We estimate a two-country open economy version of the New Keynesian dynamic stochastic general equilibrium model for the United States and the Euro area, using Bayesian techniques that allow for both determinacy and indeterminacy of the equilibrium. Empirical analysis shows that the worldwide equilibrium is indeterminate due to a passive monetary policy in the Euro area, even if U.S. policy is aggressive enough. We demonstrate that the impulse responses under indeterminacy exhibit dynamics different from those under determinacy and that sunspot shocks affect the Euro economy to a substantial degree, whereas the transmission of sunspots to the United States is limited.