Efficient Estimation with Many Weak Instruments Using Regularization Techniques

Marine Carrasco and Guy Tchuente

Econometric Reviews, 2016, vol. 35, issue 8-10, 1609-1637

Abstract: The problem of weak instruments is due to a very small concentration parameter. To boost the concentration parameter, we propose to increase the number of instruments to a large number or even up to a continuum. However, in finite samples, the inclusion of an excessive number of moments may be harmful. To address this issue, we use regularization techniques as in Carrasco (2012) and Carrasco and Tchuente (2014). We show that normalized regularized two-stage least squares (2SLS) and limited maximum likelihood (LIML) are consistent and asymptotically normally distributed. Moreover, our estimators are asymptotically more efficient than most competing estimators. Our simulations show that the leading regularized estimators (LF and T of LIML) work very well (are nearly median unbiased) even in the case of relatively weak instruments. An application to the effect of institutions on output growth completes the article.

Date: 2016
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Working Paper: Efficient estimation with many weak instruments using regularization techniques (2015)
Working Paper: Efficient estimation with many weak instruments using regularization techniques (2013)
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DOI: 10.1080/07474938.2015.1092806

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