The Gravity Equation In International Trade: An Explanation
The gravity equation uses Newton’s law of gravitation to explain the patterns of bilateral aggregate trade flows between two countries as comparative to the gross national products from each country. While also explaining how it is inversely comparative to the distance between them. This equation has proven to be shockingly stable over the years and across different tests of countries. The distance elasticity is outstandingly stable as it lingers around -1 for over a century and a half of data. The role of economic size is well comprehended while there is still no explanation for the role of distance.
This equation survived more than a century of changes in the technology of transportation, the political barriers to trade, the type of the goods traded or the relative importance of the countries trading goods. The geography of firm level trade could experience major changes and the gravity equation for aggregate trade will remain constant. Latest discoveries in trade theory have shifted the focus of trade economists toward properties of the size distribution of firms. Trade frictions force too narrow a structure on the arrangements of firm level trade and the requirements for the -1 distance elasticity of trade are generally not fulfilled.
The role of economic size, typically measured as GDP, has been well understood since 1980. When the population of a country doubles, production doubles resulting in exports doubling. Consumption doubles which leads to imports doubling. The flexibility of aggregate trade with regard to importer and exporter size is expected to be near to one. There are three conditions sufficient for the gravity equation in international trade to hold. The first condition that needs to hold is firms sizes follow a Pareto distribution over [Kmin, +] with shape parameter 1. The second condition is the average squared distance of exports is an increasing power function of firm size. The third condition is 1+. There is sufficient evidence that the distribution of firm sizes can be approximated by a Pareto distribution. Zipf’s law is 1. If Zipf’s law holds then condition three is easily fulfilled.
Under conditions one and two, the distance elasticity of aggregate trade is either continuous or asymptotically continuous and equal to -1 under Zipf’s law. Zipf’s law is about how much different firms are selling while the gravity equation is about where different countries are exporting to. The particulars of the geography of firm level trade past condition two are not that important. Firm level trade can be a mass point, uniform distribution or an exponential distribution. Each type differs primarily from the continuous distance elasticity of the gravity equation. Not all firms of a particular size export to the same locations. Some may do short or long distances. Condition three enforces only that among a set of firms of size K, the average squared distance of exports is a power function of K.
If small firms mostly export over short distances and large firms mostly over long distances, then aggregate exports toward remote locations are mainly coming from large firms. The more large firms there are compared to small firms or the faster the distance of firm level trade rises with firm size, the gentler the negative impact of distance on aggregate trade. The world is made of a variety of locations. Within each location, there is a variety of firms, starting up at a constant rate. Once started, a firm slowly obtains new trading partners in progressively isolated locations. A firm trades transitional inputs with all its trading associates. Older firms have more trading associates so that they are larger and export more and over lengthier distances.
Firms are consistently distributed over an infinite one dimensional continuous space represented by R. Time is continuous, with new firms starting at a rate in each location. So at time t, there is similar density of firms in each location. When a firm first starts, it trials a bulk of connections among other newly started firms only. Firms are infinitely resided. All outcomes conduct through with exogenous Poisson fatal shocks. New connections are always being created. At any point in time, each existing connection may reveal one if its own connections according to a Poisson process with arrival rate. Meaning a firm directly learns about new connections from the connections of its existing connections. Existing contacts are constantly gone to an exogenous Poisson shock with rate. As a result of informational conflicts, a firm sells its output only to its remaining connections. The number of connections of a firm, K, is also a measure of its size. The main assumptions of the model are resilient to allowing a functional rigorous margin of shipments. Age fully establishes size and the geography of trade. A discrete and stochastic type of this model would break the strong bond between age and firm features.
As a firm continues to grow larger, it meets the connections of its connections. Information about distant connections circulates through this network of firm to firm trade. Any singular firm progressively escapes gravity. The distribution of its connections congregates to what resembles an identical distribution over the whole real line. The world becomes “flat” for individual firms as they grow to become large. This does not mean the world becomes “flat” in the aggregate. As a firm ages and acquires more connections, those connections become increasingly dispersed over space. The result of this is that a firm’s first connections are some space away. Each movement of new connections comes from firms that are themselves further away, so each new movement is geographically more isolated than the last one. In dissimilarity to existing models, this explanation is exempt to the analysis that the effect of distance on trade should progress with transformations in the technology for trading goods, types of goods traded, the political obstacles to trade, countries involved in trade etc. As long as the distribution of firm sizes is secure and larger firms export over longer distances than smaller ones, aggregate trade should be close to inversely relative to distance.
