IDEAS home Printed from https://ideas.repec.org/a/taf/emetrv/v26y2007i2-4p221-252.html
   My bibliography  Save this article

Normalization in Econometrics

Author

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

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.

Suggested Citation

  • James D. Hamilton & Daniel F. Waggoner & Tao Zha, 2007. "Normalization in Econometrics," Econometric Reviews, Taylor & Francis Journals, vol. 26(2-4), pages 221-252.
  • Handle: RePEc:taf:emetrv:v:26:y:2007:i:2-4:p:221-252
    DOI: 10.1080/07474930701220329
    as

    Download full text from publisher

    File URL: http://www.tandfonline.com/doi/abs/10.1080/07474930701220329
    Download Restriction: Access to full text is restricted to subscribers.
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Waggoner, Daniel F. & Zha, Tao, 2003. "Likelihood preserving normalization in multiple equation models," Journal of Econometrics, Elsevier, vol. 114(2), pages 329-347, June.
    2. 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.
    3. 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.
    4. 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.
    5. Chib, Siddhartha & Greenberg, Edward, 1996. "Markov Chain Monte Carlo Simulation Methods in Econometrics," Econometric Theory, Cambridge University Press, vol. 12(3), pages 409-431, August.
    6. 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.
    7. 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.
    8. 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.
    9. Andrew Harvey (ed.), 1994. "Time Series," Books, Edward Elgar Publishing, volume 0, number 599.
    10. 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.
    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 357-384, March.
    13. 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.
    14. 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.
    15. Gregory, Allan W & Veall, Michael R, 1985. "Formulating Wald Tests of Nonlinear Restrictions," Econometrica, Econometric Society, vol. 53(6), pages 1465-1468, November.
    16. 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.
    17. Nobile, Agostino, 2000. "Comment: Bayesian multinomial probit models with a normalization constraint," Journal of Econometrics, Elsevier, vol. 99(2), pages 335-345, December.
    18. 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.
    19. Geweke, John, 1996. "Bayesian reduced rank regression in econometrics," Journal of Econometrics, Elsevier, vol. 75(1), pages 121-146, November.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Leeper, Eric M. & Zha, Tao, 2003. "Modest policy interventions," Journal of Monetary Economics, Elsevier, vol. 50(8), pages 1673-1700, November.
    2. Chew Lian Chua & Sarantis Tsiaplias, 2014. "A Bayesian Approach to Modelling Bivariate Time-Varying Cointegration and Cointegrating Rank," Melbourne Institute Working Paper Series wp2014n27, Melbourne Institute of Applied Economic and Social Research, The University of Melbourne.
    3. Karlsson, Sune, 2013. "Forecasting with Bayesian Vector Autoregression," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 2, chapter 0, pages 791-897, Elsevier.
    4. Gary Koop & Rodney Strachan & Herman van Dijk & Mattias Villani, 2004. "Bayesian Approaches to Cointegration," Discussion Papers in Economics 04/27, Division of Economics, School of Business, University of Leicester.
    5. Sims, Christopher A. & Waggoner, Daniel F. & Zha, Tao, 2008. "Methods for inference in large multiple-equation Markov-switching models," Journal of Econometrics, Elsevier, vol. 146(2), pages 255-274, October.
    6. Waggoner, Daniel F. & Wu, Hongwei & Zha, Tao, 2016. "Striated Metropolis–Hastings sampler for high-dimensional models," Journal of Econometrics, Elsevier, vol. 192(2), pages 406-420.
    7. Mark Bognanni & Edward Herbst, 2014. "Estimating (Markov-Switching) VAR Models without Gibbs Sampling: A Sequential Monte Carlo Approach," Working Papers (Old Series) 1427, Federal Reserve Bank of Cleveland.
    8. Amisano, Gianni, 2003. "Bayesian inference in cointegrated systems," Research in Economics, Elsevier, vol. 57(4), pages 287-314, December.
    9. Strachan, Rodney W. & Inder, Brett, 2004. "Bayesian analysis of the error correction model," Journal of Econometrics, Elsevier, vol. 123(2), pages 307-325, December.
    10. Mattias Villani, 2009. "Steady-state priors for vector autoregressions," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 24(4), pages 630-650.
    11. Raggi, Davide & Bordignon, Silvano, 2012. "Long memory and nonlinearities in realized volatility: A Markov switching approach," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3730-3742.
    12. Candelon, Bertrand & Lieb, Lenard, 2013. "Fiscal policy in good and bad times," Journal of Economic Dynamics and Control, Elsevier, vol. 37(12), pages 2679-2694.
    13. Eliana González & Luis F. Melo & Viviana Monroy & Brayan Rojas, 2009. "A Dynamic Factor Model For The Colombian Inflation," BORRADORES DE ECONOMIA 005273, BANCO DE LA REPÚBLICA.
    14. Penelope A. Smith & Peter M. Summers, 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.
    15. Francisco Peñaranda, 2004. "Are Vector Autoregressions an Accurate Model for Dynamic Asset Allocation?," Working Papers wp2004_0419, CEMFI.
    16. Aßmann, Christian & Boysen-Hogrefe, Jens & Pape, Markus, 2012. "The directional identification problem in Bayesian factor analysis: An ex-post approach," Kiel Working Papers 1799, Kiel Institute for the World Economy (IfW).
    17. Guilhem Bascle, 2008. "Controlling for endogeneity with instrumental variables in strategic management research," Post-Print hal-00576795, HAL.
    18. Sylvia Kaufmann, 2002. "Is there an asymmetric effect of monetary policy over time? A Bayesian analysis using Austrian data," Empirical Economics, Springer, vol. 27(2), pages 277-297.
    19. Ioannis Ntzoufras & Claudia Tarantola, 2012. "Conjugate and Conditional Conjugate Bayesian Analysis of Discrete Graphical Models of Marginal Independence," Quaderni di Dipartimento 178, University of Pavia, Department of Economics and Quantitative Methods.
    20. Kappe, Eelco & Stadler Blank, Ashley & DeSarbo, Wayne S., 2018. "A random coefficients mixture hidden Markov model for marketing research," International Journal of Research in Marketing, Elsevier, vol. 35(3), pages 415-431.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:taf:emetrv:v:26:y:2007:i:2-4:p:221-252. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: . General contact details of provider: http://www.tandfonline.com/LECR20 .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (email available below). General contact details of provider: http://www.tandfonline.com/LECR20 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.