Gravity model of trade
Encyclopedia
The gravity model of trade in international economics
, similar to other gravity model
s 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 Tinbergen in 1962. The basic theoretical model for trade between two countries (i and j) 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
(NAFTA) and the World Trade Organization
(WTO).
, 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 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, 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.
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 (see McCallum Border puzzle).
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. A non-linear system of equations are used by Anderson and van Wincoop(2003) 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(Baier and Bergstrand (2009)), 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.
,
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 (note: constant G becomes part of
):
.
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 (2006) that estimating the log-linearized equation by least squares
(OLS) can lead to significative 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 (PPML) estimator usually used for count data (see the original paper for details). One of the authors' more surprising findings was that, when controlling for sharing a common language, having past colonial ties does not increase trade—a finding which contrasts with what more basic methods, such as OLS or even scatter plots of trade data, would indicate. Martin and Pham (2008) 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 (2011), who pointed out that the simulation results of Martin and Pham (2008) are based on misspecified models and confirmed 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, tariff
s, contiguity, access to sea, colonial history, exchange rate regimes, and other variables of interest.
International economics
International economics is concerned with the effects upon economic activity of international differences in productive resources and consumer preferences and the institutions that affect them...
, similar to other gravity model
Gravity model
Gravity models are used in various social sciences to predict and describe certain behaviors that mimic gravitational interaction as described in Isaac Newton's law of gravity...
s 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 Tinbergen in 1962. The basic theoretical model for trade between two countries (i and j) 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
International relations
International relations is the study of relationships between countries, including the roles of states, inter-governmental organizations , international nongovernmental organizations , non-governmental organizations and multinational corporations...
to evaluate the impact of treaties and alliances
Alliances
Alliances may refer to:* The plural of alliance, an agreement between two or more parties* Airline alliances, agreements between two or more airlines to cooperate on a substantial level...
on trade
Trade
Trade is the transfer of ownership of goods and services from one person or entity to another. Trade is sometimes loosely called commerce or financial transaction or barter. A network that allows trade is called a market. The original form of trade was barter, the direct exchange of goods and...
, and it has been used to test the effectiveness of trade agreements and organizations such as the North American Free Trade Agreement
North American Free Trade Agreement
The North American Free Trade Agreement or NAFTA is an agreement signed by the governments of Canada, Mexico, and the United States, creating a trilateral trade bloc in North America. The agreement came into force on January 1, 1994. It superseded the Canada – United States Free Trade Agreement...
(NAFTA) and the World Trade Organization
World Trade Organization
The World Trade Organization is an organization that intends to supervise and liberalize international trade. The organization officially commenced on January 1, 1995 under the Marrakech Agreement, replacing the General Agreement on Tariffs and Trade , which commenced in 1948...
(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 tradeTrade
Trade is the transfer of ownership of goods and services from one person or entity to another. Trade is sometimes loosely called commerce or financial transaction or barter. A network that allows trade is called a market. The original form of trade was barter, the direct exchange of goods and...
, 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
Heckscher-Ohlin model
The Heckscher–Ohlin model is a general equilibrium mathematical model of international trade, developed by Eli Heckscher and Bertil Ohlin at the Stockholm School of Economics. It builds on David Ricardo's theory of comparative advantage by predicting patterns of commerce and production based...
. 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, 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
Wassily Leontief
Wassily Wassilyovich Leontief , was a Russian-American economist notable for his research on how changes in one economic sector may have an effect on other sectors. Leontief won the Nobel Committee's Nobel Memorial Prize in Economic Sciences in 1973, and three of his doctoral students have also...
found that the United States
United States
The United States of America is a federal constitutional republic comprising fifty states and a federal district...
, 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
Leontief paradox
Leontief's paradox in economics is that the country with the world's highest capital-per worker has a lower capital/labor ratio in exports than in imports....
.
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
Economy of Germany
Germany is the largest national economy in Europe, the fourth-largest by nominal GDP in the world, and fifth by GDP in 2008. Since the age of industrialisation, the country has been a driver, innovator, and beneficiary of an ever more globalised economy...
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
Linder hypothesis
The Linder hypothesis is a economics conjecture about international trade patterns: The more similar the demand structures of countries, the more they will trade with one another...
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
Elhanan Helpman
Elhanan Helpman is an Israeli-American economist who works in the field of international trade, political economy and economic growth.-Biography:...
and Paul Krugman
Paul Krugman
Paul Robin Krugman is an American economist, professor of Economics and International Affairs at the Woodrow Wilson School of Public and International Affairs at Princeton University, Centenary Professor at the London School of Economics, and an op-ed columnist for The New York Times...
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
Jeffrey Frankel
Jeffrey Alexander "Jeff" Frankel is the James W. Harpel Professor of Capital Formation and Growth at Harvard University's Kennedy School of Government. A member of the Council of Economic Advisors under President Bill Clinton, Frankel is a noted international macroeconomist...
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
Alan Deardorff
Alan V. Deardorff is the John W. Sweetland Professor of International Economics and a Professor of Economics and Public Policy at the University of Michigan, Ann Arbor. He is also the Associate Dean at the Gerald R. Ford School of Public Policy. Former Chair of the Economics Department, Professor...
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
James Anderson
- Arts :*James K Anderson , American actor*James Anderson , British actor*James Arthur Anderson , American writer*James Anderson , American television writer...
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 (see McCallum Border puzzle).
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. A non-linear system of equations are used by Anderson and van Wincoop(2003) 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(Baier and Bergstrand (2009)), 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.
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.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 (note: constant G becomes part of
):.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 (2006) that estimating the log-linearized equation by least squaresLeast squares
The method of least squares is a standard approach to the approximate solution of overdetermined systems, i.e., sets of equations in which there are more equations than unknowns. "Least squares" means that the overall solution minimizes the sum of the squares of the errors made in solving every...
(OLS) can lead to significative 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 (PPML) estimator usually used for count data (see the original paper for details). One of the authors' more surprising findings was that, when controlling for sharing a common language, having past colonial ties does not increase trade—a finding which contrasts with what more basic methods, such as OLS or even scatter plots of trade data, would indicate. Martin and Pham (2008) 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 (2011), who pointed out that the simulation results of Martin and Pham (2008) are based on misspecified models and confirmed 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
Language
Language may refer either to the specifically human capacity for acquiring and using complex systems of communication, or to a specific instance of such a system of complex communication...
relationships, tariff
Tariff
A tariff may be either tax on imports or exports , or a list or schedule of prices for such things as rail service, bus routes, and electrical usage ....
s, contiguity, access to sea, colonial history, exchange rate regimes, and other variables of interest.
Information
- World Bank presentation on the gravity model
- A page on the implementation of the Poisson pseudo-maximum likelihood estimator