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Inference with Weak Instruments

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Abstract

This paper reviews recent developments in methods for dealing with weak instruments (IVs) in IV regression models. The focus is more on tests (and confidence intervals derived from tests) than estimators. The paper also presents new testing results under "many weak IV asymptotics," which are relevant when the number of IVs is large and the coefficients on the IVs are relatively small. Asymptotic power envelopes for invariant tests are established. Power comparisons of the conditional likelihood ratio (CLR), Anderson-Rubin, and Lagrange multiplier tests are made. Numerical results show that the CLR test is on the asymptotic power envelope. This holds no matter what the relative magnitude of the IV strength to the number of IVs.

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File URL: http://cowles.econ.yale.edu/P/cd/d15a/d1530.pdf
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Bibliographic Info

Paper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 1530.

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Length: 68 pages
Date of creation: Aug 2005
Date of revision:
Publication status: Published in R. Blundell, W.K. Newey, and T. Persson, eds., Advances in Economics and Econometrics, Theory and Applications: Ninth World Congress of the Econometric Society, Vol. III, Cambridge University Press, 2007, Ch. 6
Handle: RePEc:cwl:cwldpp:1530

Note: CFP 1249.
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Web page: http://cowles.econ.yale.edu/
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Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

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Keywords: Conditional likelihood ratio test; instrumental variables; many instrumental variables; power envelope; weak instruments;

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