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The LIML estimator has finite moments!

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  • Anderson, T.W.

Abstract

The Limited Information Maximum Likelihood estimator of the vector of coefficients of a structural equation in a simultaneous equation model is the vector that defines the linear combination maximizing the effect variance relative to the error variance. If this "eigenvector" solution is normalized by setting a designated coefficient equal to 1, the second-order moment of the estimator may be unbounded. However, the second-order moment is finite if the normalization sets the sample error variance of the linear combination equal to 1.

Suggested Citation

  • Anderson, T.W., 2010. "The LIML estimator has finite moments!," Journal of Econometrics, Elsevier, vol. 157(2), pages 359-361, August.
    • Handle: RePEc:eee:econom:v:157:y:2010:i:2:p:359-361
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    References listed on IDEAS

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    1. Fuller, Wayne A, 1977. "Some Properties of a Modification of the Limited Information Estimator," Econometrica, Econometric Society, vol. 45(4), pages 939-953, May.
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    Cited by:

    1. Gareth Liu-Evans & Garry DA Phillips, 2023. "The Bias of the Modified Limited Information Maximum Likelihood Estimator (MLIML) in Static Simultaneous Equation Models," Working Papers 202303, University of Liverpool, Department of Economics.
    2. Carrasco, Marine & Tchuente, Guy, 2015. "Regularized LIML for many instruments," Journal of Econometrics, Elsevier, vol. 186(2), pages 427-442.
    3. J'er^ome R. Simons, 2023. "Hypothesis testing on invariant subspaces of non-diagonalizable matrices with applications to network statistics," Papers 2303.18233, arXiv.org, revised Oct 2025.
    4. Eric Blankmeyer, 2020. "NISE Estimation of an Economic Model of Crime," Papers 2003.07860, arXiv.org.
    5. Blankmeyer, Eric, 2021. "Explorations in NISE Estimation," MPRA Paper 108179, University Library of Munich, Germany.
    6. Phillips, Garry D.A. & Liu-Evans, Gareth, 2016. "Approximating and reducing bias in 2SLS estimation of dynamic simultaneous equation models," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 734-762.
    7. Simons, J. R., 2025. "Hypothesis Testing on Invariant Subspaces of Non-Symmetric Matrices with Applications to Network Statistics," Cambridge Working Papers in Economics 2530, Faculty of Economics, University of Cambridge.

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