Gravity Redux: Measuring International Trade Costs with Panel Data

Gravity Redux: Measuring International Trade Costs with Panel Data Dennis Novy y University of Warwick April 2008 Abstract Barriers to international trade are known to be large. But have they become smaller over time? Building on the gravity framework by Anderson and van Wincoop (2003), I derive an analytical solution for time-varying and observable multilateral resistance variables. This solution gives rise to a micro-founded gravity equation from which bilateral trade costs can be directly inferred. This approach is easy to implement and obviates the need to impose arbitrary trade cost functions. As an illustration, I show that U.S. trade costs with major trading partners declined on average by about 40 percent between 970 and 2000, with Mexico and Canada experiencing the biggest reductions. JEL classi cation: F0, F5 Keywords: Trade Costs, Gravity, Multilateral Resistance I am grateful to participants at the 2007 NBER Summer Institute (International Trade and Investment), in particular James Harrigan, David Hummels, Nuno Limão and Peter Neary. I am also grateful to Iwan Barankay, Je rey Bergstrand, Natalie Chen, Alejandro Cuñat, Robert Feenstra, David Jacks, Chris Meissner, Niko Wolf, Adrian Wood, seminar participants at Oxford University and at the European Trade Study Group. y Department of Economics, University of Warwick, Coventry CV4 7AL, United Kingdom. d.novy@warwick.ac.uk and http://www2.warwick.ac.uk/fac/soc/economics/sta /faculty/novy/

Introduction Barriers to international trade are large and of considerable interest to policymakers. The tool that economists use most frequently to calculate the magnitude of trade barriers is the gravity equation. The typical gravity equation relates two countries bilateral trade ows to their economic size and to various bilateral trade barriers such as distance, linguistic di erences, tari s and exchange rate volatility. It is the aim of most empirical gravity work to identify and measure such bilateral trade barriers. However, in order to infer such bilateral trade barriers, researchers must also account for countries average trade barriers. In an important and highly in uential paper, James Anderson and Eric van Wincoop (2003) demonstrate that it is not only bilateral trade barriers but also multilateral trade barriers that determine the trade ows between two countries. For example, trade between the U.S. and Canada is not only in uenced by the U.S.-Canadian trade barrier. If U.S. trade barriers go down with all countries in the world except for Canada, then some U.S. trade will be diverted away from Canada although the bilateral U.S.-Canadian barrier itself has not changed. What matters therefore is the bilateral relative to the multilateral trade barrier. The purpose of this paper is to develop a methodology for measuring bilateral trade barriers. The contribution of the paper is twofold. First, building on the gravity model by Anderson and van Wincoop (2003) I derive an analytical solution for time-varying multilateral trade barriers, or multilateral resistance variables, that only depends on observable trade data. These multilateral trade barriers have been acknowledged for some time, for example by Anderson (979), Bergstrand (985) and Anderson and van Wincoop (2003), but so far it has been either impossible or very cumbersome to solve for them. Second, with the solution for multilateral resistance variables at hand, I am able to derive a theoretically consistent gravity equation that implies a micro-founded trade cost measure. This trade cost measure controls for multilateral resistance and can be directly computed from observable trade data without imposing a trade cost function that is assumed to rely on distance or other trade cost proxies. Generalizing the approach by Anderson and van Wincoop (2003), who only consider cross-sectional data, the trade cost measure is able to capture how trade costs change over time and can therefore be used with time series and panel data. Another advantage of the trade cost measure is that it captures a wide range of trade cost components including those that are not typically considered in standard gravity regressions. For example, the measure can capture informational trade costs as identi ed by Portes and Rey (2005) as well as hidden transaction costs due to poor security as

