I propose to identify an SVAR, up to shock ordering, using the autocovariance structure of the squared innovations, implied by an arbitrary stochastic process for the shock variances. These higher moments are available without parametric assumptions on the variance process. In contrast, previous approaches exploiting heteroskedasticity rely on the path of innovation covariances, which can only be recovered from the data under specific parametric assumptions on the variance process. The conditions for identification are testable. I compare the identification scheme to existing approaches in simulations and provide guidance for estimation and inference. I use the methodology to estimate fiscal multipliers peaking at 0.86 for tax cuts and 0.75 for government spending. I find that tax shocks explain more variation in output at longer horizons. The empirical implications of my estimates are more consistent with theory and the narrative record than those based on some leading approaches.