The Gravity Equation in International Trade: Some Microeconomic Foundations and Empirical Evidence
TL;DR: The gravity equation has been widely recognized for its consistent empirical success in explaining many different types of flows, such as migration, commuting, tourism, and commodity shipping as mentioned in this paper, but its use for predictive purposes has been inhibited owing to an absence of strong theoretical foundations.
Abstract: 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.
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TL;DR: This article showed that the gravity model usually estimated does not correspond to the theory behind it and showed that national borders reduce trade between the US and Canada by about 44% while reducing trade among other industrialized countries by about 30%.
Abstract: The gravity model has been widely used to infer substantial trade flow effects of institutions such as customs unions and exchange rate mechanisms. McCallum [1995] found that the US-Canada border led to trade between provinces that is a factor 22 (2,200%) times trade between states and provinces, a spectacular puzzle in light of the low formal barriers on this border. We show that the gravity model usually estimated does not correspond to the theory behind it. We solve the 'border puzzle' by applying the theory seriously. We find that national borders reduce trade between the US and Canada by about 44%, while reducing trade among other industrialized countries by about 30%. McCallum's spectacular headline number is the result of a combination of omitted variables bias and the small size of the Canadian economy. Within-Canada trade rises by a factor 6 due to the border. In contrast, within-US trade rises 25%.
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TL;DR: In this article, a method that consistently and efficiently estimates a theoretical gravity equation and correctly calculates the comparative statics of trade frictions was developed to solve the famous McCallum border puzzle.
Abstract: Gravity equations have been widely used to infer trade flow effects of various institutional arrangements. We show that estimated gravity equations do not have a theoretical foundation. This implies both that estimation suffers from omitted variables bias and that comparative statics analysis is unfounded. We develop a method that (i) consistently and efficiently estimates a theoretical gravity equation and (ii) correctly calculates the comparative statics of trade frictions. We apply the method to solve the famous McCallum border puzzle. Applying our method, we find that national borders reduce trade between industrialized countries by moderate amounts of 20-50 percent.
4,997 citations
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TL;DR: In this paper, the gravity equation for trade was used to provide new estimates of this equation, and significant differences between the estimated estimator and those obtained with the traditional method were found.
Abstract: Although economists have long been aware of Jensen's inequality, many econometric applications have neglected an important implication of it: the standard practice of interpreting the parameters of log-linearized models estimated by ordinary least squares as elasticities can be highly misleading in the presence of heteroskedasticity. This paper explains why this problem arises and proposes an appropriate estimator. Our criticism to conventional practices and the solution we propose extends to a broad range of economic applications where the equation under study is log-linearized. We develop the argument using one particular illustration, the gravity equation for trade, and apply the proposed technique to provide new estimates of this equation. We find significant differences between estimates obtained with the proposed estimator and those obtained with the traditional method. These discrepancies persist even when the gravity equation takes into account multilateral resistance terms or fixed effects
4,492 citations
Cites background from "The Gravity Equation in Internation..."
...1 In its simplest form, the gravity equation for trade 1See, for example, Anderson (1979), Helpman and Krugman (1985), Bergstrand (1985), Davis (1995), Deardoff (1998), and Anderson and van Wincoop (2003)....
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TL;DR: In this paper, the authors address the endogeneity of free trade agreements using instrumental-variable (IV) techniques, control function (CF) techniques and panel-data techniques; IV and CF approaches do not adjust for endogeneity well, but a panel data approach does.
2,163 citations
TL;DR: In this article, a general equilibrium model of world trade with two differentiated-product industries and two factors is developed to illustrate how the gravity equation, including exporter and importer populations, as well as incomes, "fits in" with the Heckscher-Ohlin model of inter-industry trade and the Helpman-Krugman-Markusen models of intraindustry trade.
Abstract: A general equilibrium model of world trade with two differentiated-product industries and two factors is developed to illustrate how the gravity equation, including exporter and importer populations, as well as incomes, "fits in" with the Heckscher-Ohlin model of interindustry trade and the Helpman-Krugman-Markusen models of intraindustry trade. The study extends the microeconomic foundations for a generalized gravity equation in Bergstrand (1985) to incorporate relative factor-endowment differences and nonhomothetic tastes. Empirical estimates of this generalized gravity equation for single-digit Standard Industrial Trade Classification industry groups yield plausible inferences of their capital-labor intensities. Copyright 1989 by MIT Press.
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TL;DR: In this paper, the impact of the European Economic Community (EEC) and the European Free Trade Association (EFTA) on member trade over the period 1951-67 is investigated.
Abstract: Utilizing a cross-sectional trade flow model of the type developed by Hans Linnemann and Jan Tinbergen, this study attempts to isolate empirically the major forces which have shaped European trade relations over the period 1951-67. We first estimate via the use of dummy variables the impact of the European Economic Community (EEC) and the European Free Trade Association (EFTA) on member trade. For each year of the European integration period (1959-67), a crosssectional equation is estimated ancl used to test for the existence and approximate size of the respective integration effects. The equation is also calculated for the eight years prior to the integration period to obtain a clear picture of the forces which were at work before the formation of the EEC. Secondly, a base year equation is used to make projection estimates of the gross trade creation and European trade diversion effects of the two communities.