identi ed by Anderson and Marcouiller (2002). As an illustration I compute U.S. bilateral trade costs with a number of major trading partners. Over the period 970-2000 U.S. trade costs declined by about 40 percent, consistent with improvements in transportation and communication technology and the formation of free trade agreements such at NAFTA. In addition, I show that if multilateral resistance variables are misspeci ed as constants, trade cost estimates are likely to be biased because they will fail to account for secular trends in multilateral resistance. The paper is organized as follows. Building on the model by Anderson and van Wincoop (2003) I show in Section 2 how multilateral resistance variables can be expressed as a function of observable trade data. I also show how this expression can in turn be used to derive the micro-founded measure of bilateral trade costs. As an illustration Section 3 presents U.S. bilateral trade costs for a number of major trading partners. In Section 4 I provide a brief discussion of the results before concluding in Section 5. 2 International Trade with Trade Costs 2. The Anderson and van Wincoop Gravity Model Anderson and van Wincoop (2003) develop a multi-country general equilibrium model of international trade. Each country is endowed with a single good that is di erentiated from those produced by other countries. Optimizing individual consumers enjoy consuming a large variety of domestic and foreign goods. Their preferences are assumed to be identical across countries and are captured by constant elasticity of substitution utility. As the key element in their model, Anderson and van Wincoop (2003) introduce exogenous bilateral trade costs. When a good is shipped from country i to j, bilateral variable transportation costs and other variable trade barriers drive up the cost of each unit shipped. 2 As a result of trade costs, goods prices can di er across countries. Specifically, if p i is the net supply price of the good originating in country i, then p ij = p i t ij is the price of this good faced by consumers in country j, where t ij is the gross bilateral trade cost factor (one plus the tari equivalent). Based on this framework Anderson and van Wincoop (2003) derive a micro-founded Anderson and van Wincoop (2003) refer to regions instead of countries but this is irrelevant for the subsequent analysis. 2 Modeling trade costs in this way is well established in the literature. It is consistent with the iceberg formulation of trade costs that portrays trade costs as if an iceberg were shipped across the ocean and partly melted in transit (e.g., Samuelson, 954 and Krugman, 980). 2

gravity equation with trade costs: x ij = y iy j y W tij i P j () where x ij denotes nominal exports from i to j, y i is nominal income of country i and y W is world income de ned as y W P j y j. > is the elasticity of substitution across goods. i and P j are country i s and country j s price indices. The gravity equation implies that all else being equal, bigger countries trade more with each other. Bilateral trade costs t ij decrease bilateral trade but they have to be measured against the price indices i and P j. Anderson and van Wincoop (2003) call these price indices multilateral resistance variables because they include trade costs with all other partners and can be interpreted as average trade costs. Their exact expressions are P i = X j j = X i P j j t ij 8i (2) i i t ij 8j (3) where j is the world income share of country j de ned as j y j =y W. i is the outward multilateral resistance variable as it includes bilateral trade costs t ij summed over and weighted by all destination countries j, whereas P j is the inward multilateral resistance variable as it includes bilateral trade costs t ij summed over and weighted by all origin countries i. Thus, an important insight from gravity equation () is that bilateral trade ows do not only depend on the bilateral trade barrier but also on the multilateral trade barriers of the two countries involved. What matters is the relative trade barrier. 2.2 The Link between Multilateral Resistance and Intranational Trade It has been a problem in the literature to nd appropriate expressions for the multilateral resistance variables in equations (2) and (3). Anderson and van Wincoop (2003) point out that in general i and P j should not be interpreted as consumer price indices. For example, a home bias in preferences would yield the same gravity equation as () and the same expressions for i and P j as in equations (2) and (3). But then i and P j would include the nonpecuniary home bias and could therefore no longer be regarded as consumer price indices. 3

