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Finite-Sample Instrumental Variables Inference Using An Asymptotically Pivotal Statistic

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  • Bekker, Paul
  • Kleibergen, Frank

Abstract

We consider the K-statistic, Kleibergen s (2002, Econometrica 70, 1781 1803) adaptation of the Anderson Rubin (AR) statistic in instrumental variables regression. Whereas Kleibergen (2002) especially analyzes the asymptotic behavior of the statistic, we focus on finite-sample properties in a Gaussian framework. The AR statistic then has an F-distribution. The finite-sample distribution of the K-statistic is, however, affected by nuisance parameters. We consider two extreme cases for the nuisance parameters, 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. We thus provide tight bounds for exact confidence sets based on the K-statistic. Asymptotically the two bounds converge, except when there is a large number of redundant instruments.The authors research documented in this paper has been funded by the NWO Vernieuwingsimpuls research grant Empirical Comparison of Economic Models.

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Bibliographic Info

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. Nelson, C.R. & Startz, R. & Zivot, E., 1996. "Valid Confidence Intervals and Inference in the Presence of Weak Instruments," Discussion Papers in Economics at the University of Washington 96-15, Department of Economics at the University of Washington.
  2. Douglas Staiger & James H. Stock, 1997. "Instrumental Variables Regression with Weak Instruments," Econometrica, Econometric Society, vol. 65(3), pages 557-586, May.
  3. Frank Kleibergen, 2000. "Pivotal Statistics for Testing Structural Parameters in Instrumental Variables Regression," Tinbergen Institute Discussion Papers 00-055/4, Tinbergen Institute.
  4. Charles R. Nelson & Richard Startz, 1988. "Some Further Results on the Exact Small Sample Properties of the Instrumental Variable Estimator," NBER Technical Working Papers 0068, National Bureau of Economic Research, Inc.
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Cited by:
  1. D. S. Poskitt & C. L. Skeels, 2005. "Small Concentration Asymptotics and Instrumental Variables Inference," Monash Econometrics and Business Statistics Working Papers 4/05, Monash University, Department of Econometrics and Business Statistics.
  2. Frank Kleibergen, 2004. "Expansions of GMM statistics that indicate their properties under weak and/or many instruments and the bootstrap," Econometric Society 2004 North American Summer Meetings 408, Econometric Society.
  3. Whitney Newey & Frank Windmeijer, 2005. "GMM with many weak moment conditions," CeMMAP working papers CWP18/05, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  4. Bekker, Paul A. & Lawford, Steve, 2008. "Symmetry-based inference in an instrumental variable setting," Journal of Econometrics, Elsevier, vol. 142(1), pages 28-49, January.
  5. Dufour, Jean-Marie & Taamouti, Mohamed, 2007. "Further results on projection-based inference in IV regressions with weak, collinear or missing instruments," Journal of Econometrics, Elsevier, vol. 139(1), pages 133-153, July.

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