Excess shocks can limit the economic interpretation

Abstract

When a model has more shocks than observed variables (excess shocks) the Estimated Model (EM) shock innovations will be correlated. These correlations limit the usefulness of variance and variable decompositions, as the latter use the EM shock innovations. Furthermore, any such correlations limit the ability to directly test the assumptions made about the Assumed Model (AM) shocks. These need to be correct in order to interpret impulse responses. A partial interpretation of the data may be possible if some AM shocks can be recovered. An approach to determining which shocks can be recovered when using either the current and past or all data is presented, unifying the existing methods for asse..