Chapter Title: the Six Major Puzzles in International Macroeconomics: Is There a Common Cause? International Macroeconomics: I S There a Common Cause?

The central claim in this paper is that by explicitly introducing costs of international trade (narrowly, transport costs, but more broadly, tariffs, nontariff barriers, and other trade costs), one can go far toward explaining a great number of the main empirical puzzles that international macroeconomists have struggled with over twenty-five years. Our approach elucidates J. McCallum's home-bias-in-trade puzzle, the Feldstein-Horioka saving-investment puzzle, the French-Poterba equity-home-bias puzzle, and the Backus-Kehoe-Kydland consumption-correlations puzzle. That one simple alteration to an otherwise canonical international macroeconomic model can help substantially to explain such a broad range of empirical puzzles, including some that previously seemed intractable, suggests a rich area for future research. We also address a variety of international pricing puzzles, including the purchasing-power-parity puzzle emphasized by Rogoff, and what we term the exchange-rate disconnect puzzle. The latter category of riddles includes the Meese-Rogoff exchange-rate forecasting puzzle and the Baxter-Stockman neutrality-of-exchange-rate-regime puzzle. Here, although many elements need to be added to our extremely simple model, trade costs still play an essential role.

understanding all of these puzzles, in which the key friction is a (significant but plausible) level of international trade costs in goods markets. These trade costs may include transport costs but also tariffs, nontariff barriers, and possibly other broader factors that impede trade.
We do not pretend to be the first to make this connection. In a fundamental contribution to the literature on international trade and finance, Samuelson (1954) argued that the existence of an international transfer problem depends critically on whether there is a home bias in consumption, and he showed explicitly how a home bias could be derived from transport costs.1 In subsequent research, however, Samuelson's straightforward approach has generally been abandoned in favor of a more stylized paradigm based on breaking up a country's products into two dichotomous categories, traded and nontraded goods.2 The analysis of the present paper suggests that for many purposes, this dichotomous grouping is far less helpful than the natural alternative of simply introducing trade costs.
Especially in our treatment of capital-market anomalies, the approach in this paper differs from the one that is conventionally taken in the literature. Typically, an author chooses from a menu of plausible capitalmarket imperfections the one best suited to explain a particular puzzle. We do not deny the importance of a variety of imperfections peculiar to international asset markets. Our goal here, however, is to show how far one can go in elucidating major empirical riddles without appealing to intrinsically international capital-market imperfections. Remarkably, we find that once one allows for trade costs in goods markets, many of the main empirical objections to the canonical models of international macroeconomics disappear. Our approach, which is based on a very simple stylized model, seems to be particularly successful in resolving the realside quantity puzzles. To explain adequately the various pricing puzzles, we would need to develop a much richer framework featuring imperfect , who find that their approximate method for incorporating small trade costs does not resolve the consumption correlations puzzle in a calibrated one-good global real-business-cycle model. Another is Dumas (1992), who looks at a dynamic, stochastic, one-good open economy model with transport costs and explores a number of issues, including the forward exchange-rate premium. His work is theoretical and qualitative, however, and he does not calibrate his model's empirical implications for the various puzzles we look at here. Also, our main points in this paper really require an extension to the multigood case. In a more recent contribution, Ravn and Mazzenga (1999)  Thus, 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 conservative when applied to all of GNP) and 0 = 6, then CH/pCF = 4.2. This ratio is consistent with those we observe for many OECD countries, and the degree of home bias can easily be made larger by raising 7, raising 0, or assuming that the home country is a small one trading with many likesized foreign partners.

THE NONLINEAR RELATIONSHIP BETWEEN TRADE COSTS AND HOME BIAS IN TRADE
The higher trade costs (the closer 7 is to 1), the greater the impact of a 1% reduction in r on home bias: Obviously, this example is wildly oversimplified. It implicitly assumes a common substitution elasticity across any individual pair of home and foreign goods, and similarly lumps all goods together as having common trade costs. It ignores the potential importance of substitution between domestic and foreign inputs in production. Nevertheless, it neatly illustrates how a high elasticity of substitution can explain a large observed home trade bias even with low trade costs. What then are plausible values for the parameters r and 0?

EMPIRICAL ESTIMATES OF 0
Though there is a range of estimates for 0, recent trade studies typically find values for the elasticity of import demand with respect to price (relative to the overall domestic consumption basket) in the neighborhood of 5 to 6. Examples include Trefler and Lai (1999), who present panel estimates over 1972-1992 for a panel of 28 industries in 36 countries; their preferred estimate is 5.3. That average number reflects estimated disaggregated substitution elasticities as high as 21.4 (for industrial chemicals) and 18.9 (for electrical machinery and electronics) but as low as 1.2 (for printing and publishing). Harrigan (1993) looks at threedigit 1983 SITC data for 13 OECD countries representing 90% of OECD output and finds elasticities in the range of 5 to 12.
Recognizing that much of trade involves imperfectly competitive industries, one can attempt to infer the value of 0 by looking at markups of price over marginal cost. Using that approach, Cheung, Chinn, and Fujii (1999) look at two-digit industry level data for a range of OECD countries, and impute elasticities typically in the range of 3.5 to 4. Hummels (1999a) tries to disentangle the effects of trade elasticities from those of substitution elasticities within a cross-section framework. Using linear least squares, he comes up with an average markup of 22%, translating into a 0 of 5.6, although other of his estimates of 0 are higher. Finally, in their classic article on the demand for automobiles-including both domestic and foreign makes-Berry, Levinsohn, and Pakes (1995) find price elasticities of demand between 3.1 and 6.4.5 Of course, these studies refer to goods actually traded. As Hummels emphasizes, one would expect that elasticities of substitution would be higher on average for goods that are not traded. In this case, an estimate 5. Studies of monopoly markups in domestic sales, while not necessarily directly applicable 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 subsequent discussion, Rotemberg and Woodford (1995) argue that there is great uncertainty about 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. of 0 = 20, as Wei proposes, does not seem so wild-eyed. Brown and Stern (1989) use 6 = 15 for their policy experiments.

EMPIRICAL ESTIMATES OF TRADE COSTS T
There is far less consensus about the size of trade costs, which include (among other things), tariffs, nontariff barriers, and transport costs. For 1993, average tariffs, on a domestic-production-weighted basis, were 4.9% for the United States, 7.7% for the European Union, 3.5% for Japan, and 8.9% for Canada.6 As for nontariff barriers, official statistics only give information on their existence, not their effectiveness, which must be estimated using an economic model. Anderson and Neary (1998) use a simple computable general equilibrium model to estimate uniform tariff equivalents for nontariff barriers for a broad range of countries, and typically find estimates on the same order of magnitude as for tariffs, larger of course for some countries (such as Japan) than for others (such as the United States). This result is also consistent with the trade-equation estimates of Lee and Swagel (1997).7 Differential international transportation costs are also an important potential element of 7.8 If one looks across all commodities on a valueweighted basis, freight and insurance charges for U.S. imports averaged 3.6% in 1995, and 3.3% in 1996 and 1997.9 But these numbers considerably understate average costs in international shipping. First, As Hummels (1999a) shows, average costs are much higher for many other countries (the United States has a vast coastline, and sea shipping tends to be much cheaper than shipping by land). Second, these numbers do not include other considerable costs of international shipping, including preparing the paperwork (bills of lading) needed to clear international customs, and the costs of delays either in transit or at port of entry.
Just as empirical measures of the elasticity of substitution between home and foreign goods may be biased downwards, it is also likely that simple estimates of average transport costs grossly understate average r across all goods in the economy (due to substitution effects). Table 1 is drawn 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 and transportation costs. 8. Recall that Helliwell's and McCallum's estimates use distance in an attempt to control for 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 freight charges 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 of arrival. gregated 10-digit data. We see from the table that shipping costs for many categories of goods are quite a bit larger than the average (tradeweighted) shipping costs-and this table excludes goods that are not traded 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 unions trade two to three times as much with each other as countries with separate currencies. Certainly, currency conversion costs and exchangerate uncertainty can add to trade costs. While exchange-rate variability can have direct negative effects on capital flows, any direct negative effect on trade flows will result in an additional, indirect source of capitalmarket imperfection according to our analysis. A similar point can be made for various informational costs of international trade; see Rauch (1999) and  for discussion and some empirical evidence.10 Differences in legal and payments systems may also add to r.
Last, but not least, it is important to emphasize that our analysis has assumed no home bias in preferences. Suppose we replace the representative home agent's utility function (1) with 10. Anderson and Marcouiller (1999) argue that corruption and imperfect contract enforcement are major factors in disrupting trade, especially in developing countries. Since our main focus is on industrialized countries, we will not consider these categories of trade cost further here.

U = (C(H )/ + wC 1)/)?/0-1) (7)
and the representative foreign agent's utility function with U* = (wC *(-1)/S + CF-'/1)/0)-1) One can easily show that the effects of home bias in preferences (w < 1) can be isomorphic to the effects of trade costs r. Helpman (1999) argues that once one controls for income, there is no clear evidence of home bias in preferences. Indeed, it is more illuminating to derive trade biases from other frictions. Nevertheless, it is important to recognize that a home bias in demand for goods can work similarly to trade costs, at least for the trade and portfolio-bias puzzles.

OTHER REAL-TRADE PU7ZI7.S
Though international-finance puzzles are our main focus, we note that trade costs can explain a number of real-trade puzzles as well. For example, Trefler's (1995) favored explanation of the "missing trade" puzzle combines Hicks-neutral productivity differences across countries with a home bias in consumption (which, per our discussion above, may be induced by transport costs).ll Deardorff (1998) points out that with transport costs, the standard conditions for factor-price equalization in a Heckscher-Ohlin world break down, also implying greater specialization. Since factor-price equalization fails miserably empirically, this implies another important puzzle that can be at least partially resolved by transport costs. Anderson (1979), Deardorff (1998), and others have shown that transport costs can help explain the surprising empirical robustness of the gravity equation of trade flows. Not only do trade costs help to resolve a number of puzzles in the data, they also seem to be important in determining economic performance. Radelet and Sachs (1998) argue that countries that have high shipping costs due to adverse geography (for example, high mountains or limited port access) grow much more slowly than countries with natural transport advantages. Finally, we note that evidence on international price differentials seems quite consistent with the high degree of market segmentation evinced on the quantities side; we shall refer to this work later in discussing puzzles 5 and 6. Armed with a simple understanding of how plausible trade costs together with high elasticities of substitution in consumption can explain 11. "Missing trade" is how Trefler describes the puzzle that the imputed factor content of trade does not seem to reflect comparative advantage. substantial home biases in trade, we are ready to explore the linkages to other macro puzzles.