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TL;DR: This article showed that exchange rate changes substantially alter the relative dollar-equivalent prices of the most narrowly defined domestic and foreign manufactured goods for which prices can readily be matched, and that these relative price effects seem to persist for at least several years and cannot be shrugged off as transitory.
Abstract: Students exposed to the pure theory of international trade have been seduced by visions of an imaginary world with few goods, each typically produced by several countries but nevertheless homogeneous. In the assumed absence of transport costs and trade restrictions, perfect commodity arbitrage insures that each good is uniformly priced (in common currency units) throughout the world-the "law of one price" prevails. In reality the law of one price is flagrantly and systematically violated by ernpirical data. This paper presents evidence that exchange rate changes substantially alter the relative dollar-equivalent prices of the most narrowly defined domestic and foreign manufactured goods for which prices can readily be matched. Moreover, these relative price effects seem to persist for at least several years and cannot be shrugged off as transitory. In other words, for manufactured goods selected from the most disaggregated commodity lists for which U.S. and foreign prices can be matched, the products of different countries exhibit relative price behavior which marks them as differentiated products, rather than nearperfect substitutes. To clarify discussion it is useful to distinguish two contexts in which the law of one price is valid from a third context in which the law of one price does not hold. First, in a comparison of U.S., European, and Japanese prices of various well-defined steel items (plate, galvanized sheet, coldrolled sheet, and hot-rolled sheet) c.i.f. for delivery in a common port, Laurence Rosenberg found that relative dollar prices charged by different countries were fairly constant over time and were not significantly affected by exchange rate realignments. The dollar prices of primary commodities are also generally considered to be fairly independent of country of origin.' These are cases in which the products of different countries are close to identical, or near-perfect substitutes, so that any price disparities would be rapidly eliminated by commodity arbitrage. Second, in the absence of restrictions on commodity arbitrage, a product of any single country sold competitively in two different markets (foreign or domestic) would also obey the law of one price in the sense that its dollarequivalent prices in the two markets could not differ by more than the cost of transportation between these markets. Many U.S. manufactured goods do not have near-perfect substitutes on the lists of products manufactured abroad, however, and in this third context the law of one price is denied as an empirical proposition. Agricultural tilling machinery produced in the United States, for example, is apparently not a close substitute for agricultural tilling machinery produced in Germany. More generally, the most disaggregated groupings of manufactured goods for which both U.S. and German prices are readily available are dominated by products for which German dollar price indexes diverge over time from U.S. dollar price indexes2 in a manner that is strongly correlated with exchange rate movements. This divergence is evident in comparisons of U.S. wholesale transactions prices and German export transactions prices for various 2and 3-digit sectors of the WPI industry breakdown (Section I),
647 citations
TL;DR: In this paper, the authors examined the direction and level of aggregate bilateral trade flows in a multi-country trade network and incorporated economic variables for both the importing and exporting countries, including demand and supply conditions and trade resistance factors, in particular, the costs of transportation.
Abstract: T HIS study examines the direction and level of aggregate bilateral trade flows in a multi-country trade network. We are not so much concerned with an explanation of a country's total imports as with the geographical pattern of its imports from among its trading partners. We therefore incorporate economic variables for both the importing and exporting countries, including demand and supply conditions and "trade resistance factors," in particular, the costs of transportation. The latter are incorporated into the analysis through an errorsin-variables specification. Our study begins on familiar ground. Similar models have been proposed and tested by Tinbergen (1962), Poyhonen (1963a, b), Pulliainen (1963), Linnemann (1966) and others. The key difference between our study and previous ones lies in the treatment of the costs of transportation. Previous studies have used distance as a proxy for transport costs, but that has some serious limitations. First, the cost of transportation is influenced by other factors such as the value of the commodity being transported.1 For example, Moneta (1959) has pointed out that the effect of distance is small for high-valued commodities. Second, the use of distance imposes the assumption that the cost of transportation is the same in either direction between any pair of trading countries. This is restrictive when analyzing aggregate trade flows, since the commodity composition of trade differs by direction. Third, estimated relationships (e.g., elasticities) between trade flows and static variables such as distance are not very helpful in predicting future trade levels and thus are not very helpful in policy analysis. Finger and Yeats (1976) have shown for the United States that effective protection due to international transport costs is at least as high as tllat due to tariffs. Moreover, they indicate that the importance of transport costs has been increasing rapidly in recent years (even before full consideration of the recent petroleum price increases).2 The need to move beyond the distance specification of transport costs is clear. The fact that reliable data on transport costs are unavailable has been the primary reason for the use of distance as a proxy in the previous studies. In principle, the difference between c.i.f. and f.o.b. trade values represents the costs of freight and insurance.3 However, due to notorious measurement errors, these figures cannot be used in traditional econometric procedures. Consequently, most trade studies dealing with this subject have not utilized the differences between c.i.f. and f.o.b. values.4 Though these differences are indeed highly inaccurate measures of transport costs, they are included in our empirical analysis by applying an errorsin-variables approach. This allows the estimation of the elasticity of bilateral trade flows with respect to transport costs, which is the key product of this study. The theoretical background is introduced in section II and the empirical model is specified
171 citations