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Finite-Sample Instrumental Variables Inference using an Asymptotically Pivotal Statistic

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  • Paul A. Bekker

    (University of Groningen)

  • Frank Kleibergen

    ()
    (University of Amsterdam)

Abstract

The paper considers the K-statistic, Kleibergen’s (2000) adaptation ofthe Anderson-Rubin (AR) statistic in instrumental variables regression.Compared to the AR-statistic this K-statistic shows improvedasymptotic efficiency in terms of degrees of freedom in overidentifiedmodels and yet it shares, asymptotically, the pivotal property of theAR statistic. That is, asymptotically it has a chi-square distributionwhether or not the model is identified. This pivotal property is veryrelevant for size distortions in finite-sample tests. Whereas Kleibergen(2000) focuses especially on the asymptotic behavior of the statistic,the present paper concentrates on finite-sample properties in a Gaussianframework. In that case the AR statistic has an F-distribution.However, the K-statistic is not exactly pivotal. Its finite-sample distributionis affected by nuisance parameters. Here we consider the twoextreme cases, which provide tight bounds for the exact distribution.The first case amounts to perfect identification—which is similar tothe asymptotic case—where the statistic has an F-distribution. Inthe other extreme case there is total underidentification. For the lattercase we show how to compute the exact distribution. Thus weprovide tight bounds for exact confidence sets based on the efficientK-statistic. Asymptotically the two bounds converge, except whenthere is a large number of redundant instruments. This paper has resulted in a publication in Econometric Theory , 2003, 19, 744-53.

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Bibliographic Info

Paper provided by Tinbergen Institute in its series Tinbergen Institute Discussion Papers with number 01-055/4.

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Date of creation: 13 Jun 2001
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Handle: RePEc:dgr:uvatin:20010055

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  1. Zivot, Eric & Startz, Richard & Nelson, Charles R, 1998. "Valid Confidence Intervals and Inference in the Presence of Weak Instruments," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 1119-46, November.
  2. Nelson, C. & Startz, R., 1988. "Some Furthere Results On The Exact Small Sample Properties Of The Instrumental Variable Estimator," Discussion Papers in Economics at the University of Washington 88-06, Department of Economics at the University of Washington.
  3. Frank Kleibergen, 2000. "Pivotal Statistics for Testing Structural Parameters in Instrumental Variables Regression," Tinbergen Institute Discussion Papers 00-055/4, Tinbergen Institute.
  4. 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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Cited by:
  1. 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.
  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. D.S. Poskitt & C.L. Skeels, 2005. "Small Concentration Asymptotics and Instrumental Variables Inference," Department of Economics - Working Papers Series 948, The University of Melbourne.
  5. 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.

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