Gravity model of trade

Gravity model of trade

The gravity model of trade in international economics, similar to other gravity models in social science, predicts bilateral trade flows based on the economic sizes of (often using GDP measurements) and distance between two units. The model was first used by Walter Isard in 1954. The basic theoretical model for trade between two countries (i and j) takes the form of:

:F_{ij} = G * frac{M_i * M_j}{D_{ij

Where F is the trade flow, M is the economic mass of each country, D is the distance and G is a constant. Using logarithms, the equation can be converted to a linear form for econometric analysis. The basic model for such a test results in the following equation (note:constant G becomes part of α):

:ln(Bilateral Trade Flow) = α+βln(GDPCountry1)+βln(GDPCountry2)-βln(Distance)+ε

The model often includes variables to account for income level (GDP per capita), price levels, language relationships, tariffs, contiguity, and colonial history (whether Country1 ever colonized Country2 or vice versa). The model has also been used in international relations to evaluate the impact of treaties and alliances on trade, and it has been used to test the effectiveness of trade agreements and organizations such as the North American Free Trade Agreement (NAFTA) and the World Trade Organization (WTO).

Theoretical justifications and research

The model has been an empirical success, but the theoretical justifications for the model are the subject of some dispute. The model clearly has a relationship with a geographic view of trade, but other theoretical justifications for the model have also been proposed.

The gravity model estimates the pattern of international trade. While the model’s basic form consists of factors that have more to do with geography and spatiality, the gravity model has been used to test hypotheses rooted in purer economic theories of trade as well. One such theory predicts that trade will be based on relative factor abundances. One of the common relative factor abundance models is the Heckscher-Ohlin model. This theory would predict that trade patterns would be based on relative factor advantages. Those countries with a relative abundance of one factor would be expected to produce goods that require a relatively large amount of that factor in their production. While a generally accepted theory of trade, comparative advantage has suffered empirical problems. Investigations into real world trading patterns have produced a number of results that do not match the expectations of comparative advantage theories. Notably, a study by Wassily Leontief found that the United States, the most capital endowed country in the world actually exports more in labor intensive industries. Comparative advantage in factor endowments would suggest the opposite would occur. Other theories of trade and explanations for this relationship were proposed in order to explain the discrepancy between Leontief’s empirical findings and economic theory. The problem has become known as the Leontief paradox. An alternative theory, first proposed by Staffan Linder, predicts that patterns of trade will be determined by the aggregated preferences for goods within countries. Those countries with similar preferences would be expected to develop similar industries. With continued similar demand, these countries would continue to trade back and forth in differentiated but similar goods since both demand and produce similar products. For instance, both Germany and the United States are industrialized countries with a high preference for automobiles. Both countries have automobile industries, and both trade cars. The empirical validity of the Linder hypothesis is somewhat unclear. Several studies have found a significant impact of the Linder effect, but others have had weaker results. Studies that do not support Linder have only counted countries that actually trade; they do not input zero values for the dyads where trade could happen but does not. This has been cited as a possible explanation for their findings. Also, Linder never presented a formal model for his theory, so different studies have tested his hypothesis in different ways.

Elhanan Helpman and Paul Krugman asserted that the theory behind comparative advantage does not predict the relationships in the gravity model. Using the gravity model, countries with similar levels of income have been shown to trade more. Helpman and Krugman see this as evidence that these countries are trading in differentiated goods because of their similarities. This casts some doubt about the impact Heckscher-Ohlin has on the real world. Jeffrey Frankel sees the Helpman-Krugman set up here as distinct from Linder’s proposal. However, he does say Helpman-Krugman is different from the usual interpretation of Linder, but, since Linder made no clear model, the association between the two should not be completely discounted.
Alan Deardorff adds the possibility, that, while not immediately apparent, the basic gravity model can be derived from Heckscher-Ohlin as well as the Linder and Helpman-Krugman hypotheses. Deardorff concludes that, considering how many models can be tied to the gravity model equation, it is not useful for evaluating the empirical validity of theories.

