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Efficient estimation with many weak instruments using regularization techniques

  • Guy Tchuente
  • Marine Carrasco

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.

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File URL: http://www.cirano.qc.ca/files/publications/2013s-21.pdf
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Paper provided by CIRANO in its series CIRANO Working Papers with number 2013s-21.

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Length: 31 pages
Date of creation: 01 Jul 2013
Date of revision:
Handle: RePEc:cir:cirwor:2013s-21
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  1. Norman R. Swanson & John C. Chao & Jerry A. Hausman & Whitney K. Newey & Tiemen Woutersen, 2011. "Instrumental Variable Estimation with Heteroskedasticity and Many Instruments," Departmental Working Papers 201111, Rutgers University, Department of Economics.
  2. Antoine, Bertille & Lavergne, Pascal, 2014. "Conditional moment models under semi-strong identification," Journal of Econometrics, Elsevier, vol. 182(1), pages 59-69.
  3. Carrasco, Marine, 2012. "A regularization approach to the many instruments problem," Journal of Econometrics, Elsevier, vol. 170(2), pages 383-398.
  4. A. Belloni & D. Chen & Victor Chernozhukov & Christian Hansen, 2010. "Sparse models and methods for optimal instruments with an application to eminent domain," CeMMAP working papers CWP31/10, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  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.
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