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Normalization in Econometrics

  • James D. Hamilton
  • Daniel F. Waggoner
  • Tao Zha

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 selecting which among equivalent points to call the maximum likelihood estimate (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 an 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 from mixture models, structural vector autoregressions, and cointegration models.

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Article provided by Taylor & Francis Journals in its journal Econometric Reviews.

Volume (Year): 26 (2007)
Issue (Month): 2-4 ()
Pages: 221-252

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Handle: RePEc:taf:emetrv:v:26:y:2007:i:2-4:p:221-252
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  1. Kleibergen, F.R. & Paap, R., 1998. "Priors, posteriors and Bayes factors for a Bayesian analysis of cointegration," Econometric Institute Research Papers EI 9821, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
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  11. Nobile, Agostino, 2000. "Comment: Bayesian multinomial probit models with a normalization constraint," Journal of Econometrics, Elsevier, vol. 99(2), pages 335-345, December.
  12. Waggoner, Daniel F. & Zha, Tao, 2003. "A Gibbs sampler for structural vector autoregressions," Journal of Economic Dynamics and Control, Elsevier, vol. 28(2), pages 349-366, November.
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  15. Daniel F. Waggoner & Tao Zha, 2000. "Likelihood-preserving normalization in multiple equation models," Working Paper 2000-8, Federal Reserve Bank of Atlanta.
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