The gravity equation for international trade is probably the most important tool in international economics to explain and estimate trade ﬂows. In its simplest form, it states that the exports between any two given countries are a multiplicative function of these countries’ economic size, as measured by GDP, and their bilateral trade costs. The idea and the name is going back from the similarity to Isaac Newton’s law of gravity where the attraction force between two physical bodies equals the product of their masses divided by the squared distance between the bodies. The gravity equation in international economics becomes estimable after log-linearizing and parameterizing it. Export and GDP data are broadly available in several databases. Trade costs are not directly measurable and are therefore usually proxied by geographic distance and a set of further proxy variables like: access to the sea, common border, common language, membership in a certain group of countries, membership in a country union, and others. Trade costs proxies can be subdivided into geographical and political variables. Geographical properties of a country can hardly be changed by policy. However policymakers can influence trade costs through tariff rates, currency unions, free trade agreements, membership in certain country groups and many other measures. Since trade costs are not directly measureable, we will use a novel index of comprehensive trade costs to estimate a simultaneous system, first of a gravity equation and second of a trade cost equation for Germany. In our study, we demonstrate a new way to solve the complex equation system of multilateral resistances and compute them for a set of OECD countries.