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Assessing the magnitude of the concentration parameter in a simultaneous equations model

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Author Info
D. S. Poskitt
C. L. Skeels

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Abstract

This paper provides the practitioner with a method of ascertaining when the concentration parameter in a simultaneous equations model is small. We provide some exact distribution theory for a proposed statistic and show that the statistic possesses the minimal desirable characteristics of a test statistic when used to test that the concentration parameter is zero. The discussion is then extended to consider how to test for weak instruments using this statistic as a basis for inference. We also discuss the statistic's relationship to various other procedures that have appeared in the literature. Copyright The Author(s). Journal compilation Royal Economic Society 2009

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File URL: http://www.blackwell-synergy.com/doi/abs/10.1111/j.1368-423X.2008.00268.x
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Publisher Info
Article provided by Royal Economic Society in its journal Econometrics Journal.

Volume (Year): 12 (2009)
Issue (Month): 1 (03)
Pages: 26-44
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Handle: RePEc:ect:emjrnl:v:12:y:2009:i:1:p:26-44

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Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. D. S. Poskitt & C. L. Skeels, 2004. "Approximating the Distribution of the Instrumental Variables Estimator when the Concentration Parameter is Small," Monash Econometrics and Business Statistics Working Papers 19/04, Monash University, Department of Econometrics and Business Statistics. [Downloadable!]
  2. Mariano, Roberto S, 1982. "Analytical Small-Sample Distribution Theory in Econometrics: The Simultaneous-Equations Case," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 23(3), pages 503-33, October. [Downloadable!] (restricted)
  3. Phillips, P C B, 1980. "The Exact Distribution of Instrumental Variable Estimators in an Equation Containing n + 1 Endogenous Variables," Econometrica, Econometric Society, vol. 48(4), pages 861-78, May. [Downloadable!] (restricted)
  4. Stock, James H & Wright, Jonathan H & Yogo, Motohiro, 2002. "A Survey of Weak Instruments and Weak Identification in Generalized Method of Moments," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(4), pages 518-29, October.
  5. Phillips, P.C.B., 1983. "Exact small sample theory in the simultaneous equations model," Handbook of Econometrics, in: Z. Griliches† & M. D. Intriligator (ed.), Handbook of Econometrics, edition 1, volume 1, chapter 8, pages 449-516 Elsevier. [Downloadable!] (restricted)
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  6. Hall, Alastair R & Rudebusch, Glenn D & Wilcox, David W, 1996. "Judging Instrument Relevance in Instrumental Variables Estimation," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 37(2), pages 283-98, May.
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