Likelihood preserving normalization in multiple equation models

Issues associated with normalization in the vector autoregression literature have been largely unexplored. We show that different normalization rules can have material consequences for statistical inferences of impulse responses. The correct normalization for recursive models turns out to be, in general, inappropriate for nonrecursive models. We show that inadequate normalization rules may confound various statistical and economic interpretations. We develop a general normalization rule that preserves the likelihood shape and maintains coherent economic interpretations for both recursive and nonrecursive models.