  This paper provides three results for SVARs under the assumption that the
primitive shocks are mutually independent. First, a framework is proposed to
accommodate a disaster-type variable with infinite variance into a SVAR. We
show that the least squares estimates of the SVAR are consistent but have
non-standard asymptotics. Second, the disaster shock is identified as the
component with the largest kurtosis and whose impact effect is negative. An
estimator that is robust to infinite variance is used to recover the mutually
independent components. Third, an independence test on the residuals
pre-whitened by the Choleski decomposition is proposed to test the restrictions
imposed on a SVAR. The test can be applied whether the data have fat or thin
tails, and to over as well as exactly identified models. Three applications are
considered. In the first, the independence test is used to shed light on the
conflicting evidence regarding the role of uncertainty in economic
fluctuations. In the second, disaster shocks are shown to have short term
economic impact arising mostly from feedback dynamics. The third uses the
framework to study the dynamic effects of economic shocks post-covid.
