We propose a large structural VAR which is identified by higher moments without the need to impose economically motivated restrictions. The model scales well to higher dimensions, allowing the inclusion of a larger number of variables. We develop an efficient Gibbs sampler to estimate the model. We also present an estimator of the deviance information criterion to facilitate model comparison. Finally, we discuss how economically motivated restrictions can be added to the model. Experiments with artificial data show that the model possesses good estimation properties. Using real data we highlight the benefits of including more variables in the structural analysis. Specifically, we identify a monetary policy shock and provide empirical evidence that prices and economic output respond with a large delay to the monetary policy shock.