The Unit-effect Normalisation in Set-identified Structural Vector Autoregressions

Structural vector autoregressions that are set identified (e.g. with sign restrictions) are typically used to analyse the effects of standard deviation shocks. However, answering questions of economic interest often requires knowing the effects of a 'unit' shock. For example, central bankers want to answer questions like 'what are the effects of a 100 basis point increase in the policy rate?' The problem is that set-identifying restrictions do not always rule out the possibility that a variable does not react contemporaneously to its own shock. As a consequence, identified sets for the impulse responses to unit shocks may be unbounded, which implies that set-identifying restrictions may be extremely uninformative. Simply assuming that responses are non-zero turns out to be an arbitrary and unsatisfactory solution. I argue that it is therefore important to communicate about the extent to which the identified set may be unbounded, since this tells us about the informativeness of the identifying restrictions, and I develop tools to facilitate this. I explain how to draw useful posterior inferences about impulse responses when identified sets are unbounded with positive probability. I illustrate the empirical relevance of these issues by estimating the response of US output to a 100 basis point federal funds rate shock under different sets of identifying restrictions. Some restrictions are very uninformative about the effects of a 100 basis point shock. The output responses I obtain under a rich set of identifying restrictions lie towards the smaller end of the range of existing estimates.