The Feldstein-Horioka Puzzle (Puzzle 2)
There has been no shortage of explanations for the famous savinginvestment puzzle of Feldstein and Horioka (1980), with numerous articles on the topic having been published in most of the leading journals. The problem is that none of the explanations advanced to date (including our own attempts) has been terribly convincing. Most explanations tend to be clever but empirically inadequate and, more troublesome still, tend to fix one puzzle at the expense of creating others. The fact that the Feldstein-Horioka regularity does not seem to characterize intranational regional data suggests that factors intrinsic to trade between different nations are at work.12

STILL A PUZZLE
What Feldstein and Horioka actually demonstrated, of course, is that across OECD countries, long-period averages of national saving rates are 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 investment on saving yielded slope coefficients near unity. True, this Feldstein-Horioka coefficient-which the original work interpreted as measuring the effect of the saving rate on the investment rate, or a "savings retention" measure-has fallen over time. As Table 2 illustrates, however, it still remains large and significant. The table gives simple cross-country regressions of investment (relative to GDP) against national saving (relative to GDP), taking eight-year averages for the most recent period, 1990-1997. For the OECD countries, the coefficient (0.60) is a good deal smaller than the 0.89 found in Feldstein and Horioka's original work, but it is still larger than one might expect in a world of fully integrated capital markets where global savings should flow to the regions with the highest rates of return. The coefficient falls further once one includes countries outside the OECD (particularly poor countries), although the extended results must be viewed with extreme caution given the poor quality of national income and product data for most non-OECD countries. (The data underlying the regressions in Table 2 are reported in Table 7 in the appendix, which also describes how the countries in the sample were chosen.) The Feldstein-Horioka puzzle is durable because the core regression simply summarizes in a compact way the fact that OECD current accounts tend to be surprisingly small relative to total saving and investment, especially when one averages over any sustained period. For developing countries, notably the many that have repeatedly had trouble servicing debts, it is perhaps not so surprising that creditors prevent them from running up large sustained deficits. But it is hard to appeal to sovereign-default risk for OECD countries, especially when one considers that gross international flows of financial assets are much bigger than net international flows. Indeed, for OECD countries, asset price comparisons suggest a high degree of integration; arbitrage in similar nominally risk-free assets appears to be nearly perfect. We leave it to the reader to look at other sources (for example, Obstfeld and Rogoff, 1996, Chapter 3) for assessments of previous attempts to explain the Feldstein-Horioka conundrum.
A fair summary of the literature is that there are at least five or six leading explanations (and ten or so close seconds). All are unconvincing empirically-some because they are based on very special assumptions about the nature of the exogenous shocks (e.g., Obstfeld, 1986, or Mendoza, 1991, others because they raise collateral empirical contradictions. For example, in the asymmetric information model of Gordon and Bovenberg (1996), a "lemons" problem is invoked to explain why foreigners finance so little domestic investment, yet departures from covered interest parity must also be assumed if there is to be any foreign equity inflow at all. Explanations that try to maintain the assumption of perfect capital mobility often have the strong implication that one should also observe high saving-investment correlations across states or regions within a given country. But the partial evidence available on saving and investment by subnational regions simply does not produce the Feldstein-Horioka regularity; see, for example, Helliwell (1998, Chapter 4). We are going to propose here an entirely new explanation, based on transaction costs for international trade in goods. An especially attractive feature of our approach is that it seems to help resolve other puzzles rather than exacerbating them. It is important to emphasize that whereas our model includes trade costs for goods, it is consistent with free and costless trade in securities. Thus, it is perfectly consistent with the observation that gross international flows of securities are substantial even though net flows are small. Our account is also notable both for endogenizing the price and interest effects of trade impediments, and for showing how moderate transport costs could generate empirically significant international differences in real interest rates despite full asset-market integration.

TRANSPORT COSTS CAN INDUCE A NONLINEAR RELATIONSHIP BETWEEN THE CURRENT ACCOUNT AND THE REAL INTEREST RATE
The basic intuition of why transport costs can temper current-account imbalances can be illustrated in a standard two-period, two-good, smallcountry endowment model. It would not be difficult to endogenize the world real interest rate, or to incorporate uncertainty (as in the next section), but neither generalization is essential here. We will later discuss investment to confirm that the basic argument we make still goes through.
The model below is entirely standard except that we will again allow for Samuelsonian "iceberg" costs in trade, so that T percent of any good is lost in transit. The utility function of a representative home resident is u(C) + 8u(C2), where total real consumption C depends on consumption of the home and foreign goods, CH and CF, with constant elasticity of substitution 0 as in equation (1). The small country is endowed only with good H, with YH,1 in period 1, and YH,2 in period 2. Good F must always be imported.
(Endowing the country with both goods would not overturn our argument.) The home country is small in the sense that its actions have no effect on the world prices PH and PF, which are constant across the two periods in terms of a world unit of account (money). Nor can it affect the foreign real interest rate r* (which equals the foreign nominal interest rate assuming there is zero foreign inflation). Because of iceberg transit costs T in shipping either good, however, home consumption patterns can affect home relative prices and the home real interest rate.
Though we shall give a formal analysis below, the basic argument is simple. Suppose, for example, that the country's endowment pattern and rate of time preference 8 are such that in the first period, net exports of good H are negative (in which case intertemporal solvency dictates they must be positive in period 2). Then, as we shall shortly confirm, the relative price of good H will be higher in period 1 than in period 2. There will be expected deflation, and the home real interest rate will be above r*. The situation is reversed when the country is initially running a sufficiently large current-account surplus, so that its real consumption-based lending rate must lie below r*. As we demonstrate formally below, this effect can be quite dramatic, assuming realistic values for trade costs and the elasticity of substitution 0 (values similar to those needed to resolve the home-bias-in-trade puzzle).13

BUDGET CONSTRAINTS AND TRANSPORT COSTS
A formal analysis requires one to think carefully about the budget constraints facing the representative agent. In general, the first-period budget constraint can be written as Therefore, given a total real consumption level C in any period, the consumptions of the two individual home and foreign goods are

INFLATION
Since good F is always imported, its home price, PF =PF/(1r), must be higher than the foreign price in both periods, per equation (2). By the same logic, when good H is exported-as it must be in at least one of the two periods-its home price PH = PH(1 -T) must be lower than the foreign price, per equation (3). However, if total domestic spending is high enough relative to income in any given period, it is possible that good H is imported rather than exported (CH > YH), in which case its home price PH = PH/(1 -T) must be higher than the foreign price. As we shall see, there are also important intermediate cases where CH = YH in one period, in which case PH will turn out to lie between P*(1r) and P*/(1 -T), despite the fact that no goods roundtrip.

A GRAPHICAL ANALYSIS OF THE LINK BETWEEN REAL INTEREST RATES AND CURRENT ACCOUNTS
The link between the effective real interest rate faced by the home country and its first-period borrowing decision is illustrated in Figure 1, which plots total real consumption in period 1, C1, against the domestic real interest rate, 1 + r. (Note that the period 1 current account deficit is simply Y1 -C1). The resulting graph is a step function that can be divided up into five segments; it shows the schedule of effective real interest rates faced by the country as a function of its borrowing-lending decision.
In the first segment C1 is so low, and the period 1 current-account surplus so high, that in period 2 the country will consume an amount in segment I. If the country contemplates being a big lender, it will face an effective real interest rate significantly below the world real interest rate. Segment II starts when period 1 consumption first reaches the level Cln such that CH,2 = YH,2-In this region, PH,2 is determined by equation (8) and the first relation in equation (9), with CH,2 = YH,2 (so there is no round-tripping). Period 2 consumption of the home good remains constant at YH,2 as long as PH2 remains strictly between P((1 -T) and P*/(1 -T), but equation (9) implies that PH,2 falls as C1 rises and C2 falls, until PH,2 reaches P*(1 -T). Accordingly, the real interest rate rises over segment II.14 At the point C1 = Cm, Segment III begins as the home country becomes a period 2 exporter of its endowment good. On this stretch, 1 + r = 1 + r*. Because here, CH < YH in both periods, the overall price level is constant over time. In region III, the country is running a sufficiently small current-account surplus or deficit that there is never any reversal of the pattern of trade in either good. It is precisely in this region that trade costs have no effect on the real interest rate. At C1 = Cv, however, CH, reaches YH,, and the real interest rate begins to rise once more. In segment IV, CH, remains stuck at YH,1 as C1 rises, pushing PH,1 up with it until PH, reaches PH/(1 -7). As P,H rises along segment IV, with PH2 constant at PH(1 -T), the real interest rate rises. At Cv, however, where PH, first reaches PH/(1 -T), the country becomes a period 1 importer of its own endowment good, and the real interest rate stabilizes (along segment V) at the level The range of possible real interest rates produced by this simple example 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 interest rate is 20% (15% above the world level) while the lowest is -8% (13% below the world level). The interplay between the commodity transport costs T and the substitution elasticity 0 is similar to what we saw in the preceding section. As 0 rises, the maximum and minimum real domestic interest rates move apart-with higher substitutability, the price-level impacts of changes in P, are more pronounced. In the limiting case as 0 -oo the two goods are asymptotically perfect substitutes, in which case the country's effective real borrowing rate will be 30%, and its lending rate, -15%! Of course, the range of real domestic interest rates encompassed by Figure 1 is far greater than what we usually observe in practice, especially for OECD countries. But this simply reflects the fact that incipient real interest differentials put a sharp check on a country's incentives to run large current-account deficits or surpluses.15

EXTENSIONS AND ALTERNATIVE FORMULATIONS
The preceding account of the effect of domestic spending on real interest rates is overly stylized, but a number of obvious extensions can add to realism without diluting the main message.
3.6.1 A Continuum of Goods and Transport Costs Assume, for example, that countries are endowed with multiple goods in various proportions and that these goods display a distribution of transport costs. Then, as domestic spending rises, progressively more types of goods are imported from abroad, leading to a steadily rising real domestic interest rate. In this more realistic setup, the relationship between expenditure and 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 upwardsloping curve. With a rich enough range of goods, transport costs, and elasticities of substitution, even small current-account deficits may produce trade reversals in a small number of goods, thereby resulting in an interest-rate effect. We conjecture, though it remains to be proved, that one would obtain a similar nonlinearity to that depicted in Figure 1, with small current-account imbalances having relatively little effect on interest differentials.
3.6.2 Long-Term Borrowing and Lending An obvious question is how the results here might be tempered in a model with many periods so that there are opportunities for long-term borrowing and lending. For example, if a country ran a big current-account deficit in the initial periods, it could repay slowly over many periods. Though a more careful analysis is required than we can provide here, it seems unlikely that this consideration would overturn our basic point; there would still be a big price swing between the big deficit periods and surplus periods-which is precisely why a country would seek to avoid such swings. We note also that in a richer model with a continuum of goods, the current account would not necessarily have to swing between deficit and surplus to induce real-interest-rate effects. In general, the range and type of goods 15. The suggestion that idiosyncratic real-interest-rate developments might help explain the 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 in the literature, no one has taken the idea very seriously, since earlier models could not give any reason why the real interest rate might be so important quantitatively. Nor could they really explain the durability of the Feldstein-Horioka relationship across different time periods and regimes. being imported and/or exported will vary more or less continuously in the level of trade-balance deficit (or surplus). Thus, the real-interest-rate effect will arise along any path where there are big trade-balance swings, either over any short period, or cumulatively over any long period. This would be true even in a setting with growth in which countries could, in principle, run perpetual deficits and surpluses.

Investment How is the preceding analysis affected by introducing investment?
In the case where the country desires to be a large net borrower (segments IV and V), the real-interest-rate effect will be tempered to the extent the country can cut back on investment instead of borrowing from abroad. But that very mechanism dictates that reductions in national saving will be accompanied by reductions in domestic investment. In segments I and II, the country could channel some of its higher savings into higher investment, again tempering the fall in the effective real interest rate but creating the positive Feldstein-Horioka correlation between increases in saving and increases in investment.16

Deriving Similar Results in a More Conventional Setup with Traded and
Nontraded Goods The reader may well ask whether we needed such an extravagant formulation to make the basic point that the consumptionbased real interest rate can be linked to the current account. Couldn't we have made the same point in the context of a standard Salter-Swan model having two classes of goods, one with infinite trade costs and the other with zero trade costs (as discussed, for example, in Chapter 4 of ? Indeed, for a pure endowment case, the standard traded-nontraded model does produce a graph very much like Figure 1. Holding endowments of both goods flat, if the country chooses to run a large deficit in period 1, the price of nontraded goods will be high in that period, and low in the following period. This implies a consumption-based real interest rate above the world interest rate, just as in segments IV and V of Figure 1, and the effect can similarly be nonlinear. We prefer our formulation largely because it is much easier to think concretely about trade costs than about the arbitrary dividing line between traded and nontraded goods. Perhaps the ideal model would be a richer one incorporating a range of transport costs in which the degree of tradability is endogenous and some goods are consistently produced exclusively for the home market.

Monopoly Pricing and Sticky Prices
Our analysis assumes that prices are flexible and set in competitive markets. Introducing realistic features such as price rigidity and monopoly pricing, as in our discussion of puzzles 5 and 6, would enrich the model without overturning the main 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 monopoly power is less.

