Structural innovations in multivariate dynamic systems are typically hidden and often identified by means of a-priori economic reasoning. Under multivariate Gaussian model innovations there is no loss measure available to distinguish alternative orderings of variables or, put differently, between particular identifying restrictions and rotations thereof. Based on a non Gaussian framework of independent innovations, a loss statistic is proposed in this paper that allows to discriminate between alternative identifying assumptions on the basis of nonparametric density estimates. The merits of the proposed identification strategy are illustrated by means of a Monte Carlo study. Real data applications cover bivariate systems comprising US stock prices and total factor productivity, and four couples of international breakeven inflation rates to investigate monetary autonomy of the Bank of Canada and the Bank of England.