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Efficient Inference with Poor Instruments: a General Framework

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Abstract

We consider a general framework where weaker patterns of identifcation may arise: typically, the data generating process is allowed to depend on the sample size. However, contrary to what is usually done in the literature on weak identification, we do not give up the efficiency goal of statistical inference: even fragile information should be processed optimally for the purpose of both efficient estimation and powerful testing. Our main contribution is actually to consider that several patterns of identification may arise simultaneously. This heterogeneity of identification schemes paves the way for the device of optimal strategies for inferential use of information of poor quality. More precisely, we focus on a case where asymptotic efficiency of estimators is well-defined through the variance of asymptotically normal distributions. Standard efficient estimation procedures still hold, albeit with rates of convergence slower than usual. We stress that these are feasible without requiring the prior knowledge of the identification schemes.

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File URL: http://www.sfu.ca/econ-research/RePEc/sfu/sfudps/dp12-04.pdf
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Bibliographic Info

Paper provided by Department of Economics, Simon Fraser University in its series Discussion Papers with number dp12-04.

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Length: 58
Date of creation: Mar 2012
Date of revision:
Handle: RePEc:sfu:sfudps:dp12-04

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Postal: Department of Economics, Simon Fraser University, 8888 University Drive, Burnaby, BC, V5A 1S6, Canada
Phone: (778)782-3508
Fax: (778)782-5944
Web page: http://www.sfu.ca/economics.html
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Postal: Working Paper Coordinator, Department of Economics, Simon Fraser University, 8888 University Drive, Burnaby, BC, V5A 1S6, Canada
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Web: http://www.sfu.ca/economics/research/publications.html

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Keywords: Instrumental variable; Weak instrument; GMM;

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References

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  1. Douglas Staiger & James H. Stock, 1994. "Instrumental Variables Regression with Weak Instruments," NBER Technical Working Papers 0151, National Bureau of Economic Research, Inc.
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  14. Mehmet Caner, 2010. "Testing, Estimation in GMM and CUE with Nearly-Weak Identification," Econometric Reviews, Taylor & Francis Journals, vol. 29(3), pages 330-363.
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Cited by:
  1. Donald W. K. Andrews & Xu Cheng, 2011. "Maximum Likelihood Estimation and Uniform Inference with Sporadic Identification Failure," Cowles Foundation Discussion Papers 1824, Cowles Foundation for Research in Economics, Yale University.
  2. Donald W.K. Andrews & Xu Cheng, 2011. "GMM Estimation and Uniform Subvector Inference with Possible Identification Failure," Cowles Foundation Discussion Papers 1828, Cowles Foundation for Research in Economics, Yale University, revised Jan 2013.

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