Despite the solid theoretical foundation on which the gravity model of bilateral trade is based, empirical implementation requires several assumptions which do not follow directly from the underlying theory. First, unobserved trade costs are assumed to be a (log-)linear function of observables. Second, the effects of trade costs on trade flows are assumed to be constant across country pairs. Maintaining consistency with the underlying theory, but relaxing these assumptions, we estimate gravity models-in levels and logs-using two data sets via nonparametric methods. The results are striking. Despite the added flexibility of the nonparametric models, parametric models based on these assumptions offer equally or more reliable in-sample predictions and out-of-sample forecasts in the majority of cases, particularly in the levels model. Moreover, formal statistical tests fail to reject either parametric functional form. Thus, concerns in the gravity literature over functional form appear unwarranted, and estimation of the gravity model in levels is recommended.