World Economy Gravity Models 1

gravity models

Gravity models utilize the gravitational force concept as an analogy to explain the

volume of trade, capital flows, and migration among the countries of the world. For

example, gravity models establish a baseline for trade-flow volumes as determined by

gross domestic product (GDP), population, and distance. The effect of policies on trade

flows can then be assessed by adding the policy variables to the equation and estimating

deviations from the baseline flows. In many instances, gravity models have significant

explanatory power, leading Deardorff (1998) to refer to them as a “fact of life.”

Alternative Specifications

Gravity models begin with Newton’s Law for the gravitational force ( GFij ) between two

objects i and j. In equation form, this is expressed as:

Mi M j
GFij = i≠ j (1)
Dij

In this equation, the gravitational force is directly proportional to the masses of

the objects ( M i and M j ) and indirectly proportional to the distance between them ( Dij ).

Gravity models are estimated in terms of natural logarithms, denoted “ ln .” In this

form, what is multiplied in Equation 1 becomes added, and what is divided becomes

subtracted, translating Equation 1 into a linear equation:

ln GFij = ln M i + ln M j − ln Dij i≠ j (2)

Gravity models of international trade implement Equation 2 by using trade flows

or exports from county i to country j ( Eij ) in place of gravitational force, with arbitrarily

small numbers sometimes being used in place of any zero values. Distance is often
World Economy Gravity Models 2

measured using “great circle” calculations. The handling of mass in Equation 2 takes

place via four alternatives. In the first alternative with the most solid theoretical

foundations, mass in Equation 2 is associated with the gross domestic product (GDP) of

the countries. In this case, Equation 2 becomes:

ln E ij = α + β 1 ln GDPi + β 2 ln GDPj + β 3 ln Dil (3)

In general, the expected signs here are β 1 , β 2 > 0 . However, the economics of

Equation 3 can lead to the interpretation of GDP as income, and when applied to

agricultural goods, Engels’ Law allows for GDP in the destination country to have a

negative influence on demand for imports. Hence it is also possible that β 2 < 0 .

In the second alternative, mass in Equation 2 is associated with both GDP and

population (POP). In this case, Equation 2 becomes:

ln Eij = ϕ + γ 1 ln GDPi + γ 2 ln POPi + γ 3 ln GDPj + γ 4 POPj + γ 5 ln Dij (4)

With regard to the expected signs on the population variables, these are typically

interpreted in terms or market size and are therefore positive ( γ 2 , γ 4 > 0 ). That said,

however, there is the possibility of import substitution effects as well as market size

effects. If the import substitutions effects dominate, the expect sign is γ 4 < 0 .

In the third and fourth alternatives, mass in Equation 2 is associated with GDP

per capita and with both gross domestic product and GDP per capita, respectively. In

these cases, Equation 2 becomes one of the following:

⎛ GDPi ⎞ ⎛ GDPj ⎞
ln Eij = τ + δ 1 ln⎜ ⎟ + δ 2 ln⎜⎜ ⎟ + δ ln Dij (5)
⎝ POPi ⎠ ⎝ POPj ⎟⎠ 3
World Economy Gravity Models 3

⎛ GDPi ⎞
ln Eij = µ + ν 1 ln GDPi + ν 2 ln⎜ ⎟ + ν ln GDPj
⎝ POPi ⎠ 3
(6)
⎛ GDPj ⎞
+ ν 4 ⎜⎜ ⎟ + ν ln Dij
⎝ POPj ⎟⎠ 5

Since they involve the same variables, the parameters of Equations 4, 5, and 6 are

transformations on one another: γ 1 = δ 1 = ν 1 + ν 2 ; γ 2 = −δ 1 = −ν 2 ; γ 3 = δ 2 = ν 3 + ν 4 ;

and γ 4 = −δ 4 = −ν 4 .

Theoretical Considerations

After being introduced by Tinbergen (1962), the gravity model was considered to be a

useful physical analogy with fortunate empirical validity. Subsequently, however,

connections have been made to key elements of trade theory. The standard assumption of

the Heckscher-Ohlin model that prices of traded goods are the same in each country has

proved to be faulty due to the presence of what trade economists call “border effects.”

Properly accounting for these border effects requires prices of traded goods to differ

among the countries of the world. Gravity models have been interpreted in these terms.

Anderson (1979) was the first to do this, employing the product differentiation by

country of origin assumption, commonly known as the “Armington assumption”

(Armington, 1969). By specifying demand in these terms, Anderson helped to explain the

presence of income variables in the gravity model, as well as their multiplicative (or log

linear) form. This approach was also adopted by Bergstrand (1985) who more thoroughly

specified the supply side of economies. The result was the insight that prices in the form

of GDP deflators might be an important additional variable to include in the gravity

equations described above. Price effects have also been captured using real exchange

rates (e.g., Brun et al., 2005).

