Beyond Gravity: The Composition of Multilateral Trade

By Ahmad Lashkaripour (Indiana University Bloomington)
What type of goods does the US export to Canada? What type of goods does it export to New Zealand? Guided by a standard gravity model we know very well that the US exports more (in value terms) to Canada than New Zealand. However, gravity models tell us little about the composition of US exports across various destinations. Standard gravity models focus on the intensive margin of trade. Tracking the evolution of trade patterns and trade theory over time explains why the gravity models were constructed this way, and why it’s time to move forward.
Trade theory, before the 1980s, had a sharp focus: describing the commodity composition of trade. Classical theories described the exchange of dissimilar goods between dissimilar countries in a bilateral world. In a classical framework, the labor abundant country would export the labor-intensive good, whereas the capital abundant country would export the capital-intensive good. In the early 1980s, evidence pointed to a different –non-classical– type of trade: exchange of similar goods between similar countries. To account for this type of trade, trade theory experienced a shift in paradigm, and gravity models were born. Gravity models describe the volume of trade in a multilateral world, where both similar and dissimilar countries engage in two-way trade. In contrast to classical models, gravity models are tractable and easy to estimate in a general equilibrium multi-country setting. Tractability, however, comes at a cost. Gravity models overlook the composition margin, and do not deliver detailed predictions about what type of goods countries trade.
Two recent developments, however, point to the increasing importance of the composition margin. First, poor and remote countries have become increasingly engaged in global trade (in 2006, for the first time, the US did more trade with developing countries than with other developed nations). Second, micro-level evidence indicates that both geography (remoteness) and per capita income have systematic effects on the composition of trade. This evidence is exemplified by three basic facts:

  1. Geography systematically affects the price-composition of exports (faraway countries exchange higher price, higher quality, goods)
  1. Per capita income increases the price-composition of exports (within narrowly defined categories, rich countries export higher price, higher quality goods)
  1. Trade-to-GDP increases systematically with per capita income (rich countries import and export goods that are more tradable).

These facts are beyond the scope of both classical and gravity models. In recent years much progress has been made in explaining these facts individually.[i] Nevertheless, there remains a void. First, we do not have a unified theory that accounts for the effect of both geography and per capita income — existing theories usually confront one aspect of the data in isolation, and overlook the others. Second, to address the composition margin, existing theories generally rely on non-homothetic preferences or non-iceberg trade costs. This involves sacrificing tractability, and tractability has been a major force behind the success of gravity models.
In Lashkaripour (2015a), I confront this void. I argue that a simple extension to the theory of comparative advantage could explain both the effect of geography and the effect of per capita income on the composition of trade.[ii] Building on this idea, I develop a unified model that fully describes both the volume and the composition of trade in a multi-lateral world. Similar to standard gravity models, the unified model adopts homothetic preferences and iceberg trade costs, making it tractable and straightforward to estimate. The main insight of the paper, however, concerns the welfare gains from trade. Estimating the model reveals that the composition margin has profound effects on the gains from trade. Specifically, embedding systematic specialization into a gravity model (to account for composition) more than triples the gains from trade. Furthermore, the gains from trade systematically favor poor and remote nations. This outcome is remarkable, given that incorporating other margins such as firm heterogeneity seem to contribute minimally to the gains from trade (Arkolakis et al. (2011)).
Currently, we are equipped with a rich set of theories that shed light on the composition of trade. More importantly, depending on which theory we believe, the composition margin has deep impacts on the gains from global integration. The next major step is evaluating these theories with micro-level data. Caron et al. (2014), among others, have made notable progress on this front.[iii] Further progress in this direction would allow us to better understand the aggregate effects of global integration, especially on poor and remote nations.
Arkolakis, C., A. Costinot, and A. Rodriguez (2012). Clare, 2012, new trade models, same old gains. American Economic Review 102(1), 94.
Baldwin, R. and J. Harrigan (2011). Zeros, quality, and space: Trade theory and trade evidence. American Economic Journal: Microeconomics 3(2), 60–88.
Caron, J., T. Fally, and J. R. Markusen (2014). International trade puzzles: A solution linking production and preferences. The Quarterly Journal of Economics 129(3), 1501–1552.
Dingel, J. I. (2014). The determinants of quality specialization. Technical report, WTO Staff Working Paper.
Eaton, J. and S. Kortum (2002). Technology, geography, and trade. Econometrica 70(5), 1741–1779.
Fajgelbaum, P., G. M. Grossman, and E. Helpman (2011). Income distribution. Product Quality, and International Trade, Journal of Political Economy 118(4), 721.
Fieler, A. C. (2011). Nonhomotheticity and bilateral trade: evidence and a quantitative explanation. Econometrica 79(4), 1069–1101.
Hummels, D. and A. Skiba (2004). Shipping the good apples out? an empirical confirmation of the Alchian-Allen conjecture. Journal of Political Economy 112(6).
Lashkaripour, A. (2015a). The composition of trade in a multilateral world. Technical report, Center for Applied Economics and Policy Research, Economics Department, Indiana University Bloomington.
Lashkaripour, A. (2015b). Worth its weight in gold: Product weight, international shipping, and patterns of trade.
Melitz, M. (2003). The impact of trade on aggregate industry productivity and intra-industry reallocations. Econometrica 71(6), 1695–1725.
[i]To explain the effect of per capita income on the composition margin, many studies have embedded non-homotheticity into standard gravity models. Fieler (2011), for example, embeds non-homthetic preferences into an Eaton-Kortum model.  She assumes that rich countries consume relatively more of goods, which are more technologically differentiated. Such goods are subject to lower trade elasticities and are more tradable. This entails that rich countries import a higher share of their GDP. Another example is Fajgelbaum et al. (2011), who apply non-homotheticity to a Krugman model. In their framework the home market effect induces firms in rich countries to specialize in high-quality goods. As a result, rich countries become net exporters of high-price, high quality products.
To account for the effect of geography on the composition of trade, most studies abstract from the standard iceberg cost assumption, and assume that trade costs are additive. This approach builds on the Alchian-Allen conjecture, and is exemplified in Hummels and Skiba (2004). Baldwin and Harrigan (2011) offer an alternative theory that reconciles the effect of geography (on composition) with iceberg trade costs. Building on Melitz (2003), they develop a quality-sorting framework where high-quality firms are the most competitive and sort into the toughest, most remote markets.
[ii] I relax a commonly used “gravity” assumption that does not align with micro-level evidence. Standard gravity models assume that all goods offer the same scope for product differentiation, whereas I allow for two types of goods: a highly differentiated type and a less differentiated type. By definition, demand for the highly differentiated type is quality-intensive, whereas demand for the less differentiated type is quantity-intensive. In equilibrium, quality abundant (high-wage) and remote countries have comparative advantage in the highly differentiated type. Labor abundant (low-wage) countries, on the other hand, have comparative advantage in the less differentiated type. This leads to systematic international specialization in production. Production specialization combined with the fact that (in equilibrium) the highly differentiated type exhibits a higher markup and is more tradable, explain the composition of multi-lateral trade.
[iii]Caron et al. (2014) show that income-elastic goods are more skill-intensive. Their results imply that non-homotheticity is an important factor in explaining puzzles relating to composition. Dingel (2015) utilizes firm-level data to discriminate between two theories that explain the higher price-mix of exports from rich countries. He shows that the Home-market effect is as important as comparative advantage in explaining this pattern. In Lashkaripour (2015b), I use product level data to analyze the effect of geography on the price composition of exports. Estimation results indicate that markups are the main driver of the observed patterns.