Adding to the problem of bridging economic theory with empirical results, some economists have pointed to the possibility of intra-industry trade not as the result of differentiated goods, but because of “reciprocal dumping.” In these models, the countries involved are said to have imperfect competition and segmented markets in homogeneous goods, which leads to intra-industry trade as firms in imperfect competition seek to expand their markets to other countries and trade goods that are not differentiated yet for which they do not have a comparative advantage, since there is no specialization. This model of trade is consistent with the gravity model as it would predict that trade depends on country size. The reciprocal dumping model has held up to some empirical testing, suggesting that the specialization and differentiated goods models for the gravity equation might not fully explain the gravity equation. Feenstra, Markusen, and Rose (2001) provided evidence for reciprocal dumping by assessing the "home market effect" in separate gravity equations for differentiated and homogeneous goods. The home market effect showed a relationship in the gravity estimation for differentiated goods, but showed the inverse relationship for homogeneous goods. The authors show that this result matches the theoretical predictions of reciprocal dumping playing a role in homogeneous markets.

Past research using the gravity model has also sought to evaluate the impact of various variables in addition to the basic gravity equation. Among these, price level and exchange rate variables have been shown to have a relationship in the gravity model that accounts for a significant amount of the variance not explained by the basic gravity equation. According to empirical results on price level, the effect of price level varies according the relationship being examined. For instance, if exports are being examined, a relatively high price level on the part of the importer would be expected to increase trade with that country (Bergstrand and Summary).

United States trade

Rebecca M. Summary specifically investigated American trade in an attempt to examine the specific role of political factors on United States trade. Her model consisted of the basic gravity equation, but did not multiply GDP or population (she used these separately and excluded income level) to find an interaction since she only looked at United States data and all data would be weighted by the same, cross-sectional factor. Summary’s study concluded that American exports and imports are affected by a number of political and social factors related to business ties, alliances, and foreign policy as well as the basic factors usually included in the gravity model.


*Bergstrand, Jeffrey H. “The Gravity Equation in International Trade: Some Microeconomic Foundations and Empirical Evidence.” The Review of Economics and Statistics, Vol. 67, No. 3. (Aug., 1985), pp. 474-481.
*Caruso, R. "The impact of International Economic Sanctions on Trade. An Empirical Analysis.", Peace Economics, Peace Science and Public Policy, vol.9, no.2 (2003).
*Deardorff, Alan V. “Determinants of Bilateral Trade: Does Gravity Work in a Neoclassical World?” In The Regionalization of the World Economy, edited by J.A. Frankel. Chicago: University of Chicago Press. 1998, 21.
*Frankel, Jeffery A. Regional Trading Blocs: In the World Economic System. Washington, DC: Institute of International Economics. October 1997.
*Feenstra, Robert C., James R. Markusen, and Andrew K. Rose. “Using the Gravity Equation to Differentiate among Alternative Theories of Trade.” The Canadian Journal of Economics, Vol. 34, No. 2. (May, 2001), pp. 431.
*Isard, W., "Location Theory and Trade Theory: Short-Run Analysis". Quarterly Journal of Economics, vol. 68, 1954, p. 305- 322.
*McPherson,M. A., M. R. Redfearn and M. A. Tieslau. “A Re-examination of the Linder Hypothesis: a Random-Effects Tobit Approach.” Working Paper from the website of the Department of Economics; University of North Texas.
*Summary, Rebecca M. “A Political-Economic Model of U.S. Bilateral Trade.” The Review of Economics and Statistics, Vol. 71, No. 1. (Feb., 1989), pp. 179-182.

External links


* [ World Bank presentation on the gravity model]
* [ PDF file explaining the gravity model]


* [ World Bank's Trade and Production Database]
* [ Resources for data on trade, including the gravity model]

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