This paper is now published in AEA Papers and Proceedings.
Two recent strands of the structural vector autoregression literature use higher moments for identification, exploiting either non-Gaussianity or heteroskedasticity. These approaches achieve point identification without exclusion or sign restrictions. We review this work critically and contrast its goals with the separate research program that has pushed for macroeconometrics to rely more heavily on credible economic restrictions. Identification from higher moments imposes stronger assumptions on the shock process than second-order methods do. We recommend that these assumptions be tested. Since inference from higher moments places high demands on a finite sample, weak identification issues should be given priority by applied users.