On the impact of transportation costs on trade in a multilateral world.

Egger, Peter

1. Introduction

The consideration of transportation costs in the endowment-based model of horizontal product differentiation has been an important progression in trade theory (see Krugman 1980; Helpman and Krugman 1985; Bergstrand 1985, 1989, 1990: and Anderson and van Wincoop 2003 as some of the most important proponents). There are now numerous examples where the basic implications of the model have rather successfully been tested for bilateral trade flows. Most of these applications have built on the 2 x 2 x 2 New Trade Theory framework (1) a la Helpman and Krugman (1985) and Helpman (1987) where bilateral trade can be explained by three determinants: the difference in relative factor endowments between the countries, the similarity in country size, and the size of the bilateral economic space. Different variants of the model have been tested regarding both bilateral overall trade (Evenett and Keller 2002) and intraindustry trade (Hummels and Levinsohn 1995), widely supporting the theoretical hypotheses.

However, the reference to the two-country model had an important consequence for empirical research: It fostered the opinion that different countries would be similarly affected by identical changes in transport costs (and similarly for changes in other determinants). Anderson and van Wincoop (2003) illustrate in a one-factor general equilibrium framework that this does not hold true with respect to country size. We will see that an extension of this perspective to the case of two factors provides useful and empirically relevant further insights.

This article presents a stylized multicountry model of trade in differentiated varieties in the presence of iceberg transportation costs. For the sake of simplicity, I concentrate on a typical country's aggregate export flows in terms of the destination country's size (gross domestic product [GDP]), and hence, import shares but evaluated at free-on-board (f.o.b.) prices.

Throughout the article, I envisage the impact of transport costs on changes in this measure of trade openness. Since an analytical treatment of the model is impossible in general equilibrium, I assume that a country's producer price is given. In the comparative static analysis, four hypotheses are derived regarding interaction effects of exporter and importer characteristics and the marginal effect of trade costs. The following important conclusions arise for the empirical analysis.

A reduction in bilateral transport costs exerts a negative effect on exports as a share of importer GDP; the lower in absolute value, the better endowed with capital the exporter is and/or the higher the importer's factor and production costs (hence, GDP at given endowments). For the importer's capital-labor ratio as a measure of product diversity and the exporter's competitiveness, the opposite holds true.

Focusing on the U.S.-Canadian border case, Anderson and van Wincoop (2003) have recently motivated an interaction term between bilateral GDP and trade costs. They illustrate that the effect of a change in trade frictions is larger in absolute value for large trading partners than it is for smaller ones. Such an effect is also present in the theoretical model below, but due to the more general two-factor nature of the model it leads to both a more complex specification of the impact of trade costs and a richer set of empirically testable hypotheses. Further, I specify the gravity equation in logs, rather than in levels as Anderson and van Wincoop. The model predicts that the impact of trade frictions is smaller in absolute value for country pairs with bilateral exports, where the exporter (importer) is relatively capital-abundant (capital-scarce) and/or produces at low (high) costs.

This implies that the New Trade Theory casts doubt on the assumption of identical transport cost parameters across country pairs, suggesting four interaction terms of transport costs with the mentioned characteristics. Put simply, the importance of trade frictions rises with the level of bilateral trade in general, and this is not accounted for in typical empirical applications, which are linear in trade costs. However, it is also only partly captured by the single interaction term motivated in Anderson and van Wincoop (2003).

I assess the four hypotheses empirically. Therefore, I estimate various versions of the gravity model using a large panel of bilateral exports as a share of importer GDP over the period 1970-2000. This allows me to comprehensively account for all time-invariant influences such as historic, geographical, cultural, and other ties between countries. Also, by including fixed time effects in this setting I can control for all determinants, which are common to all country pairs, I relax the assumption that transport costs exert a similar effect on all country pairs by accounting for the above-mentioned four interaction effects in addition to the direct impact of trade frictions.

The null hypothesis of a zero impact of the interaction terms is always significantly rejected. The results suggest that a 1% reduction of trade costs on average raises bilateral export to importer GDP ratios by about 0.6%. The variance of this average marginal effect across major country blocs such as intra-OECD, OECD-Rest-of-the-World (ROW), or intra-RoW seems much less important than the variance of the impact within blocs.

The findings are extremely robust with respect to the specification choice and the included covariates. A reduction in trade frictions exerts the largest average marginal effect on OECD-RoW trade, where many relatively capital-abundant exporter to low-cost country exports arise. The impact is lowest for trade between the RoW economies due to their relative capital scarcity.

In this way, the study may contribute to the discussion about the "puzzle of home-bias," which started with McCallum (1995) and has been surveyed by Obstfeld and Rogoff (2000). It identifies a relationship between the importance of trade frictions and the characteristics of trading partners in terms of relative capital endowments or their competitiveness. The analysis suggests that restricting the impact of transport costs to be identical for all country pairs is harmful, because on average the estimated importance of transport cost reductions is downward-biased, especially for country pairs with a high level of bilateral trade.

Also, the traditional restrictive approach ignores that the marginal effect of transport cost reductions has evolved over time due to changes in capital-labor ratios and/or production costs. For instance, the findings suggest that the relevance of marginal changes in transport costs for exports as a share of importer GDP has risen by more than 8% over the last three decades for both intra-OECD and intra-RoW trade. This indicates that trade cost-reducing measures such as infrastructure investments or economic integration become more and more important, especially for trade between high-cost producers like the OECD or capital-scarce economies like the RoW.

The article is organized as follows. Section 2 presents the theoretical model. In section 3, the theoretical findings are briefly summarized and their empirical implementation is discussed. The empirical set-up is described and empirical results are presented in section 4, and section 5 concludes the article.

2. Theoretical Background

Assume a model where a single horizontally differentiated good is produced with two factors of production (capital, K, and labor, L) and traded between countries of different size and relative factor endowments. Imagine that consumer preferences are characterized by a love for variety so that the Dixit and Stiglitz (1977) constant elasticity of substitution (CES) demand assumptions apply.

A country i-based firm serves consumers at its domestic market by [x.sub.ii] and consumers at any foreign market j by [x.sub.ij]. For convenience [x.sub.ij] is the measured gross of transport costs (i.e., including the [t.sub.ij] - 1 units of the good, which melt when crossing the border). If many firms are active and engage in monopolistic competition, the elasticity of substitution between varieties ([epsilon]) is equal to the demand elasticity. Then there is a fixed mark-up over marginal costs. Country i's exports in such a model are known to be

(1) [n.sub.i][p.sub.i][x.sub.ij] = [n.sub.i][([p.sub.i][t.sub.ij]/[P.sub.j]).sup.i - [epsilon]] [y.sub.j],

where [n.sub.i] denotes the number of firmss (varieties) originating from i, [p.sub.i] is the producer price, [y.sub.j] is the total factor income (GDP) in country j. and

(2) [P.sub.j] = [(c.summation over i=1 [n.sub.i] [([p.sub.i][t.sub.ij]).sup.1 - [epsilon]).sup.1/1 - [epsilon]]

is the aggregate CES price index of country j. For the sake of simplicity, I concentrate on bilateral exports normalized by importer GDP,

(3)[n.sub.1][p.sub.i][x.sub.ij]/[y.sub.j] = [n.sub.i] [([p.sub.i][t.sub.ij]).sup.1 - [epsilon]]/[[??].sub.j],

where [[??].sub.j] = [P.sup.1p - [epsilon]/sub.j] = [summation.sup.c.sub.i=1] [n.sub.i][(p.sub.1] [t.sub.ij])].sup.1-[epsilon]] has been used to simplify the notation. In the following, I stick to the assumption that countries are small and, therefore, goods prices are exogenous. To be as close to the empirical analysis as possible, I take the log of Equation 3 in the comparative static analysis. The main results can be summarized in the following way.

