Normalization, probability distribution, and impulse responses

When impulse responses in dynamic multivariate models such as identified VARs are given economic interpretations, it is important that reliable statistical inferences be provided. Before probability assessments are provided, however, the model must be normalized. Contrary to the conventional wisdom, this paper argues that normalization, a rule of reversing signs of coefficients in equations in a particular way, could considerably affect the shape of the likelihood and thus probability bands for impulse responses. A new concept called ML distance normalization is introduced to avoid distorting the shape of the likelihood. Moreover, this paper develops a Monte Carlo simulation technique for implementing ML distance normalization.