The estimation of structural gravity models for bilateral trade flows faces methodological difficulties. These difficulties are in particular due to the multilateral resistance terms (MRT) which account for the general equilibrium constraints of global trade.
In the present paper, I show that the MRT are unique (to a harmless scale factor) and one can compute them iteratively. Based on a parallel between the MRT and the biproportional projection of matrices in the InputOutput literature, I give new insights on the econometric strategy to estimate structural gravity equations.
I extend to panels the iterative method proposed by Head and Mayer (2014), Gravity equations: Workhorse, toolkit, and cookbook, in Handbook of International Economics. This double loop procedure nests the current standard in the literature (the Poisson Pseudo Maximum Likelihood –PPMLwith dummies). I exemplify its possibilities on real data. PPML results appear not robust to a change of estimator. 
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