Gravity model of trade
The model has also been used in international relations to evaluate the impact of treaties and alliances on trade (Head and Mayer).
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.
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.
An alternative theory, first proposed by Staffan Linder, predicts that patterns of trade will be determined by the aggregated preferences for goods within countries.
Several studies have found a significant impact of the Linder effect, but others have had weaker results.
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.
Helpman and Krugman see this as evidence that these countries are trading in differentiated goods because of their similarities.
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.
A recent synthesis of empirical research using the gravity equations, however, shows that the effect of border barriers on trade is relatively modest.
[7] 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.
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 authors show that this result matches the theoretical predictions of reciprocal dumping playing a role in homogeneous markets.
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.
[8] 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.
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
Second, Santos Silva and Tenreyro (2006) argued that estimating the log-linearized equation by least squares (OLS) can lead to significant biases if the researcher believes the true model to be nonlinear in its parameters.
As shown by Santos Silva and Tenreyro (2006), PPML estimates of common gravity variables can be different from their OLS counterparts.
Martin and Pham (2008) argued that using PPML on gravity severely biases estimates when zero trade flows are frequent and reflect non-random selection.
[12] In applied work, the gravity model is often extended by including variables to account for language relationships, tariffs, contiguity, access to sea, colonial history, and exchange rate regimes.
