• Foundations of the gravity equation in international trade

    Seen Thomas Chaney (Chicago) presenting this nice paper on the foundations of the gravity equation in international trade, last Friday at Toulouse School of Economics:

    The gravity equation in international trade is one of the most robust empirical finding in economics: bilateral trade between two countries is proportional to their respective sizes, measured by their GDP, and inversely proportional to the geographic distance between them. While the role of economic size is well understood, the role played by distance remains a mystery. In this paper, I propose the first explanation for the gravity equation in international trade. This explanation is based on the emergence of a stable international network of importers and exporters. Firms can only export into markets in which they have a contact. They acquire contacts by gradually meeting the contacts of their contacts. I show that if, as observed empirically, (i) the distribution of the number of foreign countries accessed by exporters is fat tailed, (ii) there is a large turnover in exports, with firms often going in and out of individual foreign markets, and (iii) geographic distance hinders the initial acquisition of contacts in an arbitrary way, then trade is proportional to country size, and inversely proportional to distance. Data on firm level, sectoral, and aggregate trade support further predictions of the model.

    So if I understand well, the main channel is the way the structure of informational networks of firms evolves, from birth to maturity. This involves direct interactions to create new contacts. The beauty of the paper is to show that under plausible conditions, the aggregate distribution of exporting firms converges to something matching Zipf’s law (a regularity observed in aggregated empirical data), so while (in the words of the paper) “the geographic distribution of any one firm’s exports does depend on how distance affects the direct cost of creating contacts. (…) in the aggregate, the details of this distance function vanish, and the gravity equation emerges.”

    True, the data seem at first sight to fit quite well the necessary theoretical conditions, namely the fact that “the distribution of firm level total exports is close to Zipf’s law, and (…) the average (squared) distance of a firm’s exports is a power function of this firm’s number of contacts”. However, further empirical evidence will clearly be needed to give more bite to this line of explanation. As discussed during the seminar, I’ll be very interested in seeing whether some historical “natural experiments”, which could be thought of as additional constraints on the way firms expand their contacts, such as the long term isolation of some countries from the world’s markets (think of Apartheid South Africa, or communist countries being the iron curtain), or temporary disruptions (e.g., the famous closing of the Suez canal from 1967 to 1975, which is arguably an exogenous shock on distance between a number of country pairs) have affected the dynamics of trade in ways that would conform to the model’s predictions.

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