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. The benefit of this de-velopment is that empirical models which are based on few parameters explain data on bilat-eral trade flows relatively well, while being consistent with general equilibrium. The latter per-mits using the estimated parameters for comparative static analysis. In general, in the cross sec-tion such models involve country-pair-specific variables and exporter-specific as well as im-porter-specific variables. The latter are determined through structural model constraints. The dis-turbances on this model are typically assumed to be independently if not also identically dis-tributed. This paper illustrates that the assumption of independently distributed disturbances is likely flawed in practice. Ignoring such independence leads to inconsistent test statistics and standard errors of the parameters. We present a structural gravity model which permits the dis-turbances to be cross-sectionally interdependent in up to three dimensions and illustrate the consequences of doing so for inference.