Instead, Anderson and van Wincoop (2003) assume that bilateral trade costs are a function of two particular trade cost proxies - a border barrier and geographical distance. In particular, they assume the trade cost function t ij = b ij d ij where b ij is a borderrelated indicator variable, d ij is bilateral distance and is the distance elasticity. In addition, they simplify the model by assuming that bilateral trade costs are symmetric (i.e., t ij = t ji ). Under the symmetry assumption it follows that outward and inward multilateral resistance are the same (i.e., i = P i ). Thus, conditioning on these additional assumptions, Anderson and van Wincoop (2003) nd an implicit solution for multilateral resistance based on (2) and (3). But there are a number of drawbacks associated with the additional assumptions. 3 First, the chosen trade cost function might be misspeci ed. Its functional form might be incorrect and it might omit important trade cost determinants such as tari s. Second, bilateral trade costs might be asymmetric, for example if one country imposes higher tari s than the other. Moreover, in practice trade barriers are time-varying, for example when countries phase out tari s. Time-invariant trade cost proxies such as distance are therefore hardly useful in capturing trade cost changes over time. In what follows, I propose a method that helps to overcome these drawbacks by deriving an analytical solution for multilateral resistance variables. This method does not rely on any particular trade cost function and it does not impose trade cost symmetry. Instead, trade costs are inferred from time-varying trade data that are readily observable. Intuitively, our method makes use of the insight that a change in bilateral trade barriers does not only a ect international trade but also intranational trade. For example, suppose that country i s trade barriers with all other countries increase. In that case, some of the goods that i used to ship to foreign countries are now consumed domestically, i.e., intranationally. It is therefore not only the extent of international trade that depends on trade barriers with the rest of the world but also the extent of intranational trade. It turns out that there is a direct relationship between a country s multilateral resistance and its intranational trade ows. This can be seen formally by using gravity equation () to nd an expression for country i s intranational trade x ii = y iy i y W tii i P i (4) where t ii represents intranational trade costs, for example domestic transportation costs. Equation (4) can be solved for the product of outward and inward multilateral resistance 3 Anderson and van Wincoop (2003, p. 80) provide a brief discussion on this point. 4

as i P i = xii =y ( ) i tii (5) y i =y W For example, suppose two countries i and j face the same domestic trade costs t ii = t jj and are of the same size y i = y j but country i is a more closed economy, that is, x ii > x jj. It follows directly from (5) that multilateral resistance is higher for country i ( i P i > j P j ). Expression (5) implies that for given t ii it is easy to measure the change in multilateral resistance over time as P i does not depend on time-invariant trade cost proxies such as distance. Multilateral resistance can also be thought of in terms of trade diversion and trade creation. For given output y i and y W and given domestic trade costs t ii, trade diversion from one bilateral trading partner to another does not a ect domestic trade x ii and therefore neither multilateral resistance. However, trade creation implies a drop in domestic trade and therefore a drop in multilateral resistance. 2.3 A Micro-Founded Measure of Trade Costs The explicit solution for the multilateral resistance variables can be exploited to solve the general equilibrium model for bilateral trade costs. Gravity equation () contains the product of outward multilateral resistance of one country and inward multilateral resistance of another country, i P j, whereas equation (5) provides a solution for i P i. It is therefore useful to multiply gravity equation () by the corresponding gravity equation for trade ows in the opposite direction, x ji, to obtain a bidirectional gravity equation that contains both countries outward and inward multilateral resistance variables: x ij x ji = 2 yi y j tij t ji y W i P i j P j Substituting the solution from equation (5) yields tii t jj x ij x ji = x ii x jj (6) t ij t ji The size variable in gravity equation (6) is not total income y i y j as in traditional gravity equations but intranational trade x ii x jj. Intranational trade does not only control for the countries economic size, but according to equation (5) it is also directly linked to 5