EMPIRICS
The model does contain one simple prediction that can easily be checked. Countries running current-account surpluses should have lower real interest rates than countries running deficits. This connection is illustrated in the panel regression results reported in Table 3. Specification 1 regresses the domestic real interest rate, defined as the average three-month nominal interest rate in a given year less lagged annual inflation, on the ratio of the current-account surplus to GDP. Specification 2 forms real interest rates by using December average nominal interest rates in year t less year t inflation, in an attempt to capture that agents can incorporate contemporaneous information into forming inflation expectations. In both specifications we employ an autoregressive correction. We report estimates for simple ordinary least squares (OLS), a model with country fixed effects, and a model with fixed effects and time dummies (the latter to capture global influences on national real interest rates). The results show highly significant negative correlations between the current-account surplus and the real domestic interest rate, as our model suggests. However, the two specifications differ somewhat in their numerical predictions, with specification 1 giving an effect that is substantially larger than that given by specification 2. Taking the regressions with 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-account surplus is associated with roughly a 20-to 30-basis-point decline in its real interest rate.17

The Puzzle of Home Bias in Equity Portfolios (Puzzle 3)
Despite the rapid growth of international capital markets toward the close of the twentieth century and a much expanded world market for equities, stock-market investors maintain a puzzling preference for home assets. When they first highlighted the extent of the home-bias portfolio puzzle at the end of the 1980s, French and Poterba (1991) observed that Americans held roughly 94% of their equity wealth in the U.S. stock market whereas the Japanese held roughly 98% of their equity wealth at home.18 Figure 2, drawn from Tesar and Werner (1998), suggests that the home equity bias is muted for smaller countries and has shown some tendency to decline over time-by the mid-1990s about 10% of U.S. equity wealth was invested abroad. Standard models of optimal international portfolio diversification imply, however, that equity investors still have not diversified internationally nearly as much as they should, and so the puzzle remains.19 17. We experimented with a number of other specifications, expected inflation proxies, and time periods, almost always finding results similar to those reported in Table 3. Gordon and Bovenberg (1996) also establish a relationship between current accounts and real interest rates for OECD countries, but their test and their specification are motivated by a model that is very different than ours. 18. See also Golub (1990), who compared gross international asset flows with gross domestic asset creation for OECD countries. 19. University of California investment policies illustrate the extent and persistence of home bias even for large, sophisticated investors. On April 20, 2000, the U.C. regents announced a revision in investment guidelines for the university's retirement and endowment funds. The overall target portfolio share for equities remained at 65%, but the recommended target share for non-U.S. equities, previously zero, was raised From Tesar and Werner (1998) Potential explanations range from nontraded factors such as human capital (which may worsen or reduce the puzzle; see Baxter and Jermann, 1997) to nontraded consumption goods to asymmetries of information to data inadequacy. Yet it is fair to say that none of the available stories alone has provided a quantitatively satisfactory account of the observed home bias; see  for an up-to-date and thorough survey.
To set the stage for our discussion of trade costs, it is worthwhile briefly reviewing what is perhaps the leading explanation, which is based on the classic Salter-Swan traded-nontraded-goods dichotomy we have already mentioned. While these two types of goods lie at polar extremes in terms of their tradability, equity claims on either type of industry can be frictionlessly traded. Thus, even though cement is prohibitively costly to transport, there is nothing to stop foreign investors from buying shares in the domestic cement industry. Earnings, of course, must be redeemed in traded goods, since nontradables cannot be shipped to foreign equity holders by assumption. The key result one gets out of this framework is that, for the baseline case of separable to 7%. The positive target position in foreign equities, meant to "reduce risk and broaden portfolio diversification while maintaining or improving investment performance," represents a substantial advance. It still falls far short, however, of the optimal foreign equity share that simple models of international diversification would predict. preferences (across the two types of good), investors hold a globally diversified portfolio of traded-goods industries. But nontraded-goods industries are held entirely domestically. The intuition is that, since payments can only be made in traded goods and utility is separable, there is no way to enhance risk sharing in tradables by linking the allocation of tradables consumption to returns in nontraded-goods industries. (That intuition has to be modified for the case of nonseparable preferences, but it is still a useful reference point.20) Thus, if nontraded goods constitute, say, 50% of total output (a popular rule of thumb based on the fact that for many OECD countries, services, construction, and transport constitute roughly 50% of GDP; see Stockman and , then agents will (loosely speaking) hold more than half their equity 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 of explaining the 80% to 90% domestic equity shares we actually observe ( Figure 2). Second, the sharp dichotomy between traded and nontraded goods is a contrived one, since in reality transport costs differ across goods, and a particular good may or may not enter trade under different market conditions. For most goods, tradability is not absolute and tradedness is endogenous.21 Here we will take an approach based on intuition similar to that in the preceding discussion. We explore just how far can one get in explaining the home portfolio bias by explicitly introducing trade costs, rather than splitting goods into two arbitrary and dichotomous categories. What we will show is that, with a plausible elasticity of substitution across goods and reasonable-sized costs for trading them, our model can produce a very high and realistic level of home portfolio bias.

A SIMPLE MODEL
We now add uncertainty to the two-country general equilibrium version of our model, with each country having a random endowment of its distinct perishable consumption good, along the lines of Lucas (1982) or Cole and Obstfeld (1991). To keep notation simple, we again abstract from dynamics and consider a one-period portfolio problem. We assume a completely symmetric joint distribution for the national outputs

H = (1 -T)(YH -CH), CF = (1r)(YF -CF)
Four of the preceding five equations are independent and yield solutions for the consumption levels CH, CF, CH, and CF.

INTERPRETING THE MODEL
It may puzzle some readers that we focus on the Arrow-Debreu allocation when in fact we are interested in relating our analysis to observed trade in the narrower class of equity-type assets that one observes in the real world. One rationale, perhaps, is that we do not want our theoretical home bias results to be driven by ad hoc assumptions about the kinds of securities that can be traded, especially since many assets like debt and direct foreign investment have complex optionlike qualities that may be difficult to summarize in a simple model. A second, more pragmatic, rationale is that the equilibrium for the complete-markets case is relatively simple to compute. A final rationale, as we shall see, is that for realistic parameters, trade in equities alone can come quite close to attaining the complete-markets consumption allocation, so that the home bias evident under complete markets is a good guide to the home bias in an equities-only model.

EVALUATING THE HOME BIAS
It is helpful to begin by analyzing the special case p = 1/0, in which the Arrow-Debreu conditions (12) and (13) simplify enormously. One can also show that the Arrow-Debreu allocation is then identical to the one in which people can trade only straight equity shares. Given our assumption of symmetry, the equilibrium portfolio shares are where XH (XF) denotes the home agent's share of total equity in the home (foreign) industry, and XH (X*) denotes the foreigner's optimal equity shares. Note that if we were to translate these equity positions into consumption shares, we would find cF and cH lower than XF and X* by a factor of 1r, reflecting the trade costs. Of course, in the absence of trade 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 reasonable number when applied to all of output, especially compared to the usual assumption 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 implies a home equity share of 81%. If 0 = 10, then the home portfolio share of home equities is 72% even with trade costs of just 10%. (As in the case of home bias in trade, there is significant nonlinearity: the elasticity of foreign shareholdings with respect to trade costs is very high when r is near 1, but falls as trade costs fall.) The preceding calculations constrain the value of p to equal 1/0, but, as we shall now demonstrate numerically, the results turn out to be remarkably insensitive to this assumption, given realistic levels of output uncertainty.
If we relax our restriction p = 1/0, the exact conditions needed to implement the Arrow-Debreu allocation through equity trade alone are broken. Trade costs create an international wedge between marginal rates of substitution such that standard stock-market spanning theorems no longer apply.23 Nevertheless, one can still gain a good deal of insight into home bias by computing the state-contingent consumptions of the two goods in the Arrow-Debreu efficient allocation.
We can reduce the dimensionality of our numerical simulations by noting that, in equilibrium, the ratios of consumption to output, H CH/ YHJ cF CF /YF, c -CH/YH, and cF = C*/YF, depend only on the output ratio YH = YH/YF. Table 4 illustrates how the consumption ratios CH and CF differ both across states of nature and across a number of settings of the parameters r, 0, and p.24 (The values of cH and cF are apparent from the assumed symmetry of the model.) Notice that the home country's output shares decline across states of nature as its relative endowment rises. That pattern compensates the foreign country for the greater share of transport costs it must pay in states of nature such that home output is relatively high, and it is naturally more pronounced the higher the risk aversion parameter p.
For the cases in which 0 = 6 and T is 10% or 20%, the  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 our earlier calculations are indeed little affected by relaxing the assumption pO = 1. The low sensitivity to p over the range of relative output outcomes in Table 4 is consistent with the conjecture by Cole and Obstfeld (1991) that, for moderate uncertainty, the gains from global risk sharing may be so low as to be mostly offset by costs of trade. Here, the equilibrium with a rich variety of assets is not so different from the one in which individuals can hold only equity. Another conclusion we can draw from these numbers is that trade costs have to be quite large before there is a substantial discrepancy between the Arrow-Debreu consumption allocation and the one that trade in equities alone would produce. Even for trade costs of 30%, an equity allocation that gave each country the same consumption share in every state of nature as it would have in the Arrow-Debreu equilibrium only when the realization was YH = 1 would not entail a large departure from efficiency. As a result, even when pO f 1, the home bias evident in the complete-markets example is quite close to what a model of pure equity trade would imply.25 25. Backus, Kehoe, and Kydland (1992) report some relevant experiments with their calibrated two-country, complete-markets version of the Brock-Mirman stochastic growth model. It is true that they do not focus on the equity home-bias puzzle and that they allow for only a single consumption good, effectively making the elasticity of substitution between national outputs infinite. However, the fact that they find that moderate transportation costs produce an allocation close to that with full autarky is quite in accord with our results here.

CAVEATS
We do not believe that trade costs in goods markets are necessarily the whole story in explaining observed portfolio biases, and we certainly expect that the kinds of information asymmetries and legal restrictions emphasized in earlier work also play a role. These frictions can be viewed as trade costs in a broader sense, as we have noted, and they can affect portfolios through the trade-cost channel that we have emphasized in this paper. Nevertheless, it is remarkable that our simple model based on the trade-cost channel alone matches up so well to the data. As we have noted, our explanation not only has the merit of (extreme) simplicity, but is also more convincing because the same basic approach seems to help explain such a diverse range of puzzles. Finally, we note that our results are consistent with recent empirical work by . They find that international trade in both equities and goods is surprisingly well explained by an enhanced gravity model in which informational distance proxies supplement the standard set of geographical explanatory variables.26 These results are certainly in accord with our model's prediction that equity biases in large measure reflect goods-market biases.27 A caveat to our findings is that transaction costs, and the resulting home bias, would be reduced somewhat in a fully dynamic model. Investors could then reinvest dividends abroad rather than repatriating them immediately. As is true for a tax-deferred asset, they could earn dividends on wealth that would otherwise be burned up as shipping costs. The question deserves further research. Dumas and Uppal (2000) develop a dynamic two-country growth model with shipping costs, but their focus is on welfare rather than on the home-bias puzzle. (They also assume 0 = 0o throughout by positing a single consumption good.) Our guess is that trade costs will remain an important determinant of home bias even in a realistic dynamic setting.
We have used a complete-markets model to illustrate how trade costs can generate a home equity bias. By taking that modeling approach, however, we certainly do not intend to endorse an empirical view that 26. Portes and Rey (1999) report that their information variables are quite significant in explaining goods-market trade, even after controlling for geographical distance. 27. One consideration that dovetails nicely with our explanation is illustrated in the model of Martin and Rey (1999), which provides the closest antecedent to our approach. In Martin and Rey's (endogenously) incomplete-markets setup, the main driving force behind home bias is that owners of home firms retain a disproportionate share of their equity in order to extract a higher monopoly price for remaining shares from other agents. Martin and Rey focus on transaction costs in asset rather than in goods markets, in the tradition of Aiyagari and Gertler (1991). They posit an asymmetry between transaction costs for home and foreign agents, and this cost also affects share values. It does not interact with 0, however, so the effects are much smaller than here. real-world asset markets are complete or nearly complete, either domestically or internationally. The complete-markets assumption is not essential, and our arguments would go through in a fully articulated incomplete-markets model, for example, one in which households have unequal access to equity markets, so that only some hold equity (Mankiw and Zeldes, 1991). The home-equity-bias puzzle has a strong empirical basis that is independent of any narrow theoretical framework. The consumption correlations puzzle, which we turn to next, encompasses a broader notion of market completeness, but its exact formulation is also more model-specific.

