  I develop algorithms to facilitate Bayesian inference in structural vector
autoregressions that are set-identified with sign and zero restrictions by
showing that the system of restrictions is equivalent to a system of sign
restrictions in a lower-dimensional space. Consequently, algorithms applicable
under sign restrictions can be extended to allow for zero restrictions.
Specifically, I extend algorithms proposed in Amir-Ahmadi and Drautzburg (2021)
to check whether the identified set is nonempty and to sample from the
identified set without rejection sampling. I compare the new algorithms to
alternatives by applying them to variations of the model considered by Arias et
al. (2019), who estimate the effects of US monetary policy using sign and zero
restrictions on the monetary policy reaction function. The new algorithms are
particularly useful when a rich set of sign restrictions substantially
truncates the identified set given the zero restrictions.
