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The Bias of the Modified Limited Information Maximum Likelihood Estimator (MLIML) in Static Simultaneous Equation Models

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  • Gareth Liu-Evans
  • Garry DA Phillips

Abstract

A higher-order approximation is made to the bias of the modified LIML (MLIML) estimator due to Fuller. It is demonstrated via simulation that the asymptotic approximation can be used to reduce estimation bias, including in cases where instrument strength is relatively weak, and that the approximation also mirrors the behaviour of the true bias. It is possible to see via the asymptotic approximation why MLIML estimation bias is often found to be very small in two equation models where the order of overidentification is small, and to predict, in simple models where the approximation is specialised, how the order of overidentification will relate nonlinearly to the bias. An asymptotic approximation is also obtained for the pseudo-bias of the LIML estimator. Finally, the bias-corrected MLIML estimator is used to re-examine the effect on the US college graduate wage premium of shifts in the relative supply of young college workers, following Fortin (2006).

Suggested Citation

  • 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.
    • Handle: RePEc:liv:livedp:202303
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    File URL: https://www.liverpool.ac.uk/media/livacuk/schoolofmanagement/docs/ECON,WP,202303.pdf
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    References listed on IDEAS

    as
    1. Alfonso Flores-Lagunes, 2007. "Finite sample evidence of IV estimators under weak instruments," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 22(3), pages 677-694.
    2. Jinyong Hahn & Jerry Hausman & Guido Kuersteiner, 2004. "Estimation with weak instruments: Accuracy of higher-order bias and MSE approximations," Econometrics Journal, Royal Economic Society, vol. 7(1), pages 272-306, June.
    3. Carrasco, Marine & Tchuente, Guy, 2015. "Regularized LIML for many instruments," Journal of Econometrics, Elsevier, vol. 186(2), pages 427-442.
    4. Fuller, Wayne A, 1977. "Some Properties of a Modification of the Limited Information Estimator," Econometrica, Econometric Society, vol. 45(4), pages 939-953, May.
    5. Liu-Evans, Gareth & Phillips, Garry D.A., 2018. "On the use of higher order bias approximations for 2SLS and k-class estimators with non-normal disturbances and many instruments," Econometrics and Statistics, Elsevier, vol. 6(C), pages 90-105.
    6. Anderson, T.W., 2010. "The LIML estimator has finite moments!," Journal of Econometrics, Elsevier, vol. 157(2), pages 359-361, August.
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    Keywords

    LIML; Modified LIML; 2SLS; bias approximation; bias correction;
    All these keywords.

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