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Efficient estimation with many weak instruments using regularization techniques

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  • Guy Tchuente
  • Marine Carrasco

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 (is nearly median unbiased) even in the case of relatively weak instruments.

Suggested Citation

  • Guy Tchuente & Marine Carrasco, 2013. "Efficient estimation with many weak instruments using regularization techniques," CIRANO Working Papers 2013s-21, CIRANO.
    • Handle: RePEc:cir:cirwor:2013s-21
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    File URL: https://cirano.qc.ca/files/publications/2013s-21.pdf
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    References listed on IDEAS

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    1. Carrasco, Marine & Tchuente, Guy, 2015. "Regularized LIML for many instruments," Journal of Econometrics, Elsevier, vol. 186(2), pages 427-442.
    2. Guggenberger, Patrik & Smith, Richard J., 2005. "Generalized Empirical Likelihood Estimators And Tests Under Partial, Weak, And Strong Identification," Econometric Theory, Cambridge University Press, vol. 21(4), pages 667-709, August.
    3. Antoine, Bertille & Lavergne, Pascal, 2014. "Conditional moment models under semi-strong identification," Journal of Econometrics, Elsevier, vol. 182(1), pages 59-69.
    4. Carrasco, Marine, 2012. "A regularization approach to the many instruments problem," Journal of Econometrics, Elsevier, vol. 170(2), pages 383-398.
    5. Hausman, Jerry & Lewis, Randall & Menzel, Konrad & Newey, Whitney, 2011. "Properties of the CUE estimator and a modification with moments," Journal of Econometrics, Elsevier, vol. 165(1), pages 45-57.
    6. Hansen, Christian & Kozbur, Damian, 2014. "Instrumental variables estimation with many weak instruments using regularized JIVE," Journal of Econometrics, Elsevier, vol. 182(2), pages 290-308.
    7. De Mol, Christine & Giannone, Domenico & Reichlin, Lucrezia, 2008. "Forecasting using a large number of predictors: Is Bayesian shrinkage a valid alternative to principal components?," Journal of Econometrics, Elsevier, vol. 146(2), pages 318-328, October.
    8. Jerry A. Hausman & Whitney K. Newey & Tiemen Woutersen & John C. Chao & Norman R. Swanson, 2012. "Instrumental variable estimation with heteroskedasticity and many instruments," Quantitative Economics, Econometric Society, vol. 3(2), pages 211-255, July.
    9. Alexandre Dmitriev, 2013. "Institutions and growth: evidence from estimation methods robust to weak instruments," Applied Economics, Taylor & Francis Journals, vol. 45(13), pages 1625-1635, May.
    10. A. Belloni & D. Chen & V. Chernozhukov & C. Hansen, 2012. "Sparse Models and Methods for Optimal Instruments With an Application to Eminent Domain," Econometrica, Econometric Society, vol. 80(6), pages 2369-2429, November.
    11. Morimune, Kimio, 1983. "Approximate Distributions of k-Class Estimators When the Degree of Overidentifiability Is Large Compared with the Sample Size," Econometrica, Econometric Society, vol. 51(3), pages 821-841, May.
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    Cited by:

    1. Nandana Sengupta & Fallaw Sowell, 2019. "The Ridge Path Estimator for Linear Instrumental Variables," Papers 1908.09237, arXiv.org.
    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.

    More about this item

    Keywords

    Many weak instruments; LIML; 2SLS; regularization methods;

    JEL classification:

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

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