Several theoretical contributions using two-country models have combined alternative forms of pricing under nominal rigidities with different asset market structures to explain real exchange rate dynamics. We estimate a two-country model using data for the United States and the Euro Area, and study the importance of such alternative assumptions in fitting the data. A model with local currency pricing and incomplete markets does a good job in explaining real exchange rate volatility, and fits the dynamics of domestic variables well. The complete markets assumption delivers a similar fit only when the structure of shocks is rich enough. © 2009 Elsevier B.V.