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Robust estimation with many instruments
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DOI：10.1016/j.jeconom.2019.04.040.png)
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Abstract
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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. (C) 2019 Elsevier B.V. All rights reserved.
Keywords:
Instrumental variables
Generalized method of moments
Minimax estimation
Stein's method
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