We consider structural vector autoregressions that are identified through stochastic volatility under Bayesian estimation. Three contributions emerge from our exercise. First, we show that a non-centred parameterization of stochastic volatility yields a marginal prior for the conditional variances of structural shocks that is centred on homoskedasticity, with strong shrinkage and heavy tails -- unlike the common centred parameterization. This feature makes it well suited for assessing partial identification of any shock of interest. Second, Monte Carlo experiments on small and large systems indicate that the non-centred setup estimates structural parameters more precisely and normalizes conditional variances efficiently. Third, revisiting prominent fiscal structural vector autoregressions, we show how the non-centred approach identifies tax shocks that are consistent with estimates reported in the literature.

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