Algebraic Theory of Indentification in Parametric Models
Abstract
The paper presents the problem of identification in parametric models from the algebraic point of view. We argue that it is not just another perspective but the proper one. That is using our approach we can see the very nature of the identification problem, which is slightly different than that suggested in the literature. In practice it means that in many models we can unambiguously estimate parameters that have been thought as unidentifiable. This is illustrated in the case of Simultaneous Equations Model (SEM), where our analysis leads to conclusion that existing identification conditions, although correct, are based on the inappropriate premise: only the structural parameters that are in one–to–one correspondence with the reduced form parameters are identified. We will show that this is not true. In fact there are other structural parameters, which are identified, but can not be uniquely recovered from the reduced form parameters. Although we apply our theory only to SEM, it can be used in many standard econometric models.Download Info
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Paper provided by National Bank of Poland, Economic Institute in its series National Bank of Poland Working Papers with number 88.Length: 41
Date of creation: 2011
Date of revision:
Handle: RePEc:nbp:nbpmis:88
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Related research
Keywords: Identification; Group theory; Orbits; Orbit representatives; Simultaneous Equations Model; Maximal Invariant;Other versions of this item:
- Kociecki, Andrzej, 2010. "Algebraic theory of identification in parametric models," MPRA Paper 26820, University Library of Munich, Germany.
- C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
- C18 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Methodolical Issues: General
- C30 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - General
This paper has been announced in the following NEP Reports:
- NEP-ALL-2011-08-09 (All new papers)
- NEP-ECM-2011-08-09 (Econometrics)
References
References listed on IDEASPlease 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.:
- Bowden, Roger J, 1973. "The Theory of Parametric Identification," Econometrica, Econometric Society, vol. 41(6), pages 1069-74, November.
- Thomas J. Sargent & Christopher A. Sims, 1977.
"Business cycle modeling without pretending to have too much a priori economic theory,"
Working Papers
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- Tom Doan, . "RATS program to estimate observable index model from Sargent-Sims(1977)," Statistical Software Components RTZ00126, Boston College Department of Economics.
- Rothenberg, Thomas J, 1971. "Identification in Parametric Models," Econometrica, Econometric Society, vol. 39(3), pages 577-91, May.
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