Gravity Model of Trade

The gravity model of trade is an empirical model that explains the volume of trade between two countries by their economic size and the distance between them. Larger economies trade more with each other, and partners that are far apart, or separated by borders, different languages or high tariffs, trade less. The name comes from the resemblance to Newton's law of gravitation, in which attraction grows with mass and weakens with distance.

The model is among the most reliable regularities in international economics and a standard tool in econometrics. Governments, the World Trade Organization (WTO), the World Bank and academic researchers use it to estimate the effects of a free trade agreement (FTA), a currency union, economic sanctions or a new border.

Think of how often people visit shops. A big supermarket attracts more customers than a corner kiosk, and people go more often to the shop down the road than to one across the city. Two big shops next to each other will swap a lot of trade; two tiny ones far apart will hardly notice each other.

Countries behave much the same way. The United States trades heavily with Canada and Mexico, its large neighbours, and Germany with France and the Netherlands. Small, remote economies trade less with each other than with big markets nearby. Anything that makes the trip harder, such as a mountain range, customs paperwork or a tariff, acts like extra distance.

In its simplest form the model is written:

• $T_{ij}$ is trade between country $i$ and country $j$.
• $Y_i$ and $Y_j$ are the two countries' gross domestic product (GDP).
• $D_{ij}$ is the distance between them, usually between capitals or main economic centres.
• $G$ is a constant, and $\alpha$, $\beta$ and $\theta$ are estimated from data; $\alpha$ and $\beta$ are typically close to 1.

Worked example: take two pairs of countries with identical GDPs, one pair 1,000 km apart and the other 2,000 km apart. With $\theta = 1$, doubling the distance halves predicted trade. With $\theta = 0.9$, a value close to many estimates, trade falls by a factor of $2^{0.9} \approx 1.87$, so the distant pair trades about 54% as much as the close pair. In practice economists take logarithms and add variables for a shared border, common language, colonial ties, a shared currency, tariffs and membership of a trade bloc.

The Dutch economist Jan Tinbergen, later the first co-recipient of the Nobel Memorial Prize in Economic Sciences in 1969, published one of the first gravity estimates in 1962, and the Finnish economist Pentti Pöyhönen did similar work in 1963. For years the model was criticised as an empirical rule without a theory. That changed as economists derived it from standard trade models:

• Anderson (1979). James Anderson showed that a gravity equation follows from a model in which consumers value goods from different countries as distinct products.
• Anderson and van Wincoop (2003). Their paper "Gravity with Gravitas" added "multilateral resistance": trade between two countries depends on how costly it is for each to trade with everyone else, not only with each other.
• Santos Silva and Tenreyro (2006). "The Log of Gravity" showed that estimating the model in logarithms biases results and proposed Poisson pseudo-maximum likelihood (PPML), now the standard approach.

Today's "structural gravity" models are consistent with theories based on comparative advantage, differentiated products and firm-level differences.

A meta-analysis by Anne-Célia Disdier and Keith Head (2008), covering over 1,400 estimates, found an average distance elasticity close to 0.9, and found that the effect of distance had not shrunk over the twentieth century despite cheaper transport and containerization. Borders matter too: John McCallum (1995) found that in 1988 Canadian provinces traded roughly 20 times more with each other than with US states of similar size and distance, a result later revised down but not removed. Andrew Rose's 2000 estimate that sharing a currency tripled trade drew wide debate; later work using the eurozone found much smaller effects.

Gravity models help answer practical questions: how much trade a new agreement such as the United States-Mexico-Canada Agreement (USMCA) might create, how much Brexit reduced UK–EU trade, what sanctions cost, and whether a country trades less than its size and location predict, which can point to hidden barriers. The approach has been extended to foreign direct investment (FDI), migration and remittances.

Its limits are well known. "Distance" stands in for many things, from freight costs to cultural familiarity, and results depend on how variables are measured. Trade in services and digital goods may follow different patterns. Agreements are not signed at random, so estimates of their effects can be biased if countries that already trade a lot are the ones that sign them. Finally, the model predicts trade volumes, not welfare: it says little on its own about who gains, a question addressed by theories of free trade and globalization.

• WTO and UNCTAD: An Advanced Guide to Trade Policy Analysis: The Structural Gravity Model
• CEPII: Gravity database