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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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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. Marine Carrasco & Guy Tchuente, 2015. "Regularized LIML for many instruments," Studies in Economics 1515, School of Economics, University of Kent.
  2. Carrasco, Marine, 2012. "A regularization approach to the many instruments problem," Journal of Econometrics, Elsevier, vol. 170(2), pages 383-398.
  3. Hausman & Newey & Woutersen & Chao & Swanson, 2009. "Instrumental Variable Estimation with Heteroskedasticity and Many Instruments," Economics Working Paper Archive 566, The Johns Hopkins University,Department of Economics.
  4. 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.
  5. Patrik Buggenberger & Richard Smith, 2003. "Generalized empirical likelihood estimators and tests under partial, weak and strong identification," CeMMAP working papers CWP08/03, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  6. 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.
  7. Bertille Antoine & Pascal Lavergne, 2011. "Conditional Moment Models under Semi-Strong Identification," Discussion Papers dp11-04, Department of Economics, Simon Fraser University, revised Dec 2012.
  8. 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.
  9. 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 821-41, May.
  10. 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.
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