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On the Inconsistency of Instrumental Variables Estimators for the Coefficients of Certain Dummy Variables

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Abstract

In this paper we consider the asymptotic properties of the Instrumental Variables (IV) estimator of the parameters in a linear regression model with some random regressors, and other regressors that are dummy variables. The latter have the special property that the number of non-zero values is fixed, and does not increase with the sample size. We prove that the IV estimator of the coefficient vector for the dummy variables is inconsistent, while that for the other regressors is weakly consistent under standard assumptions. However, the usual estimator for the asymptotic covariance matrix of the I.V. estimator for all of the coefficients retains its usual consistency. The t-test statistics for the dummy variable coefficients are still asymptotically standard normal, despite the inconsistency of the associated IV coefficient estimator. These results extend the earlier results of Hendry and Santos (2005), which relate to a fixed-regressor model, in which the dummy variables are non-zero for just a single observation, and OLS estimation is used.

Suggested Citation

  • David E. Giles, 2011. "On the Inconsistency of Instrumental Variables Estimators for the Coefficients of Certain Dummy Variables," Econometrics Working Papers 1106, Department of Economics, University of Victoria.
  • Handle: RePEc:vic:vicewp:1106
    Note: ISSN 1485-6441
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    File URL: http://www.uvic.ca/socialsciences/economics/assets/docs/econometrics/ewp1106.pdf
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    References listed on IDEAS

    as
    1. Giles, David E. A., 1984. "Instrumental variables regressions involving seasonal data," Economics Letters, Elsevier, vol. 14(4), pages 339-343.
    2. Michael C. Lovell, 1963. "Seasonal Adjustment of Economic Time Series and Multiple Regression," Cowles Foundation Discussion Papers 151, Cowles Foundation for Research in Economics, Yale University.
    3. David F. Hendry & Carlos Santos, 2005. "Regression Models with Data-based Indicator Variables," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 67(5), pages 571-595, October.
    4. Salkever, David S., 1976. "The use of dummy variables to compute predictions, prediction errors, and confidence intervals," Journal of Econometrics, Elsevier, vol. 4(4), pages 393-397, November.
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    Blog mentions

    As found by EconAcademics.org, the blog aggregator for Economics research:
    1. Dummy Variables - Again!
      by Dave Giles in Econometrics Beat: Dave Giles' Blog on 2012-09-14 23:34:00

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    Cited by:

    1. Ambos, Tina C. & Ambos, Björn & Eich, Katharina J. & Puck, Jonas, 2016. "Imbalance and Isolation: How Team Configurations Affect Global Knowledge Sharing," Journal of International Management, Elsevier, vol. 22(4), pages 316-332.

    More about this item

    Keywords

    Dummy variables; indicator variables; instrumental variables; inconsistent estimator;

    JEL classification:

    • C20 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - General
    • C26 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Instrumental Variables (IV) Estimation
    • C49 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Other

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