An SVAR in US federal spending, federal revenue, and GDP is a standard setting for the study of the impact of fiscal shocks. An appealing feature of identifying a fiscal shock with an external instrument (proxy variable) is that one can find the effects of that shock without fully identifying the SVAR. But we show that fully or almost fully instrumenting the SVAR allows one to overidentify the model by incorporating the condition that the structural shocks are uncorrelated (via GMM). Over 1948--2019 the overidentifying restrictions are not rejected. The overidentified SVAR yields (a) greater precision in estimating impulse response functions and multipliers and (b) measures of the effects of output shocks even when there is no instrument for them.