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Efficient estimation with many weak instruments using regularization techniques

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  • Marine Carrasco
  • Guy Tchuente

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 (2013). We show that normalized regularized 2SLS and LIML are consistent and asymptotically normally distributed. Moreover, their asymptotic variances reach the semiparametric efficiency bound unlike 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 paper.

Suggested Citation

  • Marine Carrasco & Guy Tchuente, 2015. "Efficient estimation with many weak instruments using regularization techniques," Studies in Economics 1517, School of Economics, University of Kent.
    • Handle: RePEc:ukc:ukcedp:1517
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    Citations

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    Cited by:

    1. Vincent Boucher & Yann Bramoullé, 2020. "Binary Outcomes and Linear Interactions," AMSE Working Papers 2038, Aix-Marseille School of Economics, France.
    2. Berriel, Tiago & Medeiros, Marcelo C. & Sena, Marcelo J., 2016. "Instrument selection for estimation of a forward-looking Phillips Curve," Economics Letters, Elsevier, vol. 145(C), pages 123-125.
    3. Carrasco, Marine & Tchuente, Guy, 2015. "Regularized LIML for many instruments," Journal of Econometrics, Elsevier, vol. 186(2), pages 427-442.
    4. Guy Tchuente, 2021. "A Note on the Topology of the First Stage of 2SLS with Many Instruments," Papers 2106.15003, arXiv.org.
    5. Dakyung Seong, 2022. "Binary response model with many weak instruments," Papers 2201.04811, arXiv.org, revised Jun 2024.
    6. Nandana Sengupta & Fallaw Sowell, 2019. "The Ridge Path Estimator for Linear Instrumental Variables," Papers 1908.09237, arXiv.org.
    7. Nandana Sengupta & Fallaw Sowell, 2020. "On the Asymptotic Distribution of Ridge Regression Estimators Using Training and Test Samples," Econometrics, MDPI, vol. 8(4), pages 1-25, October.

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    More about this item

    Keywords

    many weak instruments; LIML; 2SLS; regularization methods;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General

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