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

• Author: 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]

   [partial derivatives]ln ([n.sub.i][p.sub.i][x.sub.ij]/[y.sub.j])/[partial derivative]ln ([n.sub.j]) = -...