In the new CAMP working paper 13/2018, Canova and Ferroni study what happens to identified shocks and to dynamic responses when the structural model features q disturbances and m endogenous variables, with q less than or equal to m, but only m_1 less than q variables are used in the empirical model.
Aggregation create problems; identified shocks do not necessarily combine structural disturbances of the same type. Instead, they are linear combinations of current and past values of all structural disturbances. The theory used to interpret the data and the disturbances it features determine whether an empirical model is too small. They highlight the magnitude of the distortions and the steps needed to reduce them with an example.