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Algebraic Theory of Indentification in Parametric Models

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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.

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File URL: http://www.nbp.pl/publikacje/materialy_i_studia/88_en.pdf
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Bibliographic Info

Paper provided by National Bank of Poland, Economic Institute in its series National Bank of Poland Working Papers with number 88.

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Length: 41
Date of creation: 2011
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Handle: RePEc:nbp:nbpmis:88

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Keywords: Identification; Group theory; Orbits; Orbit representatives; Simultaneous Equations Model; Maximal Invariant;

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  1. Bowden, Roger J, 1973. "The Theory of Parametric Identification," Econometrica, Econometric Society, vol. 41(6), pages 1069-74, November.
  2. Rothenberg, Thomas J, 1971. "Identification in Parametric Models," Econometrica, Econometric Society, vol. 39(3), pages 577-91, May.
  3. Thomas J. Sargent & Christopher A. Sims, 1977. "Business cycle modeling without pretending to have too much a priori economic theory," Working Papers 55, Federal Reserve Bank of Minneapolis.
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