant.So in fact, the puzzle concerning the relative variability of output and29. Obstfeld (1995) adds a number of caveats to some of this literature.


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372 *OBSTFELD & ROGOFFTable 6 CORRELATIONS IN PER CAPITA Y - I - G GROWTH, 1973-1992

France Germany Italy Japan U.K. U.S.Canada 0.17 0.19 0.36 -0.18 0.50 0.66France 0.13 0.34 0.20 0.02 0.11Germany 0.19 -0.19 0.13 0.18Italy -0.31 0.33 0.46Japan -0.25 -0.22U.K. 0.73Source: enn WorldTable.Correlations f log differences n percapitareal GDP net of investmentandgovernmentconsumption.Simple averageof correlation oefficientss 0.17.

consumption is not necessarily incompatible with a high level of interna-tional asset market integration. Indeed, using a dynamic new open-economy macroeconomic model, Chari, Kehoe, and McGrattan (1998)are able to produce realistic cross-country correlations of output as wellas of consumption.30 The main additional assumptions that lie behindtheir results include sticky nominal prices and, implicitly, transport costshigh enough to result in segmented national output markets. Both trans-port costs and nominal rigidities are central to the resolution of the fifthand sixth puzzles, to which we now turn.6. ThePurchasing-Power-Parityuzzle(Puzzle5) and theExchange-Rateisconnect uzzle Puzzle6)Our last two puzzles differ from the preceding ones in being fundamen-tally about the real effects of a nominal variable-the exchange rate,which is the relative price of currencies. Here, also in contrast to thepreceding four puzzles, the difficulty seems to lie primarily in explainingshort- to medium-term phenomena rather than phenomena that persistover very long periods. (The Feldstein-Horioka puzzle, for example, istypically framed using decade-average data). Finally, the last two puz-zles can be viewed as pricing puzzles, because they refer to price behav-ior, including the dynamic covariation between prices and other macro-economic variables.

Any realistic attempt to address these pricing puzzles formally wouldrequire a much more elaborate framework than the one we have used thusfar, incorporating, among other things, elements of monopoly and sticky30. In the Chari-Kehoe-McGrattan sticky-price model, highly correlated national mone-tary shocks can make national outputs covary more closely than national consump-tions. Highly correlated monetary shocks, however, also tend to reduce real-exchange-ratevariabilitycounterfactuallyn the model. Wesuspect that an extended versionofthe model couldhandle the latterproblem.


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TheSixMajorPuzzles n International acroeconomics373nominal prices for goods and/or labor. In fact, there is already a great dealof exciting research along these lines now taking place [see, for example,the recent survey by Lane (2001) on the new open-economy macro-economics]. Unfortunately, we do not have nearly enough space remain-ing here to present a fully articulated model. Nevertheless, we will try tomake clear why trade costs are as essential to resolving the pricing puzzlesas they are to resolving puzzles 1 through 4, which are quantity puzzles.The first pricing puzzle we take up is the purchasing-power-parity(PPP) puzzle (Rogoff, 1996), which highlights just how weak the connec-tion is between exchange rates and national price levels. It is based onthe observation that in hundreds of studies, using widely varying tech-niques and data sets, researchers have repeatedly found very long half-lives-on the order of 3 to 4 years-for shocks to real (CPI) exchangerates. As we shall explain, half-lives of this magnitude are hard to under-stand if financial-market disturbances with only transitory real effectsare very important in explaining short-run volatility.Our term for the second pricing puzzle is the exchange-ratedisconnectpuzzle, a name that alludes broadly to the exceedingly weak relationship(except, perhaps, in the longer run) between the exchange rate andvirtually any macroeconomic aggregates. It manifests itself in a variety ofways. For example, Meese and Rogoff (1983) showed that standardmacroeconomic exchange-rate models, even with the aid of ex post dataon the fundamentals, forecast exchange rates at short to medium hori-zons no better than a naive random walk. Baxter and Stockman (1989)argued that transitions to floating-exchange-rate regimes lead to sharpincreases in nominal- and real-exchange-rate variability with no corre-sponding changes in the distributions of fundamental macroeconomicvariables.31(The PPP puzzle is really just an example, albeit a very impor-tant one, of the broader exchange-rate disconnect puzzle.)A critical difference between the (relatively short-term) pricing puz-zles and the (longer-term) quantity puzzles is that we can no longerappeal to high elasticities of substitution to lever up the effects ofmodest-sized trade costs. (At the very least, the connection is no longeras simple and direct.) If there are only modest obstacles to short-termprice arbitrage across borders, there can be only modest short-term pricedifferentials. In fact, at the consumer level, arbitrage costs arelikely to berather large, and, after all, most goods embody very large nontradedcontent once they reach consumers at the retail level. But one cannotmake this argument for wholesale importers who trade in bulk, so here31. Flood and Rose (1995) extend Baxter and Stockman's results and arrive at similarconclusions.


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374 *OBSTFELD& ROGOFFwe need a more nuanced discussion. As we shall see, importer-levelprices do appear to exhibit somewhat less anomalous behavior than doconsumer-level prices.6.1 THEPPPPUZZLELet Q be the real exchange rate between two countries, and consider theregression equationlog Qt = a + 7qt+ y log Qt-1 + E,,where et is a random disturbance. The real exchange rate, Q, is definedas WP*/Pusing overall CPI data for price levels, where the nominalexchange rate % is the price of foreign currency in terms of home cur-rency. (In deference to conventional usage, we now switch notation anduse P to denote the domestic price level measured in home currency andP* the foreign price level measured in foreign currency.)Using monthly 1973-1995 data for Canada, France, Germany, Japan,and the United States, and constructing all 10 possible real exchangerates in this sample, we find values of y ranging from 0.99 (U.S.-Canada, implying a half-life of 69 months) to 0.97 (Germany-Japan,implying a half-life of 21 months). The mean half-life across these realexchange rates is around 39 months, or 3- years.32Such long half-lives would not necessarily be a puzzle but for theremarkable volatility of real and nominal exchange rates, volatility thatseems hard to explain without assigning a major role to monetary andfinancial shocks. If monetary and financial shocks are the predominantsource of volatility, however, it is hard to imagine what source of nomi-nal rigidity could be so persistent as to explain the prolongation of real-exchange-rate deviations. This is the PPP puzzle.6.2 THEPPPPUZZLEFORTRADABLESVERSUSNONTRADABLESOne might think that the slow mean reversion just documented appliesprimarily to goods with extremely high international trade costs,whereas, at least for goods that are heavily traded, mean reversion inrelative international consumer prices might be more rapid. That is notthe case, however, as documented most strikingly by Engel (1999).If we are willing to set our qualms aside tempor

6 major in international makro ekonomic

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