First, an unambiguously positive domestic variety expansion effect can be identified

(4) [partial derivative]ln ([n.sub.i][p.sub.i][x.sub.ij]/y.sub.j])/[partial derivative]ln ([n.sub.i]) = 1 - [n.sub.i][([p.sub.i][t.sub.ij]).sup.1 - [epsilon]]/[[??].sub.j] = [[THETA].sub.1] > 0,

which is related to the assumption of Dixit-Stiglitz (1977) preferences. Note that in Equations 9-12 below, we will make use of [[THETA].sub.1] < 1. Second, there is a negative foreign variety expansion effect, since both the domestic and foreign consumers' taste for variety implies that competition for foreign products rises in foreign product diversity:

[partial derivatives]ln ([n.sub.i][p.sub.i][x.sub.ij]/[y.sub.j])/[partial derivative]ln ([n.sub.j]) = - [n.sub.j][p.sup.1 - [epsilon]].sub.j]/[??.sub.j] = - [[THETA].sub.2] < 0.

Third, an exogenous increase in domestic prices is equivalent to a negative domestic cost expansion effect, rendering domestic goods less competitive than foreign ones

(6) [partial derivative]ln ([n.sub.i][p.sub.i][x.sub.ij]/[y.sub.j])/[partial derivative]ln([p.sub.i]) = - ([epsilon] - 1)[[THETA].sub.1] < 0.

Fourth, for the same reason there is a positive foreign cost expansion effect on foreign demand from domestic producers given by

(7) [partial derivative]ln ([n.sub.i][p.sub.i][x.sub.ij]/[y.sub.j])/[partial derivative]ln([p.sub.j]) = ([epsilon - 1)[[THETA].sub.2] > 0.

Finally and most importantly for our purpose, bilateral exports decline in bilateral trade costs:

(8) [partial derivative]ln [n.sub.i][p.sub.i][x.sub.ij]/[y.sub.j])/[partial derivative]ln (t.sub.ij] = - ([epsilon] - 1)[[THETA].sub.1] < 0.

It is obvious from Equation 4 that Equation 8 depends directly and indirectly on the respective domestic prices and the number of varieties and only indirectly on their foreign counterparts entering the price aggregator. Hence, modeling the impact of trade costs on bilateral trade in a simply log-linear fashion induces an omitted variables bias from a theoretical point of view.

The derivative of Equation 8 with respect to the four most important bilateral determinants (the log of [n.sub.i], [n.sub.j], [p.sub.j] and [p.sub.j]) obtains the theoretical hypotheses regarding the expected parameter signs of the corresponding interaction terms:

(9) [[partial derivative].sup.2]ln([n.sub.i][p.sub.i][x.sub.ij]/ [partial derivative]ln([t.sub.ij] [partial derivative]ln ([n.sub.i]) = ([epsilon] - 1)(1 - [[THETA].sub.1][[THETA].sub.1] > 0,

and

(10) [[partial derivative].sup.2]ln ([n.sub.i][p.sub.i][x.sub.ij]/[y.sub.j]/[partial derivative]ln([t.sub.ij] [partial derivative]ln([t.sub.ij][partial derivative]ln([n.sub.j] = -([epsilon]-1)(1 - [[THETA].sub.1)[[THETA].sub.2] < 0

indicate that the negative trade cost effect is weakened (reinforced) in absolute terms by the domestic (foreign) variety expansion effect at given prices. Further,

(11) [partial derivative].sup.2 ln ([n.sub.1][p.sub.i][x.sub.ij]/[y.sub.j]/[partial derivative]ln([t.sub.ij][partial derivative]ln([p.sub.j])=[([epsilon]-1).sup.2 (1-[THETA].sub.1])[THETA].sub.2] >0

and

(12) [[partial derivative].sup.2]ln([n.sub.1][p.sub.1][x.sub.ij]/[partial derivative]ln([t.sub.ij]) [partial derivative]ln([p.sub.j] = [([epsilon]-1).sup.2](1 - [[THETA].sub.2][[THETA].sub.2] > 0

illustrate that it is reinforced (weakened) by the domestic (foreign) cost expansion effect at a given number of varieties in all countries.

The basic mechanism behind these effects is simply that the marginal impact of trade frictions on trade depends on the level of trade. A higher level of domestic product diversity or foreign goods prices (i.e., a less competitive foreign supply) leads to a larger volume of bilateral exports. In this model, high trade volumes react less elastically on a marginal change in trade frictions than small ones. (2)

3. From Theory to Empirics

In the empirical analysis, one may replace [n.sub.j] and [n.sub.j] by the respective capital-labor ratios ([K.sub.i]/[L.sub.i], [K.sub.j]/[L.sub.j]) or, following the stylized fact of a high correlation between capital-labor ratios and GDP per capita data ([y.sub.i]/[L.sub.i], [y.sub.j/L.sub.j) dating back to Kaldor (1963), by GDP per capita. At given factor endowments, [p.sub.i] and [p.sub.j) reflecting a country's competitiveness in terms of production costs may be approximated by GDP ([y.sub.i] [y.sub.j]. (3) Then, the above analysis can be summarized as follows.

First, an empirical assessment of the determinants of bilateral trade motivated by Helpman and Krugman (1985) type models should account for interaction terms between the explanatory variables. Interaction terms are necessary to better approximate the inherently non-(log) linear structure of the model, and their omission likely leads to biased parameter estimates.

Second, domestic and foreign capital-labor ratios or GDP per capita stocks are positively related to domestic and foreign product diversity. Apart from their direct effect, these variables have an impact on the relevance of trade frictions. Specifically, an interaction term between bilateral trade costs and the domestic (foreign) measure of product diversity such as GDP per capita is expected to reduce (increase) the elasticity of exports with respect to trade costs. Hence, the expected parameter sign of this interaction effect is positive (negative), because a higher export volume is less sensitive to trade frictions in such a model.

Third, domestic and foreign goods prices can be substituted by domestic and foreign GDP as a measure of factor costs at given factor endowments. Besides their direct effect, these variables also change the relevance of trade frictions for bilateral trade. An interaction term between bilateral trade costs and the domestic (foreign) GDP, as an inverse measure of domestic competitiveness at given factor endowments, is expected to increase (reducee) the elasticity of bilateral exports with respect to trade frictions in absolute terms. Accordingly, the expected parameter sign of this interaction effect is negative (positive), because a higher export volume--in this case associated with a higher domestic relative to foreign competitiveness showing up in a lower domestic-to-foreign GDP ratio at given endowments--reacts again more sensitively to trade frictions.

Finally, irrespective of the relative domestic and foreign product diversity and competitiveness, the overall marginal effect of trade costs on trade is expected to be unambiguously negative.

4. Data and Estimation Results

I use a panel of bilateral real exports from country i to j in year t as a share of j's GDP ([X.sub.ijt/[y.sub.jt] = [n.sub.it][p.sub.it][x.sub.ijt]/[y.sub.jt] comprising the largest possible panel in the World Trade Data Base (UN) between 1970 and 1999 (a list of reporter and partner countries is given in the Appendix). Additionally, I use GDP per capita (y/L, as a measure of a country's range of products, n); GDP (y, given factor endowments are a proxy for a country's production cost level, both from the World Bank's World Development Indicators); and, most importantly, cost-insurance-freight (c.i.f.) to f.o.b. ratios ([t.sub.ijt]) from the UN's World Trade Data Base as a proxy for transport costs in all regressions. (4) The baseline model reads

(13) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.].

where [[mu].sub.ij] are fixed country-pair effects, which control for all time-invariant effects as cultural (language) or geographic determinants (area, borders, distance). Fixed time effects [[lambda].sub.t] guard against an omitted variables bias related to all determinants, which are common to all country pairs. For instance, at a large number of relatively similar countries, the time effects would account for the direct impact of the price aggregator [P.sub.j][[for all].sub.j]. [[epsilon].sub.ijt] is a classical error term. In all tables below, specification 13 is referred to as model 1, and we expect [[beta].sub.6], [[beta].sub.9] < 0 and [[beta].sub.7], [[beta].sub.8] > 0 due to the above arguments.

