Normal in Econometrics

• Activity Number: 14
• Type: Topic Contributed
• Date/Time: Sunday, August 8, 2004 : 2:00 PM to 3:50 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Daniel Waggoner*+ and James Hamilton and Tao Zha
• Companies: Federal Reserve Bank of Atlanta and University of California, San Diego and Federal Reserve Bank of Atlanta
• Keywords: mixture distributions ; vector autoregressions ; cointegration ; regime-switching ; numerical Bayesian methods ; weak identification

Abstract

The issue of normalization arises whenever two different values for a vector of unknown parameters imply the identical economic model. A normalization implies not just a rule for selection which among equivalent points to call the MLE, but 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, disjoint confidence intervals, 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. We illustrate these issues with examples taken form mixture models, structural VARs, and cointegration.