Structural quantitative work in international economics typically models trade costs as a log‐linear function of exogenous trade‐policy variables. We propose a structural approach that allows for a nonparametric relationship and for treating tariff and nontariff trade‐policy variables as potentially endogenous. The data reject the assumption of log‐linearity of trade costs in both tariff‐ and nontariff‐policy variables. We assess the effects of a unilateral increase of US tariffs on Chinese imports by 10 percentage points and document that the estimated effects on real bilateral trade‐flow changes would be substantially underestimated by standard approaches.