This paper examines a two-country new open economy macroeconomics model with price stickiness a la Taylor, where exporters' choice of invoicing currency is endogenous. Besides generating incomplete pass-through, the model yields four main results. First, firms' invoicing strategy is generally time-varying. Second, instant pass-through into import prices is greater than into export prices when depreciations are caused by domestic monetary expansions. Thirdly, average pass-through is asymmetric in times of persistent depreciations and depreciations. It is higher under depreciations when the destination market is more competitive. Finally, cross-country differences in money supply variability produce an origin-based asymmetry: different average pass- through rates into import and export prices.