Many improvements have been proposed for the basic gravity model specification, most of which are confirmed by standard statistical tests due to the large number of observations often used to estimate such models. We use Monte Carlo experiments to examine situations in which features of models may be found statistically significant (or insignificant) when it is known ex ante that they are absent (or present) in the underlying data process. Erroneous assumptions about the presence or absence of lagged dependent variables, fixed effects, free-trade associations and customs unions are shown to introduce economically important bias in estimates of the coefficients of interest, and in some cases to be confirmed spuriously. Policy effects, such as for free trade associations and currency unions, can also be confirmed spuriously when they do not exist in the data-generating process.