The International Consumption Correlations Puzzle (Puzzle 4)
If one believes that both domestic and international capital markets are well approximated by an Arrow-Debreu complete-markets framework, then it is a puzzle that international consumption growth correlations are not much higher than they appear to be. In an Arrow-Debreu world, country-specific output risks should be significantly pooled, and therefore domestic per capita consumption growth should not depend too heavily on country-specific income shocks. Of course, in some sense, the consumption correlations puzzle is almost a corollary of the Feldstein-Horioka and home-equity-bias puzzles. Given that the most transparent market means of consumption smoothing-debt and equity trade-are far less operative across borders than within them, it should not come as any great surprise that international consumption correlations are low. However, there are many reasons for thinking about consumption correlations independently. One is that we have only very imperfect measures of international trade in equity and debt, and another is that there may be other market channels, such as direct investment, for pooling risk.
The international consumption correlations puzzle has spawned a variety of subpuzzles. Backus, Kehoe, and Kydland (1992) highlight the fact that international output growth rates are actually more highly correlated than consumption growth rates. Backus and Smith (1993) note that in a world with traded and nontraded goods, efficient risk sharing calls for giving higher rates of consumption growth to countries that experience relative drops in the real price of consumption. (Very loosely speaking, the United States and Canada should write contracts that imply big transfers to Canada in states of nature where the Canadian dollar is very weak so that Canadians can exploit bargain Canadian prices, and vice versa when the Canadian dollar is high.) As we shall see, most consumption correlations puzzles tend to be quite model-specific (depending on factors like the completeness of markets and the exact form of the utility function), so they are not quite as 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 the world is Arrow-Debreu to think it a puzzle that agents do not take more advantage of international diversification opportunities. Nevertheless, consumption correlation puzzles play a very important role in assessing alternative general equilibrium models, and, at a more fundamental level, we can ask why consumption risk pooling tends to be higher across regions within a country's boundaries than across national boundaries.  Table 5, which gives consumption growth-rate correlations based on Penn World Table data from the Group of Seven industrial countries, illustrates. The strong prediction of equation (14) is relaxed somewhat in models where utility depends nonseparably on both consumption and leisure. However, in this case, the benchmark frictionless world economy model of Backus, Kehoe, and Kydland (1992) still predicts a crosscountry consumption correlation of almost 0.9, far above the correlations we see in the table.

THE PUZZLE OF LOW INTERNATIONAL
Since, as we have already noted, the low-consumption-correlation puzzle is virtually a corollary of the previous two puzzles we have studied, the reader will hardly be surprised when we note that introducing trade costs works just as well in explaining it. Indeed, our model of the equityhome-bias puzzle can easily generate correlations of the sort seen in Table 5.28 28.  points out that when a significant share of output is absolutely nontradable, international consumption correlations will be sharply reduced. However,

THE BACKUS-SMITH PUZZLE
Backus and Smith (1993) derive a generalization of equation (14) that holds when trade is costly and, as a consequence, national price levels for the consumption baskets entering u(C) generally differ. Let P denote the home price level and P* the foreign price level, with both price levels measured in the same numeraire currency. As in the last section, currency and securities can be traded without transport costs even though goods are costly to trade. Then complete markets in state contingent assets ensure that growth rates in the marginal utility of currency-the medium in which state-contingent insurance payments are made-are equalized across countries. If the utility-of-consumption function exhibits constant relative risk aversion and is independent of leisure, as in equation (11), that equality implies C-P / p I P* Ct+l /t+l C t+-I /Pt+1l = .
(15) CtP/Pt C / Pt( This generalizes equation (14) in that P = P* absent international trade frictions. Given the high volatility of real exchange rates under floating together with the low volatility of consumption, it is perhaps not surprising that Backus and Smith's empirical work forcefully rejects the optimal risksharing condition (15). In fact, the empirical rejection of condition (15) is Stockman and Tesar (1995) observe that, insofar as the data can be trusted, international consumption correlations for apparently tradable goods are not appreciably higher than those for goods generally classified as nontradable. Their finding supports the view that the dichotomous distinction between tradables and nontradables is overdrawn, and simultaneously suggests that there are substantial impediments to international risk sharing in traded goods. even more devastating, since even very high values of p cannot reconcile that condition with the data. One possible explanation is that their assumption that preferences are separable in consumption and leisure is too strong, so that one needs to look instead at a generalized version of (15). In our view, however, incompleteness of asset markets is the major reason why condition (15) fails so miserably in practice. Indeed, given the volatility of exchange rates, the size of transfers required for (15) to hold would require a level of risk sharing even greater than we observe in domestic markets.
The alert reader will note that a version of the Backus-Smith condition will hold in a dynamic extension of our earlier model of the home-equitybias puzzle. That model implicitly assumed flexible nominal prices, and would not produce nearly the level of real-exchange-rate volatility one sees in the data. We do not take this as damning, since for us the complete-markets assumption was only a useful device for calibration, and not a conviction. Trade costs would play essentially the same role in a world with, say, trade in debt and equities but not a complete set of Arrow-Debreu securities. Indeed, in the context of this paper, the really interesting issue is not why international consumption correlations are difficult to replicate in a complete-markets model, but the extent to which consumption risk sharing is less prevalent across distinct countries than within countries.

INCOMPLETENESS OF DOMESTIC VS. INTERNATIONAL MARKETS
Certainly, empirical studies based on domestic micro data reject resoundingly the proposition that markets are complete. For example, Attanasio and Davis (1996) find that consumption risk sharing is strikingly incomplete within the United States, and for reasons that apparently are unrelated to asymmetric information. The question the present paper raises is whether risk sharing is even more impaired internationally than domestically due to costs of specifically international trade. Our discussion of home equity bias, which does not rely fundamentally on a completemarkets assumption, suggests that this should be the case, since regional equity bias seems to be far less than the strong national home bias that we see in international data. Backus and Smith's theoretical proposition points in the same direction.
A growing body of empirical evidence supports the prediction that financial markets are less effective in promoting risk sharing among countries than among regions within a country. A full review of this literature would take us too far afield, but we can mention briefly a few relevant papers. Atkeson and Bayoumi (1993), in one of the first empirical studies in this area, find that regional financial transfers within the United States are much larger than those among the major industrial countries. A comparison 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 bigger role in consumption smoothing among U.S. states than is the case among industrial countries. Crucini (1999), using an alternative method, concludes that Canadian provinces pool risks more effectively than U.S. regions, and that either country shows more internal risk pooling than does the sample of industrial countries. Bayoumi and Klein (1997) find that Canadian provinces display more financial integration with each other than with the outside world.29 So there indeed is a puzzle as to why intranational consumption risk sharing is more efficient than international risk sharing, but it can be resolved in the same manner as we have resolved the home-bias and Feldstein-Horioka puzzles.

THE RELATIVE CORRELATIONS OF INTERNATIONAL CONSUMPTION AND OUTPUT GROWTH RATES
Backus, Kehoe and Kydland (1992) emphasize the puzzle that empirical consumption correlations are actually lower than output correlations. That pattern holds in the Penn World Table data analyzed here: the average international correlation in per capita real GDP growth rates is 0.53 over 1973-1992, while the corresponding average consumption correlation is only 0.40.
Our model, on its own, does not offer a new rationalization of their finding. However, we do not consider this to be a fundamental problem, since the existence of international risk sharing need not generate higher correlation among consumptions than outputs across countries. The reason is that only the output remaining after investment and government consumption can be shared by private consumers. Thus, a more appropriate comparison to assess the degree of global risk sharing is that between international consumption correlations and correlations in growth rates of output net of investment and government consumption (Y -I -G). Table 6 reports these correlations for the same sample period and data set used to construct Table 5. The average international correlation in the growth of Y -I -G is 0.17, far below the average correlation 0.40 of international consumption growth rates. For six of the 21 country pairs that ranking is reversed, but in most of these cases the discrepancy is not significant.
So in fact, the puzzle concerning the relative variability of output and 29. Obstfeld (1995) adds a number of caveats to some of this literature.

The Purchasing-Power-Parity Puzzle (Puzzle 5) and the Exchange-Rate Disconnect Puzzle (Puzzle 6)
Our last two puzzles differ from the preceding ones in being fundamentally about the real effects of a nominal variable-the exchange rate, which is the relative price of currencies. Here, also in contrast to the preceding four puzzles, the difficulty seems to lie primarily in explaining short-to medium-term phenomena rather than phenomena that persist over very long periods. (The Feldstein-Horioka puzzle, for example, is typically framed using decade-average data). Finally, the last two puzzles can be viewed as pricing puzzles, because they refer to price behavior, including the dynamic covariation between prices and other macroeconomic variables. Any realistic attempt to address these pricing puzzles formally would require a much more elaborate framework than the one we have used thus far, incorporating, among other things, elements of monopoly and sticky 30. In the Chari-Kehoe-McGrattan sticky-price model, highly correlated national monetary shocks can make national outputs covary more closely than national consumptions. Highly correlated monetary shocks, however, also tend to reduce real-exchangerate variability counterfactually in the model. We suspect that an extended version of the model could handle the latter problem.
nominal prices for goods and/or labor. In fact, there is already a great deal of exciting research along these lines now taking place [see, for example, the recent survey by Lane (2001) on the new open-economy macroeconomics]. Unfortunately, we do not have nearly enough space remaining here to present a fully articulated model. Nevertheless, we will try to make clear why trade costs are as essential to resolving the pricing puzzles as 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 connection is between exchange rates and national price levels. It is based on the observation that in hundreds of studies, using widely varying techniques and data sets, researchers have repeatedly found very long halflives-on the order of 3 to 4 years-for shocks to real (CPI) exchange rates. As we shall explain, half-lives of this magnitude are hard to understand if financial-market disturbances with only transitory real effects are very important in explaining short-run volatility.
Our term for the second pricing puzzle is the exchange-rate disconnect puzzle, a name that alludes broadly to the exceedingly weak relationship (except, perhaps, in the longer run) between the exchange rate and virtually any macroeconomic aggregates. It manifests itself in a variety of ways. For example, Meese and Rogoff (1983) showed that standard macroeconomic exchange-rate models, even with the aid of ex post data on the fundamentals, forecast exchange rates at short to medium horizons no better than a naive random walk. Baxter and Stockman (1989) argued that transitions to floating-exchange-rate regimes lead to sharp increases in nominal-and real-exchange-rate variability with no corresponding changes in the distributions of fundamental macroeconomic variables.31 (The PPP puzzle is really just an example, albeit a very important one, of the broader exchange-rate disconnect puzzle.) A critical difference between the (relatively short-term) pricing puzzles and the (longer-term) quantity puzzles is that we can no longer appeal to high elasticities of substitution to lever up the effects of modest-sized trade costs. (At the very least, the connection is no longer as simple and direct.) If there are only modest obstacles to short-term price arbitrage across borders, there can be only modest short-term price differentials. In fact, at the consumer level, arbitrage costs are likely to be rather large, and, after all, most goods embody very large nontraded content once they reach consumers at the retail level. But one cannot make this argument for wholesale importers who trade in bulk, so here 31. Flood and Rose (1995) extend Baxter and Stockman's results and arrive at similar conclusions.
we need a more nuanced discussion. As we shall see, importer-level prices do appear to exhibit somewhat less anomalous behavior than do consumer-level prices.

