Efficient estimation with many weak instruments using regularization techniques
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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| Length: | 31 pages |
| Date of creation: | 01 Jul 2013 |
| Date of revision: | |
| Handle: | RePEc:cir:cirwor:2013s-21 |
| Contact details of provider: | Postal: Phone: (514) 985-4000 Fax: (514) 985-4039 Web page: http://www.cirano.qc.ca/Email: More information through EDIRC
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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- 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.
- 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, 07.
- Jerry Hausman & Whitney Newey & Tiemen Woutersen & John Chao & Norman Swanson, 2007. "Instrumental variable estimation with heteroskedasticity and many instruments," CeMMAP working papers CWP22/07, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
- 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.
- Antoine, Bertille & Lavergne, Pascal, 2014.
"Conditional moment models under semi-strong identification,"
Journal of Econometrics,
Elsevier, vol. 182(1), pages 59-69.
- 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.
- Carrasco, Marine, 2012. "A regularization approach to the many instruments problem," Journal of Econometrics, Elsevier, vol. 170(2), pages 383-398.
- 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.
- 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.
- 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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