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Asymptotic variance under many instruments: Numerical computations

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  • Abutaliev, Albert
  • Anatolyev, Stanislav

Abstract

In models with many instruments, the asymptotic variance of the LIML estimator contains four components. Apart from the traditional variance, one term is due to instrument numerosity, and the last two appear if the model errors are non-normal. For a stylized instrumental variables model, we compute numerical values of these components to uncover how the four components are related to each other in magnitude.

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  • Abutaliev, Albert & Anatolyev, Stanislav, 2013. "Asymptotic variance under many instruments: Numerical computations," Economics Letters, Elsevier, vol. 118(2), pages 272-274.
  • Handle: RePEc:eee:ecolet:v:118:y:2013:i:2:p:272-274 DOI: 10.1016/j.econlet.2012.11.003
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    References listed on IDEAS

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    1. Paul A. Bekker & Jan Ploeg, 2005. "Instrumental variable estimation based on grouped data," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 59(3), pages 239-267.
    2. Anderson, T.W. & Kunitomo, Naoto & Matsushita, Yukitoshi, 2010. "On the asymptotic optimality of the LIML estimator with possibly many instruments," Journal of Econometrics, Elsevier, vol. 157(2), pages 191-204, August.
    3. Hasselt, Martijn van, 2010. "Many Instruments Asymptotic Approximations Under Nonnormal Error Distributions," Econometric Theory, Cambridge University Press, vol. 26(02), pages 633-645, April.
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    5. Jerry A. Hausman & Whitney K. Newey & Tiemen Woutersen & John C. Chao & Norman R. Swanson, 2012. "Instrumental variable estimation with heteroskedasticity and many instruments," Quantitative Economics, Econometric Society, vol. 3(2), pages 211-255, July.
    6. Anatolyev, Stanislav & Gospodinov, Nikolay, 2011. "Specification Testing In Models With Many Instruments," Econometric Theory, Cambridge University Press, vol. 27(02), pages 427-441, April.
    7. Jinyong Hahn & Atsushi Inoue, 2002. "A Monte Carlo Comparison Of Various Asymptotic Approximations To The Distribution Of Instrumental Variables Estimators," Econometric Reviews, Taylor & Francis Journals, vol. 21(3), pages 309-336.
    8. Hansen, Christian & Hausman, Jerry & Newey, Whitney, 2008. "Estimation With Many Instrumental Variables," Journal of Business & Economic Statistics, American Statistical Association, vol. 26, pages 398-422.
    9. Adelchi Azzalini & Antonella Capitanio, 2003. "Distributions generated by perturbation of symmetry with emphasis on a multivariate skew "t"-distribution," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(2), pages 367-389.
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