A systematic comparison is made of parametric (i.e., ordinary least-squares regressions and related generalizations) and nonparametric (i.e., kernel regressions and regression trees) log-linear gravity models for reproducing international trade. Experiments were conducted to estimate a log-linear gravity model reproducing import and export trade flows in quantity between Italy and 13 world economic zones, based on a panel estimation data set. The best parametric regression model was estimated to define a baseline reference model. Some specifications of nonparametric models, belonging to the categories of kernel regressions and regression trees, were also estimated. The performance of parametric and nonparametric models is contrasted through a comparison of goodness-of-fit measures (R², mean absolute percentage error) both in estimation and in hold-out sample validation. To assess the differences in model elasticity and forecasts, both parametric and nonparametric models are applied to future scenarios and the corresponding results compared.