A Characterization of Identified Impulse Response Sets in Linear State-Space Models

This paper characterizes, for an arbitrary linear state-space model with autoregressive representation of the observables and for an arbitrary set of identification restrictions, the set of impulse vectors consistent with the proposed identification scheme. For identification procedures that afford point identification this means recovery of the unique identified impulse vector; for set-identifying restrictions, this means recovery of an entire set of identified impulse vectors. Success or failure of a given identification scheme against an underlying data-generating process can then be judged through the overlap (or lack thereof) between the identified set of impulse vectors and the impulse vector of interest. The main application of the methodology is a re-interpretation of the findings in Uhlig (2005). I argue that, against a range of entirely conventional underlying structural models, his identification procedure tends to pick out positive demand and supply shocks jointly masquerading as monetary policy shocks. His failure to reject monetary policy non-neutrality in the data is thus exactly what simple sticky-price models with money non-neutrality would lead us to expect. †I am very grateful to Harald Uhlig, Chris Sims and Mark Watson for many useful comments and suggestions.