multilateral resistance. (6) can be rearranged as t ij t ji t ii t jj = xii x jj x ij x ji (7) As shipping costs between i and j can be asymmetric (t ij 6= t ji ) and as domestic trade costs can di er across countries (t ii 6= t jj ), it is useful to take the geometric mean of the barriers in both directions. It is also useful to deduct one to get an expression for the tari equivalent. I denote the resulting micro-founded trade cost measure as ij : tij t ji ij t ii t jj 2 xii x jj = x ij x ji 2( ) (8) ij measures bilateral trade costs t ij t ji relative to domestic trade costs t ii t jj. It therefore does not impose frictionless domestic trade and captures what makes international trade more costly over and above domestic trade. 4 The intuition behind ij is straightforward. If bilateral trade ows x ij x ji increase relative to domestic trade ows x ii x jj, it must have become easier for the two countries to trade with each other. This is captured by a decrease in ij, and vice versa. The measure can thus be interpreted as a gravity residual that comprises trade costs comprehensively de ned. This includes trade cost elements which can be observed directly, e.g., transportation costs and tari s, as well as trade cost elements that are unobservable such as informational barriers. The implied bilateral trade costs ij can be directly computed from observable trade data. Since these vary over time, trade costs ij can be computed not only for crosssectional data but also for time series and panel data. This is an advantage over the procedure adopted by Anderson and van Wincoop (2003) who only use cross-sectional data. It is important to stress that the trade cost measure ij is consistent with trade imbalances. As can be readily seen from gravity equation (), all else being equal asymmetric bilateral trade costs (t ij 6= t ji ) imply unbalanced bilateral trade ows (x ij 6= x ji ). ij indicates the geometric average of bilateral trade barriers in both directions. 5 But it is 4 ij can also be interpreted as a measure of the international component of trade costs net of distribution trade costs in the destination country. Formally, suppose total gross shipping costs t ij can be decomposed into gross shipping costs up to the border of j, denoted by t ij, times the gross shipping costs within j, denoted by t jj, where t jj is the same for all origins of shipment. It follows t ij = t ij t jj and t ji = t ji t ii so that ij = p t ij t ji. 5 This interpretation follows Anderson and van Wincoop (2003, p. 75). 6

not possible to infer the extent of the asymmetry from ij. 3 Illustration 3. U.S. Trade Costs As an illustration of trade costs ij given in (8), I compute U.S. bilateral trade costs for a number of major trading partners. I focus on how these bilateral trade costs have evolved over time. Due to market clearing intranational trade x ii can be rewritten as total income minus total exports, x ii = y i x i. 6 Total exports x i are de ned as the sum of all exports from country i, x i P j6=i x ij. All trade data are taken from the IMF Direction of Trade Statistics (DOTS) and denominated in U.S. dollars. GDP data are not suitable as y i because they are based on value added, whereas the trade data are reported as gross shipments. data. 7 In addition, GDP data include services that are not covered by the trade To get the shipment counterpart of GDP excluding services I follow Shang-Jin Wei (996) in constructing y i as total goods production based on the OECD s Structural Analysis (STAN) database. 8 The production data are converted into U.S. dollars by the period average exchange rate taken from the IMF International Financial Statistics (IFS). I consider annual data for 970-2000. In order to remain as close to existing trade cost measures as possible, I follow Anderson and van Wincoop (2004) in setting = 8 for the elasticity of substitution. 9 Figure illustrates U.S. bilateral trade costs with its two biggest trading partners, Canada and Mexico. U.S. trade costs fell dramatically with Mexico (from 96 to 33 percent) and also with Canada (from 50 to 25 percent). The U.S. experienced clear downward trends in trade costs with both its neighbors already prior to the North American Free Trade Agreement (NAFTA, e ective from 994), the Canada-U.S. Free Trade Agreement (CUSFTA, e ective from 989) and unilateral Mexican trade liberalization (from 985). Table reports the levels and the percentage decline in U.S. bilateral trade costs between 970 and 2000 with its six biggest export markets as of 2000. In descending order these are Canada, Mexico, Japan, the UK, Germany and Korea. 0 The decline 6 See equation (8) in Anderson and van Wincoop (2003). 7 Anderson (979) acknowledges nontradable services and models the spending on tradables as y i, where is the fraction of total income spent on tradables. But y i would still be based on value added. 8 Wei (996) uses production data for agriculture, mining and total manufacturing. 9 See Section 4 for a discussion of. 0 These six countries are those for which the 2000 share of U.S. exports exceeded 3 percent. Between 7

