Controlling for Heterogeneity in Gravity Models of Trade

GDPs, their populations, and the distance between them. Thus, the augmented CS model (CSa)assumes that in a given year trade flows from exporting country i to importing country j can beestimated using: 8ln Xij= α + β1 lnYi+ β2lnYj+ β3ln Ni+ β4ln Nj+ δ1ln Dij+ δ2Cij+ λLij+ εij; (2)where Y i andY j are the two countries’ GDPs;Nianddistance between their economic centers (their capital cities);N are their populations, D is thejC ij is a contiguity dummy; and Lijis a common-language dummy. As trade flows are expected to be positively related to nationalincomes, and negatively related to distance, it is expected that β 1, β 2 , and δ 2 are positive, andthat δ 1 is negative. Also, estimation typically yields a negative sign for β 3 , which wouldindicate that exported goods tend to be capital-intensive. It is also common to obtain a negativesign for β 4 , which would indicate that traded goods tend to have income-elastic demands.Finally, because Lijis meant to capture cultural and historical similarities between the tradingSDLUVZKLFKDUHWKRXJKWWRLQFUHDVHWKHYROXPHRIWUDGH LVH[SHFWHGWREHSRVLWLYHThe basic version of the gravity model does not include the populations of the twocountries, so it can be viewed as a special case of the augmented model in which the coefficientson population are restricted to zero. Thus, the basic CS model (CSb) assumes that bilateral tradecan be estimated with the following regression:ln Xij= α + β1 lnYi+ β2lnYj+ δ1ln Dij+ δ2Cij+ λLij+ εij.(3)The expected signs for the coefficients are as in the augmented model.ij8 Note that because ln ( per capita incomei ) = ln Yi − ln N , the regression could be suitably rearrangedito instead obtain the augmented model with per capita income.8