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Finite-sample instrumental variables inference using an asymptotically pivotal statistic


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  • Bekker, Paul A.
  • Kleibergen, Frank

    (Groningen University)


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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Bibliographic Info

Paper provided by University of Groningen, CCSO Centre for Economic Research in its series CCSO Working Papers with number 200109.

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Date of creation: 2001
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Handle: RePEc:dgr:rugccs:200109

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  1. Nelson, C. & Startz, R., 1988. "Some Furthere Results On The Exact Small Sample Properties Of The Instrumental Variable Estimator," Working Papers, University of Washington, Department of Economics 88-06, University of Washington, Department of Economics.
  2. Frank Kleibergen, 2002. "Pivotal Statistics for Testing Structural Parameters in Instrumental Variables Regression," Econometrica, Econometric Society, Econometric Society, vol. 70(5), pages 1781-1803, September.
  3. Charles R. Nelson & Richard Startz & Eric Zivot, 1996. "Valid Confidence Intervals and Inference in the Presence of Weak Instruments," Econometrics, EconWPA 9612002, EconWPA.
  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. Bekker, Paul A. & Lawford, Steve, 2008. "Symmetry-based inference in an instrumental variable setting," Journal of Econometrics, Elsevier, Elsevier, vol. 142(1), pages 28-49, January.
  2. D.S. Poskitt & C.L. Skeels, 2005. "Small Concentration Asymptotics and Instrumental Variables Inference," Department of Economics - Working Papers Series, The University of Melbourne 948, The University of Melbourne.
  3. Whitney Newey & Frank Windmeijer, 2005. "GMM with many weak moment conditions," CeMMAP working papers, Centre for Microdata Methods and Practice, Institute for Fiscal Studies CWP18/05, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  4. 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.
  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, Elsevier, vol. 139(1), pages 133-153, July.


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