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Robust estimation with many instruments

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  • Sølvsten, Mikkel
Abstract
Linear instrumental variables models are widely used in empirical work, but often associated with low estimator precision. This paper proposes an estimator that is robust to outliers and shows that the estimator is minimax optimal in a class of estimators that includes the limited maximum likelihood estimator (LIML). Intuitively, this optimal robust estimator combines LIML with Winsorization of the structural residuals and the Winsorization leads to improved precision under thick-tailed error distributions. Consistency and asymptotic normality of the estimator are established under many instruments asymptotics and a consistent variance estimator which allows for asymptotically valid inference is provided.

Suggested Citation

  • Sølvsten, Mikkel, 2020. "Robust estimation with many instruments," Journal of Econometrics, Elsevier, vol. 214(2), pages 495-512.
    • Handle: RePEc:eee:econom:v:214:y:2020:i:2:p:495-512
    DOI: 10.1016/j.jeconom.2019.04.040
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    More about this item

    Keywords

    Instrumental variables; Generalized method of moments; Minimax estimation; Stein’s method;
    All these keywords.

    JEL classification:

    • C26 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Instrumental Variables (IV) Estimation
    • C36 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Instrumental Variables (IV) Estimation

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