  We consider structural vector autoregressions identified through stochastic
volatility. Our focus is on whether a particular structural shock is identified
by heteroskedasticity without the need to impose any sign or exclusion
restrictions. Three contributions emerge from our exercise: (i) a set of
conditions under which the matrix containing structural parameters is partially
or globally unique; (ii) a statistical procedure to assess the validity of the
conditions mentioned above; and (iii) a shrinkage prior distribution for
conditional variances centred on a hypothesis of homoskedasticity. Such a prior
ensures that the evidence for identifying a structural shock comes only from
the data and is not favoured by the prior. We illustrate our new methods using
a U.S. fiscal structural model.