It is noteworthy that Glick and Rose (2002) and others estimate a restricted form of specification 13 where exporter and importer GDP (GDP per capita) exert the same impact ([[beta].sub.1] = [[beta].sub.2] and [[beta].sub.3] = [[beta].sub.4]) and [[beta].sub.k] = 0 for k = 6, ..., 9. I refer to the related specification but with [[beta].sub.k] [not equal to] 0 for k = 6, ..., 9 as model 2 in all tables. However, the restriction of equal parameters is testable, and if it is rejected, other coefficients of interest (such as those of the transport cost interaction terms and the corresponding marginal effect of trade frictions) might be biased.

Further, I apply Helpman's (1987) specification (model 3), which uses overall bilateral country size, ln([y.sub.it] + [y.sub.jt]) the similarity in bilateral county size, ln[1 - ([[y.sub.it]/([y.sub.it] + [(y.sub.jt])].sup.2] - [[y.sub.it]/([y.sub.it] + [[y.sub.jt])].sup.2]] and the difference in capital-labor ratios approximated by ln|([y.sub.it]/[L.sub.it] - ([y.sub.jt/[L.sub.jt]| as regressors:

(14) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.].

For comparison, I also estimate Equation 13 without the interaction effects by setting [[beta].sub.k] = 0 for k = 6, ..., 9 (model 4). To ensure robust results, I check for the influence of extreme outliers and exclude those with residuals larger than 2.5 standard errors in all regressions (see Belsley, Kuh, and Welsch 1980). Further, I look for potential efficiency gains from treating fixed country-pair effects as random. Finally, I only report heteroscedasticity robust test statistics and standard errors in the fixed effects regressions.

Table 1 summarizes the results from regressions of the previously mentioned four variants of the gravity model, using GDP per capita to approximate the scope of a country's product differentiation. In Table A1 of the Appendix, I provide the results for model 1 where capital-labor ratios are used instead. However, the findings are very similar and the use of capital stocks invokes the disadvantage of losing observations (see the Appendix for details).

After excluding outliers, the data set covers more than 14,000 country-pair relations and about 121,000 observations. In all regressions, the fit is well and the adjusted [R.sup.2] amounts to about 0.95. In any case, the omission of either the time effects or the country-pair effects would result in biased parameters. As indicated by the significant Hausman test statistics, one should not treat the country-pair effects as random (although both the random effects model coefficients and the pooled OLS parameters are virtually similar to their fixed effects counterparts). Model 2 is rejected against model 1, and the adjusted [R.sup.2] is also highest for model 1 among the estimated ones. Accordingly, we speak of this model as the preferred specification.

A comparison of the remaining covariates' parameters with other studies is difficult for two reasons: (i) I normalize bilateral exports by importer GDP, and (ii) I account for the interaction terms between transport costs and exporter and importer GDP and GDP per capita to be in line with the discussed approach.

Concerning the negative marginal impact of importer GDP per capita (not reported), Anderson and Marcouiller (2002) mention that an appropriate set of controls (which accounts for risk and uncertainty) tends to result in negative coefficients. Regarding the relative factor endowment parameter in the Helpman (1987) specification, we would conclude that the results point more to supporting Linder's hypothesis, rather than that of Heckscher and Ohlin.

It is noteworthy that the point estimates of all interaction term parameters are in line with the theoretical predictions, indicating that the importance of trade costs rises with the bilateral export volume, showing up in a negative (positive) parameter estimate of interaction terms 1 and 4 (2 and 3). This extends the insights provided by Anderson and van Wincoop (2003) in a one-factor general equilibrium model for the case of two factors but under the assumption of exogenous prices and numbers of variants (scope of diversity) and in a model in log form.

We should not interpret the (positive) direct impact of transport costs separately, but only look at the marginal effect, evaluated at some point--usually the mean--of the distribution of GDP per capita and of GDP. For the present purpose, it is of special interest whether the estimated marginal effect of trade frictions is generally negative as predicted by Equation 8 in section 2 and how its impact varies in the sample. The latter provides insight into the importance of the bias related to the omission of the interaction terms in model 4 as compared with model 1. The marginal effect of trade costs in our models is defined as

(15) [partial derivative]ln([X.sub.ijt]/[y.sub.jt)/[partial derivative]ln([t.sub.ijt) = [[beta].sub.5] + [[beta].sub.6]ln([y.sub.it]/[L.sub.it]) + [[beta].sub.7]ln([y.sub.jt]/[L.sub.jt]) + [[beta].sub.8]ln([y.sub.it]) + [[beta].sub.9]ln([y.sub.jt],

and

(16) [partial derivative]ln([X.sub.ijt]/[y.sub.jt])/[partial derivative]ln([t.sub.ijt]) = [[gamma].sub.4] + [[gamma].sub.5]ln([y.sub.it/[L.sub.it]) + [[gamma].sub.6]ln([y.sub.jt]) + [[gamma].sub.7]ln([y.sub.jt]), + 8 ln([y.sub.jt]),

respectively. The average marginal effect of transport costs is about -0.6% (see the reported estimates on top of the model characteristics in Table 1). Hence, a decrease in transport costs by 1% raises bilateral trade openness by about 0.6%. Since trade growth is slightly less than twice as large as importer GDP growth in the sample, we could say that a 1% rise in trade costs stimulates trade (rather than trade openness) by about 1.2%. This is considerably lower than the finding of Baler and Bergstrand (2001). However, I should mention that they have focused on an earlier time span and a narrow country sample consisting only of OECD economies. In fact, an elasticity of trade of 1.2% with respect to transport costs comes close to what others have found for distance (as a proxy of transport costs) in cross-section and pooled OLS studies (see Oguledo and MacPhee 1994 for an overview).

To illustrate the importance of the finding that the impact of transport costs on openness (and trade volumes) depends not only on GDP per capita (as a measure of the scope of diversity) but also on competitiveness (being negatively related to GDP at given factor endowments and product diversity), I compute the marginal effect for three blocs of bilateral relations: (i) trade between developed economies (intra-OECD trade), (it) trade between the developed and the developing economies (OECD-RoW trade), and (iii) trade between developing countries (intra-RoW trade). In any case, I evaluate the marginal effect of the country group specific means of GDP per capita and GDP between 1970 and 2000.

For this, I rely on bloc-specific parameter estimates, since pooling the parameters across these blocs of country pairs is rejected according to an F-test (see the bottom line in Table 1). The parameter estimates for models 1-4 and the corresponding marginal effects evaluated at the respective sample means are summarized in Table 2.

Three things are worth noting. First, the marginal effects are extremely robust with respect to the specification choice. Second, they are lowest in absolute value for intra-RoW relations and highest for trade of OECD economies with non-OECD countries. One reason for the latter is that the "typical" country pair is one with a large difference in both capital-labor ratios and production costs. Finally, the variance of the marginal effects within the mentioned country bloc samples is generally much larger than the variance of the average across the samples. The latter is best inferred in Figure 1, which displays Kernel density plots of the point estimates of marginal effects for the whole sample (based on preferred model 1 in Table 1) and for each bloc separately (based on the respective preferred model 1 in Table 2).