00% 80% U.S. Canada CUSFTA NAFTA 00% 80% U.S. Mexico Unilateral Mexican trade liberalization NAFTA Tariff equivalent τ 60% 40% Tariff equivalent τ 60% 40% 20% 20% 0 970 980 990 2000 0 970 980 990 2000 Figure : U.S. bilateral trade costs with Canada and Mexico. has been most dramatic with Mexico and Canada and has been sizeable with Korea, the UK, Germany and Japan. The trade-weighted average of U.S. trade costs declined by 44 percent between 970 and 2000, corresponding to an annualized decline of :9 percent per year. Its 2000 level stands at 42 percent. It is important to stress that the trade cost measure ij does not only capture trade costs in the narrow sense of transportation costs and tari s. ij also comprises trade cost components such as language barriers and currency barriers. In their survey on trade costs, Anderson and van Wincoop (2004) show that such non-tari barriers are substantial. The magnitudes of the bilateral trade costs in Table are entirely consistent with previous cross-sectional evidence. But the main advantage of ij over previous trade cost measures is that ij can be easily tracked over time. For the year 993 only, Anderson and van Wincoop (2004) report a 46 percent tari equivalent of overall U.S.-Canadian trade costs, compared to 3:2 percent in Figure. 2 The reason why the number reported by Anderson and van Wincoop (2004) is somewhat higher is that they use GDP data as opposed to production data to compute trade costs. In fact, when using GDP data I obtain U.S.-Canadian trade costs of 47:4 percent for 993, almost exactly the number reported 970 and 2000 their combined share of U.S. exports uctuated between 43 and 58 percent. x = 0:09 is the solution to 42 = 74 ( + x) 30. 2 Anderson and van Wincoop (2004) calculate the tari equivalent as the trade-weighted average barrier for trade between U.S. states and Canadian provinces relative to the trade-weighted average barrier for trade within the United States and Canada, using a trade cost function that includes a border-related dummy variable and distance. 8

Table : U.S. Bilateral Trade Costs Tari equivalent Partner country 970 2000 Percentage change Canada 50 25 50 Germany 95 70 26 Japan 85 65 24 Korea 07 70 35 Mexico 96 33 66 UK 95 63 34 Plain average 88 54 38 Trade-weighted average 74 42 44 All numbers are in percent and rounded o to integers. Countries listed are the six biggest U.S. export markets as of 2000. Computations based on (8). by Anderson and van Wincoop (2004). 3 But GDP data tend to overstate the extent of intranational trade and thus the level of trade costs because they include services. 4 I therefore follow Wei (996) in using merchandise production data to match the trade data more accurately. Furthermore, Eaton and Kortum (2002) report bilateral tari equivalents based on data for 9 OECD countries in 990. For countries that are 750-500 miles apart, an elasticity of substitution of = 8 implies a trade cost range of 58-78 percent, consistent with the magnitudes in Table. But an advantage of ij is that it can be easily computed for speci c country pairs. In summary, Figure and Table demonstrate that trade costs are large but generally experienced a substantial decline between 970 and 2000. They exhibit considerable heterogeneity across country pairs that would be masked by a one- ts-all measure of trade costs. 5 3 For = 5 and = 0 Anderson and van Wincoop (2004, Table 7) report 993 U.S.-Canadian trade cost tari equivalents of 9 and 35 percent, respectively. The corresponding numbers based on (8) are 97 and 35 percent when using GDP data and 6 and 24 percent when using production data. See Section 4 for a discussion of. 4 Speci cally, intranational trade is given by x ii = y i x i. As GDP data include services and as the service share of GDP has continually grown, the use of GDP data for y i overstates x ii compared to the use of production data despite the fact that imported intermediate goods are included in the trade data (see Helliwell, 2005). Novy (2008) develops a trade cost model with nontradable goods, showing that only the tradable part of output enters the model s micro-founded gravity equation. 5 For a comparison of the period 950-2000 to the period 870-93, see Jacks, Meissner and Novy (2008). 9

