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The Asymptotic Variance Bound for Instrumental Variables Estimators

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  • Yun-Yeong Kim
  • Joon Y. Park

    ()

Abstract

The paper derives the asymptotic variance bound for instrumental variables (IV) estimators, and extends the Gauss-Markov theorem for the regressions with correlated regressors and regression errors. For some special class of models, the usual IV estimator attains the lower bound and becomes the best linear consistent estimator (BLCE). In general, however, the IV estimator has asymptotic variance strictly larger than the lower bound that we obtained. Out lower bound can be consistently estimated, so that we may compute the asymptotic relative efficiency (ARE) of the IV estimator. The notion of ARE can be used to evaluate th IV practice. This is illustrated with an application of our method to the Klein's simultaneous equations model.

Suggested Citation

  • Yun-Yeong Kim & Joon Y. Park, 1999. "The Asymptotic Variance Bound for Instrumental Variables Estimators," Working Paper Series no10, Institute of Economic Research, Seoul National University.
  • Handle: RePEc:snu:ioerwp:no10
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    File URL: http://econ.snu.ac.kr/~ecores/activity/paper/no10.pdf
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    References listed on IDEAS

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    1. Nelson, Charles R & Startz, Richard, 1990. "Some Further Results on the Exact Small Sample Properties of the Instrumental Variable Estimator," Econometrica, Econometric Society, vol. 58(4), pages 967-976, July.
    2. Arthur Lewbel, 1997. "Constructing Instruments for Regressions with Measurement Error when no Additional Data are Available, with an Application to Patents and R&D," Econometrica, Econometric Society, vol. 65(5), pages 1201-1214, September.
    3. Buse, A, 1992. "The Bias of Instrumental Variable Estimators," Econometrica, Econometric Society, vol. 60(1), pages 173-180, January.
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    Keywords

    Instrumental variables estimator; asymptotic variance bound; best linear consistent estimator; asymptotic relative efficiency; simultaneous equations model;

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