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Ignoring such independence leads to inconsistent test statistics and standard errors of the parameters. This paper illustrates that the assumption of independently distributed disturbances is likely flawed in practice. The disturbances on this model are typically assumed to be independently if not also identically distributed. The latter are determined through structural model constraints. In general, in the cross section such models involve country-pair-specific variables and exporter-specific as well as importer-specific variables. The latter permits using the estimated parameters for comparative static analysis.

The benefit of this development is that empirical models which are based on few parameters explain data on bilateral trade flows relatively well, while being consistent with general equilibrium. Since the publication of the paper by Anderson and van Wincoop (J Econ Litt 42:691–751, 2004), the estimation of gravity models has turned increasingly structural.