3.2 What Happens When Multilateral Resistance is Misspeci- ed? I now demonstrate why estimated changes in trade costs over time can be biased if they ignore the fact that multilateral trade barriers change over time. Take the trade cost measure from (8) xii x jj ij = x ij x ji 2( ) and substitute expression (4) for x ii and x jj to arrive at ij = y i y j =y W 2 x ij x ji! 2( ) i P i j P j t ii t jj 2 (9) The variables in the second pair of parentheses of (9) are frequently ignored or misspeci ed in standard gravity equations, that is, the multilateral resistance variables and domestic trade costs are not properly taken into account. But an analytical solution for these terms follows directly from equation (5) as i P i t ii 2 xii =y 2( ) i = i (0) y i =y W where i is de ned as the geometric average of country i s outward and inward multilateral trade barriers normalized by domestic trade costs. Note that i can be computed directly from the data without imposing a trade cost function that includes distance or other trade cost proxies. Equation (9) can then be rewritten as ij = y i y j =y W 2 x ij x ji! 2( ) i j () Equation () is now used to examine the consequences of two types of misspeci cation. The rst misspeci cation is to completely ignore the multilateral resistance variables and domestic trade costs. The second misspeci cation is to regard multilateral resistance variables and domestic trade costs as constants, for example in the form of time-invariant country xed e ects. The rst type of misspeci cation is to implicitly assume i = j =. 6 As i is 6 i = P i = t ii = i = holds in a frictionless equilibrium. See Anderson and van Wincoop (2003, p. 76). 0

generally greater than unity, the assumption of i = j = leads to an underestimation of bilateral trade costs ij according to equation (). Intuitively, bilateral trade ows are determined by bilateral relative to multilateral barriers. If one underestimates the level of a country s multilateral barriers, one will also underestimate the level of its bilateral barriers. As to the second type of misspeci cation, incorrectly specifying multilateral resistance variables and domestic trade costs as constants is equivalent to assuming i = i and j = j. As one can see from (), in that case changes in multilateral resistance variables and domestic trade costs will not be re ected by bilateral trade costs. This implies that if the multilateral resistance variables relative to domestic trade costs follow a secular trend, then the resulting estimated trend of bilateral trade costs will be biased. Figure 2 illustrates the second mistake. The left-hand side panels plot i for the U.S., Canada and Korea, computed on the basis of (0). 7 The right-hand side panels plot the correct trade costs based on time-varying multilateral resistance variables as well as the incorrect trade costs based on constant multilateral resistance variables. 8 Both the U.S. and the Canadian s happen to be fairly stable over time. 9 This means that for those two countries multilateral resistance and domestic trade costs changed at a roughly equal rate. As a result, there is hardly a di erence between the correct and incorrect trade costs in the right-hand side panels. But Korean multilateral resistance declined markedly over time relative to domestic trade costs such that the misspeci ed U.S.-Korean trade costs would fail to re ect their actual decline. In fact, the misspeci ed measure reports a decline in trade costs from 07 to only 98 percent between 970 and 2000, whereas actual trade costs declined from 07 to 70 percent (see Table ). Ignoring the fact that Korean multilateral resistance dropped over time relative to domestic trade costs thus leads to a miscalculation of the time trend by almost 30 percentage points. Korea serves as a clear example of a country that has experienced a striking drop in general trade costs and thus a striking drop in its multilateral resistance. Although the decrease in multilateral resistance might not 7 Annual world income y W is constructed as the combined production data of Belgium, Canada, Denmark, Finland, France, Germany, Italy, Japan, Korea, Mexico, the Netherlands, Norway, Sweden, the UK and the U.S. 8 In this example the multilateral resistance variables are held constant at their 970 levels but this particular normalization is irrelevant for the argument. 9 i represents multilateral resistance relative to domestic trade costs (i.e. t ii ), whereas Anderson and van Wincoop (2004, Table 8) normalize trade costs within Maryland to zero (i.e. t ii = ) and report multilateral resistance relative to this trade barrier within Maryland. They therefore obtain multilateral resistance variables for U.S. states and Canadian provinces that are higher than those reported for the U.S. and Canada in Figure 2.

