I show that endogenously persistent output dynamics are not a puzzle for the standard sticky-price model once openness of the economy is taken into account. I make this point using a two-country, monetary model of macroeconomic interdependence under internationally incomplete asset markets with stationary net foreign asset dynamics. If asset markets are incomplete, price stickiness generates endogenous persistence in the cross-country GDP differential by introducing persistence in the dynamics of the relative price differential between the two economies. This results in the dependence of the current real GDP differential on its past value, as well as on the stock of net foreign assets accumulated in the previous period. The elasticity of the current GDP differential to its past value is sizable for standard parameter values, implying a quantitatively significant persistence effect through this channel. Endogenous persistence yields hump-shaped responses of GDP to productivity and monetary policy shocks.