Preference shocks for domestic and foreign households in a small open economy

Hi all,
I’m looking at an early version of Justiniano and Preston’s paper “Monetary Policy and uncertainty in an empirical small open economy”, found here:
The optimization problems for domestic and foreign households both contain preference shocks - but in a log-linearized equation following from the assumption of identical preferences in domestic and foreign households (eq.4 and eq.17), only the preference shock of domestic households prevails.
Is there any specific reason for this; should one avoid having different shocks in the same equation?
I would really appreciate it if anyone could please explain this for me.


To me this seems to be an assumption. Equation 4 does not contain a preference shock. My guess is that they forgot it on the left-hand side and that they abstract from preference shocks in the foreign economy as the output shocks they assume are sufficient.

I discovered that there is no preference shock in the foreign household’s euler equation, so you’re right about the assumption. Thanks for clarifying.