Figure 1 illustrates that intra-OECD and OECD-with-RoW relations are characterized by a relatively high intrasample variability of the marginal transport cost effect. Specifically, the latter sample exhibits a relatively fat tail at the lower bound. Accordingly, trade costs are relatively high for a considerable portion of OECD-RoW country pairs. The country pair-specific marginal effect of transport costs lies between about 1.09% (see the lower tail in the lower left panel) and -0.19% (see the upper tail in the upper right panel). Hence, the maximum range of the impact of trade costs amounts to about 100-|(1.09-0.19)/-0.6| = 150% of the corresponding average effect, which underpins the hamlful consequences of "pooling" by an omission of the interaction terms in a traditional approach, being log-linear in variables.

Further, both GDP and GDP per capita grew persistently in the last three decades. Accordingly, we should expect that the impact of transport costs has developed and that this has been different across country blocs. Table 3 provides insights into the development of marginal effects, average annual changes in transport costs, and the predicted annual change in exports over importer GDP. Because of the rejection of the pooling of parameters across blocs in Table 1, I again rely on the Table 2-based bloc-specific parameters of the preferred model 1 in Table 3.

First, the marginal impact of a change in trade frictions became more important over the three decades, irrespective of which country bloc we look at (see the first row in the last column after each country bloc heading in Table 3). Second, in any phase the marginal impact was largest for OECDRoW relations and smallest for intra-RoW relations. Finally, the marginal effect of transport costs has grown in absolute value by more than 8% between 1970 and 2000 for both intra-OECD and intraRoW relations and by about 2% for OECD-RoW trade.

In the data, I observe an average annual reduction of trade costs of between 0.21% (intra-OECD) and 0.90% (intra-RoW) over these three decades. In the 1970s, the actual trade cost induced change in the dependent variable of interest (bilateral aggregate exports over importer GDP) was highest (lowest) for intra-RoW (intra-OECD) trade with 0.41% (0.07%), irrespective of the considerably higher marginal effect for OECD-RoW relations. Hence, the impact in the 1970s was about six times stronger for intra-RoW trade flows than for intra-OECD relations, and it was about three times stronger for OECD-RoW relations than for intra-OECD trade. The reason for the latter is that the actual change in trade costs between RoW economies has outweighed the relatively lower marginal effect as compared with OECD-RoW trade. However, by the end of the 1990s the observed annual reduction in trade costs between RoW economies on the one hand and between OECD and RoW countries on the other account for an annual change in export openness of about 0.28%, which is more than triple as much as the effect of trade costs on intra-OECD trade.

From a political economy point of view this pattern suggests that transport cost reductions are most "efficient" for OECD-RoW trade relationships, because the marginal trade cost effect is highest there. In general, we observe that the actual contribution of trade cost reductions to the bilateral growth of OECD countries' trade (with OECD and RoW economies) has risen in the last three decades. Infrastructure investments and other means of trade cost reductions predominantly took place between OECD and RoW economies, where they also have their largest impact. In general, the findings suggest that the same trade liberalization and a reduction in trade frictions now is considerably more effective than it was 30 years ago.

4. Conclusions

Previous empirical research on the determinants of bilateral trade volumes assumed that marginal effects of the included explanatory variables are generally identical across bilateral relationships. This study concentrates on the analysis of bilateral export-to-importer GDP shares and investigates the role of transport costs in the estimation of gravity models. A simple multiregion New Trade Theory model is used to illustrate that the importance of a reduction in trade costs is positively related to the level of trade. Therefore, four interaction terms with trade costs are motivated: one with exporter GDP per capita or its capital-labor ratio as a measure of the scope of product diversity, a second one with importer GDP per capita or capital labor ratio, a third one with exporter GDP as a proxy of the (factor income and) production cost level being negatively related to the country's competitiveness, and a fourth one with importer GDP as an inverse measure of foreign competitiveness. We expect a positive (negative) sign of the first and the fourth (the second and the third) interaction term parameter.

I find strong support for this reasoning in a large panel of country-pair trade flows over 1970 2000, where the theoretical hypothesis is accounted for by including the mentioned interaction terms. The identified effects are robust with respect to the chosen empirical specification and across major country blocs. The same transport cost reduction is found to have the strongest impact on average for trade openness between OECD and non-OECD economies. The results also suggest that the importance of changes in trade costs has significantly risen in the course of years, making any reduction in trade frictions now more effective than three decades ago.

Appendix A.1: Country Sample

Afghanistan, Albania, Algeria, American Samoa, Andorra, Angola, Anguilla, Antarctica, Antigua, Argentina, Armenia, Aruba, Australia, Austria, Azerbaijan, Bahamas, Bahrain, Bangladesh, Barbados, Belarus, Belgium, Belize, Benin, Bermuda, Bhutan, Bolivia, Bosnia and Herzegovina, Botswana, British Antarctic Territory, British Indian Ocean Territory, British Virgin Islands, Brazil, Brunet, Bulgaria, Bunkers, Burkina Faso, Burundi, Cambodia, Cameroon, Canada, Cape Verde, Cayman Islands, Central Africa, Chad, Chile, China, Cocos Islands, Colombia, Comoros, Congo, Cook Islands, Costa Rica, Cote d'Ivoire, Croatia, Cuba, Cyprus, Czech Republic, Czechoslovakia, Denmark, Djibouti, Dominican Republic, East Timor, Ecuador, Egypt, El Salvador, Equatorial Guinea, Eritrea, Estonia, Ethiopia, Former Yugoslavia, Former Ethiopia, Faeroe Islands, Falkland Islands, Fiji, Finland, Former Germany, Former Panama, Former USSR. Former Vietnam, Former Yemen, French Guiana, French Polynesia, French Southern Antarctic Territory, France, Gabon, Gambia, Georgia, Germany, Ghana, Gibraltar, Greece, Greenland, Grenada, Guadeloupe, Guam, Guatemala, Guinea, Guinea Bissao, Guyana, Haiti, Holy See, Honduras, Hong Kong, Hungary, Iceland, India, Indonesia, Iran, Iraq, Ireland, Israel, Italy, Jamaica, Japan, Jordan, Kazakhstan, Kenya, Kiribati, Korea Democratic Republic of, Korea Republic of, Kuwait, Kyrgyzstan, Laos, Latvia, Lebanon, Lesotho, Liberia, Libya, Liechtenstein, Lithuania, Luxembourg, Macau, Madagascar, Malawi, Malaysia, Maldives, Mali, Malta, Marshall Islands, Martinique, Mauritania, Mauritius, Mayotte, Mexico, Micronesia, Midway, Moldavia Republic of, Mongolia, Montserrat, Morocco, Mozambique, Myanmar. Namibia, Nauru, Nepal. Netherlands Antilles, Netherlands. New Caledonia, New Zealand, Nicaragua, Niger, Nigeria, Norfolk, Norway, Oceania, Oman, Pakistan, Palau, Panama, Papua New Guinea, Paraguay, Peru, Philippines, Pitcairn, Poland, Portugal, Qatar, Reunion, Romania, Russian Federation, Rwanda, Ryukyu, South Africa, Samoa, San Marino, Sao Tome and Principe, Saudi Arabia, Senegal, Seychelles, Sierra Leone, Singapore, Slovakia, Slovenia, Solomon Islands, Somalia, Spain, Sri Lanka, St. Helena. St. Kitts and Nevis, St. Lucia. St. Pier, St. Vincent's and the Grenadines, Sudan, Suriname, Svalbard, Swaziland, Sweden, Switzerland, Syria, TFYR Macedonia, Tajikistan. Tangany, Tanzania. Thailand, Togo, Tokelau, Tonga, Trinidad and Tobago, Tunisia, Turkey, Turkmenistan, Turks, Tuvalu, U.S. Virgin Islands, United States of America, Uganda, Ukraine, United Kingdom, United Arab Emirates, Uruguay, Uzbekistan, Vanuatu, Venezuela, Vietnam, Wake Islands, Wallis, Western Samoa, Yemen, Yugoslavia, Zambia, Zanzibar, Zimbabwe.

