### Gravity model

The gravity model is most commonly used by international and regional economists to study trade.4 The classic early application of the model was by Linnemann (1966), who continued work first reported in Tinbergen (1962) and then in Pöyhönen (1963). Some of the most recent work on the application of the model was Frankel et al. (1997a, 1997b)Frankel et al. (1997a)Frankel et al. (1997b), Rauch (1999), and Rose (2004), among others. Generally, a gravity model assumes that the volume of trade between any two economies will be directly proportional to the product of their economic masses (measured by gross domestic product [GDP] or gross national product [GNP]) and inversely proportional to the distance between them. Per capita incomes (measured by product of per capita GDPs or GNPs) have become a standard covariate in the gravity models of, for example, Eaton and Tamura (1994), Frankel et al. (1997a, 1997b)Frankel et al. (1997a)Frankel et al. (1997b), and Rauch (1999).

In addition to “distance,” “adjacency” (i.e., the country pair shares a common land border) and “cultural links” also influence trade (see, e.g., Rauch and Trindade, 2002; Noland, 2005; Guiso et al., 2006; and Guo, 2009, pp. 77–102). The basic form of the gravity model to be used in our empirical analysis of interprovincial trade is as the following:(4.1)ln(TRADEij)=α0+α1ln(GDPiGDPj)+α2ln(GDPPCiGDPPCj)+α3lnDISTANCEij+α4ADJACENTij+α5ETHNIC56ij

In Equation 4.1, ln represents natural logarithm; TRADEij, measured in thousand tons, is the total freight exchange between provinces i and j. GDPiGDPj is the product of GDP (in Chinese currency) of the ith and jth provinces. GDPPCiGDPPCj is the product of GDP per capita (in Chinese currency) of the ith and jth provinces. DISTANCEij represents the distance between the geographical centers of gravity of the ith and jth provinces (in kilometers). ADJACENTij is a dummy variable, which takes the value of 1 for provinces i and j to have a common border and 0 otherwise.

natural logarithm