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 and distance between two units. The model was first used by
Jan Tinbergen in 1962. The basic model for trade between two countries takes
the form of: Where F is the trade flow, M is the
economic mass of each country, D is the distance and G is a constant. 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 and the World Trade Organization.
The model has also been applied to other bilateral flow data such as migration,
traffic, remittances and foreign direct investment.
Theoretical justifications and research The model has been an empirical success
in that it accurately predicts trade flows between countries for many goods
and services, but for a long time some scholars believed that there was no
theoretical justification for the gravity equation. However, a gravity
relationship can arise in almost any trade model that includes trade costs
that increase with distance. 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 abundance. 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, many
economists in the Chicago School believed that the Heckscher-Ohlin model
alone was sufficient to describe all trade, while Bertil Ohlin himself argued
that in fact the world is more complicated. 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
setup 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. Bridging economic theory with empirical
tests, James Anderson and Jeffrey Bergstrand develop econometric models,
grounded in the theories of differentiated goods, which measure the
gains from trade liberalizations and the magnitude of the border barriers on
trade. 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 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 to 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. A non-linear system of
equations are used by Anderson and van Wincoop to account for the endogenous
change in these price terms from trade liberalization. A more simple method is
to use a first order log-linearization of this system of equations), or
exporter-country-year and importer-country-year dummy variables.
For counterfactual analysis, however, one would still need to account for the
change in world prices. Econometric Estimation of Gravity
Equations Since the gravity model for trade does
not hold exactly, in econometric applications it is customary to specify
where represents volume of trade from country to country , and typically
represent the GDPs for countries and , denotes the distance between the two
countries, and represents an error term with expectation equal to 1.
The traditional approach to estimating this equation consists in taking logs of
both sides, leading to a log-log model of the form:
However, this approach has two major problems. First, it obviously cannot be
used when there are observations for which is equal to zero. Second, it has
been argued by Santos Silva and Tenreyro that estimating the log-linearized
equation by least squares can lead to significant biases. As an alternative,
these authors have suggested that the model should be estimated in its
multiplicative form, i.e., using a Poisson pseudo-maximum
likelihood estimator usually used for count data. One of the authors' more
surprising findings was that, when controlling for sharing a common
language, having past colonial ties does not increase trade. This is despite the
fact that simpler methods, such as taking simple averages of trade shares
of countries with and without former colonial ties suggest that countries
with former colonial ties continue to trade more. Santos Silva and Tenreyro
did not explain where their result came from and even failed to realize their
results were highly anomalous. Martin and Pham argued that using PPML on
gravity severely biases estimates when zero trade flows are frequent. However,
their results were challenged by Santos Silva and Tenreyro, who argued that the
simulation results of Martin and Pham are based on misspecified models and
showed that the PPML estimator performs well even when the proportions of zeros
is very large. In applied work, the model is often
extended by including variables to account for language relationships,
tariffs, contiguity, access to sea, colonial history, exchange rate regimes,
and other variables of interest. Dynamic Gravity Equation
The gravity equation of international trade is often motivated using New Trade
Theory models, which are models of increasing returns. Many increasing
returns models feature costs that either fixed or sunk, while it has long been
known that trade is a dynamic process. Recently, several authors have proposed
a dynamic gravity equation in place of the traditional static gravity equation,
including Yotov and Olivero, Campbell, and Campbell. The dynamic gravity
equation, in its most general form, posits that bilateral trade between
country i and j is a function of the size of each country, the current trade
costs, and the past trade costs. Empirically, the idea that trade flows
are determined by historical forces is confirmed by the evidence offered in
Eichengreen and Irwin, Campbell, and Campbell. Campbell shows that empirical
estimations using a dynamic gravity equation can have an enormous impact on
the measured impact of policy variables, such as the impact of currency unions on
trade. See also
Internationalization Notes
References Anderson, J., van Wincoop, E. "Gravity
with Gravitas: A Solution to the Border Puzzle." American Economic Review.
SL Baier, JH Bergstrand. "Bonus Vetus OLS:"A Simple Method for Approximating
International Trade-Cost Effects Using the Gravity Equation." Journal of
International Economics. 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., 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. http:www.bepress.comvol91/
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., pp. 431.
Hacker, R Scott, Einarsson, Henrik. “The Pattern, Pull, and Potential of Baltic
Sea Trade.” The Annals of Regional Science, Vol. 37, No. 1, pp. 15–29.
Isard, W., "Location Theory and Trade Theory: Short-Run Analysis". Quarterly
Journal of Economics, vol. 68, 1954, p. 305- 322.
Martin, William and Cong S. Pham, "Estimating the Gravity Model When Zero
Trade Flows are Frequent." Working Paper. .
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.
Santos Silva, J.M.C. and Tenreyro, Silvana, “The Log of Gravity,” The
Review of Economics and Statistics, 88(4), pp. 641–658.
Santos Silva, J.M.C. and Tenreyro, Silvana, Further simulation evidence on
the performance of the Poisson pseudo-maximum likelihood estimator,
Economics Letters, 112(2), pp. 220–222. Summary, Rebecca M. “A
Political-Economic Model of U.S. Bilateral Trade.” The Review of
Economics and Statistics, Vol. 71, No. 1., pp. 179–182.
Balding, C., & Dauchy, E. P.. Asymmetric Trade Estimator in Modified Gravity:
Corporate Tax Rates and Trade in OECD Countries. Available at SSRN 2249536.
External links = Information =
World Bank presentation on the gravity model
Global multi-market simulation using World Bank's World Integrated Trade
Solution *Global Tariff Cuts and Trade Simulator
A page on the implementation of the Poisson pseudo-maximum likelihood
estimator = Data =
World Bank's Trade and Production Database
Resources for data on trade, including the gravity model
UNESCAP dataset for gravity model