Table A.1.
Fixed Effects Panel Regression Results Using Capital Stocks to
Approximate [n.sub.i] and [n.sub.j]; (Model 1)

 All
 Theory countries Developed

Log exporter capital stock: 0.67 *** 0.13 ***
 ln([K.sub.it]) 43.09 4.13
Log importer capital stock: 0.30 *** 0.21 ***
 n([K.sub.jt]) 19.72 8.11
Log exporter GDP/capita: 0.19 *** 0.60 ***
 ln([y.sub.it]/[L.sub.it]) 15.09 25.78
Log importer GDP/capita: -0.28 *** -0.21 ***
 ln([y.sub.jt/[L.sub.jt]) 25.08 9.97
Log c.i.f./f.o.b. ratio (transport 0.22 ** -0.36
 costs): ln([t.sub.ijt]) 2.24 0.84
Interaction term 1: ln([t.sub.ijt]) + 0.03 *** 0.10 ***
 X ln[([K.sub.it]/[L.sub.it])] 7.53 5.12
Interaction term 2: ln([t.sub.ijt]) - -0.07 *** -0.08 ***
 X ln[([K.sub.jt]/[L.sub.jt])] 21.31 4.70
Interaction term 3: ln([t.sub.ijt]) - -0.02 *** -0.05 ***
 X ln([y.sub.it]) 7.25 4.77
Interaction term 4: ln([t.sub.ijt]) + 0.00 0.04 ***
 X ln([y.sub.jt]) 0.18 3.31
Marginal effect of transport costs - -0.62 *** -0.62 ***
p-value 0.00 0.00
Observations 98,271 13,079
Country pairs 10,557 646
Adjusted [R.sup.2] 0.95 0.98
Joint significance of interaction
 X ln([y.sub.jt]) (F-statistic) 187.13 *** 21.07 ***
p-value 0.00 0.00
Hausman test
 ([chi square] statistic) 1,358.73 *** 5,857.77 ***
p-value 0.00 0.00
Country pair effects (F-statistic) 67.48 *** 369.06 ***
p-value 0.00 0.00
Time effects (F-statistic) 31.90 *** 28.77 ***
p-value 0.00 0.00
Pooling across country blocs
 (F-statistic) 19.38 *** --
p-value 0.00 --

 Developed-
 with-
 Theory developing Developing

Log exporter capital stock: 0.61 *** 0.81 ***
 ln([K.sub.it]) 31.68 21.40
Log importer capital stock: 0.30 *** 0.11 ***
 n([K.sub.jt]) 17.12 2.82
Log exporter GDP/capita: 0.31 *** -0.08 **
 ln([y.sub.it]/[L.sub.it]) 20.46 2.43
Log importer GDP/capita: -0.22 *** -0.24 ***
 ln([y.sub.jt/[L.sub.jt]) 16.03 8.08
Log c.i.f./f.o.b. ratio (transport 0.15 0.04
 costs): ln([t.sub.ijt]) 0.96 0.25
Interaction term 1: ln([t.sub.ijt]) + 0.04 *** 0.01
 X ln[([K.sub.it]/[L.sub.it])] 8.47 1.13
Interaction term 2: ln([t.sub.ijt]) - -0.06 *** -0.05 ***
 X ln[([K.sub.jt]/[L.sub.jt])] 11.97 8.51
Interaction term 3: ln([t.sub.ijt]) - -0.02 *** -0.02 ***
 X ln([y.sub.it]) 5.59 3.92
Interaction term 4: ln([t.sub.ijt]) + -0.01 0.01
 X ln([y.sub.jt]) 1.39 1.50
Marginal effect of transport costs - -0.62 *** -0.63 ***
p-value 0.00 0.00
Observations 51,314 34,197
Country pairs 4,739 5,178
Adjusted [R.sup.2] 0.96 0.91
Joint significance of interaction
 X ln([y.sub.jt]) (F-statistic) 123.69 *** --
p-value 0.00 --
Hausman test
 ([chi square] statistic) 1,522.51 *** 424.58 ***
p-value 0.00 0.00
Country pair effects (F-statistic) 70.20 *** 37.67 ***
p-value 0.00 0.00
Time effects (F-statistic) 43.49 *** 25.02 ***
p-value 0.00 0.00
Pooling across country blocs
 (F-statistic) -- --
p-value -- --

Note: Figures below coefficients are t-statistics.

** Significant at 5%.

*** Significant at 1%.

Appendix A.2: Using Capital Stocks as a Measure of Product Diversity

Capital stocks for a large cross-section of economies must be computed according to the perpetual inventory method as outlined in Learner (1984). Following Learner, I have assumed a depreciation rate of 13.3% and relied on annual gross fixed capital formation data available from the World Bank's World Development Indicators to estimate country-specific capital stocks at an annual basis. However, investment data are available for a smaller number of countries than GDP data, so that about 20% of the observations are lost. However. Table A1 reports both the overall and the bloc-specific estimation results for model 1 if a country's scope of product diversity is approximated by capital stocks rather than GDP. The results are obviously very similar to those reported in Tables 1 and 2.

Table 1. Fixed Effects Panel Regression Results (Log Bilateral Exports
over Importer GDP; 1970-1999)

 Full Sample

 Theory Model 1 Model 2

Log exporter GDP: ln([y.sub.it]) 0.82 *** 0.63 ***
 21.02 21.84
Log importer GDP: ln([y.sub.jt]) 0.37 *** 0.63 ***
 9.91 21.84
Log exporter GDP/capita: -0.27 *** -0.45 ***
 ln([y.sub.it]/[L.sub.it]) 7.47 17.01
Log importer GDP/capita: -0.51 *** -0.45 ***
 ln([y.sub.jt]/[L.sub.jt]) 15.25 17.01
Log exporter plus importer GDP: -- --
 ln([y.sub.it] + [y.sub.jt]) -- --
Log bilateral similarity in GDP: -- --
 ln {1 - [[[y.sub.it]/([y.sub.it]
 + [y.sub.jt])].sup.2]
 + [[[y.sub.it]/([y.sub.it]
 + [y.sub.jt])].sup.2]] -- --
Log absolute difference in -- --
 bilateral GDP/capita:
 ln[abosulute value of [y.sub.it]/
 [L.sub.it] - [y.sub.jt]/
 [L.sub.jt]] -- --
Log c.i.f./f.o.b. ratio 0.32 *** 0.44 ***
 (transport costs):
 ln([t.sub.ijt]) 4.46 6.03
Interaction term l: + 0.05 *** 0.05 ***
 ln([t.sub.ijt]) X ln[([y.sub.it]/
 [L.sub.it])] 17.17 18.07
Interaction term 2: - -0.07 *** -0.07 ***
 ln([t.sub.ijt]) X ln[([y.sub.jt]/
 [L.sub.jt])] 24.72 26.18
Interaction term 3: - -0.04 *** -0.04 ***
 ln([t.sub.ijt]) X
 ln[([y.sub.it])] 15.43 16.35
Interaction term 4: + 0.00 0.00
 ln([t.sub.ijt]) X
 ln[([y.sub.jt])] 0.88 0.17
Marginal effect of transport costs - -0.62 *** -0.62 ***
p-value 0.00 0.00
Observations 121,746 121,706
Country pairs 14,070 14,071
Adjusted [R.sup.2] 0.95 0.95
Joint significance of interaction
 terms (F-statistic) 289.94 *** 331.81 ***
p-value 0.00 0.00
Hausman test
 ([chi square]-statistic) 2,087.85 *** 4,690.96 ***
p-value 0.00 0.00
Country pair effects (F-statistic) 60.92 *** 114.61 ***
p-value 0.00 0.00
Time effects (F-statistic) 63.30 *** 55.64 ***
p-value 0.00 0.00
Pooling across country blocs
 (F-statistic) 22.38 *** 22.45***
p-value 0.00 0.00