THE PPP PUZZLE
Let Q be the real exchange rate between two countries, and consider the regression equation log Qt = a + 7qt + y log Qt-1 + E,, where et is a random disturbance. The real exchange rate, Q, is defined as WP*/P using overall CPI data for price levels, where the nominal exchange rate % is the price of foreign currency in terms of home currency. (In deference to conventional usage, we now switch notation and use P to denote the domestic price level measured in home currency and P* 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 exchange rates 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 real exchange rates is around 39 months, or 3years.32 Such long half-lives would not necessarily be a puzzle but for the remarkable volatility of real and nominal exchange rates, volatility that seems hard to explain without assigning a major role to monetary and financial shocks. If monetary and financial shocks are the predominant source of volatility, however, it is hard to imagine what source of nominal rigidity could be so persistent as to explain the prolongation of realexchange-rate deviations. This is the PPP puzzle.

THE PPP PUZZLE FOR TRADABLES VERSUS NONTRADABLES
One might think that the slow mean reversion just documented applies primarily to goods with extremely high international trade costs, whereas, at least for goods that are heavily traded, mean reversion in relative international consumer prices might be more rapid. That is not the case, however, as documented most strikingly by Engel (1999).
If we are willing to set our qualms aside temporarily and adopt a conventional dichotomy of traded versus nontraded consumer goods, we can use Figure 3 to illustrate the empirical significance of the distinc-32. Data on end-of-month nominal exchange rates and on consumer price indexes come from International Financial Statistics. tion for real-exchange-rate dynamics. The figure is based on monthly 1962-1995 data from Engel (1999, Section I) for the United States, France, Germany, and Japan. The overall real exchange rate Q = WP*/P is compared with relative price indexes for tradables and nontradables, *P~/PT and fPN/PN, where we adopt Engel's disaggregation of OECD sectoral CPI data into tradable and nontradable subindexes.33 Each panel of the figure plots the correlations of percentage changes between pairs of relative prices, where the number of months over which the data are differenced is measured on the horizontal axis. Consistent with Engel's results, the data reveal no significant difference between short-term and long-term correlations, indicating extremely slow mean reversion in shocks to the relative prices of tradables. Interestingly, it seems to make rather little difference whether we use tradables or nontradables prices to compute real exchange rates: all the price ratios are highly correlated with each other even out to horizons of five years. Engel's results focused on the U.S. real exchange rate against various trading partners, but as one can see from the figure, the results are (almost) as striking for a pairing of Germany and Japan. Other non-U.S. pairings that we have examined look similar.
We have argued that the traded-nontraded-goods distinction is much too finely drawn-at the retail level, many "traded" goods already embody very large nontraded components, and the dividing line is arbitrary and likely endogenous. It is nevertheless surprising just how little difference there is between the measures of real exchange rates in Figure  3. These findings probably cannot be ascribed merely to price aggregation problems, since many researchers report similar sluggish responses even for relatively disaggregated data on consumer goods that are commonly perceived as highly tradable. (See, for example, Isard, 1977; Giovannini, 1988; and Engel and Rogers, 1996.) The results certainly seem to suggest that even over the medium term, the consumer prices of supposedly tradable goods are nearly as insulated from the forces of international arbitrage as are the consumer prices of nontradables.

ADJUSTMENT IS FASTER AT THE PRODUCER LEVEL
It is important to emphasize that there seems to be considerably more adjustment of prices to exchange-rate changes at the importer level than at the consumer level. In their excellent survey of the empirical literature on exchange rates and international prices, Goldberg and Knetter (1997) conclude that the passthrough of exchange rates to relative international prices is about 50% after one year, much faster than what we have just

See Appendix A of Engel (1999). Figure 3 looks much the same if attention is restricted
to data from the floating-exchange-rate period, 1973-1995. They find that this does not seem to be the case empirically, and instead find significant support for the conventional view-that exchange-rate depreciation worsens the term of trade of the depreciating country.

TRADE COSTS AND PRICING TO MARKET
Whereas the home bias in trade could, in principle, be explained simply by a home bias in preferences, the failure of markets to arbitrage international price differentials for seemingly identical goods cannot. The most popular explanation of persistent international price differentials argues that most goods are supplied monopolistically, and that (by assumption) monopoly producers have very broad scope to price to market by charging different prices in home and foreign markets (see, for example, Dornbusch, 1987; Krugman, 1987; Betts and Devereux, 1996; Bergin and

Feenstra, 2000; or Devereux and Engel, 2000). Goldberg and Knetter (1997) survey a large body of supportive empirical evidence. This explanation of international price differences for very similar or identical goods is appealing, but incomplete. What is to prevent consumers from arbitraging between home and foreign prices? Any explanation-and the pricing-to-market literature offers many; see Dornbusch (1987)-has to be consistent with the tenuous connection between exchange rates and the relative prices for virtually any type of consumer good.
Rationales for pricing to market that might make sense for bigticket items such as cars (the steering wheels on American and Japanese cars are on opposite sides, dealers can refuse warranty service for vehicles purchased abroad, etc.) are not very appealing when applied to, say, basic clothing items.
In our view, trade costs simply must play a central role in any explanation of international price differentials. However, to make sense of the price data, we must refine our earlier discussion of trade costs to distinguish between bulk wholesale and individual consumer trade costs. We must also think carefully about the ability of producers to control international distribution chains at the wholesale level. Otherwise-if the only wedge between home and foreign markets were moderate trade costs-one would only observe moderate price differentials.

WHOLESALE BULK VS. RETAIL INDIVIDUAL TRANSSHIPPING COSTS
At the consumer level, it is likely that for many goods, trading costs are in fact quite large, and far, far larger than trading costs faced by bulk wholesale shippers. (Individual consumers cannot profitably arbitrage even large differences in Coca-Cola prices across countries, but bulk wholesalers can.) The real question is what prevents international price arbitrage at the wholesale level. One answer is that in many cases, a firm can establish legal rights to control distribution of its product in different countries. Exclusive national marketing licenses are extremely common. For example, to protect its ability to price-discriminate across home and foreign markets, the Coca-Cola company sued a couple of small American wholesalers who, during the late 1990s, were trying to arbitrage the difference between Coca-Cola's $11.50-per-case wholesale price in Japan (as of January 2000) and its wholesale $5.50-per-case price in the United States-a differential far in excess of bulk shipping costs.34 True, for small firms, the costs of establishing sole country distribution rights, and even more the legal costs of enforcing such rights, are likely to be prohibitive. Such firms also are likely to deal only with a very small number of bulk wholesalers, however, so it is still quite possible that they can pricediscriminate, either by exploiting long-term relationships with their downstream wholesalers or even by taking over more portions of their wholesale distribution network.

PRICING TO MARKET AND THE PPP PUZZLE
To explain the data adequately, one must flesh out many details that we are omitting here. Very simple models of the kind we used in the first four sections are simply not adequate. For example, it is well known that with constant elasticities of demand, a monopolist may charge different prices in different countries, but exchange-rate changes will not cause fluctuations in relative prices charged [see Dornbusch (

THE EXCHANGE-RATE DISCONNECT PUZZLE
The same reasoning we have applied to thinking about the PPP puzzle can be applied to a much broader range of puzzles, all relating to the remarkably weak short-term feedback links between the exchange rate and the rest of the economy. We term this broader class of puzzles the exchange-rate disconnect puzzle. In a sense, the PPP puzzle is simply a very important special example of this broader class of phenomena. Of course, one may well ask why the exchange-rate disconnect puzzle should be any different from the stock-price disconnect puzzle, that is, the fact that stock markets seem to gyrate wildly without having any sizable contemporaneous effects on the real economy. We ourselves (Obstfeld and Rogoff, 1996, Chapter 9) have argued that to understand exchangerate volatility, one ultimately needs a broader model that explains the high volatility we seem to observe in all asset markets. While we still maintain that view, it is also true that the links between the exchange rate and the real economy are much more direct than for stock prices. In most economies, the exchange rate is the single most important relative price, one that potentially feeds back immediately into a large range of transactions. Because the potential links are so direct, it is surprising indeed that they are not stronger.
Though much work remains to be done, it appears to us that a framework such as the one we have outlined earlier in this section (under puzzle 5) holds great potential for explaining the other disconnect puzzles as well. For example, exchange rates are remarkably volatile relative to any model we have of underlying fundamentals such as interest rates,

Working in a competitive flexible-price model with transport costs, Ravn and Mazzenga
(1999) are also unable to rationalize both the real-exchange-rate volatility and the realexchange-rate persistence in the data. Ohanian and Stockman ( outputs, and money supplies, and no model seems to be very good at explaining exchange rates even ex post. The traditional thinking is that even though a broad range of goods is nontraded, there is always a broad range of goods that are traded, and these tie down the exchange rate. But a recurring theme here is that markets for most "traded" goods are not fully integrated, and segmentation due to various trade costs can be quite pervasive. In fact, the spectrum of goods subject to low trade costs may be very narrow.
In the type of model we described earlier in this section, a financialmarket shock that moves the exchange rate may have little economic effect even over a fairly long horizon. With pervasive pricing to market at the retail level, consumers will be largely insulated from exchange-rate effects until these have had the time to feed through to wholesale import prices and, from there, to retailers. The magnitude of the PPP puzzle suggests how long that process might take.
Thus, interacting with the segmentation caused by trade costs, nominal price rigidities can produce a disconnect in which the exchange rate responds wildly to shocks. With the prices of most goods preset in local currency and real variables such as aggregate consumption largely insulated from exchange rates in the short run, exchange-rate adjustments have minimal short-run economic effects and therefore must be huge to clear financial markets. Only gradually will the responses of importers and exporters feed through to the retail level-and the adjustments might well be too slow to be picked up in the kinds of tests performed by Baxter and Stockman (1989). High volatility and the exchange-rate disconnect therefore both result from a combination of trade costs (costs that are especially high for consumers), monopoly, and pricing to market in local currency. A full model would incorporate those factors, while also modeling fully the dynamics of price adjustment through retail distribution networks, as well as other channels through which exchange rates might affect the real economy. 37 We do not have space to explore the many implications that this intriguing class of models suggests. Can heightened exchange-rate volatility due to transport costs act to further segment markets internationally, with a resulting multiplier effect on volatility?38 What are the welfare 37. Engel (1996) proposes that if all consumer prices are preset in local currency and firms fully hedge currency risks, exchange-rate changes will have no real effects and therefore exchange rates will be indeterminate. Hau (2000b) develops a new open-economy macroeconomic model in which exchange-rate volatility is decreasing in the degree of openness to international trade. 38. The theoretical work of Bacchetta and van Wincoop (1998) and Rogoff (1998, 2000) and the empirical work of Obstfeld and Taylor (1997) and Rose (2000) suggest that currency volatility may itself act as a barrier to international trade.
costs of the exchange-rate disconnect? But the general approach strikes us as a very promising and realistic way to think about a host of exchange-rate volatility puzzles.

Conclusions
The need for research on the effects of trade costs in standard models of international finance seems compelling to us. We find that introducing plausible proportional (iceberg) trade costs into the most standard international macroeconomics models substantially resolves many of the core empirical puzzles in the field, including especially the (seemingly intractable) Feldstein-Horioka puzzle, the home-bias-in-equities puzzle, the home-bias-in-trade puzzle, and the low-consumption-correlations puzzle. We cannot claim the same degree of success in elucidating pricing puzzles as in the case of quantity puzzles, at least not with the kind of very simple models we have featured here. To tackle the PPP puzzle and the exchange-rate disconnect puzzle properly, a much richer framework featuring imperfect competition and wage-price rigidities is needed (therefore one in which, at a very fundamental level, neither domestic nor international markets are perfect). It is also necessary to build in a distinction between retail and wholesale pricing to account for the sharply different behavior of terms-of-trade indexes vs. consumer price indexes in response to exchange-rate changes (see Rogoff, 2000, andTille, 2000). We have argued, however, that introducing trade costs (implicitly or explicitly) must be an essential ingredient in resolving the international pricing puzzles as well. Richer models might consider fixed costs of trade as well as the proportional costs on which we have focused here.39 Although we take an eclectic perspective on the degree of completeness of international capital markets, our analysis does not rely on the assumption that their performance is intrinsically inferior to that of domestic capital markets (at least not in analyzing data for OECD countries). Our focus, instead, is on the distinctive ramifications for assetmarket performance of the imperfect integration of goods markets. One attractive feature of our approach is that it is entirely consistent with the observation that gross flows in international capital markets are much larger than the small net flows.
An obvious potential criticism of our central theme is that transport technology has been steadily improving over the past half century, and tariffs have fallen dramatically, especially among the OECD countries. Has the home bias in trade and equities lessened, and are the consump- (1997) give an example of a theoretical model of price arbitrage involving fixed as well as variable costs.

