The Gravity Equation in International Trade: Some Microeconomic Foundations and Empirical Evidence

Despite the gravity equation's empirical success in "explaining" trade flows, the model's predictive potential has been inhibited by an absence of strong theoretical foundations. A general equilibrium world trade model is presented from which a gravity equation is derived by making certain assumptions, including perfect international product substitutability. If, however, trade flows are differentiated by origin as evidence suggests, the typical gravity equation is misspecified, omitting certain price variables. The last section presents empirical evidence supporting the notion that the gravity equation is a reduced form from a partial equilibrium subsystem of a general equilibrium model with nationally differentiated products. THE "gravity equation" has been long recognized for its consistent empirical success in explaining many different types of flows, such as migration, commuting, tourism, and commodity shipping. Typically, the log-linear equation specifies that a flow from origin i to destination j can be explained by economic forces at the flow's origin, economic forces at the flow's destination, and economic forces either aiding or resisting the flow's movement from origin to destination. In international trade, bilateral gross aggregate trade flows are explained commonly using the following specification: PXi, = fo(yi) (I? ) 2(Dij )3(A 1)4u (1) where PXij is the U.S. dollar value of the flow from country i to country j, Yi (Y1) is the U.S. dollar value of nominal GDP in i (j), Dij is the distance from the economic center of i to that of j, Aij is any other factor(s) either aiding or resisting trade between i and j, and u is a log-normally distributed error term with E(ln uij) = 0. This specification was used in Tinbergen (1962), Poyhonen (1963a, 1963b), Pulliainen (1963), Geraci and Prewo (1977), Prewo (1978), and Abrams (1980). 1 Table I presents results from estimating a gravity equation similar to (1) for 15 OECD countries' trade flows.2 Coefficient estimates are stable across years and are representative of trade gravity equations. Despite the model's consistently high statistical explanatory power, its use for predictive purposes has been inhibited owing to an absence of strong theoretical foundations. The most common justification-used in Linnemann (1966), Aitken (1973), Geraci and Prewo (1977), Prewo (1978), Abrams (1980), and Sapir (1981)-was developed by Linnemann and asserts that the gravity model is a reduced form from a four-equation partial equilibrium model of export supply and import demand. Prices are always excluded since "they merely adjust to equate supply and demand. "3 However, critics have argued that this approach is "loose" and does not explain the multiplicative functional form.4 This study addresses these and other issues in developing further the microeconomic foundations of the gravity equation. The "looseness" critique is addressed by systematically describing assumptions necessary to generate a gravity equation similar to (1) from a general equilibrium framework. Specific, yet intuitively plausible, functions for utility and production generate the equation's multiplicative form. Section I presents a general equilibrium model of world trade derived from utilityand profit-maximizing agent behavior in N countries assuming a single factor of production in Received for publication June 16, 1983. Revision accepted for publication December 12, 1984. *Federal Reserve Bank of Boston. The author is very grateful to J. David Richardson, Robert Baldwin, Rachel McCulloch, James Alm, Saul Schwartz and two anonymous referees for helpful comments on earlier drafts, and Doug Cleveland for research assistance. All errors remain the author's responsibility. The views expressed do not necessarily reflect the views of the Federal Reserve Bank of Boston or the Federal Reserve System. 'Linnemann (1966), Aitken (1973), Sattinger (1978) and Sapir (1981) used the same general specification, but also included exporter and importer populations. Microeconomic foundations of this alternative specification are discussed in Bergstrand (1984). 2The countries are Canada, United States, Japan, BelgiumLuxembourg, Denmark, France, West Germany, Italy, Netherlands, United Kingdom, Austria, Norway, Spain, Sweden, and Switzerland. The adjacency, EEC, and EFTA dummies are explained in the appendix. 3Linnemann (1966), p. 41; Leamer and Stern (1970), p. 146; (Geraci and Prewo (1977), p. 68; Prewo (1978), p. 344; and Sapir (1981), p. 341. 4See, for example, Anderson (1979), p. 106 and Leamer and Stern (1970), p. 158.