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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 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, 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. The authors illustrate these issues with examples taken from mixture models, structural VARs, and cointegration.

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Paper provided by Federal Reserve Bank of Atlanta in its series FRB Atlanta Working Paper with number 2004-13.

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Date of creation: 2004
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Handle: RePEc:fip:fedawp:2004-13
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  1. Ng, Serena & Perron, Pierre, 1997. "Estimation and inference in nearly unbalanced nearly cointegrated systems," Journal of Econometrics, Elsevier, vol. 79(1), pages 53-81, July.
  2. Kleibergen, Frank & Paap, Richard, 2002. "Priors, posteriors and bayes factors for a Bayesian analysis of cointegration," Journal of Econometrics, Elsevier, vol. 111(2), pages 223-249, December.
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  6. Alonso-Borrego, Cesar & Arellano, Manuel, 1999. "Symmetrically Normalized Instrumental-Variable Estimation Using Panel Data," Journal of Business & Economic Statistics, American Statistical Association, vol. 17(1), pages 36-49, January.
  7. Gregory, Allan W & Veall, Michael R, 1985. "Formulating Wald Tests of Nonlinear Restrictions," Econometrica, Econometric Society, vol. 53(6), pages 1465-68, November.
  8. 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.
  9. Andrew Harvey (ed.), 1994. "Time Series," Books, Edward Elgar Publishing, volume 0, number 599.
  10. Penelope A. Smith & Peter M. Summers, 2004. "Identification and normalization in Markov switching models of "business cycles"," Research Working Paper RWP 04-09, Federal Reserve Bank of Kansas City.
  11. Matthew Stephens, 2000. "Dealing with label switching in mixture models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(4), pages 795-809.
  12. Hamilton, James D, 1989. "A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle," Econometrica, Econometric Society, vol. 57(2), pages 357-84, March.
  13. Daniel F. Waggoner & Tao Zha, 2000. "Likelihood-preserving normalization in multiple equation models," FRB Atlanta Working Paper 2000-8, Federal Reserve Bank of Atlanta.
  14. Otrok, C. & Whiteman, C.H., 1996. "Bayesian Leading Indicators: Measuring and Predicting Economic Conditions in Iowa," Working Papers 96-14, University of Iowa, Department of Economics.
  15. Peter C.B. Phillips, 1992. "Some Exact Distribution Theory for Maximum Likelihood Estimators of Cointegrating Coefficients in Error Correction Models," Cowles Foundation Discussion Papers 1039, Cowles Foundation for Research in Economics, Yale University.
  16. Fruhwirth-Schnatter S., 2001. "Markov Chain Monte Carlo Estimation of Classical and Dynamic Switching and Mixture Models," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 194-209, March.
  17. Motohiro Yogo, 2004. "Estimating the Elasticity of Intertemporal Substitution When Instruments Are Weak," The Review of Economics and Statistics, MIT Press, vol. 86(3), pages 797-810, August.
  18. Nobile, Agostino, 2000. "Comment: Bayesian multinomial probit models with a normalization constraint," Journal of Econometrics, Elsevier, vol. 99(2), pages 335-345, December.
  19. Peter Lenk & Wayne DeSarbo, 2000. "Bayesian inference for finite mixtures of generalized linear models with random effects," Psychometrika, Springer;The Psychometric Society, vol. 65(1), pages 93-119, March.
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