O'Connell and Wei
tion-correlations and Feldstein-Horioka puzzles less acute than they were half a century ago? The short answer is that trade, capital movements, and equity flows all have expanded sharply since 1950, so the major quantity puzzles are less acute. For example, the ratio of total trade (the sum of imports and exports) to GDP has roughly doubled across the OECD between 1950 and 1995; for the United States, it has risen from 9% in 1950 to 24% in 1995.40 (This calculation may significantly understate the true growth rate, since a large fraction of trade is in manufactures, the relative price of which has been falling over time.) And, as we have already seen, OECD savings-investment correlations have fallen significantly (from 0.89 for 1960-1974 to 0.60 for 1990-1997), while holdings of foreign equity have risen sharply (for the United States, from a 4% share in 1987 to a 10% share in 1996). At the same time, while transport technology has steadily improved, labor costs have risen sharply, so there is actually some debate about whether net transport costs have fallen. Hummels (1999b) argues that, until recently, the overall effect has been relatively small, with shipping costs falling sharply for bulk commodities but actually rising for manufactures, which account for over 70% of OECD trade. Greenspan (1989), on the other hand, emphasizes that trade is getting lighter, as many of the goods and services being traded today are highly knowledge-intensive. Overall, the data for the past half century certainly do not provide any prima facie case against our approach. It would be interesting to look at time spans beyond just the past fifty years, so that trend declines in trade costs become more pronounced. Williamson (2000) calculates that transport costs for internationally traded goods fell by 1.5% per annum in real terms from 1850 to 1913, with the rate slowing down substantially over 1913-1950. Although prewar data are much thinner than postwar, and although there are many other factors to control for (large fluctuations in tariff rates, decolonization, wars, changes in the international monetary regime, etc.), this would nevertheless be a useful exercise. Cross-sectional empirical work is also needed.
Finally, a small apology to readers who were expected us also to address the forward-premium puzzle. We simply have not yet tackled this particular pricing puzzle, which we regard as much more of a pure finance question than a macroeconomic puzzle (and hence this paper's title). We note, however, that Dumas (1992) has produced a model of the forward premium in which trade costs do pull in the right direction, so getting a trade-cost model with the right quantitative effects may indeed be possible. 40 Table 7 presents saving and investment rates by country for 1990-1997.

on NS and Y are from the OECD database. For non-OECD countries, NS was constructed, from International Financial Statistics (IMF), as follows: NS = GNPprivate consumptiongovernment consumption. Our measure of NS for non-OECD countries does not exactly match the theoretical definition. The main difference is that it does not take account of the balance-of-payments component "net current transfers from abroad." Most of the countries that report data to the IMF and are not in the sample were excluded for one of four reasons: (1) IFS has data only for GDP and not GNP; (2) there are no IFS data on inventory investment; (3) there is a significant statistical discrepancy either between GDP and its components (more than 3%), or between GNP and the sum of GDP and net factor income/ payments from abroad (more than 2%); (4) population is under 1 million. I/Y: investment/GDP, average over 1990-1997. Investment is the sum of gross fixed capital formation and increase (decrease) in inventory stocks. Sources are as in note a.
CThe OECD sample of countries includes those that were members in 1995. dGNP per capita measured in U.S. dollars, for 1997. eNo data for 1996 and 1997. fNo data for 1997. gNo data for 1991.

Introduction
One of the pleasures in reading this paper is that it has the flavor of a conspiracy theory. It explains a set of apparently unconnected and unexplained phenomena in terms of a single cause, which, the authors argue, is not as implausible as it sounds. And they succeed at least in instilling doubts-this on the basis of careful theoretical reasoning and some empirical evidence. This is a thought-provoking paper, which I expect to be influential and inspire a number of theoretical and empirical papers: it raises a number of hypotheses that are both theoretically intriguing and potentially testable. The thesis in this paper is that the main puzzles in international macroeconomics can be explained as the result of costs in the trade of goods and services. The paper nicely weaves together empirical evi-

Introduction
One of the pleasures in reading this paper is that it has the flavor of a conspiracy theory. It explains a set of apparently unconnected and unexplained phenomena in terms of a single cause, which, the authors argue, is not as implausible as it sounds. And they succeed at least in instilling doubts-this on the basis of careful theoretical reasoning and some empirical evidence. This is a thought-provoking paper, which I expect to be influential and inspire a number of theoretical and empirical papers: it raises a number of hypotheses that are both theoretically intriguing and potentially testable. The thesis in this paper is that the main puzzles in international macroeconomics can be explained as the result of costs in the trade of goods and services. The paper nicely weaves together empirical evi-dence and theoretical arguments, some of which are explicitly modeled with the pedagogic elegance that is one of the authors' trademarks. Obstfeld and Rogoff (OR) start with the rather uncontroversial point that trade costs can generate a significant degree of segmentation in the goods market, before moving to the more provocative part of their thesis: the international segmentation of asset markets could result from the same trade costs. In other words, it might be unnecessary to invoke the many frictions specific to the asset markets that have been discussed in the literature.1 I shall focus my comments on the Feldstein-Horioka puzzle, the international-consumption-correlation puzzle, and the exchange-rate disconnect puzzle, since this is where OR are more innovative and provocative. It is rather uncontroversial in principle that trade costs can generate a significant degree of international segmentation in the goods market, especially if goods are sufficiently substitutable and if trade costs are defined in a sufficiently broad way. OR go beyond this theoretical remark, and convincingly argue, on the basis of estimates for transportation costs and the elasticity of substitution between goods, that trade costs can explain a large degree of international segmentation in trade. An important challenge, for the scholars who will pursue this line of reasoning, will be to refine the mapping between the various trade costs (distinguishing, in particular, between those that are border-related and those that are not) and the pattern of trade segmentation that we observe in the real world.

Explaining Asset Market Segmentation by Trade Costs
OR's discussion of the different channels by which frictions can spill over from goods markets to asset markets is truly impressive in its theoretical breadth and originality of insight. I shall restrict the scope of my comments to the two channels which OR have chosen to model explicitly. The first model is presented by OR in connection with the Feldstein-Horioka puzzle; it relies on an implicit wedge in the real-interest-rate parity condition. The second model attempts to explain the home bias in equity portfolios; it looks at the implication of nontraded goods for portfolio choice.
1. The home bias in equity portfolios has been attributed to informational asymmetries , cultural and linguistic barriers, and differences in national tax systems and regulations .  show that in a portfolio perspective the Feldstein-Horioka puzzle can be viewed as a direct consequence of the home bias in asset portfolios.
The link between nontraded goods and portfolio choice is the object of a growing literature, which is difficult to review in a short space. Let me simply note that this literature may seem a bit less optimistic, in its most recent developments, than OR in this paper. In her recent review,  underlines several shortcomings of the approach; in particular, she argues that a key prediction of OR's Section 4 model-that investors hold a globally diversified portfolio of traded-good industries, but nontraded-good industries are held entirely domestically-is not supported by casual empiricism. Pesenti and Van Wincoop (1996) apply a model of optimal portfolio choice with nontraded goods to fourteen OECD countries, and find that it can explain only a small fraction of the home bias. The model presented here by OR differs from the previous literature by assuming a trade cost which applies to all domestic output, rather than drawing an arbitrary line between tradables and nontradables. It remains to be seen whether endogenizing the frontier between traded and nontraded goods significantly improves the model's ability to explain the home bias in equity portfolios. I was more intrigued by the first channel, "an entirely new explanation, based on transaction costs for international trade in goods," (Section 3.1) and shall spend, accordingly, the rest of this section commenting on it.

TRADE COSTS AND INTERTEMPORAL PRICE WEDGES: A ONE-GOOD MODEL
In their explanation of the Feldstein-Horioka puzzle OR present a model of the consumption-saving choice in a small open economy with trade costs. First, let me rephrase OR's main point in the context of a one-good model (this is the limit of their two-good model where the two goods are perfectly substitutable). The one-good model is less general but makes the logic of OR's point more transparent.2 I keep the same notation as OR except that the subscripts denoting the difference between home and foreign goods are dropped. For convenience, the representative agent's psychological discount rate is assumed to be equal to the world real interest rate.
The good can be exported to or imported from a global perfectly competitive market, where its price, P*, is fixed in terms of the world currency unit. Because a fraction T of the good "melts" in transit, the home price of the good (where home means net of trade costs) is given by It is interesting to note that these results do not hinge on particular assumptions on the time structure. The two periods could be separated by one month or one generation. If the model had more than two periods, or time were continuous, the no-trade region would still be characterized by a condition like (1). The model predicts that there is no international trade as long as domestic income does not deviate too much from its average level.  for an arbitrary continuous time path of domestic output. As long as domestic output remains in the no-trade region, the trade balance is equal to zero and the fluctuations in consumption mirror those of output. By contrast, consumption is completely smoothed when output takes extreme values outside the no-trade region. As a result, the correlation between domestic output and domestic consumption is equal to 1 in the no-trade region and equal to 0 outside. If output remains in the no-trade region most of the time, the observed average correlation will be close to 1. This might seem like a puzzle to the outside observer, who would expect consumption to be smoothed all the time, given that the capital market is perfectly integrated internationally (this is one way to define the international-consumption-correlation puzzle).
Explaining the Feldstein-Horioka puzzle by the same logic requires an explicit consideration of investment opportunities at home and abroad. Assume for example that residents have access to domestic investment opportunities with decreasing returns. If, in the two-period model, the return on the marginal domestic investment remains between (1r)2 and (1 -T)-2 times the return on investments abroad, then the represen-tative domestic agent invests all his savings at home, and domestic saving and investment behave in the same way as under autarky. Domestic saving will be perfectly correlated with domestic investment, as in the Feldstein-Horioka puzzle.

THE MULTI-GOOD CASE
In order to explain the low correlation of international consumption (the Feldstein-Horioka puzzle), OR need trade costs to generate a wedge between the domestic real interest rate and the world real interest rate. In other words, they need the instantaneous price wedge generated by trade costs-which they use to explain the home bias in trade-to be augmented by an intertemporal wedge. As OR's two-good model shows, this intertemporal wedge can arise under more complex goods structures than the one-good model I have just presented, although in that case the analysis is more complicated.
Introducing a second good into the model allows us to focus on the composition of the country's imports and exports. In OR's two-good model the home and foreign goods are both exchanged in global competitive markets at given prices in terms of foreign currency units. While the foreign good is always imported, the home good may be exported or imported in equilibrium. Whether the home good is imported or exported, moreover, is crucial for the model's ability to produce a wedge between the domestic real interest rate and the world interest rate.
As OR show, if the trade balance involves a round trip in the home good-i.e., if this good is exported at one period and imported at the other-there is a wedge between the domestic real interest rate and the world interest rate.4 In this case the consumption-saving behavior of domestic residents can be analyzed in the same terms as in the one-good model, the home good playing the same role as the single good in the one-good model. By contrast, if the domestic country exports the home good in both periods, there is no wedge in the real-interest-rate parity condition, and the intertemporal current account behaves in the same way, qualitatively, as in the absence of trade costs.5 Although trade costs distort the relative price of the home and foreign goods in each period, they do not change the intertemporal rate of substitution of home consumption between period 1 and period 2.
This raises the question of the robustness of OR's explanation for the Felstein-Horioka puzzle to changes in the underlying assumptions on the goods structure. In particular, it would be interesting to explore how easily the logic of OR's argument can be transposed to a framework where international trade involves differentiated goods. The transposition is not trivial, because trade in differentiated goods cannot exhibit the round trips which seem to play a role in OR's results. While a carproducing country may have a trade deficit or a trade surplus in cars at any given period, it is impossible by construction for this country's trade balance to exhibit a round trip in any of the differentiated goods, or brands, that compose the composite good "car." France, say, always exports Renaults and always imports Fords or Volkswagens.
Generalizing OR's model to differentiated goods would also enhance its empirical relevance. It is well known that most of the trade between industrial countries involves differentiated goods. This stylized fact has been widely documented in the literature on international trade under imperfect competition, for which it provided the founding motivation. It would be important to understand how the logic of OR's argument applies to this case, since it is precisely for developed economies that the Felstein-Horioka puzzle and the international-consumption-correlation puzzle are most puzzling (for less developed economies other factors, such as country risk, can be invoked, as OR note).

