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On the structure of IV estimands

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  • Andrews, Isaiah

Abstract

When the overidentifying restrictions of the constant-effect linear instrumental variables model fail, common IV estimators converge to different probability limits. I characterize the estimands of two stage least squares, two step GMM, and limited information maximum likelihood as functions of the single-instrument estimands from the just-identified IV regressions which consider each instrument separately. The limited information maximum likelihood estimand is found to be discontinuous on a set of dimension equal to the number of instruments minus one, and to equal the full parameter space on a set of dimension equal to the number of instruments minus two.

Suggested Citation

  • Andrews, Isaiah, 2019. "On the structure of IV estimands," Journal of Econometrics, Elsevier, vol. 211(1), pages 294-307.
    • Handle: RePEc:eee:econom:v:211:y:2019:i:1:p:294-307
    DOI: 10.1016/j.jeconom.2018.12.017
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    References listed on IDEAS

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    1. 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.
    2. Hall, Alastair R. & Inoue, Atsushi, 2003. "The large sample behaviour of the generalized method of moments estimator in misspecified models," Journal of Econometrics, Elsevier, vol. 114(2), pages 361-394, June.
    3. Magne Mogstad & Andres Santos & Alexander Torgovitsky, 2018. "Using Instrumental Variables for Inference About Policy Relevant Treatment Parameters," Econometrica, Econometric Society, vol. 86(5), pages 1589-1619, September.
    4. Imbens, Guido W & Angrist, Joshua D, 1994. "Identification and Estimation of Local Average Treatment Effects," Econometrica, Econometric Society, vol. 62(2), pages 467-475, March.
    5. James H. Stock & Jonathan Wright, 2000. "GMM with Weak Identification," Econometrica, Econometric Society, vol. 68(5), pages 1055-1096, September.
    6. Gary Chamberlain, 2007. "Decision Theory Applied to an Instrumental Variables Model," Econometrica, Econometric Society, vol. 75(3), pages 609-652, May.
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    Cited by:

    1. Hwang, Jungbin & Kang, Byunghoon & Lee, Seojeong, 2022. "A doubly corrected robust variance estimator for linear GMM," Journal of Econometrics, Elsevier, vol. 229(2), pages 276-298.
    2. Isaiah Andrews & Anna Mikusheva, 2022. "GMM is Inadmissible Under Weak Identification," Papers 2204.12462, arXiv.org, revised May 2023.

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    More about this item

    Keywords

    Instrumental variables; Misspecification;

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C26 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Instrumental Variables (IV) Estimation

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