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Normalization in Econometrics

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Author Info
James D. Hamilton
Daniel F. Waggoner
Tao Zha

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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 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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Publisher Info
Article provided by Taylor and 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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Related research
Keywords: Cointegration; Local identification; Mixture distributions; Maximum likelihood estimate; Numerical Bayesian methods; Regime-switching; Small sample distributions; Vector autoregressions; Weak identification;

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References listed on IDEAS
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  4. Geweke, John, 1996. "Bayesian reduced rank regression in econometrics," Journal of Econometrics, Elsevier, vol. 75(1), pages 121-146, November. [Downloadable!] (restricted)
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  7. 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.
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  9. 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. [Downloadable!] (restricted)
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  10. Phillips, Peter C B, 1994. "Some Exact Distribution Theory for Maximum Likelihood Estimators of Cointegrating Coefficients in Error Correction Models," Econometrica, Econometric Society, vol. 62(1), pages 73-93, January. [Downloadable!] (restricted)
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  11. 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. [Downloadable!] (restricted)
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  13. Gregory, Allan W & Veall, Michael R, 1985. "Formulating Wald Tests of Nonlinear Restrictions," Econometrica, Econometric Society, vol. 53(6), pages 1465-68, November. [Downloadable!] (restricted)
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(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Driffill, John & Kenc, Turalay & Sola, Martin & Spagnolo, Fabio, 2004. "On Model Selection and Markov Switching: A Empirical Examination of Term Structure Models with Regime Shifts," CEPR Discussion Papers 4165, C.E.P.R. Discussion Papers. [Downloadable!] (restricted)
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  2. Peter M. Summers & Penelope A. Smith, 2005. "How well do Markov switching models describe actual business cycles? The case of synchronization," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 20(2), pages 253-274. [Downloadable!]
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  3. Ai Deng & Pierre Perron, 2005. "A Comparison of Alternative Asymptotic Frameworks to Analyze a Structural Change in a Linear Time Trend," Boston University - Department of Economics - Working Papers Series WP2005-030, Boston University - Department of Economics. [Downloadable!]
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  4. Pierre Perron & Tatsuma Wada, 2005. "Let’s Take a Break: Trends and Cycles in US Real GDP," Boston University - Department of Economics - Working Papers Series wp2009-006, Boston University - Department of Economics, revised Feb 2009. [Downloadable!]
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  5. Tatsuma Wada & Pierre Perron, 2005. "An Alternative Trend-Cycle Decomposition using a State Space Model with Mixtures of Normals: Specifications and Applications to International Data," Boston University - Department of Economics - Working Papers Series WP2005-44, Boston University - Department of Economics. [Downloadable!]
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  6. B. D. McCullough & H. D. Vinod, 2004. "Verifying the Solution from a Nonlinear Solver: A Case Study: Reply," American Economic Review, American Economic Association, vol. 94(1), pages 391-396, March. [Downloadable!]
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  7. Markku Lanne, 2006. "Nonlinear dynamics of interest rate and inflation," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(8), pages 1157-1168. [Downloadable!]
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  8. 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. [Downloadable!]
  9. Thomas Sargent & Noah Williams & Tao Zha, 2006. "The conquest of South American inflation," Working Paper 2006-20, Federal Reserve Bank of Atlanta. [Downloadable!]
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  10. Andrea Carriero & George Kapetanios & Massimiliano Marcellino, 2009. "Forecasting Large Datasets with Bayesian Reduced Rank Multivariate Models," Economics Working Papers ECO2009/31, European University Institute. [Downloadable!]
  11. Jeroen V.K. Rombouts & Lars Stentoft, 2009. "Bayesian Option Pricing Using Mixed Normal Heteroskedasticity Models," CREATES Research Papers 2009-07, School of Economics and Management, University of Aarhus. [Downloadable!]
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  12. Pablo A. Guerron, 2006. "Time-Dependent Portfolio Adjustment: Yet Another Look at the Dynamics," Working Paper Series 006, North Carolina State University, Department of Economics, revised Aug 2006. [Downloadable!]
  13. Christopher A. Sims & Tao Zha, 2004. "Were there regime switches in U.S. monetary policy?," Working Paper 2004-14, Federal Reserve Bank of Atlanta. [Downloadable!]
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  14. Jeroen V.K. Rombouts & Lars Stentoft, 2009. "Bayesian Option Pricing Using Mixed Normal Heteroskedasticity," Cahiers de recherche 0926, CIRPEE. [Downloadable!]
  15. Juan Francisco Rubio-Ramírez & Daniel Waggoner & Tao Zha, 2005. "Markov-switching structural vector autoregressions: theory and application," Working Paper 2005-27, Federal Reserve Bank of Atlanta. [Downloadable!]
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  16. Daniel L. Thornton & Giorgio Valente, 2009. "Revisiting the predictability of bond risk premia," Working Papers 2009-009, Federal Reserve Bank of St. Louis. [Downloadable!]
  17. George Monokroussos, 2005. "Dynamic Limited Dependent Variable Modeling and US Monetary Policy," Computing in Economics and Finance 2005 460, Society for Computational Economics. [Downloadable!]
  18. Thomas Sargent & Noah Williams & Tao Zha, 2006. "Shocks and Government Beliefs: The Rise and Fall of American Inflation," American Economic Review, American Economic Association, vol. 96(4), pages 1193-1224, September. [Downloadable!]
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