 Full Sample

 Theory Model 3 Model 4

Log exporter GDP: ln([y.sub.it]) -- 0.78 ***
 -- 19.72
Log importer GDP: ln([y.sub.jt]) -- 0.42 ***
 -- 10.97
Log exporter GDP/capita: -- -0.21 ***
 ln([y.sub.it]/[L.sub.it]) -- 5.68
Log importer GDP/capita: -- -0.57 ***
 ln([y.sub.jt]/[L.sub.jt]) -- 16.75
Log exporter plus importer GDP: 0.11 *** --
 ln([y.sub.it] + [y.sub.jt]) 6.28 --
Log bilateral similarity in GDP: -0.31 *** --
 ln {1 - [[[y.sub.it]/([y.sub.it]
 + [y.sub.jt])].sup.2]
 + [[[y.sub.it]/([y.sub.it]
 + [y.sub.jt])].sup.2]} 24.98 --
Log absolute difference in -0.04 *** --
 bilateral GDP/capita:
 ln[abosulute value of [y.sub.it]/
 [L.sub.it] - [y.sub.jt]/
 [L.sub.jt]] 8.55 --
Log c.i.f./f.o.b. ratio 0.37 *** -0.63 ***
 (transport costs):
 ln([t.sub.ijt]) 5.03 173.70
Interaction term l: + 0.05 *** --
 ln([t.sub.ijt]) X ln[([y.sub.it]/
 [L.sub.it])] 18.70 --
Interaction term 2: - -0.07 *** --
 ln([t.sub.ijt]) X ln[([y.sub.jt]/
 [L.sub.jt])] 25.54 --
Interaction term 3: - -0.04 *** --
 ln([t.sub.ijt]) X
 ln[([y.sub.it])] 15.86 --
Interaction term 4: + 0.00 --
 ln([t.sub.ijt]) X
 ln[([y.sub.jt])] 0.31 --
Marginal effect of transport costs - -0.62 *** -0.63 ***
p-value 0.00 0.00
Observations 121,731 121,776
Country pairs 14,067 14,071
Adjusted [R.sup.2] 0.95 0.95
Joint significance of interaction
 terms (F-statistic) 317.96 *** --
p-value 0.00 --
Hausman test
 ([chi square]-statistic) 4,958.70 *** 1,718.92 ***
p-value 0.00 0.00
Country pair effects (F-statistic) 93.44 *** 60.57 ***
p-value 0.00 0.00
Time effects (F-statistic) 56.44 *** 65.00 ***
p-value 0.00 0.00
Pooling across country blocs
 (F-statistic) 24.12 *** 28.23 ***
p-value 0.00 0.00

Figures below coefficients are t-statistics.

*** Significant at 1%.

Table 2. Country Bloc-specific Fixed Effects Panel Regression Results
(Log Bilateral Exports over Importer GDP; 1970-1999)

 Developed Countries

 Theory Model 1 Model 2

Log exporter GDP: ln([y.sub.it]) 1.17 *** 1.19 ***
 10.57 15.36
Log importer GDP: ln([y.sub.jt]) 1.25 *** 1.19 ***
 13.25 15.36
Log exporter GDP/capita: -0.46 *** -0.89 ***
 ln([y.sub.it]/[L.sub.it]) 4.32 11.76
Log importer GDP/capita: -1.32 *** -0.89 ***
 ln([y.sub.jt]/[L.sub.jt]) 14.44 11.76
Log exporter plus importer GDP: -- --
 ln([y.sub.it] + [y.sub.jt]) -- --
Log bilateral similarity in GDP: --
 ln {1 - [[[y.sub.it]/([y.sub.it] -- --
 + [y.sub.jt])].sup.2] --
 + [[[y.sub.it]/([y.sub.it]
 + [y.sub.jt])].sup.2]} --
Log absolute difference in -- --
 bilateral GDP/capita:
 ln[abosulute value of [y.sub.it]/
 [L.sub.it] - [y.sub.jt]/
 [L.sub.jt]]
Log c.i.f./f.o.b. ratio 0.07 0.11
 (transport costs): 0.21 0.36
 ln([t.sub.ijt])
Interaction term 1: + 0.08 *** 0.09 ***
 ln([t.sub.ijt]) X ln[([y.sub.it]/ 4.04 5.01
 [L.sub.it])]
Interaction term 2: - -0.08 *** -0.12 ***
 ln([t.sub.ijt]) X ln[([y.sub.jt]/ 4.46 6.87
 [L.sub.jt])]
Interaction term 3: - -0.06 *** -0.05 ***
 ln([t.sub.ijt]) X 5.73 4.26
 ln[([y.sub.it])]
Interaction term 4: + 0.04 *** 0.03 ***
 ln([t.sub.ijt]) X 3.59 2.61
 ln[([y.sub.jt])]
Marginal effect
 of transport costs - -0.61 *** -0.61***
p-value 0.00 0.00
Observations 13,555 13,543
Country pairs 646 646
Adjusted [R.sup.2] 0.98 0.98
Joint significance of interaction
 terms (F-statistic) 23.33 *** 23.53 ***
p-value 0.00 0.00
Hausman test
 ([chi square]-statistic) 2,687.46 *** 245.28 ***
p-value 0.00 0.00
Country pair effects (F-statistic) 338.49 *** 576.48 ***
p-value 0.00 0.00
Time effects (F-statistic) 43.41 *** 39.72 ***
p-value 0.00 0.00

 Developed Countries

 Theory Model 3 Model 4

Log exporter GDP: ln([y.sub.it]) -- 1.18 ***
 -- 10.91
Log importer GDP: ln([y.sub.jt]) -- 1.28 ***
 -- 13.75
Log exporter GDP/capita: -- -0.48 ***
 ln([y.sub.it]/[L.sub.it]) -- 4.51
Log importer GDP/capita: -- -1.37 ***
 ln([y.sub.jt]/[L.sub.jt]) -- 15.25
Log exporter plus importer GDP: 0.28 *** --
 ln([y.sub.it] + [y.sub.jt]) 9.22 --
Log bilateral similarity in GDP: -0.38 *** --
 ln {1 - [[[y.sub.it]/([y.sub.it] 14.13 --
 + [y.sub.jt])].sup.2] -0.01 *** --
 + [[[y.sub.it]/([y.sub.it]
 + [y.sub.jt])].sup.2]}
Log absolute difference in 3.58 --
 bilateral GDP/capita:
 ln[abosulute value of [y.sub.it]/
 [L.sub.it] - [y.sub.jt]/
 [L.sub.jt]]
Log c.i.f./f.o.b. ratio -0.25 -0.61 ***
 (transport costs): 0.72 37.63
 ln([t.sub.ijt])
Interaction term 1: + 0.10 *** --
 ln([t.sub.ijt]) X ln[([y.sub.it]/ 5.14 --
 [L.sub.it])]
Interaction term 2: - -0.12 *** --
 ln([t.sub.ijt]) X ln[([y.sub.jt]/ 6.60 --
 [L.sub.jt])]
Interaction term 3: - -0.05 *** --
 ln([t.sub.ijt]) X 4.15 --
 ln[([y.sub.it])]
Interaction term 4: + 0.04 *** --
 ln([t.sub.ijt]) X 3.85 --
 ln[([y.sub.jt])]
Marginal effect
 of transport costs - -0.58 *** -0.61 ***
p-value 0.00 0.00
Observations 13,539 13,549
Country pairs 646 646
Adjusted [R.sup.2] 0.98 0.98
Joint significance of interaction
 terms (F-statistic) 23.80 *** --
p-value 0.00 --
Hausman test
 ([chi square]-statistic) 96.78 *** 4,151.32 ***
p-value 0.00 0.00
Country pair effects (F-statistic) 474.56 *** 336.68 ***
p-value 0.00 0.00
Time effects (F-statistic) 28.43 *** 41.91 ***
p-value 0.00 0.00