Multilateral resistance Φ.4.3.2. Canada U.S. U.S. Canada 970 980 990 2000 Tariff equivalent τ 00% 80% 60% 40% 20% U.S. Canada Φ s correct Φ s time invariant 0 970 980 990 2000 Multilateral resistance Φ.4.3.2. Korea U.S. U.S. Korea 970 980 990 2000 Tariff equivalent τ 00% 80% 60% 40% 20% U.S. Korea Φ s time invariant Φ s correct 0 970 980 990 2000 Figure 2: Multilateral resistance variables and U.S. bilateral trade costs based on correct time-varying and incorrect time-invariant multilateral resistance variables. be as strong for other countries, in general the bias is likely to go in the direction of underestimating the decline in trade costs. 4 Discussion The trade cost measure in (8) captures what makes international trade more costly over and above domestic trade. It is a comprehensive measure that captures a wide range of trade cost components such as transportation costs and tari s, but also components that are not directly observable such as the costs associated with language barriers and red tape. It should therefore be regarded as an upper bound. Instead, direct measures of speci c trade cost components can be seen as a lower bound of trade costs, for example international transportation costs provided by Hummels (2007) relative to domestic 2

transportation costs. The precise level of trade costs depends of course on the elasticity of substitution. Table and Figures and 2 are based on = 8, which is in the middle of the common empirical range of 5 to 0, as surveyed by Anderson and van Wincoop (2004). For = 8 the trade-weighted average of U.S. bilateral trade costs in Table falls from 74 to 42 percent, a decline of 44 percent. It follows from equation (8) that a higher value of would lead to lower trade cost levels. Higher elasticities of substitution mean that goods are not as di erentiated so that consumers are more price-sensitive. In the case of a higher elasticity of substitution, a given observed level of domestic to bilateral trade therefore implies that bilateral and domestic trade costs are not too di erent so that ij is not as high. It turns out that although the elasticity of substitution a ects the level of ij, it hardly a ects the change of ij over time. For example, in the case of = 0 the tradeweighted average falls from 54 to 3 percent, a similar decline of 42 percent. In the case of = 5 the trade-weighted average falls from 67 to 87 percent, a decline of 48 percent. Following the approach of Feenstra (994), Broda and Weinstein (2006) estimate elasticities of substitution based on demand and supply relationships for disaggregated U.S. imports. When comparing the period 972-988 with 990-200, they nd that the median elasticity fell marginally but the di erence is not signi cant for all levels of disaggregation. Nevertheless, this result might suggest that trade costs could have declined slightly less than indicated in Table but quantitatively, this e ect is unlikely to be large. Novy (2008) develops a general equilibrium model of trade that incorporates trade costs as well as the fact that some goods are nontradable. However, he nds that estimated trade costs are barely a ected when the share of nontradable goods is allowed to vary over time. 5 Conclusion This paper develops a measure of international trade costs without imposing any trade cost function that uses distance, borders barriers or other trade cost proxies. Building on the gravity model by Anderson and van Wincoop (2003), I show how intranational trade ows can be used to express multilateral resistance terms as a function of observable trade data. Given this expression for time-varying multilateral resistance terms, I am able to derive a micro-founded gravity equation from which international trade costs can be directly computed for speci c country pairs. This trade cost measure is valid for both cross-sectional and time series data. 3

As an illustration I compute U.S. bilateral trade costs for a number of major trading partners. I nd that the trade-weighted average of these trade costs declined by about 40 percent between 970 and 2000. The decline of U.S. trade costs has been particularly strong with its neighbors Mexico and Canada. I also show that if multilateral resistance variables are misspeci ed as constants, bilateral trade cost estimates will fail to capture the decline in multilateral resistance and thus understate the true fall in trade costs over time. 4

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