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Inference on a Structural Parameter in Instrumental Variables Regression with Weak Instruments


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  • Jiahui Wang

    (Department of Economics University of Washington)

  • Eric Zivot


In this paper we consider the problem of making inference on a structural parameter in instrumental variables regression when the instruments are only weakly correlated with the endogenous explanatory variables. Adopting a local-to-zero assumption as in Staiger and Stock (1994) on the coefficients of the instruments in the first stage equation, the asymptotic distributions of various test statistics are derived under a limited information framework. We show that Wald-type test statistics are not pivotal, thus (1-a)*100% confidence intervals implied by those test statistics can have zero coverage probability if the standard asymptotic distribution theory is used. In contrast, the likelihood type test statistics are pivotal when the model is just identified, thus providing valid confidence intervals. Even the model is overidentified, we show that the distributions of the likelihood type test statistics are bounded above by a Chi-Square distribution with degrees of freedom given by the number of instruments. Hence, we can always invert the likelihood type test statistics to obtain valid, although conservative, confidence intervals. The confidence intervals obtained by using this bounding distribution are compared with those obtained by using the standard Chi-Square 1 asymptotic distribution and an alternative bounding distribution, a transformation of the distribution of the Wilks statistic, suggested by Dufour (1994) . Confidence intervals based on our Chi-Square bounding distribution are shown to be tighter than those based on the Wilks bounding distribution by Monte Carlo experiments.

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Bibliographic Info

Paper provided by EconWPA in its series Econometrics with number 9610005.

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Length: 30 pages
Date of creation: 24 Oct 1996
Date of revision:
Handle: RePEc:wpa:wuwpem:9610005

Note: Type of Document - Adobe pdf file; prepared on Unix using TeX; to print on Postscript; pages: 30; figures: 5 pages of tables. 30 pages, Adobe pdf file translated from Unix TeX file.
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Keywords: confidence intervals; GMM; hypothesis testing; instrumental variables; maximum likelihood estimation; non-identified models.;

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Cited by:
  1. Zivot, E & Startz, R & Nelson, C-R, 1997. "Valid Confidence Intervals and Inference in the Presence of Weak Instruments," Discussion Papers in Economics at the University of Washington 97-17, Department of Economics at the University of Washington.
  2. Adrian Pagan, 2007. "Weak Instruments: A Guide to the Literature," NCER Working Paper Series 13, National Centre for Econometric Research.


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