International trade flows show strong persistence over time. Standard static gravity models cannot rationalize this persistence and lack a micro-foundation for including lagged trade flows as a determinant of current trade. We develop a structural dynamic gravity framework in which persistence arises from firms' sluggish adjustment of destination-specific prices, analogous to sticky prices in macroeconomics but operating at the bilateral level. The model delivers a gravity equation with lagged trade flows as a structural feature rather than an ad hoc add-on. We propose a novel estimation approach for dynamic gravity models that explicitly accounts for persistence. Empirically, we show that ignoring persistence can lead standard gravity estimates to substantially understate the effects of trade policy changes. As an application, we find that the estimated trade impact of regional trade agreements can increase by 30 percent or more once persistence is taken into account.