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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 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 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. 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. [Downloadable!] (restricted)
  2. 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. [Downloadable!] (restricted)
  3. Waggoner, Daniel F. & Zha, Tao, 2003. "Likelihood preserving normalization in multiple equation models," Journal of Econometrics, Elsevier, vol. 114(2), pages 329-347, June. [Downloadable!] (restricted)
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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)
  5. 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, 03. [Downloadable!] (restricted)
  6. Jinyong Hahn & Jerry Hausman, 2002. "A New Specification Test for the Validity of Instrumental Variables," Econometrica, Econometric Society, vol. 70(1), pages 163-189, January. [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.
  8. Otrok, Christopher & Whiteman, Charles H, 1998. "Bayesian Leading Indicators: Measuring and Predicting Economic Conditions in Iowa," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 997-1014, November.
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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)
  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)
  12. 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. [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)
  14. Peter Lenk & Wayne DeSarbo, 2000. "Bayesian inference for finite mixtures of generalized linear models with random effects," Psychometrika, Springer, vol. 65(1), pages 93-119, March. [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)
  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. Christopher A. Sims & Tao Zha, 2004. "MCMC method for Markov mixture simultaneous-equation models: a note," Working Paper 2004-15, Federal Reserve Bank of Atlanta. [Downloadable!]
  4. 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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  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!]
  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!] (restricted)
  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. 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!]
  11. Thomas Sargent & Noah Williams & Tao Zha, 2004. "Shocks and government beliefs: the rise and fall of American inflation," Working Paper 2004-22, Federal Reserve Bank of Atlanta. [Downloadable!]
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  12. 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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  13. 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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  14. George Monokroussos, 2005. "Dynamic Limited Dependent Variable Modeling and US Monetary Policy," Computing in Economics and Finance 2005 460, Society for Computational Economics. [Downloadable!]
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