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Higher Order Approximation of IV Estimators with Invalid Instruments

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  • Byunghoon Kang

Abstract

This paper considers the instrument selection problem in instrumental variable (IV) regression model when there is a large set of instruments with potential invalidity. I derive higher-order mean square error (MSE) approximation of two-stage least squares (2SLS), limited information maximum likelihood (LIML), Fuller (FULL) and bias-adjusted 2SLS (B2SLS) estimators with allowing for local violation of the instrument-exogeneity conditions. Based on the approximation to the higher-order MSE, I propose instrument selection criteria that are robust to potential invalidity of instruments. Furthermore, I also show the optimality results of instrument selection criteria in Donald and Newey (2001, Econometrica) under faster than N^(-1/2) locally invalid instruments specication.

Suggested Citation

  • Byunghoon Kang, 2018. "Higher Order Approximation of IV Estimators with Invalid Instruments," Working Papers 257105320, Lancaster University Management School, Economics Department.
    • Handle: RePEc:lan:wpaper:257105320
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    File URL: http://www.lancaster.ac.uk/media/lancaster-university/content-assets/documents/lums/economics/working-papers/LancasterWP2019_001.pdf
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    References listed on IDEAS

    as
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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.

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    More about this item

    Keywords

    Instrument selection; Invalid instruments; Many instruments; 2SLS; LIML; Fuller estimator; Bias-adjusted 2SLS;
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