We study what happens to identified shocks and to dynamic responses when the data generating process features q disturbances but less than q variables are used in the empirical model. Identified shocks are mongrels: they are linear combinations of current and past values of all structural disturbances and do not necessarily combine disturbances of the same type. Sound restrictions may be insufficient to obtain structural dynamics. The theory used to interpret the data and the disturbances it features determine whether an empirical model is too small. An example shows the magnitude of the distortions and the steps needed to reduce them. We revisit the evidence regarding the transmission of house price and of uncertainty shocks.
Deformation state variables dynamic responses structural models house price shocks uncertainty shocks