The issue of normalization arises whenever two different values for a vector of unknown
parameters imply the identical economic model. A normalization does not just imply a rule for selecting
which point, among equivalent ones, to call the maximum likelihood estimator (MLE). It also governs the
topography of the set of points that go into a small-sample confidence interval associated with that MLE. A
poor normalization can lead to multimodal distributions, confidence intervals that are disjoint, and very
misleading characterizations of the true statistical uncertainty. This paper introduces the identification
principle as a framework upon which a normalization should be imposed, according to which the
boundaries of the allowable parameter space should correspond to loci along which the model is locally
unidentified. The authors illustrate these issues with examples taken from mixture models, structural
VARs, and cointegration.