Normalization in econometrics
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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- 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.
- Ng, S. & Perron, P., 1995. "Estimation and Inference in Nearly Unbalanced, Nearly Cointegrated Systems," Cahiers de recherche 9534, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
- Ng, S. & Perron, P., 1995. "Estimation and Inference in Nearly Unbalanced, Nearly Cointegrated Systems," Cahiers de recherche 9534, Universite de Montreal, Departement de sciences economiques.
- 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.
- Otrok, C. & Whiteman, C.H., 1996.
"Bayesian Leading Indicators: Measuring and Predicting Economic Conditions in Iowa,"
96-14, University of Iowa, Department of Economics.
- 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.
- 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.
- 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.
- 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.
- Jinyong Hahn & Jerry Hausman, 1999.
"A New Specification Test for the Validity of Instrumental Variables,"
99-11, Massachusetts Institute of Technology (MIT), Department of Economics.
- 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.
- 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.
- Siddhartha Chib & Edward Greenberg, 1994.
"Markov Chain Monte Carlo Simulation Methods in Econometrics,"
9408001, EconWPA, revised 24 Oct 1994.
- Chib, Siddhartha & Greenberg, Edward, 1996. "Markov Chain Monte Carlo Simulation Methods in Econometrics," Econometric Theory, Cambridge University Press, vol. 12(03), pages 409-431, August.
- Gregory, Allan W & Veall, Michael R, 1985. "Formulating Wald Tests of Nonlinear Restrictions," Econometrica, Econometric Society, vol. 53(6), pages 1465-68, November.
- Waggoner, Daniel F. & Zha, Tao, 2003.
"Likelihood preserving normalization in multiple equation models,"
Journal of Econometrics,
Elsevier, vol. 114(2), pages 329-347, June.
- Daniel F. Waggoner & Tao Zha, 2000. "Likelihood-preserving normalization in multiple equation models," Working Paper 2000-8, Federal Reserve Bank of Atlanta.
- Geweke, John, 1996.
"Bayesian reduced rank regression in econometrics,"
Journal of Econometrics,
Elsevier, vol. 75(1), pages 121-146, November.
- 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.
- 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.
- 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.
- Nobile, Agostino, 2000. "Comment: Bayesian multinomial probit models with a normalization constraint," Journal of Econometrics, Elsevier, vol. 99(2), pages 335-345, December.
- 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.
- 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.
- 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.
- 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.
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