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Approximating the Distribution of the Instrumental Variables Estimator when the Concentration Parameter is Small

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Abstract

This paper presents a new approximation to the exact sampling distribution of the instrumental variables estimator in simultaneous equations models. It differs from many of the approximations currently available, Edgeworth expansions for example, in that it is specifically designed to work well when the concentration parameter is small. The approximation is remarkable for the simplicity of its final form, for its accuracy and for its ability to capture those stylized facts that characterize lack of identification and weak instrument scenarios. The development leading to the approximation is also novel in that it introduces techniques of some independent interest not seen in this literature hitherto.

Suggested Citation

  • 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.
    • Handle: RePEc:msh:ebswps:2004-19
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    File URL: http://www.buseco.monash.edu.au/ebs/pubs/wpapers/2004/wp19-04.pdf
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    References listed on IDEAS

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    Cited by:

    1. D. S. Poskitt & C. L. Skeels, 2009. "Assessing the magnitude of the concentration parameter in a simultaneous equations model," Econometrics Journal, Royal Economic Society, vol. 12(1), pages 26-44, March.
    2. 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.
    3. Poskitt, D.S. & Skeels, C.L., 2008. "Conceptual frameworks and experimental design in simultaneous equations," Economics Letters, Elsevier, vol. 100(1), pages 138-142, July.
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    More about this item

    Keywords

    concentration parameter; IV estimator; simultaneous equations model; t approximation; weak instruments.;
    All these keywords.

    JEL classification:

    • C16 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Econometric and Statistical Methods; Specific Distributions
    • C30 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - General

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