A regularization approach to the many instruments problem

Marine Carrasco

Journal of Econometrics, 2012, vol. 170, issue 2, 383-398

Abstract: This paper focuses on the estimation of a finite dimensional parameter in a linear model where the number of instruments is very large or infinite. In order to improve the small sample properties of standard instrumental variable (IV) estimators, we propose three modified IV estimators based on three different ways of inverting the covariance matrix of the instruments. These inverses involve a regularization or smoothing parameter. It should be stressed that no restriction on the number of instruments is needed and that all the instruments are used in the estimation. We show that the three estimators are asymptotically normal and attain the semiparametric efficiency bound. Higher-order analysis of the MSE reveals that the bias of the modified estimators does not depend on the number of instruments. Finally, we suggest a data-driven method for selecting the regularization parameter. Interestingly, our regularization techniques lead to a consistent nonparametric estimation of the optimal instrument.

Keywords: Many instruments; Mean square error; Regularization methods (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (75)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:econom:v:170:y:2012:i:2:p:383-398

DOI: 10.1016/j.jeconom.2012.05.012

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