Gravity Equations and Economic Frictions in the World Economy

Abstract

At the same time that the modern theory of international trade due to comparative advantage developed in the post-World War II era to explain the patterns of international trade using 2 × 2 × 2 general equilibrium models, a small and separate line of empirical research in international trade emerged to ‘explain’ statistically actual aggregate bilateral trade flows among large numbers of countries. Drawing upon analogy to Isaac Newton’s Law of Gravitation, these international trade economists noted that observed bilateral aggregate trade flows between any pair of countries i and j could be explained very well using statistical methods by the product of the economic sizes of the two countries (GDP _i GDP _j ) divided by the distance between the country pair’s major economic centers (DIST _ij ). Specifically, these researchers conjectured that:

$$P{X_{ij}} = {\beta _0}{(GD{P_i})^{{\beta _1}}}{(GD{P_j})^{{\beta _2}}}{(DIS{T_{ij}})^{{\beta _3}}}{\varepsilon _{ij}}$$

(1)

or

$$\ln P{X_{ij}} = ln{\beta _0} + {\beta _1}ln{\mkern 1mu} {\text{GD}}{{\text{P}}_i} + {\beta _2}ln{\mkern 1mu} {\text{GD}}{{\text{P}}_j} + {\beta _3}ln{\mkern 1mu} {\text{DIS}}{{\text{T}}_{ij}} + ln{\mkern 1mu} {\varepsilon _{ij}},$$

(2)

where PX _ij is the value (in current prices) of the merchandise trade flow from exporter i to importer j, GDP _i (GDP _j ) is the level of nominal gross domestic product in country i (j), DIST _ij is the bilateral physical distance between the economic centers of countries i and j, and ε _ij is assumed to be a log normally distributed error term. In equation (2), ln refers to the natural logarithm. Intuition suggested that β₁ > 0, β₂ > 0, and β₃ < 0. In the 1960s, equations (1) and (2) came to be known among international trade economists as the ‘gravity equation’ — owing to its obvious similarity to Newton’s gravity equation in physics.