We propose to exploit stochastic volatility for statistical identification of structural vector autoregressive models (SV-SVAR). We discuss full and partial identification of the model and develop efficient EM algorithms for maximum likelihood inference. Simulation evidence suggests that the SV-SVAR works well in identifying structural parameters also under misspecification of the variance process, particularly if compared to alternative heteroscedastic SVARs. We apply the model to study the importance of oil supply shocks for driving oil prices. Since shocks identified by heteroscedasticity may not be economically meaningful, we exploit the framework to test instrumental variable restrictions which are overidentifying in the heteroscedastic model. Our findings suggest that conventional supply shocks are negligible, while news shocks about future supply account for almost all the variation in oil prices.
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