A LOOK AT THE DATA
Although it remains to be seen whether OR's analysis is robust to monopolistic competition, their assumptions seem plausible for international trade in raw commodities, which are generally exchanged in very competitive markets. Their model predicts that because of trade costs, we should observe few round trips in raw commodities. Is this prediction borne out by the data? Table 1 provides evidence on the occurrence of round trips for a sample of ten countries and five raw commodities. The table is constructed using the United Nations annual trade data set over the period 1988-1998. The + (-) sign indicates that the country has been an exporter (importer) of the commodity over the whole period, i.e., every single year from 1988 to 1998. The sign + indicates that at least one round trip (change in the sign of the trade balance in the commodity) has been observed.
The results reported in Table 1 are consistent with the model's prediction. Of the 42 country-commodity pairs for which data are available, almost 90% do not show any round trip. This finding could be interpreted as evidence in favor of OR's hypothesis that round trips are discouraged by trade costs. However, it could also reflect the fact that trade in primary commodities is driven by comparative advantage, not by intertemporal consumption smoothing. In a world where comparative advantage is the driving force, we would observe very few round trips even in the absence of trade costs.

The Exchange-Rate Disconnect Puzzle
OR present very stimulating developments on exchange-rate excess volatility and what they call the exchange-rate disconnect. Their point can be loosely summarized as follows: because of the combination of nominal stickiness and pricing to market at the level of the domestic consumers, the exchange rate matters very little for anything real in the domestic economy (at least in the short run), so that it can wander around under the impact of small shocks. OR's "disconnect" is between the exchangerate and goods markets. OR's point is related to an old question in exchange-rate economics: Should one view exchange rates primarily as asset prices or primarily as the determinants of relative prices in goods markets? Of course they are both to some extent, and one way to view the history of exchangerate theory-from its early developments to the "new open macroeconomics"-is as a long struggle to integrate both aspects of exchangerate determination in a coherent framework. The substance of the question, however, was in the adverb primarily. To rephrase the question: Is it practically more relevant to think of exchange rates as asset prices, or as determinants of relative prices in the markets for goods-if, leaving general equilibrium aside, one had to choose between the two views? I interpret OR's "exchange-rate disconnect" as the idea that exchange rates matter so little for relative prices that they can best be viewed as asset prices-at least to a first approximation. Let us now consider the case where the international exchange of good is prevented in period 1 by infinite trade costs (r1 = +oo). Then the law of one price no longer holds at period 1 and domestic consumption is equal to domestic output in both periods: cl = y, and c = y' = 0. Taking the expectation of money demand at period 2 gives s2 = m2, so that the nominal exchange rate at period 1 must satisfy

A MODEL
Simple manipulations of the remaining equations then give the following reduced-form expression for the exchange rate: Comparing equations (2) and (4) brings out the implication of trade costs for the determination of the exchange rate in this model. In the absence of trade costs the exchange rate is determined in the goods market: Equation (2) is an arbitrage condition between the domestic and the foreign price of the good. By contrast, in the presence of (high enough) trade costs, the exchange rate is determined in the asset market. Equation (4) is an arbitrage condition between domestic currency and foreign currency bonds. In this simple setup, infinite trade costs produce a complete exchange-rate disconnect at period 1 (in the sense that the exchange rate has no direct connection with domestic output or the domestic price level), and as a result, the equation for the exchange rate becomes a pure asset-pricing equation.7

CAN THE EXCHANGE-RATE DISCONNECT EXPLAIN EXCESSIVE EXCHANGE-RATE VOLATILITY?
Does the exchange rate become more volatile as a result of trade costs? Comparing equation (3) and equation (5) shows that the answer is yes if, and only if, (1 + po-)/(l + r-) > 1/(1 + o-/2), i.e.,

p > + (6)
High trade costs increase exchange-rate volatility if the intertemporal substitutability of consumption, l/p, is low enough. This is because a lower intertemporal substitutability of consumption makes the interest rate-and so the exchange rate, when it is determined as an asset price-more volatile. There is another sense in which trade costs can generate an exchangerate disconnect in this model. If international trade involves a cost not only at period 1 but also at period 2 (T2 t 0), then the nominal exchange may become indeterminate in both periods over some range of parameter values. This point is extremely easy to see in the extreme case where trade costs are infinite in both periods. Then the law of one price is removed from the set of equations (S) and there is nothing to pin down the exchange rate. Indeterminacy can be a significant cause of volatility if the exchange rate fluctuates widely in the range of indeterminacy, under the influence of market sentiments and other nonfundamental factors.8 7. The asset market is in equilibrium, and the.interest parity condition holds, irrespective of trade costs. Under the exchange-rate disconnect, however, the interest parity condition endogenizes the exchange rate after the nominal interest rate has been solved for using the other equations. Under perfect trade integration it endogenizes the nominal interest rate after the exchange rate. 8. The intuition behind the exchange-rate indeterminacy can be conveyed by the following parable. Assume that humans come into contact with an extraterrestrial civilization with which telecommunications are easy, but the exchange of goods is ruled out forever because of the enormous distance between them and us. Assume that in a misconceived attempt to extend the reach of liberal capitalism to outer space, an electronic market for the exchange of extraterrestrial and terrestrial currencies and nominal bonds is estab- The notion that exchange rates can be indeterminate, and that this indeterminacy could generate excess volatility, is not new.9 From a theoretical point of view, moreover, indeterminacy is a rather brittle property of this model. It hinges on a complete and permanent absence of international trade. The certainty that countries will exchange at least one good, even in the distant future and in very small quantities, suffices to pin down the exchange rate-making indeterminacy an unconvincing explanation for excess exchange-rate volatility in a world where countries routinely trade with each other. Still the model may have some pedagogical value, if only to make the point that although their short-run dynamics may obey the rules of asset pricing, exchange rates are ultimately pinned down by international trade in goods.
Another question is the extent to which the exchange-rate disconnect makes the high volatility of exchange rates observed in the data less puzzling. This is not entirely clear to me. The only substantial implication of the exchange-rate disconnect for exchange-rate volatility, if I understand OR correctly, is that the volatility of exchange rates should be thought of in the same way as the price volatility of other assets.10 The asset perspective, however, is precisely the one adopted by most of the empirical literature on the excess volatility of exchange rates.ll The exchange-rate disconnect, then, just leaves us with the more general question: why are asset prices so volatile? Answering this question is likely to require departures from key assumptions (such as common knowledge or rational expectations) on which most exchange-rate models, including those in this paper, are based.

Introduction
Obstfeld and Rogoff have once again written an important paper that undoubtedly will be highly influential in developing our understanding of many of the major puzzles in international macroeconomics. They highlight the fact that goods markets for consumers appear to be very far from being perfectly integrated, and show how this imperfection can help provide a unified understanding of the puzzles that have eluded satisfactory explanation. These goods-market imperfections are a plausible direction to look toward because the empirical evidence suggests they are significant in magnitude. And Obstfeld and Rogoff (referred to as OR hereinafter) provide us with models that make sense at an intuitive level.
My comments primarily focus on three issues:

Introduction
Obstfeld and Rogoff have once again written an important paper that undoubtedly will be highly influential in developing our understanding of many of the major puzzles in international macroeconomics. They highlight the fact that goods markets for consumers appear to be very far from being perfectly integrated, and show how this imperfection can help provide a unified understanding of the puzzles that have eluded satisfactory explanation. These goods-market imperfections are a plausible direction to look toward because the empirical evidence suggests they are significant in magnitude. And Obstfeld and Rogoff (referred to as OR hereinafter) provide us with models that make sense at an intuitive level. My comments primarily focus on three issues: In reviewing some of the existing literature, it appears to me that trade frictions alone do not explain the puzzles. While they move things in the right direction, quantitatively goods frictions are insufficient. OR provide us with extraordinary intuition for why goods markets move things in the right direction, but we need more study to be able to reconcile their compelling but simplified examples with the results that emerge from simulation of more fully specified dynamic models. This very much reminds me of the literature on one puzzle that OR do not try to resolve-the forward-premium puzzle. There, the easy explanation that was proposed is that a foreign-exchange risk premium can lead to biased forecasts of the forward premium. But when researchers tried to embed risk premiums into calibrated equilibrium models and assess the size of that effect, they found that the risk premium was far too small to explain the magnitude of the deviations from uncovered interest parity. The parallel is that the literature so far has not found that goods-market imperfections alone can quantitatively explain the OR puzzles.
There is another parallel with the literature on the forward-premium puzzle. When researchers finally were able to construct models that got close to matching the magnitude and sign of the deviation from uncovered interest parity, they found that their models had a very unpleasant implication about the moments of another variable. In that case, the problem was that the models implied nominal-interest-rate volatility that was much greater than what is found in the data. The parallel here is that the models that OR propose imply a high correlation of real exchange rates with relative consumption levels across countries. OR call this the "Backus-Smith" problem. They appear to dismiss this issue, but in doing so leave me puzzled as to how we can reconcile the implications of their approach with the data.
My comments will focus on puzzles 2-4 of OR (which I call the core puzzles): the Feldstein-Horioka puzzle, the home-bias-in-equity-port-folios puzzle, and the international-consumption-correlations puzzle. These three puzzles are linked in that they can best be understood as pointing toward a surprising lack of risk sharing internationally. I comment only briefly on the other three puzzles.
To reiterate, I do think that costs of trade are fundamental in understanding these puzzles. Capital-market imperfections alone are not the answer. OR provide new insight into how trade costs can help resolve the puzzles, and should help to focus future research endeavors in this promising direction.

The Core Puzzles
To my tastes, the clearest way to demonstrate the claim that trade costs alone can explain the core puzzles would be to use the model of complete asset markets and no trade frictions as the benchmark, and show how far trade costs get us. For example, the home-bias-in-portfolios puzzle is no puzzle at all if the null model is one in which there are restrictions on asset trade or missing asset markets.
Let me briefly review the three core puzzles to help clarify. We find very low correlations of consumption internationally. That is puzzling because it seems to imply that there is very little sharing of idiosyncratic shocks to income. To me (and to OR) the puzzle is not that there is an absence of complete risk sharing. The puzzle is that there appears to be so little risk sharing-much less than we would expect given the wide array of assets that allow us to hedge risk. But how can we measure the ability of trade costs to explain the low correlation of consumption levels? The natural way to me (and apparently to OR) is to assess the effects of introducing trade costs into a model with complete asset markets. We know that the free-trade, complete-markets model implies perfect correlation-so how far does that correlation fall when there are plausible trade costs?
Home bias in portfolios is puzzling at an intuitive level. Investors could more effectively hedge risk by balancing their portfolios among assets from countries around the globe. Diversification is the fundamental principle of risk management. Again, however, it is helpful to have a benchmark to assess the effects of trade costs. In general, full diversification of equity holdings does not achieve complete risk sharing, but OR quite naturally focus on special models where that does occur. This special case is appealing because it gives us a simple benchmark to compare the effects of market imperfections against. Furthermore, as OR show in this paper (and in their 1996 textbook), "for realistic parameters, trade in equities alone can come quite close to attaining the complete-markets consumption allocation, so that the home bias evident under complete markets is a good guide to the home bias in an equitiesonly model." The Feldstein-Horioka paradox has been a hard one to pin down. Why is the finding of low correlation of saving and investment a puzzle? OR's (1996) textbook has, for my tastes, the clearest explanation of the puzzle. In a Walrasian model with no trade barriers and complete asset markets, the amount of investment in a country's capital stock should be independent of the parameters that determine the country's consumption level. The simplest way to see this is to think of the special cases in which a diversified portfolio of equities mimics complete markets. In that case, the firm's decision to add to capital must be independent of the consumption choices of the individuals who live in the country where the firm produces. The firm is owned globally, so why would the consumption or saving decisions of the residents of the country where the firm is located have any special influence on its investment decision? So, again, a natural benchmark to compare the effects of trade costs alone is the free-trade, complete-markets Walrasian model.

