Controlling for Heterogeneity in Gravity Models of Trade

independent variables are assumed to be correlated withwhich can be estimated using OLS.α ij , and is a classical regression modelBayoumi and Eichengreen (1997) and Mátyás (1997) have also proposed models tohandle country-pair heterogeneity, each of which can be modeled as a restricted version of the FEmodel. In the Bayoumi and Eichengreen (BE) model the differences in the dependent andindependent variables are used to eliminate the fixed variables, including the country-pairdummies and distance. Specifically,∆lnijt 0 tijt ijtX = γ + γ + ∆Z + µ , t = 1, ..., T; (BE)ZKHUH LVWKHGLIIHUHQFHRSHUDWRUDQG γ0+ γt= αt− αt−1. In this model the intercept has twoparts: γ0is the change in the period-specific effect that is common across years, and γtis thechange that is specific to year t. As is well known, when there are no time dummies, such adifferencing model should yield results identical to a model with dummy variables to control forfixed effects. However, with time dummies it is necessary to impose restrictions on the timeeffects so as to avoid collinearity, which in turn makes the BE model a restricted form of the FEmodel. If the collinearity restriction is that the first time dummy in the BE model is equal tozero, this is equivalent to restricting the common component of the change in the period-specificeffects as equal to the difference in the first two period-specific effects, i.e. γ = α − . If0 2α1instead the collinearity restriction is that the sum of the time dummies in the BE model is zero,this is equivalent to restricting the common component as equal to the difference between thefirst and last time dummies, i.e. γ = α − .0 Tα 16