The monopolistic competition model of new trade theory has been another

approach to providing theoretical foundations to the gravity model (Helpman, 1987 and

Bergstrand, 1989). Here, the product differentiation by country of origin approach is

replaced by product differentiation among producing firms, and the empirical success of

the gravity model is considered to be supportive of the monopolistic competition

explanation of intra-industry trade. However, Deardorff (1998) and Feenstra (2004) have

cast doubt on this interpretation, noting the compatibility of the gravity equation with

some forms of the Heckscher-Ohlin model and, consequently, the need for empirical

evidence to distinguish among potential theoretical bases: product differentiation by

country of origin; product differentiation by firm; and particular forms of Heckscher-

Ohlin-based comparative advantage. In each of these cases, the common denominator is

complete specialization by countries in a particular good. Without this feature, bilateral

trade tends to become indeterminate.

Alternatively, there are other approaches to gravity-based explanations of bilateral

trade that do not depend on compete specialization. As emphasized by Haveman and

Hummels (2004), this involves accounting for trade frictions in the form of distance-

based shipping costs or other trade costs, as well as policy-based trade barriers. Distance

costs can also be augmented to account for infrastructure, oil price, and trade composition

as in Brun et al. (2005). The two approaches (complete vs. incomplete specialization) can

be empirically distinguished by category of good, namely differentiated vs.

homogeneous, as in Feenstra, Markusen and Rose (2001).

Assessment

Due to its log-linear structure, the coefficients of the gravity model are in terms of

elasticities or ratios of percentage changes. These “unitless” measures are comparable

across countries and goods and give us direct measures of the responsiveness of trade

flows to the trade potential variables of Equations 3-6. For GDP and distance, estimated

elasticities tend to be close to 1.0 in value. For distance, comparison across groups of

countries gives a measure of the degree of integration in the world economy. In addition

to these standard variables, the coefficients of policy variables help us to understand the

impacts of the represented policies on trade flows. It is also possible to obtain estimates

of border effects independently of distance and other variables, as well as to investigate

some issues in economic geography as in Redding and Venables (2004). Despite some

ambiguity regarding its theoretical foundations, then, the gravity model is an important

empirical tool to help us understand trade and other economic flows in the world

economy.

See also: Applied General Equilibrium Models, Heckscher-Ohlin Model, Intra-Industry

Trade, Monopolistic Competition Model, New Trade Theory, Partial Equilibrium

Models, Revealed Comparative Advantage

Further Reading

Anderson, James E. 1979. A Theoretical Foundation for the Gravity Equation. American

Economic Review 69(1): 106-116. A first attempt to provide theoretical

foundations to the gravity model.

Armington, Paul. 1969. A Theory of Demand for Products Distinguished by Place of

Production. IMF Staff Papers 16(3): 159-176. The key contribution on product

differentiation by country of origin.

Bergstrand, Jeffrey H. 1985. The Gravity Equation in International Trade: Some

Microeconomic Foundations and Empirical Evidence. Review of Economics and

Statistics 67(3): 474-481. A second attempt to provide theoretical foundations to

the gravity model.

Bergstrand, Jeffrey H. 1989. The Generalized Gravity Equation, Monopolistic

Competition, and the Factor-Proportions Theory in International Trade. Review of

Economics and Statistics 71(1): 143-153. An interpretation of the gravity model

in terms of monopolistic competition.

Brun, Jean-François, Céline Carrère, Patrick Guillaumont, and Jaime de Melo (2005) Has

Distance Died? Evidence from a Panel Gravity Model. World Bank Economic

Review 19(1): 99-120. A useful exploration of distance in gravity models.

Deardorff, Alan V. 1998. Determinants of Bilateral Trade: Does Gravity Work in a

Neoclassical World? In Jeffrey A. Frankel, ed., The Regionalization of the World

Economy. Chicago: University of Chicago Press. A helpful review and assessment

of the gravity model.

Feenstra, Robert C. 2004. Advanced International Trade: Theory and Evidence.

Princeton: Princeton University Press. Chapter 5 of this book reviews the gravity

model in light of trade theory and also delves into a number of key estimation

issues.
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Feenstra, Robert.C., James R. Markusen and Andrew K. Rose. 2001. Using the Gravity

Equation to Differentiate among Alternative Theories of Trade. Canadian Journal

of Economics 34 (2): 430-447. Tests the gravity model over differentiated and

homogenous goods, focusing on differences in estimated parameter values.

Helpman, Elhanan. 1987. Imperfect Competition and International Trade: Evidence from

Fourteen Industrial Countries. Journal of the Japanese and International

Economies 1(1): 62-81. A claim for monopolistic competition models of intra-

industry trade using gravity model evidence.

Haveman, Jon and David Hummels. 2004. Alternative Hypotheses and the Volume of

Trade: The Gravity Equation and the Extent of Specialization. Canadian Journal

of Economics 37(1): 199-218. Explores gravity model explanations both in terms

of complete specialization such as in monopolistic competition models and

incomplete specialization with trade frictions.

Redding, Stephen and Anthony J. Venables. 2004. Economic Geography and

International Inequality. Journal of International Economics 62(1): 53-82. An

application of the gravity framework to economic geography.

Tinbergen, Jan. 1962. Shaping the World Economy: Suggestions for an International

Economic Policy. New York: The Twentieth Century Fund. The first use of a

gravity model to analyze international trade flows.

Kenneth A. Reinert, School of Public Policy, George Mason University