 Developed with
 Developing Countries

 Theory Model 1 Model 2

Log exporter GDP: ln([y.sub.it]) 0.60 *** 0.40 ***
 10.64 8.41
Log importer GDP: ln([y.sub.jt]) 0.15 *** 0.40 ***
 2.92 8.41
Log exporter GDP/capita: 0.07 -0.15 ***
 ln([y.sub.it]/[L.sub.it]) 1.36 3.25
Log importer GDP/capita: -0.23 *** -0.15 ***
 ln([y.sub.jt]/[L.sub.jt]) 4.95 3.25
Log exporter plus importer GDP: -- --
 ln([y.sub.it] + [y.sub.jt]) -- --
Log bilateral similarity in GDP: -- --
 ln {1 - [[[y.sub.it]/([y.sub.it] -- --
 + [y.sub.jt])].sup.2] -- --
 + [[[y.sub.it]/([y.sub.it]
 + [y.sub.jt])].sup.2]}
Log absolute difference in -- --
 bilateral GDP/capita:
 ln[abosulute value of [y.sub.it]/
 [L.sub.it] - [y.sub.jt]/
 [L.sub.jt]]
Log c.i.f./f.o.b. ratio 0.20 * 0.43 ***
 (transport costs): 1.90 4.00
 ln([t.sub.ijt])
Interaction term 1: + 0.08 *** 0.08 ***
 ln([t.sub.ijt]) X ln[([y.sub.it]/ 18.27 18.28
 [L.sub.it])]
Interaction term 2: - -0.05 *** -0.06 ***
 ln([t.sub.ijt]) X ln[([y.sub.jt]/ 12.25 14.95
 [L.sub.jt])]
Interaction term 3: - -0.04 *** -0.05 ***
 ln([t.sub.ijt]) X 12.91 14.16
 ln[([y.sub.it])]
Interaction term 4: + 0.00 0.00
 ln([t.sub.ijt]) X 0.75 1.11
 ln[([y.sub.jt])]
Marginal effect
 of transport costs - -0.65 *** -0.65 ***
p-value 0.00 0.00
Observations 63,241 63,218
Country pairs 6,093 6,090
Adjusted [R.sup.2] 0.96 0.96
Joint significance of interaction
 terms (F-statistic) 197.54 *** 237.36 ***
p-value 0.00 0.00
Hausman test
 ([chi square]-statistic) 1,431.55*** 240.72 ***
p-value 0.00 0.00
Country pair effects (F-statistic) 63.86 *** 174.59 ***
p-value 0.00 0.00
Time effects (F-statistic) 54.65 *** 43.63 ***
p-value 0.00 0.00

 Developed with
 Developing Countries

 Theory Model 3 Model 4

Log exporter GDP: ln([y.sub.it]) -- 0.58 ***
 -- 10.19
Log importer GDP: ln([y.sub.jt]) -- 0.17 ***
 -- 3.36
Log exporter GDP/capita: -- 0.12 **
 ln([y.sub.it]/[L.sub.it]) -- 2.30
Log importer GDP/capita: -- -0.26 ***
 ln([y.sub.jt]/[L.sub.jt]) -- 5.50
Log exporter plus importer GDP: 0.38 *** --
 ln([y.sub.it] + [y.sub.jt]) 15.42 --
Log bilateral similarity in GDP: -0.32 *** --
 ln {1 - [[[y.sub.it]/([y.sub.it] 22.54 --
 + [y.sub.jt])].sup.2] -0.09 *** --
 + [[[y.sub.it]/([y.sub.it]
 + [y.sub.jt])].sup.2]}
Log absolute difference in 10.53 --
 bilateral GDP/capita:
 ln[abosulute value of [y.sub.it]/
 [L.sub.it] - [y.sub.jt]/
 [L.sub.jt]]
Log c.i.f./f.o.b. ratio 0.31 *** -0.69 ***
 (transport costs): 2.88 138.48
 ln([t.sub.ijt])
Interaction term 1: + 0.08 *** --
 ln([t.sub.ijt]) X ln[([y.sub.it]/ 19.53 --
 [L.sub.it])]
Interaction term 2: - -0.06 *** --
 ln([t.sub.ijt]) X ln[([y.sub.jt]/ 14.63 --
 [L.sub.jt])]
Interaction term 3: - -0.04 *** --
 ln([t.sub.ijt]) X 13.60 --
 ln[([y.sub.it])]
Interaction term 4: + 0.00 --
 ln([t.sub.ijt]) X 0.74 --
 ln[([y.sub.jt])]
Marginal effect
 of transport costs - -0.64 *** -0.69 ***
p-value 0.00 0.00
Observations 63,204 63,211
Country pairs 6,090 6,090
Adjusted [R.sup.2] 0.96 0.96
Joint significance of interaction
 terms (F-statistic) 245.68 *** --
p-value 0.00 --
Hausman test
 ([chi square]-statistic) 795.81 *** 1,718.92 ***
p-value 0.00 0.00
Country pair effects (F-statistic) 120.80 *** 60.57 ***
p-value 0.00 0.00
Time effects (F-statistic) 39.22 *** 65.00 ***
p-value 0.00 0.00

