This paper generalizes the standard methods of solving rational expectations models to the case of time-varying nonstochastic parameters, recurring in a finite cycle. Such a specification occurs in a simple stylized New Keynesian model of the euro area when we combine the rotation in the ECB Governing Council (as constituted by the Treaty of Nice) and home bias in the interest rate decisions taken by its members. In small and mid-size economies, this combination slightly increases output and inflation volatility, as compared to a monetary policy setup without rotation. The method of Christiano (2002) has also been applied to solve the model when we assume a lagged perception of foreign macroeconomic shocks by domestic agents. When the cross-country synchronization of shocks is low or moderate and when these shocks are relatively persistent, the exclusion of contemporaneous foreign shocks from domestic agents' information sets may raise the volatility of output. There is also some tentative evidence that this effect could particularly affect mid-size economies.