A gravity model of immigration

Immigration is a controversial issue in many countries, and economists are increasingly called on to explain its causes and consequences. Most economic studies of immigration, such as Friedberg and Hunt (1995), Card (2001), and Borjas (2003), use a standard labor market model in which immigrant workers respond to differences in wages between countries. Many other factors influence immigration, however. This paper offers an adaptable regression model, based on the popular gravity model of international trade, with which to test hypothesized influences on immigration.

The gravity model of trade specifies trade as a positive function of the attractive “mass” of two economies and a negative function of distance between them. Defining TRADE_ij as total trade between countries i and j, DIST_ij as the distance between the two countries, and the gravitational “mass” as the product of gross domestic products of countries i and j, the gravity model of trade is${\mathrm{TRADE}}_{ij}=f\left[\left({\mathrm{GDP}}_i\cdot {\mathrm{GDP}}_j\right)/{\mathrm{DIST}}_{ij}\right]\text{.}$

Showing natural logs in lower case, the regression equation is commonly specified as${\mathrm{trade}}_{ij}=a_0+a_1({\mathrm{gdp}}_i\cdot {\mathrm{gdp}}_j)+a_2\left({\mathrm{dist}}_{ij}\right)+u_{ij}\text{.}$

Researchers using the gravity model to explain trade often include variables to control for demographic, geographic, ethnic/linguistic, and economic conditions, as for example${\mathrm{trade}}_{ij}=a_0+a_1\left({\mathrm{gdp}}_i\cdot {\mathrm{gdp}}_j\right)+a_2\left({\mathrm{pop}}_i\cdot {\mathrm{pop}}_j\right)+a_3\left({\mathrm{dist}}_{ij}\right)+a_4{\mathrm{BLOC}}_{ij}+a_5{\mathrm{LANG}}_{ij}+a_6{\mathrm{CONT}}_{ij}+a_7{\mathrm{LINK}}_{ij}+u_{ij}\text{.}$

In (3), BLOC, LANG, CONT, and LINK are dummy variables for pairs of countries that share membership in a free trade area, a common language, a contiguous border, and colonial links, respectively, and pop_i · pop_j is the log of the product of the populations.

Tinbergen (1962) first used the gravity model to explain international trade patterns, and economists have consistently found it to explain a large proportion of the variation in international trade flows, making the model attractive for testing the marginal influence of other hypothesized variables on international trade. Theoretical justifications for the model have been provided by Linnemann (1966), Anderson (1979), and Deardorff (1998).