 Developing Countries

 Theory Model 1 Model 2

Log exporter GDP: ln([y.sub.it]) 0.66 *** 0.45 ***
 6.15 6.02
Log importer GDP: ln([y.sub.jt]) 0.20 * 0.45 ***
 1.88 6.02
Log exporter GDP/capita: -0.33 *** -0.41 ***
 ln([y.sub.it]/[L.sub.it]) 3.17 5.98
Log importer GDP/capita: -0.44 *** -0.41 ***
 ln([y.sub.jt]/[L.sub.jt]) 4.52 5.98
Log exporter plus importer GDP: -- --
 ln([y.sub.it] + [y.sub.jt]) -- --
Log bilateral similarity in GDP: -- --
 ln {1 - [[[y.sub.it]/([y.sub.it] -- --
 + [y.sub.jt])].sup.2] -- --
 + [[[y.sub.it]/([y.sub.it]
 + [y.sub.jt])].sup.2]}
Log absolute difference in -- --
 bilateral GDP/capita:
 ln[abosulute value of [y.sub.it]/
 [L.sub.it] - [y.sub.jt]/
 [L.sub.jt]]
Log c.i.f./f.o.b. ratio 0.23 * 0.25 **
 (transport costs): 1.90 2.09
 ln([t.sub.ijt])
Interaction term 1: + 0.03 *** 0.03 ***
 ln([t.sub.ijt]) X ln[([y.sub.it]/ 6.16 6.63
 [L.sub.it])]
Interaction term 2: - -0.05 *** -0.05 ***
 ln([t.sub.ijt]) X ln[([y.sub.jt]/ 11.02 11.34
 [L.sub.jt])]
Interaction term 3: - -0.03 *** -0.03 ***
 ln([t.sub.ijt]) X 9.36 9.25
 ln[([y.sub.it])]
Interaction term 4: + 0.01 ** 0.01
 ln([t.sub.ijt]) X 1.99 1.54
 ln[([y.sub.jt])]
Marginal effect
 of transport costs - -0.59 *** -0.59 ***
p-value 0.00 0.00
Observations 45,259 45,255
Country pairs 7,343 7,342
Adjusted [R.sup.2] 0.91 0.91
Joint significance of interaction
 terms (F-statistic) 58.33 *** 60.27 ***
p-value 0.00 0.00
Hausman test
 ([chi square]-statistic) 1,516.92 *** 1,075.60***
p-value 0.00 0.00
Country pair effects (F-statistic) 36.00 *** 50.39 ***
p-value 0.00 0.00
Time effects (F-statistic) 23.36 *** 23.66 ***
p-value 0.00 0.00

 Developing Countries

 Theory Model 3 Model 4

Log exporter GDP: ln([y.sub.it]) -- 0.68 ***
 -- 6.32
Log importer GDP: ln([y.sub.jt]) -- 0.24 **
 -- 2.31
Log exporter GDP/capita: -- -0.34 ***
 ln([y.sub.it]/[L.sub.it]) -- 3.30
Log importer GDP/capita: -- -0.49 ***
 ln([y.sub.jt]/[L.sub.jt]) -- 4.99
Log exporter plus importer GDP: -0.12 *** --
 ln([y.sub.it] + [y.sub.jt]) 3.68 --
Log bilateral similarity in GDP: -0.35 *** --
 ln {1 - [[[y.sub.it]/([y.sub.it] 12.56 --
 + [y.sub.jt])].sup.2] -0.01 --
 + [[[y.sub.it]/([y.sub.it]
 + [y.sub.jt])].sup.2]}
Log absolute difference in 1.60 --
 bilateral GDP/capita:
 ln[abosulute value of [y.sub.it]/
 [L.sub.it] - [y.sub.jt]/
 [L.sub.jt]]
Log c.i.f./f.o.b. ratio 0.23 * -0.58 ***
 (transport costs): 1.89 104.63
 ln([t.sub.ijt])
Interaction term 1: + 0.03 *** --
 ln([t.sub.ijt]) X ln[([y.sub.it]/ 6.51 --
 [L.sub.it])]
Interaction term 2: - -0.05 *** --
 ln([t.sub.ijt]) X ln[([y.sub.jt]/ 11.13 --
 [L.sub.jt])]
Interaction term 3: - -0.03 *** --
 ln([t.sub.ijt]) X 9.25 --
 ln[([y.sub.it])]
Interaction term 4: + 0.01 * --
 ln([t.sub.ijt]) X 1.75 --
 ln[([y.sub.jt])]
Marginal effect
 of transport costs - -0.59 *** -0.58 ***
p-value 0.00 0.00
Observations 45,257 45,273
Country pairs 7,341 7,342
Adjusted [R.sup.2] 0.91 0.91
Joint significance of interaction
 terms (F-statistic) 59.09 *** --
p-value 0.00 --
Hausman test
 ([chi square]-statistic) 492.12 *** 900.43 ***
p-value 0.00 0.00
Country pair effects (F-statistic) 42.11 *** 35.66 ***
p-value 0.00 0.00
Time effects (F-statistic) 39.52 *** 21.93 ***
p-value 0.00 0.00

Figures below coefficients are r-statistics.

* Significant at 10%.

** Significant at 5%.

*** Significant at 1%.

Table 3. Development of the Marginal Transport Cost Effect 1970-2000
(Based on Model 1 Parameters in Table 2)

 1970-1980 1981-1990

Intra-OECD relations
 Marginal transport cost effect -0.58 *** -0.60 ***
 p-value 0.00 0.00
 Average annual change in trade costs in % -0.17 -0.26
 Average annual trade cost induced
 exports/importer GDP effect in % 0.07 0.12

OECD-RoW relations
 Marginal transport cost effect -0.64 *** -0.64 ***
 p-value 0.00 0.00
 Average annual change in trade costs in % -0.46 -0.58
 Average annual trade cost induced
 exports/importer GDP effect in % 0.22 0.28

Intra-RoW relations
 Marginal transport cost effect -0.50 *** -0.53 ***
 p-value 0.00 0.00
 Average annual change in trade costs in % -0.97 -0.90
 Average annual trade cost induced
 exports/importer GDP effect in % 0.41 0.40

 Change in %
 1991-2000 (1970-2000)

Intra-OECD relations
 Marginal transport cost effect -0.63 *** 8.19
 p-value 0.00 --
 Average annual change in trade costs in % -0.19 --
 Average annual trade cost induced
 exports/importer GDP effect in % 0.09 --

OECD-RoW relations
 Marginal transport cost effect -0.65 *** 1.96
 p-value 0.00 --
 Average annual change in trade costs in % -0.59 --
 Average annual trade cost induced
 exports/importer GDP effect in % 0.28 --

Intra-RoW relations
 Marginal transport cost effect -0.54 *** 9.82
 p-value 0.00 --
 Average annual change in trade costs in % -0.64 --
 Average annual trade cost induced
 exports/importer GDP effect in % 0.29 --

*** Significant at 1%.

(1) Two goods (one homogeneous, one horizontally differentiated); two factors (labor, capital); and two countries.

(2) It can be shown in simulations that this holds also in general equilibrium.

(3) Note that this becomes immediately obvious if we assume that only L serves in the production process and only capital is used to invent varieties. In the simplest possible formulation, we obtain [K.sub.i] = [n.sub.i] and exhibits a unitary elasticity with respect to the exogenous ln(p.sub.i]) [for all]i. However. I should note that GDP is not necessarily a proxy of prices only. It may also be seen as a measure of a Country's overall endowments. Especially in models of at least two factors and less restrictive technology assumptions as the ones adopted here, and particularly if the small country assumption is valid (i.e., at exogenous goods prices), this interpretation seems important.

(4) One should be cautious about using c.i.f./f.o.b. ratios as a proxy for trade cost levels. Hummels and Lugovskyy (2003) provide recent evidence that these data tend to be biased, especially for the developing economies (see Yeats 1978 for an earlier investigation). However, they conclude (ibid., p. 15) that c.i.f./f.o.b. ratios may nevertheless "be useful as a rough control variable for aggregate bilateral transportation costs." Hummels and Lugovskyy indicate that the use of variation (rather than levels) in c.i.f./f.o.b. ratios is informative and systematically and plausibly related to determinants like geographical distance between country pairs (see also Geraci and Prewo 1977 for the explanation of c.i.f./f.o.b. ratios). This is exactly what is exploited in the fixed country pair effects estimates (also referred to as analysis of covariance) adopted below.

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Peter Egger, University of Munich and Ifo Institute, Poschingerstrasse 5, D-81679 Munich, Germany; E-mail egger@ifo.de.

I am grateful to Jeff Bergstrand, Wilhelm Kohler, Michael Pfuffermayr, Alan Winters, participants at the 2002 ETSG conference in Brussels, and two anonymous referees for helpful comments. Of course, any remaining errors are my own.

Received October 2001; accepted May 2004.