Adam Smith on the gravity model of trade

I've written a number of posts that reference gravity models, including a lot of my own research. For example, see here for a post about my own research using the gravity model of internal migration flows, or here for a post about joint work with one of my PhD students on using the gravity model of international trade flows. Essentially, a gravity model suggests that the flow (of people in a migration model, or goods and services in a trade model) between two regions is positively related to the 'economic mass' (usually measured as population in a migration model, or economic output or GDP in a trade model) of the origin and the 'economics mass' of the destination, and negatively related to the distance between the two places. This idea of gravity models in migration goes back to work by Ernst Georg Ravenstein in the 1880s, and then developed mathematically by George Kingsley Zipf in the 1940s. In trade, the mathematical gravity model is usually attributed to Walter Isard in the 1950s.

So, the gravity model is old. But, as the inside joke among economists goes, there's been nothing new in economics since Adam Smith. And it turns out that Smith had a number of things to say in his most famous 1776 book The Wealth of Nations, as related by Bruce Elmslie (University of New Hampshire, and previously a visitor at Waikato) in this 2018 article published in the Journal of Economic Perspectives (open access). Elmslie notes a number of places where Smith alludes to gravity in the context of international trade, in Book IV, Chapter III, Part II of the Wealth of Nations. Elmslie writes that:

Smith (1776, pp. 624–25; emphases added) compares the trade that could take place between England and France if his system of natural liberty prevailed versus the forced, policy-driven trade between England and the North American colonies, and between France and its colonies:

[T]he commerce of France might be more advantageous to Great Britain than that of any other country, and for the same reason that of Great Britain to France. France is the nearest neighbor to Great Britain. In the trade between the southern coast of England and the northern and north-western coasts of France, the returns might be expected, in the same manner as in the inland trade, four, five, or six times in the year. The capital, therefore, employed in this trade, could in each of the two countries keep in motion four, five, or six times the quantity of industry, and afford employment and subsistence to four, five, or six times the number of people, which an equal capital could do in the greater part of the other branches of foreign trade. . . . It would be, at least, three times more advantageous, than the boasted trade with our North American colonies . . . France, besides, is supposed to contain twenty-four millions of inhabitants. Our North American colonies were never supposed to contain more than three millions: And France is a much richer country than North America; . . . France therefore could afford a market at least eight times more extensive, and, on account of the superior frequency of the returns, four-and-twenty times more advantageous, than that which our North American colonies ever afforded. The trade of Great Britain would be just as advantageous to France, and, in proportion to the wealth, population and proximity of the respective countries...

Thus, Smith holds that if the trade volume between two countries is determined by each country’s consideration of “their real interest, without either mercantile jealousy or national animosity” (p. 624), it will be in relation to the size of the national produce of each country and the distance or proximity between them.

Notice that the three passages that Elmslie has emphasised in italics in the quote from Adam Smith all seem to relate to the gravity model of trade. How did Smith come upon the gravity model? Interestingly, Elmslie notes that:

Smith did not use the “gravity” terminology explicitly, but it is intriguing that for the determinants of the volume of trade Smith emphasized mass and distance, which is of course similar to Isaac Newton’s theory of gravity. Smith gives no direct indication that he had Newton’s gravity model in mind, but a connection is not implausible. Newton’s work had a significant impact on Smith’s methodology in the Wealth of Nations... In an earlier work written prior to 1758, Smith (1795) calls Newton’s theory of gravity “the greatest discovery that ever was made by man”...

So, there you have it. Adam Smith may actually have laid some of the initial foundations for the gravity model of trade (and migration), having been inspired by the work of Sir Isaac Newton.