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Finite-Sample Instrumental Variables Inference Using An Asymptotically Pivotal Statistic

  • Bekker, Paul
  • Kleibergen, Frank

The paper considers the K-statistic, Kleibergen’s (2000) adaptation of the Anderson-Rubin (AR) statistic in instrumental variables regression. Compared to the AR-statistic this K-statistic shows improved asymptotic efficiency in terms of degrees of freedom in overidenti?ed models and yet it shares, asymptotically, the pivotal property of the AR statistic. That is, asymptotically it has a chi-square distribution whether or not the model is identi?ed. This pivotal property is very relevant for size distortions in ?nite-sample tests. Whereas Kleibergen (2000) focuses especially on the asymptotic behavior of the statistic, the present paper concentrates on finite-sample properties in a Gaussian framework. In that case the AR statistic has an F-distribution. However, the K-statistic is not exactly pivotal. Its finite-sample distribution is affected by nuisance parameters. Here we consider the two extreme cases, which provide tight bounds for the exact distribution. The first case amounts to perfect identification —which is similar to the asymptotic case—where the statistic has an F-distribution. In the other extreme case there is total underidentification. For the latter case we show how to compute the exact distribution. Thus we provide tight bounds for exact con?dence sets based on the efficient K-statistic. Asymptotically the two bounds converge, except when there is a large number of redundant instruments.

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Article provided by Cambridge University Press in its journal Econometric Theory.

Volume (Year): 19 (2003)
Issue (Month): 05 (October)
Pages: 744-753

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Handle: RePEc:cup:etheor:v:19:y:2003:i:05:p:744-753_19
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  1. Douglas Staiger & James H. Stock, 1997. "Instrumental Variables Regression with Weak Instruments," Econometrica, Econometric Society, vol. 65(3), pages 557-586, May.
  2. 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.
  3. Nelson, C. & Startz, R., 1988. "Some Furthere Results On The Exact Small Sample Properties Of The Instrumental Variable Estimator," Working Papers 88-06, University of Washington, Department of Economics.
  4. repec:dgr:uvatin:20000055 is not listed on IDEAS
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