The Literature
There are two reasons why I emphasize that the complete-asset-markets model is a natural benchmark. First, there actually exists a literature that looks into trade costs as an explanation for these puzzles. Using complete markets as the benchmark, introducing trade costs alone does not appear to get us very far in resolving the puzzles. The second reason I emphasize it is that while OR naturally gravitate toward the completemarkets model as a benchmark, in several instances they subsequently inveigh against that model on the grounds essentially that in the real world markets are not complete. True, but the complete-markets model is a useful benchmark. I address the literature in this section. In Section 5, I return to the benchmark issue.
The careful reader might have noticed footnote 2 in OR. It makes reference to Backus, Kehoe, and Kydland (1992), which is the piece that brought the consumption correlation puzzle to the attention of the profession. That paper actually devotes an entire section to whether the introduction of trade costs of precisely the type OR propose can explain the consumption correlation puzzle. Their model is a fairly detailed Walrasian, complete-markets model. They can assess directly the effect of trade costs on consumption correlations. And they find that the introduction of trade costs into their model actually makes the consumption correlation puzzle worse, not better. Further investigation by the same authors in a subsequent study using alternative specifications of trading costs  confirms that the consumption correlation puzzle is not solved by trading costs.
In fact, however, the Feldstein-Horioka problem is partly explained by Backus, Kydland, and Kehoe when trading costs are introduced. And, as OR note in footnote 25, one can interpret some of their results as supporting the contention that moderate transportation costs help resolve the home-bias-in-equities puzzle. However, this illustrates where we need to go with the observations of OR. Does the solution to one puzzle make things worse for the others? When Backus, Kydland, and Kehoe build a benchmark complete-markets free-trade Walrasian model, they find that introducing trade costs helps in some dimensions but not others. And, as I shall discuss in the next section, there are some other dimensions along which the trade costs make things much worse.
I agree with OR that the dichotomy in many papers between traded goods and nontraded goods is not a useful one. As they say, we can probably think of all consumer goods as having a nontradable component. The problems they discuss in Sections 6.2-6.5 ought to be at the core of what we do research on in international macroeconomics. But, still, one wonders whether the literature in which nontraded goods are introduced as an explanation for these puzzles might be instructive as to how far trade costs will get us. By and large, the nontraded-goods models have not been particularly useful in resolving these puzzles. OR do provide a helpful description of the shortcomings of the nontradedgoods model with the portfolio diversification paradox, and show how trade costs might get us further. But what about the other core puzzles? And what about the Backus-Smith paradox?

Other Variables
As OR note in equation (15), the complete-markets models they introduce imply perfect correlation of the log of relative consumption levels internationally with real exchange rates. Backus and Smith (1993) were the first to derive this implication in a model with trade imperfections. (Theirs was a model with nontraded goods.) But the condition arises in a wide variety of contexts in which the law of one price fails.
The problem is that in the data there is virtually no correlation between relative consumption levels and real exchange rates. Backus and Smith document this in a fairly simple way for G7 countries. But Kollmann (1995) and  thoroughly demolish the notion that these two variables are connected. Kollman shows that, generally for advanced countries, real exchange rates and relative consumption levels are not cointegrated and that there is no discernible short-run relationship.
Of course, models sometimes have ancillary implications that are not supported by the data but are not critical to the issue of interest. But here, the implication is central to the resolution of the puzzles. In the OR models of this paper, trade costs lead to deviations from the law of one price, and deviations from the law of one price are the sole reason for the failure of purchasing-power parity. The changes in the real exchange rate that are generated are, in turn, what break the link between consumption levels across countries. That is, it is precisely the nonconstancy of real exchange rates in their models that explains why there does not appear to be a great deal of risk sharing.
My sense is that it is knowledge of the empirical findings of Backus and Smith (1993) and Kollmann (1995) that has convinced researchers that trade costs per se, or more generally models with law-of-one-price deviations, are not the sole solution to these riddles. Perhaps researchers should not have been scared away from this avenue, but OR do little to help us out on this problem. They say that "Trade costs would play essentially the same role in a world with, say, trade in debt and equities but not a complete set of Arrow-Debreu securities." That may be true, but it needs to be demonstrated. Can trade costs play a quantitatively significant role in resolving the puzzles in such a model? At this stage, this seems not much more than a conjecture. The models that are presented in this paper all have the implication that relative consumption levels are perfectly correlated with real exchange rates. OR provide us with no evidence about models in which this link is broken.
It is also a bit disconcerting that OR focus exclusively on the implications of their models for the puzzles that the model is meant to address, and not on other implications of the model. The type of discipline that we rightly demand from the purveyors of general equilibrium Walrasian models (that is, the RBCers) is that they show us that the models can explain moments of some variables without generating unreasonable correlations among other variables. For example, would the OR models with trade costs imply negative correlation of inputs, such as arise in many of the RBC models (with and without trade frictions or nontraded goods)?

The Benchmark
OR seem to shrug off the Backus-Smith puzzle: "We do not take this as damning, since for us the complete-markets assumption was only a useful device for calibration, and not a conviction." Of course that is true for me too. But, where are we left? Apparently we need to concede that there is some deviation from complete markets to be able to accommodate the Backus-Smith problem. How far from completeness do they have to be? At what point have we stepped over the line and made capital-market imperfections part of the solution to the problem? In short, how can OR say that we can solve these riddles "without appealing to capital-market imperfections"?

The Other Puzzles
Let me briefly comment on some of the other issues raised by OR. First, I am not convinced that allowing for high elasticities of substitution goes that far in solving the home-bias-in-trade puzzle. There are small frictions in within-country trade as well, and one would suspect that goods produced within a country's borders are even closer substitutes than internationally traded goods. Yet, the small intranational trading costs do not seem to impose much of a barrier to intranational trade. Indeed, the revised version of  concludes that the story in which "high border effects arise almost entirely from high elasticities of substitution provides at best a partial explanation" of the home bias in trade.
The misleading thing about the OR examples in this regard is that there are no intranational frictions in trade. So they tell us that 0.25 is a modest value for proportional international trade costs, but implicitly assume that 0 is a modest value of intranational trade costs. It is easy to set up a model parallel to the one described in equations (1)-(6) of OR, but with two regions within each of two countries. Consider their calibration, allowing the elasticity of substitution intranationally and internationally to be equal to 6, but introduce within-country trade costs of 0.10. Then the ratio of intranational trade to international trade in the model falls to 2.5. If, in addition, one allows the intranational elasticity of substitution to be greater than the international elasticity (equal to 12 instead of 6), the trade-costs model goes only a small way toward explaining the home trade bias. The ratio of international to within-country trade explained by the model is merely 1.3. I found OR's discussion of the final two puzzles engaging and stimulating. Let me make just two comments. First, I think even in trying to explain exchange-rate volatility it might turn out that we need more than just goods-market imperfections. Here is why I make this conjecture.  consider exchange-rate volatility in which consumer goods markets are completely segmented and the law of one price fails. In their static model, indeed they find exchange-rate volatility is much larger (6 times larger) than a parallel model in which the law of one price and PPP hold. But when they move to a dynamic model with capital mobility , the volatility effect is much smaller. The exchange-rate variance is only 1.7 times larger in the segmented-markets model than in the model with integrated goods market. OR's intuition is that the goods-market frictions modify the dampening effect that capital markets have on exchange-rate fluctuations. But, in a dynamic setting, Betts and Devereux's results suggest that the modification may not be large.
The second comment is that I think it is a mistake to link the exchangerate disconnect puzzle with exchange-rate volatility. One way of putting it is that the exchange-rate disconnect puzzle is about why exchange rates are not correlated with fundamentals. It is a puzzle about correlations, not variances. In other words, I believe the case that OR are trying to make is that unobserved shocks might have a large effect on exchange rates if exchange rates are highly volatile. But observed shocks in the money supply and other fundamentals also should have large effects. It is not immediately clear that high volatility in the exchange rate implies a weak link between the exchange rate and fundamentals (which is what the exchange-rate disconnect puzzle is all about).

Concluding Comments
I think there may be a close link between the type of goods-market frictions OR describe and possible failures in the capital markets. Because the discipline imposed by goods markets on the equilibrium exchange rate is so weak, there may be more room (particularly in the short run) for noise in exchange rates. That is, "chartists" as in , or noise traders as in Jeanne and Rose (1999), or order flow from foreignexchange traders as in , might influence the exchange rate in the short run because misalignments in the exchange rate do not provoke a large immediate response from the real side of the economy. OR may be hinting at this in their Section 6.7 (or they may not be). I think this is a promising avenue to explore to help understand exchange-rate volatility and the disconnect between exchange rates and fundamentals. But it will require formal modeling and testing.
While it may seem that I am very skeptical of the ideas OR have presented here, I am not. My hunch is that their view and mine on these issues are very close (at least compared to the huge lack of consensus in international macroeconomics). I am more cautious than OR about the degree to which trade costs alone have solved the puzzles. But this difference in tone probably mostly reflects the differing roles of paper writers and paper discussants.

Discussion ?411
One final thought: it may be that over the next 50 years or so, international goods markets will become much more integrated and efficient through cyberspace, making the types of goods-market frictions that OR discuss less important over time. By the time we have built the models that explain the puzzles, the models and the puzzles may be obsolete. same results as with moderate trade costs, it might be necessary to assume that a very large fraction of goods are nontraded.
Michael Klein observed that trading costs, broadly construed, seem to be declining over time, which should imply that some of the puzzles are becoming less pronounced. Maury Obstfeld agreed and cited results in the literature to the effect that home biases in asset holdings and consumption have become smaller recently. Valerie Ramey suggested that immigration patterns and policies may affect trading costs, as immigrants are often effective middlemen for trade between their country of origin and their current residence. Richard Portes agreed with discussant Charles Engel that a full explanation of asset-market puzzles would require asset-market as well as goods-market imperfections, such as asymmetric information.
Alberto Alesina asked how broadly trade costs should be defined. For example, do they include costs arising from different currencies, languages, and legal systems? Obstfeld said that they were comfortable with a quite broad interpretation of trade costs. Alesina also noted that the number of countries in the world is rising, which is a negative development if cross-border costs are high. Obstfeld replied that Alesina's own work suggests that countries are proliferating in part because national independence confers greater flexibility in establishing trading and other economic relationships; so perhaps this is not a concern.
Allan Drazen objected to the use of iceberg costs on the grounds that the most important effects empirically are not distance effects but border effects. Further, many trading costs are not exogenous but are endogenously chosen, e.g., trade barriers. He suggested that European economic integration provides an excellent test case to study the effects of falling trade costs. Obstfeld agreed that border-related trade costs are quite important; the decision to use iceberg costs was based primarily on considerations of tractability.
John Leahy expressed the concern that the effects identified in this paper might turn out to be quantitatively small in a realistically calibrated model. The authors agreed that more work needed to be done to flesh out their story but noted that their model differs in important ways from those previously studied in the literature.