This paper is devoted to fiscal shock identification based on the assumption of non-Gaussianity of the errors, which can be easily tested. We use additional co-kurtosis conditions in GMM estimation of the AB-model to estimate the dynamic effects of fiscal shocks and find fiscal multipliers in the U.S. economy. Our approach results in higher tax multipliers on average relative to Blanchard and Perotti (2002) and Leeper et al. (2013). Testing the restrictions, we are not able to reject them in the Blanchard and Perotti (2002) model. Once we control for fiscal foresight, we can reject restrictions both individually and altogether. Finally, comparing elasticities of tax revenue to output to elasticities found in the literature, rejecting most of them, we are not able to reject the one of Caldara and Kamps (2017).