Are the shocks obtained from SVAR fundamental?

This paper provides new conditions under which the shocks recovered from the estimates of structural vector autoregressions are fundamental. I prove that the Wold innovations are unpredictable if and only if the model is fundamental. I propose a test based on a generalized spectral density to check the unpredictability of the Wold innovations. The test is applied to study the dynamic effects of government spending on economic activity. I find that standard SVAR models commonly employed in the literature are non-fundamental. Moreover, I formally show that introduction of a narrative variable that measures anticipation restores fundamentalness.